Post on 02-Dec-2021
DISTRIBUTION NETWORK
AUTOMATION FOR MULTI-
OBJECTIVE OPTIMISATION
A thesis submitted to The University of Manchester for the degree of
Doctor of Philosophy
in the Faculty of Science and Engineering
2018
BOYI ZHANG
SCHOOL OF ELECTRICAL AND ELECTRONIC ENGINEERING
Page | 2
List of Contents
List of Contents 2
List of Figures 7
List of Tables 10
List of Abbreviations 14
Abstract 16
Declaration 17
Copyright Statement 18
Acknowledgements 19
CHAPTER 1 20
INTRODUCTION 20
11 Motivation 20
12 Objectives 22
13 Contribution of the work 23
14 Structure of the thesis 25
CHAPTER 2 28
DISTRIBUTION AUTOMATION 28
21 Introduction 28
22 Distribution Network Configurations 29
23 Switchgear for Distribution Network 30
231 Reclosers 30
232 Sectionalising Switches 31
233 Tie-switches 31
24 Transformer Economic Operation 31
241 Basic Concepts 31
242 Literatures on Transformer Economic Operation 33
25 Distribution Network Reconfiguration 35
251 Basic Concepts 35
252 Literatures on Distribution Network Reconfiguration 36
26 Placement of Sectionalising Switches 38
261 Basic Concepts 38
262 Literatures on Sectionalising Switch Placement 41
Page | 3
27 Transformer Loss Assessment 42
271 Operating Principles 42
272 Transformer Quantities Measurement 43
273 Integrated Transformer Loss 46
28 Feeder Loss Assessment 47
29 Reliability Evaluation 48
291 Reliability Indices 48
292 Reliability Evaluation Methods 50
210 Multi-objective Optimisation 53
2101 Single Objective Function 54
2102 Single Fuzzy Satisfaction Objective Function 54
2103 Multi-objective Formulation in the Pareto Optimality Framework 56
211 Summary 58
CHAPTER 3 60
OPTIMISATION TECHNIQUES 60
31 Introduction 60
32 Monte Carlo Method 61
33 Ant Colony Optimisation 62
34 AIS-ACO Hybrid Algorithm 65
341 Artificial Immune Systems 65
342 Proposed AIS-ACO Hybrid Algorithm 66
35 Summary 68
CHAPTER 4 70
TRANSFORMER ECONOMIC OPERATION amp DISTRIBUTION NETWORK
RECONFIGURATION FOR TRANSFORMER LOSS REDUCTION 70
41 Introduction 70
42 Load Model 72
43 Problem Formulation 73
44 Methodology 73
441 Transformer Economic Operation 73
442 Distribution Network Reconfiguration 76
45 Application Studies 77
451 Test Case 1 77
452 Test Case 2 85
Page | 4
46 Summary 90
CHAPTER 5 92
DISTRIBUTION NETWORK RECONFIGURATION amp DG ALLOCATION FOR
FEEDER LOSS REDUCTION 92
51 Introduction 92
52 Problem Formulation 93
53 Solution Method 94
531 Distribution Network Reconfiguration 94
532 Applying ACO to DNR and DGs Placement 95
54 Application Studies 99
541 33-bus System 99
542 69-bus System 105
55 Summary 109
CHAPTER 6 111
DISTRIBUTION NETWORK RECONFIGURATION amp TRANSFORMER
ECONOMIC OPERATION FOR NETWORK LOSS REDUCTION 111
61 Introduction 111
62 Time-varying Load Model 112
63 Problem Formulation 113
64 Applying ACO to DNR and TEO 114
65 Application Studies 118
651 Test Case 1 122
652 Test Case 2 123
653 Test Case 3 124
66 Summary 126
CHAPTER 7 128
OPTIMAL PLACEMENT OF SECTIONALISING SWITCHES FOR
RELIABILITY IMPROVEMENT 128
71 Introduction 128
72 Problem Formulation 129
721 Weighted Aggregation 129
722 Single Fuzzy Satisfaction Objective Function with Two Parameters 130
723 Single Fuzzy Satisfaction Objective Function with Three Parameters 131
Page | 5
724 Evaluation of ECOST 132
725 Evaluation of SAIDI 133
726 Evaluation of Switch Costs 133
73 Applying ACO to Sectionalising Switch Placement Problem 134
74 Benefit-to-cost Analysis 135
75 Application Studies 136
751 Test Case 1 138
752 Test Case 2 147
753 Test Case 3 147
76 Summary 148
CHAPTER 8 150
DISTRIBUTION NETWORK RECONFIGURATION FOR LOSS REDUCTION amp
RELIABILITY IMPROVEMENT 150
81 Introduction 150
82 Problem Formulation 152
821 Multi-objective Reconfiguration Problem 152
822 Best Compromise Solution 153
83 Solution Methodology 154
831 Applying MOACO to Multi-objective DNR Problem 154
832 Applying AIS-ACO to Multi-objective DNR Problem 158
84 Application Studies 161
85 Best Compromise Solution 163
86 Summary 164
CHAPTER 9 166
MULTI-OBJECTIVE DISTRIBUTION NETWORK RECONFIGURATION amp DG
ALLOCATION CONSIDERING LOSS VOLTAGE DEVIATION AND LOAD
BALANCING 166
91 Introduction 166
92 Problem Formulation 168
921 Single Fuzzy Satisfaction Objective Function 168
922 Multi-objective Reconfiguration Problem Using Pareto Optimality 170
93 Solution methodology 171
931 Applying ACO to DNR and DG Allocation in the Fuzzy Domain 171
932 Applying AIS-ACO to Multi-objective DNR and DG Allocation Using
Pareto Optimality 171
Page | 6
94 Application Studies 171
941 33-bus System 172
942 69-bus System 180
95 Summary 187
CHAPTER 10 189
CONCLUSION amp FUTURE WORK 189
101 Conclusion 189
102 Future Work 193
References 195
APPENDIX A Network Model Data 204
APPENDIX B Simulation Results 209
APPENDIX C Control Parameters of Algorithms 221
APPENDIX D List of Publications 224
Word count 51012
Page | 7
List of Figures
Fig 2-1 Typical Distribution network [27] 29
Fig 2-2 Recloser operation 30
Fig 2-3 Transformer loss versus transformer load 32
Fig 2-4 Daily load curve of a typical substation before and after load smoothing [38]
34
Fig 2-5 Radial test system 35
Fig 2-6 Fully automated distribution feeder 40
Fig 2-7 Partially automated distribution feeder 41
Fig 2-8 Elements of a single phase transformer [33] 43
Fig 2-9 Construction of a three-phase transformer [33] 43
Fig 2-10 The open-circuit test [33] 44
Fig 2-11 The short-circuit test [33] 45
Fig 2-12 Simple two-bus network 47
Fig 2-13 Reliability model for static components 51
Fig 2-14 Procedure for reliability evaluation 52
Fig 2-15 Sample network 53
Fig 2-16 Linear membership function 54
Fig 3-1 Example of ant colony system [69] 63
Fig 3-2 Flowchart of the ant colony algorithm 65
Fig 3-3 Flowchart of the AIS-ACO algorithm 67
Fig 4-1 Procedure of domestic electricity demand profile generation 72
Fig 4-2 Monte Carlo simulation platform for three transformer operation modes
comparison 74
Fig 4-3 Flowchart of transformer loss assessment 75
Fig 4-4 Monte Carlo simulation platform for distribution network reconfiguration 76
Fig 4-5 Generic distribution network topology 78
Fig 4-6 Transformer load factor variation 79
Fig 4-7 Transformer loss variations in different scenarios 80
Fig 4-8 11 kV 4th
feeder voltage profiles in different scenarios 81
Fig 4-9 Voltage profiles of Load 4_1 in different scenarios 82
Fig 4-10 Voltage profiles of Load 4_8 in different scenarios 83
Page | 8
Fig 4-11 11 kV 4th
feeder mean voltage profile of various TCLFs 84
Fig 4-12 Test system 86
Fig 4-13 Daily load variations for different load groups 87
Fig 4-14 Mean voltage profiles in S1 S2 and S3 89
Fig 4-15 Mean voltage profiles in S1 S4 and S7 89
Fig 5-1 Search space of DNR and DGs Placement 95
Fig 5-2 Flowchart of the ACO applied to DNR and DGs placement 98
Fig 5-3 33-bus system 100
Fig 5-4 33-bus system for feeder loss minimisation Case II 101
Fig 5-5 33-bus system for feeder loss minimisation Case III 102
Fig 5-6 33-bus system for feeder loss minimisation Case IV 103
Fig 5-7 Comparison of feeder loss for different DG capacities before and after
simultaneous reconfiguration and DG allocation 104
Fig 5-8 Comparison of voltage profiles in different cases of 33-node system 104
Fig 5-9 69-bus system 105
Fig 5-10 69-bus system for feeder loss minimisation Case II 106
Fig 5-11 69-bus system for feeder loss minimisation Case III 107
Fig 5-12 69-bus system for feeder loss minimisation Case IV 107
Fig 5-13 Comparison of feeder loss for different DG capacities before and after
simultaneous reconfiguration and DG allocation 108
Fig 5-14 Comparison of voltage profiles in different cases of 69-node system 109
Fig 6-1 The reconfiguration hours for a typical day 113
Fig 6-2 Search space of DNR and TEO 115
Fig 6-3 Sample network with three substations 116
Fig 6-4 Flowchart of the ACO applied to DNR and TEO for a specific type of day
117
Fig 6-5 Distribution feeder connected to RBTS Bus 4 118
Fig 6-6 Daily load profile of residential consumers 119
Fig 6-7 Daily load profile of commercial consumers 120
Fig 6-8 Daily load profile of industrial consumers 120
Fig 6-9 Daily load profile (MW) of the main feeder 120
Fig 6-10 Annual energy loss with different DG capacities 123
Fig 6-11 Annual energy loss in uncoordinated charging strategy 125
Fig 6-12 Annual energy loss in coordinated charging strategy 126
Page | 9
Fig 7-1 Membership function for SAIDI and switch cost reduction 131
Fig 7-2 Membership function for ECOST reduction 132
Fig 7-3 Search space of sectionalising switch placement 134
Fig 7-4 Distribution feeder connected to RBTS Bus 4 with 6 sectionalising switches
136
Fig 7-5 Optimal relocation of sectionalising switches in Test Case 11 139
Fig 7-6 Optimal installation of sectionalising switches in Test Case 12 141
Fig 7-7 Optimal installation and relocation of sectionalising switches in Test Case
13 142
Fig 7-8 BCR versus years 143
Fig 7-9 Variation of cost versus change in CDF 144
Fig 7-10 Number of installed sectionalising switches versus change in CDF 145
Fig 8-1 Flowchart of the MOACO algorithm applied to multi-objective DNR
problem 157
Fig 8-2 Flowchart of the AIS-ACO algorithm applied to multi-objective DNR
problem 158
Fig 8-3 Distribution feeder connected to RBTS Bus 4 161
Fig 8-4 Pareto solutions obtained (minimisation of feeder loss ECOST and SAIDI)
162
Fig 9-1 Membership function for feeder loss reduction 168
Fig 9-2 Membership function for maximum node voltage deviation reduction 169
Fig 9-3 Membership function for load balancing index reduction 170
Fig 9-4 33 bus-system for fuzzy multi-objective optimisation Case II 173
Fig 9-5 Pareto front obtained for 33-bus system in Case II 174
Fig 9-6 33 bus-system for fuzzy multi-objective optimisation Case III 175
Fig 9-7 Pareto front obtained for 33-bus system in Case III 176
Fig 9-8 33 bus-system for fuzzy multi-objective optimisation Case IV 178
Fig 9-9 Pareto front obtained for 33-bus system in Case IV 178
Fig 9-10 69 bus system for fuzzy multi-objective optimisation Case II 180
Fig 9-11 Pareto front obtained for 69-bus system in Case II 181
Fig 9-12 69-bus system for fuzzy multi-objective optimisation Case III 183
Fig 9-13 Pareto front obtained for 69-bus system in Case III 183
Fig 9-14 69-bus system for fuzzy multi-objective optimisation Case IV 185
Fig 9-15 Pareto front obtained for 69-bus system in Case IV 186
Page | 10
List of Tables
Table 2-1 Transformer economic operation area 33
Table 2-2 Transformer technical specifications and costs 35
Table 3-1 Relationship of 119911 lowast and 119862 62
Table 4-1 Household size by number of people in household as a proportion [103] 72
Table 4-2 Parameters of a typical 3311 kV two-winding transformer [106] 78
Table 4-3 Daily transformer loss in different scenarios 80
Table 4-4 Transformer loss with different TCLF 85
Table 4-5 Average number of switching operations with different TCLF 85
Table 4-6 Transformer loss in Test Case 2 88
Table 5-1 Results of different cases for the 33-bus system 100
Table 5-2 Comparison of simulation results for 33-bus system in Case II 101
Table 5-3 Comparison of ACO with CGA and CSA for the 33-bus system in Case II
102
Table 5-4 Results of different cases for the 69-bus system 105
Table 5-5 Comparison of simulation results for 69-bus system in Case II 106
Table 6-1 Revised customer data (peak load) 119
Table 6-2 The distribution of load types for a whole year 121
Table 6-3 Results of DNR and TEO with different load types in Test Case 1 122
Table 6-4 Characteristics of EV 124
Table 7-1 Customer data (Average load) 137
Table 7-2 Sector interruption cost estimation ($kW) 138
Table 7-3 Results of sectionalising switches relocation in Test Case 11 140
Table 7-4 Results of sectionalising switches installation in Test Case 12 141
Table 7-5 Results of sectionalising switches relocation and installation in Test Case
13 143
Table 7-6 Impacts of 120588 variation on objective function 119869 146
Table 7-7 Impacts of variation in number of ants on objective function 119869 146
Table 7-8 Results of sectionalising switches relocation and installation in Test Case
2 147
Table 7-9 Results of sectionalising switches installation and relocation in Test Case
3 148
Page | 11
Table 8-1 Revised customer data (Average load) 162
Table 8-2 Mean and standard deviation of Pareto Front (loss ECOST and SAIDI)
163
Table 8-3 Minimum solutions along each objective (loss ECOST and SAIDI) 163
Table 8-4 Best compromise solutions (loss ECOST and SAIDI) 164
Table 9-1 Results of DNR in fuzzy multi-objective formulation for 33-bus system in
Case II 173
Table 9-2 Mean and standard deviations of Pareto Front for 33-bus system in Case II
174
Table 9-3 Minimum solutions along each objective for 33-bus system in Case II 175
Table 9-4 Results of DNR in fuzzy multi-objective formulation for 33-bus system in
Case III 176
Table 9-5 Mean and standard deviations of Pareto Front for 33-bus system in Case
III 176
Table 9-6 Minimum solutions along each objective for 33-bus system in Case III 177
Table 9-7 Results of DNR and DG allocation in fuzzy multi-objective formulation
for 33-bus system in Case IV 178
Table 9-8 Mean and standard deviations of Pareto Front for 33-bus system in Case
IV 179
Table 9-9 Minimum solutions along each objective for 33-bus system in Case IV 179
Table 9-10 Results of DNR in fuzzy multi-objective formulation for 69-bus system
in Case II 181
Table 9-11 Mean and standard deviations of Pareto Front for 69-bus system in Case
II 181
Table 9-12 Minimum solutions along each objective for 69-bus system in Case II 182
Table 9-13 Results of DNR in fuzzy multi-objective formulation for 69-bus system
in Case III 183
Table 9-14 Mean and standard deviations of Pareto Front for 69-bus system in Case
III 184
Table 9-15 Minimum solutions along each objective for 69-bus system in Case III
184
Table 9-16 Results of DNR and DGs allocation in fuzzy multi-objective formulation
for 69-bus system in Case IV 185
Page | 12
Table 9-17 Mean and standard deviations of Pareto Front for 69-bus system in Case
IV 186
Table 9-18 Minimum solutions along each objective for 69-bus system in Case IV
187
Table A-1 Typical configurations and parameters of 11 kV triplex cables in the UK
204
Table A-2 Line and load data of 33-bus system 205
Table A-3 Line and load data of 69-bus system 206
Table A-4 Feeder data of RBTS Bus 4 207
Table A-5 Reliability Data for RBTS Bus 4 208
Table B-1 The locations of tie-switch in Scenario 9 209
Table B-2 Mean voltage profiles at each node in the linked feeder 210
Table B-3 95th
voltage profiles at each node in the linked feeder 210
Table B-4 Network losses in each branch of 33-bus system 211
Table B-5 Network losses in each branch of 69-bus system 212
Table B-6 Pareto optimal solutions of multi-objective DNR (loss ECOST and
SAIDI) 214
Table B-7 Pareto optimal solutions of multi-objective DNR (loss maximum node
voltage deviation feeder load balancing index) for 33-bus system in Case II 215
Table B-8 Pareto optimal solutions of multi-objective DNR (loss maximum node
voltage deviation feeder load balancing index) for 33-bus system in Case III 215
Table B-9 Pareto optimal solutions of multi-objective DNR (loss maximum node
voltage deviation feeder load balancing index) for 33-bus system in Case IV 216
Table B-10 Pareto optimal solutions of multi-objective DNR (loss maximum node
voltage deviation feeder load balancing index) for 69-bus system in Case II 218
Table B-11 Pareto optimal solutions of multi-objective DNR (loss maximum node
voltage deviation feeder load balancing index) for 69-bus system in Case III 218
Table B-12 Pareto optimal solutions of multi-objective DNR (loss maximum node
voltage deviation feeder load balancing index) for 69-bus system in Case IV 219
Table C-1 ACO parameters for distribution network reconfiguration and DG
allocation in Test Case 2amp3 221
Table C-2 ACO parameters for distribution network reconfiguration and DG
allocation in Test Case 4 221
Page | 13
Table C-3 ACO parameters for distribution network reconfiguration and transformer
economic operation 221
Table C-4 ACO parameters for sectionalising switch placement in Test Case 1 222
Table C-5 ACO parameters for sectionalising switch placement in Test Case 2amp3222
Table C-6 MOACO parameters for multi-objective distribution network
reconfiguration (loss ECOST and SAIDI) 222
Table C-7 AIS-ACO parameters for multi-objective distribution network
reconfiguration (loss ECOST and SAIDI) 223
Table C-8 ACO parameters for multi-objective DNR (loss maximum node voltage
deviation feeder load balancing index) 223
Table C-9 AIS-ACO parameters for multi-objective DNR (loss maximum node
voltage deviation feeder load balancing index) 223
Page | 14
List of Abbreviations
Abbreviations Definition
ACO Ant Colony Optimisation
ACS Ant Colony System
AENS Average Energy Not Supplied
AIS Artificial Immune Systems
AIS-ACO Artificial Immune Systems-Ant Colony Optimisation
ANN Artificial Neutral Network
ASP Active Server Pages
BCR Benefit-to-cost Ratio
BEM Branch Exchange Method
BPSO Binary Particle Swarm Optimisation
CDF Customer Damage Function
CGA Continuous Genetic Algorithm
CSA Cuckoo Search Algorithm
DA Distribution Automation
DNO Distribution Network Operator
DNR Distribution Network Reconfiguration
DG Distributed Generation
DPSO Discrete Particle Swarm Optimisation
ECOST Expected Customer Damaged Cost
EDNS Expected Demand Not Supplied
ENS Energy not supplied
EV Electric Vehicle
FMEA Failure-mode-and-effect Analysis
FWA Firework Algorithm
FRTU Feeder Remote Terminal Unit
GA Genetic Algorithm
HC Hyper Cube
HSA Harmony Search Algorithm
HV High Voltage
Page | 15
IWO Invasive Weed Optimisation
LV Low Voltage
MDC Maximum Driving Capability
MILP Mixed Integer Linear Programming
MOACO Multi-objective Ant Colony Optimisation
MV Medium Voltage
PSO Particle Swarm Optimisation
RBTS Roy Billinton Test System
RGA Refined Genetic Algorithm
SA Simulated Annealing
SAIDI System Average Interruption Duration Index
SAIFI System Average Interruption Frequency Index
SCADA Supervisory Control and Data Acquisition
SSP Sectionalising Switch Placement
TS Tabu Search
TCLF Transformer Critical Load Factor
TEO Transformer Economic Operation
TOM Transformer Operation Mode
VML Vector Markup Language
Page | 16
Abstract
The University of Manchester
Submitted by Boyi Zhang
for the degree of Doctor of Philosophy
Distribution Network Automation for Multi-objective Optimisation
December 2017
Asset management and automation are acknowledged by distribution utilities as a
useful strategy to improve service quality and reliability However the major
challenge faced by decision makers in distribution utilities is how to achieve long-
term return on the projects while minimising investment and operation costs
Distribution automation (DA) in terms of transformer economic operation (TEO)
distribution network reconfiguration (DNR) and sectionalising switch placement
(SSP) is recognised as the most effective way for distribution network operators
(DNOs) to increase operation efficiency and reliability Automated tie-switches and
sectionalising switches play a fundamental role in distribution networks
A method based on the Monte Carlo simulation is discussed for transformer loss
reduction which comprises of profile generators of residential demand and a
distribution network model The ant colony optimisation (ACO) algorithm is then
developed for optimal DNR and TEO to minimise network loss An ACO algorithm
based on a fuzzy multi-objective approach is proposed to solve SSP problem which
considers reliability indices and switch costs Finally a multi-objective ant colony
optimisation (MOACO) and an artificial immune systems-ant colony optimisation
(AIS-ACO) algorithm are developed to solve the reconfiguration problem which is
formulated within a multi-objective framework using the concept of Pareto
optimality The performance of the optimisation techniques has been assessed and
illustrated by various case studies on three distribution networks The obtained
optimum network configurations indicate the effectiveness of the proposed methods
for optimal DA
Page | 17
Declaration
No portion of the work referred to in the thesis has been submitted in support of an
application for another degree or qualification of this or any other university or other
institute of learning
Page | 18
Copyright Statement
i The author of this thesis (including any appendices andor schedules to this
thesis) owns certain copyright or related rights in in (the ldquoCopyrightrdquo) she
has given The University of Manchester certain rights to use such Copyright
including for administrative purposes
ii Copies of this thesis either in full or in extracts and whether in hard or
electronic copy may be made only in accordance with the Copyright
Designs and Patents Act 1988 (as amended) and regulations issued under it
or where appropriate in accordance with licensing agreements which the
University has from time to time This page must form part of any such
copies made
iii The ownership of certain Copyright patents designs trademarks and other
intellectual property (the ldquoIntellectual Propertyrdquo) and any reproductions of
copyright works in the thesis for example graphs and tables
(ldquoReproductionsrdquo) which may be described in this thesis may not be owned
by the author and may be owned by third parties Such Intellectual Property
and Reproductions cannot and must not be made available for use without the
prior written permission of the owner(s) of the relevant Intellectual Property
andor Reproductions
iv Further information on the conditions under which disclosure publication
and commercialisation of this thesis the Copyright and any Intellectual
Property andor Reproductions described in it may take place is available in
the University IP Policy (see
httpdocumentsmanchesteracukDocuInfoaspxDocID=24420) in any
relevant Thesis restriction declarations deposited in the University Library
The University Libraryrsquos regulations (see
httpwwwlibrarymanchesteracukaboutregulations) and in The
Universityrsquos policy on Presentation of Theses
Page | 19
Acknowledgements
First and foremost I would like to express my deepest gratitude to my supervisor
Prof Peter Crossley for his invaluable guidance and continuous encouragement
throughout the project
I would like to thank my friends and colleagues in the Ferranti Building at The
University of Manchester Prof Zhongdong Wang and Dr Qiang Liu for the fruitful
research discussions and their encouragement throughout the period of my PhD
I wish to thank North China Electric Power University PR China for the 2+2
course and also to Prof Chunming Duan and Prof Sangao Hu for their help and
encouragement
I also wish to thank Prof Bo Zhang Prof Jianguo Zhao and Prof Li Zhang from
Shandong University PR China who continued to support my research with their
valuable feedback and advice
Finally I would like to express my gratitude to my parents for their encouragement
and support
Page | 20
CHAPTER 1
INTRODUCTION
11 Motivation
The electricity ldquoutilityrdquo distribution network is part of a power system that carries
electricity from a high voltage transmission grid to industrial commercial and
residential customers [1] In England and Wales the voltage level of distribution
networks ranges from 132 kV to 230 V [2] Generally most distribution networks
operating at voltages below 25 kV are designed in closed loop but are operated
radially due to the simplicity of operation the ease of protection coordination and
the minimisation of overall economics [3] [4]
The electric power generation transmission and distribution companies are not only
energy producers but also significant power consumers Power loss occurs when
electricity is supplied to customers In 2013 the total distribution losses of GBrsquos
networks were estimated to be 196 TWh which indicates that about 6 of the total
power generation is wasted in the form of losses at distribution level [5] Utility
statistics also indicate that distribution transformers account for approximately 22
of these losses and the line and cable losses make up the remaining 78 Reduction
in active power loss can help distribution network operators (DNOs) save costs and
increase profits
The expression ldquoPower quality = Voltage qualityrdquo has been widely accepted as the
wave shape and magnitude of voltage that strongly influences the power quality
Chapter 1 Introduction
Page | 21
received by customers [6] According to the EN50160 standard [7] under normal
conditions at least 95 of the mean 10 minutes average rms voltage magnitudes in
an 11 kV electricity distribution network should be within the range 09 pu to 11 pu
during one week
Distribution network reliability has proved to be another fundamental attribute for
the safe operation of any modern power system [8] Data show that about 80 of
customer outages are due to distribution system failures [9] Based on the resource
from [10] in 2011 the average number of minutes of lost supply per customer in GB
is 70 minutes According to [11] electricity breakdowns cost the United States
around $80 billion per year With improved reliability the DNOs can save expenses
that are spent on networkrsquos maintenances after a failure [12]
The major challenge faced by DNOs is how to distribute the power in a low-cost
reliable and efficient way Distribution automation (DA) is recognised as the most
effective method for DNOs to increase operation efficiency and reliability The three
main parts of DA are transformer economic operation (TEO) distribution network
reconfiguration (DNR) and sectionalising switch placement (SSP) TEO refers to the
optimum selection of the transformers needed to supply each feeder This is related
to the economic evaluation of network performance and the resilience of the
network DNR is a process that involves changing the network topology by altering
the openclose status of sectionalising (normally closed) and tie (normally open)
switches [13] [14] Installation of new sectionalising switches and relocation of
existing sectionalising switches are defined as SSP
Mathematically DA is a discrete non-linear constrained combinational optimisation
problem that is subject to operating constraints As it is not a practical solution to
investigate all possible network configurations ant colony optimisation (ACO)-
based heuristic search algorithms have been developed
To build a cleaner climate-friendly community the European Union has set a target
on carbon emissions for a 40 60 and 80 below 1990 levels by 2030 2040
and 2050 respectively [15] Therefore a large number of renewable distributed
generations (DGs) are deployed DG is a small electric generation unit that is
connected directly to the distribution network or appears on side of the meter
accessed by the customer [16] Since the number of DGs has increased in recent
Chapter 1 Introduction
Page | 22
years this has resulted in bidirectional power flows and locally looped networks [17]
The integration of high numbers of DGs strongly affects network operation and
planning Therefore optimal placement and sizing of DGs strongly improve
distribution network performance
12 Objectives
The aim of this research is to improve service quality and efficiency based on the
results of DA To achieve this aim the objectives of this thesis are as follows
To review distribution networks DA loss and reliability assessment and
optimisation functions
To propose three optimisation techniques namely the Monte Carlo Method the
ACO algorithm and the artificial immune systems-ant colony optimisation (AIS-
ACO) algorithm
To develop an optimal strategy consisting of TEO and DNR for transformer loss
reduction Statistic models of customer electrical demands should be established
to evaluate their impact from the perspective of probability
To assess the DNR and DG placement problems simultaneously in terms of
distribution feeder loss minimisation
To assess the TEO and DNR problem simultaneously in terms of distribution
network loss minimisation including transformer loss and feeder loss under
different load scenarios
To assess the SSP problem simultaneously based on three objectives namely
reduction of unserved energy cost decrease in the average time that a customer is
interrupted and minimisation of switch costs and using the fuzzy set theory
To propose a benefit-to-cost analysis to justify whether the benefits of installing
and relocating sectionalising switches can justify the cost or not
To formulate the optimal network reconfiguration problem within a multi-
objective framework using the Pareto optimality concept where network loss
and reliability indices are simultaneously optimised
Chapter 1 Introduction
Page | 23
To assess the DNR and DG allocation problem in terms of three conflicting
objectives optimisation network loss maximum node voltage deviation and
load balancing index in order to obtain a set of non-dominated solutions
13 Contribution of the work
This thesis has presented three methodologies of DA All of them are designed to
achieve service quality and efficiency improvement
The contributions of this thesis are summarised below
Load profiles In most literatures the load variations are ignored in their studies
which could underestimate the total energy loss for the utility [18] The
stochastic nature associated with load variety is considered in Chapter 4 In this
chapter the value of the load associated with domestic demand profiles are
obtained from the research described in [19] this can produce a random 1-min
resolution model for UK households A pool of load profiles is randomly
generated by this model in MATLAB Following this each node in the feeders
from the system is assigned with residential demand profiles from the pool based
on the Monte Carlo methodology
In Chapter 6 the distribution loads experience daily and seasonal variations The
study considers the daily load curves of different types of consumers (residential
commercial and industrial) In addition the days are divided into eight types
spring weekdays spring weekends summer weekdays summer weekends
autumn weekdays autumn weekends winter weekdays and winter weekends
Optimisation problems Previously it was observed that sufficient work has
been completed in terms of examining the TEO and the DNR problems
separately In Chapter 4 and 6 both the TEO and network reconfiguration
problems are integrated to benefit the whole distribution network effectively
Different combinations of locations of tie-switches in the network and operation
modes of all transformers in the substations represent different network
configurations Network reconfiguration and transformer operation modes
variation are dealt simultaneously using the ACO algorithm with an objective of
network loss minimisation as presented in Chapter 6
Chapter 1 Introduction
Page | 24
Most research projects have focused only on the optimisation of either the DNR
or the DG allocation problem An ACO algorithm is proposed in Chapter 5 to
deal with the DNR and DG allocation problems simultaneously in terms of
feeder loss minimisation In Chapter 9 the study aims to determine the optimum
network configurations and DG locations that minimise the active power loss
maximum node voltage deviation and feeder load balancing simultaneously
Multi-objective optimisation framework When there are multiple and
conflicting objectives that need to be satisfied all objective can be converted into
a single objective function which reflects a compromise among all objectives
The single objective function has two forms weighted aggregation and fuzzy
satisfaction objective function The selection of the form depends on the number
of objectives as well as their units and dimensions In Chapter 7 the system
expected outage cost to customers (ECOST) and switch costs can be converted
into a single objective function by aggregating these objectives in a weighted
function However as system interruption duration index (SAIDI) and switch
costs have different dimensions and units the two conflicting objectives are
modelled with fuzzy sets and then combined into a single objective function
Also a fuzzy membership function based on max-min principle is presented for
optimising ECOST SAIDI and switch costs simultaneously In Chapter 9 a new
operator called lsquomax-geometric meanrsquo has been introduced to determine the
degree of overall fuzzy satisfaction
However the above simple optimisation processes only obtain a compromise
solution It is no longer suitable if the DNO wishes to obtain all possible optimal
solutions for all the conflicting objectives at the same time [20] Therefore a set
of Pareto optimal solutions is introduced in this study And the corresponding
objective values constitute the Pareto front It allows decision makers to select
the most suitable topology from the Pareto optimal solutions for implementation
depending on the utilitiesrsquo priorities In Chapter 8 the study formulates the
optimal network reconfiguration problem within a multi-objective framework
using the concept of Pareto optimality where network loss and reliability indices
are simultaneously optimised In Chapter 9 active power loss maximum node
voltage deviation and feeder load balancing are optimised simultaneously
After obtaining the Pareto optimal solutions the best compromise solution
among the multiple objectives can be selected by comparing the fitness value of
Chapter 1 Introduction
Page | 25
each member in the Pareto front The best compromise solution is varied by
changing the values of weighting factors based on the tendencies of the network
decision makers A set of best compromise solutions can be obtained by varying
the weighing factors of each objective function and this is presented in Chapter 8
Proposal of ACO-based algorithms for assessment of optimisation problems
The ACO algorithm is a population-based approach based on the behaviour of
real ants [14] The proposed algorithm is not only used for assessment of the
TEO problem but also with DNR DG allocation and SSP problems The ACO
control parameters are different for each test case The selection of parameters is
a balance between the convergence rate and the global search ability of the
algorithm They are set experimentally using information from several trial runs
The results obtained by the ACO algorithm have been compared to those from
other algorithms in Chapter 5 and the ACO parameter sensitivity analysis is
provided in Chapter 7
In Chapter 8 the multi-objective ant colony optimisation (MOACO) and AIS-
ACO algorithms have been proposed and compared for assessment of multi-
objective DNR problems Both algorithms focus on problems in terms of Pareto
optimality where the objective functions are multidimensional and not scalar
A full list of publications resulting from this thesis is included in Appendix D
14 Structure of the thesis
The thesis is organised as follows
Chapter 2 introduces the distribution network configurations and associated
equipment It also gives a comprehensive literature survey which reviews the
existing knowledge and research activities in the distribution automation (DA)
including transformer economic operation (TEO) distribution network
reconfiguration (DNR) and sectionalising switch placement (SSP) The assessment
of transformer loss feeder loss and reliability indices as well as the multi-objective
optimisation functions are also described in this chapter
Chapter 3 summarises the optimisation techniques for assessment of the multi-
objective problem The Monte Carlo Method ACO algorithm and AIS-ACO hybrid
algorithm are described in detail
Chapter 1 Introduction
Page | 26
Chapter 4 proposes two methodologies for transformer loss reduction whilst
maintaining satisfactory voltages which are TEO and DNR The demand profiles are
randomly generated by the profile generators in MATLAB Following this each
node in the feeders from the system is assigned with demand profiles based on the
Monte Carlo Method The effectiveness of the two investigated methods
implemented either alone or together are presented and discussed
Chapter 5 describes an ACO algorithm to assess the network reconfiguration and
DG placement problems simultaneously in terms of distribution feeder loss
minimisation The results of four scenarios carried out on two standard IEEE 33-
node and 69-node systems are presented to show the effectiveness of the proposed
approach The effect of DG capacities on DNR for feeder loss reduction is also
discussed Moreover the results obtained by ACO algorithm have been compared to
those from other algorithms in the literature
Chapter 6 presents the ACO algorithm for minimisation of the losses associated
with a network loss including transformer loss and feeder loss under different load
scenarios This is achieved by the optimum selection of which transformers need to
supply each feeder and by determining the optimal locations of the tie-switches The
performance of this approach to minimise power loss is assessed and illustrated by
various case studies on a typical UK distribution network The impact of DGs and
electrical vehicles (EVs) in reducing the loss is also discussed
Chapter 7 explores an ACO-based methodology for the placement of sectionalising
switches in distribution networks The objectives of the proposed sectionalising
switch placement problem are reduction of unserved energy costs decrease in the
average time that a customer is interrupted and minimisation of switch costs These
objectives are formulated in either a single objective function or a fuzzy satisfaction
objective function The performance of the proposed methodology is assessed and
illustrated by various test cases on a well-known reliability test system
Chapter 8 formulates the optimal network reconfiguration problem within a multi-
objective framework using the Pareto optimality concept where network loss and
reliability indices are simultaneously optimised The MOACO algorithm and AIS-
ACO algorithm are proposed and compared for assessment of DNR problems The
Chapter 1 Introduction
Page | 27
proposed approaches are tested on Bus 4 of the RBTS and a set of high quality non-
dominated solutions are obtained
Chapter 9 addresses two algorithms to assess the DNR and DG allocation problems
in terms of the three conflicting objectives minimisation network loss maximum
node voltage deviation and load balancing index The ACO algorithm is used to
solve the problem in the fuzzy domain and the AIS-ACO algorithm is adopted to
obtain a set of non-dominated solutions using the concept of Pareto optimality The
effectiveness and the efficiency of the proposed methods are implemented on two
standard test systems as case studies
Chapter 10 concludes the thesis by summarising the main findings of the work
Finally possible future research ideas associated with this thesis are proposed
All the network models are built in OpenDSS and all the algorithms are coded in
MATLAB They are carried on a 340-GHz processor with 16 GBs of RAM memory
for all studies
Page | 28
CHAPTER 2
DISTRIBUTION AUTOMATION
21 Introduction
Distribution automation (DA) is an important part of a Smart Grid [21] It enables a
distribution network operator (DNO) to monitor coordinate and operate distribution
components in real-time from a remote control centre [22] [23] This improves the
reliability performance and operational efficiency of the electrical distribution
system and helps increase the market penetration of distributed generations (DGs)
and electrical vehicles (EVs) [24]ndash[26]
The remainder of this chapter is structured as follows Sections 22-23 introduce the
network configurations and associated equipment Sections 24-26 present the three
main parts of DA namely transformer economic operation (TEO) distribution
network reconfiguration (DNR) and sectionalising switch placement (SSP)
Transformer loss feeder loss and reliability indices assessments are described in
Sections 27-29 Three methods for assessment of multi-objective optimisation
problems are reviewed in Section 210 A summary of the main conclusions in this
chapter is given in Section 211
Chapter 2 Distribution Automation
Page | 29
Tie-switch
Sectionalising switch
22 Distribution Network Configurations
In England and Wales the voltage level of distribution networks ranges from 132 kV
to 230 V [2] Generally most distribution networks are designed in closed loop but
are operated radially due to the simplicity of operation the ease of protection
coordination and the minimisation of overall economics [3] [4]
There are three typical system configurations shown in Fig 2-1 [27] The radial
system in Fig 2-1 (a) is common in rural areas but does not include any backup
supplies Consequently the lack of feeder interconnections means a short-circuit
fault will interrupt power to all the downstream customers and power will not be
restored until the faulted equipment is repaired The tie-switches (normally open) in
Fig 2-1 (b) connect two feeders and make the system radial in a primary loop There
are multiple tie-switches between multiple feeders in distribution systems Fig 2-1 (c)
describes a link arrangement and during normal conditions the systems are operated
radially However when a fault occurs the part affected by the fault is isolated by
tripping the breakers The unaffected areas can then be restored from a different
busbar by closing the tie-switches and feeding the supply
(a) Radial system (b) Primary loop (c) Link Arrangement
Fig 2-1 Typical Distribution network [27]
Chapter 2 Distribution Automation
Page | 30
23 Switchgear for Distribution Network
There is a large variety of switchgears used in distribution networks this includes
reclosers sectionalising switches tie-switches fuses and circuit breakers This
section mainly focuses on reclosers sectionalising switches and tie-switches
231 Reclosers
Reclosers are automatic self-contained protection devices installed on main feeders
and operate as a part of the protection schemes [28] [29] They are a type of circuit
breakers with control measurement and automatic re-closing functions Most faults
on distribution feeders are temporary ie they last from a few cycles to a few
seconds and are cleared by protection tripping a circuit breaker [1] Reclosers
normally count the number of overcurrent pulses followed by the line de-
energisation sequences [1] They always coordinate with other types of protection
equipment These include such as fuses and sectionalising switches for the purpose
of fault isolation and system restoration The process of recloser operation is shown
in Fig 2-2 The time between reclosures and the time of the reclose can be
programmed If the fault is transient the recloser will operate 1-3 times and then
restore service quickly If the fault is permanent after a pre-set number of trip-
reclose operations the recloser is locked and the recloser interrupter triggers a final
trip
Fig 2-2 Recloser operation
Time between reclosures
Time of the reclose Fault current
Recloser locks
out on 2nd
reclose
as programmed
Recloser opens
Recloser recloses
fault still present
Recloser recloses
fault still present
Recloser re-opens
fault still present
Load current
Chapter 2 Distribution Automation
Page | 31
232 Sectionalising Switches
Sectionalising switches are the protective devices that operate in conjunction with
backup circuit breakers or reclosers [25] They are isolating devices that
automatically isolate the faulted sections from a distribution network after a
permanent fault has occurred and after the line is de-energised by the feeder breaker
[1] This is because sectionalising switches are not designed to interrupt the fault
current and must be used with the feeder breaker that can break and reclose a circuit
under all conditions ie normal or faulty operating conditions [25] [30] A detailed
operation of sectionalising switches is presented in Section 26
233 Tie-switches
Tie-switches refer to the normally open switches of the network By closing the
opened tie-switch the load is transferred from one feeder to another but this requires
an appropriate sectionalising switch to be opened to restore the radial topology [31]
The tie-switch placement should follow certain principles ie all the loads are
energised and the network is operated in radial configurations The tie-switches are
designed to operate in normal condition but are not suitable for the interruption of
fault currents They are designed to operate after a switching device (circuit breaker
of fuse) has interrupted the fault current
24 Transformer Economic Operation
241 Basic Concepts
Power transformers are the interface between the generators and the transmission
lines and between lines operating at different voltage levels [32] They are a critical
part of an electric power system and transform the ac voltage based on the principle
of electromagnetic induction A step-up transformer ensures the efficient
transmission of power ie high voltage-low current and a step-down transformer
permits the transmitted power to be used at a lower and safer voltage [33]
Distribution transformers are used to reduce the primary system voltages to the
Chapter 2 Distribution Automation
Page | 32
Tran
sfo
rme
r Lo
ss
Transformer Load Factor
1 Transformer
2 Transformers
utilisation voltages [25] normally 132 kV for high voltage (HV) 11 kV-33 kV for
medium voltage (MV) and 400 V for low voltage (LV) in UK distribution networks
For transformers currently in operation developing a new strategy for transformer
loss reduction is required rather than replacing them with high efficiency
transformers [34] Transformer economic operation refers to the optimum selection
of transformers needed to supply each feeder This is related to the economic
evaluation of network performance and the resilience of the network
In order to meet reliability requirements the load factor of each transformer should
not go beyond 50 when two transformers are operated in parallel In other words
the transformer load factor must be within 100 in separate operation modes
The integrated power loss curves of onetwo transformers in operations are shown in
Fig 2-3 The intersection of the two curves is 119878119871 which is called the transformer
critical load factor (TCLF) Therefore it can be concluded that
When the total load 119878 lt 119878119871 a single transformer produces less integrated
power loss than parallel transformers
When 119878 gt 119878119871 parallel operation of transformer is more economical
When 119878 = 119878119871 the losses in single or parallel operation modes are identical
Fig 2-3 Transformer loss versus transformer load
119878119871
Core loss for 2 transformers
Core loss for 1 transformer
Chapter 2 Distribution Automation
Page | 33
As a result Table 2-1 presents the transformer commercial operation area
Table 2-1 Transformer economic operation area
Operation modes Single Transformer Two Parallel Transformers
Economic operation area 0 ~ 119878119871 119878119871 ~ 119878
242 Literatures on Transformer Economic Operation
Several papers that discuss research on transformer economic operation not only
focuse on transformer loss reduction but also discuss cost reduction and reliability
improvement
The papers concerned with transformer economic operation based on loss reduction
were presented in [35]ndash[37] Wang and Liu [35] used the ASP (Active Server Pages)
language as a foundation to analyse transformer economic operation on-line The
operation curves and interval graph of commercial operation were achieved from the
VML (Vector Markup Language) and the simulation results In the interest of the
economical and profitable operation of transformer real-time data was obtained
using the SCADA (Supervisory Control and Data Acquisition) and this included the
measurement of active power load and voltage [36] [37] Then the transformers
were monitored in real-time and the methods used to ensure their economical and
profitable operation were suggested online
However if the active power loss of transformers was measured based on the real-
time load data transformers would frequently be switched to a new state associated
with instantaneous economical and profitable operation As the number of switching
operations increases the lifetime of the transformers decreases As a result Song and
Zhang [38] developed a load smoothing algorithm to reduce the number of switching
operations of the transformer effectively The curves of transformer loads before and
after smoothing are presented in Fig 2-4 Table 2-2 and 2-3 illustrate the transformer
operation mode variation before and after smoothing respectively The results show
that the active loss achieved when using the load smoothing algorithm was a little
higher than when smoothing was not used However the total number of switching
operations of transformers with load smoothing was reduced from 6 to 2 which
would expand the transformer life cycle
Chapter 2 Distribution Automation
Page | 34
(a) Before load smoothing (b) After load smoothing
Fig 2-4 Daily load curve of a typical substation before and after load smoothing [38]
Table 2-2 Transformer operation mode variation before load smoothing
Time Transformer operation mode The sum of active power loss
(Kw)
000-300 1 transformer in operation 12363
300-1600 2 transformer in operation
1600-2100 Parallel operation
2100-2400 2 transformer in operation
Table 2-3 Transformer operation mode variation before load smoothing
Time Transformer operation mode The sum of active power loss
(Kw)
000-600 2 transformer in operation 12768
600-2100 Parallel operation
2100-2400 2 transformer in operation
Generally the cost of the energy loss of a transformer over its service life is much
higher than its initial capital price As a result the transformer selection decision is
based not only on the purchase price but also includes the cost of installation
maintenance and loss over the lifetime of the equipment [39]
Amoiralis etc [40] have investigated the cost of two transformers that have the same
capacity but different specifications The transformers were loaded at 50 of full
load and with an increase of 37 for each year The technical characteristics and the
costs associated with the two transformers are presented in Table 2-4 The total cost
is the summation of loss and capital cost of a transformer over 30 years Purchasing a
Chapter 2 Distribution Automation
Page | 35
transformer with low efficiency (Transformer A) reduced the initial cost but resulted
in higher energy costs during the transformer lifetime in comparison with
Transformer B The economic approach in [41] and [42] were used to determine the
suitable size of transformers in Thailand The choice of a high capacity transformer
could improve voltage profiles and provide extra room for emergency conditions and
load increments in the future
Table 2-4 Transformer technical specifications and costs [40]
Transformer Size
(kVA)
No load loss
(kW)
Load loss
(kW)
Capital
price (euro)
Cost of loss
(euro)
Total cost
(euro)
A 1000 11 9 9074 34211 43285
B 1000 094 76 11362 28986 40348
25 Distribution Network Reconfiguration
251 Basic Concepts
DNR refers to a process that involves changing the network topology at normal and
abnormal operating conditions by altering the openclose status of sectionalising
(normally closed) and tie (normally open) switches [13] [14] In fact DNR can be
used as a tool for distribution network planning and real-time operation [14]
As presented in Fig 2-5 the openclosed status of the tie switches and sectionalising
switches determines the structure of the system To achieve a new system
configuration the tie-switch 3 is closed which will create a new loop In order to
restore the network back to a radial structure a switch from 1 2 4 and 5 is selected
and opened
Fig 2-5 Radial test system
Chapter 2 Distribution Automation
Page | 36
Since there are various combinations of switching DNR is treated as a discrete and
constrained optimisation problem Recently optimal DNR strategies discussed in
many literatures have been implemented to achieve active power loss reduction and
system reliability improvement
252 Literatures on Distribution Network Reconfiguration
Network reconfiguration was first introduced by Merlin and Back [43] using a
discrete branch and bound optimisation method to reduce network loss Firstly all
the switches were closed to build a meshed network and then in each step one
branch was removed until the radial configuration was found
Another early study on loss reduction through network reconfiguration was
presented in [44] which discussed how to achieve minimum power loss in
distribution feeders through feeder reconfiguration It is possible to determine loss
variation by analysing the load flow results This involved simulating the system
configuration before and after the feeder was reconfigured [44] It was based on a
single pair switch operation per iteration The relevant results showed that the loss
was reduced only if the voltage across the tie-switch was significant and if the loads
connected at the lower voltage side were transferred to the other side [44] This
criterion was developed to eliminate undesirable switching options The best
switching option was then obtained from the results of load flow studies simulating
all feasible feeder configurations
Zehra etc [31] have proposed a branch exchange algorithm based on two stages of
the solution methodology It started with a feasible network operating in a radial
configuration The first step determined the loop that achieved maximum loss
reduction by comparing the circle sizes for each loop The largest circle indicated the
maximum loss reduction The second phase determined the switching options to be
operated in that loop to provide maximum loss reduction The smallest circle was
identified for the best solution In comparison with [44] the introduction of the
branch exchange method allowed the number of load flow solutions related to the
computation time to be greatly reduced However the results were strongly related to
the initial configuration of the electrical network [45] The above methodologies [31]
[43] [44] were able to obtain the global optimal solution but were only applied to
simplified network models
Chapter 2 Distribution Automation
Page | 37
Later on the artificial intelligent and modern heuristic optimisation algorithms such
as genetic algorithm (GA) [46]ndash[49] simulated annealing (SA) [50] [51] tabu
search (TS) [52]ndash[54] and particle swarm optimisation (PSO) [55] etc were
developed with minor computational effort These intelligent techniques which are
affected by the selection of parameters are able to obtain the optimum solution of
good quality The GA based network reconfiguration method was presented and
tested in a real 136-bus distribution network in [13] Various radial topologies were
generated after the implementation of the genetic operators and the search space was
enlarged by a local improvement method The results show that after network
reconfiguration the power loss is reduced from 3203 kW to 2801 kW which
amounts to a 1255 reduction
Other important objectives including reliability improvement and service restoration
by DNR were mentioned in [56]ndash[58] An intelligent binary particle swarm
optimisation (BPSO) based search method was presented in [57] for assessment of
the DNR problem in terms of reliability improvement The failure of all distribution
equipment such as transformers feeders breakers etc was considered In this paper
the reliability index was in the form of expected demand not supplied (EDNS) The
EDNS of the original configuration is 1008 kW and after reconfiguration the best
result is reached with 849 kW
Network reconfiguration can be formulated not only as a single objective problem
but also as a multi-objective problem that considers various parameters
simultaneously [45] [59]ndash[62] In [59] the objective function was to minimise the
combination of loss cost and consumer interruption cost thus the multiple objectives
were aggregated into an single objective function In order to achieve optimal DNR
a new method was proposed in [60] using a fuzzy multi-objective function to
balance feeder loads and reduce power loss of the distribution systems Depending
on the operatorrsquos preferences the weighting factors of each of the variables could be
varied Das [61] introduced another fuzzy membership formulation to handle the
multiple objectives In this work the degree of overall satisfaction was the minimum
of all the above membership values and the final optimal solution was the maximum
of all such overall degrees of satisfaction [61] Mendoza etc [62] introduced a
micro-genetic algorithm to deal with the trade-offs between the power loss and
reliability indices in order to obtain a set of optimal network configurations using
Chapter 2 Distribution Automation
Page | 38
the concept of Pareto optimality Andervazh etc [45] have presented another Pareto-
based multi-objective DNR method using discrete PSO The objectives were the
minimisation of power loss bus voltage deviations and number of switching
operations
In addition an optimal planning strategy based on network reconfiguration and DGs
placement was presented in [16] The primary objective was power loss reduction
and voltage stability improvement The performance of the methodology was tested
on a 33-bus network and three DGs were installed The power loss was reduced by
3093 by DNR 5624 by DG installation and 6689 by employing
reconfiguration and DG installation simultaneously
26 Placement of Sectionalising Switches
261 Basic Concepts
The implementation of DA requires the installation of various new devices [63]
Among other things DA involves the placement of sectionalising switches ie the
installation of new switches and relocation of existing switches DA in terms of
automatic and remote controlled sectionalising switch placement brings major
benefits to distribution network operators (DNOs) [64] [65] The duration and
number of outages per year determines the annual interruption time of customers
[66] It is possible to shorten outage duration by decreasing the restoration time and
to reduce the number of outages by improving failure rates [67] SSP is useful for the
reduction of the time required to detect and locate a fault and the improvement of
the speed of isolating the faulty sections in the primary distribution network [64]
The effectiveness of these objectives depends on the number and location of
sectionalising switches
In a distribution feeder the section is defined as a group of line segments between
adjacent sectionalising switches [68] And the equivalent load of the section is the
sum of the individual load points in this section [69] When a permanent fault occurs
the switch actions need to respond as follows
Chapter 2 Distribution Automation
Page | 39
1 Detect and locate the fault and initiate tripping to clear the fault A transient
fault is normally cleared by two or three trips and reclose cycles
2 However if the fault persists beyond the predefined cycles reclosure will be
inhibited and the protection will initiate a final trip The load breaker will open and
all the downstream loads will be de-energised
3 The faulty section is then isolated by opening the upstream and downstream
sectionalising switches located next to the fault
4 Restore the loads in the healthy area by closing the upstream and downstream
circuit breakers automatically
5 Repair the faulty section of the feeder and manually restore the loads (ie
reconnect loads to the supply)
A fully and a partially automated distribution feeder are shown in Fig 2-6 and Fig
2-7 respectively The fault occurs on line section 4 It can be clearly seen in Fig 2-6
that all loads are restored after the faulty area is isolated and the total outage time is
the same as the switching time of circuit breakers and sectionalising switches [64]
However as shown in Fig 2-7 only Loads LP1 LP5 LP6 are restored after the
isolation of the faulty section the outage duration of other loads is equal to the repair
time ie significantly longer than the switching time As a result the installation of
sectionalising switches could increase the network reliability as well as the
investment and operation cost of automation [64]
Chapter 2 Distribution Automation
Page | 40
LP1 LP2 LP3 LP4 LP5 LP6
1 2 3 4 5 6 7
LP1 LP2 LP3 LP4 LP5 LP6
1 2 3 4 5 6 7
LP1 LP2 LP3 LP4 LP5 LP6
1 2 3 4 5 6 7
LP1 LP2 LP3 LP4 LP5 LP6
1 2 3 4 5 6 7
Fault occurred on line section 4
CB1 opened
Sectionalising switches adjacent to the faulted area are opened
Energy restored to un-faulted area by closing CB1 and CB2
CB1 CB2
CB1CB2
CB1 CB2
CB1 CB2
Normally closed circuit breaker
Normally open circuit breaker
Closed sectionalising switch
Open sectionalising switch
Interrupted
load
Fig 2-6 Fully automated distribution feeder
Chapter 2 Distribution Automation
Page | 41
LP1 LP2 LP3 LP4 LP5 LP6
1 2 3 4 5 6 7
LP1 LP2 LP3 LP4 LP5 LP6
1 2 3 4 5 6 7
LP1 LP2 LP3 LP4 LP5 LP6
1 2 3 4 5 6 7
LP1 LP2 LP3 LP4 LP5 LP6
1 2 3 4 5 6 7
Fault occurred on line section 4
CB1 opened
Sectionalising switches adjacent to the faulted area are opened
Energy restored to un-faulted area by closing CB1 and CB2
CB1 CB2
CB1CB2
CB1 CB2
CB1 CB2
Normally closed circuit breaker
Normally open circuit breaker
Closed sectionalising switch
Open sectionalising switch
Interrupted
load
Fig 2-7 Partially automated distribution feeder
262 Literatures on Sectionalising Switch Placement
The earliest work that discussed SSP in distribution networks was presented by
Miranda [70] A fuzzy-logic-based optimisation technique has been used to
determine the location of sectionalising switches
In [69] the optimum sectionalising switch relocation problem has been solved by
using the ant colony system (ACS) based method to reduce feeder interruption costs
Chapter 2 Distribution Automation
Page | 42
after a fault In this work it is assumed that there were no additional capital
investments brought by switch relocation However the investment and operation
cost of a sectionalising switch is an important issue which cannot be ignored when
considering the problem of unsupplied energy costs minimisation since they conflict
with each other Therefore the information provided by the multi-objective model is
more valuable than the traditional mono-objective model Abiri-Jahromi etc [64]
have developed a mixed-integer linear programming (MILP) to deal with the new
sectionalising switch installation problem which considers customer outage costs as
well as switch capital operation and maintenance costs After the placement of
sectionalising switches the total system cost over the life period of the switches was
greatly reduced [64] In addition the impacts of customer damage function and load
density variations on SSP were also investigated through sensitivity analysis
The impacts of DG on the optimal number and location of sectionalising switches
were discussed in [71] The introduction of DGs connects a mono-source distribution
network to a multi-source one [66] This potentially improves network reliability
since it reduces the duration and restoration time of interruptions Many loads can be
restored through DGs when operating in islanding mode A mathematical
optimisation methodology has been proposed to minimise the reliability cost when
operating with a minimum number of sectionalising switches The results indicate
the reliability indices of distribution networks are affected by the number and
location of sectionalising switches
27 Transformer Loss Assessment
271 Operating Principles
A transformer has three essential elements a primary winding a secondary winding
and a core [33] As shown in Fig 2-8 the winding connected to the electrical source
is called the primary winding and the secondary winding is linked with the loads All
the windings are connected by the common magnetic flux in the core
Chapter 2 Distribution Automation
Page | 43
Fig 2-8 Elements of a single phase transformer [33]
Usually the power is generated and distributed in a three-phase system Therefore it
is necessary to use a three-phase transformer to increasedecrease the voltage The
structure of the three-phase transformer is presented in Fig 2-9
Fig 2-9 Construction of a three-phase transformer [33]
272 Transformer Quantities Measurement
The transformer quantities present the self-loss during power transmission which
consists of active power loss together with increase in the reactive power of the
network unit [72]
Open-circuit test
The equivalent circuit for the open-circuit test is shown in Fig 2-10 The test is made
on the low-voltage side by applying rated voltage at rated frequency with the high-
voltage winding open [33] The input power and current are measured which are
named no-load loss 119875119874119862 and no-load current 119868119874119862
Chapter 2 Distribution Automation
Page | 44
(a) Test circuit
(b) Equivalent circuit
Fig 2-10 The open-circuit test [33]
As the secondary is open the primary current is equal to the no-load current The no-
load current is used to produce the primary magnetic flux when the transformer is in
no-load operation which is also called the exciting current The voltage drops in the
primary winding can be ignored so the no-load loss is the summation of hysteresis
and eddy current losses [33] The input power is practically equal to the no-load loss
at rated voltage and frequency
119875119874119862 = 119875ℎ+119890 =119880119874119862
2
119877119888119871119881= 119880119874119862119868ℎ+119890 (2-1)
where 119877119888119871119881 is the resistance referred to the low-voltage side 119868ℎ+119890 is the core loss
current
Short-circuit test
The short-circuit test is used to measure the equivalent resistance and reactance of
the winding [6] As shown in Fig 2-11 the low-voltage terminal is shorted together
and the high-voltage side of the transformer is connected to a low-voltage high-
119880119900119888
119868ℎ+119890 119868120601
119868119900119888 119885119890119902 119871119881
119877119888 119871119881 119883119898 119871119881
Chapter 2 Distribution Automation
Page | 45
current source at rated frequency [33] The source voltage is increased until the short
circuit current reaches the rated value At this time value of the source voltage is
known as the short-circuit source voltage 119880119878119862
(a) Test circuit
(b) Equivalent circuit
Fig 2-11 The short-circuit test [33]
As the secondary side is shorted the voltage applied to the full load current is low
compared to the rated voltage and the exciting current 119868119890119909 is negligible during this
test [33] Since the rated current is used the input power is equal to the full-load loss
and expressed as
119875119878119862 = 1198681198781198622 119877119890119902119867119881 (2-2)
where 119877119890119902119867119881 is the winding resistance referred to the high voltage side
As the full-load loss depends on the value of the full load current the loss in the
winding resistance is varied under different loading conditions
119880119904119888
119868119890119909
119868119904119888 119877119890119902 119867119881 119883119890119902 119867119881
(119899119890119892119897119890119888119905)
Chapter 2 Distribution Automation
Page | 46
Active power loss
The active power loss ∆119875 of a two-winding transformer is decided by the no-load
loss 119875119874119862 full-load loss 119875119878119862 and the transformer load factor [73]
∆119875 = 119875119874119862 + 1205732119875119878119862 (2-3)
where 120573 =119878119871
119878119873 represents the transformer load factor 119878119871 is the transformer actual
loading (kVA) 119878119873 is the transformer rated capacity (kVA) Assuming the voltages
are held constant at 10 pu
Reactive power loss
The no-load current 119868119900119888 and short-circuit source voltage 119880119878119862 represent the change of
reactive power ∆119876 in other words the reactive power loss which can be simplified
as
∆119876 = 119876119874119862 + 1205732119876119878119862 (2-4)
119876119874119862 = 119878119874119862 =119868119874119862
119868119873∙ 119878119873 (2-5)
119876119878119862 = 119878119878119862 = 119880119878119862
119880119873∙ 119878119873 (2-6)
273 Integrated Transformer Loss
In general the power loss of a transformer is related to the active power [74]
However if a transformer draws reactive power (it takes current) this causes real
power loss in the network The integrated power loss refers to the sum of active
power loss of the transformer and the increased active power loss contributed by the
reactive power of the transformer [72]
The integrated power loss of a two-winding transformer is calculated by
1198791198711 = 11988002119875119885119874119862 +
1205732
11988002 119875119885119878119862 (2-7)
119875119885119874119862 = 119875119874119862 + 119870119876119876119874119862 (2-8)
Chapter 2 Distribution Automation
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119875119885119878119862 = 119875119878119862 + 119870119876119876119878119862 (2-9)
where 119875119885119874119862 and 119875119885119878119862 are the integrated no-load loss (kW) and the full-load loss (kW)
120573 =119878119871
119878119873 represents the transformer load factor 119878119871 is the transformer actual loading
(kVA) 119878119873 is the rated capacity of the transformer (kVA) 119875119874119862 and 119876119874119862 are the no-
load active power loss (kW) and no-load reactive power loss (kVAr) 119875119878119862 and 119876119878119862
are the full load active power loss (kW) and full load reactive power loss (kVAr) 119870119876
represents the reactive equivalent which is the ratio of increased active power loss to
the change of the node reactive power (kWkVAr) [72] 1198800 is the operational voltage
of the transformer low voltage side in per unit
The no-load and full-load power losses are obtained from the open-circuit and short-
circuit test separately
For two transformers operating in parallel with the same capacity the current
flowing through each transformer is reduced by half Thus the full-load loss of each
transformer becomes a quarter of the previous case The total integrated power loss
is twice the no-load loss and half (2 times1
4) of the full-load loss of one transformer
1198791198712 = 211988002119875119885119874119862 +
1
2
1205732
11988002 119875119885119878119862 (2-10)
28 Feeder Loss Assessment
The distribution network power loss is mainly due to resistive loss in distribution
feeders which is obtained through a power flow study [75] The calculation of
power loss is explained using a two-bus network as shown in Fig 2-12
Fig 2-12 Simple two-bus network
Chapter 2 Distribution Automation
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Assume there is no capacitance on either the sending or receiving bus and 119868119887119904 =
119868119887119903 = 119868119887 As a result the current flowing through branch b and the real power loss
are derived using the following equations
119875119887119877 + 119895119876119887119877 = 119887119877 times 119868lowast (2-11)
119875119887 = 1198681198872 times 119877119887 (2-12)
From (2-11) and (2-12) it is calculated as
119875119887 =119875119887119877
2 +1198761198871198772
1198811198871198772 times 119877119887 (2-13)
where 119875119887 is the real power loss of branch b (W) 119875119887119877 and 119876119887119877 are the real power (W)
and reactive power (VAr) at the receiving end of branch b 119881119887119877 represents the rms
voltage at the receiving end of branch b (V) 119868119887 is the rms current through branch b
(A) and 119877119887 is the resistance of branch b (Ω)
The real power losses in the other branches are evaluated similarly and the network
real loss is the sum of the power losses in all branches as presented in (2-14)
119864119871 = sum 119875119887119899119873119887119899 (2-14)
where 119873119887 is the set of all the distribution network branches
29 Reliability Evaluation
291 Reliability Indices
Reliability is a fundamental attribute for the safe operation of any modern power
system [8] A distribution network which is directly connected to customers has a
large impact on power reliability Distribution reliability primarily relates to
equipment outages and customer interruptions [76] The reliability indices of
distribution network can be classified into two groups ie load point reliability
indices and system reliability indices [77]
Chapter 2 Distribution Automation
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The three primary load point reliability indices average failure rate (120582) average
annual outage time (119880) and average outage time (119903) are calculated by [73]
120582 = sum 120582119895119895 (2-15)
119880 = sum 120582119895119895 119903119895 (2-16)
119903 =119880
120582 (2-17)
where 120582119895 and 119903119895 are the failure rate and outage time of contingency j for this load
point
The system reliability indices mainly include system average interruption frequency
index (SAIFI) system average interruption duration index (SAIDI) average energy
not supplied (AENS) and expected customer damaged cost (ECOST) [78] The
Formulae for these reliability indicators are presented in (2-18) to (2-21) [78]
119878119860119868119865119868 =sum 120582119894119873119894119894
sum 119873119894119894 (2-18)
119878119860119868119863119868 =sum 119880119894119873119894119894
sum 119873119894119894 (2-19)
119860119864119873119878 =sum 119880119894119871119894119894
sum 119873119894119894 (2-20)
119864119862119874119878119879 = sum 119888119898(119889119898)119891119898119871119898119872119898=1 (2-21)
where 119873119894 is the total number of customers of load point 119894 120582119894 119880119894 and 119871119894is the failure
rate outage time and average load connected to load point i 119872 is quantity of load
outage events 119871119898 is load curtailed (kW) due to outage event m 119891119898 and 119889119898 are the
frequency and duration of outage event m 119888119898(119889119898) is the outage cost (poundkW) of
outage duration 119889119898 using the customer damage function (CDF)
SAIFI is a measure of the number of outages an average customer will experience
SAIDI states the average interruption hours for a customer in the system AENS
presents the effect of interruptions on the energy that is not supplied to the customers
during failures [79] ECOST is the index that connects reliability with economics
Chapter 2 Distribution Automation
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292 Reliability Evaluation Methods
The methods used to calculate reliability indicators for distribution network are
classified into two groups namely the simulation method and analytical method
Simulation method
The simulation method has better scalability and flexibility when incorporating
complex considerations in comparison with the analytical technique And it is more
capable of dealing with large-scale power systems and the variation of load points
[77] The Monte Carlo method is a typical example of a simulation method and
takes into account the time varying and stochastic nature of load models in
evaluating the power system reliability [80] Vitorino etc [12] proposed a non-
sequential Monte Carlo method based on branch reliability to estimate energy not
supplied (ENS) index Contingencies were simulated by randomly selecting a faulty
branch from a candidate network pool based on failure probabilities [12] However
although the Monte Carlo method can simulate the behaviour of a complex system
with a high degree of accuracy it requires a considerable amount of CPU time and
memory
Analytical method
The first step of an analytical technique is to build a reliability probabilistic model
for the system according to network topology as well as the relationships between
the system and components [77] The model is then solved by calculating the
reliability indices in iterations [77] The most common analytical methods are
minimal path method minimal cutset method and failure-mode-and-effect analysis
(FMEA)
In [81] the minimal path method which identifies the shortest paths from a node to
a source and between any two nodes was described The minimal path of the source
node to the load points was obtained by searching for the upstream node from the
load points [82] As the distribution network was radial each node had only one
upstream node The sections out of service after a fault occurred were identified and
separate subsystems were formed The nodes were classified in terms of the effect of
a failure on them Using the node class and amount of load shedding data the
reliability indexes could then be evaluated [81]
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FMEA is a classical analytical algorithm for distribution network reliability
evaluation based on the analysis of all the failure modes of each static component
[82] As shown in Fig 2-13 there are four failure modes which are 1) active failure
2) transient failure 3) passive failure and 4) maintenance The active and transient
failures can cause the operation of breakers and hence the healthy components can
be removed from service [75] The passive failures are similar to maintenance outage
and have no effect on the protection system and remaining heathy zone [82]
Fig 2-13 Reliability model for static components
The proposed reliability evaluation method is based on the N-1 criterion and its
computation procedure is demonstrated in Fig 2-14
Normal operation
Active
failure
Transient
failure
Passive
failure
Maintenance
120582119860 120582119879 120582119875 120582119872
120583119860 120583119879 120583119875
120583119872
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Start
Read system topology load
data and reliability parameters
Initialise failure number i=1
All failures are considered
Search for the upstream feeder breaker
Search for the upstream and downstream
sectionalising switches and tie-switch
The load points are classified into three categories
Evaluate the reliability of load points
and whole system when fault at line i
Next failure i=i+1
Calculate the reliability of the whole system
End
No
Yes
Fig 2-14 Procedure for reliability evaluation
The system failure events are enumerated first For a failure event the scope of the
failure is determined by searching for the adjacent circuit breaker or tie switch The
isolation zone is then confirmed by the location of the upstream and downstream
sectionalising switches and the appropriate tie-switch Subsequently all the load
points are classified based on their interruption times Finally the consequence of
each contingency and a value for total system reliability are evaluated
When a fault occurs all the load points can be categorised as follows
Healthy points are load points not affected by the fault and refer to upstream
nodes of the upstream circuit breaker or downstream nodes of the
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downstream circuit breaker or tie-switch For example when a fault occurs at
L2 in Fig 2-15 LP1 and LP5 are healthy points
Temporary damaged points when the protection systems are in operation
they cause the load points to be interrupted but the load points can be
restored by isolating the faulty area and by using a supply through another
path When a fault occurs at L2 in Fig 2-15 LP2 and LP4 are isolated by
opening the sectionalising switches S1 and S2 LP2 is restored by closing B1
and LP4 is supplied by closing the tie-switch As a result LP2 and LP4 are
temporary damaged points The interruption time is 119879119878 which is the average
switching time after failure
Permanent damaged points are load points that are interrupted by the
operation of protection devices and cannot be restored until the fault is
cleared [82] When a fault occurs at L2 in Fig 2-15 LP3 is the permanent
damaged point The interruption time is 119879119877 which is the average repair time
after failure
Fig 2-15 Sample network
Overall the analytical method which is based on a reliability model of each
component evaluates system reliability by enumeration of all failure states However
the increasing number of devices in a complex system results in an increase in the
quantity of failure states and the complexity of calculation As such the scale of the
network might be limited
210 Multi-objective Optimisation
The aim of this section is to provide fundamental information in order to assess
multi-objective optimisation problems The objectives are conflicting and can be
Chapter 2 Distribution Automation
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0
1
converted into three forms which are 1) single objective function 2) single fuzzy
satisfaction objective function and 3) Pareto front
2101 Single Objective Function
The single objective function is generally done by simply aggregating the objectives
with the same dimension and transforming others into constraints [83] It can be
solved by traditionally scalar-valued optimisation techniques However this function
has several limits 1) it results in only one solution 2) the analysis of the objectives
that are converted into constraints is limited
In [64] a sectionalising switch placement strategy was proposed to minimise the
sum of ECOST and sectionalising switch costs The above mentioned objectives
were simply aggregated and calculated in US dollars Other objectives such as the
number of available switches were converted into constraints
2102 Single Fuzzy Satisfaction Objective Function
In the fuzzy domain each variable is associated with a membership function varying
from zero to unity which indicates the satisfaction level of the objective [84] The
higher the membership value is the better the solution is Generally the linear
membership function is formulated as given in (2-22) and is presented in Fig 2-16
120572 =
1 119883 le 119883119898119894119899119883119898119886119909minus119883
119883119898119886119909minus119883119898119894119899119883119898119894119899 lt 119883 lt 119883119898119886119909
0 119883 ge 119883119898119886119909
(2-22)
Fig 2-16 Linear membership function
If 119883 is equal or less than 119883119898119894119899 the membership value is one As 119883 becomes greater
than 119883119898119894119899 the degree of satisfaction decreases This decrease is continued until 119883
reaches 119883119898119886119909 and the membership function becomes zero
120572
119883119898119894119899 119883119898119886119909 119883
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The fuzzy-based optimisation procedure is used for handling multiple conflicting
objectives with different dimensions and units [66] The degrees of satisfaction level
can be formulated into a single objective function in three methods which are 1)
weighted aggregation 2) max-min method 3) max-geometric-mean method The
objective is to maximise such degree of satisfaction
Weighted aggregation
In this method the degree of satisfaction level is the weighted aggregation of the
membership values of all objectives [85] Thus the final compromise solution for
multi-objective functions is described as follows
119872119886119909 119869 = 12059611205721 + 12059621205722 + ⋯ + 120596119899120572119899 (2-23)
where 120596119894 is the constant weighting factor for each of the membership values and
they should meet the condition sum 120596119894119894 = 1
The weighting factors are decided by the decision makers and a higher weighting
factor indicates that this parameter is more important However the disadvantage of
this technique is that DNOs may have difficulty in obtaining enough information
about the relative importance of each objective to determine the trade-offs among the
selected objectives
Saffar etc [60] have developed a network reconfiguration technique to reduce power
loss and equal load balancing of feeders As these objectives had different
dimensions and units they were transformed into a single objective function with
fuzzy variables A set of compromised solutions was obtained by varying the
weighting factors of each element
Max-min method
In this technique the degree of overall satisfaction is the minimal value among the
membership values of all objectives [85] Thus the final compromise solution for
multi-objective functions is described as follows
119872119886119909 119869 = min 1205721 1205722 hellip 120572119899 (2-24)
The solution is optimised by maximising the overall satisfaction of all objectives
However the max-min method might not predict the best compromise solution
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because even if one membership value is weak it does not necessarily mean that
other membership values are also weak [86]
The max-min principle was adopted in [84] for the multi-objective optimisation with
fuzzy sets The aim was to minimise real power loss and the absolute value of branch
current as well as to minimise nodes voltage deviation Finally an optimal solution
was obtained which indicated a concession among all the objectives The results also
revealed that although network reconfiguration resulted in a significant reduction in
total system loss the loss allocated to a certain number of customers increased [84]
It is important to change the tariff structure for these consumers so that they are not
obliged to pay more for the increase in loss allocation as a result of network
reconfiguration
Max-geometric-mean method
Like the above max-min method the geometric-mean function is also used to
evaluate the degree of overall fuzzy satisfaction but in different forms The objective
is computed as follows
119872119886119909 119869 = (1205721 ∙ 1205722 ∙ hellip ∙ 120572119873)1 119899frasl (2-25)
In [86] firstly all the variables (real power loss branch current loading maximum
voltage deviation and switching numbers) were assigned by truncated sinusoidal
fuzzy membership functions The overall degree of satisfaction was the geometric
mean of all fuzzy membership values [86] The best compromise solution was then
obtained by maximising this satisfaction level
2103 Multi-objective Formulation in the Pareto Optimality
Framework
All the studies mentioned above are solved by a single-objective optimisation
technique In contrast a Pareto optimal solution is provided for the treatment of
multi-objective problems This produces a range of solutions rather than just one
which represents a compromise that goes some way to optimise objective functions
[87] [88] The Pareto optimal solution is based on a dominance concept The
solution 119883 dominates 119884 means that 119865(119883) is no worse than 119865(119884) for all objectives
Chapter 2 Distribution Automation
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and there is at least one objective for which 119865(119883) is better than 119865(119884) as expressed in
(2-26) and (2-27) The following conditions should be satisfied concurrently
forall 119894 = 12 hellip 119873119900119887119895 119865119894(119883) le 119865119894(119884) (2-26)
exist 119894 = 12 hellip 119873119900119887119895 119865119894(119883) lt 119865119894(119884) (2-27)
where 119873119900119887119895 is the number of objective functions
If a solution 119883 and solution 119884 do not dominate each other these two solutions are
incomparable For example the objective is to minimise 1198911 and 1198912 and there are
three solutions whose objective function values are 119865(119883) = (24) 119865(119884) = (44)
119865(119885) = (52) It can be seen that 119883 dominates 119884 as 1198911(119883) lt 1198911(119884) and 1198912(119883) le
1198912(119884) And the solution 119883 and 119885 are incomparable because 1198911(119883) lt 1198911(119885) and
1198912(119883) gt 1198912(119885) Similarly solutions 119884 and 119885 are also incomparable
A solution belongs to Pareto optimal solutions if there is no other solution that can
improve at least one objective without degradation of any other objectives [83] In
other words there is no another solution that dominates it The Pareto set is the set of
all non-dominated solutions and its corresponding objective values constitute the
Pareto front [88] The goal of the multi-objective optimisation is to select the most
suitable one from the Pareto set for implementation according to decision makersrsquo
preferences
In [45] the study proposed a Pareto-based multi-objective DNR method using a
discrete PSO algorithm It aims to reduce power loss voltage deviations and the
number of switching operations Firstly each objective function was optimised
separately and the best results were found All objectives were then optimised
simultaneously and the Pareto optimal set was obtained The best results for each
objective were included in the Pareto front and the corresponding solutions were
stored in the Pareto optimal set Finally the best compromise solutions among the
multiple objectives were derived Different scenarios were modelled by assigning
different weighting factors based on the preferences of the decision makers
Chapter 2 Distribution Automation
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211 Summary
Generally most distribution networks are designed in closed loop but are operated
radially There are three typical distribution network topologies which are the radial
system primary loop and link arrangement The descriptions of three switchgears ie
recloser sectionalising switch and tie-switch are also included in this chapter
TEO DNR and SSP are the three main parts of DA In this chapter there are several
reviews of these techniques TEO which refers to optimum selection of which
transformers need to supply each feeder can not only reduce loss but also reduce
total costs and improve network reliability DNR is defined as a process that
involves changing the network topology under normal and abnormal operating
conditions by relocation of tie-switches [13] [14] The methodologies from a branch
and bound optimisation method to modern heuristic optimisation algorithms
designed for loss reduction are reviewed In addition DNR is also able to improve
service quality and efficiency at the same time The placement of sectionalising
switches refers to the installation of new switches and relocation of existing switches
It is used for distribution network reliability improvement and service restoration
However so far few studies have been carried out that consider the combination of
the above three techniques
The major challenge facing DNOs is how to distribute the power in a low-cost
reliable and efficient way Thus the assessments of transformer loss feeder loss and
reliability indices are proposed in Section 27-29 The integrated transformer loss
consists of not only real power loss but also reactive power loss The transformer
quantities such as no-load loss and full-load loss are obtained from open-circuit test
and short-circuit test The distribution network power loss is achieved through power
flow study The reliability indices can be calculated through reliability evaluation
methods namely simulation methods and analytical methods The most common one
is FMEA which is also used for reliability evaluation in this thesis Although there
are many research projects that consider feeder loss and reliability simultaneously
few consider transformer loss and feeder loss at the same time
Three objective functions for optimising multiple conflicting objectives are 1) single
objective function 2) single fuzzy satisfaction objective function and 3) Pareto front
Chapter 2 Distribution Automation
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The single objective function is generally done by simply aggregating some
objectives and transforming others into constraints In the fuzzy objective function
each variable is associated with a membership function and then aggregated into a
single objective function [84] The first two functions only obtain a single solution
However Pareto optimal solutions can obtain a set of non-dominated solutions
rather than one which represents a compromise that goes some way to optimising
objective functions In this thesis all three objectives functions will be studied and
results will be presented in the following chapters
This thesis will deal with single objective and multiple objectives through different
methods of DA based on various algorithms The next chapter will introduce the
Monte Carlo method and modern heuristic optimisation algorithms such as ant
colony optimisation (ACO) and artificial immune systems (AIS)
Page | 60
CHAPTER 3
OPTIMISATION TECHNIQUES
31 Introduction
Mathematically distribution automation (DA) is categorised as a discrete non-linear
constrained and combinational optimisation problem since the problem is to
determine the status of all transformers and switches In general the optimisation
techniques for assessment of this problem can be divided into two large groups 1)
simulation methods and 2) analytical methods
The Monte Carlo method is a typical example of a simulation method which will be
discussed in Section 32 in detail It can handle uncertainties and solve the
probabilistic optimal power flow [89] In a complex system with hundreds of
switches although the Monte Carlo method can find the best solution with a high
degree of accuracy it is generally not practical to carry out an extensive search of all
possible configurations as it consumes a great deal of CPU time and memory [88]
Therefore most DA problems are solved by analytical methods
The analytical methods can obtain a solution of good quality or even the global
optimal solution of the problem [13] It can be classified into four types 1) branch
and bound 2) optimal flow pattern 3) branch exchange and 4) metaheuristic
techniques Recently the last type has become the most popular
Chapter 3 Optimisation Techniques
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The metaheuristic method is a process that attempts to find a solution to the problem
beginning from a starting point or a set of starting points and exploring all the search
space [13] It also includes a strategy to explore the search space and provide an
escape from the local optimal This process does not guarantee a globally optimal
solution but can offer near optimal solutions with a reasonable computational effort
This includes genetic algorithm (GA) ant colony optimisation (ACO) particle
swarm optimisation (PSO) and artificial immune systems (AIS) Different
metaheuristic techniques use different strategies that pass through and explore the
search space [13]
As for the remainder of the chapter the Monte Carlo method is discussed in Section
32 Section 33 presents the proposed ACO algorithm Section 34 discusses a new
hybrid AIS-ACO framework and the summary of this chapter is provided in Section
35
32 Monte Carlo Method
The Monte Carlo method is a simulation algorithm that can be carried out many
times to produce numerical samples that accurately reflect the probability
distribution of the real results [90] [91] This method is always used to solve power
system issues involving uncertain parameters [92] The uncertainties are allocated
randomly and each simulation is operated numerous times In theory the more
simulations are running the less deviation error between actual mean value and
sample mean value Therefore it is important to determine the overall running times
of the Monte Carlo simulation The convergence or stopping criteria is used to
determine the simulation times required to obtain acceptable accurate results
The confidence interval acts as a good estimate of the unknown parameters The
probability that the true parameter remains in the confidence interval is calculated as
follows [93]
119862 = 119875(119883 minus 119871 le 120583 le 119883 + 119871) = int 119866(119883)119889119909119883+119871
119883minus119871 (3-1)
119871 = 119911lowast 120590
radic119899 (3-2)
Chapter 3 Optimisation Techniques
Page | 62
where 119862 is the degree of confidence is the estimated mean value 119871 is the
confidence interval which provides an estimate range of values which probably
contains an unknown population parameter 120583 is the true population mean value
119866(119883) is the Gaussian distribution 120590 is the sample standard deviation and 119899 is the
number of samples the estimation of 119911lowast is based on the degree of confidence 119862 as
presented in Table 3-1 The most common 119911lowast is 196 and the corresponding 119862 is
095
Table 3-1 Relationship of 119911lowast and 119862
119862 09 095 099 0999
119911lowast 1645 1960 2576 3291
The required number of samples could be expressed as
119899 = (119911lowast120590
119871)2 (3-3)
There are several methods used to determine the sample size and to obtain results
with acceptable accuracy One is by predefining the maximum sample size 119873 when
119899 reaches 119873 the simulation is stopped Another one is by using the degree of
confidence 119862 The confidence interval 119871 is calculated and compared with the
predefined 119871 for each sample and the simulation reaches the stopping criteria when
the confidence interval is less than the critical value
33 Ant Colony Optimisation
The ant colony optimisation method is one of the metaheuristic techniques that has
been employed for the solution of combinational optimisation problems in recent
years [60] The ant colony system (ACS) simulates the behaviour of real ants [94]
[95] The moving paths of artificial ants construct the candidate solutions to a
problem [96] The ants communicate with other ants by a chemical substance called
pheromones [97] Originally all the ants start from their nest and search for their
food in a random manner When the food source is found the ants leave a chemical
Chapter 3 Optimisation Techniques
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substance trail on the way home The pheromone deposited by the ants is used as the
primary guide function for the other ants The pheromones will then evaporate after a
period of time As all of the ants travel approximately at the same speed the shortest
path has the largest probability to contain more pheromones because more ants
choose this one The ants tend to follow the path that has more pheromones than
others After a brief period the shortest path with the most intensity of pheromones
could attract more and more ants providing feedback to the system that promotes the
use of best paths [98] Fig 3-1 represents the behaviours of real ants [69]
Fig 3-1 Example of ant colony system [69]
As shown in Fig 3-1 (a) all the ants are travelling in the same path which connects
point A and point B by a straight line The environment is changed due to the
occurrence of an obstacle in Fig 3-1 (b) and (c) At first all the ants choose the left
or right path randomly because they have no guide It is assumed that they move
through path C or D with the same probability Later on the ants that choose path C
will move faster than that choose path D As a result the pheromones deposited on
path C accumulate faster than those on the path D and this attracts more ants to
choose path C Finally all the ants tend to choose the shortest path (path C) as this
contains the most pheromones
The flowchart of ACO algorithm is shown in Fig 3-2 and the main stages of the
algorithm are presented as follows [69] [94] [95] [97] [98]
Initialisation In this stage the trail intensity on each edge in the search
space is initialised to a constant positive value and all the ants are located in
Chapter 3 Optimisation Techniques
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the nest
Ant Dispatch In this step each ant begins its tour at the starting point and
chooses the next node to move to according to a probabilistic selection rule
which involves the intensity of pheromones deposited on each node by other
ants [88] [99] The ants prefer to choose the path with a higher pheromones
This process is repeated until all the ants have reached the food source
Quality Function Evaluation After all the ants have completed a tour the
relevant quality function of the optimisation problem is calculated to evaluate
the performance of each ant If any constraint is violated the configuration is
discarded Otherwise the objective function is evaluated
Trail Intensity Update There are two pheromone updating rules applied in
this step One is called the global pheromone update It accumulates the
pheromone values on the high-quality solution path to improve convergence
However the pheromone intensity of each edge evaporates over time due to
another rule called the local pheromone update This update is used to
enlarge the search space and to avoid premature convergence for local
minima Ants travelling between two nodes update the relevant pheromone
intensity in the corresponding edge
Convergence Determination This process is operated until the maximum
iteration number is reached or all the ants choose the same path between their
home colony and food source
Chapter 3 Optimisation Techniques
Page | 65
Start
Set Iteration n=1
Maximum iteration
reached
End
No
Yes
Initialise the parameters for ACO algorithm
searching space and build graph of the tours
Dispatch ants based on the
amount of pheromones on edges
Quality function evaluation
Trail intensity update
Record the high quality solutions of this
iteration and empty all location lists
n=n+1
Fig 3-2 Flowchart of the ant colony algorithm
The above procedure should be modified to a computational procedure to solve
different optimisation problems and this is discussed in the following chapters
Several factors need to be taken into account when designing an ACO algorithm
such as search space transition probability etc
34 AIS-ACO Hybrid Algorithm
341 Artificial Immune Systems
The immune system acts as a defensive barrier to recognise and eliminate foreign
antigens ie bacteria virus etc B lymphocytes are the main immune cells in the
biological immune system and originate in the bone marrow Being exposed to an
Chapter 3 Optimisation Techniques
Page | 66
antigen a specific antibody is produced on the surfaces of B cells and an immune
response is elicited to make antibodies recognise and bind the antigen [88] [100]
Those B cells whose antibodies best match the antigen are activated and cloned
several times [88] This process is called cloning To identify the most suitable
antibodies for the antigen it is necessary to cause the antibody and the antigen to
interact more closely with each other This is achieved through a process call
hypermutation in which random changes are introduced into the genes of the cloned
B cells [88] One such change might lead to an increase or decrease in the closeness
between antibody and antigen [88] The new B cells can only survive if they are
closely related to the antigen and therefore the B cells that are closely related are
then chosen to enter the pool of memory cells [100] These cloning hypermutation
and selection processes are called the clonal selection principle [101] By repeating
this principle a number of times the immune system learns to respond more
efficiently for the same antigen
Several computational models of the AIS have been developed recently as the
immune system is an adaptive learning system that has the following specifications
learning memory recognition of foreigners and pattern recognition [102]
342 Proposed AIS-ACO Hybrid Algorithm
The proposed AIS-ACO hybrid algorithm combines the advantages of AIS and ACO
The hypermutation developed from the AIS is used as a random operator by
adopting random changes to perturb a solution and hence to enlarge the search space
However the pheromones provided by the ACO can store information about the
quality of solution components for improving the objective functions [88] In
addition the information obtained from pheromone updating guides the algorithm in
its search and improves the convergence rate [88]
The limitation of ACO is that the algorithm can easily fall into a local optimum
which might be due to an insufficient range of candidate solutions This can be made
up by the random changes of solutions in AIS through hypermutation Also the
weakness of the global searching ability in AIS is improved by the pheromone tables
in ACO Thus the new hybrid AIS-ACO framework based on the pheromone-based
hypermutation method has better diversity and convergence in comparison with
either the AIS or ACO algorithms
Chapter 3 Optimisation Techniques
Page | 67
Start
Cloning
Maximum iteration
reached
End
No
Yes
Initialise and set iteration number n=1
Hypermutation
Fitness evaluation
Non-dominated solutions extraction
Pheromone updating
n=n+1
Record the Pareto front and
Pareto optimal solutions
In this thesis the AIS-ACO hybrid approach is used to generate a set of non-
dominated solutions The antigen is the multi-objective function and the antibody is
the solution to the problem The affinity between the antibody and the antigen is the
Pareto dominance among solutions which indicates the quality of the solution [88]
All the non-dominated solutions experience cloning hypermutation and selection
until the maximum number of iterations is reached The flowchart of the AIS-ACO
algorithm for Pareto optimality is presented in Fig 3-3
Fig 3-3 Flowchart of the AIS-ACO algorithm
Chapter 3 Optimisation Techniques
Page | 68
The key parts of the algorithm are explained as follows
Initialisation At the beginning of this algorithm a set of initial solutions is
generated These solutions should meet the condition of constraints The
information related to each objective is represented by an individual
pheromone table Each pheromone value represents the probability of
selection of the corresponding edge in the network model [88] All
pheromone values are initially set as the same value
Cloning The number of clones for each non-dominated solution should be
the same as the number of objectives and also as the number of pheromone
tables [88]
Hypermutation The selection of an edge in each cloned solution for
hypermutation is dependent on its pheromone values [88] A higher
pheromone value of a cell in the table indicates that the corresponding edge
in the network is more likely to be selected
Non-dominated solutions extraction This is the process of selecting non-
dominated solutions according to their affinity value [99] All the solutions
are compared as presented in Section 2103 and all the non-dominated
solutions are then extracted for the next iteration
Pheromone updating The aim of this stage is to accumulate the pheromone
values on the edges that belong to a part of the non-dominated solutions and
this is called the global pheromone update However the pheromone
intensity of all edges will evaporate over time by the local pheromone update
This update is used to explore the entire search space
Termination This process is operated until the maximum iteration number
is reached The set of final non-dominated solutions is called the Pareto set
which is used to solve the problem [88]
35 Summary
This chapter introduces the techniques for assessment of mono-objectivemulti-
objective optimisation problems The optimisation techniques are categorised into
two groups simulation methods and analytical methods
Chapter 3 Optimisation Techniques
Page | 69
The Monte Carlo method is a typical simulation technique and is generally used to
handle uncertain parameters It can find the best solution with a high degree of
accuracy but requires a considerable amount of CPU time and memory The
application of this methodology is discussed in Chapter 4 In that chapter an
efficient methodology based on the Monte Carlo Method is proposed for finding
transformer economic operation modes and optimal tie-switch placement strategies
to minimise transformer loss
The ACO algorithm is one of the metaheuristic techniques designed for assessment
of distribution automation (DA) problems It simulates the behaviour of artificial
ants with positive feedback and distributed computation The positive feedback
enhances the search speed in order to find the global solution and the distributed
computation explores the search space The ACO algorithm is able to find the global
solution in a reasonable computation time It is used for either loss reduction or
reliability improvement as discussed in Chapter 5-7 In addition a new multi-
objective ACO (MOACO) algorithm for assessment of multi-objective DNR
problems in terms of Pareto optimality is provided in Chapter 8
The AIS-ACO hybrid algorithm is a combination of AIS and ACO Hypermutation
is used in AIS as a random operator by using random changes to perturb a solution to
maintain the diversity of the solutions avoiding premature convergence for local
minima The pheromone tables used in the ACO are used to direct the algorithm
towards high quality solutions [88] The AIS-ACO hybrid algorithm is always used
for assessing the DA problem in terms of multiple objectives optimisation in order
to obtain a set of non-dominated solutions In addition the advantages of the AIS-
ACO algorithm over the MOACO algorithm for the assessment of multi-objective
optimisation problems are also discussed in Chapter 8
Page | 70
CHAPTER 4
TRANSFORMER ECONOMIC
OPERATION amp DISTRIBUTION
NETWORK RECONFIGURATION FOR
TRANSFORMER LOSS REDUCTION
41 Introduction
The electrical power generation transmission and distribution companies are not
only energy producers but also significant power consumers Energy loss occurs in
the process of power transfer and takes place in all electrical equipment including
generators power lines and transformers The large number and power capacity of
transformers used in a transformer and distribution network means transformer loss
is a significant component in energy loss The lifetime cost of energy loss in a
transformer is significant especially when one considers rising electricity demand
and the cost of the energy supplied For this reason it is important to tackle the
causes of transformer loss and the problems which then ensue so that energy
consumption can be reduced To support this statement several research projects
that have focused on transformer loss reduction are discussed in Section 242
Chapter 4 Transformer Economic Operation amp Distribution Network
Reconfiguration for Transformer Loss Reduction
Page | 71
An efficient methodology based on the Monte Carlo Method for the 3311 kV
transformer loss reduction with consideration of the voltage issues observed on a
distribution network is proposed in this chapter For a substation with two
transformers there are three operation modes that can occur 1) single transformer in
separate operation 2) two transformers in parallel operation 3) transformer
economic operation (TEO) as mentioned in Section 24 With regard to the load
models which are also discussed in this chapter a database containing numerous
domestic electricity demand profiles is imported into MATLAB to work as the
profile generators A Monte Carlo simulation platform is established by combining
the residential demand profiles with a 3311 kV distribution network model built in
OpenDSS Based on this platform the impacts of three operation modes of
transformers on transformer loss minimisation are investigated and compared
In addition an enumeration approach used for the optimum relocation of tie-switches
in a linked 11 kV distribution network is also suggested The process that involves
changing the distribution network topology by relocation of tie-switches is called
distribution network reconfiguration (DNR) [13] [14] The control centre can
change the location of tie-switches and the transformer operation modes (TOMs) in
each substation based on load data and simulated power loss from the test system at
each time interval The proposed approach is applied to the test system and the
effectiveness of an optimal planning strategy using TEO and DNR to achieve
minimum transformer loss is demonstrated through the results obtained
The remainder of this chapter is structured as follows Section 42 explains the load
models Section 43 describes the mathematical formulation of transformer loss
Section 44 analyses the methodology used to minimise transformer loss whilst
maintaining satisfactory voltages and the case studies and the results are presented
and discussed in Section 45 Finally the main conclusions are summarised in
Section 46
Chapter 4 Transformer Economic Operation amp Distribution Network
Reconfiguration for Transformer Loss Reduction
Page | 72
42 Load Model
In order to access the performance of the distribution feeders with different operation
modes of transformers in the substation the time-series behaviour of loads has to be
modelled
The value of the load associated with domestic electricity demand customers has
been obtained from the research described in [19] this can produce a random 1-min
resolution model for UK households There are six steps for creating a domestic
electricity demand model as shown in Fig 4-1 Table 4-1 presents the proportion of
household sizes based on UK statistics [103]
Fig 4-1 Procedure of domestic electricity demand profile generation
Table 4-1 Household size by number of people in household as a proportion [103]
Number of people
in household
1 2 3 4 ge5
Percentage () 3058 341 1557 1288 686
A pool of 10000 different load profiles covering 24 hours in a typical February
weekday are generated by this model For computation reasons the 1440 1-min
time-step load profiles are integrated as 144 10-min resolution profiles in this study
Specify the number of residents in the house from 1 to 5
Specify either a weekday or
weekend
Select the month of the year from 1 to
12
Random allocate appliances to the
dwelling
Run the active occupancy model
Run the electricity demand simulation
Chapter 4 Transformer Economic Operation amp Distribution Network
Reconfiguration for Transformer Loss Reduction
Page | 73
(active power is recorded for each minute and then averaged at intervals of 10
minutes) The power factors of all the loads are set to 095
43 Problem Formulation
The objective of this study is to minimise transformer loss through TEO and optimal
DNR The energy loss of the transformer is related to active power However as a
transformer draws reactive power (it takes current) it causes real power loss in the
network The integrated power loss refers to the sum of active power loss of the
transformer itself and the increased active power loss contributed by reactive power
loss of the transformer [73] The mathematical formulation can be expressed as
follows
Minimise 119891 = 1198800
2119875119885119874119862 +1205732
11988002 119875119885119878119862 119905119903119886119899119904119891119900119903119898119890119903 119894119899 119904119894119899119892119897119890 119900119901119890119903119886119905119894119900119899
211988002119875119885119874119862 +
1
2
1205732
11988002 119875119885119878119862 119905119903119886119899119904119891119900119903119898119890119903119904 119894119899 119901119886119903119886119897119897119890119897 119900119901119890119903119886119905119894119900119899
(4-1)
where 119875119885119874119862 and 119875119885119878119862 are the integrated no-load loss (kW) and the full-load loss (kW)
120573 =119878119871
119878119873 represents the transformer load factor S is the transformer actual loading
(kVA) 119878119873 is the transformer rated capacity (kVA) 1198800 is the operational voltage of
the transformer secondary side in per unit
44 Methodology
In this study there are two methodologies used for transformer loss reduction which
are called TEO and DNR
441 Transformer Economic Operation
In this section a Monte Carlo simulation platform for three TOMs comparison is
established as shown in Fig 4-2 and the flowchart of the transformer loss assessment
is presented in Fig 4-3
Chapter 4 Transformer Economic Operation amp Distribution Network
Reconfiguration for Transformer Loss Reduction
Page | 74
Fig 4-2 Monte Carlo simulation platform for three transformer operation modes comparison
Firstly a pool of 10000 10-min daily domestic electricity demand profiles is
randomly generated by the profile generators in MATLAB Following this each
node in the feeders from the system is assigned with residential demand profiles
from the pool using the Monte Carlo Method Theses profiles and one of the TOMs
are then imported into the distribution network model built in OpenDSS After this a
sequential load flow calculation is performed and the simulation results are returned
including voltage profiles and transformer losses to MATLAB The obtained
results are then analysed and compared with the system constraints for each time
step In this study for each TOM the calculation is set to be repeated 10000 times
in order to satisfy the convergence criteria When the losses of all TOMs are
calculated the minimum transformer loss and its associated operation mode are
obtained
Profile
generator of
domestic
electricity
demand profiles
Transformer
operation
modes
MATLAB
Distribution
network
model built
in OpenDSS
Analyse and
compare
simulation
results in
MATLAB
Load flow calculation
Chapter 4 Transformer Economic Operation amp Distribution Network
Reconfiguration for Transformer Loss Reduction
Page | 75
Start
Monte Carlo trail number N=1
All transformer operation
modes considered
End
No
Yes
Select demand profiles to each
customer randomly
Select transformer operation
mode
Sequentially run power flow
calculation for 144 10-minute time step
Record results
Change
transformer
operation
mode
N=N+1
Maximum iteration reached
Minimum transformer loss and its associated
transformer operation mode are obtained
No
Yes
Load and aggregate the domestic
electricity demand profiles pool
(144 10-minute time steps)
Fig 4-3 Flowchart of transformer loss assessment
Chapter 4 Transformer Economic Operation amp Distribution Network
Reconfiguration for Transformer Loss Reduction
Page | 76
442 Distribution Network Reconfiguration
Reconfiguration of radial distribution system is achieved by local control of tie-
switches located in linked feeders The Monte Carlo simulation platform through
DNR is presented in Fig 4-4
Fig 4-4 Monte Carlo simulation platform for distribution network reconfiguration
In the proposed strategy the tie-switch status is modified by the control centre and
the detailed control algorithm is discussed below
Step 1 Random load profiles are first selected
Step 2 When the load profiles have been imported into the network model a
sequential load flow calculation is performed to calculate and compare the
transformer loss under different network configurations (different tie-switches
location) at each time interval
Step 3 Minimum transformer loss and its associated network configuration are
obtained
Step 4 Location of tie-switches based on minimum transformer loss over a whole
day is recorded
Step 5 Optimal DNR strategy is obtained
Profile
generator of
domestic
electricity
demand profiles
Tie-switch
status
MATLAB
Distribution
network
model built
in OpenDSS
Analyse and
compare
simulation
results in
MATLAB
Load flow calculation
Chapter 4 Transformer Economic Operation amp Distribution Network
Reconfiguration for Transformer Loss Reduction
Page | 77
45 Application Studies
To demonstrate the impact of TOMs and DNR on transformer loss the proposed
methodologies are applied to two test networks Several scenarios are tested and the
results are analysed and reported
451 Test Case 1
The single line diagram of the network shown in Fig 4-5 is developed from the UK
generic distribution network [104] The network model is built to incorporate a 3311
kV substation supplying the downstream loads in the OpenDSS software
environment The two transformers have the same specifications and their
characteristics are presented in Table 4-2 The corresponding TCLF is calculated as
5244 The 11 kV network is represented by four outgoing feeders from a single
busbar For computation reasons three of the feeders are simplified lumped loads
whilst the 4th
feeder is modelled in detail The 4th
11 kV feeder consists of eight
nodes which represents a small system with a total of 252 domestic single phase
house loads connected on each node A Monte Carlo simulation approach is
implemented to select these load profiles randomly from a pool of domestic
electricity demand profiles Each house in the 4th
feeder is then assigned with a
residential demand profile The loads in the other three feeders are then lumped with
the same daily profile of the 4th
feeder All the values of the network components are
based on a broad collection from [104] [105] and are recorded in Appendix A1
In this test a comparison of the three TOM methods for transformer loss
minimisation is provided A time-series load flow algorithm is implemented to
quantify the changes in feeder voltage and transformer loss in the previous described
3311 kV UK distribution network for different TOMs In this test three scenarios
are studied and summarised as follows
Scenario 1 Single transformer in separate operation
Scenario 2 Two transformers in parallel operation
Scenario 3 Transformer economic operation in this mode if the transformer load
factor is less than TCLF only one transformer remains in service if the transformer
load factor is higher than TCLF two transformers are operated in parallel
Chapter 4 Transformer Economic Operation amp Distribution Network
Reconfiguration for Transformer Loss Reduction
Page | 78
A
A
A
A
B
B
B
B
Load1Load2Load3Load4_1
Load4_2
Load4_3
Load4_4
Load4_5
Load4_6
Load4_7
Load4_8
75 MVA
33 kV
11 kV
33 kV
Voltage
Source
75 MVA
Fig 4-5 Generic distribution network topology
Table 4-2 Parameters of a typical 3311 kV two-winding transformer [106]
Sub-
sector
Transf
Rating
(kVA)
Conn Tapping
Range
Load
Losses
at
75
(kW)
No-
Load
Losses
(kW)
Impedance voltage
at rated current for
the principle
tapping
()
Reference
standard
Urban 7500 YY0 plusmn75
6 steps of 25
Each
50
75
835 BS 171 amp
IEC 60076
1) Test 1-1 Base Case
The simulation results of transformer load factor variation are shown in Fig 4-6 and
the transformer loss variation curves are presented in Fig 4-7 It is observed that the
transformer loss in Scenario 3 is the same as in Scenario 1 between 000 to 630 and
Chapter 4 Transformer Economic Operation amp Distribution Network
Reconfiguration for Transformer Loss Reduction
Page | 79
0
10
20
30
40
50
60
70
80
90
100
0 2 4 6 8 10 12 14 16 18 20 22
Tran
sfo
rme
r Lo
ad F
acto
r
Time (h)
0
10
20
30
40
50
60
70
0 2 4 6 8 10 12 14 16 18 20 22
Tran
sfo
rme
r Lo
sse
s (k
W)
Time (h)
0
10
20
30
40
50
60
70
0 2 4 6 8 10 12 14 16 18 20 22
Tran
sfo
rme
r Lo
sse
s (k
W)
Time (h)
the same in Scenario 2 from 1800 to 2200 With the introduction of Scenario 3 the
minimum loss is around 9 kW at 000 which is below the 18 kW of Scenario 2 The
maximum loss of Scenario 3 is nearly 40 kW at 1900 which is far below the 60 kW
of Scenario 1
Fig 4-6 Transformer load factor variation
(a) Scenario 1
(b) Scenario 2
Chapter 4 Transformer Economic Operation amp Distribution Network
Reconfiguration for Transformer Loss Reduction
Page | 80
0
10
20
30
40
50
60
70
0 2 4 6 8 10 12 14 16 18 20 22
Tran
sfo
rme
r Lo
sse
s (k
W)
Time (h)
(c) Scenario 3
Fig 4-7 Transformer loss variations in different scenarios
The mean values of 3311 kV transformer energy loss during one day under different
scenarios are presented in Table 4-3 As shown in Fig 4-6 the average transformer
load factor during a whole day is slightly below the TCLF (5244 in this test) This
situation is more suitable for a single transformer than two transformers The loss in
Scenario 3 reaches the lowest value and results in a reduction of 1133 and 1441
in comparison with Scenario 1 and Scenario 2
Table 4-3 Daily transformer loss in different scenarios
Scenario 1 Scenario 2 Scenario 3
Transformer losses (kWh) 53982 55922 47865
According to the EN50160 standard [7] under normal conditions at least 95 of the
10-min average mean rms voltage magnitude in the 11 kV electricity distribution
network should be within the range 09 pu to 11 pu over one week In other words
the 95th
percentile voltage profile is compared with the allowed voltage range to
check the networkrsquos reliability
The mean and 95th
percentile voltage profiles at each node in the fourth feeder are
presented in Fig 4-8 It can be seen that the voltage level at each node can change
considerably after the scenario changes It also appears that the nodes in Scenario 1
experience the most severe voltage drop in comparison with the other two scenarios
The worst 95 voltage value of the node lsquoLoad4_8rsquo at the end of the studied feeder
in Scenario 1 is around 098 pu which is not as satisfactory as the results of 0987 pu
and 0984 pu observed in Scenario 2 and Scenario 3
Chapter 4 Transformer Economic Operation amp Distribution Network
Reconfiguration for Transformer Loss Reduction
Page | 81
0976
0978
098
0982
0984
0986
0988
099
0992
Load4_1 Load4_2 Load4_3 Load4_4 Load4_5 Load4_6 Load4_7 Load4_8
Vo
ltag
e (
pu
)
Scenario1
Scenario2
Scenario3
0974
0976
0978
098
0982
0984
0986
0988
099
Load4_1 Load4_2 Load4_3 Load4_4 Load4_5 Load4_6 Load4_7 Load4_8
Vo
ltag
e (
pu
)
Scenario1
Scenario2
Scenario3
(a) Mean value
(b) 95th
value
Fig 4-8 11 kV 4th
feeder voltage profiles in different scenarios
To show in detail the voltage profiles affected by different TOMs the load at the
start of the 4th
feeder lsquoLoad4_1rsquo and the end one lsquoLoad4_8rsquo have been selected
Since the Monte Carlo method produces many loss and voltage values it is
preferable to present the averages of all these values and their deviations
As shown in the charts from Fig 4-9 and Fig 4-10 the voltage drops severely from
1800 to 2000 which is also the maximum daily demand period It also appears that
the voltage profile in Scenario 3 is the same as in Scenario 1 between 000 to 630
and the same as in Scenario 2 from 1800 to 2200 With the introduction of Scenario
Chapter 4 Transformer Economic Operation amp Distribution Network
Reconfiguration for Transformer Loss Reduction
Page | 82
088
09
092
094
096
098
1
0 2 4 6 8 10 12 14 16 18 20 22
Bu
s V
olt
age
(p
u)
Time (h)
088
09
092
094
096
098
1
0 2 4 6 8 10 12 14 16 18 20 22
Bu
s V
olt
age
(p
u)
Time (h)
088
09
092
094
096
098
1
0 2 4 6 8 10 12 14 16 18 20 22
Bu
s V
olt
age
(p
u)
Time (h)
3 the lowest voltage of lsquoLoad4_8rsquo is around 097 pu which is significantly above
the lower limit 090 pu
(a) Scenario 1
(b) Scenario 2
(c) Scenario 3
Fig 4-9 Voltage profiles of Load 4_1 in different scenarios
Lower Limit
Lower Limit
Lower Limit
Chapter 4 Transformer Economic Operation amp Distribution Network
Reconfiguration for Transformer Loss Reduction
Page | 83
088
09
092
094
096
098
1
0 2 4 6 8 10 12 14 16 18 20 22
Bu
s V
olt
age
(p
u)
Time (h)
088
09
092
094
096
098
1
0 2 4 6 8 10 12 14 16 18 20 22
Bu
s V
olt
age
(p
u)
Time (h)
088
09
092
094
096
098
1
0 2 4 6 8 10 12 14 16 18 20 22
Bu
s V
olt
age
(p
u)
Time (h)
(a) Scenario 1
(b) Scenario 2
(c) Scenario 3
Fig 4-10 Voltage profiles of Load 4_8 in different scenarios
Lower Limit
Lower Limit
Lower Limit
Chapter 4 Transformer Economic Operation amp Distribution Network
Reconfiguration for Transformer Loss Reduction
Page | 84
0976
0978
098
0982
0984
0986
0988
099
0992
Load4_1 Load4_2 Load4_3 Load4_4 Load4_5 Load4_6 Load4_7 Load4_8
0 25
5244 75
100
As most people are sleeping late at night and the transformer load factor is less than
the TCLF transformers are in individual operation mode When most people are at
home again from 1800 the transformer load factor increases beyond the TCLF As a
result the voltage profiles are improved when transformers are operated in parallel
In conclusion when the transformer load factor is less than the TCLF transformers
in a separate service result in less loss but more voltage dips however transformers
operating in parallel cause lower voltage drops but more loss When the transformer
load factor is higher than the TCLF transformers in parallel operation cause less loss
and lower voltage drops As a result based on the economic operation theory the
transformer in Scenario 3 significantly reduces transformer loss and maintains the
voltages at a satisfactory level
2) Test 1-2 TCLF Sensitivity Analysis
In this test the value of TCLF used to distinguish whether the transformer should be
in separate or parallel operation is discussed The complete process presented
previously is carried out again but takes into account the effect of different critical
values 0 25 5244 75 and 100
Fig 4-11 shows the effect on the mean voltage magnitudes of various TCLFs The
results indicate that the voltage profile is closely related to the TCLF and the TCLF
should be decreased to increase the region in which transformers operate in parallel
This will improve the voltage profiles
Fig 4-11 11 kV 4th
feeder mean voltage profile of various TCLFs
Chapter 4 Transformer Economic Operation amp Distribution Network
Reconfiguration for Transformer Loss Reduction
Page | 85
Table 4-4 describes the effect on the transformer loss when TCLF is changed It
reaches the lowest value when TCLF is 5244 If the TCLF is decreased or
increased above this value the loss increases Overall the TCLF should be set to
5244 in order to minimise transformer loss
Table 4-4 Transformer loss with different TCLF
TCLF () 0 25 5244 75 100
Transformer loss
(kWh)
55922 50783 47865 49414 53982
As presented in Table 4-5 the average number of switching operations is increased
as the TCLF is approached to its optimum value
Table 4-5 Average number of switching operations with different TCLF
TCLF () 0 25 5244 75 100
Average number of
switching operations
0 2 4 2 0
452 Test Case 2
The impacts of TOMs and DNR on transformer loss are evaluated in this section As
presented in Fig 4-12 the model of the test system is developed from the
duplication of the generic distribution network shown in Fig 4-5 All the values of
the network parameters are obtained from [104]ndash[106] The system is supplied by
two 3311 kV substations and each bus has four feeders There is one linked feeder
with nine tie-switches Tie-switches refer to the switches of the network that are
normally open The function of the tie-switches is to alter the network topology to
provide various routes for supplying loads In order to feed all loads and keep the
systemrsquos radial topology only one tie-switch is open and all the others are closed
Chapter 4 Transformer Economic Operation amp Distribution Network
Reconfiguration for Transformer Loss Reduction
Page | 86
0
02
04
06
08
1
12
14
16
0 2 4 6 8 10 12 14 16 18 20 22
Act
ive
Po
we
r (k
W)
Time (h)
TW1 TW2 TW3 TW4 TW5
A1
A2
A3
A4_1 A4_2 A4_3 A4_4 A4_5 A4_6 A4_7 A4_8 B4_8 B4_7 B4_6 B4_5 B4_4 B4_3 B4_2 B4_1
B1
B2
B3
EndA EndB
TW9TW8TW7TW6
Tie-Switch (close) Tie-Switch (open)
Fig 4-12 Test system
For simplicity the daily load variations in each feeder are the same and the load
profiles of each node in the linked feeder are also the same Therefore the loads
could be categorised into two groups
Group 1 A1 A2 A3 B1 B2 B3
Group 2 A4_1 A4_2 A4_3 A4_4 A4_5 A4_6 A4_7 A4_8 B4_1 B4_2
B4_3 B4_4 B4_5 B4_6 B4_7 B4_8
On the basis of transformer load factor variation shown in Fig 4-6 the relevant 10-
min resolution load models of the two groups are presented in Fig 4-13 The power
factors of all the loads are set to 095
(a) Group 1
Chapter 4 Transformer Economic Operation amp Distribution Network
Reconfiguration for Transformer Loss Reduction
Page | 87
0
002
004
006
008
01
012
014
016
018
02
0 2 4 6 8 10 12 14 16 18 20 22
Act
ive
Po
we
r (k
W)
Time (h)
(b) Group 2
Fig 4-13 Daily load variations for different load groups
As this test system is developed from the duplication of the generic distribution
network and all the loads have the same profiles the position of the tie-switch is
selected from lsquoTW1rsquo to lsquoTW5rsquo For example the tie-switch located in lsquoTW1rsquo has the
same effect as lsquoTW9rsquo The control strategy is used to quantify the changes in feeder
voltage and transformer loss in the previously described test system under different
scenarios which could be categorised as
Scenario 1 each end has one transformer in operation and the tie-switch is located
at TW1 ie entire feeder supplied from end B
Scenario 2 each end has one transformer in operation and the tie-switch is located
in TW5 ie feeder split at mid-point
Scenario 3 each end has one transformer in operation and the location of the tie-
switch is based on minimum transformer loss operation
Scenario 4 each end has two transformers in operation and the tie-switch is located
at TW1
Scenario 5 each end has two transformers in operation and the tie-switch is located
at TW5
Scenario 6 each end has two transformers in operation and the location of the tie-
switch is based on minimum transformer loss operation
Chapter 4 Transformer Economic Operation amp Distribution Network
Reconfiguration for Transformer Loss Reduction
Page | 88
Scenario 7 each end has onetwo transformers in operation based on the transformer
load factor and the tie-switch is located at TW1
Scenario 8 each end has onetwo transformers in operation based on the transformer
load factor and the tie-switch is located at TW5
Scenario 9 each end has onetwo transformers in operation based on the transformer
load factor and the location of the tie-switch is based on minimum transformer loss
operation
Table 4-6 indicates the mean value of 3311 kV transformer loss during one day
under different scenarios As can be seen from the table when the tie-switches have
the same location TW1 transformer loss in Scenario 7 results in a reduction of
1396 and 1456 in comparison with Scenario 1 and Scenario 4 In conclusion
the mode introducing a flexible number of transformers in operation based on TCLF
reduces the loss In addition the transformer loss in Scenario 9 is 9528 kWh per day
which is 217 and 014 lower than Scenario 7 and Scenario 8 As a result the
variation of tie-switch locations could reduce transformer loss The detailed location
of the tie-switch in Scenario 9 is included in Appendix B1
Table 4-6 Transformer loss in Test Case 2
Scenarios S1 S2 S3 S4 S5 S6 S7 S8 S9
Loss
(kWhday)
11319 10848 10848 11399 11162 11162 9739 9572 9528
The graph presented in Fig 4-14 illustrates the voltage variation caused by the tie-
switch relocation The node voltages in Scenario 1 experience the worst profile
which increases to a peak of 09749 pu from 09675 pu along the linked feeder In
order to reduce the loss the tie-switch is always located in the middle of the feeder
TW5 in Scenario 3 As a result the voltage profiles of Scenario 2 and Scenario 3 are
the same It should be noted that Scenario 2 experiences a slight drop from 09787 pu
to 0972 pu and then climbs back to 09827 pu It can also be clearly seen that the
voltage reaches the lowest value where the tie-switch is located The further away
the nodes are from the tie-switch the better the voltage profiles that can be obtained
In addition when the tie-switch moves closer to the middle of the linked feeder the
Chapter 4 Transformer Economic Operation amp Distribution Network
Reconfiguration for Transformer Loss Reduction
Page | 89
096
0962
0964
0966
0968
097
0972
0974
0976
0978
098
A4_1A4_2A4_3A4_4A4_5A4_6A4_7A4_8B4_8B4_7B4_6B4_5B4_4B4_3B4_2B4_1
Vo
ltag
e (
pu
)
Scenario1
Scenario2
Scenario3
0955
096
0965
097
0975
098
0985
099
A4_1A4_2A4_3A4_4A4_5A4_6A4_7A4_8B4_8B4_7B4_6B4_5B4_4B4_3B4_2B4_1
Vo
ltag
e (
pu
)
Scenario1
Scenario4
Scenario7
voltage performance is improved And the detailed voltage values at each node in the
linked feeder for different scenarios are presented in Appendix B1
Fig 4-14 Mean voltage profiles in S1 S2 and S3
As shown in Fig 4-15 the voltage variation is due to a change in TOMs
Fig 4-15 Mean voltage profiles in S1 S4 and S7
As in the case of the tie-switch located in lsquoTW1rsquo all the node voltages experience a
rise along the linked feeder from lsquoEndArsquo to lsquoEndBrsquo It should be noted that the node
voltages in Scenario 4 achieve the best profile which increase to a peak of 0984 pu
from 0976 pu As discussed in Test Case 1 the transformers in parallel operation
could improve the voltage profiles In addition the flexible number of transformers
Chapter 4 Transformer Economic Operation amp Distribution Network
Reconfiguration for Transformer Loss Reduction
Page | 90
in operation based on TCLF (Scenario 7) shows a slight difference in voltage from
that in Scenario 4
As discussed above the location of the tie-switch and the change of TOMs have an
impact on the feeder voltage variation The tie-switch located in the middle of the
feeder and transformers with parallel operation defines the best voltage profiles
46 Summary
This chapter illustrates why transformer economic operation (TEO) is an economical
solution to reduce transformer loss The substation composed of two transformers
with the same characteristics has been used as an example to introduce the general
approach of determining the TCLF and TEO area A Monte Carlo simulation
platform was established to tackle load uncertainties A methodology to prove that
the TOM variation affects the performance of the 11kV distribution network is
discussed and analysed The TEO mode with minimum loss and satisfactory voltages
is achieved depending on the the transformer load factors by operating with either
one or two transformers and can be summarised as when the transformer load factor
is less than the TCLF transformers should be in separate operation when the
transformer load factor is higher than the TCLF transformers are recommended to
operate in parallel This results in a reduction of 1441 over the conventional
transformer loss ie when two transformers are in parallel operation However
simulation studies also indicate voltage profiles are improved when transformers
operate in parallel Therefore a slight reduction in TCLF results in an increased loss
but an improvement in voltage performance
The effectiveness of a DNR strategy has also been proposed through the results
obtained The presented results illustrate the impact of different TOMs in each
substation and tie-switch statuses on transformer loss and the voltages measured
along the feeder during a 24 hour operating period The optimal economic operation
strategy with TEO and DNR have successfully reduced the transformer loss and
improved the voltage profiles The further away the nodes are from the tie-switch
the better the voltage profiles obtained In addition when the tie-switch moves closer
to the middle of the linked feeder the voltage performance is improved
Chapter 4 Transformer Economic Operation amp Distribution Network
Reconfiguration for Transformer Loss Reduction
Page | 91
In normal operating conditions transformers operate in parallel and the tie-switch is
located in the middle of the linked feeder As indicated by Table 46 the daily
energy loss in Scenario 5 is 11162 kWh After the introduction of Scenario 9 the
annual saving energy could be 59641 kWh
Page | 92
CHAPTER 5
DISTRIBUTION NETWORK
RECONFIGURATION amp DG ALLOCATION
FOR FEEDER LOSS REDUCTION
51 Introduction
Distribution networks generally operate in radial configuration to ease protection
coordination and to reduce short circuit current [107] Distribution feeders can be
reconfigured to alter the network topology at normal and abnormal operating
conditions by changing the openclose status of switches to satisfy the operatorrsquos
objectives [13] [14]
DG is a small electric generation unit that is connected directly to the distribution
network or appears on side of the meter accessed by the customer [16] With the
increasing number of DGs bidirectional power flows have appeared and locally
looped networks have become inevitable [17] Therefore the type size and location
of DGs in the distribution networks strongly affect power system operation and
planning
The studies in [5] indicate that about 5 of the total power generation is wasted in
the form of feeder loss at the distribution level Reduction in active power loss can
help distribution network operators (DNOs) save costs and increase profits The
Chapter 5 Distribution Network Reconfiguration amp DG Allocation for Feeder Loss
Reduction
Page | 93
optimal distribution network reconfiguration (DNR) placement and sizing of DGs
strategies should be used to reduce feeder loss while satisfying the operating
constraints
The ant colony optimisation (ACO) developed by M Dorigo is a metaheuristic
algorithm for the assessment of optimisation problems [94] It is based on the
pheromones deposited by ants as a guide for finding the shortest path between a food
source and their home colony The detailed description of ACO algorithm has been
presented in Section 33 In this chapter an ACO algorithm is proposed to solve the
network reconfiguration and DG placement problems simultaneously based on
distribution feeder loss minimisation The proposed technique is tested on two
standard IEEE 33-node and 69-node systems and the simulation results show the
performance and effectiveness of the proposed method Four scenarios are
considered during network reconfiguration and DG allocation The impacts of DG
capacity on assessing the DNR and DG allocation problems in terms of feeder loss
reduction are also studied Moreover the results obtained by ACO algorithm have
been compared to those from other algorithms in the literature
As for the remainder of this chapter the mathematical formulation of the objective
function and its constraints are explained in Section 52 Section 53 discusses the
application of ACO algorithms in order to solve the problem Section 54 provides a
detailed analysis of the numerical results and Section 55 provides the final
conclusions
52 Problem Formulation
The proposed objective function (F) of the problem is formulated to minimise the
feeder loss of a distribution network which is described as follows
119872119894119899119894119898119894119904119890 119891 = sum 119896119894119877119894(119875119894
2+1198761198942
1198801198942 )
119873119887119894=1 (5-1)
where 119877119894 is the resistance of the ith branch 119875119894 and 119876119894 are the real power (W) and
reactive power (VAr) at the receiving end of branch i 119880119894 represents the rms voltage
at the receiving end of branch i (V) 119896119894 is a binary variable 119896119894 = 0 indicates that
Chapter 5 Distribution Network Reconfiguration amp DG Allocation for Feeder Loss
Reduction
Page | 94
branch 119894 is open and 119896119894 = 1 indicates that branch 119894 is closed The detailed feeder loss
assessment has been given in Section 28
Subject to
∆119881119899 le ∆119881119898119886119909 for all load points (5-2)
119868119887 le 119868119898119886119909 for all branches (5-3)
119875119894 le 119875119894119898119886119909 (5-4)
det(119860) = 1 119900119903 minus 1 (5-5)
Constraints (5-2) ndash (5-3) represent the computed voltages and currents and should be
in their permissible range Constraint (5-4) indicates that the power flow at all
branches should be within the limits defined for each branch Constraint (5-5)
ensures the radial topology of the network [32] The branch to node incidence matrix
Arsquo has one row for each branch and one column for each node 119886119894119895 represents the
coefficient in row i and column j 119886119894119895 = 0 if branch i is not connected with node j
119886119894119895 = 1 if branch i is directed away from node j and 119886119894119895 = minus1 if branch i is directed
towards node j When the column corresponding to the reference node and the rows
of open branches are deleted from matrix Arsquo a new square branch-to-node matrix A
is obtained Then the determinant of A is calculated If det(A) is 1 or -1 the system is
radial Otherwise the system is not radial
53 Solution Method
531 Distribution Network Reconfiguration
With regard to the DNR problem each solution is represented by a string of integers
which indicates the location of tie-switches As the number of tie-switches that keep
the network radial is always constant the number of the solutionrsquos elements is equal
to the number of tie-switches in the network
Chapter 5 Distribution Network Reconfiguration amp DG Allocation for Feeder Loss
Reduction
Page | 95
Home
1 2 NP1NP1-1
1 2 NP1-1 NP1
1 2 NP1NP1-1
1 2 NP2-1 NP2
1 2 NP2NP2-1
1 2 NP2-1 NP2
1 2 NP2NP2-1
1 2 NP2-1 NP2
Food
Stage
1
2
NT-1
NT
NT+1
NT+2
NT+NDG-1
NT+NDG
Part 1 Number of
existing tie-switches
Part 2 Number
of DGs
532 Applying ACO to DNR and DGs Placement
In this chapter an ACO algorithm is adopted to find the optimum locations of tie-
switches and sites of DGs placement in the network in terms of feeder loss
minimisation When the locations of tie-switches and DGs are changed a new
network configuration will be formed For each network configuration the feeder
loss is evaluated by using the approach presented in Section 52
Fig 5-1 Search space of DNR and DGs Placement
Chapter 5 Distribution Network Reconfiguration amp DG Allocation for Feeder Loss
Reduction
Page | 96
The search space of the DNR and DG allocation problems is modelled as a directed
graph as shown in Fig 5-1 In Part I the states signify the location of tie switches
and the sites for DGs installation are represented by states in Part II The number of
stages in this graph is the sum of the amount of existing tie-switches 119873119905 and the
number of installed DGs 119873119863119866 1198731199011is the number of possible locations for the tie-
switches relocation and 1198731199012 is the number of candidate buses for DGs installation
Artificial ants start their tours at home moving along the paths in the graph and end
at the food source Each location list consists of a string of integers and represents a
solution to the problem Different orders of the solutionrsquos elements indicate different
routes However several routes might indicate a certain solution as the order of the
solutionrsquos elements makes no difference to the network configuration For example
the solution vector (1 2 3) represents the same network configuration as the solution
vector (3 2 1) And the objective functions of these two routes are the same In this
study the first route that the ants found will be chosen as the feasible solution The
flowchart of the proposed ACO algorithm is presented in Fig 5-2 and is expressed in
five steps
Step 1 Initialisation First of all all the ants are initially located at home The
pheromone values of the edges in the search space are all set to a small positive
constant value
Step 2 Ant Dispatch All the ants are sent in parallel from the home colony and one
of the states is chosen in the next stage according to a probabilistic selection rule
which involves the intensity of pheromones deposited on the states [66] The
locations of the tie-switches are determined first and the sites for the DGs
installation are then selected The probability of an ant choosing state j of the next
stage y is
119875119895119910(119873) =
120591119895119910
(119873)
sum 120591119895119910
(119873)ℎisin∆119910
(5-6)
where 120591119895119910
(119873) is the pheromone value of state j of stage y at iteration N ∆119910 is the set
of available states which an ant can choose at stage y
Chapter 5 Distribution Network Reconfiguration amp DG Allocation for Feeder Loss
Reduction
Page | 97
Step 3 Objective Function Evaluation After all the ants have completed their tour
the location list and corresponding objective function in (5-1) for each ant are
evaluated If any constraint in (5-2) - (5-5) is violated the corresponding solution is
assigned with a huge value and is discarded If not all the objective functions are
assessed and the best configuration of the Nth iteration with minimum objective
function 119891119887119890119904119905(119873) is recorded This should be compared to the best configuration
obtained so far 119891119887119890119904119905 if 119891119887119890119904119905(119873) lt 119891119887119890119904119905 the best solution should be updated such
that 119891119887119890119904119905 = 119891119887119890119904119905(119873) [14] If not the best configuration found in the previous
iteration is retained After this the location list is emptied and all the ants are free to
choose a new trail
Step 4 Pheromone Updating The aim of this step is to favour transitions towards
states involving high quality solutions with greater pheromones There are two rules
of pheromone updating the local rule and global rule
Local rule The amount of pheromone deposited in the search space should be
evaporated to make paths less attractive The local pheromone update rule is
calculated as following
120591119895119910
(119873) = (1 minus 120588)120591119895119910
(119873 minus 1) + 120591119888 (5-7)
where 120588 is the pheromone evaporation rate which is set between 0 and 1 120591119888 is a
small positive constant value Even if the amount of pheromone deposited on an
edge is at the lowest value of 120591119888 there is a slight chance that an ant will still choose
this edge
Global rule The global pheromone updating rule involves ants depositing large
amounts of pheromone to the edges that belong to the highest quality solution per
iteration This rule is to guide the search to find the global optimal solution The
pheromones of those edges can be modified by
120591119895119910(119873) = 120591119895
119910(119873) + 120588119891119887119890119904119905
119891119887119890119904119905(119873) (5-8)
After applying the local and global pheromone updating rules the method Max-Min
ACO algorithm is integrated into the proposed approach
120591119895119910(119873) = 120591119898119886119909 119894119891 120591119895
119910(119873) ge 120591119898119886119909 (5-9)
120591119895119910(119873) = 120591119898119894119899 119894119891 120591119895
119910(119873) le 120591119898119894119899 (5-10)
Chapter 5 Distribution Network Reconfiguration amp DG Allocation for Feeder Loss
Reduction
Page | 98
Start
Set Iteration n=1
Maximum iteration
reached
Output best
configuration and end
No
Yes
Initialise the parameters for ACO algorithm
searching space and build graph of the tours
Dispatch ants based on the
amount of pheromones on edges
Relocate tie-switches and DGs by location lists
Calculate the objective function for each ant
The pheromones are updated according
to local and global rules
n=n+1
Record the best solution so far and empty
all location lists
Read system topology
and load data
where 120591119898119886119909and 120591119898119894119899 are the higher and lower bound of the pheromone level on each
edge respectively The trail limit of the pheromone ensures the probabilities of all
the edges are greater than zero which maintains the diversity of the solutions and
avoids premature convergence for local minima
Step 5 Termination The computation continues until the predefined maximum
number iterations is reached The best tour selected among all iterations implies the
optimal solution
Fig 5-2 Flowchart of the ACO applied to DNR and DGs placement
Chapter 5 Distribution Network Reconfiguration amp DG Allocation for Feeder Loss
Reduction
Page | 99
54 Application Studies
To demonstrate the performance and effectiveness of the proposed technique in
assessing the network reconfiguration and placement of DG problems
simultaneously the proposed ACO is implemented on two 1266 kV test systems
consisting of 33 and 69 buses The network models are built in OpenDSS and the
solution algorithm is developed in MATLAB For both test systems the substation
voltage is assumed to be 10 pu and all the branches and buses are considered as
candidate locations for tie-switches and DG placement respectively In this study
for simplicity the number of installed DGs is three All the DGs are synchronous
generators and are represented as PQ models with a 100 kVA capability and a
power factor equal to 10 For the purpose of better illustration and comparison four
cases are considered to analyse the superiority and performance of the proposed
method
Case I System is without reconfiguration and has no DGs (base case)
Case II System is optimally reconfigured and has no DGs
Case III System is optimally reconfigured after DGs are placed at certain buses
Case IV System is optimally reconfigured and DGs are optimally placed
simultaneously
It is to be noted that the ACO control parameters are different for each test case
They are set experimentally using information from several trial runs The final
combinations that provide the best results for all of the above tests are given in
Appendix C1
541 33-bus System
In this section the proposed procedure is implemented on a 33-bus 1266 kV radial
distribution system with 37 branches and 5 tie-switches whose single-line diagram
is shown in Fig 5-3 The tie-switches are located at L33 to L37 represented by red
dotted lines The data of line and load are taken from [108] and summarised in
Appendix A2 The total real and reactive power loads of the system are 3715 kW
and 2300 kVAr respectively The performance of the presented method for the four
Chapter 5 Distribution Network Reconfiguration amp DG Allocation for Feeder Loss
Reduction
Page | 100
10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
18 19 20 21
22 23 24
25 26 27 28 29 30 31 32
L1 L2 L3 L4 L5 L6 L7 L8 L9 L10 L11 L12 L13 L14 L15 L16 L17
L18
L19 L20 L21
L22
L23 L24
L25
L26 L27 L28 L29 L30 L31 L32
L33
L34
L35
L36
L37
cases is given in Table 5-1 The network losses in each branch for all test cases are
listed in Appendix B2
Fig 5-3 33-bus system
Table 5-1 Results of different cases for the 33-bus system
Case Active feeder
loss (kW)
Minimum voltage
(pu)
(Bus No)
Location of tie-switches
on Fig 53
DG location
Case I 20314 09116 (B17) L33 L34 L35 L36 L37 NA
Case II 13981 09361 (B31) L7 L9 L14 L32 L37 NA
Case III 11753 09357 (B31) L7 L9 L14 L28 L31 B17 B21 B24
Case IV 10844 09462 (B32) L7 L9 L14 L32 L37 B30 B31 B31
Case I base case
For the base case without reconfiguration and DGs the initial active feeder loss of
this system is 20314 kW The lowest bus voltage is 09116 pu and this occurs at
Bus 17
Case II with reconfiguration only (no DGs)
In this case only reconfiguration is considered and no DGs are installed The
network configuration after DNR is shown in Fig 5-4 The number of the solutionrsquos
elements for this case is 5 which is the number of tie-switches After DNR the total
feeder loss is 13981 kW which corresponds to a 3118 reduction in loss In
addition the minimum voltage also increases from 09116 pu to 09361 pu
Chapter 5 Distribution Network Reconfiguration amp DG Allocation for Feeder Loss
Reduction
Page | 101
10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
18 19 20 21
22 23 24
25 26 27 28 29 30 31 32
L1 L2 L3 L4 L5 L6 L7 L8 L9 L10 L11 L12 L13 L14 L15 L16 L17
L18
L19 L20 L21
L22
L23 L24
L25
L26 L27 L28 L29 L30 L31 L32
L33
L34
L35
L36
L37
Fig 5-4 33-bus system for feeder loss minimisation Case II
To illustrate the performance of the proposed ACO the results are compared with
the results obtained using the branch exchange method (BEM) [109] harmony
search algorithm (HSA) [110] fireworks algorithm (FWA) [16] particle swarm
optimisation (PSO) [55] and invasive weed optimisation (IWO) [111] these are all
described in the literature and are presented in Table 5-2 It is observed that the
results obtained from the ACO are identical to those from the HAS PSO and IWO
but better than the results from the BEM and FWA This is because that BEM and
FWA have plunged into a local optimal solution and they lack the ability to escape
from it
Table 5-2 Comparison of simulation results for 33-bus system in Case II
Method Feeder loss
(kW)
Loss reduction
()
Tie-switches location Minimum
voltage (pu)
The proposed ACO 13981 3118 L7 L9 L14 L32 L37 09361
BEM [109] 14054 3082 L7 L10 L14 L32 L37 09361
HSA [110] 13981 3118 L7 L9 L14 L32 L37 09361
FWA [16] 14026 3095 L7 L9 L14 L28 L32 09396
PSO [55] 13981 3118 L7 L9 L14 L32 L37 09361
IWO [111] 13981 3118 L7 L9 L14 L32 L37 09361
Moreover both the continuous genetic algorithm (CGA) [112] and cuckoo search
algorithm (CSA) [113] are implemented to further investigate the performance of the
proposed ACO It is important to note that the performance of the ACO CGA and
CSA depends on the selection of their control parameters All three algorithms are
solved 100 times The average maximum minimum and standard deviation of the
100 runs are compared and shown in Table 5-3 The convergence number is defined
Chapter 5 Distribution Network Reconfiguration amp DG Allocation for Feeder Loss
Reduction
Page | 102
10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
18 19 20 21
22 23 24
25 26 27 28 29 30 31 32
L1 L2 L3 L4 L5 L6 L7 L8 L9 L10 L11 L12 L13 L14 L15 L16 L17
L18
L19 L20 L21
L22
L23 L24
L25
L26 L27 L28 L29 L30 L31 L32
L33
L34
L35
L36
L37
DG2
DG1
DG3
as the number of the iterations when the objective function is convergence It can be
seen that all three algorithms have obtained the same minimum loss However the
proposed ACO method has a higher probability in finding the global optimum
solution as the mean and standard deviation of the fitness values of the ACO
algorithm are less than those obtained by the other algorithms Furthermore as the
average value of convergence number of the ACO is less than that of the other two
algorithms this means the proposed algorithm has a higher convergence rate In
terms of the computation times the proposed ACO runs faster when compared with
CGA and CSA
Table 5-3 Comparison of ACO with CGA and CSA for the 33-bus system in Case II
Method Feeder loss (kW) Convergence number Average
computation
times
(second)
AVG MAX MIN STD AVG STD
ACO 13981 13981 13981 0 228 821 1448
CGA [112] 14002 14619 13981 12121 5463 2986 3926
CSA [113] 13986 14028 13981 01328 8363 3425 7258
AVG MAX MIN and STD mean the average maximum minimum and standard deviation of the 100 runs
Case III with reconfiguration only (with DGs)
In this case the three DGs are located at the end of the feeders ie Bus 17 21 24
The network configuration after DNR is illustrated in Fig 5-5 As shown in Table 5-
1 the network reconfiguration results in a reduction of 4214 in feeder loss in
comparison with the original network without DGs and a reduction of 1594 in
comparison with the reconfigured system without DGs
Fig 5-5 33-bus system for feeder loss minimisation Case III
Chapter 5 Distribution Network Reconfiguration amp DG Allocation for Feeder Loss
Reduction
Page | 103
10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
18 19 20 21
22 23 24
25 26 27 28 29 30 31 32
L1 L2 L3 L4 L5 L6 L7 L8 L9 L10 L11 L12 L13 L14 L15 L16 L17
L18
L19 L20 L21
L22
L23 L24
L25
L26 L27 L28 L29 L30 L31 L32
L33
L34
L35
L36
L37
DG2DG1
DG3
Case IV with reconfiguration and DG allocation
Fig 5-6 illustrates the optimal network configuration and DG locations The network
is reconfigured and DGs are allocated simultaneously in this case Therefore the
number of the solutionrsquos elements for this case becomes 8 which is the sum of the
number of tie-switches and DGs The results show the final configuration with a
feeder loss of 10844 kW with 4662 2244 and 773 reduction in comparison
with that in Case I Case II and Case III respectively
Fig 5-6 33-bus system for feeder loss minimisation Case IV
In this case the impacts of DG capacity on assessing the DNR and DG allocation
problems in terms of feeder loss reduction are also studied The capacity of each DG
is set as 100 400 700 and 1000 kVA respectively The feeder losses for different
DG capacities are shown in Fig 5-7 Before simultaneous reconfiguration and DG
allocation the feeder loss decreases from 1783 kW to 1023 kW when the capacity
of DG is increased from 100 kVA to 700 kVA However the feeder loss increases to
1042 kW if the capacity of DG continuously grows to 1000 kVA The inappropriate
network configuration and DG location might result in loss increment when the size
of the DG is increased However with the introduction of network reconfiguration
and DG allocation feeder loss is reduced no matter what the capacity of DG is This
proves that the proposed methodology can reduce the total feeder loss by
determining the most suitable network topology and DG locations in comparison
with the original configuration
Chapter 5 Distribution Network Reconfiguration amp DG Allocation for Feeder Loss
Reduction
Page | 104
086
088
09
092
094
096
098
1
102
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32
Vo
ltag
e (
pu
)
Bus No
Case I
Case II
Case III
Case IV
0
20
40
60
80
100
120
140
160
180
200
100 400 700 1000
Fee
de
r lo
ss (
kW)
DG Capacity (kVA)
Before simultaneousreconfiguration and DG allocation
After simultaneous reconfigurationand DG allocation
Fig 5-7 Comparison of feeder loss for different DG capacities before and after simultaneous
reconfiguration and DG allocation
The voltage profiles of four cases are compared and shown in Fig 5-8 It can be seen
that the voltage profiles at most buses in Case IV have been improved in comparison
with the other three cases In terms of Case III and Case IV the buses which inject
DGs show the improvement in voltage profiles ie the voltage of Bus 31 is
improved from 09357 pu in Case III to 09537 pu in Case IV In Case IV as Bus 32
is the furthest bus being supplied its voltage is the lowest value among all buses In
conclusion the systemrsquos voltage profiles are improved by optimal DNR and DG
allocation
Fig 5-8 Comparison of voltage profiles in different cases of 33-node system
Chapter 5 Distribution Network Reconfiguration amp DG Allocation for Feeder Loss
Reduction
Page | 105
10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
27
28
29
30
31 32 33 34
35
36
37
38 39 40 41 42 43 44 45
46 47 48 49
50
51
52
53 54 55 56 57 58 59 60 61 62 63 64
65 66
67 68
L1 L2 L3 L4 L5 L6 L7 L8 L9 L10 L11 L12 L13 L14 L15 L16 L17 L18 L19 L20 L21 L22 L23 L24 L25 L26
L27
L28
L29
L30
L31 L32 L33 L34
L35
L36
L37
L38 L39 L40 L41 L42 L43 L44 L45
L46
L47 L48 L49
L50
L51
L52
L53 L54 L55 L56 L57 L58 L59 L60 L61 L62 L63 L64
L65
L66
L67
L68
L69
L70
L71
L72L73
542 69-bus System
This is a large-scale radial distribution system consisting of 73 branches and 5 tie-
switches whose single-line diagram is shown in Fig 5-9 The tie-switches are
located at L69 to L73 represented by red dotted lines The line and load data of the
system are taken from [84] and summarised in Appendix A3 The total power loads
are 379589 kW and 26891 kVAr respectively Similar to 33-bus system this
system is also simulated for four cases and the results are given in Table 5-4 The
network losses in each branch for all test cases are listed in Appendix B2
Fig 5-9 69-bus system
Table 5-4 Results of different cases for the 69-bus system
Case Active feeder
loss (kW)
Minimum voltage
(pu)
(Bus No)
Tie-switches location DG location
Case I 22562 09072 (B64) L69 L70 L71 L72 L73 NA
Case II 9885 09476 (B60) L14 L55 L61 L71 L72 NA
Case III 8758 09477 (B60) L13 L55 L61 L71 L72 B26 B45 B64
Case IV 7397 09571 (B60) L14 L55 L61 L71 L72 B60 B60 B60
Case I base case
Base case active feeder loss in the system is 22562 kW The lowest bus voltage is
09072 pu and occurs at bus 64
Chapter 5 Distribution Network Reconfiguration amp DG Allocation for Feeder Loss
Reduction
Page | 106
10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
27
28
29
30
31 32 33 34
35
36
37
38 39 40 41 42 43 44 45
46 47 48 49
50
51
52
53 54 55 56 57 58 59 60 61 62 63 64
65 66
67 68
L1 L2 L3 L4 L5 L6 L7 L8 L9 L10 L11 L12 L13 L14 L15 L16 L17 L18 L19 L20 L21 L22 L23 L24 L25 L26
L27
L28
L29
L30
L31 L32 L33 L34
L35
L36
L37
L38 L39 L40 L41 L42 L43 L44 L45
L46
L47 L48 L49
L50
L51
L52
L53 L54 L55 L56 L57 L58 L59 L60 L61 L62 L63 L64
L65
L66
L67
L68
L69
L70
L71
L72L73
Case II with reconfiguration only (no DGs)
After DNR switches at L14 L55 L61 L71 and L72 are opened as shown in Fig 5-
10 The total feeder loss is reduced by 5619 and the minimum voltage is
increased to 09476 pu in comparison with the base case
Fig 5-10 69-bus system for feeder loss minimisation Case II
The comparisons of results among the proposed ACO with FWA [16] HSA [110]
and genetic algorithm (GA) [110] are presented in Table 5-5 It is observed that the
results obtained from the ACO are better than those from the FWA HSA and GA
as these algorithms are trapped into the local optimal solution
Table 5-5 Comparison of simulation results for 69-bus system in Case II
Method Feeder loss
(kW)
Loss reduction
()
Tie-switches location Minimum
voltage (pu)
The proposed ACO 9885 5619 L14 L55 L61 L71 L72 09476
FWA [16] 9886 5618 L14 L56 L61 L71 L72 09476
HSA [110] 10546 5326 L13 L18 L56 L61 L72 09475
GA [110] 10242 5461 L14 L53 L61 L71 L72 09462
Case III with reconfiguration only (with DGs)
In this case the three DGs are located at the end of the feeders ie Bus 26 45 64
The network configuration after DNR is illustrated in Fig 5-11 As shown in Table
Chapter 5 Distribution Network Reconfiguration amp DG Allocation for Feeder Loss
Reduction
Page | 107
10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
27
28
29
30
31 32 33 34
35
36
37
38 39 40 41 42 43 44 45
46 47 48 49
50
51
52
53 54 55 56 57 58 59 60 61 62 63 64
65 66
67 68
L1 L2 L3 L4 L5 L6 L7 L8 L9 L10 L11 L12 L13 L14 L15 L16 L17 L18 L19 L20 L21 L22 L23 L24 L25 L26
L27
L28
L29
L30
L31 L32 L33 L34
L35
L36
L37
L38 L39 L40 L41 L42 L43 L44 L45
L46
L47 L48 L49
L50
L51
L52
L53 L54 L55 L56 L57 L58 L59 L60 L61 L62 L63 L64
L65
L66
L67
L68
L69
L70
L71
L72L73
DG3
DG1
DG2
10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
27
28
29
30
31 32 33 34
35
36
37
38 39 40 41 42 43 44 45
46 47 48 49
50
51
52
53 54 55 56 57 58 59 60 61 62 63 64
65 66
67 68
L1 L2 L3 L4 L5 L6 L7 L8 L9 L10 L11 L12 L13 L14 L15 L16 L17 L18 L19 L20 L21 L22 L23 L24 L25 L26
L27
L28
L29
L30
L31 L32 L33 L34
L35
L36
L37
L38 L39 L40 L41 L42 L43 L44 L45
L46
L47 L48 L49
L50
L51
L52
L53 L54 L55 L56 L57 L58 L59 L60 L61 L62 L63 L64
L65
L66
L67
L68
L69
L70
L71
L72L73
DG3DG1
DG2
5-5 the network reconfiguration results in a reduction of 6118 in feeder losses as
compared with the original network without DGs and a reduction of 1140 in
comparison with the reconfigured system without DGs
Fig 5-11 69-bus system for feeder loss minimisation Case III
Case IV with reconfiguration and DG allocation
Fig 5-12 illustrates the optimal network configuration and DG locations In this case
the results show the final configuration with a feeder loss of 7397 kW with 6721
2517 and 1554 reduction in comparison with that in Case I Case II and Case
III respectively
Fig 5-12 69-bus system for feeder loss minimisation Case IV
Chapter 5 Distribution Network Reconfiguration amp DG Allocation for Feeder Loss
Reduction
Page | 108
0
50
100
150
200
250
100 400 700 1000
Fee
de
r lo
ss (
kW)
DG Capacity (kVA)
Before simultaneousreconfiguration and DG allocation
After simultaneous reconfigurationand DG allocation
In this case the impacts of DG capacity on assessing the DNR and DG allocation
problems in terms of feeder loss reduction are also studied The capacity of each DG
is set as 100 500 900 and 1300 kVA respectively The feeder loss curves for
different DG capacities are shown in Fig 5-13 After simultaneous reconfiguration
and DG allocation the feeder loss decreases from 7397 kW to 873 kW when the
DG capacity is increased from 100 kVA to 900 kVA However the loss bounces
back to 114 kW if the DG capacity continues to increase to 1300 kVA This means
that the capability of network reconfiguration and DG allocation on feeder loss
reduction is limited when the size of DGs is large But the proposed methodology
can still reduce the total feeder loss for all DG capacities by determining the most
suitable network topology and DG locations in comparison with the original
configuration
Fig 5-13 Comparison of feeder loss for different DG capacities before and after simultaneous
reconfiguration and DG allocation
Fig 5-14 shows the voltage profile of the 69-bus system It can be seen that the
voltage profiles at most buses in Case IV have been improved in comparison with
the other three cases Compared with Case III and Case IV the buses which inject
DGs show improvement in voltage profiles ie the voltage of Bus 60 is improved
from 09477 pu in Case III to 09571 pu in Case IV In Case IV although there are
three DGs connected as Bus 60 as the value of load connected at this bus is the
largest (1244 kW) this bus voltage is the lowest among all buses In conclusion the
systemrsquos voltage profiles are improved by optimal DNR and DG allocation
Chapter 5 Distribution Network Reconfiguration amp DG Allocation for Feeder Loss
Reduction
Page | 109
086
088
09
092
094
096
098
1
102
0 5 10 15 20 25 30 35 40 45 50 55 60 65
Vo
ltag
e (
pu
)
Bus No
Case I
Case II
Case III
Case IV
Fig 5-14 Comparison of voltage profiles in different cases of 69-node system
55 Summary
In this chapter the application of optimal planning using DNR and DG allocation for
the problem of distribution feeder loss minimisation has been implemented The
method based on ACO has been successfully applied to the 1266 kV 33-bus and 69-
bus systems to find the optimum system configuration and DG locations
There are four cases used to analyse the superiority and performance of the proposed
method The proposed ACO is capable of finding the optimal solutions in all cases
In Case IV the feeder losses are reduced by 4662 and 6721 for the 33-bus and
69-bus system respectively in comparison with the base case Therefore Case IV is
found to be more effective in minimising the total loss and improving voltage
profiles compared to the other cases The numerical results show that for best
performance the existing tie-switches are relocated and the DGs are optimally
placed in comparison with the original network In addition the impacts of DG
capacity on assessing the DNR and DG allocation problems in terms of feeder loss
reduction are also studied The inappropriate network configuration and DG location
might result in loss increment when the size of DG is increased The proposed
methodology has successfully reduced the total feeder loss for different capacities of
DG by determining the most suitable network topology and the DG locations
Chapter 5 Distribution Network Reconfiguration amp DG Allocation for Feeder Loss
Reduction
Page | 110
compared to the original configuration The minimum loss obtained by DNR and DG
allocation decreases as the capacities of DGs are increased However this decrease
stops when DGs can supply all the loads without the main supply After that the
minimum loss increases as the capacities of DGs are increased
Moreover the simulation results have been compared with other classical methods in
literature and the proposed ACO is more efficient and is more likely to obtain the
global optimum solution
Page | 111
CHAPTER 6
DISTRIBUTION NETWORK
RECONFIGURATION amp TRANSFORMER
ECONOMIC OPERATION FOR NETWORK
LOSS REDUCTION
61 Introduction
Rapid increases in electricity demand have forced electric power utilities throughout
the world into major reconstructing processes As a significant proportion of electric
energy is dissipated in the operation of a distribution network the reduction of loss
should be considered an important problem for the economic operation of the overall
system [82]
Load variations have been disregarded in most studies on distribution automation
(DA) problems ie average loads were used in their reconfiguration schemes In this
chapter distribution loads experience daily and seasonal variations The study
considers the daily load curves of different types of consumers (residential
commercial and industrial) and in addition the days are divided into eight types
spring weekdays spring weekends summer weekdays summer weekends autumn
Chapter 6 Distribution Network Reconfiguration amp Transformer Economic
Operation for Network Loss Reduction
Page | 112
weekdays autumn weekends winter weekdays and winter weekends The best
reconfiguration hours during each of these typical days are then selected
The objective function for finding the best configuration of the network when
considering feeder loss and transformer loss will be studied in this chapter Different
combinations of locations of tie-switches in the network and operation modes of all
transformers in the substations represent different network configurations An Ant
colony optimisation (ACO) algorithm is adopted on an 11 kV distribution network
developed from Bus 4 of the Roy Billinton Test System (RBTS) to determine the
optimal network configuration during each type of day Furthermore the effects of
DGs and EVs in solving distribution network reconfiguration (DNR) and
transformer economic operation (TEO) based on network loss reduction are also
investigated
This chapter is organised as follows the next section discusses the variation of loads
and the reconfiguration hours Section 63 presents the objective function and
constraints for DNR Section 64 describes the application of ACO algorithms to the
problem Numerical studies are presented and discussed in Section 65 and finally
Section 66 summarises the main conclusions
62 Time-varying Load Model
As distribution loads experience daily and seasonal variations the optimum network
configuration constantly changes [82] However it is not reasonable to reconfigure a
network frequently ie based on hourly schedule since each switch has a maximum
number of allowable switching operations during its lifetime and frequent switching
actions will increase its maintenance costs [82]
However infrequent actions cause the system to work well below its optimum state
In order to determine the best reconfiguration time during a day the daily load
profiles should be smoothed In other words the daily load curves are divided into a
number of periods As the maintenance cost of a switch increases with the increasing
number of switching actions the number of intervals is a trade-off between the
optimum reconfiguration and switch cost As there is a peak and a valley of network
Chapter 6 Distribution Network Reconfiguration amp Transformer Economic
Operation for Network Loss Reduction
Page | 113
Actual daily load curve
Smoothed daily load curve
load variations during a day it is appropriate to divide the 24 hours daily load curves
into two periods Increasing the number of intervals will not change the nature of the
problem but will increase its complexity
Fig 6-1 The reconfiguration hours for a typical day
As the difference between 1198751 and 1198752 is increased the effect of DNR on loss
reduction increases where 1198751 and 1198752 are the average active power of the loads
during the first and second time periods respectively As shown in Fig 6-1 hours
1199051and 1199052 are calculated to maximise |1198751 minus 1198752| It should also be noted that the above
load smoothing methodology is only used to determine the reconfiguration intervals
and the active power loss during each interval is calculated based on the actual daily
load curve [82]
63 Problem Formulation
In this study the 24 hours of a typical day is divided into two periods The first time
period is 0000 to 1199051 and 1199052 to 2400 and the second time period is between 1199051 and 1199052
The following objective function is calculated for all possible network configurations
during each time interval and the one that minimises the total power loss and
satisfies all constraints is selected The energy losses of the distribution network over
the first and second time interval are presented in (6-1) and (6-2) the objective
function (6-3) is to minimise f the sum of f1 and f2
P1
P2
1199051 1199052 Time (h)
Chapter 6 Distribution Network Reconfiguration amp Transformer Economic
Operation for Network Loss Reduction
Page | 114
1198911 = sum (119864119871119905 + 119879119871119905)1199051minus1119905=1 + sum (119864119871119905 + 119879119871119905) 1199051
24119905=1199052 isin 1 2 hellip 24 (6-1)
1198912 = sum (119864119871119905 + 119879119871119905)1199052minus1119905=1199051 1199052 isin 1 2 hellip 24 (6-2)
Min 119891 = 1198911 + 1198912 (6-3)
where 119864119871119905 is the feeder loss of the distribution network during hour t (kWh) 119879119871119905
represents the transformer loss during hour t (kWh) The detailed calculation of
transformer loss and feeder loss are presented in Section 27 and 28 respectively
The computed voltages currents and the power flow at all branches should be kept
in their permissible range and the network should be operated in radial The
configurations that violate any constraint are assigned with huge objective functions
and are disregarded
64 Applying ACO to DNR and TEO
In this chapter the objective of simultaneous reconfiguring network and changing
transformer operation modes is to deal with energy loss minimisation including
transformer loss and feeder loss To implement the optimisation problem the
developed ACO algorithm is adopted to find the optimum location of tie-switches
and transformer operation modes in the network When the location of tie-switches
and operation modes of transformers are changed a new network configuration will
be formed For each network configuration the objective function is evaluated by
using the approach presented in Section 63
The search space of the DNR and TEO problems is modelled as a directed graph as
shown in Fig 6-2 Each solution is represented by a string of integers which
indicates the transformer operation modes and the location of tie-switches The
number of the solutionrsquos elements is equal to the number of stages in this graph
which is the sum of the amount of main feeders (the number of transformer pairs 119873119904)
and the number of existing tie-switches 119873119905
Chapter 6 Distribution Network Reconfiguration amp Transformer Economic
Operation for Network Loss Reduction
Page | 115
Home
0 1
0 1
0 1
0 1
1 2 NPNP-1
1 2 NP-1 NP
1 2 NPNP-1
1 2 NP-1 NP
Food
Stage
1
2
Ns-1
Ns
Ns+1
Ns+2
Ns+Nt-1
Ns+Nt
Part 1
Number of
substations
Ns
Part 2 Number
of existing tie-
switches Nt
Number of candidate locations for the tie-switches NP
Fig 6-2 Search space of DNR and TEO
As shown in Fig 6-3 the number of transformer pairs is 3 and the number of
existing tie-switches is 4 Therefore the number of the solutionrsquos elements for this
system is 7 In addition the possible branches for tie-switch placement are 4
Chapter 6 Distribution Network Reconfiguration amp Transformer Economic
Operation for Network Loss Reduction
Page | 116
Tie-switch
Transformer
Fig 6-3 Sample network with three substations
For transformer operation mode selection in Part I the ACO algorithm is applied to
assign each bit of the front part of the solution vector to the status of substations and
hence the number of transformers in operation in each substation can be represented
as a binary vector
State 0 this substation has one transformer in operation
State 1 this substation has two transformers in operation
However for the relocation of existing tie-switches in Part II the states indicate the
location of switches Artificial ants will start their tours at home move along the
paths in the graph and end at the food source
The 24 hour load curve is divided into two time intervals for all load types in terms
of the principle presented in Section 62 Fig 6-4 demonstrates the computation
procedure for the transformer operation mode selection and tie-switches relocation
problem at each of the time interval The application of the ACO algorithm to the
TEO and DNR problem is similar to that in Section 532 For each time interval the
operation modes of the transformers are selected first and the locations of tie-
switches are then determined
Chapter 6 Distribution Network Reconfiguration amp Transformer Economic
Operation for Network Loss Reduction
Page | 117
Start
Set time interval T=1
Maximum iteration
reached
Output best
configuration and end
No
Yes
Divide the 24-h daily load curve into two
intervals using the technique in Section 62
Iteration N=1
Initialise the parameters for ACO
algorithm searching space
Dispatch ants based on the amount
of pheromone on edges
Relocate tie-switches and select the
number of transformers to be operated in
all substations by location lists
N=N+1
Calculate the objective function
for each ant at this time interval
Read system topology
and load data
The pheromones are updates
according to local and global rules
Record the best solution so far
and empty all location lists
T=T+1
Tgt2
Yes
t=t+1
No
Fig 6-4 Flowchart of the ACO applied to DNR and TEO for a specific type of day
Chapter 6 Distribution Network Reconfiguration amp Transformer Economic
Operation for Network Loss Reduction
Page | 118
LP11 LP12 LP13 LP14 LP15 LP16 LP17
LP8 LP9 LP10
LP1 LP2 LP3 LP4 LP5 LP6 LP7
LP32 LP33 LP34 LP35 LP36 LP37 LP38
LP29 LP30 LP31
LP26 LP27 LP28
LP18 LP19 LP20 LP21 LP22 LP23 LP24 LP25
19
20
21
22
23
24
26
25 27
28
29 30
71
13 15
14 16
17
18
69
1 3
2
5
4
7
6 8
10
9
68
11 12
56
57
58 60
59 61 62
65
64 66 67
50 52
51
54
53 55
44
45
46
47
48
49
70
31
32
33
34
36
35
39
37 38 40
41
42 43
63
F3
F2
F1
F7
F6
F5
F4
Normally Open Circuit BreakerNormally Closed Circuit Breaker
Subbus1
Subbus2
Subbus3
T1
T3
T5
Main
feeder
Main
feeder
Main
feeder
T2
T4
T6
65 Application Studies
In this study the proposed methodology is applied to an 11 kV distribution network
developed from Bus 4 of the RBTS a single-line diagram of the network is shown in
Fig 6-5 The network consists of 38 load points and 4 tie-switches the associated
data can be found in [114] The types and lengths of 11 kV feeders are listed in
Appendix A4 The network built in OpenDSS incorporates three 3311 kV double
transformer substations supplying the downstream loads
Fig 6-5 Distribution feeder connected to RBTS Bus 4
This typical urban distribution network supplies residential commercial and
industrial consumers The maximum value of active and reactive power and the
Chapter 6 Distribution Network Reconfiguration amp Transformer Economic
Operation for Network Loss Reduction
Page | 119
customer type of each node are modified from the original values and the new values
are listed in Table 6-1
Table 6-1 Revised customer data (peak load)
Number
of load
points
Load points Customer type P
(kW)
Q
(kVAr)
Number of
customers
4 1-2 9-10 residential 8869 8426 220
6 3-5 13-15 residential 8137 7731 200
12 6-7 16-17 23-25 28
30-31 37-38
commercial 6714 6378 10
6 8 11 18 26 32-33 industrial 2445 23228 1
10 12 19-22 27 29 34-
36
industrial 1630 15485 1
The days of the year are divided into eight categories spring weekdays spring
weekends summer weekdays summer weekends autumn weekdays autumn
weekends winter weekdays and winter weekends Typical loads profiles for
different consumer types are shown in Fig 6-6-6-8 which are multiplied by the
values of Table 6-1 to obtain the real demand of each node [82] In order to find the
reconfiguration hours for each day type the aggregated load profiles of the main
feeder shown in Fig 6-9 are used
Fig 6-6 Daily load profile of residential consumers
Chapter 6 Distribution Network Reconfiguration amp Transformer Economic
Operation for Network Loss Reduction
Page | 120
Fig 6-7 Daily load profile of commercial consumers
Fig 6-8 Daily load profile of industrial consumers
Fig 6-9 Daily load profile (MW) of the main feeder
Chapter 6 Distribution Network Reconfiguration amp Transformer Economic
Operation for Network Loss Reduction
Page | 121
In this case eight types of day and two time intervals for each of them are
considered As a result the optimisation problem has to be solved 16 times to obtain
a yearly reconfiguration scheme The distribution of load types for a whole year is
shown in Table 6-2
Table 6-2 The distribution of load types for a whole year
Load Types Number of days Total days
Spring
(Mar Apr May)
Weekdays 66 92
Weekends 26
Summer
(Jun Jul Aug)
Weekdays 66 92
Weekends 26
Autumn
(Sep Oct Nov)
Weekdays 65 91
Weekends 26
Winter
(Dec Jan Feb)
Weekdays 64 90
Weekends 26
Year 365 Days
For the purpose of better illustration and comparison three test cases are considered
to analyse the superiority and performance of the proposed method
Test Case 1 The system is optimally reconfigured and has no DGs and EVs
Test Case 2 The system is optimally reconfigured after DGs are placed at certain
buses
Test Case 3 The system is optimally reconfigured after integration of EVs
The proposed ACO algorithm is coded in the MATLAB to obtain the location of tie-
switches and operation modes of transformers for the optimum configuration The
settings of the ACO parameters that provided the optimum solution for these three
cases are presented in Appendix C2 The selection of parameters is a balance
between the convergence rate and the global search ability of the algorithm
Chapter 6 Distribution Network Reconfiguration amp Transformer Economic
Operation for Network Loss Reduction
Page | 122
651 Test Case 1
In this test the tie-switches are relocated and the operation modes of transformers in
all substations are changed to obtain the best network configuration with minimum
network loss
Table 6-3 Results of DNR and TEO with different load types in Test Case 1
As shown in Fig 6-5 the tie-switches are located in L68-71 and each substation has
two transformers operating in parallel for the base network configuration The test
results with different load conditions are presented in Table 6-3 Reconfiguration of
the network and changes in the operation modes of transformers in all substations
using the proposed algorithm result in a reduction of loss for all load conditions As
a result the annual energy loss is reduced from 4337150 kWh to 4117681 kWh
which amounts to a 506 reduction Both transformer loss and feeder loss are
reduced through this optimal planning using DNR and TEO It can be noted that on
winter weekdays the loading of the main feeders is very high from 800 to 2100
Spring
weekday
Spring
weekend
Summer
weekday
Summer
weekend
Autumn
weekday
Autumn
weekend
Winter
weekday
Winter
weekend
Before
Reconfiguration
Whole Day Open branches L68L69
L70L71
L68L69
L70L71
L68L69
L70L71
L68L69
L70L71
L68L69
L70L71
L68L69
L70L71
L68L69
L70L71
L68L69
L70L71
Number of operated
transformers
1st substation 2 2 2 2 2 2 2 2
2nd substation 2 2 2 2 2 2 2 2
3rd substation 2 2 2 2 2 2 2 2
Loss
(kWh)
Cable 9233 3498 8050 3151 9660 3665 11009 4080
Transformer 4301 3410 4109 3350 4372 3437 4597 3507
Total 13534 6908 12159 6501 14032 7102 15606 7587
After
Reconfiguration
1st interval Time (h) 0-7
23-24
0-6 0-7
23
0-7 0-7
22-23
0-6
0-7
22-23
0-6
Open branches L48L68
L69L71
L68L69
L70L71
L17L68
L70L71
L17L68
L70L71
L17L68
L70L71
L68L69
L70L71
L17L68
L70L71
L68L69
L70L71
Number of operated
transformers
1st substation 1 1 1 1 1 1 1 1
2nd substation 1 1 1 1 1 1 1 1
3rd substation 1 1 1 1 1 1 1 1
2nd interval Time (h) 8-22 7-23 8-22 8-23 8-21 7-23 8-21 7-23
Open branches L17L41
L65L70
L68L69
L70L71
L41L48
L65L69
L68L69
L70L71
L17L41
L65L70
L68L69
L70L71
L17L41
L65L70
L68L69
L70L71
Number of operated
transformers
1st substation 2 2 2 2 2 2 2 2
2nd substation 2 1 2 1 2 1 2 1
3rd substation 2 1 2 1 2 1 2 1
Loss
(kWh)
Cable 9043 3516 7851 3169 9519 3685 10845 4103
Transformer 3955 2616 3759 2517 4036 2656 4264 2755
Total 12998 6132 11610 5686 13479 6341 15109 6858
Chapter 6 Distribution Network Reconfiguration amp Transformer Economic
Operation for Network Loss Reduction
Page | 123
0
05
1
15
2
25
3
35
4
45
05 1 15 2 25 3
Before reconfiguration
After reconfiguration
Thus transformers in all substations are operated in parallel However during spring
weekends from 000 to 700 as the loadings supplied by all feeders are lower than
the critical transformer load factor (TCLF) and hence transformers in all substations
are operated in single In addition the loadings supplied by Feeder 4 are much larger
than that of Feeder 3 in summer weekdays between 800 to 2200 Thus the tie-
switch is moved from L71 to L41 and LP24amp25 are moved from Feeder 4 to Feeder
3 This ensures balancing of the loads between the two feeders
652 Test Case 2
In this test the presence of three DG units is taken into consideration The effect of
DGs on assessing the DNR and TEO problems in terms of loss minimisation is
studied The introduction of DGs converts a mono-source distribution network to a
multi-source one [66] The three DGs are located at the end of the feeders ie Bus
17 41 and 65 All the DGs are synchronous generators and considered as PQ models
The capacity of DG is assumed to be 05 1 15 2 25 and 3 MVA respectively
The results are shown in Fig 6-10 and show that the proposed methodology has
successfully reduced the total energy loss for different capacities of DG by
determining the most suitable network topology
Fig 6-10 Annual energy loss with different DG capacities
To
tal
loss
(G
Wh
)
DG Capacity (MW)
Chapter 6 Distribution Network Reconfiguration amp Transformer Economic
Operation for Network Loss Reduction
Page | 124
653 Test Case 3
The objective of this section is to illustrate the behaviour of the proposed
optimisation process when EVs are integrated into the existing distribution network
The impacts of EV penetration levels and charging strategies are studied This
section utilises the optimal planning using DNR and TEO as a technique to decrease
network loss whilst respecting the operation constraints It is assumed that the
battery starts charging once the EV is connected to the charger at home
The charging duration can be calculated according to the following formula [89]
119905119888 =119862119864119881times(1minus119878119874119862)times119863119874119863
120578times119875119862 (6-4)
where 119862119864119881 is the battery capacity In this section EVs are divided into four types
with different market shares and batteries as in Table 6-4 [115] 119863119874119863 and 120578 are
depth of discharge and charger efficiency (assumed to be 80 and 90 separately)
Two types of chargers with different charging rates (119875119862) are commonly used for
consumer EVs at home charging points this study assumes that 80 of EVs are
charged at 3kW (13A) and 20 at 7kW (30A) [92] SOC is state-of-charge and is
defined as the ratio of available energy to maximum battery capacity [89] It is
determined by the distance covered by the EV in terms of number of miles during
the day
Table 6-4 Characteristics of EV
Types 119862119864119881 (kWh) Maximum driving
capability (mile)
Market share ()
Micro car 12 50 20
Economy car 14 53 30
Mid-size car 18 56 30
Light truck SUV 23 60 20
According to [116] the average number of miles covered by a vehicle was reported
to be 2164 milesday in 2014 Then the SOC for an EV is calculated based on
number of miles (m) and the maximum driving capability (MDC) as follows
Chapter 6 Distribution Network Reconfiguration amp Transformer Economic
Operation for Network Loss Reduction
Page | 125
4
42
44
46
48
5
30 60 90
Before reconfiguration
After reconfiguration
119878119874119862 = 0 119898 gt 119872119863119862
119872119863119862minus119898
119872119863119862 119898 le 119872119863119862 (6-5)
As mentioned before the EVs are distributed over all the residential load points The
number of customers of residential loads is given in Table 6-1 It is reported that
each customer has 15 vehicles [92] The problem is solved for three different
penetration levels of EVs in the test network 30 60 and 90 respectively In
addition two charging strategies are introduced (1) uncoordinated charging and (2)
coordinated charging The thermal problems of cables which caused by high
penetration levels of EVs are ignored in this study
1) Uncoordinated Charging Strategy
In this part all EVs are plugged in and immediately start charging when they arrive
home In most cases the EV plug-in time is modelled by normal distribution which
increases uncertainty However in order to simplify the discussion the charging start
time is assumed to be 1800 when most people are back home from work The total
losses in the network for the different penetration levels of EVs are compared in Fig
6-11 It can be seen that as the penetration of EVs is increased the total loss also
increases But the total loss for all penetration levels decreases by implementing the
optimal planning strategy in comparison with the original network
Fig 6-11 Annual energy loss in uncoordinated charging strategy
To
tal
loss
(G
Wh
)
Penetration level ()
Chapter 6 Distribution Network Reconfiguration amp Transformer Economic
Operation for Network Loss Reduction
Page | 126
4
42
44
46
48
5
30 60 90
Before reconfiguration
After reconfiguration
2) Coordinated Charging Strategy
In this case the DNOs tend to charge the EVs during off-peak hours to avoid a clash
with the evening peak hours As a result the charging start time is delayed to 0100
when most people are sleeping The total network loss for different EV penetrations
is compared in Fig 6-12 The results show that the postponement of charging time
and optimal planning strategy has been successful in reducing the total energy loss in
comparison with the uncoordinated charging method
Fig 6-12 Annual energy loss in coordinated charging strategy
66 Summary
This study has presented a new optimal planning strategy using DNR and TEO for
distribution network loss minimisation including transformer loss and feeder loss In
this study the distribution loads experience daily and seasonal variations The day is
divided into two periods The proposed ACO algorithm has been successfully
applied to the modified Bus 4 of the RBTS to find the optimum network
configuration and economic operation mode of transformers in all substations during
each time interval Using the results obtained for reconfiguration the existing tie-
switches are relocated and the transformer operation modes are changed
Furthermore the simulation results obtained with numerical studies further
demonstrate the capability of applying the ACO algorithm to distribution network
planning including networks with DGs and EVs The proposed methodology has
successfully reduced the total network loss for different capacities of DG and
To
tal
loss
(G
Wh
)
Penetration level ()
Chapter 6 Distribution Network Reconfiguration amp Transformer Economic
Operation for Network Loss Reduction
Page | 127
different penetration levels of EVs by determining the most suitable network
topology compared to the original configuration The benefits associated with the
increasing capacity of DGs and increasing penetration levels of EVs are also
presented Comparative results show that coordinated charging of EVs results in less
energy loss compared to uncoordinated charging plan with the same EV penetration
level This is due to the postponement of charging time which avoids a clash with
the peak power demand times
The proposed ACO algorithm is suitable for planning a future network based on the
load estimation results Hence there is no limitation on the calculation time An
additional interesting point about DNR and TEO is that although the opening and
closing of switches and transformers result in the life reduction of plants the
additional costs for utilities is insignificant in comparison with the benefits they
bring All the results have proved that a distribution network can be reconfigured and
the operation modes of transformers can be changed to reduce network power loss
which can increase the profits of the distribution utilities
Page | 128
CHAPTER 7
OPTIMAL PLACEMENT OF
SECTIONALISING SWITCHES FOR
RELIABILITY IMPROVEMENT
71 Introduction
Failures in the distribution network cause the majority of service interruptions [78]
And reliability improvement becomes a motivation for distribution utilities to launch
research and demonstration projects [64] An effective method to reduce customer
minutes lost is the greater and more effective use of automated and remote controlled
sectionalising switches and feeder breaker automation This approach will reduce
customer restoration time and minimise the region of a network affected by a short-
circuit fault The effectiveness depends on the number location and type of
sectionalising switches and feeder breakers
Reliability improvement by reduction of expected customer damaged cost (ECOST)
and system interruption duration index (SAIDI) as well as the minimisation of
switch costs are considered in formulating the objective function used in this study
When there are multiple objectives to be considered a compromise solution has to
be made to obtain the best solution ECOST and switch costs can be converted into a
single objective function by aggregating these objectives in a weighted function
Chapter 7 Optimal Placement of Sectionalising Switches for Reliability
Improvement
Page | 129
However as SAIDI and switch costs have different dimensions and units a single
fuzzy satisfaction objective function is used to transform the two conflicting
objectives into fuzzy memberships and then finally to combine them into a single
objective function Also a fuzzy membership function based on the max-min
principle is presented for optimising ECOST SAIDI and switch costs
simultaneously These are achieved by the optimal installation of new switches and
the relocation of existing switches Therefore identifying the number and location of
switches becomes an optimisation problem The ant colony optimisation (ACO) is
adopted which has the ability to find near optimal solutions close to the global
minimum in a finite number of steps This algorithm is proposed for the assessing
the sectionalising switch placement (SSP) problem based on reliability improvement
and switch costs minimisation using a multi-objective function with fuzzy variables
The impact of benefit-to-cost analysis is then investigated to justify investment
expenses Furthermore the importance of the customer damage function (CDF)
variation in determining the SSP is investigated through sensitivity analysis And the
ACO parameter sensitivity analysis is also provided in this study
The mathematical formulation of the objective function is presented in Section 72
and in Section 73 the applied ACO algorithm used to address the problems of SSP
is discussed Section 74 describes the benefit-cost analysis and the numerical case
studies are presented and discussed in Section 75 The main conclusions of the study
are summarised in Section 76
72 Problem Formulation
The primary objective of this study is to resolve the three conflicting objectives
reduction of unserved energy cost decrease in the average time a customer is
interrupted and minimisation of switch costs Three formulations of objective
functions are presented and the solution is a trade-off between each objective
721 Weighted Aggregation
As ECOST and switch costs have the same units and dimensions they are
transformed into a single objective function by aggregating all the objectives in a
weighted function
Chapter 7 Optimal Placement of Sectionalising Switches for Reliability
Improvement
Page | 130
119872119894119899 119869 = micro1 ∙ 119864119862119874119878119879 + micro2 ∙ 119878119862 (7-1)
where ECOST is the system expected outage cost to customers ($) and SC is the cost
of sectionalising switches ($) micro1and micro2 are the weighting factors given to the
reliability index and the cost of switches
722 Single Fuzzy Satisfaction Objective Function with Two
Parameters
SAIDI and switch costs are associated with a membership function in a fuzzy
domain due to different dimensions The satisfaction level of each objective is
represented by the membership function [66] The higher the membership value is
the better the solution is The two objectives are combined into a fuzzy environment
and a final objective function is formulated as follows
119872119886119909 119870 = 1205961 ∙ 120572119878119860 + 1205962 ∙ 120572119878119862 (7-2)
where 120572119878119860 is the membership function value to distribution reliability improvement
by SAIDI reduction 120572119878119862 is the value of membership function for a decrease in the
switch costs 1205961and 1205962 are the constant weighting factors for each of the parameters
The optimisation process can be changed for different purposes by varying the
values of weighting factors which should satisfy the condition 1205961 + 1205962 = 1 A
higher weighting factor indicates that this parameter is more important [66] In the
fuzzy domain each objective has a membership value varying from zero to unity
[66] The proposed membership function for each objective is described below
Membership function for SAIDI reduction
The basic purpose of this membership function is to improve reliability or obtain the
minimum SAIDI Therefore the placement of sectionalising switches with a lower
SAIDI value obtains a higher membership value The membership function for
reliability improvement is formulated in (7-3) and presented in Fig 7-1 (a) As
SAIDI becomes greater than 119878119860119868119863119868119898119894119899 the degree of satisfaction is decreased This
reduction is continued until SAIDI reaches 119878119860119868119863119868119900119903119894
Chapter 7 Optimal Placement of Sectionalising Switches for Reliability
Improvement
Page | 131
0
1
0
1
120572119878119860 =
1 119878119860119868119863119868 le 119878119860119868119863119868119898119894119899119878119860119868119863119868119900119903119894minus119878119860119868119863119868
119878119860119868119863119868119900119903119894minus119878119860119868119863119868119898119894119899119878119860119868119863119868119898119894119899 lt 119878119860119868119863119868 lt 119878119860119868119863119868119900119903119894
0 119878119860119868119863119868 ge 119878119860119868119863119868119900119903119894
(7-3)
where 119878119860119868119863119868119900119903119894 is the SAIDI of the original network 119878119860119868119863119868119898119894119899 is the minimum
value of SAIDI which is obtained by placing sectionalising switches in all candidate
locations As it is not appropriate for decision makers to obtain a combination of
sectionalising switches which reduces reliability after switch placement the
minimum value of 120572119878119860 is selected as 0 if SAIDI is greater than or equal to 119878119860119868119863119868119900119903119894
(a) SAIDI reduction (b) SC reduction
Fig 7-1 Membership function for SAIDI and switch cost reduction
Membership function for switch cost reduction
The membership function for switch costs reduction is shown in Fig 7-1(b) The
mathematical equation is presented below
120572119878119862 =
1 119878119862 le 119878119862119900119903119894119878119862119898119886119909minus119878119862
119878119862119898119886119909minus119878119862119900119903119894119878119862119900119903119894 lt 119878119862 lt 119878119862119898119886119909
0 119878119862 ge 119878119862119898119886119909
(7-4)
where 119878119862119900119903119894 and 119878119862119898119886119909 are the original and maximum value of switch costs
respectively The maximum switch costs are obtained by installing sectionalising
switches in all candidate sites
723 Single Fuzzy Satisfaction Objective Function with Three
Parameters
When there are more than two objectives with different dimensions and units to be
satisfied simultaneously a single fuzzy satisfaction objective function based on the
120572119878119860
119878119860119868119863119868119898119894119899 119878119860119868119863119868119900119903119894 119878119860119868119863119868
120572119878119862
119878119862119900119903119894 119878119862119898119886119909 119878119862
Chapter 7 Optimal Placement of Sectionalising Switches for Reliability
Improvement
Page | 132
0
1
max-min principle is considered The three conflicting objectives to be optimised are
ECOST SAIDI and switch costs The membership functions for SAIDI and switch
costs are presented in the previous section The function for ECOST is shown in Fig
7-2 and expressed as
120572119864119862 =
1 119864119862119874119878119879 le 119864119862119874119878119879119898119894119899119864119862119874119878119879119900119903119894minus119864119862119874119878119879
119864119862119874119878119879119900119903119894minus119864119862119874119878119879119898119894119899119864119862119874119878119879119898119894119899 lt 119864119862119874119878119879 lt 119864119862119874119878119879119900119903119894
0 119864119862119874119878119879 ge 119864119862119874119878119879119900119903119894
(7-5)
where 119864119862119874119878119879119900119903119894 and 119864119862119874119878119879119898119894119899 are the original and minimum value of ECOST
respectively The minimum ECOST is obtained by installing sectionalising switches
in all candidate locations
Fig 7-2 Membership function for ECOST reduction
The degree of overall satisfaction for these objective functions is the minimum value
of all the membership functions [85] The fuzzy decision for a final compromised
solution is the maximum degree of overall satisfaction and is formulated in (7-6)
Max 119871 = min (120572119878119860 120572119878119862 120572119864119862) (7-6)
724 Evaluation of ECOST
ECOST is an index that combines reliability with economics The best way to
present customer interruption costs is in the form of CDF A CDF provides the
interruption cost versus interruption duration for a various class of customers and
can be aggregated to produce a composite CDF at any particular load point [67] [69]
Generally ECOST is used to represent the customer outage costs since it not only
considers the effects of the system configuration interruption durations load
variations and equipment failure probability but also accounts for the various
customer types and their damage functions [52]
120572119864119862
119864119862119874119878119879119898119894119899 119864119862119874119878119879119900119903119894 119864119862119874119878119879
Chapter 7 Optimal Placement of Sectionalising Switches for Reliability
Improvement
Page | 133
The calculation of ECOST of the total system over T years is based on failure-mode-
and-effect analysis (FMEA) and can be quantified as follows
1 ( 1)
1 1 1 1 1 1
( ) ( ) ( ) ( ) (1 ) (1 )b b b b bN CT NR CT NST
t t
b b k R k s
t b k j k j
ECOST L P k j C d P k j C d IR DR
(7-7)
where T is time period (year) 119873119887 is the total number of branches 120582119887and 119871119887 are the
average failure rate (failurekm-year) and length (km) of branch b 119862119879119887 119873119877119887 and
119873119878119887 are the total number of customer types permanent damaged and temporary
damaged load points when the fault is at branch b P(k j) is the average load of the
kth-type customers at the jth load point (kW) 119862119896(119889) is the CDF for kth-type
customer lasting d hours ($kW) 119889119877 and 119889119878 are the average repair time and the
switch time after failure IR and DR are the annual load increase rate and discount
rate
725 Evaluation of SAIDI
The SAIDI which represents the average outage duration time of each customer
over T years can be expressed as
119878119860119868119863119868 = sum sum 120582119887∙119871119887[sum 119889119877
119873119862119877(119887)119899=1 +sum 119889119878
119873119862119878(119887)119899=1 ]
119873119887119887=1
119873119862119905119900119905119886119897119879
119905=1 (7-8)
where 119873119862119877(119887) and 119873119862119878(119887) are the number of permanent damaged and temporary
damaged customers when the fault is at branch b 119873119862119905119900119905119886119897 is the total number of
served customers SAIDI is measured in hours
726 Evaluation of Switch Costs
In this study reliability is improved by the installation of new sectionalising
switches and relocation of existing switches Thus the total cost of switches can be
determined as following
119878119862 = 119862119868119878 ∙ 119873119899119890119908 + 119862119877119878 ∙ 119873119903119890119897 + sum 119872119862119879119905=1 ∙ (119873119899119890119908 + 119873119890119909119894119904) ∙ (1 + 119863119877)minus(119905minus1) (7-9)
where CIS is the investment and installation cost of a new sectionalising switch ($)
119873119899119890119908 119873119903119890119897 and 119873119890119909119894119904 are the number of newly installed relocated and existing
sectionalising switches respectively CRS is the relocation cost of an existing
Chapter 7 Optimal Placement of Sectionalising Switches for Reliability
Improvement
Page | 134
Home
0
1
0
1
0
1
0
1
Food
Number of candidate locations for sectionalising switches
sectionalising switch ($) and MC is the maintenance and operation cost of a
sectionalising switch ($)
73 Applying ACO to Sectionalising Switch Placement
Problem
This study uses ACO algorithm for distribution automation in terms of the
installation of new sectionalising switches and relocation of existing switches When
the locations of sectionalising switches are changed a new network configuration
will be formed The search method is used for finding the optimal value of objective
functions as presented in Section 721-723
The search space of the automation problem in terms of SSP is modelled as a
directed graph as shown in Fig 7-3 The number of stages is the candidate locations
for all the sectionalising switches 119873119878 For this problem the switch status can be
represented as a binary vector in each stage State 0 ldquono sectionalising switch in this
locationrdquo State 1 is ldquoa sectionalising switch in this locationrdquo The artificial ant
searches for the values of the bits and produces a solution to the problem after it
completes a tour between the home and food source which is similar to the process
described in Section 532
Fig 7-3 Search space of sectionalising switch placement
Chapter 7 Optimal Placement of Sectionalising Switches for Reliability
Improvement
Page | 135
74 Benefit-to-cost Analysis
The benefit-to-cost analysis is a financial term that describes the expected balance of
benefits made from the investment and costs incurred during the production process
It helps predict if an investmentdecision is feasible and whether its benefits
outweigh the costs during a predefined time interval [82]
In this study the benefit-to-cost ratio (BCR) offers a comparison between ECOST
and SC The benefit to the distribution network operator (DNO) is the reduction of
ECOST which is equal to
119887119890119899119890119891119894119905 = sum119864119862119874119878119879119887119886119904119890
119905 minus119864119862119874119878119879119900119901119905119905
(1+119863119877)119905119879119905=1 (7-10)
where 119864119862119874119878119879119887119886119904119890119905 and 119864119862119874119878119879119900119901119905
119905 are the value of ECOST of year t before and after
the placement of switches ($)DR is the annual discount rate
The cost for the DNO is the total switching cost including investment maintenance
and operation cost as presented in (7-9) and BCR is defined as
119861119862119877 =119887119890119899119890119891119894119905
119878119862 (7-11)
A higher value for BCR indicates that the benefits relative to the costs are greater
The investment return time refers to the time when BCR starts to exceed 10 If the
investment return time is less than the lifetime of a switch adding a switch will bring
benefits to the investors
Chapter 7 Optimal Placement of Sectionalising Switches for Reliability
Improvement
Page | 136
LP11 LP12 LP13 LP14 LP15 LP16 LP17
LP8 LP9 LP10
LP1 LP2 LP3 LP4 LP5 LP6 LP7
LP32 LP33 LP34 LP35 LP36 LP37 LP38
LP29 LP30 LP31
LP26 LP27 LP28
LP18 LP19 LP20 LP21 LP22 LP23 LP24 LP25
9 10 11 12 13 33
6 7 8 31
1 2 3 4 5 30
25 26 27 29
22 23 24
19 20 21
32
14 15 16 17 18
28
F3
F2
F1
F7
F6
F5
F4
Normally Open Circuit BreakerNormally Closed Circuit Breaker
Subbus1
Subbus2
Subbus3
T1
T3
T5
Main
feeder
Main
feeder
Main
feeder
T2
T4
T6
75 Application Studies
In this study the proposed methodology is applied to an 11 kV distribution network
developed from Bus 4 of the Roy Billinton Test System (RBTS) The single-line
diagram of the network with 6 existing sectionalising switches is shown in Fig 7-4
Fig 7-4 Distribution feeder connected to RBTS Bus 4 with 6 sectionalising switches
In this study there are 51 locations considered as candidates for switch placement
[114] All the values of the required data ie feeder type and length as well as
component failure rate are available in [114] and summarised in Appendix A4 The
failure rate of the feeders is proportional to their physical length and all other
Chapter 7 Optimal Placement of Sectionalising Switches for Reliability
Improvement
Page | 137
components ie transformers buses and breakers are assumed to be completely
reliable This typical urban distribution network supplies residential commercial and
industrial consumers The average value of active power and the customer type of
each node were also found in [114] and listed in Table 7-1 The power factors of all
the loads are set to 10
Table 7-1 Customer data (Average load)
Number
of load
points
Load points Customer type P
(kW)
Number of
customers
15 1-4 11-13 18-21 32-35 residential 545 220
7 5 14 15 22 23 36 37 residential 500 200
7 8 10 26-30 industrial 1000 1
2 9 31 industrial 1500 1
7 6 7 16 17 24 25 38 commercial 415 10
The relocation cost of a sectionalising switch is US $ 500 The investment and
installation cost of a sectionalising switch is US $ 4700 [64] The annual
maintenance and operation cost is considered to be 2 of the investment cost [64]
All the sectionalising switches and circuit breakers are remotely controlled The
costs of the feeder terminal unit which is used for data acquisition of the switch
status and communication equipment have also been added to the automated
sectionalising switches The overall switching time of sectionalising switch and
circuit breakers for temporary damage load points in other words the time between
the occurrence of a fault and the restoration of energy to unaffected areas is set to 10
minutes [64] And the average repair time of the permanent faulty section is assumed
to be 5 hours The lifetime of a switch depends on various factors such as the
maximum number of allowable switching operations the number of annual
switching operations of the switch etc Based on these factors the life period of the
switches is calculated to be 15 years The load growth rate and the annual interest
rate are set to 3 and 8 respectively The CDF data are extracted from [64] and
summarised in Table 7-2
Chapter 7 Optimal Placement of Sectionalising Switches for Reliability
Improvement
Page | 138
Table 7-2 Sector interruption cost estimation ($kW)
User Sector Interruption Duration
10 min 1 hour 2 hour 4 hour 5 hour 10 hour
Residential 006 11 16 26 316 5
Industrial 288 806 95 124 1387 276
Commercial 205 96 125 185 2151 6306
The proposed ACO algorithm was coded in the MATLAB to obtain the location of
the sectionalising switches In this study three cases with different objective
functions are considered to analyse the superiority and performance of the proposed
method
Test Case 1 Minimisation of ECOST and switch costs
Test Case 2 Minimisation of SAIDI and switch costs
Test Case 3 Minimisation of ECOST SAIDI and switch costs
The final combinations of the ACO control parameters that provide the best results
for all the above tests are given in Appendix C3
751 Test Case 1
In this test the minimisation of ECOST and switch costs are considered in the
formulation of a single objective function this involves aggregating the objective
functions as presented in Section 721 For simplicity both weighting factors micro1
and micro2 are set to 1 ie these two objectives are assumed to be equally important
Three cases are studied as follows
Case 11 Optimal relocation of existing sectionalising switches
Case 12 Optimal installation of new sectionalising switches
Case 13 Optimal installation of new sectionalising switches and relocation of
existing sectionalising switches
Chapter 7 Optimal Placement of Sectionalising Switches for Reliability
Improvement
Page | 139
LP11 LP12 LP13 LP14 LP15 LP16 LP17
LP8 LP9 LP10
LP1 LP2 LP3 LP4 LP5 LP6 LP7
LP32 LP33 LP34 LP35 LP36 LP37 LP38
LP29 LP30 LP31
LP26 LP27 LP28
LP18 LP19 LP20 LP21 LP22 LP23 LP24 LP25
9 10 11 12 13 33
6 7 8 31
1 2 3 4 5 30
25 26 27 29
22 23 24
19 20 21
32
14 15 16 17 18
28
F3
F2
F1
F7
F6
F5
F4
Normally Open Circuit BreakerNormally Closed Circuit Breaker
Subbus1
Subbus2
Subbus3
T1
T3
T5
Main
feeder
Main
feeder
Main
feeder
T2
T4
T6
Case 11 Optimal relocation of existing sectionalising switches
The objective of this case is to investigate the optimum sectionalising switch
relocation problem The optimal locations of sectionalising devices are shown in Fig
7-5 Before relocation the total cost including ECOST operation and maintenance
cost of existing switches over 15 years is US $ 477090 After relocation the total
cost including the addition of relocation cost obtained by the ACO approach is US
$ 343620 which amounts to a reduction of 2798
Fig 7-5 Optimal relocation of sectionalising switches in Test Case 11
Chapter 7 Optimal Placement of Sectionalising Switches for Reliability
Improvement
Page | 140
In comparison with the original configuration 4 switches change their locations The
optimal locations of sectionalising switches and the number and types of loads
adjacent to each switch are presented in Table 7-3 The results indicate that each
feeder attempts to have at least one switch As there are 6 switches and 7 feeders
and the total load level of Feeder 5 is 3000 kW which is the lowest value for all the
feeders no switch is placed on Feeder 5 It should also be noted that the load
density and customer types play an important role in determining the locations of
sectionalising switches For instance the adjacent load of Switch 1 is LP6 and LP7
which has the highest CDF value (commercial load) and relatively high load levels
In addition Switch 2 is placed on 7D whose adjacent load is LP9 and this has the
largest load density
Table 7-3 Results of sectionalising switches relocation in Test Case 11
Switch
No
Feeder Location Total Feeder
Load (kW)
Adjacent Load Adjacent Load Levels (kW) and
Type
1 1 5D 3510 LP6 LP7 415 (commercial) 415 (commercial)
2 2 7D 3500 LP9 1500 (industrial)
3 3 13D 3465 LP16 LP17 415 (commercial) 415 (commercial)
4 4 18D 4010 LP24 LP25 415 (commercial) 415 (commercial)
5 6 23D 3500 LP30 1000 (industrial)
6 7 28D 3595 LP36 500 (commercial)
( Each section has two candidate locations for sectionalising switch placement U means upstream side of the section and D
means downstream side of the section)
Case 12 Optimal installation of new sectionalising switches
In this case the effect of installing new sectionalising switches without relocating
the existing switches is studied As shown in Fig 7-6 there are 11 new
sectionalising switches installed
The detailed results of ECOST capital and installation as well as the operation and
maintenance cost of sectionalising switches over 15 years are shown in Table 7-4
After the installation of sectionalising switches the total system cost is decreased
from US $ 477090 to US $ 286980 ie a reduction of 3984
Chapter 7 Optimal Placement of Sectionalising Switches for Reliability
Improvement
Page | 141
LP11 LP12 LP13 LP14 LP15 LP16 LP17
LP8 LP9 LP10
LP1 LP2 LP3 LP4 LP5 LP6 LP7
LP32 LP33 LP34 LP35 LP36 LP37 LP38
LP29 LP30 LP31
LP26 LP27 LP28
LP18 LP19 LP20 LP21 LP22 LP23 LP24 LP25
9 10 11 12 13 33
6 7 8 31
1 2 3 4 5 30
25 26 27 29
22 23 24
19 20 21
32
14 15 16 17 18
28
F3
F2
F1
F7
F6
F5
F4
Normally Open Circuit BreakerNormally Closed Circuit Breaker
Subbus1
Subbus2
Subbus3
T1
T3
T5
Main
feeder
Main
feeder
Main
feeder
T2
T4
T6
Fig 7-6 Optimal installation of sectionalising switches in Test Case 12
Table 7-4 Results of sectionalising switches installation in Test Case 12
ECOST
($)
Number of
installed
switches
Capital and
installation cost
($)
Maintenance
and operation
cost ($)
Total system
cost ($)
Before switches
installation
472260 0 0 4830 477090
After switches
installation
221610 11 51700 13670 286980
Chapter 7 Optimal Placement of Sectionalising Switches for Reliability
Improvement
Page | 142
LP11 LP12 LP13 LP14 LP15 LP16 LP17
LP8 LP9 LP10
LP1 LP2 LP3 LP4 LP5 LP6 LP7
LP32 LP33 LP34 LP35 LP36 LP37 LP38
LP29 LP30 LP31
LP26 LP27 LP28
LP18 LP19 LP20 LP21 LP22 LP23 LP24 LP25
9 10 11 12 13 33
6 7 8 31
1 2 3 4 5 30
25 26 27 29
22 23 24
19 20 21
32
14 15 16 17 18
28
F3
F2
F1
F7
F6
F5
F4
Normally Open Circuit BreakerNormally Closed Circuit Breaker
Subbus1
Subbus2
Subbus3
T1
T3
T5
Main
feeder
Main
feeder
Main
feeder
T2
T4
T6
Case 13 Optimal relocation and installation of sectionalising switches
A Base case
The main objective of this test is to reduce the total system cost including ECOST
and switch costs by the relocation of existing sectionalising switches and the
installation of new ones The switch locations are presented in Fig 7-7
Fig 7-7 Optimal installation and relocation of sectionalising switches in Test Case 13
In comparison with the original configuration there are 8 new sectionalising
switches installed and 5 existing switches relocated As expected the sectionalising
switches are placed adjacent to the load centres with either the highest load density
Chapter 7 Optimal Placement of Sectionalising Switches for Reliability
Improvement
Page | 143
0
1
2
3
4
5
6
7
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
BC
R
Years
or the highest CDF For example the adjacent load of switch 13D is LP6 and LP7
which has the highest CDF value (commercial loads) In addition switch 7D is
placed adjacent to LP9 which has the largest load density The detailed results for
ECOST and switch costs are shown in Table 7-5 After the installation and relocation
of the switches the total system cost is decreased from US $ 477090 to US
$ 272480 ie a reduction of 4289
Table 7-5 Results of sectionalising switches relocation and installation in Test Case 13
ECOST
($)
Number of
relocated
switches
Relocation
cost ($)
Number of
installed
switches
Capital and
installation
cost ($)
Maintenance
and operation
cost ($)
Total
system
cost ($)
Before switch
placement
472260 0 0 0 0 4830 477090
After switch
placement
221120 5 2500 8 37600 11260 272480
B Benefit-to-Cost analysis
BCR analysis is used to verify the benefits and costs of sectionalising switch
placement for distribution operators The results are presented in Fig 7-8 The
benefits and costs are accumulated during the predefined life period There is no
return on investment for the first year as the BCR for Year 1 is 055 However the
BCR for Year 2 is 108 which means the investors start to get benefits in Year 2 In
addition switch placement proved to be a feasible investment since the BCR is
increased to 620 when the switch achieves its service life 15 years in this study
Fig 7-8 BCR versus years
Chapter 7 Optimal Placement of Sectionalising Switches for Reliability
Improvement
Page | 144
0
20
40
60
80
100
120
140
160
05 1 15 2 25 3 35 4 45 5 55 6 65 7 75 8
Co
st (
th
ou
san
d $
)
CDF multiplier
ECOST
Switch costs
Total costs
C Sensitivity analysis
To demonstrate the impact of changing the values of different parameters on the
corresponding results several sensitivity analysis studies are discussed
CDF variation sensitivity analysis
The main objective of this test is to assess the behaviour of the proposed approach
when the CDF (customer damage function) is varied The CDF is increased from 50
to 800 of its initial value in 50 increments The original value of the CDF
multiplier is 100 The effect of variation in the CDF on the ECOST switching
costs and the total system cost is plotted in Fig 7-9 Switch costs include
sectionalising switch installation relocation operation and maintenance cost The
ECOST and switching costs increase as the CDF is increased However the
difference between ECOST and switching costs is also increased
Fig 7-9 Variation of cost versus change in CDF
Variations of the optimal number of installed sectionalising switches versus the CDF
are presented in Fig 7-10 The optimal number of newly installed switches increases
from 7 to 34 as the CDG multiplier is increased from 05 to 8 This indicates the
network needs to be more automated especially if the consequence of customer
damage becomes more serious However the growth in the optimal number of
sectionalising switches is slowing down As shown in Fig 7-10 when the CDF
multiplier increases above 3 the number of sectionalising switches remains at 32 as
Chapter 7 Optimal Placement of Sectionalising Switches for Reliability
Improvement
Page | 145
0
5
10
15
20
25
30
35
40
05 1 15 2 25 3 35 4 45 5 55 6 65 7 75 8
Nu
mb
er
of
swit
che
s
CDF multiplier
the reduction of ECOST brought by installing a sectionalising switch is small
compared to the increase in switch costs Only when the CDF multiplier reaches 55
does the reduction of ECOST outweigh the installation cost of a switch and hence
acquiring a sectionalising switch is a cost-effective investment This is due to the fact
that the installation of the first sectionalising switch has the largest effect on
reducing the total system cost and the impact of sectionalising switch installation on
ECOST decreases as the network becomes more automated
Fig 7-10 Number of installed sectionalising switches versus change in CDF
ACO parameters sensitivity analysis
The ACO parameter analysis is provided in this section In each test only one
parameter is changed whilst the others remain constant The convergence number is
defined as the number of the iterations when the objective function is convergence
The assessment of the impact of the pheromone evaporation rate ρ on the proposed
algorithm is presented in Table 7-6 The number of ants is 200 and the iteration time
is 400 Parameter ρ is varied from 01 to 06 with an increment of 01 For each ρ the
test is run 100 times Table 7-6 shows the impacts of the ρ variation on the objective
function J It can be seen the evaporation rate ρ has a considerable impact on the
convergence performance of the ACO algorithm When ρ is small the residual
pheromone on the path is dominant and the positive feedback of pheromone is weak
This results in an increment in the stochastic performance and global search ability
Chapter 7 Optimal Placement of Sectionalising Switches for Reliability
Improvement
Page | 146
of the ACO algorithm but a reduction in the convergence rate When ρ is large the
positive feedback of the pheromone is dominant which results in an improvement in
the convergence rate but a reduction in the search ability of the algorithm In other
words the algorithm is more easily trapped into a local optimal solution In summary
the selection of ρ is based on two factors of the algorithm 1) convergence rate 2)
global search ability As shown in the table the best value of ρ for this case is 04
which results in the minimum average value and has a suitable convergence rate
Table 7-6 Impacts of 120588 variation on objective function 119869
120588 Objective function value Average convergence
number Average Maximum Minimum
01 273120 274810 272480 223
02 273400 275960 272480 175
03 273480 274810 272480 132
04 273100 274810 272480 110
05 273550 274810 272480 94
06 273440 274810 272480 81
Table 7-7 presents the impacts of the variation in the number of ants on objective
function J The evaporation rate is 04 and the iteration number is 400 The number
of ants is changed from 100 to 500 with an increment of 100 The greater the
number of ants the more likely the global optimum value is achieved This is due to
the growth in global search capability However the convergence rate decreases To
balance the global search ability and convergence rate the number of ants is set to
400
Table 7-7 Impacts of variation in number of ants on objective function 119869
Number of ants Objective function value Average convergence
number Average Maximum Minimum
100 273865 276120 272480 91
200 273100 274810 272480 110
300 273030 274370 272480 135
400 272820 274230 272480 168
500 273170 274230 272480 245
Chapter 7 Optimal Placement of Sectionalising Switches for Reliability
Improvement
Page | 147
However in this study the proposed approach is used for planning a future network
Thus the computation time is not an issue The number of ants and iteration should
be large enough for the ACO algorithm to find the global optimum solution
752 Test Case 2
The objective of this test is to minimise SAIDI and switch costs by maximising the
fuzzy bi-objective function as presented in Section 722 The results of the
membership values of objectives SAIDI as well as switch costs are listed in Table
7-8 The weighting factors of the system objectives can be changed by the network
operator which make it possible to give preference to one over the other Three
cases are studied in which the weighting factors 1205961and 1205962vary from 01 to 09
As shown in the table as the weighing factor of SAIDI 1205961 is increased more
sectionalising switches are installed and reliability is improved The results show the
algorithm can adapt itself to the variation of the weighting factors For decision
making appropriate weighting factors for each objective are selected and a
compromised switch placement plan is obtained using the proposed approach
Table 7-8 Results of sectionalising switches relocation and installation in Test Case 2
Test Cases 1205961 1205962 120572119878119860 120572119878119862 Objective
Function
SAIDI
(hrscustomer)
Switch costs ($)
Case 21 01 09 04909 09970 09464 1157 68275
Case 22 05 05 08456 09061 08758 556 67378
Case 23 09 01 09384 07761 09221 39936 153950
( Each section has two candidate locations for sectionalising switch placement U means upstream side of the section and D
means downstream side of the section)
753 Test Case 3
In this test the three objective functions of the problem to be optimised are ECOST
SAIDI and switch costs The detailed test results before and after switch placement
are listed in Table 7-9 The placement of sectionalising switches results in a
reduction of 60 in ECOST and 7148 in SAIDI It is observed that the
installation and relocation of sectionalising switches has obtained a compromise
solution of three objectives optimisation
Chapter 7 Optimal Placement of Sectionalising Switches for Reliability
Improvement
Page | 148
Table 7-9 Results of sectionalising switches installation and relocation in Test Case 3
Objective
Function
120572119864119862 120572119878119860 120572119878119862 ECOST
($)
SAIDI
(hrscustomer)
Switch costs
($)
Before
switch
placement
0 0 0 1 472260 1989 4830
After switch
placement
08327 08327 08392 08384 188950 56723 112410
76 Summary
This study has presented an ACO algorithm for assessing the SSP problem in terms
of three conflicting objectives optimisation reduction of unserved energy cost
decrease in the average time that a customer is interrupted and minimisation of
switch costs The proposed model has been successfully applied on Bus 4 of the
RBTS In comparison with the original system the existing sectionalising switches
are relocated and new automatic switches are installed The effectiveness of the
proposed approach has been demonstrated through the results obtained which
indicates switch placement using the ACO algorithm reduces the customer outage
costs and interruption duration times during fault contingencies Furthermore the
importance of the CDF variation in determining the SSP is investigated through
sensitivity analysis The impact of installing sectionalising switches on reducing the
total system costs decreases as the number of sectionalising switches is increased As
the parameters of ACO algorithm affect the performance of the proposed method an
ACO parameter sensitivity analysis is also provided in this study The selection of
pheromone evaporation rate and number of ants is a trade-off between the global
search ability and convergence rate of the algorithm In addition a benefit-to-cost
analysis is implemented and used to prove switch investment is profitable The
procedure is used for system planning and is applied off-line so there is no
limitation in calculation times
The main contribution of this study is the conversion of all the multiple objectives
into a single objective function in two forms weighted aggregation and fuzzy
satisfaction objective function considering ECOST SAIDI and cost of
sectionalising switches simultaneously The selection of each form depends on the
Chapter 7 Optimal Placement of Sectionalising Switches for Reliability
Improvement
Page | 149
number of objectives as well as their units and dimensions Another contribution is
the incorporation of FMEA to evaluate the impact on distribution system reliability
of increased automation
Page | 150
CHAPTER 8
DISTRIBUTION NETWORK
RECONFIGURATION FOR LOSS
REDUCTION amp RELIABILITY
IMPROVEMENT
81 Introduction
Optimal distribution network reconfiguration (DNR) can not only solve a single
objective function such as feeder loss minimisation but can also deal with multiple
objectives The presence of multiple objectives raises the issue of how to consider
them simultaneously [117] In the previous section the multiple objectives are
transformed into a single equation using fuzzy logic based approaches The
optimisation is then formulated either as the weighted sum of the fuzzy membership
functions or with the application of the max-min principle
However the above simple optimisation processes only find a compromise solution
It is no longer acceptable for a system with multiple conflicting objectives if the
distribution network operator (DNO) desires to know all possible optimal solutions
for all the objectives simultaneously [20] Therefore a set of trade-off solutions
using the Pareto optimality concept is now proposed These solutions can be
Chapter 8 Distribution Network Reconfiguration for Loss Reduction amp Reliability
Improvement
Page | 151
compared by using the concept of dominance [88] In this concept a solution is non-
dominated when no other solution exists with better values for all the individual
objectives The Pareto set is the set of all non-dominated solutions and the
corresponding objective values constitute the Pareto front [88] This allows the
DNOs to select the most suitable one for implementation depending on the utilitiesrsquo
priorities Pareto analysis is suitable for addressing problems whose conflicting
solutions cannot be addressed using a single solution [117]
This study formulates the optimal network reconfiguration problem within a Pareto
optimal framework where feeder loss and system reliability indices are
simultaneously optimised Two types of reliability indices are considered system
expected outage costs to customers (ECOST) and system interruption duration index
(SAIDI) The multi-objective ant colony optimisation (MOACO) and artificial
immune systems-ant colony optimisation (AIS-ACO) algorithms are proposed and
compared for the assessment of DNR problems Both algorithms focus on problems
in terms of Pareto optimality where the objective functions are multidimensional In
MOACO each objective function is assigned with a pheromone matrix and all
values from multiple pheromone matrices are aggregated into a single pheromone
value by a weighted sum [96] In AIS-ACO the quality of elements that make up the
solution to the problem is represented by the pheromones developed from the ACO
And the hypermutation from the AIS is used as a random operator to enlarge the
search space [88] To verify the suitability of the proposed algorithms they have
been tested on Bus 4 of the Roy Billinton Test System (RBTS) system and the Pareto
set is obtained
The remaining parts of this chapter are organised as follows Section 82 deals with
the framework of multi-objective optimisation and DNR problem formulation The
implementation details of the MOACO and AIS-ACO algorithms to the problem are
discussed in Section 83 The simulation results and the best compromise solutions
are presented and discussed in Section 84 and 85 Section 86 summarises the main
conclusions
Chapter 8 Distribution Network Reconfiguration for Loss Reduction amp Reliability
Improvement
Page | 152
82 Problem Formulation
This section formulates the DNR problems in the Pareto optimal framework
821 Multi-objective Reconfiguration Problem
In this study three objectives are considered and they are feeder loss unserved
energy cost and the average time that a customer is interrupted Therefore the multi-
objective DNR problem can be defined as the minimisation of the vector
119865(119866) = [1198911(119866)1198912(119866)1198913(119866)]119879 (8-3)
where 1198911(119866) 1198912(119866) and 1198913(119866) are described below for a given network
configuration G
8211 Minimisation of feeder loss
The total feeder loss of the network is formulated as
1198911(119866) = sum 119896119894119877119894(119875119894
2+1198761198942
1198801198942 )
119873119887119894=1 (8-4)
where 119877119894 is the resistance of the ith branch 119875119894 and 119876119894 are the real power (W) and
reactive power (VAr) at the receiving end of branch i 119880119894 represents the rms voltage
at the receiving end of branch i (V) 119896119894 is a binary variable 119896119894 = 0 indicates that
branch 119894 is open and 119896119894 = 1 indicates that branch 119894 is closed The detailed feeder loss
assessment is presented in Section 28
8212 Minimisation of ECOST
The ECOST represents the unserved energy cost and is described as
1 ( 1)
1 1 1 1 1 1
( ) ( ) ( ) ( ) (1 ) (1 )b b b b bN CT NR CT NST
t t
b b k R k s
t b k j k j
ECOST L P k j C d P k j C d IR DR
(8-5)
where T is time period (year) 119873119887 is the total number of branches 120582119887and 119871119887 are the
average failure rate (failurekm-year) and length (km) of branch b 119862119879119887 119873119877119887 and
119873119878119887 are the total number of customer types permanent damaged and temporary
Chapter 8 Distribution Network Reconfiguration for Loss Reduction amp Reliability
Improvement
Page | 153
damaged load points when the fault is at branch b P(k j) is the average load of the
kth-type customers at the jth load point (kW) 119862119896(119889) is the customer damage
function for kth-type customer lasting d hours ($kW) 119889119877 and 119889119878 are the average
repair time and the switch time after failure IR and DR are the annual load increase
rate and discount rate
8213 Minimisation of SAIDI
The average time that a customer is interrupted is represented by a reliability index
SAIDI and is defined as
119878119860119868119863119868 = sum sum 120582119887∙119871119887[sum 119889119877
119873119862119877(119887)119899=1 +sum 119889119878
119873119862119878(119887)119899=1 ]
119873119887119887=1
119873119862119905119900119905119886119897119879
119905=1 (8-6)
where 119873119862119877(119887) and 119873119862119878(119887) are the number of permanent damaged and temporary
damaged customers when the fault is at branch b 119873119862119905119900119905119886119897 is the total number of
served customers SAIDI is measured in hours
8214 Constraints
The computed voltages currents and the power flow at all branches should be kept
in their permissible range and the network should be operated in radial The
configurations that violate any constraint should be disregarded
822 Best Compromise Solution
After obtaining the Pareto set the best compromise solution among the multiple
objectives can be selected by comparing the fitness value of each member in the
Pareto front as follows [45]
119891119901119904(119894) = sum 120596119895max(119900119891119895)minus119900119891119895(119875119878119894)
max(119900119891119895)minusmin (119900119891119895)
119873119900119887119895
119895=1 (8-7)
where 119873119900119887119895 is the number of objectives which is three in this study max(119900119891119895) and
min(119900119891119895) are the maximum and minimum value of the jth objective function
obtained by all the members in the Pareto front respectively 1205961 1205962 and 1205963 are the
weighting factor for feeder loss ECOST and SAIDI respectively
The best compromise solution is varied by changing the values of the weighting
factors based on the tendencies of the decision makers
Chapter 8 Distribution Network Reconfiguration for Loss Reduction amp Reliability
Improvement
Page | 154
83 Solution Methodology
In this study there are two methodologies proposed for generating the Pareto set to
the multi-objective DNR problem which are MOACO and AIS-ACO algorithm
Each solution is represented by a string of integers which indicates the locations of
tie-switches
831 Applying MOACO to Multi-objective DNR Problem
Generally ACO algorithm is developed for the assessment of a single objective
optimisation problem However a MOACO algorithm is proposed for assessing
multiple objective functions in the Pareto optimality framework which can generate
diverse solutions rather than just one The flowchart of the MOACO algorithm is
presented in Fig 8-1 and is divided into six steps
Step 1 Initialisation First of all all the ants are initially located at home The
number of pheromone matrices is equal to the number of objectives Each
pheromone matrix has 33 rowsstates (candidate locations for tie-switches) and 4
columnsstages (number of tie-switches) The pheromone values of the edges in the
search space are all initialised at an equal value which is a small positive constant
number
Step 2 Pheromone matrix generation and ant dispatch As there are multiple
pheromone matrices 1205911 1205912 and 1205913 are associated with feeder loss ECOST and
SAIDI respectively All matrices are aggregated into a single pheromone matrix by
weighted sum as
120591119894119909 = 1199011 ∙ 1205911198941199091 + |1199011 minus 1199012| ∙ 120591119894119909
2 + (1 minus 1199012) ∙ 1205911198941199093 (8-8)
where 1205911198941199091 120591119894119909
2 and 1205911198941199093 are the levels of pheromone deposited on state i of stage x for
feeder loss ECOST and SAIDI respectively where 1199011 and 1199012 are uniform random
numbers between 0 and 1 and 1199011 is less than 1199012 This ensures the selection of the
three pheromone matrices all have the same probability and can be used to build the
new matrix
All the ants begin their tours from the home colony and choose the next node to
move to based on the intensity of pheromones from a new pheromone matrix They
Chapter 8 Distribution Network Reconfiguration for Loss Reduction amp Reliability
Improvement
Page | 155
experience different pheromone matrices according to the random variation of
weights The probability of an ant choosing state i of stage x is
119875119894119909(119873) =120591119894119909(119873)
sum 120591119894119909(119873)ℎisin∆119909
(8-9)
where 120591119894119909(119873) is the level of pheromone deposited on state i of stage x at iteration
N ∆119909 is the set of available states which an ant can choose at stage x
Step 3 Objective Function Evaluation After all the ants have completed their tour
the location list and corresponding objective functions in (8-3) for each ant are
evaluated If any constraint is violated the corresponding solutions are discarded
Step 4 Non-dominated Solutions Extraction and Diversity Measure The non-
dominated solutions extraction extracts solutions from a pool based on the concept
of dominance as presented in Section 821 The crowding distance is used to
measure the extent to which non-dominated solutions are spread over the objective
space [20] As there are three objectives to be optimised the crowding distance of a
solution is equal to the side length of the cuboid which is built by two adjacent
solutions [88] Regarding the boundary solutions (the corner solutions) they are
assigned with an infinite distance The solutions are assigned with a small distance
value if they are located in a crowded area The decision makers tend to choose the
solutions from less crowded regions of the search space (with higher crowding
distance) if the maximum number of non-dominated solutions is restricted to a
certain number [88]
Step 5 Pheromone Updating The aim of this step is to favour transitions towards
states by non-dominated solutions with greater pheromone values There are two
rules of pheromone updating the local rule and global rule
Local rule The pheromones deposited in the search space should be evaporated to
make the paths less attractive The local pheromone update rule is calculated as
follow
120591119894119909119899 (119873) = (1 minus 120588)120591119894119909
119899 (119873 minus 1) + 120591119888 (8-10)
where 120588 is the pheromone evaporation rate which is set between 0 and 1 120591119894119909119899 (119873 minus
1) is pheromone value deposited on state i of stage x of matrix n at iteration N-1 120591119888
Chapter 8 Distribution Network Reconfiguration for Loss Reduction amp Reliability
Improvement
Page | 156
is a small positive constant value Even if the amount of pheromone deposited on an
edge is at the lowest value of 120591119888 there is a slight chance that an ant will still choose
this edge
Global rule The global pheromone updating rule involves ants depositing large
amounts of pheromone to the edges that belong to the corner non-dominated
solutions which are the solutions that have minimum values along each objective
The pheromones of those edges can be updated by
120591119894119909119899 (119873) = 120591119894119909
119899 (119873) + 120588119891119887119890119904119905
119899 (119873)
119891119887119890119904119905119899 (119873minus1)
(8-11)
where 119891119887119890119904119905119899 (119873 minus 1) and 119891119887119890119904119905
119899 (119873) are the minimum values of objective function n
obtained by the non-dominated solutions at iteration N-1 and N respectively
After applying the local and global pheromone updating rules the method Max-Min
ACO algorithm is integrated into the proposed approach
120591119894119909119899 (119873) = 120591119898119886119909 119894119891 120591119894119909
119899 (119873) ge 120591119898119886119909 (8-12)
120591119894119909119899 (119873) = 120591119898119894119899 119894119891 120591119894119909
119899 (119873) le 120591119898119894119899 (8-13)
where 120591119898119886119909and 120591119898119894119899 are the higher and lower bound of pheromone level on each
edge respectively Even if the amount of pheromone deposited to a path is at the
lowest value 120591119898119894119899 there is a slight chance that an ant will still choose this path This
enlarges the search space and prevents convergence from occurring too rapidly
After this the non-dominated solutions with their location lists and corresponding
fitness values in the current iteration are retained and all the ants are free to choose a
new path for the next iteration
Step 6 Termination The computation continues until the predefined maximum
number of iterations is reached The final non-dominated solutions are considered as
the Pareto set to the multi-objective DNR problem
Chapter 8 Distribution Network Reconfiguration for Loss Reduction amp Reliability
Improvement
Page | 157
Start
Iteration N=1
Maximum ant number
reaches
Output Pareto
optimal set and end
No
Yes
Initialise the parameters for MOACO
algorithm search space
Ant number m=1
Random select weights and
aggregate multiple pheromone
matrices into one
Dispatch the ant based on the
amount of pheromone on edges
Calculate the multiple objective functions
for this ant
N=N+1
Read system topology
and load data
Diversity measure and extract non-
dominated solutions
Maximum iteration
reaches
Yes
m=m+1
No
The pheromones are updated according
to local and global rules
Fig 8-1 Flowchart of the MOACO algorithm applied to multi-objective DNR problem
Chapter 8 Distribution Network Reconfiguration for Loss Reduction amp Reliability
Improvement
Page | 158
Start
Cloning
Maximum iteration
reached
Output Pareto
optimal set and end
No
Yes
Initialise and set iteration n=1
Pheromone based hypermutation
Diversity measure and extract non-
dominated solutions
The pheromones are updated according to
local and global rules
n=n+1
832 Applying AIS-ACO to Multi-objective DNR Problem
The general description of AIS-ACO algorithm is presented in Section 34 In this
study the AIS-ACO hybrid approach is used to handle multi-objective formulation
using the Pareto optimality concept The antigen is the multi-objective function and
the antibody is the solution to the problem The affinity between the antibody and the
antigen is the Pareto dominance among solutions which indicates the quality of the
solution [88] The information related to each objective is represented by an
individual pheromone table All the non-dominated solutions experience cloning
hypermutation selection and updating until the maximum number of iterations is
reached The flowchart of the AIS-ACO algorithm for Pareto optimality is presented
in Fig 8-2
Fig 8-2 Flowchart of the AIS-ACO algorithm applied to multi-objective DNR problem
Chapter 8 Distribution Network Reconfiguration for Loss Reduction amp Reliability
Improvement
Page | 159
The key parts of the algorithm are explained as follows
Step 1 Initialisation At the beginning of this algorithm a set of initial solutions is
generated These solutions should satisfy the constraints An individual pheromone
table is also built for each objective Each pheromone table has 33 cells (candidate
locations for tie-switches) The pheromone value of each cell represents the
probability of selecting the corresponding switch to be opened in the network model
The pheromone values of all cells are initially set at the same value
Step 2 Cloning All the non-dominated solutions are subjected to cloning In this
study as there are three objectives to be optimised the number of clones for each
non-dominated solution is three
Step 3 Hypermutation The selection of a cell in each clone for hypermutation is
obtained by applying a roulette wheel on its pheromone table [88] The probability of
selecting a cell is dependent on its pheromone intensity A higher pheromone value
of a cell in the table indicates that the corresponding edge in the network is more
likely to be selected The probability of selection cell i in table n is given by
119901119894119899 =
120591119894119899
sum 120591119895119899
119895 (8-14)
where 120591119894119899 is the pheromone value of cell i in table n sum 120591119895
119899119895 represents the sum of
pheromone values of all cells in table n
Step 4 Non-dominated Solutions Extraction and Diversity Measure This step is
same to the step which has been discussed in Section 831
Step 5 Pheromone Updating The aim of this step is to favour transitions toward
non-dominated solutions with great pheromone values There are two rules of
pheromone updating the local rule and global rule
Local rule Pheromones deposited in the search space should be evaporated to make
the paths less attractive The local pheromone update rule is calculated as follows
120591119894119899(119873) = 119898119886119909 (1 minus 120588)120591119894
119899(119873 minus 1) 120591119898119894119899 (8-15)
where 120588 is the pheromone evaporation rate which is set between 0 and 1 120591119894119899(119873 minus 1)
is pheromone value deposited on cell i of table n at iteration N-1 120591119898119894119899 is the lower
Chapter 8 Distribution Network Reconfiguration for Loss Reduction amp Reliability
Improvement
Page | 160
bound of pheromone level on each edge Even if the amount of pheromone deposited
to a path is at the lowest value 120591119898119894119899 there is a slight chance that an ant will still
choose this path This enlarges the entire search space
Global rule The global pheromone updating rule involves depositing large amounts
of pheromone to the edges that are a part of all the non-dominated solutions in the
current iteration [88] At iteration N the edges of the non-dominated solutions can be
updated as
120591119894119899(119873) = 119898119894119899120591119894
119899(119873) + 120588min (119891119899(119866))
119891119899(119866) 120591119898119886119909 (8-16)
where each 119894 isin edge set of G 119899 isin objective set and 119866 isin non-dominated solutions set
119891119899(119866) is the value of objective function n obtained by the non-dominated solution G
120591119898119886119909 is the higher bound of pheromone level on each edge
After this the non-dominated solutions with their location lists and fitness values in
the current iteration are retained and all the ants are free to choose a new path for the
next iteration
Step 6 Termination The computation continues until the predefined maximum
number iteration is reached The final non-dominated solutions are considered as the
Pareto set to the multi-objective DNR problem
Chapter 8 Distribution Network Reconfiguration for Loss Reduction amp Reliability
Improvement
Page | 161
LP11 LP12 LP13 LP14 LP15 LP16 LP17
LP8 LP9 LP10
LP1 LP2 LP3 LP4 LP5 LP6 LP7
LP32 LP33 LP34 LP35 LP36 LP37 LP38
LP29 LP30 LP31
LP26 LP27 LP28
LP18 LP19 LP20 LP21 LP22 LP23 LP24 LP25
19
20
21
22
23
24
26
25 27
28
29 30
71
13 15
14 16
17
18
69
1 3
2
5
4
7
6 8
10
9
68
11 12
56
57
58 60
59 61 62
65
64 66 67
50 52
51
54
53 55
44
45
46
47
48
49
70
31
32
33
34
36
35
39
37 38 40
41
42 43
63
F3
F2
F1
F7
F6
F5
F4
Normally Open Circuit BreakerNormally Closed Circuit Breaker
Subbus1
Subbus2
Subbus3
T1
T3
T5
Main
feeder
Main
feeder
Main
feeder
T2
T4
T6
84 Application Studies
The proposed MOACO and AIS-ACO algorithms have been tested on an 11 kV
distribution network developed from Bus 4 of the Roy Billinton Test System (RBTS)
a single-line diagram of the network is shown in Fig 8-3 The network consists of 38
load points and 4 tie-switches the associated data can be found in [114] The types
and lengths of 11 kV feeders are listed in Appendix A4 The network built in
OpenDSS incorporates three 3311 kV double transformer substations supplying the
downstream loads
Fig 8-3 Distribution feeder connected to RBTS Bus 4
This typical urban distribution network supplies residential commercial and
industrial consumers The average value of active and reactive power and the
customer type of each node are modified from the original values and the new values
are listed in Table 8-1
Chapter 8 Distribution Network Reconfiguration for Loss Reduction amp Reliability
Improvement
Page | 162
300
350
400
450
4
45
5
55
6
x 104
08
09
1
11
12
13
14
15
Feeder loss (kW)ECOST ($yr)
SA
IDI
(hrs
custo
mer
yr)
Table 8-1 Revised customer data (Average load)
Number
of load
points
Load points Customer type P
(kW)
Q
(kVAr)
Number of
customers
4 1-2 9-10 residential 545 51775 220
6 3-5 13-15 residential 500 475 200
12 6-7 16-17 23-25 28 30-
31 37-38
commercial 415 39425 10
6 8 11 18 26 32-33 industrial 1500 1425 1
10 12 19-22 27 29 34-36 industrial 1000 950 1
The proposed MOACO and AIS-ACO algorithms are coded in the MATLAB to
obtain the location of tie-switches for the optimum configuration The settings of the
algorithm parameters that provided the optimum solution for these two cases are
presented in Appendix C4
The number of Pareto optimal solutions obtained by the two algorithms is 26 and its
Pareto front is presented in Fig 8-4 in three dimensions The Pareto set is listed in
Appendix B3 in detail These solutions provide the network operator with various
configurations for the system to choose from Both algorithms have obtained the
same results However for 100 runs the average computation time of AIS-ACO
algorithm is 402s which is significantly lower than the MOCAO algorithm 1053s
Fig 8-4 Pareto solutions obtained (minimisation of feeder loss ECOST and SAIDI)
Chapter 8 Distribution Network Reconfiguration for Loss Reduction amp Reliability
Improvement
Page | 163
Table 8-2 presents the mean and standard deviation of the Pareto front
Table 8-2 Mean and standard deviation of Pareto Front (loss ECOST and SAIDI)
Feeder loss (kW) ECOST ($yr) SAIDI (hrscustomeryr)
Mean
38074 48139 09975
Standard deviation
3431 5291 01165
The corner non-dominated solutions representing minimum feeder loss minimum
ECOST and minimum SAIDI are marked by the red circle yellow circle and green
circle respectively as shown in Fig 8-4 The objective values of these solutions and
relevant tie-switches locations are presented in Table 8-3 It is obvious that the three
objectives are conflicting with each other and the algorithm is able to find the global
optimal solution for each objective function The minimum loss configuration is the
base configuration of RBTS-Bus4 In minimum ECOST solution the unserved
energy cost is reduced by 1133 in comparison with that in the original network
The minimum SAIDI solution shows a reduction of 3695 in the average time that
a customer is interrupted
Table 8-3 Minimum solutions along each objective (loss ECOST and SAIDI)
Feeder loss (kW) ECOST ($yr) SAIDI
(hrscustomeryr)
Tie-switches location
Minimum Loss
32142 46404 13090 68 69 70 71
Minimum ECOST
35409 41145 10586 10 17 41 70
Minimum SAIDI
43523 57891 08253 7 26 54 69
85 Best Compromise Solution
After obtaining the Pareto set the best compromise solution is the member which
has the largest fitness value as calculated in Eq (8-7) The results are presented in
Table 8-4 The importance of each objective function is represented by its weighting
Chapter 8 Distribution Network Reconfiguration for Loss Reduction amp Reliability
Improvement
Page | 164
factor which ranges from 1 to 10 A higher weighing factor indicates this objective
function is more important It can be seen that the solutions are different if the
weighing factors of each objective function are varied based on the tendencies of
DNO For example as shown in the table Case 2 (1205961 = 10 1205962 = 1 1205963 = 1)
indicates that the importance of feeder loss reduction is higher than the other two
objectives and hence the best compromise solution for this case obtains the
minimum loss among all the solutions which is the same as the results obtained
from Table 8-3 In comparison of Case 5 with Case 2 as the importance of ECOST
reduction is increased the network is reconfigured and its feeder loss increases by
588 to compensate for a 1045 decrease in the ECOST If there is no preferred
objective the best solution is obtained by setting 1205961 = 1205962 = 1205963 (Case 1)
Table 8-4 Best compromise solutions (loss ECOST and SAIDI)
Case No Weighting factors Best
compromise
solution
Feeder
loss
(kW)
ECOST
($yr)
SAIDI
(hrscustomeryr) 1205961 1205962 1205963
1 10 10 10 10 41 69 70 34033 41553 10996
2 10 1 1 68 69 70 71 32142 46404 13090
3 1 10 1 10 17 41 70 35409 41145 10586
4 1 1 10 7 26 54 69 43523 57891 08253
5 10 10 1 10 41 69 70 34033 41553 10996
6 10 1 10 10 54 69 71 34759 46644 10217
7 1 10 10 7 17 41 70 40368 43329 09570
86 Summary
The MOACO and AIS-ACO algorithms have been presented in this study for the
assessment of the multi-objective DNR problem using the Pareto optimality concept
The proposed DNR problem is formulated taking into account three objectives to be
minimised feeder loss ECOST and SAIDI The algorithms have been successfully
tested in an RBTS-Bus 4 network The results illustrate that the proposed algorithm
is able to generate a set of non-dominated solutions with high quality and great
diversity This set of solutions represent different trade-offs among the objective
functions And the corner non-dominated solutions which represent the minimum
Chapter 8 Distribution Network Reconfiguration for Loss Reduction amp Reliability
Improvement
Page | 165
value of each objective function are presented in the Pareto front chart By varying
the weighting factors for the parameters the decision makers can select the best
compromise strategy among the three objectives for implementation depending on
the utilitiesrsquo priorities
According to the obtained results both algorithms have obtained the same Pareto
optimal solutions but the AIS-ACO algorithm performs better in comparison with
the MOACO algorithm in terms of computation time The pheromone tables in AIS-
ACO algorithm are used to guide the search process and improve the solution quality
In addition the hypermutation is used as a random operator to enlarge the search
space and to prevent the algorithm from easily falling into the local optimum Future
work could include the assessment of the DNR problem with other objectives such
as balancing loads on feeders and minimising the maximum node voltage deviation
The AIS-ACO algorithm can also be applied to larger systems
Page | 166
CHAPTER 9
MULTI-OBJECTIVE DISTRIBUTION
NETWORK RECONFIGURATION amp DG
ALLOCATION CONSIDERING LOSS
VOLTAGE DEVIATION AND LOAD
BALANCING
91 Introduction
As discussed in the previous chapters distribution network reconfiguration (DNR)
can not only be used for single objective optimisation but also multi-objective
optimisation The study aims to determine a system topology that simultaneously
minimises feeder loss maximum node voltage deviation and feeder load balancing
This is achieved by optimal DNR and DG allocation
There are two methods presented in this chapter that tackle these objectives a single
fuzzy satisfaction objective function is used to transform the three conflicting
objectives into fuzzy memberships and then finally to combine them into a single
function The ultimate goal is to find a solution that maximises this single objective
while maintaining the constraints of the network [20] In Chapter 7 the degree of
Chapter 9 Multi-objective Distribution Network Reconfiguration amp DG Allocation
Considering Loss Voltage Deviation and Load Balancing
Page | 167
overall fuzzy satisfaction is determined by the max-min principle However there is
no guarantee that if one membership value is weaker than the other membership
values then for the same option the optimised single function will also be weak [86]
Therefore the max-min principle may not predict the best compromise solution In
this study a new operator called lsquomax-geometric meanrsquo has been introduced to
determine the degree of overall fuzzy satisfaction
Another methodology used for assessing the multi-objective DNR and DG allocation
problem is based on the Pareto optimality concept The proposed method provides a
set of non-dominated solutions with high quality and great diversity This constructs
a full Pareto front which represents different trade-offs among the objective
functions It allows the decision makers to select the most suitable one from all the
non-dominated solutions and use this for implementation which depends on the
utilitiesrsquo priorities
The optimisation algorithms for DNR and DG allocation can be classified into two
groups
Ant colony optimisation (ACO) algorithm which is used to solve the
problem in the fuzzy domain
Artificial immune systems-ant colony optimisation (AIS-ACO) algorithm
which is adopted to formulate the optimal network reconfiguration problem
within a multi-objective framework based on the Pareto optimality concept
The effectiveness and the efficiency of the proposed methods are implemented on
two standard IEEE 33-node and 69-node systems as case studies
The remainder of this chapter is organised as follows in Section 92 the
mathematical models of the problem are developed Then the solution procedures
are presented in Section 93 Numerical studies are presented and discussed in
Section 94 and finally Section 95 summarises the main conclusions
Chapter 9 Multi-objective Distribution Network Reconfiguration amp DG Allocation
Considering Loss Voltage Deviation and Load Balancing
Page | 168
0
1
92 Problem Formulation
The primary objective of this study is to minimise the three conflicting objectives
feeder loss maximum node voltage deviation and the feeder load balancing index
Two formulations of objective functions are presented as follow
921 Single Fuzzy Satisfaction Objective Function
In this study the three conflicting objectives are transformed into a single objective
function in the fuzzy domain The best compromise solution is obtained using a
lsquomax-geometric meanrsquo principle and is formulated as follows
Max 119871 = (120572119871 times 120572119881 times 120572119861)1 3frasl (9-1)
where 120572119871 120572119881 120572119861 represents the value of the membership functions for the feeder loss
the maximum node voltage deviation and the feeder load balancing index
respectively
The membership functions used to describe the three objectives of the DNR and DG
allocation problem are presented in the following sections
Membership function for feeder loss reduction
The calculation of feeder loss has been discussed in Section 28 The basic purpose
of this membership function is to reduce feeder loss Therefore the network
topology with a lower loss value obtains a higher membership value The
membership function for loss reduction is formulated in (9-2) and presented in Fig
9-1
Fig 9-1 Membership function for feeder loss reduction
As feeder loss becomes greater than 119871119874119878119878119898119894119899 the degree of satisfaction decreases
This reduction is continued until feeder loss reaches 119871119874119878119878119900119903119894
120572119871
119871119874119878119878119898119894119899 119871119874119878119878119900119903119894 119871119874119878119878
Chapter 9 Multi-objective Distribution Network Reconfiguration amp DG Allocation
Considering Loss Voltage Deviation and Load Balancing
Page | 169
0
1
120572119871 =
1 119871119874119878119878 le 119871119874119878119878119898119894119899119871119874119878119878119900119903119894minus119871119874119878119878
119871119874119878119878119900119903119894minus119871119874119878119878119898119894119899119871119874119878119878119898119894119899 lt 119871119874119878119878 lt 119871119874119878119878119900119903119894
0 119871119874119878119878 ge 119871119874119878119878119900119903119894
(9-2)
where 119871119874119878119878119900119903119894 is the loss of the original network 119871119874119878119878119898119894119899 is the minimum loss that
a network can achieve As it is not appropriate for decision makers to obtain a
network topology which increases loss after DNR and DG allocation the minimum
value of 120572119871 is selected as 0 if the loss is greater than or equal to 119871119874119878119878119900119903119894
Membership function for maximum node voltage deviation reduction
The maximum deviation of bus voltages from their rated values is formulated as
119881119863 = max|119881119903119890119891 minus 119898119894119899(119881119894)| |119881119903119890119891 minus 119898119886119909(119881119894)| 119894 120598 1 2 hellip 119873119887 (9-2)
where 119881119903119890119891 is the reference value for the node voltage which is the substation voltage
it is assumed to be 10 per unit in this study 119881119894 is the voltage at the ith node and 119873119887
is the number of nodes
The membership function for maximum node voltage deviation is shown in Fig 9-2
Fig 9-2 Membership function for maximum node voltage deviation reduction
The mathematical equation is presented below
120572119881 =
1 119881119863 le 119881119863119898119894119899119881119863119900119903119894minus119881119863
119881119863119900119903119894minus119881119863119898119894119899119881119863119898119894119899 lt 119881119863 lt 119881119863119900119903119894
0 119881119863 ge 119881119863119900119903119894
(9-3)
where 119881119863119900119903119894 and 119881119863119898119894119899 are the original and minimum values of the maximum node
voltage deviation respectively
120572119881
119881119863119898119894119899 119881119863119900119903119894 119881119863
Chapter 9 Multi-objective Distribution Network Reconfiguration amp DG Allocation
Considering Loss Voltage Deviation and Load Balancing
Page | 170
0
1
Membership function for feeder load balancing index reduction
The feeder load balancing index is calculated as
119871119861119868 = 119881119886119903[1198681
1198681119898119886119909
1198682
1198682119898119886119909 hellip
119868119894
119868119894119898119886119909 hellip
119868119899
119868119899119898119886119909] (9-4)
where 119868119894 is the current flowing through branch 119894 119868119894119898119886119909 represents the maximum
current limit of branch 119894
The function for feeder load balancing index is shown in Fig 9-3 and expressed as
120572119861 =
1 119871119861119868 le 119871119861119868119898119894119899119871119861119868119900119903119894minus119871119861119868
119871119861119868119900119903119894minus119871119861119868119898119894119899119871119861119868119898119894119899 lt 119871119861119868 lt 119871119861119868119900119903119894
0 119871119861119868 ge 119871119861119868119900119903119894
(9-5)
where 119871119861119868119900119903119894 and 119871119861119868119898119894119899 are the original and minimum values of the feeder load
balancing index respectively
Fig 9-3 Membership function for load balancing index reduction
922 Multi-objective Reconfiguration Problem Using Pareto
Optimality
In this study the multi-objective DNR problem can be defined as the minimisation
of the vector
119865(119866) = [1198911(119866)1198912(119866)1198913(119866)]119879 (9-6)
where 1198911(119866) 1198912(119866) and 1198913(119866) are feeder loss maximum node voltage deviation and
feeder load balancing index respectively The calculation of these three parameters
is discussed in Section 921
120572119861
119871119861119868119898119894119899 119871119861119868119900119903119894 119871119861119868
Chapter 9 Multi-objective Distribution Network Reconfiguration amp DG Allocation
Considering Loss Voltage Deviation and Load Balancing
Page | 171
93 Solution methodology
931 Applying ACO to DNR and DG Allocation in the Fuzzy
Domain
In this study the objective of reconfiguring the network and allocating DGs
simultaneously is to deal with the single fuzzy satisfaction objective function In
order to tackle this optimisation problem an ACO algorithm is adopted to find the
optimum configuration of tie-switches and the location of DGs in the network When
the locations of tie-switches and DGs are changed a new network configuration will
be formed For each network configuration the overall satisfaction of the plan is
calculated using Eq (9-1) The search space of the DNR and DG allocation problems
is modelled as a directed graph as shown in Fig 5-1 The flowchart of the proposed
ACO algorithm is presented in Fig 5-2
932 Applying AIS-ACO to Multi-objective DNR and DG
Allocation Using Pareto Optimality
The application of the AIS-ACO algorithm to the multi-objective DNR and DG
allocation problem using the concept of Pareto optimality is similar to that in Section
832 with an additional process for DG allocation
94 Application Studies
To demonstrate the performance and effectiveness of the proposed techniques in
solving the network reconfiguration and placement of DG problems simultaneously
the proposed ACO and AIS-ACO are implemented on two 1266 kV test systems
consisting of 33 and 69 buses The network models are built in OpenDSS and the
solution algorithms are developed in MATLAB For both test systems the substation
voltage is assumed to be 10 pu and all the sections and buses are considered as
candidate locations for tie-switches and DG placement respectively In this study
for simplicity the number of installed DGs is three All the DGs are synchronous
generators and are represented as PQ models with a 100 kVA and a power factor
Chapter 9 Multi-objective Distribution Network Reconfiguration amp DG Allocation
Considering Loss Voltage Deviation and Load Balancing
Page | 172
equal to 10 However the proposed methodology can be implemented for any
number of DGs For the purpose of better illustration and comparison four cases are
considered to analyse the superiority and performance of the proposed methods
Case I System is without reconfiguration and has no DGs (base case)
Case II System is optimally reconfigured and has no DGs
Case III System is optimally reconfigured after DGs are placed at certain buses
Case IV System is optimally reconfigured and DGs are optimally placed
simultaneously
It is to be noted that the ACO and AIS-ACO control parameters are different for
each test case They are set experimentally using information from several trial runs
The final combinations that provide the best results for all of the above tests are
given in Appendix C5 And the Pareto sets for all test cases are listed in Appendix
B4 in detail
941 33-bus System
In this section the proposed procedure is implemented on a 33-bus 1266 kV radial
distribution system with 37 branches and 5 tie-switches whose single line diagram is
shown in Fig 5-3 The tie-switches are located at L33 to L37 represented by red
dotted lines The data of lines and loads are taken from [108] and summarised in
Appendix A2 The current carrying capacity of all branches is 255A The total real
and reactive power loads of the system are 3715 kW and 2300 kVAr respectively
Case I base case
For the base case without reconfiguration and DGs the initial active feeder loss
maximum node voltage deviation and feeder load balancing index of this system are
20314 kW 00884 pu and 00419 respectively
Chapter 9 Multi-objective Distribution Network Reconfiguration amp DG Allocation
Considering Loss Voltage Deviation and Load Balancing
Page | 173
10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
18 19 20 21
22 23 24
25 26 27 28 29 30 31 32
L1 L2 L3 L4 L5 L6 L7 L8 L9 L10 L11 L12 L13 L14 L15 L16 L17
L18
L19 L20 L21
L22
L23 L24
L25
L26 L27 L28 L29 L30 L31 L32
L33
L34
L35
L36
L37
Case II with reconfiguration only (no DGs)
In this case only reconfiguration is considered and no DGs are installed
After DNR the best compromise solution obtained using ACO algorithm in a single
fuzzy satisfaction objective function is presented in Table 9-1 It can be seen that the
DNR has resulted in a reduction of 2956 in feeder loss 2930 in maximum node
voltage deviation and 3556 in feeder load balancing index compared to the base
case This solution is one of the Pareto optimal solutions which are obtained by
using AIS-ACO algorithm And the network configuration after DNR is shown in
Fig 9-4
Table 9-1 Results of DNR in fuzzy multi-objective formulation for 33-bus system in Case II
Objective function Feeder loss
(kW)
Maximum node
voltage deviation
(pu)
Feeder Load
balancing index
Tie-switches
location
08734 14310 00625 00270 6 9 14 32 37
Fig 9-4 33 bus-system for fuzzy multi-objective optimisation Case II
The number of Pareto optimal solutions obtained using AIS-ACO algorithm is 21
and its Pareto front is presented in Fig 9-5 in three dimensions Table 9-2 presents
the mean and standard deviations of the objective values of the Pareto solutions
Chapter 9 Multi-objective Distribution Network Reconfiguration amp DG Allocation
Considering Loss Voltage Deviation and Load Balancing
Page | 174
120140
160180
200220
006
008
01
012
014
016
0022
0024
0026
0028
003
0032
0034
0036
Feeder loss (kW)Maximum node voltage deviation (pu)
Feeder
load b
ala
ncin
g index
Fig 9-5 Pareto front obtained for 33-bus system in Case II
Table 9-2 Mean and standard deviations of Pareto Front for 33-bus system in Case II
Feeder loss (kW) Maximum node voltage
deviation (pu)
Feeder Load balancing index
Mean
15499 00815 00256
Standard deviation
1549 00194 00023
The corner non-dominated solutions which represent minimum feeder loss
minimum voltage deviation and minimum feeder load balancing index are marked
by the red circle yellow circle and green circle respectively as shown in Fig 9-5
The objective values of these solutions and relevant tie-switches locations are
presented in Table 9-3 In minimum loss solution the feeder loss is reduced by 3118
compared to the initial state If improving voltage profiles is the principle objective
the solution with maximum node voltage deviation of 00604 pu is optimum which
represents a 3167 improvement compared to the base case If balancing feeder
Chapter 9 Multi-objective Distribution Network Reconfiguration amp DG Allocation
Considering Loss Voltage Deviation and Load Balancing
Page | 175
10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
18 19 20 21
22 23 24
25 26 27 28 29 30 31 32
L1 L2 L3 L4 L5 L6 L7 L8 L9 L10 L11 L12 L13 L14 L15 L16 L17
L18
L19 L20 L21
L22
L23 L24
L25
L26 L27 L28 L29 L30 L31 L32
L33
L34
L35
L36
L37
DG2
DG1
DG3
load is the main objective the solution with load balancing index of 00223 is
optimum where the index decreases by 4678 in comparison with the initial case
Table 9-3 Minimum solutions along each objective for 33-bus system in Case II
Feeder loss (kW) Maximum node
voltage deviation (pu)
Feeder Load balancing
index
Tie-switches location
Minimum Loss
13981 00639 00280 7 9 14 32 37
Minimum Voltage Deviation
14026 00604 00310 7 9 14 28 32
Minimum Feeder Load Balancing Index
20248 01309 00223 7 30 34 35 37
Case III with reconfiguration only (with DGs)
In this case the three DGs are located at the end of the feeders ie Bus 17 21 24
The feeder loss maximum node voltage deviation and feeder load balancing of the
original network with DGs are 17831 kW 00823 pu and 00389 pu respectively
After DNR the best compromise solution obtained using ACO algorithm in a single
fuzzy satisfaction objective function is presented in Table 9-4 Compared to the Case
I feeder loss maximum node voltage deviation and feeder load balancing decrease
by 3893 3281 and 4511 respectively This solution belongs to the Pareto
set which are obtained by using AIS-ACO algorithm Fig 9-6 illustrates the optimal
network configuration
Fig 9-6 33 bus-system for fuzzy multi-objective optimisation Case III
Chapter 9 Multi-objective Distribution Network Reconfiguration amp DG Allocation
Considering Loss Voltage Deviation and Load Balancing
Page | 176
110120
130140
150160
170
004
006
008
01
0120018
002
0022
0024
0026
0028
003
Feeder loss (kW)Maximum node voltage deviation (pu)
Feeder
load b
ala
ncin
g index
Table 9-4 Results of DNR in fuzzy multi-objective formulation for 33-bus system in Case III
Objective function Feeder loss
(kW)
Maximum node
voltage deviation
(pu)
Feeder Load
balancing index
Tie-switches
location
08590 12405 00594 00230 6 8 14 32 37
Fig 9-7 shows the Pareto front obtained by the AIS-ACO method and the number
of Pareto optimal solutions for this case is 28 The mean and standard deviations of
the objective values of the Pareto solutions are listed in Table 9-5
Fig 9-7 Pareto front obtained for 33-bus system in Case III
Table 9-5 Mean and standard deviations of Pareto Front for 33-bus system in Case III
Feeder loss (kW) Maximum node voltage
deviation (pu)
Feeder load balancing index
Mean
12850 00711 00231
Standard deviation
1003 00166 00029
Chapter 9 Multi-objective Distribution Network Reconfiguration amp DG Allocation
Considering Loss Voltage Deviation and Load Balancing
Page | 177
The corner non-dominated solutions which represent minimum feeder loss
minimum voltage deviation and minimum feeder load balancing index are marked
by the red circle yellow circle and green circle respectively as shown in Fig 9-7
Table 9-6 presents the objective values of these solutions and relevant tie-switches
locations In minimum loss solution the network reconfiguration results in a
reduction of 4214 in feeder loss compared to the original network and a
reduction of 1594 compared to the reconfigured network without DGs If
improving voltage profiles is the principle objective the solution with maximum
node voltage deviation of 00567 pu is optimum which represents a 3586 and
613 improvement compared to Case I and Case II If balancing feeder load is the
main objective the solution with load balancing index of 00189 is optimum where
the index decreases by 5489 and 1525 in comparison with Case I and Case II
Table 9-6 Minimum solutions along each objective for 33-bus system in Case III
Feeder loss (kW) Maximum node
voltage deviation (pu)
Feeder Load balancing
index
Tie-switches location
Minimum Loss
11753 00643 00241 7 9 14 28 31
Minimum Voltage Deviation
12592 00567 00265 6 8 14 28 32
Minimum Feeder Load Balancing Index
16419 01139 00189 7 21 30 35 37
Case IV with reconfiguration and DG allocation
The network is reconfigured and DGs are allocated simultaneously in this case The
best compromise solution obtained using the proposed algorithm in a single fuzzy
satisfaction objective function after DNR and DG allocation is presented in Table 9-
7 Feeder loss maximum node voltage deviation and feeder load balancing decrease
by 4645 4355 and 4463 respectively in comparison with the base case
This solution is one of the Pareto optimal solutions which are obtained by using
AIS-ACO algorithm Fig 9-8 illustrates the optimal network configuration and DG
locations
Chapter 9 Multi-objective Distribution Network Reconfiguration amp DG Allocation
Considering Loss Voltage Deviation and Load Balancing
Page | 178
10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
18 19 20 21
22 23 24
25 26 27 28 29 30 31 32
L1 L2 L3 L4 L5 L6 L7 L8 L9 L10 L11 L12 L13 L14 L15 L16 L17
L18
L19 L20 L21
L22
L23 L24
L25
L26 L27 L28 L29 L30 L31 L32
L33
L34
L35
L36
L37
DG1
DG3
DG2
100110
120130
140150
160
004
006
008
01
012
0016
0018
002
0022
0024
0026
0028
Feeder loss (kW)Maximum node voltage deviation (pu)
Feeder
load b
ala
ncin
g index
Table 9-7 Results of DNR and DG allocation in fuzzy multi-objective formulation for 33-bus system
in Case IV
Objective
function
Feeder loss
(kW)
Maximum node
voltage
deviation (pu)
Feeder Load
balancing
index
Tie-switches
location
DGs location
08961 10878 00499 00232 7 9 14 36 37 B32 B32 B32
Fig 9-8 33 bus-system for fuzzy multi-objective optimisation Case IV
The number of non-dominated solutions obtained by the AIS-ACO algorithm is 295
However the maximum number for Pareto optimal solutions is restricted to 50
Therefore the solutions with a high value of crowding distance are selected Fig 9-9
shows the Pareto front obtained by the proposed method
Fig 9-9 Pareto front obtained for 33-bus system in Case IV
Chapter 9 Multi-objective Distribution Network Reconfiguration amp DG Allocation
Considering Loss Voltage Deviation and Load Balancing
Page | 179
The mean and standard deviations of the Pareto front are listed in Table 9-8
Table 9-8 Mean and standard deviations of Pareto Front for 33-bus system in Case IV
Feeder loss (kW) Maximum node voltage
deviation (pu)
Feeder Load balancing index
Mean
13295 00873 00194
Standard deviation
1354 00179 00019
The corner non-dominated solutions which represent minimum feeder loss
minimum voltage deviation and minimum feeder load balancing index are marked
by the red circle yellow circle and green circle respectively as shown in Fig 9-9
The objective values of these solutions and relevant tie-switches locations are
presented in Table 9-9 In minimum loss solution the network reconfiguration and
DG allocation result in a reduction of 4662 2244 and 773 in feeder loss
compared to Case I Case II and Case III respectively If improving voltage profiles
is the principle objective the solution with maximum node voltage deviation of
00490 pu is optimum which represents a 4457 1887 and 1358
improvement compared to Case I Case II and Case III respectively If balancing
feeder load is the main objective the solution with load balancing index of 00178 is
optimum where the index decreases by 5752 2018 and 582 in comparison
with Case I Case II and Case III respectively
Table 9-9 Minimum solutions along each objective for 33-bus system in Case IV
Feeder loss (kW) Maximum node
voltage deviation
(pu)
Feeder Load
balancing index
Tie-switches
location
DGs location
Minimum Loss
10844 00538 00228 7 9 14 32 37 B30 B31 B31
Minimum Voltage Deviation
11020 00490 00259 7 9 14 28 36 B31 B31 B32
Minimum Feeder Load Balancing Index
15443 01090 00178 7 30 34 35 37 B8 B9 B12
Chapter 9 Multi-objective Distribution Network Reconfiguration amp DG Allocation
Considering Loss Voltage Deviation and Load Balancing
Page | 180
10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
27
28
29
30
31 32 33 34
35
36
37
38 39 40 41 42 43 44 45
46 47 48 49
50
51
52
53 54 55 56 57 58 59 60 61 62 63 64
65 66
67 68
L1 L2 L3 L4 L5 L6 L7 L8 L9 L10 L11 L12 L13 L14 L15 L16 L17 L18 L19 L20 L21 L22 L23 L24 L25 L26
L27
L28
L29
L30
L31 L32 L33 L34
L35
L36
L37
L38 L39 L40 L41 L42 L43 L44 L45
L46
L47 L48 L49
L50
L51
L52
L53 L54 L55 L56 L57 L58 L59 L60 L61 L62 L63 L64
L65
L66
L67
L68
L69
L70
L71
L72L73
942 69-bus System
This is a large-scale radial distribution system consisting of 73 branches and 5 tie-
switches whose single-line diagram is shown in Fig 5-9 The tie-switches are
located at L69 to L73 represented by red dotted lines The line and load data of the
system are taken from [84] and summarised in Appendix A3 The current carrying
capacity of the branches 1-9 is 400 A 46-49 and 52-64 is 300 A and for all other
branches it is 200 A The total power loads are 379589 kW and 26891 kVAr
respectively
Case I base case
For the base case without reconfiguration and DGs the initial active feeder loss
maximum node voltage deviation and feeder load balancing index of this system are
22562 kW 00928 pu and 00259 respectively
Case II with reconfiguration only (no DGs)
In this case only reconfiguration is considered and no DGs are installed After DNR
the best compromise solution obtained using ACO algorithm in a single fuzzy
satisfaction objective function is presented in Table 9-10 and the network
configuration is shown in Fig 9-10 Reconfiguring the network brings a reduction of
5619 4353 and 2355 in feeder loss maximum node voltage deviation and
feeder load balancing index respectively compared to the base case This solution
belongs to the Pareto set which are obtained by using AIS-ACO algorithm
Fig 9-10 69 bus system for fuzzy multi-objective optimisation Case II
Chapter 9 Multi-objective Distribution Network Reconfiguration amp DG Allocation
Considering Loss Voltage Deviation and Load Balancing
Page | 181
80
100
120
140
160
005
006
007
0080016
0018
002
0022
0024
0026
0028
Feeder loss (kW)Maximum node voltage deviation (pu)
Feeder
load b
ala
ncin
g index
Table 9-10 Results of DNR in fuzzy multi-objective formulation for 69-bus system in Case II
Objective function Feeder loss
(kW)
Maximum node
voltage deviation
(pu)
Feeder Load
balancing index
Tie-switches
location
09676 9885 00524 00195 14 55 61 71 72
The number of Pareto optimal solutions obtained by the AIS-ACO algorithm is 12
and its Pareto front are presented in Fig 9-11 in three dimensions
Fig 9-11 Pareto front obtained for 69-bus system in Case II
The mean and standard deviations of the objective values of the Pareto solutions are
listed in Table 9-11
Table 9-11 Mean and standard deviations of Pareto Front for 69-bus system in Case II
Feeder loss (kW) Maximum node voltage
deviation (pu)
Feeder Load balancing index
Mean
12535 00605 00192
Standard deviation
2458 00085 00028
Chapter 9 Multi-objective Distribution Network Reconfiguration amp DG Allocation
Considering Loss Voltage Deviation and Load Balancing
Page | 182
The corner non-dominated solutions which represent minimum feeder loss
minimum voltage deviation and minimum feeder load balancing index are marked
by the red circle yellow circle and green circle respectively as shown in Fig 9-11
The objective values of these solutions and relevant tie-switches locations are
presented in Table 9-12 In minimum loss solution the feeder loss is reduced by
5619 compared to the initial state If improving voltage profiles is the principle
objective the solution with maximum node voltage deviation of 00523 pu is
optimum which represents a 4364 improvement compared to the base case If
balancing feeder load is the main objective the solution with load balancing index of
00161 is optimum where the index decreases by 3784 in comparison with the
initial case
Table 9-12 Minimum solutions along each objective for 69-bus system in Case II
Feeder loss (kW) Maximum node
voltage deviation (pu)
Feeder load balancing
index
Tie-switches location
Minimum Loss
9885 00524 00195 14 55 61 71 72
Minimum Voltage Deviation
10535 00523 00242 9 14 55 61 71
Minimum Feeder Load Balancing Index
15051 00701 00161 14 61 69 71 72
Case III with reconfiguration only (with DGs)
In this case the three DGs are located at the end of the feeders ie Bus 26 45 64
The feeder loss maximum node voltage deviation and feeder load balancing of the
original network with DGs are 19472 kW 00855 pu and 00234 pu respectively
After DNR Table 9-13 presents the best compromise solution obtained using ACO
algorithm in a single fuzzy satisfaction objective function and the optimal network
configuration is shown in Fig 9-12 Compared to the base case feeder loss
maximum node voltage deviation and feeder load balancing decrease by 6118
4364 and 3282 respectively This solution is one of the Pareto optimal
solutions which are obtained by using AIS-ACO algorithm
Chapter 9 Multi-objective Distribution Network Reconfiguration amp DG Allocation
Considering Loss Voltage Deviation and Load Balancing
Page | 183
10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
27
28
29
30
31 32 33 34
35
36
37
38 39 40 41 42 43 44 45
46 47 48 49
50
51
52
53 54 55 56 57 58 59 60 61 62 63 64
65 66
67 68
L1 L2 L3 L4 L5 L6 L7 L8 L9 L10 L11 L12 L13 L14 L15 L16 L17 L18 L19 L20 L21 L22 L23 L24 L25 L26
L27
L28
L29
L30
L31 L32 L33 L34
L35
L36
L37
L38 L39 L40 L41 L42 L43 L44 L45
L46
L47 L48 L49
L50
L51
L52
L53 L54 L55 L56 L57 L58 L59 L60 L61 L62 L63 L64
L65
L66
L67
L68
L69
L70
L71
L72L73
DG3
DG1
DG2
8090
100110
120130
140
005
006
007
008
0014
0016
0018
002
0022
0024
Feeder loss (kW)Maximum node voltage deviation (pu)
Feeder
load b
ala
ncin
g index
Table 9-13 Results of DNR in fuzzy multi-objective formulation for 69-bus system in Case III
Objective function Feeder loss
(kW)
Maximum node
voltage deviation
(pu)
Feeder Load
balancing index
Tie-switches
location
08829 8758 00523 00174 14 55 61 71 72
Fig 9-12 69-bus system for fuzzy multi-objective optimisation Case III
Fig 9-13 shows the Pareto front obtained by the AIS-ACO method and the number
of Pareto optimal solutions for this case is 19
Fig 9-13 Pareto front obtained for 69-bus system in Case III
Chapter 9 Multi-objective Distribution Network Reconfiguration amp DG Allocation
Considering Loss Voltage Deviation and Load Balancing
Page | 184
The mean and standard deviations of the objective values of the Pareto solutions are
listed in Table 9-14
Table 9-14 Mean and standard deviations of Pareto Front for 69-bus system in Case III
Feeder loss (kW) Maximum node voltage
deviation (pu)
Feeder Load balancing index
Mean
10707 00576 00183
Standard deviation
2042 00071 00029
The corner non-dominated solutions which represent minimum feeder loss
minimum voltage deviation and minimum feeder load balancing index are marked
by the red circle yellow circle and green circle respectively as shown in Fig 9-13
Table 9-15 presents the objective values of these solutions and relevant tie-switches
locations are presented In minimum loss solution the network reconfiguration
results in a reduction of 6118 in feeder loss compared to the original network and
a reduction of 1140 compared to the reconfigured network without DGs If
improving voltage profiles is the principle objective the solution with maximum
node voltage deviation of 00522 pu is optimum which represents a 4375 and
019 improvement compared to Case I and Case II If balancing feeder load is the
main objective the solution with load balancing index of 00147 is optimum where
the index decreases by 4324 and 745 in comparison with Case I and Case II
Table 9-15 Minimum solutions along each objective for 69-bus system in Case III
Feeder loss (kW) Maximum node
voltage deviation (pu)
Feeder Load balancing
index
Tie-switches location
Minimum Loss
8758 00523 00174 13 55 61 71 72
Minimum Voltage Deviation
9729 00522 00226 7 12 55 61 71
Minimum Feeder Load Balancing Index
13686 00681 00147 11 61 69 71 72
Chapter 9 Multi-objective Distribution Network Reconfiguration amp DG Allocation
Considering Loss Voltage Deviation and Load Balancing
Page | 185
10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
27
28
29
30
31 32 33 34
35
36
37
38 39 40 41 42 43 44 45
46 47 48 49
50
51
52
53 54 55 56 57 58 59 60 61 62 63 64
65 66
67 68
L1 L2 L3 L4 L5 L6 L7 L8 L9 L10 L11 L12 L13 L14 L15 L16 L17 L18 L19 L20 L21 L22 L23 L24 L25 L26
L27
L28
L29
L30
L31 L32 L33 L34
L35
L36
L37
L38 L39 L40 L41 L42 L43 L44 L45
L46
L47 L48 L49
L50
L51
L52
L53 L54 L55 L56 L57 L58 L59 L60 L61 L62 L63 L64
L65
L66
L67
L68
L69
L70
L71
L72L73
DG3DG1
DG2
Case IV with reconfiguration and DGs allocation
In this case the network is reconfigured and DGs are allocated simultaneously
Table 9-16 presents the best compromise solution obtained using the ACO algorithm
in a single fuzzy satisfaction objective function after DNR and DGs allocation and
the optimal network configuration and DG locations are shown in Fig 9-14 Feeder
loss maximum node voltage deviation and feeder load balancing decrease by
6721 5377 and 3840 respectively in comparison with the base case This
solution is one of the Pareto optimal solutions which are obtained by using AIS-
ACO algorithm
Table 9-16 Results of DNR and DGs allocation in fuzzy multi-objective formulation for 69-bus
system in Case IV
Objective
function
Feeder loss
(kW)
Maximum
node voltage
deviation (pu)
Feeder Load
balancing
index
Tie-switches
location
DGs location
08882 7397 00429 00158 14 55 61 71 72 B60 B60 B60
Fig 9-14 69-bus system for fuzzy multi-objective optimisation Case IV
The number of non-dominated solutions obtained by the AIS-ACO algorithm is 46
Fig 9-15 shows the Pareto front obtained by the proposed method The mean and
standard deviations of the objective values of the Pareto solutions are listed in Table
9-17
Chapter 9 Multi-objective Distribution Network Reconfiguration amp DG Allocation
Considering Loss Voltage Deviation and Load Balancing
Page | 186
70
80
90
100
110
120
004
0045
005
0055
006
0012
0013
0014
0015
0016
0017
0018
0019
Feeder loss (kW)Maximum node voltage deviation (pu)
Feeder
load b
ala
ncin
g index
Fig 9-15 Pareto front obtained for 69-bus system in Case IV
Table 9-17 Mean and standard deviations of Pareto Front for 69-bus system in Case IV
Feeder loss (kW) Maximum node voltage
deviation (pu)
Feeder Load balancing index
Mean
9872 00520 00147
Standard deviation
1491 00055 00013
The corner non-dominated solutions which represent minimum feeder loss
minimum voltage deviation and minimum feeder load balancing index are marked
by the red circle yellow circle and green circle respectively as shown in Fig 9-15
The objective values of these solutions and relevant tie-switches locations are
presented in Table 9-18 In minimum loss solution the network reconfiguration and
DG allocation result in a reduction of 6721 2517 and 1554 in feeder loss
compared to Case I Case II and Case III respectively If improving voltage profiles
is the principle objective the solution with maximum node voltage deviation of
00428 is optimum which represents a 5388 1816 and 1801 improvement
compared to Case I Case II and Case III respectively If balancing feeder load is the
Chapter 9 Multi-objective Distribution Network Reconfiguration amp DG Allocation
Considering Loss Voltage Deviation and Load Balancing
Page | 187
main objective the solution with load balancing index of 00125 pu is optimum
where the index decreases by 5174 2236 and 1497 in comparison with Case
I Case II and Case III respectively
Table 9-18 Minimum solutions along each objective for 69-bus system in Case IV
Feeder loss (kW) Maximum node
voltage deviation
(pu)
Feeder Load
balancing index
Tie-switches
location
DGs location
Minimum Loss
7397 00429 00158 14 55 61 71 72 B60 B60 B60
Minimum Voltage Deviation
8032 00428 00183 11 55 61 71 72 B60 B60 B60
Minimum Feeder Load Balancing Index
10962 00577 00125 14 63 69 71 72 B62 B62 B62
95 Summary
In this study the DNR and DG allocation problem is formulated either within a
fuzzy satisfaction objective function or within a multi-objective Pareto optimal
framework This formulation incorporates the minimisation of three conflicting
objectives feeder loss maximum node voltage deviation and feeder load balancing
index In the fuzzy multi-objective formulation all three objectives are transformed
into a single fuzzy satisfaction objective function and the ACO algorithm is used to
provide decision support The AIS-ACO algorithm has been presented in this study
for the assessment of the multi-objective DNR problem from a Pareto optimality
point of view The proposed methods have been successfully applied on a 33-bus and
a 69-bus radial distribution system The results illustrate that the proposed algorithm
is able to generate a set of non-dominated solutions with high quality and great
diversity This allows the network operators to choose any one from the non-
dominated solutions for implementation based on utilitiesrsquo priorities And the corner
non-dominated solutions which represent the minimum value of each objective
function are presented in the Pareto front chart
Chapter 9 Multi-objective Distribution Network Reconfiguration amp DG Allocation
Considering Loss Voltage Deviation and Load Balancing
Page | 188
Future work could include the assessment of the DNR and DG allocation problem
with more than three objectives These objectives may include balancing loads on
transformers minimising the number of switching operations etc The proposed
methodologies can be evaluated further by applying them to actual systems
Page | 189
CHAPTER 10
CONCLUSION amp FUTURE WORK
101 Conclusion
The aim of this thesis is to improve service efficiency and quality in distribution
networks Optimal distribution automation (DA) is one of the best solutions to
achieve this goal The multiple objectives are transformed into different forms based
on utilitiesrsquo priorities For this purpose the Monte Carlo method is used to solve
power system issues involving uncertain load values And a set of ant colony
optimisation (ACO)-based algorithms has been developed for objectives
optimisation This section summarises the conclusions drawn from the research
results
A comprehensive review of the network configurations switchgears DA
assessment of loss and reliability indices and different forms of multi-objective
functions was provided in Chapter 2 This has demonstrated the need for DA to
provide a reliable and high efficiency power supply to all customers with a minimum
cost
In Chapter 3 the thesis reviewed the techniques for the assessment of mono-
objectivemulti-objective optimisation problems which were categorised into two
groups simulation methods and analytical methods The Monte Carlo method is a
typical simulation technique and is generally used to deal with power system
calculations involving uncertain parameters It can find the best solution with a high
Chapter 10 Conclusion amp Future Work
Page | 190
degree of accuracy but requires a considerable amount of CPU time and memory
The ant colony optimisation (ACO) algorithm is one of the metaheuristic techniques
designed for assessing the DA problems It can find the global optimum solution in a
reasonable computation time The artificial immune systems (AIS)-ACO hybrid
algorithm was used for assessing the DA problems in order to obtain a set of non-
dominated solutions by using the concept of Pareto dominance
The thesis illustrates why transformer economic operation (TEO) is an economical
solution to reduce transformer loss The TEO mode with minimum loss and
satisfactory voltages is achieved by operating with one or two transformers This
can be summarised as when the transformer load factor is less than the TCLF
transformers should operate separately However when the transformer load factor is
higher than the TCLF it is recommended that transformers operate in parallel In
Chapter 4 a Monte Carlo simulation platform was established to tackle load
uncertainties A methodology based on TEO to reduce transformer loss was then
described This results in a reduction over the conventional transformer loss ie
when two transformers are in parallel operation However simulation studies also
indicate voltage profiles are improved when transformers operate in parallel
Therefore a slight reduction in TCLF results in an increased loss but an
improvement in voltage performance
In Chapter 4 the thesis also demonstrates why distribution network reconfiguration
(DNR) is an effective strategy for transformer loss reduction The presented results
illustrate the optimal locations of tie-switch statuses have successfully reduced the
transformer losses and improved the voltages profiles during a 24 hour operating
period The further away the nodes are from the tie-switch the better the voltage
profiles obtained In addition when the tie-switch moves closer to the middle of the
linked feeder the voltage performance is improved In this case the daily energy
loss in Scenario 5 is 11162 kWh After the introduction of Scenario 9 the annual
saving energy could be 59641 kWh
One conclusion of this thesis is that the network can be reconfigured and DGs can be
relocated simultaneously for feeder loss reduction In Chapter 5 an ACO algorithm
was used for assessing the DNR and DG allocation problems in terms of feeder loss
reduction The numerical results showed that for best performance the existing tie-
Chapter 10 Conclusion amp Future Work
Page | 191
switches were relocated and DGs were optimally placed at the same time The feeder
losses are reduced by 4662 and 6721 for the 33-bus and 69-bus system
respectively The inappropriate network configuration and DG location might result
in loss increment when the size of DG is increased The proposed methodology has
also successfully reduced the total feeder loss and improved the voltage profiles for
different capacities of DG by determining the most suitable network topology and
the DG locations In addition the simulation results have been compared with other
classical methods in literature and it is demonstrated that the proposed ACO is more
efficient and is more likely to obtain the global optimum solution
Another conclusion of this thesis is that the distribution network loss including
transformer loss and feeder loss can be minimised by using a new optimal planning
strategy This strategy is a combination of TEO and network reconfiguration as
presented in Chapter 6 In this chapter the distribution loads experience daily and
seasonal variations and the day is divided into two periods The proposed ACO
algorithm has successfully found the optimum network configuration and economic
operation mode of transformers in all substations during each time interval The
annual energy loss is reduced by 506 compared to the original network Both
transformer loss and feeder loss are reduced through this optimal planning using
DNR and TEO Furthermore simulation results obtained with numerical studies
have demonstrated the capability of applying the ACO algorithm to distribution
network planning including networks with DGs and EVs The proposed
methodology has successfully reduced the total network loss for different capacities
of DG and different penetration levels of EVs by determining the most suitable
network topology compared to the original configuration Comparative results also
show that coordinated charging plan results in less energy loss compared to
uncoordinated charging strategy with the same EV penetration level This is due to
the postponement of charging time which avoids a clash with the peak power
demand times
The thesis develops an effective strategy of sectionalising switch placement (SSP)
for system reliability improvement This is achieved by installing new switches and
relocating existing switches In Chapter 7 an ACO algorithm was proposed for the
assessment of the SSP problem based on reliability improvement and switch costs
minimisation using either a single objective function with weighted aggregation of a
Chapter 10 Conclusion amp Future Work
Page | 192
multi-objective function with fuzzy variables The selection of pheromone
evaporation rate and number of ants is a trade-off between the global search ability
and convergence rate of the ACO algorithm In comparison with the original system
existing sectionalising switches were relocated and new automatic switches were
installed For this practical system the total system costs are reduced by 4289
compared to the original network The impact of installing sectionalising switches on
reducing the total system costs decreases as the number of sectionalising switches is
increased Furthermore a benefit-to-cost analysis which offered a comparison
between ECOST and switch costs was implemented The analysis reveals that the
installing and relocating sectionalising switches is a profitable investment In
addition a set of compromise solutions was obtained by assessing the SSP problem
in terms of ECOST and SAIDI reduction during fault contingencies The placement
of sectionalising switches results in a reduction of 60 in ECOST and 7148 in
SAIDI
The thesis also proposes a strategy for assessing the DNR problems if the
distribution network operator (DNO) desires to know all possible optimal solutions
for all the multiple conflicting objectives simultaneously This formulates the DNR
problem within a multi-objective formulation in the Pareto optimal framework In
Chapter 8 The MOACO and AIS-ACO algorithms were used for assessing this
problem in terms of loss reduction and reliability improvement Both algorithms
have obtained the same Pareto optimal solutions but the AIS-ACO algorithm
performs better in comparison with the MOACO algorithm in terms of computation
time Feeder loss maximum node voltage deviation and feeder load balancing were
simultaneous optimised in Chapter 9 A set of non-dominated solutions with high
quality and great diversity was obtained This set of solutions represent different
trade-offs among the objective functions And the corner non-dominated solutions
which represent the minimum value of each objective function are presented in the
Pareto front chart For IEEE 69-bus system compared to the base case the network
reconfiguration and DG allocation result in a reduction of 6721 in minimum loss
solution If improving the voltage profiles is the principle objective the best solution
represents a 5388 improvement of this index If balancing feeder load is the main
objective this index decreases by 5174 By varying the weighting factors for the
Chapter 10 Conclusion amp Future Work
Page | 193
parameters the decision makers can select the best compromise among the three
objectives for implementation depending on the utilitiesrsquo priorities
102 Future Work
Based on the findings of this project the suggestions for future work are
In this thesis the transformers have the same characteristics In the future as the
cost of replacing an existing transformer with a new one is cheaper than
replacing both transformers the situation that two transformers with different
characteristics in a substation is not uncommon Therefore an optimisation
method for two transformers with different characteristics will be investigated
and four operation modes can occur
1) First transformer operates alone
2) Second transformer operates alone
3) Two transformers operate in parallel
4) Optimisation mode optimum selection of the transformers needed to
supply each feeder
At present in the UK customers pay for losses in the network In this thesis the
losses are analysed as a whole without allocating them to the users in the network
In the future a loss allocation scheme to customers in the distribution network
will be developed However after reconfiguration the total network loss is
reduced but the loss allocation to some customers may increase The customers
with more loss allocated will be dissatisfied with the network reconfiguration It
is therefore important to change the tariff structure for these customers so that
they are not obliged to pay more for the increase in loss allocation as a result of
network reconfiguration
In this thesis the maximum number of objectives to be optimised simultaneously
is three However the work could be extended to solve the DA problem with
more than three objectives These objectives may include balancing load on
transformers minimising the number of switch operations and maximising the
load on feeders
Chapter 10 Conclusion amp Future Work
Page | 194
The optimal DNR DG allocation TEO and SSP will be combined together to
solve the multi-objective optimisation problem The proposed methodologies
could be tested in large-scale practical systems
In this thesis the evaluation of reliability indices only considers the faults in the
line sections And all the feeders are supposed to have the same parameters and
hence the same failure rates However historical data shows the failure rates of a
feeder vary with geographical location and the weather Therefore different
types of feeders and seasonal varying data of feeder section failure rates will be
considered in future work Moreover the impacts of contingencies on the system
such as faults in the transformers and protective devices could also be considered
The integration of large number of electric vehicles (EVs) into the distribution
network places an extra burden on the electricity grid such as increases in energy
loss overloading in feeders decrease in reliability and power quality Therefore
network reconfiguration techniques and smart charging strategies will be
proposed to moderate the charging effects of EVs In addition the vehicle-to-grid
(V2G) technique which returns electricity to the gird will also be studied The
bi-directional of EVs in the network can provide power to improve load
balancing by ldquovalley fillingrdquo (charging) and ldquopeak shavingrdquo (discharging) [118]
The simulation results show ACO-based algorithms could find a set of good
solutions within a reasonable computation time The ACO control parameters are
set experimentally using information from several trial runs More work is
needed to improve the performance of the proposed algorithms by determining
the optimum set of parameter values It is expected that new ACO-based
algorithms will outperform any existing ones or at worst match their results
In the future a multi-objective stochastic optimal flow problem with the
consideration of load DG EV uncertainties will be addressed The load DG
and EV models are obtained by using a Monte Carlo probabilistic power flow
The objectives are then optimised by using a suitable metaheuristic technique
Page | 195
References
[1] L M Faulkenberry Electrical power distribution and transmission Pearson
Education India 1996
[2] Parliamentary Office of Science and Technology ldquoUK Electricity Networksrdquo
2001
[3] R Das et al ldquoDistribution automation strategies evolution of technologies
and the business caserdquo IEEE Trans Smart Grid vol 6 no 4 pp 2166ndash2175
2015
[4] P Balakrishna K Rajagopal and K S Swarup ldquoApplication benefits of
Distribution Automation and AMI systems convergence methodology for
distribution power restoration analysisrdquo Sustain Energy Grids Networks vol
2 pp 15ndash22 2015
[5] ofgem ldquoEnergy Efficiency Directive An assessment of the energy efficiency
potential of Great Britainrsquos gas and electricity infrastructurerdquo 2015
[6] R C Dugan M F McGranaghan and H W Beaty ldquoElectrical power
systems qualityrdquo 1996
[7] British Standards Institution DECC UK Office for National Statistic and
Met Office UK ldquoVoltage characteristics of electricity supplied by public
distribution systemsrdquo Whether and Climate change no December pp 1ndash18
2010
[8] Y F Niu Z Y Gao and W H K Lam ldquoEvaluating the reliability of a
stochastic distribution network in terms of minimal cutsrdquo Transp Res Part E
Logist Transp Rev vol 100 pp 75ndash97 2017
[9] R Billinton and J E Billinton ldquoDistribution system reliability indicesrdquo
IEEE Trans Power Deliv vol 4 no 1 pp 561ndash568 1989
[10] Ofgem ldquoElectricity Distribution Annual Report for 2010-11rdquo 2012
[11] J Hamachi K Eto ldquoUnderstanding the Cost of Power Interruption to US
Electric Consumers LBNL-55718rdquo 2004
[12] R M Vitorino H M Jorge and L P Neves ldquoLoss and reliability
optimization for power distribution system operationrdquo Elsevier BV 2013
[13] E M Carreno R Romero and A Padilha-Feltrin ldquoAn efficient codification
to solve distribution network reconfiguration for loss reduction problemrdquo
IEEE Trans Power Syst vol 23 no 4 pp 1542ndash1551 2008
[14] A Y Abdelaziz R A Osama and S M El-Khodary ldquoReconfiguration of
distribution systems for loss reduction using the hyper-cube ant colony
optimisation algorithmrdquo IET Gener Transm Distrib vol 6 no 2 p 176
References
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2012
[15] European commission ldquoRoadmap for moving to a low-carbon economy in
2050rdquo DG Clim Action portal pp 1ndash2 2011
[16] A Mohamed Imran M Kowsalya and D P Kothari ldquoA novel integration
technique for optimal network reconfiguration and distributed generation
placement in power distribution networksrdquo Int J Electr Power Energy Syst
vol 63 pp 461ndash472 2014
[17] W Guan Y Tan H Zhang and J Song ldquoDistribution system feeder
reconfiguration considering different model of DG sourcesrdquo Int J Electr
Power Energy Syst vol 68 pp 210ndash221 2015
[18] S A Yin and C N Lu ldquoDistribution feeder scheduling considering variable
load profile and outage costsrdquo IEEE Trans Power Syst vol 24 no 2 pp
652ndash660 2009
[19] I Richardson M Thomson D Infield and C Clifford ldquoDomestic electricity
use A high-resolution energy demand modelrdquo Energy Build vol 42 no 10
pp 1878ndash1887 2010
[20] K Deb A Pratap S Agarwal and T Meyarivan ldquoA fast and elitist
multiobjective genetic algorithm NSGA-IIrdquo IEEE Trans Evol Comput vol
6 no 2 pp 182ndash197 2002
[21] M E Elkhatib R El Shatshat and M M A Salama ldquoDecentralized reactive
power control for advanced distribution automation systemsrdquo IEEE Trans
Smart Grid vol 3 no 3 pp 1482ndash1490 2012
[22] C-L Su and J-H Teng ldquoOutage costs quantification for benefitndashcost
analysis of distribution automation systemsrdquo Int J Electr Power Energy
Syst vol 29 no 10 pp 767ndash774 2007
[23] I Goroohi Sardou M Banejad R Hooshmand and a Dastfan ldquoModified
shuffled frog leaping algorithm for optimal switch placement in distribution
automation system using a multi-objective fuzzy approachrdquo IET Gener
Transm Distrib vol 6 no 6 p 493 2012
[24] C L Smallwood and J Wennermark ldquoBenefits of distribution automationrdquo
IEEE Ind Appl Mag vol 16 no 1 pp 65ndash73 2010
[25] T Goumlnen Electric power distribution system engineering McGraw-Hill New
York 1986
[26] V Madani et al ldquoDistribution automation strategies challenges and
opportunities in a changing landscaperdquo IEEE Trans Smart Grid vol 6 no 4
pp 2157ndash2165 2015
[27] J J Burke ldquoPower distribution engineering fundamentals and applicationsrdquo
1994
[28] A Elmitwally E Gouda and S Eladawy ldquoRestoring recloser-fuse
coordination by optimal fault current limiters planning in DG-integrated
References
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distribution systemsrdquo Int J Electr Power Energy Syst vol 77 pp 9ndash18
2016
[29] L He J R Mayor R G Harley H Liles G Zhang and Y Deng ldquoMulti-
physics modeling of the dynamic response of a circuit breaker recloser
Systemrdquo in IEEE International Electric Machines amp Dirves Conference 2013
vol 1 pp 1001ndash1008
[30] J M Gers and E J Holmes Protection of electricity distribution networks
vol 47 The Institution of Electrical Engineers 2004
[31] E-J-A Zehra M Moghavvemi M M I Hashim and M Kashem ldquoNetwork
reconfiguration using PSAT for loss reduction in distribution systemsrdquo in 1st
International Conference on Energy Power and Control (EPC-IQ) 2010 pp
62ndash66
[32] J J S Grainger W D J J Grainger and W D Stevenson Power system
analysis McGraw-Hill New York 1994
[33] R D Laramore An introduction to electrical machines and transformers
Wiley 1990
[34] D Borge-Diez A Colmenar-Santos M Castro-Gil and J Carpio-Ibaacutentildeez
ldquoParallel distribution transformer loss reductions A proposed method and
experimental validationrdquo Int J Electr Power Energy Syst vol 49 no 1 pp
170ndash180 2013
[35] Y Wang and hui chao Liu ldquoThe information system for economic operation
of transformer based on ASPrdquo in Intertational Power Engineering
Conference 2007 pp 1914ndash1917
[36] X Chen and Z Guo ldquoEconomic operation of power transformer based on real
time parameter checkingrdquo in Power Engineering Society General Meeting
2006 pp 4ndash6
[37] W Yuan and Y Zhang ldquoEconomic operation of transformers in the area
power network based on real-time analysis and controlrdquo in China
International Conference on Electricity Distribution 2008 pp 1ndash5
[38] R Song and X Zhang ldquoThe application research of load smoothing algorithm
in the transformer economic operationrdquo in International Conference on
Energy and Environment Technology 2009 vol 2 pp 328ndash331
[39] C Mamane ldquoTransformer loss evaluation user-manufacturer
communicationsrdquo IEEE Trans Ind Appl vol IA-20 no 1 pp 11ndash15 1984
[40] E I Amoiralis M A Tsili and A G Kladas ldquoEconomic evaluation of
transformer selection in electrical power systemsrdquo in 19th International
Conference on Electrical Machines 2010 pp 1ndash5
[41] B Suechoey J Ekburanawat N Kraisnachinda S Banjongjit C Chompoo
and M Kando ldquoAn analysis and selection of distribution transformer for
losses reductionrdquo in IEEE Power Engineering Society Winter Meeting 2000
pp 2290ndash2293
References
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[42] B Suechoey S Bunjongjit and M Kando ldquoThe result analysis of economic
distribution transformer design in Thailandrdquo in Transmission and Distribution
Conference and Exhibition 2002 pp 1820ndash1823
[43] A Merlin and H Back ldquoSearch for a minimal-loss operating spanning tree
configuration in an urban power distribution systemrdquo in Proc 5th Power
System Computation Conf 1975 pp 1ndash18
[44] S Civanlar J J Grainger H Yin and S S H Lee ldquoDistribution feeder
reconfiguration for loss reductionrdquo IEEE Trans Power Deliv vol 3 no 3
pp 1217ndash1223 1988
[45] M-R Andervazh J Olamaei and M-R Haghifam ldquoAdaptive multi-
objective distribution network reconfiguration using multi-objective discrete
particles swarm optimisation algorithm and graph theoryrdquo IET Gener Transm
Distrib vol 7 no 12 pp 1367ndash1382 2013
[46] K Nara A Shiose M Kitagawa and T Ishihara ldquoImplementation of genetic
algorithm for distribution systems loss minimum re-configurationrdquo IEEE
Trans Power Syst vol 7 no 3 pp 1044ndash1051 1992
[47] J Z Zhu ldquoOptimal reconfiguration of electrical distribution network using
the refined genetic algorithmrdquo Electr Power Syst Res vol 62 no 1 pp 37ndash
42 2002
[48] B Enacheanu B Raison R Caire O Devaux W Bienia and N HadjSaid
ldquoRadial network reconfiguration using genetic algorithm based on the matroid
theoryrdquo IEEE Trans Power Syst vol 23 no 1 pp 186ndash195 2008
[49] J C Cebrian and N Kagan ldquoReconfiguration of distribution networks to
minimize loss and disruption costs using genetic algorithmsrdquo Electr Power
Syst Res vol 80 no 1 pp 53ndash62 2010
[50] H D Chiang and R Jean-Jumeau ldquoOptimal network reconfigurations in
distribution systems part 1 A new formulation and a solution methodologyrdquo
IEEE Trans Power Deliv vol 5 no 4 pp 1902ndash1909 1990
[51] Y J Jeon J C Kim and J O Kim ldquoAn efficient simulted annealing
algorithm for network reconfiguration in large-scale distribution systemsrdquo
IEEE Trans Power Deliv vol 17 no 4 pp 1070ndash1078 2002
[52] H Mori and Y Ogita ldquoA parallel tabu search based method for
reconfigurations of distribution systemsrdquo in Power Engineering Society
Summer Meeting 2000 pp 73ndash78
[53] D Zhang Z Fu and L Zhang ldquoAn improved TS algorithm for loss-
minimum reconfiguration in large-scale distribution systemsrdquo Electr Power
Syst Res vol 77 no 5ndash6 pp 685ndash694 2007
[54] A Y Abdelaziz F M Mohamed S F Mekhamer and M A L Badr
ldquoDistribution system reconfiguration using a modified Tabu Search algorithmrdquo
Electr Power Syst Res vol 80 no 8 pp 943ndash953 2010
[55] A Y Abdelaziz F M Mohammed S F Mekhamer and M A L Badr
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ldquoDistribution systems reconfiguration using a modified particle swarm
optimization algorithmrdquo Electr Power Syst Res vol 79 no 11 pp 1521ndash
1530 2009
[56] A Skoonpong and S Sirisumrannukul ldquoNetwork reconfiguration for
reliability worth enhancement in distribution systems by simulated annealingrdquo
5th Int Conf Electr Eng Comput Telecommun Inf Technol ECTI-CON pp
937ndash940 2008
[57] S Elsaiah M Benidris and J Mitra ldquoReliability improvement of power
distribution system through feeder reconfigurationrdquo in 13th International
Conference on Probabilistic Methods Applied to Power Systems 2014
[58] A Kavousi-Fard and T Niknam ldquoOptimal distribution feeder reconfiguration
for reliability improvement considering uncertaintyrdquo IEEE Trans Power
Deliv vol 29 no 3 pp 1344ndash1353 2014
[59] S Ghasemi ldquoBalanced and unbalanced distribution networks reconfiguration
considering reliability indicesrdquo Ain Shams Eng J 2015
[60] A Saffar R Hooshmand and A Khodabakhshian ldquoA new fuzzy optimal
reconfiguration of distribution systems for loss reduction and load balancing
using ant colony search-based algorithmrdquo Appl Soft Comput J vol 11 no 5
pp 4021ndash4028 2011
[61] D Das ldquoA fuzzy multiobjective approach for network reconfiguration of
distribution systemsrdquo IEEE Trans Power Deliv vol 21 no 1 pp 202ndash209
2006
[62] J E Mendoza E A Loacutepez M E Loacutepez and C A Coello Coello
ldquoMicrogenetic multiobjective reconfiguration algorithm considering power
losses and reliability indices for medium voltage distribution networkrdquo IET
Gener Transm Distrib vol 3 no 9 pp 825ndash840 2009
[63] K M Muttaqi J Aghaei V Ganapathy and A E Nezhad ldquoTechnical
challenges for electric power industries with implementation of distribution
system automation in smart gridsrdquo Renew Sustain Energy Rev vol 46 pp
129ndash142 2015
[64] A Abiri-Jahromi M Fotuhi-Firuzabad M Parvania and M Mosleh
ldquoOptimized sectionalizing switch placement strategy in distribution systemsrdquo
IEEE Trans Power Deliv vol 27 no 1 pp 362ndash370 2012
[65] J Northcote-Green and R G Wilson Control and automation of electrical
power distribution systems vol 28 CRC Press 2006
[66] H Falaghi M R Haghifam and C Singh ldquoAnt colony optimization-based
method for placement of sectionalizing switches in distribution networks
using a fuzzy multiobjective approachrdquo IEEE Trans Power Deliv vol 24
no 1 pp 268ndash276 2009
[67] M Nematollahi and M Tadayon ldquoOptimal sectionalizing switches and DG
placement considering critical system conditionrdquo in 21st Iranian Conference
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on Electrical Engineering 2013 pp 1ndash6
[68] J H Teng and C N Lu ldquoFeeder-switch relocation for customer interruption
cost minimizationrdquo IEEE Trans Power Deliv vol 17 no 1 pp 254ndash259
2002
[69] J H Teng and Y H Liu ldquoA novel ACS-based optimum switch relocation
methodrdquo IEEE Trans Power Syst vol 18 no 1 pp 113ndash120 2003
[70] V Miranda ldquoUsing fuzzy reliability in a decision aid environment for
establishing interconnection and switching location policiesrdquo in CIRED 1991
pp 1ndash6
[71] A Heidari V G Agelidis and M Kia ldquoConsiderations of sectionalizing
switches in distribution networks with distributed generationrdquo IEEE Trans
Power Deliv vol 30 no 3 pp 1401ndash1409 2015
[72] I v Zhezhelenko Y Papaika and others ldquoEstimating economic equivalent of
reactive power in the systems of enterprise electric power supplyrdquo Sci Bull
Natl Min Univ no 5 2016
[73] L Li and R Li ldquoStudy on the analysis software of economic operation of
transformerrdquo Adv Mater Res vol 1008ndash1009 pp 497ndash500 2014
[74] J Shang Z Tan C Zhang and L Ju ldquoThe transformer equipment selectionrsquos
update decision technical and economic analysis modelrdquo in Energy and
Power Engineering 2013 vol 5 no 4 pp 143ndash147
[75] B Amanulla S Chakrabarti and S N Singh ldquoReconfiguration of power
distribution systems considering reliability and power lossrdquo IEEE Trans
Power Deliv vol 27 no 2 pp 918ndash926 2012
[76] R E Brown Electric power distribution reliability CRC press 2008
[77] P Zhou R Y Jin and L W Fan ldquoReliability and economic evaluation of
power system with renewables A reviewrdquo Renew Sustain Energy Rev vol
58 pp 537ndash547 2016
[78] R Billington and R N Allan Reliability evaluation of power systems
Plenum Publishing Corp New York NY 1996
[79] N G Paterakis et al ldquoMulti-objective reconfiguration of radial distribution
systems using reliability indicesrdquo IEEE Trans Power Syst vol 31 no 2 pp
1048ndash1062 2016
[80] B Sultana M W Mustafa U Sultana and A R Bhatti ldquoReview on
reliability improvement and power loss reduction in distribution system via
network reconfigurationrdquo Renew Sustain Energy Rev vol 66 pp 297ndash310
2016
[81] K Xie J Zhou and R Billinton ldquoReliability evaluation algorithm for
complex medium voltage electrical distribution networks based on the shortest
pathrdquo IEE Proceedings-Generation Transm Distrib vol 150 no 6 pp
686ndash690 2003
References
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[82] Z Ghofrani-Jahromi M Kazemi and M Ehsan ldquoDistribution switches
upgrade for loss reduction and reliability improvementrdquo IEEE Trans Power
Deliv vol 30 no 2 pp 684ndash692 2015
[83] P Ngatchou A Zarei and A El-Sharkawi ldquoPareto multi objective
optimizationrdquo in Proceedings of the 13th International Conference on
Intelligent Systems Application to Power Systems 2005 pp 84ndash91
[84] J S Savier and D Das ldquoImpact of network reconfiguration on loss allocation
of radial distribution systemsrdquo IEEE Trans Power Deliv vol 22 no 4 pp
2473ndash2480 2007
[85] T T Nguyen T T Nguyen A V Truong Q T Nguyen and T A Phung
ldquoMulti-objective electric distribution network reconfiguration solution using
runner-root algorithmrdquo Appl Soft Comput J vol 52 pp 93ndash108 2017
[86] N Gupta A Swarnkar R C Bansal and K R Niazi ldquoMulti-objective
reconfiguration of distribution systems using adaptive genetic algorithm in
fuzzy frameworkrdquo IET Gener Transm Distrib vol 4 no 12 pp 1288ndash1298
2010
[87] M R Narimani A Azizi Vahed R Azizipanah-Abarghooee and M
Javidsharifi ldquoEnhanced gravitational search algorithm for multi-objective
distribution feeder reconfiguration considering reliability loss and operational
costrdquo IET Gener Transm Distrib vol 8 no 1 pp 55ndash69 2014
[88] A Ahuja S Das and A Pahwa ldquoAn AIS-ACO hybrid approach for multi-
objective distribution system reconfigurationrdquo IEEE Trans Power Syst vol
22 no 3 pp 1101ndash1111 2007
[89] M Rostami A Kavousi-Fard and T Niknam ldquoExpected cost minimization
of smart grids with plug-in hybrid electric vehicles using optimal distribution
feeder reconfigurationrdquo Ind Informatics IEEE Trans vol 11 no 2 pp
388ndash397 2015
[90] S Oh J Kim S Kwon and S Chung ldquoMonte Carlo simulation of
phytosanitary irradiation treatment for mangosteen using MRI-based
geometryrdquo vol 39 no 3 pp 205ndash214 2014
[91] N HadjSaid and J C Sabonnadiere Electrical Distribution Networks
London ISTE Ltd 2011
[92] Y Li ldquoVoltage balancing on three-phase low voltage feederrdquo The Univerisity
of Manchester 2015
[93] K Bell and P R Allan ldquoComputation of the Value of Securityrdquo 1999
[94] M Dorigo V Maniezzo and A Colorni ldquoThe ant systems optimization by a
colony of cooperative agentsrdquo IEEE Trans Syst Man Cybern B vol 26 no
1 pp 1ndash13 1996
[95] M Dorigo and L M Gambardella ldquoAnt colony system a cooperative
learning approach to the traveling salesman problemrdquo IEEE Trans Evol
Comput vol 1 no 1 pp 53ndash66 1997
References
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[96] M Lopez-Ibanez and T Stuetzle ldquoThe automatic design of multiobjective ant
colony optimization algorithmsrdquo IEEE Trans Evol Comput vol 16 no 6
pp 861ndash875 2012
[97] L Charles Daniel and S Ravichandran ldquoDistribution network reconfiguration
for loss reduction using ant colony system algorithmrdquo in IEEE Indicon 2005
Conference 2005 pp 1ndash4
[98] J F Goacutemez et al ldquoAnt colony system algorithm for the planning of primary
distribution circuitsrdquo IEEE Trans Power Syst vol 19 no 2 pp 996ndash1004
2004
[99] J Lu N Wang J Chen and F Su ldquoCooperative path planning for multiple
UCAVs using an AIS-ACO hybrid approachrdquo Proc 2011 Int Conf Electron
Mech Eng Inf Technol EMEIT 2011 vol 8 no 2 pp 4301ndash4305 2011
[100] J E Hunt and D E Cooke ldquoAn adaptive distributed learning system based
on the immune systemrdquo 1995 IEEE Int Conf Syst Man Cybern Intell Syst
21st Century vol 3 pp 2494ndash2499 1995
[101] C A C Coello and N C Cortes ldquoSolving multiobjective optimization
problems using an artificial immune systemrdquo Genet Program Evolvable
Mach vol 6 no 2 pp 163ndash190 2005
[102] L N De Castro and F J Von Zuben ldquoLearning and optimization using the
clonal selection principlerdquo IEEE Trans Evol Comput vol 6 no 3 pp 239ndash
251 2002
[103] Office for National Statistics Population and household estimates for the
United Kingdom UK 2011
[104] S Ingram S Probert and K Jackson ldquoThe impact of small scale embedded
generation on the operating parameters of distribution networksrdquo Department
of Trade and Industry (DTI) 2003 [Online] Available
httpwebarchivenationalarchivesgovuk20100919182407httpwwwensg
govukassets22_01_2004_phase1b_report_v10b_web_site_finalpdf
[105] 63 EDS 02-0027 Engineering design standard EDS 02-007 11 kV Triplex
Cable 2012
[106] TTH ldquo75 MVA-33-11 KV-GTP TTHrdquo 2014 [Online] Available
httpwwwtranstechtransformerscompdf75mva3311kvgtptth24012008pdf
[107] A M Tahboub V R Pandi and H H Zeineldin ldquoDistribution system
reconfiguration for annual energy loss reduction considering variable
distributed generation profilesrdquo IEEE Trans Power Deliv vol 30 no 4 pp
1677ndash1685 2015
[108] M E Baran and F F Wu ldquoNetwork reconfiguration in distribution systems
for loss reduction and load balancingrdquo Power Deliv IEEE Trans vol 4 no
2 pp 1401ndash1407 1989
[109] D Shirmohammadi and H W Hong ldquoReconfiguration of electric distribution
networks for resistive line losses reductionrdquo IEEE Trans Power Deliv vol 4
References
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no 2 pp 1492ndash1498 1989
[110] R S Rao K Ravindra K Satish and S V L Narasimham ldquoPower loss
minimization in distribution system using network reconfiguration in the
presence of distributed generationrdquo IEEE Trans Power Syst vol 28 no 1
pp 1ndash9 2012
[111] D Sudha Rani N Subrahmanyam and M Sydulu ldquoMulti-objective invasive
weed optimization - an application to optimal network reconfiguration in
radial distribution systemsrdquo Int J Electr Power Energy Syst vol 73 pp
932ndash942 2015
[112] R L Haupt and S E Haupt Practical genetic algorithms John Wiley amp
Sons 2004
[113] X S Yang and S Deb ldquoCuckoo search via Levy flightsrdquo 2009 World Congr
Nat Biol Inspired Comput NABIC 2009 - Proc pp 210ndash214 2009
[114] R N Allan R Billinton I Sjarief L Goel and K S So ldquoA reliability test
system for educational purposes-basic distribution system data and resultsrdquo
IEEE Trans Power Syst vol 6 no 2 pp 813ndash820 1991
[115] G Li and X-P Zhang ldquoModeling of plug-in hybrid electric vehicle charging
demand in probabilistic power flow calculationsrdquo Smart Grid IEEE Trans
vol 3 no 1 pp 492ndash499 2012
[116] UK Department for Transport ldquoNational Travel Survey England 2013 -
Statistical Releaserdquo no July p 26 2014
[117] A Mazza G Chicco and A Russo ldquoOptimal multi-objective distribution
system reconfiguration with multi criteria decision making-based solution
ranking and enhanced genetic operatorsrdquo Int J Electr Power Energy Syst
vol 54 pp 255ndash267 2014
[118] E Sortomme and M A El-Sharkawi ldquoOptimal charging strategies for
unidirectional vehicle-to-gridrdquo IEEE Trans Smart Grid vol 2 no 1 pp
119ndash126 2011
Page | 204
APPENDIX A Network Model Data
A1 UK generic distribution network
The line parameters given here is related to the single line diagram of the network
shown in Fig 45 which are used in the simulation study in Section 451 and 452
Table A-1 Typical configurations and parameters of 11 kV triplex cables in the UK
11 kV line type Cross
Sectional
Area
(CSA)
Positive sequence
Z
Zero-phase
sequence
Z
Approximate
Capacitance
C
Id Configuration Rph Xph R0 X0 C
(mm2) (Ωkm) (μFkm)
A Nexans
635011000
Volt Triplex
Cable
185 0415 0112 0988 0236 036
B 95 0220 0012 0530 0102 028
Appendix A Network Data
Page | 205
A2 33-bus system
Table A-2 Line and load data of 33-bus system
Branch
number
Sending end
node
Receiving end
node
R
(Ω)
X
(Ω)
P at receiving
end (kW)
Q at receiving
end (kVAr)
1 0 1 00922 0047 100 60
2 1 2 04930 02511 90 40
3 2 3 03660 01864 120 80
4 3 4 03811 01941 60 30
5 4 5 08190 07070 60 20
6 5 6 01872 06188 200 100
7 6 7 07114 02351 200 100
8 7 8 10300 07400 60 20
9 8 9 10440 07400 60 20
10 9 10 01966 00650 45 30
11 10 11 03744 01238 60 35
12 11 12 14680 11550 60 35
13 12 13 05416 07129 120 80
14 13 14 05910 05260 60 10
15 14 15 07463 05450 60 20
16 15 16 12890 17210 60 20
17 16 17 03720 05740 90 40
18 17 18 01640 01565 90 40
19 18 19 15042 13554 90 40
20 19 20 04095 04784 90 40
21 20 21 07089 09373 90 40
22 21 22 04512 03083 90 50
23 22 23 08980 07091 420 200
24 23 24 08960 07011 420 200
25 24 25 02030 01034 60 25
26 25 26 02842 01447 60 25
27 26 27 10590 09337 60 20
28 27 28 08042 07006 120 70
29 28 29 05075 02585 200 600
30 29 30 09744 09630 150 70
31 30 31 03105 03619 210 100
32 31 32 03410 05362 60 40
33 7 20 2 2 -- --
34 11 21 2 2 -- --
35 8 14 2 2 -- --
36 17 32 05 05 -- --
37 24 28 05 05 -- --
Appendix A Network Data
Page | 206
A3 69-bus system
Table A-3 Line and load data of 69-bus system
Branch
number
Sending end
node
Receiving end
node
R
(Ω)
X
(Ω)
P at receiving
end (kW)
Q at receiving
end (kVAr)
1 0 1 00005 00012 0 0
2 1 2 00005 00012 0 0
3 2 3 00015 00036 0 0
4 3 4 00251 00294 0 0
5 4 5 0366 01864 26 22
6 5 6 0381 01941 404 30
7 6 7 00922 0047 75 54
8 7 8 00493 00251 30 22
9 8 9 0819 02707 28 19
10 9 10 01872 00619 145 104
11 10 11 07114 02351 145 104
12 11 12 103 034 8 5
13 12 13 1044 0345 8 55
14 13 14 1058 03496 0 0
15 14 15 01966 0065 455 30
16 15 16 03744 01238 60 35
17 16 17 00047 00016 60 35
18 17 18 03276 01083 0 0
19 18 19 02106 0069 1 06
20 19 20 03416 01129 114 81
21 20 21 0014 00046 5 35
22 21 22 01591 00526 0 0
23 22 23 03463 01145 28 20
24 23 24 07488 02475 0 0
25 24 25 03089 01021 14 10
26 25 26 01732 00572 14 10
27 26 27 00044 00108 26 186
28 27 28 0064 01565 26 186
29 28 29 03978 01315 0 0
30 29 30 00702 00232 0 0
31 30 31 0351 0116 0 0
32 31 32 0839 02816 14 10
33 32 33 1708 05646 195 14
34 33 34 1474 04873 6 4
35 34 35 00044 00108 26 1855
36 35 36 0064 01565 26 1855
37 36 37 01053 0123 0 0
38 37 38 00304 00355 24 17
39 38 39 00018 00021 24 17
40 39 40 07283 08509 12 1
41 40 41 031 03623 0 0
Appendix A Network Data
Page | 207
42 41 42 0041 00478 6 43
43 42 43 00092 00116 0 0
44 43 44 01089 01373 3922 263
45 44 45 00009 00012 3922 263
46 45 46 00034 00084 0 0
47 46 47 00851 02083 79 564
48 47 48 02898 07091 3847 2745
49 48 49 00822 02011 3847 2745
50 49 50 00928 00473 405 283
51 50 51 03319 01114 36 27
52 51 52 0174 00886 435 35
53 52 53 0203 01034 264 19
54 53 54 02842 01447 24 172
55 54 55 02813 01433 0 0
56 55 56 159 05337 0 0
57 56 57 07837 0263 0 0
58 57 58 03042 01006 100 72
59 58 59 03861 01172 0 0
60 59 60 05075 02585 1244 888
61 60 61 00974 00496 32 23
62 61 62 0145 00738 0 0
63 62 63 07105 03619 227 162
64 63 64 1041 05302 59 42
65 64 65 02012 00611 18 13
66 65 66 00047 00014 18 13
67 66 67 07394 02444 28 20
68 67 68 00047 00016 28 20
69 49 58 2 1 -- --
70 26 64 1 05 -- --
71 12 20 05 05 -- --
72 10 42 05 05 -- --
73 14 45 1 05 -- --
A4 RBTS Bus 4 system
Table A-4 Feeder data of RBTS Bus 4
Feeder
Type
Length
(km)
Feeder section number
1 060 2 6 10 14 17 21 25 28 30 34 38 41 43 46 49 51 55 58 61 64 67
68 69 70 71
2 075 1 4 7 9 12 16 19 22 24 27 29 32 3537 40 42 45 48 50 53 56 60
63 65
3 080 3 5 8 11 13 15 18 20 23 26 31 33 36 3944 47 52 54 57 59 62 66
Appendix A Network Data
Page | 208
Table A-5 Reliability Data for RBTS Bus 4
Equipment λA λP λM λt R RM
Lines 004 0 0 0 5 0
Buses 0001 0 1 001 2 8
Switches 0004 0002 1 006 4 72
Distribution Transformers 0015 0 1 0 200 120
λA Active failure rate in (fryrkm) for lines and (fryr) for other components
λP Passive failure rate in (fryrkm) for lines and (fryr) for other components
λM Maintenance outage rate in (fryrkm) for lines and (fryr) for other components
λP Transient failure rate in (fryrkm) for lines and (fryr) for other components
R Repair time of failures in (hr)
RM Maintenance outage time in (hr)
Page | 209
APPENDIX B Simulation Results
B1 Simulation results of Chapter 4
B11Tie-switch location
As discussed in Section 452 the location of tie-switch in Scenario 9 is changeable
and the relevant results are presented in Table B-1 It can be clearly seen that the
NOP is located in lsquoTW1rsquo between 0730 and 1000 1600 and 1630 while in lsquoTW5rsquo
for the rest of the day
Table B-1 The locations of tie-switch in Scenario 9
Time Loc Time Loc Time Loc Time Loc Time Loc Time Loc
0000 TW5 0400 TW5 0800 TW1 1200 TW5 1600 TW1 2000 TW5
0010 TW5 0410 TW5 0810 TW1 1210 TW5 1610 TW1 2010 TW5
0020 TW5 0420 TW5 0820 TW1 1220 TW5 1620 TW1 2020 TW5
0030 TW5 0430 TW5 0830 TW1 1230 TW5 1630 TW1 2030 TW5
0040 TW5 0440 TW5 0840 TW1 1240 TW5 1640 TW5 2040 TW5
0050 TW5 0450 TW5 0850 TW1 1250 TW5 1650 TW5 2050 TW5
0100 TW5 0500 TW5 0900 TW1 1300 TW5 1700 TW5 2100 TW5
0110 TW5 0510 TW5 0910 TW1 1310 TW5 1710 TW5 2110 TW5
0120 TW5 0520 TW5 0920 TW1 1320 TW5 1720 TW5 2120 TW5
0130 TW5 0530 TW5 0930 TW1 1330 TW5 1730 TW5 2130 TW5
0140 TW5 0540 TW5 0940 TW1 1340 TW5 1740 TW5 2140 TW5
0150 TW5 0550 TW5 0950 TW1 1350 TW5 1750 TW5 2150 TW5
0200 TW5 0600 TW5 1000 TW1 1400 TW5 1800 TW5 2200 TW5
0210 TW5 0610 TW5 1010 TW5 1410 TW5 1810 TW5 2210 TW5
0220 TW5 0620 TW5 1020 TW5 1420 TW5 1820 TW5 2220 TW5
0230 TW5 0630 TW5 1030 TW5 1430 TW5 1830 TW5 2230 TW5
0240 TW5 0640 TW5 1040 TW5 1440 TW5 1840 TW5 2240 TW5
0250 TW5 0650 TW5 1050 TW5 1450 TW5 1850 TW5 2250 TW5
0300 TW5 0700 TW5 1100 TW5 1500 TW5 1900 TW5 2300 TW5
0310 TW5 0710 TW5 1110 TW5 1510 TW5 1910 TW5 2310 TW5
0320 TW5 0720 TW5 1120 TW5 1520 TW5 1920 TW5 2320 TW5
0330 TW5 0730 TW1 1130 TW5 1530 TW5 1930 TW5 2330 TW5
0340 TW5 0740 TW1 1140 TW5 1540 TW5 1940 TW5 2340 TW5
0350 TW5 0750 TW1 1150 TW5 1550 TW5 1950 TW5 2350 TW5
Appendix B Simulation Results
Page | 210
B12 Voltage variations
For Test Case 2 in Section 452 the detailed voltage values of the mean and the
corresponding 95th
profiles at each node in the linked feeder are recorded in Table
B-2 and Table B-3
Table B-2 Mean voltage profiles at each node in the linked feeder
Node
No
Scenarios
S1 S2 S3 S4 S5 S6 S7 S8 S9
A4_1 09675 09787 09787 09766 09859 09859 09748 09825 09815
A4_2 09676 09784 09784 09766 09856 09856 09748 09822 09813
A4_3 09677 09782 09782 09767 09854 09854 09749 09819 09811
A4_4 09678 09780 09780 09768 09851 09851 09750 09817 09810
A4_5 09681 09777 09777 09771 09849 09849 09753 09814 09808
A4_6 09685 09775 09775 09775 09846 09846 09757 09812 09807
A4_7 09689 09773 09773 09779 09845 09845 09762 09811 09807
A4_8 09694 09772 09772 09784 09844 09844 09767 09810 09807
B4_8 09700 09772 09772 09790 09844 09844 09773 09810 09808
B4_7 09707 09773 09773 09797 09845 09845 09779 09811 09810
B4_6 09714 09775 09775 09804 09846 09846 09787 09812 09813
B4_5 09722 09777 09777 09813 09849 09849 09795 09814 09816
B4_4 09731 09780 09780 09821 09851 09851 09804 09817 09820
B4_3 09737 09782 09782 09827 09854 09854 09809 09819 09823
B4_2 09743 09784 09784 09833 09856 09856 09815 09822 09826
B4_1 09749 09787 09787 09839 09859 09859 09821 09825 09830
Table B-3 95th
voltage profiles at each node in the linked feeder
Node
No
Scenarios
S1 S2 S3 S4 S5 S6 S7 S8 S9
A4_1 09352 09573 09573 09537 09721 09721 09537 09721 09715
A4_2 09353 09567 09567 09537 09715 09715 09537 09715 09709
A4_3 09355 09562 09562 09539 09711 09711 09539 09711 09704
A4_4 09357 09558 09558 09541 09707 09707 09541 09707 09702
A4_5 09363 09553 09553 09547 09701 09701 09547 09701 09679
A4_6 09370 09548 09548 09555 09697 09697 09555 09697 09694
A4_7 09379 09545 09545 09563 09694 09694 09563 09794 09691
A4_8 09389 09544 09544 09573 09692 09692 09573 09792 09692
B4_8 09400 09544 09544 09585 09692 09692 09585 09792 09692
B4_7 09413 09545 09545 09598 09694 09694 09598 09794 09694
B4_6 09427 09548 09548 09613 09697 09697 09613 09697 09697
B4_5 09443 09553 09553 09628 09701 09701 09628 09701 09701
B4_4 09460 09558 09558 09646 09707 09707 09646 09707 09707
Appendix B Simulation Results
Page | 211
B4_3 09471 09562 09562 09656 09711 09711 09656 09711 09711
B4_2 09482 09567 09567 09668 09715 09715 09668 09715 09715
B4_1 09494 09573 09573 09680 09721 09721 09680 09721 09721
B2 Simulation results of Chapter 5
The network losses in each branch for all test cases of 33-bus system and 69-bus
system are listed in Table B-4 and Table B-5 respectively
Table B-4 Network losses in each branch of 33-bus system
Branch number Feeder loss (kW)
Case I Case II Case III Case IV
1 1227 1189 1010 1003
2 5192 2686 2051 2060
3 1995 756 112 490
4 1874 667 074 415
5 3833 1321 122 807
6 192 006 006 006
7 484 0 0 0
8 418 124 211 124
9 357 0 0 0
10 055 001 001 001
11 088 003 003 003
12 267 045 045 045
13 073 008 008 008
14 036 0 0 0
15 028 045 092 045
16 025 048 115 048
17 003 007 022 007
18 016 226 232 226
19 083 1809 1859 1808
20 01 424 436 423
21 004 118 071 118
22 319 316 914 315
23 516 512 1618 510
24 129 128 869 128
25 26 224 005 124
26 334 285 003 155
27 1133 962 003 510
28 786 664 0 345
29 391 326 199 159
30 160 110 018 003
Appendix B Simulation Results
Page | 212
31 021 012 0 000
32 001 0 013 0
33 0 563 809 563
34 0 215 215 215
35 0 174 320 174
36 0 002 033 002
37 0 0 263 0
Total 20314 13981 11753 10844
Table B-5 Network losses in each branch of 69-bus system
Branch number Feeder loss (kW)
Case I Case II Case III Case IV
1 008 007 006 006
2 008 007 006 006
3 020 012 012 010
4 194 011 011 011
5 2829 159 155 159
6 2939 164 160 164
7 691 035 034 035
8 338 012 012 012
9 477 143 137 142
10 101 029 027 028
11 219 032 030 032
12 128 000 000 000
13 124 000 0 000
14 120 0 000 0
15 022 083 043 083
16 032 138 067 138
17 000 001 001 001
18 010 080 032 080
19 007 052 021 052
20 011 083 033 083
21 000 003 001 002
22 001 022 006 022
23 001 049 013 049
24 001 091 021 091
25 000 037 009 037
26 000 019 004 019
27 000 000 000 000
28 000 000 000 000
29 001 001 001 001
30 000 000 000 000
31 001 001 001 001
Appendix B Simulation Results
Page | 213
32 001 001 001 001
33 001 001 001 001
34 000 000 000 000
35 000 003 001 003
36 001 041 019 041
37 002 064 028 064
38 000 018 008 018
39 000 001 000 001
40 005 391 161 391
41 002 166 068 166
42 000 022 009 022
43 000 005 002 005
44 001 057 023 057
45 000 000 000 000
46 002 017 017 013
47 058 416 416 316
48 164 1321 1321 991
49 012 253 253 178
50 000 000 000 000
51 000 000 000 000
52 580 001 001 001
53 673 001 001 000
54 916 000 000 000
55 882 0 0 0
56 4986 000 000 000
57 2458 000 000 000
58 954 000 000 000
59 1071 627 626 379
60 1408 824 823 498
61 011 0 0 0
62 014 000 000 000
63 066 001 001 001
64 004 071 069 071
65 000 000 000 000
66 000 000 000 000
67 002 002 002 002
68 000 000 000 000
69 0 3783 3782 2384
70 0 102 052 102
71 0 0 0 0
72 0 0 0 0
73 0 423 252 423
Total 22562 9885 8758 7397
Appendix B Simulation Results
Page | 214
B3 Simulation results of Chapter 8
Table B-6 Pareto optimal solutions of multi-objective DNR (loss ECOST and SAIDI)
Tie-switches location Feeder loss (kW) ECOST ($yr) SAIDI
(hrscustomeryr)
70 68 71 69 321415 4640359 130895231648616
70 10 41 54 364131 431068083000 102819629963899
17 10 41 70 354092 411445783000000 105858799638989
17 26 10 70 383269 530285525000000 0968805806257521
7 26 54 69 435225 578907612000000 0825265794223827
7 54 41 69 406035 460067870000000 0915047984356197
7 26 54 70 442913 571756512000000 0836828971119134
17 10 71 70 345231 439663189000000 106361687725632
70 10 71 69 331470 443747189000000 110465057160048
70 10 41 69 340330 415529783000000 109962169073406
70 68 41 69 330274 435818516000000 130392343561974
7 54 71 69 397170 488285276000000 0920076865222623
41 10 54 69 356448 438219183000000 101663312274368
70 10 54 26 393311 549907825000000 0938414109506619
70 7 71 69 381047 465595876000000 100306543321300
70 7 41 17 403678 433294470000000 0957002858002407
70 10 54 71 355269 459285489000000 103322518050542
7 54 71 70 404856 481134176000000 0931640042117930
7 26 17 70 432867 552134212000000 0867220667870036
7 70 41 69 389911 437378470000000 0998036552346570
7 26 69 70 419096 556218212000000 0908254362214200
17 7 71 70 394813 461511876000000 0962031738868833
71 10 54 69 347586 466436589000000 102166200361011
10 26 54 69 385625 557058925000000 0926850932611312
70 26 10 69 369504 534369525000000 100983950060168
7 54 41 70 413721 452916770000000 0926611161251504
Appendix B Simulation Results
Page | 215
B4 Simulation results of Chapter 9
Table B-7 Pareto optimal solutions of multi-objective DNR (loss maximum node voltage deviation
feeder load balancing index) for 33-bus system in Case II
Tie-switches location Feeder loss
(kW)
Maximum node
Voltage deviation
Feeder load
balancing index
7 34 35 31 37 176962 0108696024464801 00228687361961248
7 11 35 32 28 143474 00613272038422790 00305387759787611
7 9 14 31 37 142477 00768537372742428 00252628392269486
6 8 12 36 37 151849 00696765908940439 00259144961258893
7 8 14 31 37 155399 00924077518455773 00239781364880477
6 8 12 31 37 169382 0104485611067200 00236077543160956
6 8 12 32 37 152876 00776641110366926 00250547432924683
33 8 14 30 37 171441 0108063061643879 00230652089068052
7 9 14 32 28 140261 00604355611623940 00310349101268755
7 11 35 32 37 143028 00639069227083702 00273727965037185
6 8 14 31 37 159752 00968913958755809 00236540473688646
6 33 35 32 37 170278 00826562726566354 00249194843739843
6 11 35 32 37 144683 00656445815841987 00261947314082027
6 8 14 32 37 146983 00705648561488426 00256096967694280
7 9 14 32 37 139815 00639015456844128 00280407351785895
6 9 14 32 37 143097 00625183468485540 00270001779728268
7 11 35 31 37 148829 00852978398065017 00245113845932977
7 34 35 30 37 202483 0130888991378581 00223050578905545
6 8 14 36 37 146991 00643933147100736 00266176555168500
6 11 35 31 37 154281 00897759906819439 00242838273201709
6 8 13 32 37 150430 00753226918458818 00253604605496161
Table B-8 Pareto optimal solutions of multi-objective DNR (loss maximum node voltage deviation
feeder load balancing index) for 33-bus system in Case III
Tie-switches location Feeder loss
(kW)
Maximum node
Voltage deviation
Feeder load
balancing index
7 14 8 32 28 121696 00575193535569366 00264544805354717
7 11 35 31 37 123007 00712785797883380 00213250141648472
6 12 8 32 37 128324 00630309398395457 00223824361844486
6 14 8 30 37 145672 0101299721228755 00194921779245086
7 33 35 32 28 130184 00583420082867310 00261406698684195
7 14 8 30 37 140274 00967924815464314 00195001911353607
7 21 35 30 37 164190 0113945920950777 00189031534924873
6 13 8 32 37 126434 00607661484850486 00227035446761735
7 14 9 32 28 117726 00575130414815478 00271215548731366
Appendix B Simulation Results
Page | 216
6 14 8 32 28 125920 00566904604559002 00265195832133384
6 12 8 31 37 137974 00889877482038002 00200083704114662
7 11 35 30 37 133030 00891516445489180 00199682922816912
6 11 35 32 37 123013 00593840879899440 00235298833627789
7 14 9 32 37 121070 00631040005210335 00255168322432724
6 14 9 32 28 123916 00566872316455769 00273594084038335
7 14 9 30 37 126587 00812324184971598 00206873922472966
7 14 9 31 28 117529 00642736861104275 00240537048868074
6 14 9 32 37 122047 00593825021727904 00240927348267257
6 11 35 32 28 124883 00566888115014094 00269082055980326
6 11 35 31 37 126802 00756552348586014 00207586957663036
6 14 8 32 37 124050 00593857418451058 00230337877365745
7 13 8 32 28 124039 00575225874614865 00262247242500743
7 11 35 32 28 119522 00575159230231156 00267430211390231
7 14 9 31 37 118759 00642740886891275 00220228862077971
6 14 8 31 37 130316 00816654599427028 00201908840890301
33 14 8 30 37 140110 00923831702765571 00197570883486903
7 12 8 32 28 125895 00587758838819431 00259864524009700
6 13 8 31 37 134936 00865715938530326 00201790772057552
Table B-9 Pareto optimal solutions of multi-objective DNR (loss maximum node voltage deviation
feeder load balancing index) for 33-bus system in Case IV
Tie-switches location DG location Feeder
loss
(kW)
Maximum node
Voltage deviation
Feeder load
balancing index
7 9 14 30 37 15 17 16 112506 00655990339384582 00207847799664288
6 8 14 31 37 14 11 15 120818 00728143829651942 00199639595336255
7 11 35 30 37 16 16 12 118637 00756705031931788 00198888055963062
6 8 14 31 37 11 29 14 125736 00822955381260978 00194988443664523
6 11 35 32 37 29 11 29 116999 00602917954784902 00213598898907595
7 9 14 31 37 15 14 16 110931 00518306996442978 00223689972435171
7 34 35 30 37 16 13 13 140652 00983575865184194 00182688360250883
7 8 14 30 37 14 11 15 128617 00876913785424229 00190954012999288
7 8 14 30 37 11 16 14 127141 00860397262006276 00191601352391895
7 9 14 36 37 30 30 29 109157 00520335391274761 00229564125698243
7 8 14 30 37 10 14 16 126706 00857230143750372 00192117850059117
7 11 35 30 37 13 16 12 121130 00786215737441328 00196617519208137
7 34 35 30 37 13 10 9 151352 0106960621828031 00178195736666725
7 34 35 30 37 10 12 9 152310 0107688512235453 00178046268710843
6 8 14 30 37 11 15 16 130550 00897068798318073 00189590122249633
6 8 14 30 37 16 14 10 130869 00901533044670202 00189271311922809
7 34 35 30 37 10 13 12 148089 0104837492639545 00178736074180585
Appendix B Simulation Results
Page | 217
7 34 35 30 37 13 11 16 143317 0100615335666250 00181553323058751
6 8 14 30 37 10 14 14 133299 00925968739633617 00188139999335965
7 34 35 30 37 13 9 12 148392 0105013682219175 00178453713901855
6 8 14 30 37 14 11 10 137593 00963962506644021 00186232592604301
6 8 14 30 37 11 8 14 136046 00951731865531927 00187106569470356
6 8 14 30 37 11 11 16 135639 00942616575802945 00187170876179048
7 8 14 30 37 15 16 14 122935 00815907052491111 00195198923102276
7 34 35 30 37 12 14 16 140640 00983915740315128 00182784576692257
6 33 35 31 37 11 11 13 146017 00888852225316270 00188548348595259
7 34 35 30 37 12 16 12 142144 00997534014352579 00181578155086060
6 8 14 30 37 14 11 15 132819 00921338781311946 00188143081376993
6 8 14 30 37 10 15 11 136651 00956093119043262 00186781475357014
7 9 14 31 37 14 14 16 111382 00525319705640723 00222591386298574
7 34 35 30 37 13 14 16 139957 00977014014811679 00183484070331887
7 34 35 30 37 12 15 16 139849 00976123852270839 00183745698300515
7 34 35 30 37 12 16 16 138589 00959671533698319 00184842191427931
7 34 35 30 37 16 13 16 137912 00952795751906571 00185525366651277
6 33 35 31 37 11 11 11 148785 00910856464605774 00187751047204272
7 34 35 30 37 12 16 13 141338 00990484927061306 00181980491991251
7 34 35 30 37 12 13 12 145536 0102926179499332 00179590185768212
6 8 14 30 37 14 10 15 132373 00918145642214576 00188660639598312
6 8 14 30 37 16 11 14 131312 00904718190224125 00188759872087077
7 34 35 30 37 13 15 16 139168 00969230570394858 00184436609617936
7 34 35 30 37 13 9 11 150730 0106620666560267 00178315514588942
6 8 14 30 37 14 11 14 133746 00929165522686308 00187615074100094
7 34 35 30 37 9 9 12 152656 0107867658396772 00178031242058681
6 8 14 30 37 10 11 16 135118 00939381882085281 00187414815201857
7 34 35 30 37 12 12 9 149341 0105739135263959 00178316539838164
7 9 14 36 28 32 32 32 110385 00489797931328652 00256323647901629
7 9 14 36 37 32 31 31 108599 00498935433820196 00235262740306846
7 9 14 32 37 31 30 31 108436 00537552050723257 00227898958267559
7 9 14 36 28 32 31 31 110203 00489682960875768 00259015702487973
7 34 35 30 37 8 12 9 154427 0108962750550623 00178021823053241
Appendix B Simulation Results
Page | 218
Table B-10 Pareto optimal solutions of multi-objective DNR (loss maximum node voltage deviation
feeder load balancing index) for 69-bus system in Case II
Tie-switches location Feeder loss
(kW)
Maximum node
Voltage deviation
Feeder load
balancing index
55 61 71 72 12 99036 00524391619987274 00196366946903149
69 61 71 9 14 145213 00664127006601768 00185315761508749
55 61 71 72 14 98845 00524393494628415 00194882148961848
69 70 71 10 14 145135 00666490251240782 00182871906896542
69 61 71 72 12 150267 00699556148777123 00161708619074924
55 61 71 10 14 104521 00524349487665904 00238104755589364
69 61 71 72 13 150383 00700225094171628 00161512783956020
55 61 71 72 13 98937 00524392488739880 00195710324132613
69 61 71 72 11 150792 00682108082577803 00171029450547815
55 61 71 9 14 105348 00524349082167884 00242117051986541
69 61 71 72 14 150513 00700911373758199 00161129748303495
55 61 71 72 11 105195 00524380932334678 00218572363716938
Table B-11 Pareto optimal solutions of multi-objective DNR (loss maximum node voltage deviation
feeder load balancing index) for 69-bus system in Case III
Tie-switches location Feeder loss
(kW)
Maximum node
Voltage deviation
Feeder load
balancing index
55 61 12 14 9 97461 00523081449765275 00226112450860475
69 61 71 14 9 130761 00662843002557533 00155527078006889
55 61 71 14 7 97263 00523080911134007 00226177446060770
55 61 12 71 72 87588 00523152959484715 00174558059214037
55 61 71 14 8 93176 00523082195004728 00211109499855264
55 61 71 13 72 87581 00523154440245970 00174392153380541
55 61 12 14 72 87755 00523153511186373 00174538759436512
55 61 12 71 7 97289 00523080869366065 00226232791264600
69 61 71 11 9 134009 00662855052002667 00154463391981039
69 61 12 14 9 130989 00662843776081034 00155381836375260
55 61 71 13 7 97273 00523080879708534 00227249951330579
55 61 71 14 9 90907 00523086904216601 00201865894567423
55 61 71 14 10 90291 00523088955157064 00199034032147027
69 61 71 14 10 130894 00665207578684145 00154263271797149
55 61 71 14 72 87582 00523156072908145 00174100597226583
69 61 71 11 10 134197 00665220013747228 00153401360203180
69 61 71 11 72 136858 00680828895070073 00147368269784675
69 61 12 14 10 131126 00665208386694061 00154135530565384
55 61 71 11 72 91274 00523126048676607 00184393848480773
Appendix B Simulation Results
Page | 219
Table B-12 Pareto optimal solutions of multi-objective DNR (loss maximum node voltage deviation
feeder load balancing index) for 69-bus system in Case IV
Tie-switches location DG location Feeder
loss
(kW)
Maximum node
Voltage deviation
Feeder load
balancing index
69 63 71 10 14 60 60 60 105879 00543213716422435 00153740505896722
69 63 12 72 71 60 62 62 109324 00575466375767690 00126779733811642
55 61 71 72 11 60 60 60 80324 00429183191505871 00183159151221229
69 63 12 72 71 61 61 62 109323 00575465740537586 00126842028893447
55 61 71 72 12 60 60 60 74165 00429193759769601 00159264876998350
69 63 14 10 71 62 62 62 106070 00543012249613587 00150279825984642
69 63 11 72 71 60 62 60 110547 00558290844078126 00139841427388105
69 63 14 9 71 62 62 62 106271 00540689205567605 00153025056850459
69 61 71 72 11 60 60 60 108838 00542584369620998 00141625735067141
55 61 71 72 14 60 56 60 75837 00436673338725839 00157367114339890
69 63 14 10 71 62 62 60 105960 00542966739560918 00151430448212008
69 61 71 10 14 60 60 60 104307 00527268149576859 00155323687715422
69 63 11 72 71 61 62 62 110652 00558333983851442 00137892112215884
69 63 13 72 71 62 62 62 109522 00576169823075075 00125440050970194
55 61 71 72 14 60 55 60 75975 00436701836501366 00156758120818947
69 63 71 10 14 60 60 62 105896 00542940500362948 00152768514567046
69 63 14 9 71 62 61 61 106159 00540643102892876 00154245882374843
55 61 71 72 13 60 60 60 74066 00429194617185072 00158554987038681
69 62 71 10 14 61 60 60 105886 00542959390978505 00153513700764165
69 63 14 72 71 62 62 62 109622 00576844280930477 00125002240983144
55 63 71 72 14 62 61 62 74382 00440379610790336 00155858821619573
69 63 71 72 11 60 60 60 110530 00558564471048234 00140822204796308
55 63 71 72 14 60 60 62 74285 00440350644694274 00157371695186626
55 63 14 72 71 62 62 62 74448 00440399072962552 00155438948075735
55 63 71 72 14 60 62 62 74344 00440368353288504 00156312863856681
69 63 71 9 14 60 61 60 105882 00542934725670071 00153515485666183
55 63 71 72 14 60 61 62 74305 00440356668532606 00156816031788752
55 61 20 72 13 60 60 60 80533 00429326269571468 00157463174391893
55 63 71 72 14 61 61 62 74343 00440367927398261 00156346520711234
69 61 71 72 14 60 60 60 107187 00561022028435777 00126909641069497
69 63 71 72 11 60 61 60 110533 00558285040786375 00140595150870697
69 63 12 72 71 62 62 62 109436 00575512407997617 00125707103016452
69 63 14 10 71 61 62 62 106000 00542983427485794 00150838099664421
69 63 11 72 71 60 61 62 110569 00558299818740340 00139149694834405
69 63 14 9 71 61 62 60 106118 00540626433897020 00154840963668230
69 61 71 72 12 60 60 60 107041 00559693311798567 00127785892138089
55 61 71 72 14 60 60 60 73974 00429195606297569 00157682511572302
69 63 14 10 71 61 61 62 105958 00542966109653011 00151492343922130
69 63 12 72 71 62 62 61 109365 00575483243249972 00126225992147273
Appendix B Simulation Results
Page | 220
69 63 11 72 71 62 62 60 110611 00558317226735644 00138490567525274
69 63 14 9 71 62 62 61 106201 00540660395254129 00153587525958041
69 63 14 10 71 61 60 62 105917 00542949434469265 00152083287358888
69 63 14 9 71 62 62 60 106160 00540643732226493 00154184014811756
69 63 11 72 71 61 61 62 110610 00558316590719640 00138552654427231
69 63 71 72 11 62 62 62 110723 00558362979744786 00137328015545176
69 61 71 72 13 60 60 60 107108 00560349171634668 00127435051911921
Page | 221
APPENDIX C Control Parameters of
Algorithms
C1 Control parameters of ACO algorithm in Chapter 5
Table C-1 ACO parameters for distribution network reconfiguration and DG allocation in Test Case
2amp3
Parameter Value
Number of ants 50
Maximum number of iteration 200
Pheromone evaporation rate 120530 03
Higher bound of pheromone level 120533119846119834119857 1
Lower bound of pheromone level 120533119846119842119847 001
Constant accumulation number 120533119836 0002
Table C-2 ACO parameters for distribution network reconfiguration and DG allocation in Test Case 4
Parameter Value
Number of ants 100
Maximum number of iteration 500
Pheromone evaporation rate 120530 03
Higher bound of pheromone level 120533119846119834119857 1
Lower bound of pheromone level 120533119846119842119847 001
Constant accumulation number 120533119836 0002
C2 Control parameters of ACO algorithm in Chapter 6
Table C-3 ACO parameters for distribution network reconfiguration and transformer economic
operation
Parameter Value
Number of ants 150
Maximum number of iteration 500
Pheromone evaporation rate 120530 03
Higher bound of pheromone level 120533119846119834119857 1
Lower bound of pheromone level 120533119846119842119847 001
Constant accumulation number 120533119836 0002
Appendix C Control Parameters of Algorithms
Page | 222
C3 Control parameters of ACO algorithm in Chapter 7
Table C-4 ACO parameters for sectionalising switch placement in Test Case 1
Parameter Value
Number of ants 400
Maximum number of iteration 400
Pheromone evaporation rate 120530 04
Higher bound of pheromone level 120533119846119834119857 1
Lower bound of pheromone level 120533119846119842119847 001
Constant accumulation number 120533119836 0002
Table C-5 ACO parameters for sectionalising switch placement in Test Case 2amp3
Parameter Value
Number of ants 500
Maximum number of iteration 200
Pheromone evaporation rate 120530 01
Higher bound of pheromone level 120533119846119834119857 1
Lower bound of pheromone level 120533119846119842119847 001
Constant accumulation number 120533119836 0002
C4 Control parameters of MOACO and AIS-ACO algorithm in
Chapter 8
Table C-6 MOACO parameters for multi-objective distribution network reconfiguration (loss
ECOST and SAIDI)
Parameter Value
Number of ants 100
Maximum number of iteration 100
Pheromone evaporation rate 120530 01
Higher bound of pheromone level 120533119846119834119857 1
Lower bound of pheromone level 120533119846119842119847 001
Constant accumulation number 120533119836 0002
Appendix C Control Parameters of Algorithms
Page | 223
Table C-7 AIS-ACO parameters for multi-objective distribution network reconfiguration (loss
ECOST and SAIDI)
Parameter Value
Maximum number of iteration 50
Pheromone evaporation rate 120530 01
Higher bound of pheromone level 120533119846119834119857 1
Lower bound of pheromone level 120533119846119842119847 001
Constant accumulation number 120533119836 0002
C5 Control parameters of ACO and AIS-ACO algorithm in
Chapter 9
Table C-8 ACO parameters for multi-objective DNR (loss maximum node voltage deviation feeder
load balancing index)
Parameter Value
Number of ants 200
Maximum number of iteration 800
Pheromone evaporation rate 120530 03
Higher bound of pheromone level 120533119846119834119857 1
Lower bound of pheromone level 120533119846119842119847 001
Constant accumulation number 120533119836 0002
Table C-9 AIS-ACO parameters for multi-objective DNR (loss maximum node voltage deviation
feeder load balancing index)
Parameter Value
Maximum number of iteration 3000
Pheromone evaporation rate 120530 01
Higher bound of pheromone level 120533119846119834119857 1
Lower bound of pheromone level 120533119846119842119847 001
Constant accumulation number 120533119836 0002
Page | 224
APPENDIX D List of Publications
1 B Zhang and P A Crossley ldquoMinimum transformer losses based on transformer
economic operation and optimized tie-switches placementrdquo in Proceedings of the 6th
International Conference on Advanced Power System Automation and Protection
(APAP) pp 1-7 20-25 September 2015
2 B Zhang and P A Crossley ldquoReliability improvement using ant colony
optimization applied to placement of sectionalizing switchesrdquo in Proceedings of the
9th
International Conference on Applied Energy (ICAE) pp 1-7 21-24 August 2017
3 B Zhang and P A Crossley ldquoMinimization of distribution network loss using
ant colony optimization applied to transformer economic operation and relocation of
tie-switchesrdquo to be submitted to IEEE Transactions on Smart Grid
4 B Zhang and PA Crossley ldquoOptimized sectionalising switch placement for
reliability improvement in distribution systemsrdquo to be submitted to IEEE
Transactions on Power Delivery
5 B Zhang and P A Crossley ldquoAn ant colony optimization ndashbased method for
multi-objective distribution system reconfigurationrdquo in Proceedings of the 14th
International Conference on Developments in Power System Protection (DPSP) pp
1-6 12-15 March 2018
Page | 2
List of Contents
List of Contents 2
List of Figures 7
List of Tables 10
List of Abbreviations 14
Abstract 16
Declaration 17
Copyright Statement 18
Acknowledgements 19
CHAPTER 1 20
INTRODUCTION 20
11 Motivation 20
12 Objectives 22
13 Contribution of the work 23
14 Structure of the thesis 25
CHAPTER 2 28
DISTRIBUTION AUTOMATION 28
21 Introduction 28
22 Distribution Network Configurations 29
23 Switchgear for Distribution Network 30
231 Reclosers 30
232 Sectionalising Switches 31
233 Tie-switches 31
24 Transformer Economic Operation 31
241 Basic Concepts 31
242 Literatures on Transformer Economic Operation 33
25 Distribution Network Reconfiguration 35
251 Basic Concepts 35
252 Literatures on Distribution Network Reconfiguration 36
26 Placement of Sectionalising Switches 38
261 Basic Concepts 38
262 Literatures on Sectionalising Switch Placement 41
Page | 3
27 Transformer Loss Assessment 42
271 Operating Principles 42
272 Transformer Quantities Measurement 43
273 Integrated Transformer Loss 46
28 Feeder Loss Assessment 47
29 Reliability Evaluation 48
291 Reliability Indices 48
292 Reliability Evaluation Methods 50
210 Multi-objective Optimisation 53
2101 Single Objective Function 54
2102 Single Fuzzy Satisfaction Objective Function 54
2103 Multi-objective Formulation in the Pareto Optimality Framework 56
211 Summary 58
CHAPTER 3 60
OPTIMISATION TECHNIQUES 60
31 Introduction 60
32 Monte Carlo Method 61
33 Ant Colony Optimisation 62
34 AIS-ACO Hybrid Algorithm 65
341 Artificial Immune Systems 65
342 Proposed AIS-ACO Hybrid Algorithm 66
35 Summary 68
CHAPTER 4 70
TRANSFORMER ECONOMIC OPERATION amp DISTRIBUTION NETWORK
RECONFIGURATION FOR TRANSFORMER LOSS REDUCTION 70
41 Introduction 70
42 Load Model 72
43 Problem Formulation 73
44 Methodology 73
441 Transformer Economic Operation 73
442 Distribution Network Reconfiguration 76
45 Application Studies 77
451 Test Case 1 77
452 Test Case 2 85
Page | 4
46 Summary 90
CHAPTER 5 92
DISTRIBUTION NETWORK RECONFIGURATION amp DG ALLOCATION FOR
FEEDER LOSS REDUCTION 92
51 Introduction 92
52 Problem Formulation 93
53 Solution Method 94
531 Distribution Network Reconfiguration 94
532 Applying ACO to DNR and DGs Placement 95
54 Application Studies 99
541 33-bus System 99
542 69-bus System 105
55 Summary 109
CHAPTER 6 111
DISTRIBUTION NETWORK RECONFIGURATION amp TRANSFORMER
ECONOMIC OPERATION FOR NETWORK LOSS REDUCTION 111
61 Introduction 111
62 Time-varying Load Model 112
63 Problem Formulation 113
64 Applying ACO to DNR and TEO 114
65 Application Studies 118
651 Test Case 1 122
652 Test Case 2 123
653 Test Case 3 124
66 Summary 126
CHAPTER 7 128
OPTIMAL PLACEMENT OF SECTIONALISING SWITCHES FOR
RELIABILITY IMPROVEMENT 128
71 Introduction 128
72 Problem Formulation 129
721 Weighted Aggregation 129
722 Single Fuzzy Satisfaction Objective Function with Two Parameters 130
723 Single Fuzzy Satisfaction Objective Function with Three Parameters 131
Page | 5
724 Evaluation of ECOST 132
725 Evaluation of SAIDI 133
726 Evaluation of Switch Costs 133
73 Applying ACO to Sectionalising Switch Placement Problem 134
74 Benefit-to-cost Analysis 135
75 Application Studies 136
751 Test Case 1 138
752 Test Case 2 147
753 Test Case 3 147
76 Summary 148
CHAPTER 8 150
DISTRIBUTION NETWORK RECONFIGURATION FOR LOSS REDUCTION amp
RELIABILITY IMPROVEMENT 150
81 Introduction 150
82 Problem Formulation 152
821 Multi-objective Reconfiguration Problem 152
822 Best Compromise Solution 153
83 Solution Methodology 154
831 Applying MOACO to Multi-objective DNR Problem 154
832 Applying AIS-ACO to Multi-objective DNR Problem 158
84 Application Studies 161
85 Best Compromise Solution 163
86 Summary 164
CHAPTER 9 166
MULTI-OBJECTIVE DISTRIBUTION NETWORK RECONFIGURATION amp DG
ALLOCATION CONSIDERING LOSS VOLTAGE DEVIATION AND LOAD
BALANCING 166
91 Introduction 166
92 Problem Formulation 168
921 Single Fuzzy Satisfaction Objective Function 168
922 Multi-objective Reconfiguration Problem Using Pareto Optimality 170
93 Solution methodology 171
931 Applying ACO to DNR and DG Allocation in the Fuzzy Domain 171
932 Applying AIS-ACO to Multi-objective DNR and DG Allocation Using
Pareto Optimality 171
Page | 6
94 Application Studies 171
941 33-bus System 172
942 69-bus System 180
95 Summary 187
CHAPTER 10 189
CONCLUSION amp FUTURE WORK 189
101 Conclusion 189
102 Future Work 193
References 195
APPENDIX A Network Model Data 204
APPENDIX B Simulation Results 209
APPENDIX C Control Parameters of Algorithms 221
APPENDIX D List of Publications 224
Word count 51012
Page | 7
List of Figures
Fig 2-1 Typical Distribution network [27] 29
Fig 2-2 Recloser operation 30
Fig 2-3 Transformer loss versus transformer load 32
Fig 2-4 Daily load curve of a typical substation before and after load smoothing [38]
34
Fig 2-5 Radial test system 35
Fig 2-6 Fully automated distribution feeder 40
Fig 2-7 Partially automated distribution feeder 41
Fig 2-8 Elements of a single phase transformer [33] 43
Fig 2-9 Construction of a three-phase transformer [33] 43
Fig 2-10 The open-circuit test [33] 44
Fig 2-11 The short-circuit test [33] 45
Fig 2-12 Simple two-bus network 47
Fig 2-13 Reliability model for static components 51
Fig 2-14 Procedure for reliability evaluation 52
Fig 2-15 Sample network 53
Fig 2-16 Linear membership function 54
Fig 3-1 Example of ant colony system [69] 63
Fig 3-2 Flowchart of the ant colony algorithm 65
Fig 3-3 Flowchart of the AIS-ACO algorithm 67
Fig 4-1 Procedure of domestic electricity demand profile generation 72
Fig 4-2 Monte Carlo simulation platform for three transformer operation modes
comparison 74
Fig 4-3 Flowchart of transformer loss assessment 75
Fig 4-4 Monte Carlo simulation platform for distribution network reconfiguration 76
Fig 4-5 Generic distribution network topology 78
Fig 4-6 Transformer load factor variation 79
Fig 4-7 Transformer loss variations in different scenarios 80
Fig 4-8 11 kV 4th
feeder voltage profiles in different scenarios 81
Fig 4-9 Voltage profiles of Load 4_1 in different scenarios 82
Fig 4-10 Voltage profiles of Load 4_8 in different scenarios 83
Page | 8
Fig 4-11 11 kV 4th
feeder mean voltage profile of various TCLFs 84
Fig 4-12 Test system 86
Fig 4-13 Daily load variations for different load groups 87
Fig 4-14 Mean voltage profiles in S1 S2 and S3 89
Fig 4-15 Mean voltage profiles in S1 S4 and S7 89
Fig 5-1 Search space of DNR and DGs Placement 95
Fig 5-2 Flowchart of the ACO applied to DNR and DGs placement 98
Fig 5-3 33-bus system 100
Fig 5-4 33-bus system for feeder loss minimisation Case II 101
Fig 5-5 33-bus system for feeder loss minimisation Case III 102
Fig 5-6 33-bus system for feeder loss minimisation Case IV 103
Fig 5-7 Comparison of feeder loss for different DG capacities before and after
simultaneous reconfiguration and DG allocation 104
Fig 5-8 Comparison of voltage profiles in different cases of 33-node system 104
Fig 5-9 69-bus system 105
Fig 5-10 69-bus system for feeder loss minimisation Case II 106
Fig 5-11 69-bus system for feeder loss minimisation Case III 107
Fig 5-12 69-bus system for feeder loss minimisation Case IV 107
Fig 5-13 Comparison of feeder loss for different DG capacities before and after
simultaneous reconfiguration and DG allocation 108
Fig 5-14 Comparison of voltage profiles in different cases of 69-node system 109
Fig 6-1 The reconfiguration hours for a typical day 113
Fig 6-2 Search space of DNR and TEO 115
Fig 6-3 Sample network with three substations 116
Fig 6-4 Flowchart of the ACO applied to DNR and TEO for a specific type of day
117
Fig 6-5 Distribution feeder connected to RBTS Bus 4 118
Fig 6-6 Daily load profile of residential consumers 119
Fig 6-7 Daily load profile of commercial consumers 120
Fig 6-8 Daily load profile of industrial consumers 120
Fig 6-9 Daily load profile (MW) of the main feeder 120
Fig 6-10 Annual energy loss with different DG capacities 123
Fig 6-11 Annual energy loss in uncoordinated charging strategy 125
Fig 6-12 Annual energy loss in coordinated charging strategy 126
Page | 9
Fig 7-1 Membership function for SAIDI and switch cost reduction 131
Fig 7-2 Membership function for ECOST reduction 132
Fig 7-3 Search space of sectionalising switch placement 134
Fig 7-4 Distribution feeder connected to RBTS Bus 4 with 6 sectionalising switches
136
Fig 7-5 Optimal relocation of sectionalising switches in Test Case 11 139
Fig 7-6 Optimal installation of sectionalising switches in Test Case 12 141
Fig 7-7 Optimal installation and relocation of sectionalising switches in Test Case
13 142
Fig 7-8 BCR versus years 143
Fig 7-9 Variation of cost versus change in CDF 144
Fig 7-10 Number of installed sectionalising switches versus change in CDF 145
Fig 8-1 Flowchart of the MOACO algorithm applied to multi-objective DNR
problem 157
Fig 8-2 Flowchart of the AIS-ACO algorithm applied to multi-objective DNR
problem 158
Fig 8-3 Distribution feeder connected to RBTS Bus 4 161
Fig 8-4 Pareto solutions obtained (minimisation of feeder loss ECOST and SAIDI)
162
Fig 9-1 Membership function for feeder loss reduction 168
Fig 9-2 Membership function for maximum node voltage deviation reduction 169
Fig 9-3 Membership function for load balancing index reduction 170
Fig 9-4 33 bus-system for fuzzy multi-objective optimisation Case II 173
Fig 9-5 Pareto front obtained for 33-bus system in Case II 174
Fig 9-6 33 bus-system for fuzzy multi-objective optimisation Case III 175
Fig 9-7 Pareto front obtained for 33-bus system in Case III 176
Fig 9-8 33 bus-system for fuzzy multi-objective optimisation Case IV 178
Fig 9-9 Pareto front obtained for 33-bus system in Case IV 178
Fig 9-10 69 bus system for fuzzy multi-objective optimisation Case II 180
Fig 9-11 Pareto front obtained for 69-bus system in Case II 181
Fig 9-12 69-bus system for fuzzy multi-objective optimisation Case III 183
Fig 9-13 Pareto front obtained for 69-bus system in Case III 183
Fig 9-14 69-bus system for fuzzy multi-objective optimisation Case IV 185
Fig 9-15 Pareto front obtained for 69-bus system in Case IV 186
Page | 10
List of Tables
Table 2-1 Transformer economic operation area 33
Table 2-2 Transformer technical specifications and costs 35
Table 3-1 Relationship of 119911 lowast and 119862 62
Table 4-1 Household size by number of people in household as a proportion [103] 72
Table 4-2 Parameters of a typical 3311 kV two-winding transformer [106] 78
Table 4-3 Daily transformer loss in different scenarios 80
Table 4-4 Transformer loss with different TCLF 85
Table 4-5 Average number of switching operations with different TCLF 85
Table 4-6 Transformer loss in Test Case 2 88
Table 5-1 Results of different cases for the 33-bus system 100
Table 5-2 Comparison of simulation results for 33-bus system in Case II 101
Table 5-3 Comparison of ACO with CGA and CSA for the 33-bus system in Case II
102
Table 5-4 Results of different cases for the 69-bus system 105
Table 5-5 Comparison of simulation results for 69-bus system in Case II 106
Table 6-1 Revised customer data (peak load) 119
Table 6-2 The distribution of load types for a whole year 121
Table 6-3 Results of DNR and TEO with different load types in Test Case 1 122
Table 6-4 Characteristics of EV 124
Table 7-1 Customer data (Average load) 137
Table 7-2 Sector interruption cost estimation ($kW) 138
Table 7-3 Results of sectionalising switches relocation in Test Case 11 140
Table 7-4 Results of sectionalising switches installation in Test Case 12 141
Table 7-5 Results of sectionalising switches relocation and installation in Test Case
13 143
Table 7-6 Impacts of 120588 variation on objective function 119869 146
Table 7-7 Impacts of variation in number of ants on objective function 119869 146
Table 7-8 Results of sectionalising switches relocation and installation in Test Case
2 147
Table 7-9 Results of sectionalising switches installation and relocation in Test Case
3 148
Page | 11
Table 8-1 Revised customer data (Average load) 162
Table 8-2 Mean and standard deviation of Pareto Front (loss ECOST and SAIDI)
163
Table 8-3 Minimum solutions along each objective (loss ECOST and SAIDI) 163
Table 8-4 Best compromise solutions (loss ECOST and SAIDI) 164
Table 9-1 Results of DNR in fuzzy multi-objective formulation for 33-bus system in
Case II 173
Table 9-2 Mean and standard deviations of Pareto Front for 33-bus system in Case II
174
Table 9-3 Minimum solutions along each objective for 33-bus system in Case II 175
Table 9-4 Results of DNR in fuzzy multi-objective formulation for 33-bus system in
Case III 176
Table 9-5 Mean and standard deviations of Pareto Front for 33-bus system in Case
III 176
Table 9-6 Minimum solutions along each objective for 33-bus system in Case III 177
Table 9-7 Results of DNR and DG allocation in fuzzy multi-objective formulation
for 33-bus system in Case IV 178
Table 9-8 Mean and standard deviations of Pareto Front for 33-bus system in Case
IV 179
Table 9-9 Minimum solutions along each objective for 33-bus system in Case IV 179
Table 9-10 Results of DNR in fuzzy multi-objective formulation for 69-bus system
in Case II 181
Table 9-11 Mean and standard deviations of Pareto Front for 69-bus system in Case
II 181
Table 9-12 Minimum solutions along each objective for 69-bus system in Case II 182
Table 9-13 Results of DNR in fuzzy multi-objective formulation for 69-bus system
in Case III 183
Table 9-14 Mean and standard deviations of Pareto Front for 69-bus system in Case
III 184
Table 9-15 Minimum solutions along each objective for 69-bus system in Case III
184
Table 9-16 Results of DNR and DGs allocation in fuzzy multi-objective formulation
for 69-bus system in Case IV 185
Page | 12
Table 9-17 Mean and standard deviations of Pareto Front for 69-bus system in Case
IV 186
Table 9-18 Minimum solutions along each objective for 69-bus system in Case IV
187
Table A-1 Typical configurations and parameters of 11 kV triplex cables in the UK
204
Table A-2 Line and load data of 33-bus system 205
Table A-3 Line and load data of 69-bus system 206
Table A-4 Feeder data of RBTS Bus 4 207
Table A-5 Reliability Data for RBTS Bus 4 208
Table B-1 The locations of tie-switch in Scenario 9 209
Table B-2 Mean voltage profiles at each node in the linked feeder 210
Table B-3 95th
voltage profiles at each node in the linked feeder 210
Table B-4 Network losses in each branch of 33-bus system 211
Table B-5 Network losses in each branch of 69-bus system 212
Table B-6 Pareto optimal solutions of multi-objective DNR (loss ECOST and
SAIDI) 214
Table B-7 Pareto optimal solutions of multi-objective DNR (loss maximum node
voltage deviation feeder load balancing index) for 33-bus system in Case II 215
Table B-8 Pareto optimal solutions of multi-objective DNR (loss maximum node
voltage deviation feeder load balancing index) for 33-bus system in Case III 215
Table B-9 Pareto optimal solutions of multi-objective DNR (loss maximum node
voltage deviation feeder load balancing index) for 33-bus system in Case IV 216
Table B-10 Pareto optimal solutions of multi-objective DNR (loss maximum node
voltage deviation feeder load balancing index) for 69-bus system in Case II 218
Table B-11 Pareto optimal solutions of multi-objective DNR (loss maximum node
voltage deviation feeder load balancing index) for 69-bus system in Case III 218
Table B-12 Pareto optimal solutions of multi-objective DNR (loss maximum node
voltage deviation feeder load balancing index) for 69-bus system in Case IV 219
Table C-1 ACO parameters for distribution network reconfiguration and DG
allocation in Test Case 2amp3 221
Table C-2 ACO parameters for distribution network reconfiguration and DG
allocation in Test Case 4 221
Page | 13
Table C-3 ACO parameters for distribution network reconfiguration and transformer
economic operation 221
Table C-4 ACO parameters for sectionalising switch placement in Test Case 1 222
Table C-5 ACO parameters for sectionalising switch placement in Test Case 2amp3222
Table C-6 MOACO parameters for multi-objective distribution network
reconfiguration (loss ECOST and SAIDI) 222
Table C-7 AIS-ACO parameters for multi-objective distribution network
reconfiguration (loss ECOST and SAIDI) 223
Table C-8 ACO parameters for multi-objective DNR (loss maximum node voltage
deviation feeder load balancing index) 223
Table C-9 AIS-ACO parameters for multi-objective DNR (loss maximum node
voltage deviation feeder load balancing index) 223
Page | 14
List of Abbreviations
Abbreviations Definition
ACO Ant Colony Optimisation
ACS Ant Colony System
AENS Average Energy Not Supplied
AIS Artificial Immune Systems
AIS-ACO Artificial Immune Systems-Ant Colony Optimisation
ANN Artificial Neutral Network
ASP Active Server Pages
BCR Benefit-to-cost Ratio
BEM Branch Exchange Method
BPSO Binary Particle Swarm Optimisation
CDF Customer Damage Function
CGA Continuous Genetic Algorithm
CSA Cuckoo Search Algorithm
DA Distribution Automation
DNO Distribution Network Operator
DNR Distribution Network Reconfiguration
DG Distributed Generation
DPSO Discrete Particle Swarm Optimisation
ECOST Expected Customer Damaged Cost
EDNS Expected Demand Not Supplied
ENS Energy not supplied
EV Electric Vehicle
FMEA Failure-mode-and-effect Analysis
FWA Firework Algorithm
FRTU Feeder Remote Terminal Unit
GA Genetic Algorithm
HC Hyper Cube
HSA Harmony Search Algorithm
HV High Voltage
Page | 15
IWO Invasive Weed Optimisation
LV Low Voltage
MDC Maximum Driving Capability
MILP Mixed Integer Linear Programming
MOACO Multi-objective Ant Colony Optimisation
MV Medium Voltage
PSO Particle Swarm Optimisation
RBTS Roy Billinton Test System
RGA Refined Genetic Algorithm
SA Simulated Annealing
SAIDI System Average Interruption Duration Index
SAIFI System Average Interruption Frequency Index
SCADA Supervisory Control and Data Acquisition
SSP Sectionalising Switch Placement
TS Tabu Search
TCLF Transformer Critical Load Factor
TEO Transformer Economic Operation
TOM Transformer Operation Mode
VML Vector Markup Language
Page | 16
Abstract
The University of Manchester
Submitted by Boyi Zhang
for the degree of Doctor of Philosophy
Distribution Network Automation for Multi-objective Optimisation
December 2017
Asset management and automation are acknowledged by distribution utilities as a
useful strategy to improve service quality and reliability However the major
challenge faced by decision makers in distribution utilities is how to achieve long-
term return on the projects while minimising investment and operation costs
Distribution automation (DA) in terms of transformer economic operation (TEO)
distribution network reconfiguration (DNR) and sectionalising switch placement
(SSP) is recognised as the most effective way for distribution network operators
(DNOs) to increase operation efficiency and reliability Automated tie-switches and
sectionalising switches play a fundamental role in distribution networks
A method based on the Monte Carlo simulation is discussed for transformer loss
reduction which comprises of profile generators of residential demand and a
distribution network model The ant colony optimisation (ACO) algorithm is then
developed for optimal DNR and TEO to minimise network loss An ACO algorithm
based on a fuzzy multi-objective approach is proposed to solve SSP problem which
considers reliability indices and switch costs Finally a multi-objective ant colony
optimisation (MOACO) and an artificial immune systems-ant colony optimisation
(AIS-ACO) algorithm are developed to solve the reconfiguration problem which is
formulated within a multi-objective framework using the concept of Pareto
optimality The performance of the optimisation techniques has been assessed and
illustrated by various case studies on three distribution networks The obtained
optimum network configurations indicate the effectiveness of the proposed methods
for optimal DA
Page | 17
Declaration
No portion of the work referred to in the thesis has been submitted in support of an
application for another degree or qualification of this or any other university or other
institute of learning
Page | 18
Copyright Statement
i The author of this thesis (including any appendices andor schedules to this
thesis) owns certain copyright or related rights in in (the ldquoCopyrightrdquo) she
has given The University of Manchester certain rights to use such Copyright
including for administrative purposes
ii Copies of this thesis either in full or in extracts and whether in hard or
electronic copy may be made only in accordance with the Copyright
Designs and Patents Act 1988 (as amended) and regulations issued under it
or where appropriate in accordance with licensing agreements which the
University has from time to time This page must form part of any such
copies made
iii The ownership of certain Copyright patents designs trademarks and other
intellectual property (the ldquoIntellectual Propertyrdquo) and any reproductions of
copyright works in the thesis for example graphs and tables
(ldquoReproductionsrdquo) which may be described in this thesis may not be owned
by the author and may be owned by third parties Such Intellectual Property
and Reproductions cannot and must not be made available for use without the
prior written permission of the owner(s) of the relevant Intellectual Property
andor Reproductions
iv Further information on the conditions under which disclosure publication
and commercialisation of this thesis the Copyright and any Intellectual
Property andor Reproductions described in it may take place is available in
the University IP Policy (see
httpdocumentsmanchesteracukDocuInfoaspxDocID=24420) in any
relevant Thesis restriction declarations deposited in the University Library
The University Libraryrsquos regulations (see
httpwwwlibrarymanchesteracukaboutregulations) and in The
Universityrsquos policy on Presentation of Theses
Page | 19
Acknowledgements
First and foremost I would like to express my deepest gratitude to my supervisor
Prof Peter Crossley for his invaluable guidance and continuous encouragement
throughout the project
I would like to thank my friends and colleagues in the Ferranti Building at The
University of Manchester Prof Zhongdong Wang and Dr Qiang Liu for the fruitful
research discussions and their encouragement throughout the period of my PhD
I wish to thank North China Electric Power University PR China for the 2+2
course and also to Prof Chunming Duan and Prof Sangao Hu for their help and
encouragement
I also wish to thank Prof Bo Zhang Prof Jianguo Zhao and Prof Li Zhang from
Shandong University PR China who continued to support my research with their
valuable feedback and advice
Finally I would like to express my gratitude to my parents for their encouragement
and support
Page | 20
CHAPTER 1
INTRODUCTION
11 Motivation
The electricity ldquoutilityrdquo distribution network is part of a power system that carries
electricity from a high voltage transmission grid to industrial commercial and
residential customers [1] In England and Wales the voltage level of distribution
networks ranges from 132 kV to 230 V [2] Generally most distribution networks
operating at voltages below 25 kV are designed in closed loop but are operated
radially due to the simplicity of operation the ease of protection coordination and
the minimisation of overall economics [3] [4]
The electric power generation transmission and distribution companies are not only
energy producers but also significant power consumers Power loss occurs when
electricity is supplied to customers In 2013 the total distribution losses of GBrsquos
networks were estimated to be 196 TWh which indicates that about 6 of the total
power generation is wasted in the form of losses at distribution level [5] Utility
statistics also indicate that distribution transformers account for approximately 22
of these losses and the line and cable losses make up the remaining 78 Reduction
in active power loss can help distribution network operators (DNOs) save costs and
increase profits
The expression ldquoPower quality = Voltage qualityrdquo has been widely accepted as the
wave shape and magnitude of voltage that strongly influences the power quality
Chapter 1 Introduction
Page | 21
received by customers [6] According to the EN50160 standard [7] under normal
conditions at least 95 of the mean 10 minutes average rms voltage magnitudes in
an 11 kV electricity distribution network should be within the range 09 pu to 11 pu
during one week
Distribution network reliability has proved to be another fundamental attribute for
the safe operation of any modern power system [8] Data show that about 80 of
customer outages are due to distribution system failures [9] Based on the resource
from [10] in 2011 the average number of minutes of lost supply per customer in GB
is 70 minutes According to [11] electricity breakdowns cost the United States
around $80 billion per year With improved reliability the DNOs can save expenses
that are spent on networkrsquos maintenances after a failure [12]
The major challenge faced by DNOs is how to distribute the power in a low-cost
reliable and efficient way Distribution automation (DA) is recognised as the most
effective method for DNOs to increase operation efficiency and reliability The three
main parts of DA are transformer economic operation (TEO) distribution network
reconfiguration (DNR) and sectionalising switch placement (SSP) TEO refers to the
optimum selection of the transformers needed to supply each feeder This is related
to the economic evaluation of network performance and the resilience of the
network DNR is a process that involves changing the network topology by altering
the openclose status of sectionalising (normally closed) and tie (normally open)
switches [13] [14] Installation of new sectionalising switches and relocation of
existing sectionalising switches are defined as SSP
Mathematically DA is a discrete non-linear constrained combinational optimisation
problem that is subject to operating constraints As it is not a practical solution to
investigate all possible network configurations ant colony optimisation (ACO)-
based heuristic search algorithms have been developed
To build a cleaner climate-friendly community the European Union has set a target
on carbon emissions for a 40 60 and 80 below 1990 levels by 2030 2040
and 2050 respectively [15] Therefore a large number of renewable distributed
generations (DGs) are deployed DG is a small electric generation unit that is
connected directly to the distribution network or appears on side of the meter
accessed by the customer [16] Since the number of DGs has increased in recent
Chapter 1 Introduction
Page | 22
years this has resulted in bidirectional power flows and locally looped networks [17]
The integration of high numbers of DGs strongly affects network operation and
planning Therefore optimal placement and sizing of DGs strongly improve
distribution network performance
12 Objectives
The aim of this research is to improve service quality and efficiency based on the
results of DA To achieve this aim the objectives of this thesis are as follows
To review distribution networks DA loss and reliability assessment and
optimisation functions
To propose three optimisation techniques namely the Monte Carlo Method the
ACO algorithm and the artificial immune systems-ant colony optimisation (AIS-
ACO) algorithm
To develop an optimal strategy consisting of TEO and DNR for transformer loss
reduction Statistic models of customer electrical demands should be established
to evaluate their impact from the perspective of probability
To assess the DNR and DG placement problems simultaneously in terms of
distribution feeder loss minimisation
To assess the TEO and DNR problem simultaneously in terms of distribution
network loss minimisation including transformer loss and feeder loss under
different load scenarios
To assess the SSP problem simultaneously based on three objectives namely
reduction of unserved energy cost decrease in the average time that a customer is
interrupted and minimisation of switch costs and using the fuzzy set theory
To propose a benefit-to-cost analysis to justify whether the benefits of installing
and relocating sectionalising switches can justify the cost or not
To formulate the optimal network reconfiguration problem within a multi-
objective framework using the Pareto optimality concept where network loss
and reliability indices are simultaneously optimised
Chapter 1 Introduction
Page | 23
To assess the DNR and DG allocation problem in terms of three conflicting
objectives optimisation network loss maximum node voltage deviation and
load balancing index in order to obtain a set of non-dominated solutions
13 Contribution of the work
This thesis has presented three methodologies of DA All of them are designed to
achieve service quality and efficiency improvement
The contributions of this thesis are summarised below
Load profiles In most literatures the load variations are ignored in their studies
which could underestimate the total energy loss for the utility [18] The
stochastic nature associated with load variety is considered in Chapter 4 In this
chapter the value of the load associated with domestic demand profiles are
obtained from the research described in [19] this can produce a random 1-min
resolution model for UK households A pool of load profiles is randomly
generated by this model in MATLAB Following this each node in the feeders
from the system is assigned with residential demand profiles from the pool based
on the Monte Carlo methodology
In Chapter 6 the distribution loads experience daily and seasonal variations The
study considers the daily load curves of different types of consumers (residential
commercial and industrial) In addition the days are divided into eight types
spring weekdays spring weekends summer weekdays summer weekends
autumn weekdays autumn weekends winter weekdays and winter weekends
Optimisation problems Previously it was observed that sufficient work has
been completed in terms of examining the TEO and the DNR problems
separately In Chapter 4 and 6 both the TEO and network reconfiguration
problems are integrated to benefit the whole distribution network effectively
Different combinations of locations of tie-switches in the network and operation
modes of all transformers in the substations represent different network
configurations Network reconfiguration and transformer operation modes
variation are dealt simultaneously using the ACO algorithm with an objective of
network loss minimisation as presented in Chapter 6
Chapter 1 Introduction
Page | 24
Most research projects have focused only on the optimisation of either the DNR
or the DG allocation problem An ACO algorithm is proposed in Chapter 5 to
deal with the DNR and DG allocation problems simultaneously in terms of
feeder loss minimisation In Chapter 9 the study aims to determine the optimum
network configurations and DG locations that minimise the active power loss
maximum node voltage deviation and feeder load balancing simultaneously
Multi-objective optimisation framework When there are multiple and
conflicting objectives that need to be satisfied all objective can be converted into
a single objective function which reflects a compromise among all objectives
The single objective function has two forms weighted aggregation and fuzzy
satisfaction objective function The selection of the form depends on the number
of objectives as well as their units and dimensions In Chapter 7 the system
expected outage cost to customers (ECOST) and switch costs can be converted
into a single objective function by aggregating these objectives in a weighted
function However as system interruption duration index (SAIDI) and switch
costs have different dimensions and units the two conflicting objectives are
modelled with fuzzy sets and then combined into a single objective function
Also a fuzzy membership function based on max-min principle is presented for
optimising ECOST SAIDI and switch costs simultaneously In Chapter 9 a new
operator called lsquomax-geometric meanrsquo has been introduced to determine the
degree of overall fuzzy satisfaction
However the above simple optimisation processes only obtain a compromise
solution It is no longer suitable if the DNO wishes to obtain all possible optimal
solutions for all the conflicting objectives at the same time [20] Therefore a set
of Pareto optimal solutions is introduced in this study And the corresponding
objective values constitute the Pareto front It allows decision makers to select
the most suitable topology from the Pareto optimal solutions for implementation
depending on the utilitiesrsquo priorities In Chapter 8 the study formulates the
optimal network reconfiguration problem within a multi-objective framework
using the concept of Pareto optimality where network loss and reliability indices
are simultaneously optimised In Chapter 9 active power loss maximum node
voltage deviation and feeder load balancing are optimised simultaneously
After obtaining the Pareto optimal solutions the best compromise solution
among the multiple objectives can be selected by comparing the fitness value of
Chapter 1 Introduction
Page | 25
each member in the Pareto front The best compromise solution is varied by
changing the values of weighting factors based on the tendencies of the network
decision makers A set of best compromise solutions can be obtained by varying
the weighing factors of each objective function and this is presented in Chapter 8
Proposal of ACO-based algorithms for assessment of optimisation problems
The ACO algorithm is a population-based approach based on the behaviour of
real ants [14] The proposed algorithm is not only used for assessment of the
TEO problem but also with DNR DG allocation and SSP problems The ACO
control parameters are different for each test case The selection of parameters is
a balance between the convergence rate and the global search ability of the
algorithm They are set experimentally using information from several trial runs
The results obtained by the ACO algorithm have been compared to those from
other algorithms in Chapter 5 and the ACO parameter sensitivity analysis is
provided in Chapter 7
In Chapter 8 the multi-objective ant colony optimisation (MOACO) and AIS-
ACO algorithms have been proposed and compared for assessment of multi-
objective DNR problems Both algorithms focus on problems in terms of Pareto
optimality where the objective functions are multidimensional and not scalar
A full list of publications resulting from this thesis is included in Appendix D
14 Structure of the thesis
The thesis is organised as follows
Chapter 2 introduces the distribution network configurations and associated
equipment It also gives a comprehensive literature survey which reviews the
existing knowledge and research activities in the distribution automation (DA)
including transformer economic operation (TEO) distribution network
reconfiguration (DNR) and sectionalising switch placement (SSP) The assessment
of transformer loss feeder loss and reliability indices as well as the multi-objective
optimisation functions are also described in this chapter
Chapter 3 summarises the optimisation techniques for assessment of the multi-
objective problem The Monte Carlo Method ACO algorithm and AIS-ACO hybrid
algorithm are described in detail
Chapter 1 Introduction
Page | 26
Chapter 4 proposes two methodologies for transformer loss reduction whilst
maintaining satisfactory voltages which are TEO and DNR The demand profiles are
randomly generated by the profile generators in MATLAB Following this each
node in the feeders from the system is assigned with demand profiles based on the
Monte Carlo Method The effectiveness of the two investigated methods
implemented either alone or together are presented and discussed
Chapter 5 describes an ACO algorithm to assess the network reconfiguration and
DG placement problems simultaneously in terms of distribution feeder loss
minimisation The results of four scenarios carried out on two standard IEEE 33-
node and 69-node systems are presented to show the effectiveness of the proposed
approach The effect of DG capacities on DNR for feeder loss reduction is also
discussed Moreover the results obtained by ACO algorithm have been compared to
those from other algorithms in the literature
Chapter 6 presents the ACO algorithm for minimisation of the losses associated
with a network loss including transformer loss and feeder loss under different load
scenarios This is achieved by the optimum selection of which transformers need to
supply each feeder and by determining the optimal locations of the tie-switches The
performance of this approach to minimise power loss is assessed and illustrated by
various case studies on a typical UK distribution network The impact of DGs and
electrical vehicles (EVs) in reducing the loss is also discussed
Chapter 7 explores an ACO-based methodology for the placement of sectionalising
switches in distribution networks The objectives of the proposed sectionalising
switch placement problem are reduction of unserved energy costs decrease in the
average time that a customer is interrupted and minimisation of switch costs These
objectives are formulated in either a single objective function or a fuzzy satisfaction
objective function The performance of the proposed methodology is assessed and
illustrated by various test cases on a well-known reliability test system
Chapter 8 formulates the optimal network reconfiguration problem within a multi-
objective framework using the Pareto optimality concept where network loss and
reliability indices are simultaneously optimised The MOACO algorithm and AIS-
ACO algorithm are proposed and compared for assessment of DNR problems The
Chapter 1 Introduction
Page | 27
proposed approaches are tested on Bus 4 of the RBTS and a set of high quality non-
dominated solutions are obtained
Chapter 9 addresses two algorithms to assess the DNR and DG allocation problems
in terms of the three conflicting objectives minimisation network loss maximum
node voltage deviation and load balancing index The ACO algorithm is used to
solve the problem in the fuzzy domain and the AIS-ACO algorithm is adopted to
obtain a set of non-dominated solutions using the concept of Pareto optimality The
effectiveness and the efficiency of the proposed methods are implemented on two
standard test systems as case studies
Chapter 10 concludes the thesis by summarising the main findings of the work
Finally possible future research ideas associated with this thesis are proposed
All the network models are built in OpenDSS and all the algorithms are coded in
MATLAB They are carried on a 340-GHz processor with 16 GBs of RAM memory
for all studies
Page | 28
CHAPTER 2
DISTRIBUTION AUTOMATION
21 Introduction
Distribution automation (DA) is an important part of a Smart Grid [21] It enables a
distribution network operator (DNO) to monitor coordinate and operate distribution
components in real-time from a remote control centre [22] [23] This improves the
reliability performance and operational efficiency of the electrical distribution
system and helps increase the market penetration of distributed generations (DGs)
and electrical vehicles (EVs) [24]ndash[26]
The remainder of this chapter is structured as follows Sections 22-23 introduce the
network configurations and associated equipment Sections 24-26 present the three
main parts of DA namely transformer economic operation (TEO) distribution
network reconfiguration (DNR) and sectionalising switch placement (SSP)
Transformer loss feeder loss and reliability indices assessments are described in
Sections 27-29 Three methods for assessment of multi-objective optimisation
problems are reviewed in Section 210 A summary of the main conclusions in this
chapter is given in Section 211
Chapter 2 Distribution Automation
Page | 29
Tie-switch
Sectionalising switch
22 Distribution Network Configurations
In England and Wales the voltage level of distribution networks ranges from 132 kV
to 230 V [2] Generally most distribution networks are designed in closed loop but
are operated radially due to the simplicity of operation the ease of protection
coordination and the minimisation of overall economics [3] [4]
There are three typical system configurations shown in Fig 2-1 [27] The radial
system in Fig 2-1 (a) is common in rural areas but does not include any backup
supplies Consequently the lack of feeder interconnections means a short-circuit
fault will interrupt power to all the downstream customers and power will not be
restored until the faulted equipment is repaired The tie-switches (normally open) in
Fig 2-1 (b) connect two feeders and make the system radial in a primary loop There
are multiple tie-switches between multiple feeders in distribution systems Fig 2-1 (c)
describes a link arrangement and during normal conditions the systems are operated
radially However when a fault occurs the part affected by the fault is isolated by
tripping the breakers The unaffected areas can then be restored from a different
busbar by closing the tie-switches and feeding the supply
(a) Radial system (b) Primary loop (c) Link Arrangement
Fig 2-1 Typical Distribution network [27]
Chapter 2 Distribution Automation
Page | 30
23 Switchgear for Distribution Network
There is a large variety of switchgears used in distribution networks this includes
reclosers sectionalising switches tie-switches fuses and circuit breakers This
section mainly focuses on reclosers sectionalising switches and tie-switches
231 Reclosers
Reclosers are automatic self-contained protection devices installed on main feeders
and operate as a part of the protection schemes [28] [29] They are a type of circuit
breakers with control measurement and automatic re-closing functions Most faults
on distribution feeders are temporary ie they last from a few cycles to a few
seconds and are cleared by protection tripping a circuit breaker [1] Reclosers
normally count the number of overcurrent pulses followed by the line de-
energisation sequences [1] They always coordinate with other types of protection
equipment These include such as fuses and sectionalising switches for the purpose
of fault isolation and system restoration The process of recloser operation is shown
in Fig 2-2 The time between reclosures and the time of the reclose can be
programmed If the fault is transient the recloser will operate 1-3 times and then
restore service quickly If the fault is permanent after a pre-set number of trip-
reclose operations the recloser is locked and the recloser interrupter triggers a final
trip
Fig 2-2 Recloser operation
Time between reclosures
Time of the reclose Fault current
Recloser locks
out on 2nd
reclose
as programmed
Recloser opens
Recloser recloses
fault still present
Recloser recloses
fault still present
Recloser re-opens
fault still present
Load current
Chapter 2 Distribution Automation
Page | 31
232 Sectionalising Switches
Sectionalising switches are the protective devices that operate in conjunction with
backup circuit breakers or reclosers [25] They are isolating devices that
automatically isolate the faulted sections from a distribution network after a
permanent fault has occurred and after the line is de-energised by the feeder breaker
[1] This is because sectionalising switches are not designed to interrupt the fault
current and must be used with the feeder breaker that can break and reclose a circuit
under all conditions ie normal or faulty operating conditions [25] [30] A detailed
operation of sectionalising switches is presented in Section 26
233 Tie-switches
Tie-switches refer to the normally open switches of the network By closing the
opened tie-switch the load is transferred from one feeder to another but this requires
an appropriate sectionalising switch to be opened to restore the radial topology [31]
The tie-switch placement should follow certain principles ie all the loads are
energised and the network is operated in radial configurations The tie-switches are
designed to operate in normal condition but are not suitable for the interruption of
fault currents They are designed to operate after a switching device (circuit breaker
of fuse) has interrupted the fault current
24 Transformer Economic Operation
241 Basic Concepts
Power transformers are the interface between the generators and the transmission
lines and between lines operating at different voltage levels [32] They are a critical
part of an electric power system and transform the ac voltage based on the principle
of electromagnetic induction A step-up transformer ensures the efficient
transmission of power ie high voltage-low current and a step-down transformer
permits the transmitted power to be used at a lower and safer voltage [33]
Distribution transformers are used to reduce the primary system voltages to the
Chapter 2 Distribution Automation
Page | 32
Tran
sfo
rme
r Lo
ss
Transformer Load Factor
1 Transformer
2 Transformers
utilisation voltages [25] normally 132 kV for high voltage (HV) 11 kV-33 kV for
medium voltage (MV) and 400 V for low voltage (LV) in UK distribution networks
For transformers currently in operation developing a new strategy for transformer
loss reduction is required rather than replacing them with high efficiency
transformers [34] Transformer economic operation refers to the optimum selection
of transformers needed to supply each feeder This is related to the economic
evaluation of network performance and the resilience of the network
In order to meet reliability requirements the load factor of each transformer should
not go beyond 50 when two transformers are operated in parallel In other words
the transformer load factor must be within 100 in separate operation modes
The integrated power loss curves of onetwo transformers in operations are shown in
Fig 2-3 The intersection of the two curves is 119878119871 which is called the transformer
critical load factor (TCLF) Therefore it can be concluded that
When the total load 119878 lt 119878119871 a single transformer produces less integrated
power loss than parallel transformers
When 119878 gt 119878119871 parallel operation of transformer is more economical
When 119878 = 119878119871 the losses in single or parallel operation modes are identical
Fig 2-3 Transformer loss versus transformer load
119878119871
Core loss for 2 transformers
Core loss for 1 transformer
Chapter 2 Distribution Automation
Page | 33
As a result Table 2-1 presents the transformer commercial operation area
Table 2-1 Transformer economic operation area
Operation modes Single Transformer Two Parallel Transformers
Economic operation area 0 ~ 119878119871 119878119871 ~ 119878
242 Literatures on Transformer Economic Operation
Several papers that discuss research on transformer economic operation not only
focuse on transformer loss reduction but also discuss cost reduction and reliability
improvement
The papers concerned with transformer economic operation based on loss reduction
were presented in [35]ndash[37] Wang and Liu [35] used the ASP (Active Server Pages)
language as a foundation to analyse transformer economic operation on-line The
operation curves and interval graph of commercial operation were achieved from the
VML (Vector Markup Language) and the simulation results In the interest of the
economical and profitable operation of transformer real-time data was obtained
using the SCADA (Supervisory Control and Data Acquisition) and this included the
measurement of active power load and voltage [36] [37] Then the transformers
were monitored in real-time and the methods used to ensure their economical and
profitable operation were suggested online
However if the active power loss of transformers was measured based on the real-
time load data transformers would frequently be switched to a new state associated
with instantaneous economical and profitable operation As the number of switching
operations increases the lifetime of the transformers decreases As a result Song and
Zhang [38] developed a load smoothing algorithm to reduce the number of switching
operations of the transformer effectively The curves of transformer loads before and
after smoothing are presented in Fig 2-4 Table 2-2 and 2-3 illustrate the transformer
operation mode variation before and after smoothing respectively The results show
that the active loss achieved when using the load smoothing algorithm was a little
higher than when smoothing was not used However the total number of switching
operations of transformers with load smoothing was reduced from 6 to 2 which
would expand the transformer life cycle
Chapter 2 Distribution Automation
Page | 34
(a) Before load smoothing (b) After load smoothing
Fig 2-4 Daily load curve of a typical substation before and after load smoothing [38]
Table 2-2 Transformer operation mode variation before load smoothing
Time Transformer operation mode The sum of active power loss
(Kw)
000-300 1 transformer in operation 12363
300-1600 2 transformer in operation
1600-2100 Parallel operation
2100-2400 2 transformer in operation
Table 2-3 Transformer operation mode variation before load smoothing
Time Transformer operation mode The sum of active power loss
(Kw)
000-600 2 transformer in operation 12768
600-2100 Parallel operation
2100-2400 2 transformer in operation
Generally the cost of the energy loss of a transformer over its service life is much
higher than its initial capital price As a result the transformer selection decision is
based not only on the purchase price but also includes the cost of installation
maintenance and loss over the lifetime of the equipment [39]
Amoiralis etc [40] have investigated the cost of two transformers that have the same
capacity but different specifications The transformers were loaded at 50 of full
load and with an increase of 37 for each year The technical characteristics and the
costs associated with the two transformers are presented in Table 2-4 The total cost
is the summation of loss and capital cost of a transformer over 30 years Purchasing a
Chapter 2 Distribution Automation
Page | 35
transformer with low efficiency (Transformer A) reduced the initial cost but resulted
in higher energy costs during the transformer lifetime in comparison with
Transformer B The economic approach in [41] and [42] were used to determine the
suitable size of transformers in Thailand The choice of a high capacity transformer
could improve voltage profiles and provide extra room for emergency conditions and
load increments in the future
Table 2-4 Transformer technical specifications and costs [40]
Transformer Size
(kVA)
No load loss
(kW)
Load loss
(kW)
Capital
price (euro)
Cost of loss
(euro)
Total cost
(euro)
A 1000 11 9 9074 34211 43285
B 1000 094 76 11362 28986 40348
25 Distribution Network Reconfiguration
251 Basic Concepts
DNR refers to a process that involves changing the network topology at normal and
abnormal operating conditions by altering the openclose status of sectionalising
(normally closed) and tie (normally open) switches [13] [14] In fact DNR can be
used as a tool for distribution network planning and real-time operation [14]
As presented in Fig 2-5 the openclosed status of the tie switches and sectionalising
switches determines the structure of the system To achieve a new system
configuration the tie-switch 3 is closed which will create a new loop In order to
restore the network back to a radial structure a switch from 1 2 4 and 5 is selected
and opened
Fig 2-5 Radial test system
Chapter 2 Distribution Automation
Page | 36
Since there are various combinations of switching DNR is treated as a discrete and
constrained optimisation problem Recently optimal DNR strategies discussed in
many literatures have been implemented to achieve active power loss reduction and
system reliability improvement
252 Literatures on Distribution Network Reconfiguration
Network reconfiguration was first introduced by Merlin and Back [43] using a
discrete branch and bound optimisation method to reduce network loss Firstly all
the switches were closed to build a meshed network and then in each step one
branch was removed until the radial configuration was found
Another early study on loss reduction through network reconfiguration was
presented in [44] which discussed how to achieve minimum power loss in
distribution feeders through feeder reconfiguration It is possible to determine loss
variation by analysing the load flow results This involved simulating the system
configuration before and after the feeder was reconfigured [44] It was based on a
single pair switch operation per iteration The relevant results showed that the loss
was reduced only if the voltage across the tie-switch was significant and if the loads
connected at the lower voltage side were transferred to the other side [44] This
criterion was developed to eliminate undesirable switching options The best
switching option was then obtained from the results of load flow studies simulating
all feasible feeder configurations
Zehra etc [31] have proposed a branch exchange algorithm based on two stages of
the solution methodology It started with a feasible network operating in a radial
configuration The first step determined the loop that achieved maximum loss
reduction by comparing the circle sizes for each loop The largest circle indicated the
maximum loss reduction The second phase determined the switching options to be
operated in that loop to provide maximum loss reduction The smallest circle was
identified for the best solution In comparison with [44] the introduction of the
branch exchange method allowed the number of load flow solutions related to the
computation time to be greatly reduced However the results were strongly related to
the initial configuration of the electrical network [45] The above methodologies [31]
[43] [44] were able to obtain the global optimal solution but were only applied to
simplified network models
Chapter 2 Distribution Automation
Page | 37
Later on the artificial intelligent and modern heuristic optimisation algorithms such
as genetic algorithm (GA) [46]ndash[49] simulated annealing (SA) [50] [51] tabu
search (TS) [52]ndash[54] and particle swarm optimisation (PSO) [55] etc were
developed with minor computational effort These intelligent techniques which are
affected by the selection of parameters are able to obtain the optimum solution of
good quality The GA based network reconfiguration method was presented and
tested in a real 136-bus distribution network in [13] Various radial topologies were
generated after the implementation of the genetic operators and the search space was
enlarged by a local improvement method The results show that after network
reconfiguration the power loss is reduced from 3203 kW to 2801 kW which
amounts to a 1255 reduction
Other important objectives including reliability improvement and service restoration
by DNR were mentioned in [56]ndash[58] An intelligent binary particle swarm
optimisation (BPSO) based search method was presented in [57] for assessment of
the DNR problem in terms of reliability improvement The failure of all distribution
equipment such as transformers feeders breakers etc was considered In this paper
the reliability index was in the form of expected demand not supplied (EDNS) The
EDNS of the original configuration is 1008 kW and after reconfiguration the best
result is reached with 849 kW
Network reconfiguration can be formulated not only as a single objective problem
but also as a multi-objective problem that considers various parameters
simultaneously [45] [59]ndash[62] In [59] the objective function was to minimise the
combination of loss cost and consumer interruption cost thus the multiple objectives
were aggregated into an single objective function In order to achieve optimal DNR
a new method was proposed in [60] using a fuzzy multi-objective function to
balance feeder loads and reduce power loss of the distribution systems Depending
on the operatorrsquos preferences the weighting factors of each of the variables could be
varied Das [61] introduced another fuzzy membership formulation to handle the
multiple objectives In this work the degree of overall satisfaction was the minimum
of all the above membership values and the final optimal solution was the maximum
of all such overall degrees of satisfaction [61] Mendoza etc [62] introduced a
micro-genetic algorithm to deal with the trade-offs between the power loss and
reliability indices in order to obtain a set of optimal network configurations using
Chapter 2 Distribution Automation
Page | 38
the concept of Pareto optimality Andervazh etc [45] have presented another Pareto-
based multi-objective DNR method using discrete PSO The objectives were the
minimisation of power loss bus voltage deviations and number of switching
operations
In addition an optimal planning strategy based on network reconfiguration and DGs
placement was presented in [16] The primary objective was power loss reduction
and voltage stability improvement The performance of the methodology was tested
on a 33-bus network and three DGs were installed The power loss was reduced by
3093 by DNR 5624 by DG installation and 6689 by employing
reconfiguration and DG installation simultaneously
26 Placement of Sectionalising Switches
261 Basic Concepts
The implementation of DA requires the installation of various new devices [63]
Among other things DA involves the placement of sectionalising switches ie the
installation of new switches and relocation of existing switches DA in terms of
automatic and remote controlled sectionalising switch placement brings major
benefits to distribution network operators (DNOs) [64] [65] The duration and
number of outages per year determines the annual interruption time of customers
[66] It is possible to shorten outage duration by decreasing the restoration time and
to reduce the number of outages by improving failure rates [67] SSP is useful for the
reduction of the time required to detect and locate a fault and the improvement of
the speed of isolating the faulty sections in the primary distribution network [64]
The effectiveness of these objectives depends on the number and location of
sectionalising switches
In a distribution feeder the section is defined as a group of line segments between
adjacent sectionalising switches [68] And the equivalent load of the section is the
sum of the individual load points in this section [69] When a permanent fault occurs
the switch actions need to respond as follows
Chapter 2 Distribution Automation
Page | 39
1 Detect and locate the fault and initiate tripping to clear the fault A transient
fault is normally cleared by two or three trips and reclose cycles
2 However if the fault persists beyond the predefined cycles reclosure will be
inhibited and the protection will initiate a final trip The load breaker will open and
all the downstream loads will be de-energised
3 The faulty section is then isolated by opening the upstream and downstream
sectionalising switches located next to the fault
4 Restore the loads in the healthy area by closing the upstream and downstream
circuit breakers automatically
5 Repair the faulty section of the feeder and manually restore the loads (ie
reconnect loads to the supply)
A fully and a partially automated distribution feeder are shown in Fig 2-6 and Fig
2-7 respectively The fault occurs on line section 4 It can be clearly seen in Fig 2-6
that all loads are restored after the faulty area is isolated and the total outage time is
the same as the switching time of circuit breakers and sectionalising switches [64]
However as shown in Fig 2-7 only Loads LP1 LP5 LP6 are restored after the
isolation of the faulty section the outage duration of other loads is equal to the repair
time ie significantly longer than the switching time As a result the installation of
sectionalising switches could increase the network reliability as well as the
investment and operation cost of automation [64]
Chapter 2 Distribution Automation
Page | 40
LP1 LP2 LP3 LP4 LP5 LP6
1 2 3 4 5 6 7
LP1 LP2 LP3 LP4 LP5 LP6
1 2 3 4 5 6 7
LP1 LP2 LP3 LP4 LP5 LP6
1 2 3 4 5 6 7
LP1 LP2 LP3 LP4 LP5 LP6
1 2 3 4 5 6 7
Fault occurred on line section 4
CB1 opened
Sectionalising switches adjacent to the faulted area are opened
Energy restored to un-faulted area by closing CB1 and CB2
CB1 CB2
CB1CB2
CB1 CB2
CB1 CB2
Normally closed circuit breaker
Normally open circuit breaker
Closed sectionalising switch
Open sectionalising switch
Interrupted
load
Fig 2-6 Fully automated distribution feeder
Chapter 2 Distribution Automation
Page | 41
LP1 LP2 LP3 LP4 LP5 LP6
1 2 3 4 5 6 7
LP1 LP2 LP3 LP4 LP5 LP6
1 2 3 4 5 6 7
LP1 LP2 LP3 LP4 LP5 LP6
1 2 3 4 5 6 7
LP1 LP2 LP3 LP4 LP5 LP6
1 2 3 4 5 6 7
Fault occurred on line section 4
CB1 opened
Sectionalising switches adjacent to the faulted area are opened
Energy restored to un-faulted area by closing CB1 and CB2
CB1 CB2
CB1CB2
CB1 CB2
CB1 CB2
Normally closed circuit breaker
Normally open circuit breaker
Closed sectionalising switch
Open sectionalising switch
Interrupted
load
Fig 2-7 Partially automated distribution feeder
262 Literatures on Sectionalising Switch Placement
The earliest work that discussed SSP in distribution networks was presented by
Miranda [70] A fuzzy-logic-based optimisation technique has been used to
determine the location of sectionalising switches
In [69] the optimum sectionalising switch relocation problem has been solved by
using the ant colony system (ACS) based method to reduce feeder interruption costs
Chapter 2 Distribution Automation
Page | 42
after a fault In this work it is assumed that there were no additional capital
investments brought by switch relocation However the investment and operation
cost of a sectionalising switch is an important issue which cannot be ignored when
considering the problem of unsupplied energy costs minimisation since they conflict
with each other Therefore the information provided by the multi-objective model is
more valuable than the traditional mono-objective model Abiri-Jahromi etc [64]
have developed a mixed-integer linear programming (MILP) to deal with the new
sectionalising switch installation problem which considers customer outage costs as
well as switch capital operation and maintenance costs After the placement of
sectionalising switches the total system cost over the life period of the switches was
greatly reduced [64] In addition the impacts of customer damage function and load
density variations on SSP were also investigated through sensitivity analysis
The impacts of DG on the optimal number and location of sectionalising switches
were discussed in [71] The introduction of DGs connects a mono-source distribution
network to a multi-source one [66] This potentially improves network reliability
since it reduces the duration and restoration time of interruptions Many loads can be
restored through DGs when operating in islanding mode A mathematical
optimisation methodology has been proposed to minimise the reliability cost when
operating with a minimum number of sectionalising switches The results indicate
the reliability indices of distribution networks are affected by the number and
location of sectionalising switches
27 Transformer Loss Assessment
271 Operating Principles
A transformer has three essential elements a primary winding a secondary winding
and a core [33] As shown in Fig 2-8 the winding connected to the electrical source
is called the primary winding and the secondary winding is linked with the loads All
the windings are connected by the common magnetic flux in the core
Chapter 2 Distribution Automation
Page | 43
Fig 2-8 Elements of a single phase transformer [33]
Usually the power is generated and distributed in a three-phase system Therefore it
is necessary to use a three-phase transformer to increasedecrease the voltage The
structure of the three-phase transformer is presented in Fig 2-9
Fig 2-9 Construction of a three-phase transformer [33]
272 Transformer Quantities Measurement
The transformer quantities present the self-loss during power transmission which
consists of active power loss together with increase in the reactive power of the
network unit [72]
Open-circuit test
The equivalent circuit for the open-circuit test is shown in Fig 2-10 The test is made
on the low-voltage side by applying rated voltage at rated frequency with the high-
voltage winding open [33] The input power and current are measured which are
named no-load loss 119875119874119862 and no-load current 119868119874119862
Chapter 2 Distribution Automation
Page | 44
(a) Test circuit
(b) Equivalent circuit
Fig 2-10 The open-circuit test [33]
As the secondary is open the primary current is equal to the no-load current The no-
load current is used to produce the primary magnetic flux when the transformer is in
no-load operation which is also called the exciting current The voltage drops in the
primary winding can be ignored so the no-load loss is the summation of hysteresis
and eddy current losses [33] The input power is practically equal to the no-load loss
at rated voltage and frequency
119875119874119862 = 119875ℎ+119890 =119880119874119862
2
119877119888119871119881= 119880119874119862119868ℎ+119890 (2-1)
where 119877119888119871119881 is the resistance referred to the low-voltage side 119868ℎ+119890 is the core loss
current
Short-circuit test
The short-circuit test is used to measure the equivalent resistance and reactance of
the winding [6] As shown in Fig 2-11 the low-voltage terminal is shorted together
and the high-voltage side of the transformer is connected to a low-voltage high-
119880119900119888
119868ℎ+119890 119868120601
119868119900119888 119885119890119902 119871119881
119877119888 119871119881 119883119898 119871119881
Chapter 2 Distribution Automation
Page | 45
current source at rated frequency [33] The source voltage is increased until the short
circuit current reaches the rated value At this time value of the source voltage is
known as the short-circuit source voltage 119880119878119862
(a) Test circuit
(b) Equivalent circuit
Fig 2-11 The short-circuit test [33]
As the secondary side is shorted the voltage applied to the full load current is low
compared to the rated voltage and the exciting current 119868119890119909 is negligible during this
test [33] Since the rated current is used the input power is equal to the full-load loss
and expressed as
119875119878119862 = 1198681198781198622 119877119890119902119867119881 (2-2)
where 119877119890119902119867119881 is the winding resistance referred to the high voltage side
As the full-load loss depends on the value of the full load current the loss in the
winding resistance is varied under different loading conditions
119880119904119888
119868119890119909
119868119904119888 119877119890119902 119867119881 119883119890119902 119867119881
(119899119890119892119897119890119888119905)
Chapter 2 Distribution Automation
Page | 46
Active power loss
The active power loss ∆119875 of a two-winding transformer is decided by the no-load
loss 119875119874119862 full-load loss 119875119878119862 and the transformer load factor [73]
∆119875 = 119875119874119862 + 1205732119875119878119862 (2-3)
where 120573 =119878119871
119878119873 represents the transformer load factor 119878119871 is the transformer actual
loading (kVA) 119878119873 is the transformer rated capacity (kVA) Assuming the voltages
are held constant at 10 pu
Reactive power loss
The no-load current 119868119900119888 and short-circuit source voltage 119880119878119862 represent the change of
reactive power ∆119876 in other words the reactive power loss which can be simplified
as
∆119876 = 119876119874119862 + 1205732119876119878119862 (2-4)
119876119874119862 = 119878119874119862 =119868119874119862
119868119873∙ 119878119873 (2-5)
119876119878119862 = 119878119878119862 = 119880119878119862
119880119873∙ 119878119873 (2-6)
273 Integrated Transformer Loss
In general the power loss of a transformer is related to the active power [74]
However if a transformer draws reactive power (it takes current) this causes real
power loss in the network The integrated power loss refers to the sum of active
power loss of the transformer and the increased active power loss contributed by the
reactive power of the transformer [72]
The integrated power loss of a two-winding transformer is calculated by
1198791198711 = 11988002119875119885119874119862 +
1205732
11988002 119875119885119878119862 (2-7)
119875119885119874119862 = 119875119874119862 + 119870119876119876119874119862 (2-8)
Chapter 2 Distribution Automation
Page | 47
119875119885119878119862 = 119875119878119862 + 119870119876119876119878119862 (2-9)
where 119875119885119874119862 and 119875119885119878119862 are the integrated no-load loss (kW) and the full-load loss (kW)
120573 =119878119871
119878119873 represents the transformer load factor 119878119871 is the transformer actual loading
(kVA) 119878119873 is the rated capacity of the transformer (kVA) 119875119874119862 and 119876119874119862 are the no-
load active power loss (kW) and no-load reactive power loss (kVAr) 119875119878119862 and 119876119878119862
are the full load active power loss (kW) and full load reactive power loss (kVAr) 119870119876
represents the reactive equivalent which is the ratio of increased active power loss to
the change of the node reactive power (kWkVAr) [72] 1198800 is the operational voltage
of the transformer low voltage side in per unit
The no-load and full-load power losses are obtained from the open-circuit and short-
circuit test separately
For two transformers operating in parallel with the same capacity the current
flowing through each transformer is reduced by half Thus the full-load loss of each
transformer becomes a quarter of the previous case The total integrated power loss
is twice the no-load loss and half (2 times1
4) of the full-load loss of one transformer
1198791198712 = 211988002119875119885119874119862 +
1
2
1205732
11988002 119875119885119878119862 (2-10)
28 Feeder Loss Assessment
The distribution network power loss is mainly due to resistive loss in distribution
feeders which is obtained through a power flow study [75] The calculation of
power loss is explained using a two-bus network as shown in Fig 2-12
Fig 2-12 Simple two-bus network
Chapter 2 Distribution Automation
Page | 48
Assume there is no capacitance on either the sending or receiving bus and 119868119887119904 =
119868119887119903 = 119868119887 As a result the current flowing through branch b and the real power loss
are derived using the following equations
119875119887119877 + 119895119876119887119877 = 119887119877 times 119868lowast (2-11)
119875119887 = 1198681198872 times 119877119887 (2-12)
From (2-11) and (2-12) it is calculated as
119875119887 =119875119887119877
2 +1198761198871198772
1198811198871198772 times 119877119887 (2-13)
where 119875119887 is the real power loss of branch b (W) 119875119887119877 and 119876119887119877 are the real power (W)
and reactive power (VAr) at the receiving end of branch b 119881119887119877 represents the rms
voltage at the receiving end of branch b (V) 119868119887 is the rms current through branch b
(A) and 119877119887 is the resistance of branch b (Ω)
The real power losses in the other branches are evaluated similarly and the network
real loss is the sum of the power losses in all branches as presented in (2-14)
119864119871 = sum 119875119887119899119873119887119899 (2-14)
where 119873119887 is the set of all the distribution network branches
29 Reliability Evaluation
291 Reliability Indices
Reliability is a fundamental attribute for the safe operation of any modern power
system [8] A distribution network which is directly connected to customers has a
large impact on power reliability Distribution reliability primarily relates to
equipment outages and customer interruptions [76] The reliability indices of
distribution network can be classified into two groups ie load point reliability
indices and system reliability indices [77]
Chapter 2 Distribution Automation
Page | 49
The three primary load point reliability indices average failure rate (120582) average
annual outage time (119880) and average outage time (119903) are calculated by [73]
120582 = sum 120582119895119895 (2-15)
119880 = sum 120582119895119895 119903119895 (2-16)
119903 =119880
120582 (2-17)
where 120582119895 and 119903119895 are the failure rate and outage time of contingency j for this load
point
The system reliability indices mainly include system average interruption frequency
index (SAIFI) system average interruption duration index (SAIDI) average energy
not supplied (AENS) and expected customer damaged cost (ECOST) [78] The
Formulae for these reliability indicators are presented in (2-18) to (2-21) [78]
119878119860119868119865119868 =sum 120582119894119873119894119894
sum 119873119894119894 (2-18)
119878119860119868119863119868 =sum 119880119894119873119894119894
sum 119873119894119894 (2-19)
119860119864119873119878 =sum 119880119894119871119894119894
sum 119873119894119894 (2-20)
119864119862119874119878119879 = sum 119888119898(119889119898)119891119898119871119898119872119898=1 (2-21)
where 119873119894 is the total number of customers of load point 119894 120582119894 119880119894 and 119871119894is the failure
rate outage time and average load connected to load point i 119872 is quantity of load
outage events 119871119898 is load curtailed (kW) due to outage event m 119891119898 and 119889119898 are the
frequency and duration of outage event m 119888119898(119889119898) is the outage cost (poundkW) of
outage duration 119889119898 using the customer damage function (CDF)
SAIFI is a measure of the number of outages an average customer will experience
SAIDI states the average interruption hours for a customer in the system AENS
presents the effect of interruptions on the energy that is not supplied to the customers
during failures [79] ECOST is the index that connects reliability with economics
Chapter 2 Distribution Automation
Page | 50
292 Reliability Evaluation Methods
The methods used to calculate reliability indicators for distribution network are
classified into two groups namely the simulation method and analytical method
Simulation method
The simulation method has better scalability and flexibility when incorporating
complex considerations in comparison with the analytical technique And it is more
capable of dealing with large-scale power systems and the variation of load points
[77] The Monte Carlo method is a typical example of a simulation method and
takes into account the time varying and stochastic nature of load models in
evaluating the power system reliability [80] Vitorino etc [12] proposed a non-
sequential Monte Carlo method based on branch reliability to estimate energy not
supplied (ENS) index Contingencies were simulated by randomly selecting a faulty
branch from a candidate network pool based on failure probabilities [12] However
although the Monte Carlo method can simulate the behaviour of a complex system
with a high degree of accuracy it requires a considerable amount of CPU time and
memory
Analytical method
The first step of an analytical technique is to build a reliability probabilistic model
for the system according to network topology as well as the relationships between
the system and components [77] The model is then solved by calculating the
reliability indices in iterations [77] The most common analytical methods are
minimal path method minimal cutset method and failure-mode-and-effect analysis
(FMEA)
In [81] the minimal path method which identifies the shortest paths from a node to
a source and between any two nodes was described The minimal path of the source
node to the load points was obtained by searching for the upstream node from the
load points [82] As the distribution network was radial each node had only one
upstream node The sections out of service after a fault occurred were identified and
separate subsystems were formed The nodes were classified in terms of the effect of
a failure on them Using the node class and amount of load shedding data the
reliability indexes could then be evaluated [81]
Chapter 2 Distribution Automation
Page | 51
FMEA is a classical analytical algorithm for distribution network reliability
evaluation based on the analysis of all the failure modes of each static component
[82] As shown in Fig 2-13 there are four failure modes which are 1) active failure
2) transient failure 3) passive failure and 4) maintenance The active and transient
failures can cause the operation of breakers and hence the healthy components can
be removed from service [75] The passive failures are similar to maintenance outage
and have no effect on the protection system and remaining heathy zone [82]
Fig 2-13 Reliability model for static components
The proposed reliability evaluation method is based on the N-1 criterion and its
computation procedure is demonstrated in Fig 2-14
Normal operation
Active
failure
Transient
failure
Passive
failure
Maintenance
120582119860 120582119879 120582119875 120582119872
120583119860 120583119879 120583119875
120583119872
Chapter 2 Distribution Automation
Page | 52
Start
Read system topology load
data and reliability parameters
Initialise failure number i=1
All failures are considered
Search for the upstream feeder breaker
Search for the upstream and downstream
sectionalising switches and tie-switch
The load points are classified into three categories
Evaluate the reliability of load points
and whole system when fault at line i
Next failure i=i+1
Calculate the reliability of the whole system
End
No
Yes
Fig 2-14 Procedure for reliability evaluation
The system failure events are enumerated first For a failure event the scope of the
failure is determined by searching for the adjacent circuit breaker or tie switch The
isolation zone is then confirmed by the location of the upstream and downstream
sectionalising switches and the appropriate tie-switch Subsequently all the load
points are classified based on their interruption times Finally the consequence of
each contingency and a value for total system reliability are evaluated
When a fault occurs all the load points can be categorised as follows
Healthy points are load points not affected by the fault and refer to upstream
nodes of the upstream circuit breaker or downstream nodes of the
Chapter 2 Distribution Automation
Page | 53
downstream circuit breaker or tie-switch For example when a fault occurs at
L2 in Fig 2-15 LP1 and LP5 are healthy points
Temporary damaged points when the protection systems are in operation
they cause the load points to be interrupted but the load points can be
restored by isolating the faulty area and by using a supply through another
path When a fault occurs at L2 in Fig 2-15 LP2 and LP4 are isolated by
opening the sectionalising switches S1 and S2 LP2 is restored by closing B1
and LP4 is supplied by closing the tie-switch As a result LP2 and LP4 are
temporary damaged points The interruption time is 119879119878 which is the average
switching time after failure
Permanent damaged points are load points that are interrupted by the
operation of protection devices and cannot be restored until the fault is
cleared [82] When a fault occurs at L2 in Fig 2-15 LP3 is the permanent
damaged point The interruption time is 119879119877 which is the average repair time
after failure
Fig 2-15 Sample network
Overall the analytical method which is based on a reliability model of each
component evaluates system reliability by enumeration of all failure states However
the increasing number of devices in a complex system results in an increase in the
quantity of failure states and the complexity of calculation As such the scale of the
network might be limited
210 Multi-objective Optimisation
The aim of this section is to provide fundamental information in order to assess
multi-objective optimisation problems The objectives are conflicting and can be
Chapter 2 Distribution Automation
Page | 54
0
1
converted into three forms which are 1) single objective function 2) single fuzzy
satisfaction objective function and 3) Pareto front
2101 Single Objective Function
The single objective function is generally done by simply aggregating the objectives
with the same dimension and transforming others into constraints [83] It can be
solved by traditionally scalar-valued optimisation techniques However this function
has several limits 1) it results in only one solution 2) the analysis of the objectives
that are converted into constraints is limited
In [64] a sectionalising switch placement strategy was proposed to minimise the
sum of ECOST and sectionalising switch costs The above mentioned objectives
were simply aggregated and calculated in US dollars Other objectives such as the
number of available switches were converted into constraints
2102 Single Fuzzy Satisfaction Objective Function
In the fuzzy domain each variable is associated with a membership function varying
from zero to unity which indicates the satisfaction level of the objective [84] The
higher the membership value is the better the solution is Generally the linear
membership function is formulated as given in (2-22) and is presented in Fig 2-16
120572 =
1 119883 le 119883119898119894119899119883119898119886119909minus119883
119883119898119886119909minus119883119898119894119899119883119898119894119899 lt 119883 lt 119883119898119886119909
0 119883 ge 119883119898119886119909
(2-22)
Fig 2-16 Linear membership function
If 119883 is equal or less than 119883119898119894119899 the membership value is one As 119883 becomes greater
than 119883119898119894119899 the degree of satisfaction decreases This decrease is continued until 119883
reaches 119883119898119886119909 and the membership function becomes zero
120572
119883119898119894119899 119883119898119886119909 119883
Chapter 2 Distribution Automation
Page | 55
The fuzzy-based optimisation procedure is used for handling multiple conflicting
objectives with different dimensions and units [66] The degrees of satisfaction level
can be formulated into a single objective function in three methods which are 1)
weighted aggregation 2) max-min method 3) max-geometric-mean method The
objective is to maximise such degree of satisfaction
Weighted aggregation
In this method the degree of satisfaction level is the weighted aggregation of the
membership values of all objectives [85] Thus the final compromise solution for
multi-objective functions is described as follows
119872119886119909 119869 = 12059611205721 + 12059621205722 + ⋯ + 120596119899120572119899 (2-23)
where 120596119894 is the constant weighting factor for each of the membership values and
they should meet the condition sum 120596119894119894 = 1
The weighting factors are decided by the decision makers and a higher weighting
factor indicates that this parameter is more important However the disadvantage of
this technique is that DNOs may have difficulty in obtaining enough information
about the relative importance of each objective to determine the trade-offs among the
selected objectives
Saffar etc [60] have developed a network reconfiguration technique to reduce power
loss and equal load balancing of feeders As these objectives had different
dimensions and units they were transformed into a single objective function with
fuzzy variables A set of compromised solutions was obtained by varying the
weighting factors of each element
Max-min method
In this technique the degree of overall satisfaction is the minimal value among the
membership values of all objectives [85] Thus the final compromise solution for
multi-objective functions is described as follows
119872119886119909 119869 = min 1205721 1205722 hellip 120572119899 (2-24)
The solution is optimised by maximising the overall satisfaction of all objectives
However the max-min method might not predict the best compromise solution
Chapter 2 Distribution Automation
Page | 56
because even if one membership value is weak it does not necessarily mean that
other membership values are also weak [86]
The max-min principle was adopted in [84] for the multi-objective optimisation with
fuzzy sets The aim was to minimise real power loss and the absolute value of branch
current as well as to minimise nodes voltage deviation Finally an optimal solution
was obtained which indicated a concession among all the objectives The results also
revealed that although network reconfiguration resulted in a significant reduction in
total system loss the loss allocated to a certain number of customers increased [84]
It is important to change the tariff structure for these consumers so that they are not
obliged to pay more for the increase in loss allocation as a result of network
reconfiguration
Max-geometric-mean method
Like the above max-min method the geometric-mean function is also used to
evaluate the degree of overall fuzzy satisfaction but in different forms The objective
is computed as follows
119872119886119909 119869 = (1205721 ∙ 1205722 ∙ hellip ∙ 120572119873)1 119899frasl (2-25)
In [86] firstly all the variables (real power loss branch current loading maximum
voltage deviation and switching numbers) were assigned by truncated sinusoidal
fuzzy membership functions The overall degree of satisfaction was the geometric
mean of all fuzzy membership values [86] The best compromise solution was then
obtained by maximising this satisfaction level
2103 Multi-objective Formulation in the Pareto Optimality
Framework
All the studies mentioned above are solved by a single-objective optimisation
technique In contrast a Pareto optimal solution is provided for the treatment of
multi-objective problems This produces a range of solutions rather than just one
which represents a compromise that goes some way to optimise objective functions
[87] [88] The Pareto optimal solution is based on a dominance concept The
solution 119883 dominates 119884 means that 119865(119883) is no worse than 119865(119884) for all objectives
Chapter 2 Distribution Automation
Page | 57
and there is at least one objective for which 119865(119883) is better than 119865(119884) as expressed in
(2-26) and (2-27) The following conditions should be satisfied concurrently
forall 119894 = 12 hellip 119873119900119887119895 119865119894(119883) le 119865119894(119884) (2-26)
exist 119894 = 12 hellip 119873119900119887119895 119865119894(119883) lt 119865119894(119884) (2-27)
where 119873119900119887119895 is the number of objective functions
If a solution 119883 and solution 119884 do not dominate each other these two solutions are
incomparable For example the objective is to minimise 1198911 and 1198912 and there are
three solutions whose objective function values are 119865(119883) = (24) 119865(119884) = (44)
119865(119885) = (52) It can be seen that 119883 dominates 119884 as 1198911(119883) lt 1198911(119884) and 1198912(119883) le
1198912(119884) And the solution 119883 and 119885 are incomparable because 1198911(119883) lt 1198911(119885) and
1198912(119883) gt 1198912(119885) Similarly solutions 119884 and 119885 are also incomparable
A solution belongs to Pareto optimal solutions if there is no other solution that can
improve at least one objective without degradation of any other objectives [83] In
other words there is no another solution that dominates it The Pareto set is the set of
all non-dominated solutions and its corresponding objective values constitute the
Pareto front [88] The goal of the multi-objective optimisation is to select the most
suitable one from the Pareto set for implementation according to decision makersrsquo
preferences
In [45] the study proposed a Pareto-based multi-objective DNR method using a
discrete PSO algorithm It aims to reduce power loss voltage deviations and the
number of switching operations Firstly each objective function was optimised
separately and the best results were found All objectives were then optimised
simultaneously and the Pareto optimal set was obtained The best results for each
objective were included in the Pareto front and the corresponding solutions were
stored in the Pareto optimal set Finally the best compromise solutions among the
multiple objectives were derived Different scenarios were modelled by assigning
different weighting factors based on the preferences of the decision makers
Chapter 2 Distribution Automation
Page | 58
211 Summary
Generally most distribution networks are designed in closed loop but are operated
radially There are three typical distribution network topologies which are the radial
system primary loop and link arrangement The descriptions of three switchgears ie
recloser sectionalising switch and tie-switch are also included in this chapter
TEO DNR and SSP are the three main parts of DA In this chapter there are several
reviews of these techniques TEO which refers to optimum selection of which
transformers need to supply each feeder can not only reduce loss but also reduce
total costs and improve network reliability DNR is defined as a process that
involves changing the network topology under normal and abnormal operating
conditions by relocation of tie-switches [13] [14] The methodologies from a branch
and bound optimisation method to modern heuristic optimisation algorithms
designed for loss reduction are reviewed In addition DNR is also able to improve
service quality and efficiency at the same time The placement of sectionalising
switches refers to the installation of new switches and relocation of existing switches
It is used for distribution network reliability improvement and service restoration
However so far few studies have been carried out that consider the combination of
the above three techniques
The major challenge facing DNOs is how to distribute the power in a low-cost
reliable and efficient way Thus the assessments of transformer loss feeder loss and
reliability indices are proposed in Section 27-29 The integrated transformer loss
consists of not only real power loss but also reactive power loss The transformer
quantities such as no-load loss and full-load loss are obtained from open-circuit test
and short-circuit test The distribution network power loss is achieved through power
flow study The reliability indices can be calculated through reliability evaluation
methods namely simulation methods and analytical methods The most common one
is FMEA which is also used for reliability evaluation in this thesis Although there
are many research projects that consider feeder loss and reliability simultaneously
few consider transformer loss and feeder loss at the same time
Three objective functions for optimising multiple conflicting objectives are 1) single
objective function 2) single fuzzy satisfaction objective function and 3) Pareto front
Chapter 2 Distribution Automation
Page | 59
The single objective function is generally done by simply aggregating some
objectives and transforming others into constraints In the fuzzy objective function
each variable is associated with a membership function and then aggregated into a
single objective function [84] The first two functions only obtain a single solution
However Pareto optimal solutions can obtain a set of non-dominated solutions
rather than one which represents a compromise that goes some way to optimising
objective functions In this thesis all three objectives functions will be studied and
results will be presented in the following chapters
This thesis will deal with single objective and multiple objectives through different
methods of DA based on various algorithms The next chapter will introduce the
Monte Carlo method and modern heuristic optimisation algorithms such as ant
colony optimisation (ACO) and artificial immune systems (AIS)
Page | 60
CHAPTER 3
OPTIMISATION TECHNIQUES
31 Introduction
Mathematically distribution automation (DA) is categorised as a discrete non-linear
constrained and combinational optimisation problem since the problem is to
determine the status of all transformers and switches In general the optimisation
techniques for assessment of this problem can be divided into two large groups 1)
simulation methods and 2) analytical methods
The Monte Carlo method is a typical example of a simulation method which will be
discussed in Section 32 in detail It can handle uncertainties and solve the
probabilistic optimal power flow [89] In a complex system with hundreds of
switches although the Monte Carlo method can find the best solution with a high
degree of accuracy it is generally not practical to carry out an extensive search of all
possible configurations as it consumes a great deal of CPU time and memory [88]
Therefore most DA problems are solved by analytical methods
The analytical methods can obtain a solution of good quality or even the global
optimal solution of the problem [13] It can be classified into four types 1) branch
and bound 2) optimal flow pattern 3) branch exchange and 4) metaheuristic
techniques Recently the last type has become the most popular
Chapter 3 Optimisation Techniques
Page | 61
The metaheuristic method is a process that attempts to find a solution to the problem
beginning from a starting point or a set of starting points and exploring all the search
space [13] It also includes a strategy to explore the search space and provide an
escape from the local optimal This process does not guarantee a globally optimal
solution but can offer near optimal solutions with a reasonable computational effort
This includes genetic algorithm (GA) ant colony optimisation (ACO) particle
swarm optimisation (PSO) and artificial immune systems (AIS) Different
metaheuristic techniques use different strategies that pass through and explore the
search space [13]
As for the remainder of the chapter the Monte Carlo method is discussed in Section
32 Section 33 presents the proposed ACO algorithm Section 34 discusses a new
hybrid AIS-ACO framework and the summary of this chapter is provided in Section
35
32 Monte Carlo Method
The Monte Carlo method is a simulation algorithm that can be carried out many
times to produce numerical samples that accurately reflect the probability
distribution of the real results [90] [91] This method is always used to solve power
system issues involving uncertain parameters [92] The uncertainties are allocated
randomly and each simulation is operated numerous times In theory the more
simulations are running the less deviation error between actual mean value and
sample mean value Therefore it is important to determine the overall running times
of the Monte Carlo simulation The convergence or stopping criteria is used to
determine the simulation times required to obtain acceptable accurate results
The confidence interval acts as a good estimate of the unknown parameters The
probability that the true parameter remains in the confidence interval is calculated as
follows [93]
119862 = 119875(119883 minus 119871 le 120583 le 119883 + 119871) = int 119866(119883)119889119909119883+119871
119883minus119871 (3-1)
119871 = 119911lowast 120590
radic119899 (3-2)
Chapter 3 Optimisation Techniques
Page | 62
where 119862 is the degree of confidence is the estimated mean value 119871 is the
confidence interval which provides an estimate range of values which probably
contains an unknown population parameter 120583 is the true population mean value
119866(119883) is the Gaussian distribution 120590 is the sample standard deviation and 119899 is the
number of samples the estimation of 119911lowast is based on the degree of confidence 119862 as
presented in Table 3-1 The most common 119911lowast is 196 and the corresponding 119862 is
095
Table 3-1 Relationship of 119911lowast and 119862
119862 09 095 099 0999
119911lowast 1645 1960 2576 3291
The required number of samples could be expressed as
119899 = (119911lowast120590
119871)2 (3-3)
There are several methods used to determine the sample size and to obtain results
with acceptable accuracy One is by predefining the maximum sample size 119873 when
119899 reaches 119873 the simulation is stopped Another one is by using the degree of
confidence 119862 The confidence interval 119871 is calculated and compared with the
predefined 119871 for each sample and the simulation reaches the stopping criteria when
the confidence interval is less than the critical value
33 Ant Colony Optimisation
The ant colony optimisation method is one of the metaheuristic techniques that has
been employed for the solution of combinational optimisation problems in recent
years [60] The ant colony system (ACS) simulates the behaviour of real ants [94]
[95] The moving paths of artificial ants construct the candidate solutions to a
problem [96] The ants communicate with other ants by a chemical substance called
pheromones [97] Originally all the ants start from their nest and search for their
food in a random manner When the food source is found the ants leave a chemical
Chapter 3 Optimisation Techniques
Page | 63
substance trail on the way home The pheromone deposited by the ants is used as the
primary guide function for the other ants The pheromones will then evaporate after a
period of time As all of the ants travel approximately at the same speed the shortest
path has the largest probability to contain more pheromones because more ants
choose this one The ants tend to follow the path that has more pheromones than
others After a brief period the shortest path with the most intensity of pheromones
could attract more and more ants providing feedback to the system that promotes the
use of best paths [98] Fig 3-1 represents the behaviours of real ants [69]
Fig 3-1 Example of ant colony system [69]
As shown in Fig 3-1 (a) all the ants are travelling in the same path which connects
point A and point B by a straight line The environment is changed due to the
occurrence of an obstacle in Fig 3-1 (b) and (c) At first all the ants choose the left
or right path randomly because they have no guide It is assumed that they move
through path C or D with the same probability Later on the ants that choose path C
will move faster than that choose path D As a result the pheromones deposited on
path C accumulate faster than those on the path D and this attracts more ants to
choose path C Finally all the ants tend to choose the shortest path (path C) as this
contains the most pheromones
The flowchart of ACO algorithm is shown in Fig 3-2 and the main stages of the
algorithm are presented as follows [69] [94] [95] [97] [98]
Initialisation In this stage the trail intensity on each edge in the search
space is initialised to a constant positive value and all the ants are located in
Chapter 3 Optimisation Techniques
Page | 64
the nest
Ant Dispatch In this step each ant begins its tour at the starting point and
chooses the next node to move to according to a probabilistic selection rule
which involves the intensity of pheromones deposited on each node by other
ants [88] [99] The ants prefer to choose the path with a higher pheromones
This process is repeated until all the ants have reached the food source
Quality Function Evaluation After all the ants have completed a tour the
relevant quality function of the optimisation problem is calculated to evaluate
the performance of each ant If any constraint is violated the configuration is
discarded Otherwise the objective function is evaluated
Trail Intensity Update There are two pheromone updating rules applied in
this step One is called the global pheromone update It accumulates the
pheromone values on the high-quality solution path to improve convergence
However the pheromone intensity of each edge evaporates over time due to
another rule called the local pheromone update This update is used to
enlarge the search space and to avoid premature convergence for local
minima Ants travelling between two nodes update the relevant pheromone
intensity in the corresponding edge
Convergence Determination This process is operated until the maximum
iteration number is reached or all the ants choose the same path between their
home colony and food source
Chapter 3 Optimisation Techniques
Page | 65
Start
Set Iteration n=1
Maximum iteration
reached
End
No
Yes
Initialise the parameters for ACO algorithm
searching space and build graph of the tours
Dispatch ants based on the
amount of pheromones on edges
Quality function evaluation
Trail intensity update
Record the high quality solutions of this
iteration and empty all location lists
n=n+1
Fig 3-2 Flowchart of the ant colony algorithm
The above procedure should be modified to a computational procedure to solve
different optimisation problems and this is discussed in the following chapters
Several factors need to be taken into account when designing an ACO algorithm
such as search space transition probability etc
34 AIS-ACO Hybrid Algorithm
341 Artificial Immune Systems
The immune system acts as a defensive barrier to recognise and eliminate foreign
antigens ie bacteria virus etc B lymphocytes are the main immune cells in the
biological immune system and originate in the bone marrow Being exposed to an
Chapter 3 Optimisation Techniques
Page | 66
antigen a specific antibody is produced on the surfaces of B cells and an immune
response is elicited to make antibodies recognise and bind the antigen [88] [100]
Those B cells whose antibodies best match the antigen are activated and cloned
several times [88] This process is called cloning To identify the most suitable
antibodies for the antigen it is necessary to cause the antibody and the antigen to
interact more closely with each other This is achieved through a process call
hypermutation in which random changes are introduced into the genes of the cloned
B cells [88] One such change might lead to an increase or decrease in the closeness
between antibody and antigen [88] The new B cells can only survive if they are
closely related to the antigen and therefore the B cells that are closely related are
then chosen to enter the pool of memory cells [100] These cloning hypermutation
and selection processes are called the clonal selection principle [101] By repeating
this principle a number of times the immune system learns to respond more
efficiently for the same antigen
Several computational models of the AIS have been developed recently as the
immune system is an adaptive learning system that has the following specifications
learning memory recognition of foreigners and pattern recognition [102]
342 Proposed AIS-ACO Hybrid Algorithm
The proposed AIS-ACO hybrid algorithm combines the advantages of AIS and ACO
The hypermutation developed from the AIS is used as a random operator by
adopting random changes to perturb a solution and hence to enlarge the search space
However the pheromones provided by the ACO can store information about the
quality of solution components for improving the objective functions [88] In
addition the information obtained from pheromone updating guides the algorithm in
its search and improves the convergence rate [88]
The limitation of ACO is that the algorithm can easily fall into a local optimum
which might be due to an insufficient range of candidate solutions This can be made
up by the random changes of solutions in AIS through hypermutation Also the
weakness of the global searching ability in AIS is improved by the pheromone tables
in ACO Thus the new hybrid AIS-ACO framework based on the pheromone-based
hypermutation method has better diversity and convergence in comparison with
either the AIS or ACO algorithms
Chapter 3 Optimisation Techniques
Page | 67
Start
Cloning
Maximum iteration
reached
End
No
Yes
Initialise and set iteration number n=1
Hypermutation
Fitness evaluation
Non-dominated solutions extraction
Pheromone updating
n=n+1
Record the Pareto front and
Pareto optimal solutions
In this thesis the AIS-ACO hybrid approach is used to generate a set of non-
dominated solutions The antigen is the multi-objective function and the antibody is
the solution to the problem The affinity between the antibody and the antigen is the
Pareto dominance among solutions which indicates the quality of the solution [88]
All the non-dominated solutions experience cloning hypermutation and selection
until the maximum number of iterations is reached The flowchart of the AIS-ACO
algorithm for Pareto optimality is presented in Fig 3-3
Fig 3-3 Flowchart of the AIS-ACO algorithm
Chapter 3 Optimisation Techniques
Page | 68
The key parts of the algorithm are explained as follows
Initialisation At the beginning of this algorithm a set of initial solutions is
generated These solutions should meet the condition of constraints The
information related to each objective is represented by an individual
pheromone table Each pheromone value represents the probability of
selection of the corresponding edge in the network model [88] All
pheromone values are initially set as the same value
Cloning The number of clones for each non-dominated solution should be
the same as the number of objectives and also as the number of pheromone
tables [88]
Hypermutation The selection of an edge in each cloned solution for
hypermutation is dependent on its pheromone values [88] A higher
pheromone value of a cell in the table indicates that the corresponding edge
in the network is more likely to be selected
Non-dominated solutions extraction This is the process of selecting non-
dominated solutions according to their affinity value [99] All the solutions
are compared as presented in Section 2103 and all the non-dominated
solutions are then extracted for the next iteration
Pheromone updating The aim of this stage is to accumulate the pheromone
values on the edges that belong to a part of the non-dominated solutions and
this is called the global pheromone update However the pheromone
intensity of all edges will evaporate over time by the local pheromone update
This update is used to explore the entire search space
Termination This process is operated until the maximum iteration number
is reached The set of final non-dominated solutions is called the Pareto set
which is used to solve the problem [88]
35 Summary
This chapter introduces the techniques for assessment of mono-objectivemulti-
objective optimisation problems The optimisation techniques are categorised into
two groups simulation methods and analytical methods
Chapter 3 Optimisation Techniques
Page | 69
The Monte Carlo method is a typical simulation technique and is generally used to
handle uncertain parameters It can find the best solution with a high degree of
accuracy but requires a considerable amount of CPU time and memory The
application of this methodology is discussed in Chapter 4 In that chapter an
efficient methodology based on the Monte Carlo Method is proposed for finding
transformer economic operation modes and optimal tie-switch placement strategies
to minimise transformer loss
The ACO algorithm is one of the metaheuristic techniques designed for assessment
of distribution automation (DA) problems It simulates the behaviour of artificial
ants with positive feedback and distributed computation The positive feedback
enhances the search speed in order to find the global solution and the distributed
computation explores the search space The ACO algorithm is able to find the global
solution in a reasonable computation time It is used for either loss reduction or
reliability improvement as discussed in Chapter 5-7 In addition a new multi-
objective ACO (MOACO) algorithm for assessment of multi-objective DNR
problems in terms of Pareto optimality is provided in Chapter 8
The AIS-ACO hybrid algorithm is a combination of AIS and ACO Hypermutation
is used in AIS as a random operator by using random changes to perturb a solution to
maintain the diversity of the solutions avoiding premature convergence for local
minima The pheromone tables used in the ACO are used to direct the algorithm
towards high quality solutions [88] The AIS-ACO hybrid algorithm is always used
for assessing the DA problem in terms of multiple objectives optimisation in order
to obtain a set of non-dominated solutions In addition the advantages of the AIS-
ACO algorithm over the MOACO algorithm for the assessment of multi-objective
optimisation problems are also discussed in Chapter 8
Page | 70
CHAPTER 4
TRANSFORMER ECONOMIC
OPERATION amp DISTRIBUTION
NETWORK RECONFIGURATION FOR
TRANSFORMER LOSS REDUCTION
41 Introduction
The electrical power generation transmission and distribution companies are not
only energy producers but also significant power consumers Energy loss occurs in
the process of power transfer and takes place in all electrical equipment including
generators power lines and transformers The large number and power capacity of
transformers used in a transformer and distribution network means transformer loss
is a significant component in energy loss The lifetime cost of energy loss in a
transformer is significant especially when one considers rising electricity demand
and the cost of the energy supplied For this reason it is important to tackle the
causes of transformer loss and the problems which then ensue so that energy
consumption can be reduced To support this statement several research projects
that have focused on transformer loss reduction are discussed in Section 242
Chapter 4 Transformer Economic Operation amp Distribution Network
Reconfiguration for Transformer Loss Reduction
Page | 71
An efficient methodology based on the Monte Carlo Method for the 3311 kV
transformer loss reduction with consideration of the voltage issues observed on a
distribution network is proposed in this chapter For a substation with two
transformers there are three operation modes that can occur 1) single transformer in
separate operation 2) two transformers in parallel operation 3) transformer
economic operation (TEO) as mentioned in Section 24 With regard to the load
models which are also discussed in this chapter a database containing numerous
domestic electricity demand profiles is imported into MATLAB to work as the
profile generators A Monte Carlo simulation platform is established by combining
the residential demand profiles with a 3311 kV distribution network model built in
OpenDSS Based on this platform the impacts of three operation modes of
transformers on transformer loss minimisation are investigated and compared
In addition an enumeration approach used for the optimum relocation of tie-switches
in a linked 11 kV distribution network is also suggested The process that involves
changing the distribution network topology by relocation of tie-switches is called
distribution network reconfiguration (DNR) [13] [14] The control centre can
change the location of tie-switches and the transformer operation modes (TOMs) in
each substation based on load data and simulated power loss from the test system at
each time interval The proposed approach is applied to the test system and the
effectiveness of an optimal planning strategy using TEO and DNR to achieve
minimum transformer loss is demonstrated through the results obtained
The remainder of this chapter is structured as follows Section 42 explains the load
models Section 43 describes the mathematical formulation of transformer loss
Section 44 analyses the methodology used to minimise transformer loss whilst
maintaining satisfactory voltages and the case studies and the results are presented
and discussed in Section 45 Finally the main conclusions are summarised in
Section 46
Chapter 4 Transformer Economic Operation amp Distribution Network
Reconfiguration for Transformer Loss Reduction
Page | 72
42 Load Model
In order to access the performance of the distribution feeders with different operation
modes of transformers in the substation the time-series behaviour of loads has to be
modelled
The value of the load associated with domestic electricity demand customers has
been obtained from the research described in [19] this can produce a random 1-min
resolution model for UK households There are six steps for creating a domestic
electricity demand model as shown in Fig 4-1 Table 4-1 presents the proportion of
household sizes based on UK statistics [103]
Fig 4-1 Procedure of domestic electricity demand profile generation
Table 4-1 Household size by number of people in household as a proportion [103]
Number of people
in household
1 2 3 4 ge5
Percentage () 3058 341 1557 1288 686
A pool of 10000 different load profiles covering 24 hours in a typical February
weekday are generated by this model For computation reasons the 1440 1-min
time-step load profiles are integrated as 144 10-min resolution profiles in this study
Specify the number of residents in the house from 1 to 5
Specify either a weekday or
weekend
Select the month of the year from 1 to
12
Random allocate appliances to the
dwelling
Run the active occupancy model
Run the electricity demand simulation
Chapter 4 Transformer Economic Operation amp Distribution Network
Reconfiguration for Transformer Loss Reduction
Page | 73
(active power is recorded for each minute and then averaged at intervals of 10
minutes) The power factors of all the loads are set to 095
43 Problem Formulation
The objective of this study is to minimise transformer loss through TEO and optimal
DNR The energy loss of the transformer is related to active power However as a
transformer draws reactive power (it takes current) it causes real power loss in the
network The integrated power loss refers to the sum of active power loss of the
transformer itself and the increased active power loss contributed by reactive power
loss of the transformer [73] The mathematical formulation can be expressed as
follows
Minimise 119891 = 1198800
2119875119885119874119862 +1205732
11988002 119875119885119878119862 119905119903119886119899119904119891119900119903119898119890119903 119894119899 119904119894119899119892119897119890 119900119901119890119903119886119905119894119900119899
211988002119875119885119874119862 +
1
2
1205732
11988002 119875119885119878119862 119905119903119886119899119904119891119900119903119898119890119903119904 119894119899 119901119886119903119886119897119897119890119897 119900119901119890119903119886119905119894119900119899
(4-1)
where 119875119885119874119862 and 119875119885119878119862 are the integrated no-load loss (kW) and the full-load loss (kW)
120573 =119878119871
119878119873 represents the transformer load factor S is the transformer actual loading
(kVA) 119878119873 is the transformer rated capacity (kVA) 1198800 is the operational voltage of
the transformer secondary side in per unit
44 Methodology
In this study there are two methodologies used for transformer loss reduction which
are called TEO and DNR
441 Transformer Economic Operation
In this section a Monte Carlo simulation platform for three TOMs comparison is
established as shown in Fig 4-2 and the flowchart of the transformer loss assessment
is presented in Fig 4-3
Chapter 4 Transformer Economic Operation amp Distribution Network
Reconfiguration for Transformer Loss Reduction
Page | 74
Fig 4-2 Monte Carlo simulation platform for three transformer operation modes comparison
Firstly a pool of 10000 10-min daily domestic electricity demand profiles is
randomly generated by the profile generators in MATLAB Following this each
node in the feeders from the system is assigned with residential demand profiles
from the pool using the Monte Carlo Method Theses profiles and one of the TOMs
are then imported into the distribution network model built in OpenDSS After this a
sequential load flow calculation is performed and the simulation results are returned
including voltage profiles and transformer losses to MATLAB The obtained
results are then analysed and compared with the system constraints for each time
step In this study for each TOM the calculation is set to be repeated 10000 times
in order to satisfy the convergence criteria When the losses of all TOMs are
calculated the minimum transformer loss and its associated operation mode are
obtained
Profile
generator of
domestic
electricity
demand profiles
Transformer
operation
modes
MATLAB
Distribution
network
model built
in OpenDSS
Analyse and
compare
simulation
results in
MATLAB
Load flow calculation
Chapter 4 Transformer Economic Operation amp Distribution Network
Reconfiguration for Transformer Loss Reduction
Page | 75
Start
Monte Carlo trail number N=1
All transformer operation
modes considered
End
No
Yes
Select demand profiles to each
customer randomly
Select transformer operation
mode
Sequentially run power flow
calculation for 144 10-minute time step
Record results
Change
transformer
operation
mode
N=N+1
Maximum iteration reached
Minimum transformer loss and its associated
transformer operation mode are obtained
No
Yes
Load and aggregate the domestic
electricity demand profiles pool
(144 10-minute time steps)
Fig 4-3 Flowchart of transformer loss assessment
Chapter 4 Transformer Economic Operation amp Distribution Network
Reconfiguration for Transformer Loss Reduction
Page | 76
442 Distribution Network Reconfiguration
Reconfiguration of radial distribution system is achieved by local control of tie-
switches located in linked feeders The Monte Carlo simulation platform through
DNR is presented in Fig 4-4
Fig 4-4 Monte Carlo simulation platform for distribution network reconfiguration
In the proposed strategy the tie-switch status is modified by the control centre and
the detailed control algorithm is discussed below
Step 1 Random load profiles are first selected
Step 2 When the load profiles have been imported into the network model a
sequential load flow calculation is performed to calculate and compare the
transformer loss under different network configurations (different tie-switches
location) at each time interval
Step 3 Minimum transformer loss and its associated network configuration are
obtained
Step 4 Location of tie-switches based on minimum transformer loss over a whole
day is recorded
Step 5 Optimal DNR strategy is obtained
Profile
generator of
domestic
electricity
demand profiles
Tie-switch
status
MATLAB
Distribution
network
model built
in OpenDSS
Analyse and
compare
simulation
results in
MATLAB
Load flow calculation
Chapter 4 Transformer Economic Operation amp Distribution Network
Reconfiguration for Transformer Loss Reduction
Page | 77
45 Application Studies
To demonstrate the impact of TOMs and DNR on transformer loss the proposed
methodologies are applied to two test networks Several scenarios are tested and the
results are analysed and reported
451 Test Case 1
The single line diagram of the network shown in Fig 4-5 is developed from the UK
generic distribution network [104] The network model is built to incorporate a 3311
kV substation supplying the downstream loads in the OpenDSS software
environment The two transformers have the same specifications and their
characteristics are presented in Table 4-2 The corresponding TCLF is calculated as
5244 The 11 kV network is represented by four outgoing feeders from a single
busbar For computation reasons three of the feeders are simplified lumped loads
whilst the 4th
feeder is modelled in detail The 4th
11 kV feeder consists of eight
nodes which represents a small system with a total of 252 domestic single phase
house loads connected on each node A Monte Carlo simulation approach is
implemented to select these load profiles randomly from a pool of domestic
electricity demand profiles Each house in the 4th
feeder is then assigned with a
residential demand profile The loads in the other three feeders are then lumped with
the same daily profile of the 4th
feeder All the values of the network components are
based on a broad collection from [104] [105] and are recorded in Appendix A1
In this test a comparison of the three TOM methods for transformer loss
minimisation is provided A time-series load flow algorithm is implemented to
quantify the changes in feeder voltage and transformer loss in the previous described
3311 kV UK distribution network for different TOMs In this test three scenarios
are studied and summarised as follows
Scenario 1 Single transformer in separate operation
Scenario 2 Two transformers in parallel operation
Scenario 3 Transformer economic operation in this mode if the transformer load
factor is less than TCLF only one transformer remains in service if the transformer
load factor is higher than TCLF two transformers are operated in parallel
Chapter 4 Transformer Economic Operation amp Distribution Network
Reconfiguration for Transformer Loss Reduction
Page | 78
A
A
A
A
B
B
B
B
Load1Load2Load3Load4_1
Load4_2
Load4_3
Load4_4
Load4_5
Load4_6
Load4_7
Load4_8
75 MVA
33 kV
11 kV
33 kV
Voltage
Source
75 MVA
Fig 4-5 Generic distribution network topology
Table 4-2 Parameters of a typical 3311 kV two-winding transformer [106]
Sub-
sector
Transf
Rating
(kVA)
Conn Tapping
Range
Load
Losses
at
75
(kW)
No-
Load
Losses
(kW)
Impedance voltage
at rated current for
the principle
tapping
()
Reference
standard
Urban 7500 YY0 plusmn75
6 steps of 25
Each
50
75
835 BS 171 amp
IEC 60076
1) Test 1-1 Base Case
The simulation results of transformer load factor variation are shown in Fig 4-6 and
the transformer loss variation curves are presented in Fig 4-7 It is observed that the
transformer loss in Scenario 3 is the same as in Scenario 1 between 000 to 630 and
Chapter 4 Transformer Economic Operation amp Distribution Network
Reconfiguration for Transformer Loss Reduction
Page | 79
0
10
20
30
40
50
60
70
80
90
100
0 2 4 6 8 10 12 14 16 18 20 22
Tran
sfo
rme
r Lo
ad F
acto
r
Time (h)
0
10
20
30
40
50
60
70
0 2 4 6 8 10 12 14 16 18 20 22
Tran
sfo
rme
r Lo
sse
s (k
W)
Time (h)
0
10
20
30
40
50
60
70
0 2 4 6 8 10 12 14 16 18 20 22
Tran
sfo
rme
r Lo
sse
s (k
W)
Time (h)
the same in Scenario 2 from 1800 to 2200 With the introduction of Scenario 3 the
minimum loss is around 9 kW at 000 which is below the 18 kW of Scenario 2 The
maximum loss of Scenario 3 is nearly 40 kW at 1900 which is far below the 60 kW
of Scenario 1
Fig 4-6 Transformer load factor variation
(a) Scenario 1
(b) Scenario 2
Chapter 4 Transformer Economic Operation amp Distribution Network
Reconfiguration for Transformer Loss Reduction
Page | 80
0
10
20
30
40
50
60
70
0 2 4 6 8 10 12 14 16 18 20 22
Tran
sfo
rme
r Lo
sse
s (k
W)
Time (h)
(c) Scenario 3
Fig 4-7 Transformer loss variations in different scenarios
The mean values of 3311 kV transformer energy loss during one day under different
scenarios are presented in Table 4-3 As shown in Fig 4-6 the average transformer
load factor during a whole day is slightly below the TCLF (5244 in this test) This
situation is more suitable for a single transformer than two transformers The loss in
Scenario 3 reaches the lowest value and results in a reduction of 1133 and 1441
in comparison with Scenario 1 and Scenario 2
Table 4-3 Daily transformer loss in different scenarios
Scenario 1 Scenario 2 Scenario 3
Transformer losses (kWh) 53982 55922 47865
According to the EN50160 standard [7] under normal conditions at least 95 of the
10-min average mean rms voltage magnitude in the 11 kV electricity distribution
network should be within the range 09 pu to 11 pu over one week In other words
the 95th
percentile voltage profile is compared with the allowed voltage range to
check the networkrsquos reliability
The mean and 95th
percentile voltage profiles at each node in the fourth feeder are
presented in Fig 4-8 It can be seen that the voltage level at each node can change
considerably after the scenario changes It also appears that the nodes in Scenario 1
experience the most severe voltage drop in comparison with the other two scenarios
The worst 95 voltage value of the node lsquoLoad4_8rsquo at the end of the studied feeder
in Scenario 1 is around 098 pu which is not as satisfactory as the results of 0987 pu
and 0984 pu observed in Scenario 2 and Scenario 3
Chapter 4 Transformer Economic Operation amp Distribution Network
Reconfiguration for Transformer Loss Reduction
Page | 81
0976
0978
098
0982
0984
0986
0988
099
0992
Load4_1 Load4_2 Load4_3 Load4_4 Load4_5 Load4_6 Load4_7 Load4_8
Vo
ltag
e (
pu
)
Scenario1
Scenario2
Scenario3
0974
0976
0978
098
0982
0984
0986
0988
099
Load4_1 Load4_2 Load4_3 Load4_4 Load4_5 Load4_6 Load4_7 Load4_8
Vo
ltag
e (
pu
)
Scenario1
Scenario2
Scenario3
(a) Mean value
(b) 95th
value
Fig 4-8 11 kV 4th
feeder voltage profiles in different scenarios
To show in detail the voltage profiles affected by different TOMs the load at the
start of the 4th
feeder lsquoLoad4_1rsquo and the end one lsquoLoad4_8rsquo have been selected
Since the Monte Carlo method produces many loss and voltage values it is
preferable to present the averages of all these values and their deviations
As shown in the charts from Fig 4-9 and Fig 4-10 the voltage drops severely from
1800 to 2000 which is also the maximum daily demand period It also appears that
the voltage profile in Scenario 3 is the same as in Scenario 1 between 000 to 630
and the same as in Scenario 2 from 1800 to 2200 With the introduction of Scenario
Chapter 4 Transformer Economic Operation amp Distribution Network
Reconfiguration for Transformer Loss Reduction
Page | 82
088
09
092
094
096
098
1
0 2 4 6 8 10 12 14 16 18 20 22
Bu
s V
olt
age
(p
u)
Time (h)
088
09
092
094
096
098
1
0 2 4 6 8 10 12 14 16 18 20 22
Bu
s V
olt
age
(p
u)
Time (h)
088
09
092
094
096
098
1
0 2 4 6 8 10 12 14 16 18 20 22
Bu
s V
olt
age
(p
u)
Time (h)
3 the lowest voltage of lsquoLoad4_8rsquo is around 097 pu which is significantly above
the lower limit 090 pu
(a) Scenario 1
(b) Scenario 2
(c) Scenario 3
Fig 4-9 Voltage profiles of Load 4_1 in different scenarios
Lower Limit
Lower Limit
Lower Limit
Chapter 4 Transformer Economic Operation amp Distribution Network
Reconfiguration for Transformer Loss Reduction
Page | 83
088
09
092
094
096
098
1
0 2 4 6 8 10 12 14 16 18 20 22
Bu
s V
olt
age
(p
u)
Time (h)
088
09
092
094
096
098
1
0 2 4 6 8 10 12 14 16 18 20 22
Bu
s V
olt
age
(p
u)
Time (h)
088
09
092
094
096
098
1
0 2 4 6 8 10 12 14 16 18 20 22
Bu
s V
olt
age
(p
u)
Time (h)
(a) Scenario 1
(b) Scenario 2
(c) Scenario 3
Fig 4-10 Voltage profiles of Load 4_8 in different scenarios
Lower Limit
Lower Limit
Lower Limit
Chapter 4 Transformer Economic Operation amp Distribution Network
Reconfiguration for Transformer Loss Reduction
Page | 84
0976
0978
098
0982
0984
0986
0988
099
0992
Load4_1 Load4_2 Load4_3 Load4_4 Load4_5 Load4_6 Load4_7 Load4_8
0 25
5244 75
100
As most people are sleeping late at night and the transformer load factor is less than
the TCLF transformers are in individual operation mode When most people are at
home again from 1800 the transformer load factor increases beyond the TCLF As a
result the voltage profiles are improved when transformers are operated in parallel
In conclusion when the transformer load factor is less than the TCLF transformers
in a separate service result in less loss but more voltage dips however transformers
operating in parallel cause lower voltage drops but more loss When the transformer
load factor is higher than the TCLF transformers in parallel operation cause less loss
and lower voltage drops As a result based on the economic operation theory the
transformer in Scenario 3 significantly reduces transformer loss and maintains the
voltages at a satisfactory level
2) Test 1-2 TCLF Sensitivity Analysis
In this test the value of TCLF used to distinguish whether the transformer should be
in separate or parallel operation is discussed The complete process presented
previously is carried out again but takes into account the effect of different critical
values 0 25 5244 75 and 100
Fig 4-11 shows the effect on the mean voltage magnitudes of various TCLFs The
results indicate that the voltage profile is closely related to the TCLF and the TCLF
should be decreased to increase the region in which transformers operate in parallel
This will improve the voltage profiles
Fig 4-11 11 kV 4th
feeder mean voltage profile of various TCLFs
Chapter 4 Transformer Economic Operation amp Distribution Network
Reconfiguration for Transformer Loss Reduction
Page | 85
Table 4-4 describes the effect on the transformer loss when TCLF is changed It
reaches the lowest value when TCLF is 5244 If the TCLF is decreased or
increased above this value the loss increases Overall the TCLF should be set to
5244 in order to minimise transformer loss
Table 4-4 Transformer loss with different TCLF
TCLF () 0 25 5244 75 100
Transformer loss
(kWh)
55922 50783 47865 49414 53982
As presented in Table 4-5 the average number of switching operations is increased
as the TCLF is approached to its optimum value
Table 4-5 Average number of switching operations with different TCLF
TCLF () 0 25 5244 75 100
Average number of
switching operations
0 2 4 2 0
452 Test Case 2
The impacts of TOMs and DNR on transformer loss are evaluated in this section As
presented in Fig 4-12 the model of the test system is developed from the
duplication of the generic distribution network shown in Fig 4-5 All the values of
the network parameters are obtained from [104]ndash[106] The system is supplied by
two 3311 kV substations and each bus has four feeders There is one linked feeder
with nine tie-switches Tie-switches refer to the switches of the network that are
normally open The function of the tie-switches is to alter the network topology to
provide various routes for supplying loads In order to feed all loads and keep the
systemrsquos radial topology only one tie-switch is open and all the others are closed
Chapter 4 Transformer Economic Operation amp Distribution Network
Reconfiguration for Transformer Loss Reduction
Page | 86
0
02
04
06
08
1
12
14
16
0 2 4 6 8 10 12 14 16 18 20 22
Act
ive
Po
we
r (k
W)
Time (h)
TW1 TW2 TW3 TW4 TW5
A1
A2
A3
A4_1 A4_2 A4_3 A4_4 A4_5 A4_6 A4_7 A4_8 B4_8 B4_7 B4_6 B4_5 B4_4 B4_3 B4_2 B4_1
B1
B2
B3
EndA EndB
TW9TW8TW7TW6
Tie-Switch (close) Tie-Switch (open)
Fig 4-12 Test system
For simplicity the daily load variations in each feeder are the same and the load
profiles of each node in the linked feeder are also the same Therefore the loads
could be categorised into two groups
Group 1 A1 A2 A3 B1 B2 B3
Group 2 A4_1 A4_2 A4_3 A4_4 A4_5 A4_6 A4_7 A4_8 B4_1 B4_2
B4_3 B4_4 B4_5 B4_6 B4_7 B4_8
On the basis of transformer load factor variation shown in Fig 4-6 the relevant 10-
min resolution load models of the two groups are presented in Fig 4-13 The power
factors of all the loads are set to 095
(a) Group 1
Chapter 4 Transformer Economic Operation amp Distribution Network
Reconfiguration for Transformer Loss Reduction
Page | 87
0
002
004
006
008
01
012
014
016
018
02
0 2 4 6 8 10 12 14 16 18 20 22
Act
ive
Po
we
r (k
W)
Time (h)
(b) Group 2
Fig 4-13 Daily load variations for different load groups
As this test system is developed from the duplication of the generic distribution
network and all the loads have the same profiles the position of the tie-switch is
selected from lsquoTW1rsquo to lsquoTW5rsquo For example the tie-switch located in lsquoTW1rsquo has the
same effect as lsquoTW9rsquo The control strategy is used to quantify the changes in feeder
voltage and transformer loss in the previously described test system under different
scenarios which could be categorised as
Scenario 1 each end has one transformer in operation and the tie-switch is located
at TW1 ie entire feeder supplied from end B
Scenario 2 each end has one transformer in operation and the tie-switch is located
in TW5 ie feeder split at mid-point
Scenario 3 each end has one transformer in operation and the location of the tie-
switch is based on minimum transformer loss operation
Scenario 4 each end has two transformers in operation and the tie-switch is located
at TW1
Scenario 5 each end has two transformers in operation and the tie-switch is located
at TW5
Scenario 6 each end has two transformers in operation and the location of the tie-
switch is based on minimum transformer loss operation
Chapter 4 Transformer Economic Operation amp Distribution Network
Reconfiguration for Transformer Loss Reduction
Page | 88
Scenario 7 each end has onetwo transformers in operation based on the transformer
load factor and the tie-switch is located at TW1
Scenario 8 each end has onetwo transformers in operation based on the transformer
load factor and the tie-switch is located at TW5
Scenario 9 each end has onetwo transformers in operation based on the transformer
load factor and the location of the tie-switch is based on minimum transformer loss
operation
Table 4-6 indicates the mean value of 3311 kV transformer loss during one day
under different scenarios As can be seen from the table when the tie-switches have
the same location TW1 transformer loss in Scenario 7 results in a reduction of
1396 and 1456 in comparison with Scenario 1 and Scenario 4 In conclusion
the mode introducing a flexible number of transformers in operation based on TCLF
reduces the loss In addition the transformer loss in Scenario 9 is 9528 kWh per day
which is 217 and 014 lower than Scenario 7 and Scenario 8 As a result the
variation of tie-switch locations could reduce transformer loss The detailed location
of the tie-switch in Scenario 9 is included in Appendix B1
Table 4-6 Transformer loss in Test Case 2
Scenarios S1 S2 S3 S4 S5 S6 S7 S8 S9
Loss
(kWhday)
11319 10848 10848 11399 11162 11162 9739 9572 9528
The graph presented in Fig 4-14 illustrates the voltage variation caused by the tie-
switch relocation The node voltages in Scenario 1 experience the worst profile
which increases to a peak of 09749 pu from 09675 pu along the linked feeder In
order to reduce the loss the tie-switch is always located in the middle of the feeder
TW5 in Scenario 3 As a result the voltage profiles of Scenario 2 and Scenario 3 are
the same It should be noted that Scenario 2 experiences a slight drop from 09787 pu
to 0972 pu and then climbs back to 09827 pu It can also be clearly seen that the
voltage reaches the lowest value where the tie-switch is located The further away
the nodes are from the tie-switch the better the voltage profiles that can be obtained
In addition when the tie-switch moves closer to the middle of the linked feeder the
Chapter 4 Transformer Economic Operation amp Distribution Network
Reconfiguration for Transformer Loss Reduction
Page | 89
096
0962
0964
0966
0968
097
0972
0974
0976
0978
098
A4_1A4_2A4_3A4_4A4_5A4_6A4_7A4_8B4_8B4_7B4_6B4_5B4_4B4_3B4_2B4_1
Vo
ltag
e (
pu
)
Scenario1
Scenario2
Scenario3
0955
096
0965
097
0975
098
0985
099
A4_1A4_2A4_3A4_4A4_5A4_6A4_7A4_8B4_8B4_7B4_6B4_5B4_4B4_3B4_2B4_1
Vo
ltag
e (
pu
)
Scenario1
Scenario4
Scenario7
voltage performance is improved And the detailed voltage values at each node in the
linked feeder for different scenarios are presented in Appendix B1
Fig 4-14 Mean voltage profiles in S1 S2 and S3
As shown in Fig 4-15 the voltage variation is due to a change in TOMs
Fig 4-15 Mean voltage profiles in S1 S4 and S7
As in the case of the tie-switch located in lsquoTW1rsquo all the node voltages experience a
rise along the linked feeder from lsquoEndArsquo to lsquoEndBrsquo It should be noted that the node
voltages in Scenario 4 achieve the best profile which increase to a peak of 0984 pu
from 0976 pu As discussed in Test Case 1 the transformers in parallel operation
could improve the voltage profiles In addition the flexible number of transformers
Chapter 4 Transformer Economic Operation amp Distribution Network
Reconfiguration for Transformer Loss Reduction
Page | 90
in operation based on TCLF (Scenario 7) shows a slight difference in voltage from
that in Scenario 4
As discussed above the location of the tie-switch and the change of TOMs have an
impact on the feeder voltage variation The tie-switch located in the middle of the
feeder and transformers with parallel operation defines the best voltage profiles
46 Summary
This chapter illustrates why transformer economic operation (TEO) is an economical
solution to reduce transformer loss The substation composed of two transformers
with the same characteristics has been used as an example to introduce the general
approach of determining the TCLF and TEO area A Monte Carlo simulation
platform was established to tackle load uncertainties A methodology to prove that
the TOM variation affects the performance of the 11kV distribution network is
discussed and analysed The TEO mode with minimum loss and satisfactory voltages
is achieved depending on the the transformer load factors by operating with either
one or two transformers and can be summarised as when the transformer load factor
is less than the TCLF transformers should be in separate operation when the
transformer load factor is higher than the TCLF transformers are recommended to
operate in parallel This results in a reduction of 1441 over the conventional
transformer loss ie when two transformers are in parallel operation However
simulation studies also indicate voltage profiles are improved when transformers
operate in parallel Therefore a slight reduction in TCLF results in an increased loss
but an improvement in voltage performance
The effectiveness of a DNR strategy has also been proposed through the results
obtained The presented results illustrate the impact of different TOMs in each
substation and tie-switch statuses on transformer loss and the voltages measured
along the feeder during a 24 hour operating period The optimal economic operation
strategy with TEO and DNR have successfully reduced the transformer loss and
improved the voltage profiles The further away the nodes are from the tie-switch
the better the voltage profiles obtained In addition when the tie-switch moves closer
to the middle of the linked feeder the voltage performance is improved
Chapter 4 Transformer Economic Operation amp Distribution Network
Reconfiguration for Transformer Loss Reduction
Page | 91
In normal operating conditions transformers operate in parallel and the tie-switch is
located in the middle of the linked feeder As indicated by Table 46 the daily
energy loss in Scenario 5 is 11162 kWh After the introduction of Scenario 9 the
annual saving energy could be 59641 kWh
Page | 92
CHAPTER 5
DISTRIBUTION NETWORK
RECONFIGURATION amp DG ALLOCATION
FOR FEEDER LOSS REDUCTION
51 Introduction
Distribution networks generally operate in radial configuration to ease protection
coordination and to reduce short circuit current [107] Distribution feeders can be
reconfigured to alter the network topology at normal and abnormal operating
conditions by changing the openclose status of switches to satisfy the operatorrsquos
objectives [13] [14]
DG is a small electric generation unit that is connected directly to the distribution
network or appears on side of the meter accessed by the customer [16] With the
increasing number of DGs bidirectional power flows have appeared and locally
looped networks have become inevitable [17] Therefore the type size and location
of DGs in the distribution networks strongly affect power system operation and
planning
The studies in [5] indicate that about 5 of the total power generation is wasted in
the form of feeder loss at the distribution level Reduction in active power loss can
help distribution network operators (DNOs) save costs and increase profits The
Chapter 5 Distribution Network Reconfiguration amp DG Allocation for Feeder Loss
Reduction
Page | 93
optimal distribution network reconfiguration (DNR) placement and sizing of DGs
strategies should be used to reduce feeder loss while satisfying the operating
constraints
The ant colony optimisation (ACO) developed by M Dorigo is a metaheuristic
algorithm for the assessment of optimisation problems [94] It is based on the
pheromones deposited by ants as a guide for finding the shortest path between a food
source and their home colony The detailed description of ACO algorithm has been
presented in Section 33 In this chapter an ACO algorithm is proposed to solve the
network reconfiguration and DG placement problems simultaneously based on
distribution feeder loss minimisation The proposed technique is tested on two
standard IEEE 33-node and 69-node systems and the simulation results show the
performance and effectiveness of the proposed method Four scenarios are
considered during network reconfiguration and DG allocation The impacts of DG
capacity on assessing the DNR and DG allocation problems in terms of feeder loss
reduction are also studied Moreover the results obtained by ACO algorithm have
been compared to those from other algorithms in the literature
As for the remainder of this chapter the mathematical formulation of the objective
function and its constraints are explained in Section 52 Section 53 discusses the
application of ACO algorithms in order to solve the problem Section 54 provides a
detailed analysis of the numerical results and Section 55 provides the final
conclusions
52 Problem Formulation
The proposed objective function (F) of the problem is formulated to minimise the
feeder loss of a distribution network which is described as follows
119872119894119899119894119898119894119904119890 119891 = sum 119896119894119877119894(119875119894
2+1198761198942
1198801198942 )
119873119887119894=1 (5-1)
where 119877119894 is the resistance of the ith branch 119875119894 and 119876119894 are the real power (W) and
reactive power (VAr) at the receiving end of branch i 119880119894 represents the rms voltage
at the receiving end of branch i (V) 119896119894 is a binary variable 119896119894 = 0 indicates that
Chapter 5 Distribution Network Reconfiguration amp DG Allocation for Feeder Loss
Reduction
Page | 94
branch 119894 is open and 119896119894 = 1 indicates that branch 119894 is closed The detailed feeder loss
assessment has been given in Section 28
Subject to
∆119881119899 le ∆119881119898119886119909 for all load points (5-2)
119868119887 le 119868119898119886119909 for all branches (5-3)
119875119894 le 119875119894119898119886119909 (5-4)
det(119860) = 1 119900119903 minus 1 (5-5)
Constraints (5-2) ndash (5-3) represent the computed voltages and currents and should be
in their permissible range Constraint (5-4) indicates that the power flow at all
branches should be within the limits defined for each branch Constraint (5-5)
ensures the radial topology of the network [32] The branch to node incidence matrix
Arsquo has one row for each branch and one column for each node 119886119894119895 represents the
coefficient in row i and column j 119886119894119895 = 0 if branch i is not connected with node j
119886119894119895 = 1 if branch i is directed away from node j and 119886119894119895 = minus1 if branch i is directed
towards node j When the column corresponding to the reference node and the rows
of open branches are deleted from matrix Arsquo a new square branch-to-node matrix A
is obtained Then the determinant of A is calculated If det(A) is 1 or -1 the system is
radial Otherwise the system is not radial
53 Solution Method
531 Distribution Network Reconfiguration
With regard to the DNR problem each solution is represented by a string of integers
which indicates the location of tie-switches As the number of tie-switches that keep
the network radial is always constant the number of the solutionrsquos elements is equal
to the number of tie-switches in the network
Chapter 5 Distribution Network Reconfiguration amp DG Allocation for Feeder Loss
Reduction
Page | 95
Home
1 2 NP1NP1-1
1 2 NP1-1 NP1
1 2 NP1NP1-1
1 2 NP2-1 NP2
1 2 NP2NP2-1
1 2 NP2-1 NP2
1 2 NP2NP2-1
1 2 NP2-1 NP2
Food
Stage
1
2
NT-1
NT
NT+1
NT+2
NT+NDG-1
NT+NDG
Part 1 Number of
existing tie-switches
Part 2 Number
of DGs
532 Applying ACO to DNR and DGs Placement
In this chapter an ACO algorithm is adopted to find the optimum locations of tie-
switches and sites of DGs placement in the network in terms of feeder loss
minimisation When the locations of tie-switches and DGs are changed a new
network configuration will be formed For each network configuration the feeder
loss is evaluated by using the approach presented in Section 52
Fig 5-1 Search space of DNR and DGs Placement
Chapter 5 Distribution Network Reconfiguration amp DG Allocation for Feeder Loss
Reduction
Page | 96
The search space of the DNR and DG allocation problems is modelled as a directed
graph as shown in Fig 5-1 In Part I the states signify the location of tie switches
and the sites for DGs installation are represented by states in Part II The number of
stages in this graph is the sum of the amount of existing tie-switches 119873119905 and the
number of installed DGs 119873119863119866 1198731199011is the number of possible locations for the tie-
switches relocation and 1198731199012 is the number of candidate buses for DGs installation
Artificial ants start their tours at home moving along the paths in the graph and end
at the food source Each location list consists of a string of integers and represents a
solution to the problem Different orders of the solutionrsquos elements indicate different
routes However several routes might indicate a certain solution as the order of the
solutionrsquos elements makes no difference to the network configuration For example
the solution vector (1 2 3) represents the same network configuration as the solution
vector (3 2 1) And the objective functions of these two routes are the same In this
study the first route that the ants found will be chosen as the feasible solution The
flowchart of the proposed ACO algorithm is presented in Fig 5-2 and is expressed in
five steps
Step 1 Initialisation First of all all the ants are initially located at home The
pheromone values of the edges in the search space are all set to a small positive
constant value
Step 2 Ant Dispatch All the ants are sent in parallel from the home colony and one
of the states is chosen in the next stage according to a probabilistic selection rule
which involves the intensity of pheromones deposited on the states [66] The
locations of the tie-switches are determined first and the sites for the DGs
installation are then selected The probability of an ant choosing state j of the next
stage y is
119875119895119910(119873) =
120591119895119910
(119873)
sum 120591119895119910
(119873)ℎisin∆119910
(5-6)
where 120591119895119910
(119873) is the pheromone value of state j of stage y at iteration N ∆119910 is the set
of available states which an ant can choose at stage y
Chapter 5 Distribution Network Reconfiguration amp DG Allocation for Feeder Loss
Reduction
Page | 97
Step 3 Objective Function Evaluation After all the ants have completed their tour
the location list and corresponding objective function in (5-1) for each ant are
evaluated If any constraint in (5-2) - (5-5) is violated the corresponding solution is
assigned with a huge value and is discarded If not all the objective functions are
assessed and the best configuration of the Nth iteration with minimum objective
function 119891119887119890119904119905(119873) is recorded This should be compared to the best configuration
obtained so far 119891119887119890119904119905 if 119891119887119890119904119905(119873) lt 119891119887119890119904119905 the best solution should be updated such
that 119891119887119890119904119905 = 119891119887119890119904119905(119873) [14] If not the best configuration found in the previous
iteration is retained After this the location list is emptied and all the ants are free to
choose a new trail
Step 4 Pheromone Updating The aim of this step is to favour transitions towards
states involving high quality solutions with greater pheromones There are two rules
of pheromone updating the local rule and global rule
Local rule The amount of pheromone deposited in the search space should be
evaporated to make paths less attractive The local pheromone update rule is
calculated as following
120591119895119910
(119873) = (1 minus 120588)120591119895119910
(119873 minus 1) + 120591119888 (5-7)
where 120588 is the pheromone evaporation rate which is set between 0 and 1 120591119888 is a
small positive constant value Even if the amount of pheromone deposited on an
edge is at the lowest value of 120591119888 there is a slight chance that an ant will still choose
this edge
Global rule The global pheromone updating rule involves ants depositing large
amounts of pheromone to the edges that belong to the highest quality solution per
iteration This rule is to guide the search to find the global optimal solution The
pheromones of those edges can be modified by
120591119895119910(119873) = 120591119895
119910(119873) + 120588119891119887119890119904119905
119891119887119890119904119905(119873) (5-8)
After applying the local and global pheromone updating rules the method Max-Min
ACO algorithm is integrated into the proposed approach
120591119895119910(119873) = 120591119898119886119909 119894119891 120591119895
119910(119873) ge 120591119898119886119909 (5-9)
120591119895119910(119873) = 120591119898119894119899 119894119891 120591119895
119910(119873) le 120591119898119894119899 (5-10)
Chapter 5 Distribution Network Reconfiguration amp DG Allocation for Feeder Loss
Reduction
Page | 98
Start
Set Iteration n=1
Maximum iteration
reached
Output best
configuration and end
No
Yes
Initialise the parameters for ACO algorithm
searching space and build graph of the tours
Dispatch ants based on the
amount of pheromones on edges
Relocate tie-switches and DGs by location lists
Calculate the objective function for each ant
The pheromones are updated according
to local and global rules
n=n+1
Record the best solution so far and empty
all location lists
Read system topology
and load data
where 120591119898119886119909and 120591119898119894119899 are the higher and lower bound of the pheromone level on each
edge respectively The trail limit of the pheromone ensures the probabilities of all
the edges are greater than zero which maintains the diversity of the solutions and
avoids premature convergence for local minima
Step 5 Termination The computation continues until the predefined maximum
number iterations is reached The best tour selected among all iterations implies the
optimal solution
Fig 5-2 Flowchart of the ACO applied to DNR and DGs placement
Chapter 5 Distribution Network Reconfiguration amp DG Allocation for Feeder Loss
Reduction
Page | 99
54 Application Studies
To demonstrate the performance and effectiveness of the proposed technique in
assessing the network reconfiguration and placement of DG problems
simultaneously the proposed ACO is implemented on two 1266 kV test systems
consisting of 33 and 69 buses The network models are built in OpenDSS and the
solution algorithm is developed in MATLAB For both test systems the substation
voltage is assumed to be 10 pu and all the branches and buses are considered as
candidate locations for tie-switches and DG placement respectively In this study
for simplicity the number of installed DGs is three All the DGs are synchronous
generators and are represented as PQ models with a 100 kVA capability and a
power factor equal to 10 For the purpose of better illustration and comparison four
cases are considered to analyse the superiority and performance of the proposed
method
Case I System is without reconfiguration and has no DGs (base case)
Case II System is optimally reconfigured and has no DGs
Case III System is optimally reconfigured after DGs are placed at certain buses
Case IV System is optimally reconfigured and DGs are optimally placed
simultaneously
It is to be noted that the ACO control parameters are different for each test case
They are set experimentally using information from several trial runs The final
combinations that provide the best results for all of the above tests are given in
Appendix C1
541 33-bus System
In this section the proposed procedure is implemented on a 33-bus 1266 kV radial
distribution system with 37 branches and 5 tie-switches whose single-line diagram
is shown in Fig 5-3 The tie-switches are located at L33 to L37 represented by red
dotted lines The data of line and load are taken from [108] and summarised in
Appendix A2 The total real and reactive power loads of the system are 3715 kW
and 2300 kVAr respectively The performance of the presented method for the four
Chapter 5 Distribution Network Reconfiguration amp DG Allocation for Feeder Loss
Reduction
Page | 100
10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
18 19 20 21
22 23 24
25 26 27 28 29 30 31 32
L1 L2 L3 L4 L5 L6 L7 L8 L9 L10 L11 L12 L13 L14 L15 L16 L17
L18
L19 L20 L21
L22
L23 L24
L25
L26 L27 L28 L29 L30 L31 L32
L33
L34
L35
L36
L37
cases is given in Table 5-1 The network losses in each branch for all test cases are
listed in Appendix B2
Fig 5-3 33-bus system
Table 5-1 Results of different cases for the 33-bus system
Case Active feeder
loss (kW)
Minimum voltage
(pu)
(Bus No)
Location of tie-switches
on Fig 53
DG location
Case I 20314 09116 (B17) L33 L34 L35 L36 L37 NA
Case II 13981 09361 (B31) L7 L9 L14 L32 L37 NA
Case III 11753 09357 (B31) L7 L9 L14 L28 L31 B17 B21 B24
Case IV 10844 09462 (B32) L7 L9 L14 L32 L37 B30 B31 B31
Case I base case
For the base case without reconfiguration and DGs the initial active feeder loss of
this system is 20314 kW The lowest bus voltage is 09116 pu and this occurs at
Bus 17
Case II with reconfiguration only (no DGs)
In this case only reconfiguration is considered and no DGs are installed The
network configuration after DNR is shown in Fig 5-4 The number of the solutionrsquos
elements for this case is 5 which is the number of tie-switches After DNR the total
feeder loss is 13981 kW which corresponds to a 3118 reduction in loss In
addition the minimum voltage also increases from 09116 pu to 09361 pu
Chapter 5 Distribution Network Reconfiguration amp DG Allocation for Feeder Loss
Reduction
Page | 101
10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
18 19 20 21
22 23 24
25 26 27 28 29 30 31 32
L1 L2 L3 L4 L5 L6 L7 L8 L9 L10 L11 L12 L13 L14 L15 L16 L17
L18
L19 L20 L21
L22
L23 L24
L25
L26 L27 L28 L29 L30 L31 L32
L33
L34
L35
L36
L37
Fig 5-4 33-bus system for feeder loss minimisation Case II
To illustrate the performance of the proposed ACO the results are compared with
the results obtained using the branch exchange method (BEM) [109] harmony
search algorithm (HSA) [110] fireworks algorithm (FWA) [16] particle swarm
optimisation (PSO) [55] and invasive weed optimisation (IWO) [111] these are all
described in the literature and are presented in Table 5-2 It is observed that the
results obtained from the ACO are identical to those from the HAS PSO and IWO
but better than the results from the BEM and FWA This is because that BEM and
FWA have plunged into a local optimal solution and they lack the ability to escape
from it
Table 5-2 Comparison of simulation results for 33-bus system in Case II
Method Feeder loss
(kW)
Loss reduction
()
Tie-switches location Minimum
voltage (pu)
The proposed ACO 13981 3118 L7 L9 L14 L32 L37 09361
BEM [109] 14054 3082 L7 L10 L14 L32 L37 09361
HSA [110] 13981 3118 L7 L9 L14 L32 L37 09361
FWA [16] 14026 3095 L7 L9 L14 L28 L32 09396
PSO [55] 13981 3118 L7 L9 L14 L32 L37 09361
IWO [111] 13981 3118 L7 L9 L14 L32 L37 09361
Moreover both the continuous genetic algorithm (CGA) [112] and cuckoo search
algorithm (CSA) [113] are implemented to further investigate the performance of the
proposed ACO It is important to note that the performance of the ACO CGA and
CSA depends on the selection of their control parameters All three algorithms are
solved 100 times The average maximum minimum and standard deviation of the
100 runs are compared and shown in Table 5-3 The convergence number is defined
Chapter 5 Distribution Network Reconfiguration amp DG Allocation for Feeder Loss
Reduction
Page | 102
10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
18 19 20 21
22 23 24
25 26 27 28 29 30 31 32
L1 L2 L3 L4 L5 L6 L7 L8 L9 L10 L11 L12 L13 L14 L15 L16 L17
L18
L19 L20 L21
L22
L23 L24
L25
L26 L27 L28 L29 L30 L31 L32
L33
L34
L35
L36
L37
DG2
DG1
DG3
as the number of the iterations when the objective function is convergence It can be
seen that all three algorithms have obtained the same minimum loss However the
proposed ACO method has a higher probability in finding the global optimum
solution as the mean and standard deviation of the fitness values of the ACO
algorithm are less than those obtained by the other algorithms Furthermore as the
average value of convergence number of the ACO is less than that of the other two
algorithms this means the proposed algorithm has a higher convergence rate In
terms of the computation times the proposed ACO runs faster when compared with
CGA and CSA
Table 5-3 Comparison of ACO with CGA and CSA for the 33-bus system in Case II
Method Feeder loss (kW) Convergence number Average
computation
times
(second)
AVG MAX MIN STD AVG STD
ACO 13981 13981 13981 0 228 821 1448
CGA [112] 14002 14619 13981 12121 5463 2986 3926
CSA [113] 13986 14028 13981 01328 8363 3425 7258
AVG MAX MIN and STD mean the average maximum minimum and standard deviation of the 100 runs
Case III with reconfiguration only (with DGs)
In this case the three DGs are located at the end of the feeders ie Bus 17 21 24
The network configuration after DNR is illustrated in Fig 5-5 As shown in Table 5-
1 the network reconfiguration results in a reduction of 4214 in feeder loss in
comparison with the original network without DGs and a reduction of 1594 in
comparison with the reconfigured system without DGs
Fig 5-5 33-bus system for feeder loss minimisation Case III
Chapter 5 Distribution Network Reconfiguration amp DG Allocation for Feeder Loss
Reduction
Page | 103
10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
18 19 20 21
22 23 24
25 26 27 28 29 30 31 32
L1 L2 L3 L4 L5 L6 L7 L8 L9 L10 L11 L12 L13 L14 L15 L16 L17
L18
L19 L20 L21
L22
L23 L24
L25
L26 L27 L28 L29 L30 L31 L32
L33
L34
L35
L36
L37
DG2DG1
DG3
Case IV with reconfiguration and DG allocation
Fig 5-6 illustrates the optimal network configuration and DG locations The network
is reconfigured and DGs are allocated simultaneously in this case Therefore the
number of the solutionrsquos elements for this case becomes 8 which is the sum of the
number of tie-switches and DGs The results show the final configuration with a
feeder loss of 10844 kW with 4662 2244 and 773 reduction in comparison
with that in Case I Case II and Case III respectively
Fig 5-6 33-bus system for feeder loss minimisation Case IV
In this case the impacts of DG capacity on assessing the DNR and DG allocation
problems in terms of feeder loss reduction are also studied The capacity of each DG
is set as 100 400 700 and 1000 kVA respectively The feeder losses for different
DG capacities are shown in Fig 5-7 Before simultaneous reconfiguration and DG
allocation the feeder loss decreases from 1783 kW to 1023 kW when the capacity
of DG is increased from 100 kVA to 700 kVA However the feeder loss increases to
1042 kW if the capacity of DG continuously grows to 1000 kVA The inappropriate
network configuration and DG location might result in loss increment when the size
of the DG is increased However with the introduction of network reconfiguration
and DG allocation feeder loss is reduced no matter what the capacity of DG is This
proves that the proposed methodology can reduce the total feeder loss by
determining the most suitable network topology and DG locations in comparison
with the original configuration
Chapter 5 Distribution Network Reconfiguration amp DG Allocation for Feeder Loss
Reduction
Page | 104
086
088
09
092
094
096
098
1
102
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32
Vo
ltag
e (
pu
)
Bus No
Case I
Case II
Case III
Case IV
0
20
40
60
80
100
120
140
160
180
200
100 400 700 1000
Fee
de
r lo
ss (
kW)
DG Capacity (kVA)
Before simultaneousreconfiguration and DG allocation
After simultaneous reconfigurationand DG allocation
Fig 5-7 Comparison of feeder loss for different DG capacities before and after simultaneous
reconfiguration and DG allocation
The voltage profiles of four cases are compared and shown in Fig 5-8 It can be seen
that the voltage profiles at most buses in Case IV have been improved in comparison
with the other three cases In terms of Case III and Case IV the buses which inject
DGs show the improvement in voltage profiles ie the voltage of Bus 31 is
improved from 09357 pu in Case III to 09537 pu in Case IV In Case IV as Bus 32
is the furthest bus being supplied its voltage is the lowest value among all buses In
conclusion the systemrsquos voltage profiles are improved by optimal DNR and DG
allocation
Fig 5-8 Comparison of voltage profiles in different cases of 33-node system
Chapter 5 Distribution Network Reconfiguration amp DG Allocation for Feeder Loss
Reduction
Page | 105
10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
27
28
29
30
31 32 33 34
35
36
37
38 39 40 41 42 43 44 45
46 47 48 49
50
51
52
53 54 55 56 57 58 59 60 61 62 63 64
65 66
67 68
L1 L2 L3 L4 L5 L6 L7 L8 L9 L10 L11 L12 L13 L14 L15 L16 L17 L18 L19 L20 L21 L22 L23 L24 L25 L26
L27
L28
L29
L30
L31 L32 L33 L34
L35
L36
L37
L38 L39 L40 L41 L42 L43 L44 L45
L46
L47 L48 L49
L50
L51
L52
L53 L54 L55 L56 L57 L58 L59 L60 L61 L62 L63 L64
L65
L66
L67
L68
L69
L70
L71
L72L73
542 69-bus System
This is a large-scale radial distribution system consisting of 73 branches and 5 tie-
switches whose single-line diagram is shown in Fig 5-9 The tie-switches are
located at L69 to L73 represented by red dotted lines The line and load data of the
system are taken from [84] and summarised in Appendix A3 The total power loads
are 379589 kW and 26891 kVAr respectively Similar to 33-bus system this
system is also simulated for four cases and the results are given in Table 5-4 The
network losses in each branch for all test cases are listed in Appendix B2
Fig 5-9 69-bus system
Table 5-4 Results of different cases for the 69-bus system
Case Active feeder
loss (kW)
Minimum voltage
(pu)
(Bus No)
Tie-switches location DG location
Case I 22562 09072 (B64) L69 L70 L71 L72 L73 NA
Case II 9885 09476 (B60) L14 L55 L61 L71 L72 NA
Case III 8758 09477 (B60) L13 L55 L61 L71 L72 B26 B45 B64
Case IV 7397 09571 (B60) L14 L55 L61 L71 L72 B60 B60 B60
Case I base case
Base case active feeder loss in the system is 22562 kW The lowest bus voltage is
09072 pu and occurs at bus 64
Chapter 5 Distribution Network Reconfiguration amp DG Allocation for Feeder Loss
Reduction
Page | 106
10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
27
28
29
30
31 32 33 34
35
36
37
38 39 40 41 42 43 44 45
46 47 48 49
50
51
52
53 54 55 56 57 58 59 60 61 62 63 64
65 66
67 68
L1 L2 L3 L4 L5 L6 L7 L8 L9 L10 L11 L12 L13 L14 L15 L16 L17 L18 L19 L20 L21 L22 L23 L24 L25 L26
L27
L28
L29
L30
L31 L32 L33 L34
L35
L36
L37
L38 L39 L40 L41 L42 L43 L44 L45
L46
L47 L48 L49
L50
L51
L52
L53 L54 L55 L56 L57 L58 L59 L60 L61 L62 L63 L64
L65
L66
L67
L68
L69
L70
L71
L72L73
Case II with reconfiguration only (no DGs)
After DNR switches at L14 L55 L61 L71 and L72 are opened as shown in Fig 5-
10 The total feeder loss is reduced by 5619 and the minimum voltage is
increased to 09476 pu in comparison with the base case
Fig 5-10 69-bus system for feeder loss minimisation Case II
The comparisons of results among the proposed ACO with FWA [16] HSA [110]
and genetic algorithm (GA) [110] are presented in Table 5-5 It is observed that the
results obtained from the ACO are better than those from the FWA HSA and GA
as these algorithms are trapped into the local optimal solution
Table 5-5 Comparison of simulation results for 69-bus system in Case II
Method Feeder loss
(kW)
Loss reduction
()
Tie-switches location Minimum
voltage (pu)
The proposed ACO 9885 5619 L14 L55 L61 L71 L72 09476
FWA [16] 9886 5618 L14 L56 L61 L71 L72 09476
HSA [110] 10546 5326 L13 L18 L56 L61 L72 09475
GA [110] 10242 5461 L14 L53 L61 L71 L72 09462
Case III with reconfiguration only (with DGs)
In this case the three DGs are located at the end of the feeders ie Bus 26 45 64
The network configuration after DNR is illustrated in Fig 5-11 As shown in Table
Chapter 5 Distribution Network Reconfiguration amp DG Allocation for Feeder Loss
Reduction
Page | 107
10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
27
28
29
30
31 32 33 34
35
36
37
38 39 40 41 42 43 44 45
46 47 48 49
50
51
52
53 54 55 56 57 58 59 60 61 62 63 64
65 66
67 68
L1 L2 L3 L4 L5 L6 L7 L8 L9 L10 L11 L12 L13 L14 L15 L16 L17 L18 L19 L20 L21 L22 L23 L24 L25 L26
L27
L28
L29
L30
L31 L32 L33 L34
L35
L36
L37
L38 L39 L40 L41 L42 L43 L44 L45
L46
L47 L48 L49
L50
L51
L52
L53 L54 L55 L56 L57 L58 L59 L60 L61 L62 L63 L64
L65
L66
L67
L68
L69
L70
L71
L72L73
DG3
DG1
DG2
10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
27
28
29
30
31 32 33 34
35
36
37
38 39 40 41 42 43 44 45
46 47 48 49
50
51
52
53 54 55 56 57 58 59 60 61 62 63 64
65 66
67 68
L1 L2 L3 L4 L5 L6 L7 L8 L9 L10 L11 L12 L13 L14 L15 L16 L17 L18 L19 L20 L21 L22 L23 L24 L25 L26
L27
L28
L29
L30
L31 L32 L33 L34
L35
L36
L37
L38 L39 L40 L41 L42 L43 L44 L45
L46
L47 L48 L49
L50
L51
L52
L53 L54 L55 L56 L57 L58 L59 L60 L61 L62 L63 L64
L65
L66
L67
L68
L69
L70
L71
L72L73
DG3DG1
DG2
5-5 the network reconfiguration results in a reduction of 6118 in feeder losses as
compared with the original network without DGs and a reduction of 1140 in
comparison with the reconfigured system without DGs
Fig 5-11 69-bus system for feeder loss minimisation Case III
Case IV with reconfiguration and DG allocation
Fig 5-12 illustrates the optimal network configuration and DG locations In this case
the results show the final configuration with a feeder loss of 7397 kW with 6721
2517 and 1554 reduction in comparison with that in Case I Case II and Case
III respectively
Fig 5-12 69-bus system for feeder loss minimisation Case IV
Chapter 5 Distribution Network Reconfiguration amp DG Allocation for Feeder Loss
Reduction
Page | 108
0
50
100
150
200
250
100 400 700 1000
Fee
de
r lo
ss (
kW)
DG Capacity (kVA)
Before simultaneousreconfiguration and DG allocation
After simultaneous reconfigurationand DG allocation
In this case the impacts of DG capacity on assessing the DNR and DG allocation
problems in terms of feeder loss reduction are also studied The capacity of each DG
is set as 100 500 900 and 1300 kVA respectively The feeder loss curves for
different DG capacities are shown in Fig 5-13 After simultaneous reconfiguration
and DG allocation the feeder loss decreases from 7397 kW to 873 kW when the
DG capacity is increased from 100 kVA to 900 kVA However the loss bounces
back to 114 kW if the DG capacity continues to increase to 1300 kVA This means
that the capability of network reconfiguration and DG allocation on feeder loss
reduction is limited when the size of DGs is large But the proposed methodology
can still reduce the total feeder loss for all DG capacities by determining the most
suitable network topology and DG locations in comparison with the original
configuration
Fig 5-13 Comparison of feeder loss for different DG capacities before and after simultaneous
reconfiguration and DG allocation
Fig 5-14 shows the voltage profile of the 69-bus system It can be seen that the
voltage profiles at most buses in Case IV have been improved in comparison with
the other three cases Compared with Case III and Case IV the buses which inject
DGs show improvement in voltage profiles ie the voltage of Bus 60 is improved
from 09477 pu in Case III to 09571 pu in Case IV In Case IV although there are
three DGs connected as Bus 60 as the value of load connected at this bus is the
largest (1244 kW) this bus voltage is the lowest among all buses In conclusion the
systemrsquos voltage profiles are improved by optimal DNR and DG allocation
Chapter 5 Distribution Network Reconfiguration amp DG Allocation for Feeder Loss
Reduction
Page | 109
086
088
09
092
094
096
098
1
102
0 5 10 15 20 25 30 35 40 45 50 55 60 65
Vo
ltag
e (
pu
)
Bus No
Case I
Case II
Case III
Case IV
Fig 5-14 Comparison of voltage profiles in different cases of 69-node system
55 Summary
In this chapter the application of optimal planning using DNR and DG allocation for
the problem of distribution feeder loss minimisation has been implemented The
method based on ACO has been successfully applied to the 1266 kV 33-bus and 69-
bus systems to find the optimum system configuration and DG locations
There are four cases used to analyse the superiority and performance of the proposed
method The proposed ACO is capable of finding the optimal solutions in all cases
In Case IV the feeder losses are reduced by 4662 and 6721 for the 33-bus and
69-bus system respectively in comparison with the base case Therefore Case IV is
found to be more effective in minimising the total loss and improving voltage
profiles compared to the other cases The numerical results show that for best
performance the existing tie-switches are relocated and the DGs are optimally
placed in comparison with the original network In addition the impacts of DG
capacity on assessing the DNR and DG allocation problems in terms of feeder loss
reduction are also studied The inappropriate network configuration and DG location
might result in loss increment when the size of DG is increased The proposed
methodology has successfully reduced the total feeder loss for different capacities of
DG by determining the most suitable network topology and the DG locations
Chapter 5 Distribution Network Reconfiguration amp DG Allocation for Feeder Loss
Reduction
Page | 110
compared to the original configuration The minimum loss obtained by DNR and DG
allocation decreases as the capacities of DGs are increased However this decrease
stops when DGs can supply all the loads without the main supply After that the
minimum loss increases as the capacities of DGs are increased
Moreover the simulation results have been compared with other classical methods in
literature and the proposed ACO is more efficient and is more likely to obtain the
global optimum solution
Page | 111
CHAPTER 6
DISTRIBUTION NETWORK
RECONFIGURATION amp TRANSFORMER
ECONOMIC OPERATION FOR NETWORK
LOSS REDUCTION
61 Introduction
Rapid increases in electricity demand have forced electric power utilities throughout
the world into major reconstructing processes As a significant proportion of electric
energy is dissipated in the operation of a distribution network the reduction of loss
should be considered an important problem for the economic operation of the overall
system [82]
Load variations have been disregarded in most studies on distribution automation
(DA) problems ie average loads were used in their reconfiguration schemes In this
chapter distribution loads experience daily and seasonal variations The study
considers the daily load curves of different types of consumers (residential
commercial and industrial) and in addition the days are divided into eight types
spring weekdays spring weekends summer weekdays summer weekends autumn
Chapter 6 Distribution Network Reconfiguration amp Transformer Economic
Operation for Network Loss Reduction
Page | 112
weekdays autumn weekends winter weekdays and winter weekends The best
reconfiguration hours during each of these typical days are then selected
The objective function for finding the best configuration of the network when
considering feeder loss and transformer loss will be studied in this chapter Different
combinations of locations of tie-switches in the network and operation modes of all
transformers in the substations represent different network configurations An Ant
colony optimisation (ACO) algorithm is adopted on an 11 kV distribution network
developed from Bus 4 of the Roy Billinton Test System (RBTS) to determine the
optimal network configuration during each type of day Furthermore the effects of
DGs and EVs in solving distribution network reconfiguration (DNR) and
transformer economic operation (TEO) based on network loss reduction are also
investigated
This chapter is organised as follows the next section discusses the variation of loads
and the reconfiguration hours Section 63 presents the objective function and
constraints for DNR Section 64 describes the application of ACO algorithms to the
problem Numerical studies are presented and discussed in Section 65 and finally
Section 66 summarises the main conclusions
62 Time-varying Load Model
As distribution loads experience daily and seasonal variations the optimum network
configuration constantly changes [82] However it is not reasonable to reconfigure a
network frequently ie based on hourly schedule since each switch has a maximum
number of allowable switching operations during its lifetime and frequent switching
actions will increase its maintenance costs [82]
However infrequent actions cause the system to work well below its optimum state
In order to determine the best reconfiguration time during a day the daily load
profiles should be smoothed In other words the daily load curves are divided into a
number of periods As the maintenance cost of a switch increases with the increasing
number of switching actions the number of intervals is a trade-off between the
optimum reconfiguration and switch cost As there is a peak and a valley of network
Chapter 6 Distribution Network Reconfiguration amp Transformer Economic
Operation for Network Loss Reduction
Page | 113
Actual daily load curve
Smoothed daily load curve
load variations during a day it is appropriate to divide the 24 hours daily load curves
into two periods Increasing the number of intervals will not change the nature of the
problem but will increase its complexity
Fig 6-1 The reconfiguration hours for a typical day
As the difference between 1198751 and 1198752 is increased the effect of DNR on loss
reduction increases where 1198751 and 1198752 are the average active power of the loads
during the first and second time periods respectively As shown in Fig 6-1 hours
1199051and 1199052 are calculated to maximise |1198751 minus 1198752| It should also be noted that the above
load smoothing methodology is only used to determine the reconfiguration intervals
and the active power loss during each interval is calculated based on the actual daily
load curve [82]
63 Problem Formulation
In this study the 24 hours of a typical day is divided into two periods The first time
period is 0000 to 1199051 and 1199052 to 2400 and the second time period is between 1199051 and 1199052
The following objective function is calculated for all possible network configurations
during each time interval and the one that minimises the total power loss and
satisfies all constraints is selected The energy losses of the distribution network over
the first and second time interval are presented in (6-1) and (6-2) the objective
function (6-3) is to minimise f the sum of f1 and f2
P1
P2
1199051 1199052 Time (h)
Chapter 6 Distribution Network Reconfiguration amp Transformer Economic
Operation for Network Loss Reduction
Page | 114
1198911 = sum (119864119871119905 + 119879119871119905)1199051minus1119905=1 + sum (119864119871119905 + 119879119871119905) 1199051
24119905=1199052 isin 1 2 hellip 24 (6-1)
1198912 = sum (119864119871119905 + 119879119871119905)1199052minus1119905=1199051 1199052 isin 1 2 hellip 24 (6-2)
Min 119891 = 1198911 + 1198912 (6-3)
where 119864119871119905 is the feeder loss of the distribution network during hour t (kWh) 119879119871119905
represents the transformer loss during hour t (kWh) The detailed calculation of
transformer loss and feeder loss are presented in Section 27 and 28 respectively
The computed voltages currents and the power flow at all branches should be kept
in their permissible range and the network should be operated in radial The
configurations that violate any constraint are assigned with huge objective functions
and are disregarded
64 Applying ACO to DNR and TEO
In this chapter the objective of simultaneous reconfiguring network and changing
transformer operation modes is to deal with energy loss minimisation including
transformer loss and feeder loss To implement the optimisation problem the
developed ACO algorithm is adopted to find the optimum location of tie-switches
and transformer operation modes in the network When the location of tie-switches
and operation modes of transformers are changed a new network configuration will
be formed For each network configuration the objective function is evaluated by
using the approach presented in Section 63
The search space of the DNR and TEO problems is modelled as a directed graph as
shown in Fig 6-2 Each solution is represented by a string of integers which
indicates the transformer operation modes and the location of tie-switches The
number of the solutionrsquos elements is equal to the number of stages in this graph
which is the sum of the amount of main feeders (the number of transformer pairs 119873119904)
and the number of existing tie-switches 119873119905
Chapter 6 Distribution Network Reconfiguration amp Transformer Economic
Operation for Network Loss Reduction
Page | 115
Home
0 1
0 1
0 1
0 1
1 2 NPNP-1
1 2 NP-1 NP
1 2 NPNP-1
1 2 NP-1 NP
Food
Stage
1
2
Ns-1
Ns
Ns+1
Ns+2
Ns+Nt-1
Ns+Nt
Part 1
Number of
substations
Ns
Part 2 Number
of existing tie-
switches Nt
Number of candidate locations for the tie-switches NP
Fig 6-2 Search space of DNR and TEO
As shown in Fig 6-3 the number of transformer pairs is 3 and the number of
existing tie-switches is 4 Therefore the number of the solutionrsquos elements for this
system is 7 In addition the possible branches for tie-switch placement are 4
Chapter 6 Distribution Network Reconfiguration amp Transformer Economic
Operation for Network Loss Reduction
Page | 116
Tie-switch
Transformer
Fig 6-3 Sample network with three substations
For transformer operation mode selection in Part I the ACO algorithm is applied to
assign each bit of the front part of the solution vector to the status of substations and
hence the number of transformers in operation in each substation can be represented
as a binary vector
State 0 this substation has one transformer in operation
State 1 this substation has two transformers in operation
However for the relocation of existing tie-switches in Part II the states indicate the
location of switches Artificial ants will start their tours at home move along the
paths in the graph and end at the food source
The 24 hour load curve is divided into two time intervals for all load types in terms
of the principle presented in Section 62 Fig 6-4 demonstrates the computation
procedure for the transformer operation mode selection and tie-switches relocation
problem at each of the time interval The application of the ACO algorithm to the
TEO and DNR problem is similar to that in Section 532 For each time interval the
operation modes of the transformers are selected first and the locations of tie-
switches are then determined
Chapter 6 Distribution Network Reconfiguration amp Transformer Economic
Operation for Network Loss Reduction
Page | 117
Start
Set time interval T=1
Maximum iteration
reached
Output best
configuration and end
No
Yes
Divide the 24-h daily load curve into two
intervals using the technique in Section 62
Iteration N=1
Initialise the parameters for ACO
algorithm searching space
Dispatch ants based on the amount
of pheromone on edges
Relocate tie-switches and select the
number of transformers to be operated in
all substations by location lists
N=N+1
Calculate the objective function
for each ant at this time interval
Read system topology
and load data
The pheromones are updates
according to local and global rules
Record the best solution so far
and empty all location lists
T=T+1
Tgt2
Yes
t=t+1
No
Fig 6-4 Flowchart of the ACO applied to DNR and TEO for a specific type of day
Chapter 6 Distribution Network Reconfiguration amp Transformer Economic
Operation for Network Loss Reduction
Page | 118
LP11 LP12 LP13 LP14 LP15 LP16 LP17
LP8 LP9 LP10
LP1 LP2 LP3 LP4 LP5 LP6 LP7
LP32 LP33 LP34 LP35 LP36 LP37 LP38
LP29 LP30 LP31
LP26 LP27 LP28
LP18 LP19 LP20 LP21 LP22 LP23 LP24 LP25
19
20
21
22
23
24
26
25 27
28
29 30
71
13 15
14 16
17
18
69
1 3
2
5
4
7
6 8
10
9
68
11 12
56
57
58 60
59 61 62
65
64 66 67
50 52
51
54
53 55
44
45
46
47
48
49
70
31
32
33
34
36
35
39
37 38 40
41
42 43
63
F3
F2
F1
F7
F6
F5
F4
Normally Open Circuit BreakerNormally Closed Circuit Breaker
Subbus1
Subbus2
Subbus3
T1
T3
T5
Main
feeder
Main
feeder
Main
feeder
T2
T4
T6
65 Application Studies
In this study the proposed methodology is applied to an 11 kV distribution network
developed from Bus 4 of the RBTS a single-line diagram of the network is shown in
Fig 6-5 The network consists of 38 load points and 4 tie-switches the associated
data can be found in [114] The types and lengths of 11 kV feeders are listed in
Appendix A4 The network built in OpenDSS incorporates three 3311 kV double
transformer substations supplying the downstream loads
Fig 6-5 Distribution feeder connected to RBTS Bus 4
This typical urban distribution network supplies residential commercial and
industrial consumers The maximum value of active and reactive power and the
Chapter 6 Distribution Network Reconfiguration amp Transformer Economic
Operation for Network Loss Reduction
Page | 119
customer type of each node are modified from the original values and the new values
are listed in Table 6-1
Table 6-1 Revised customer data (peak load)
Number
of load
points
Load points Customer type P
(kW)
Q
(kVAr)
Number of
customers
4 1-2 9-10 residential 8869 8426 220
6 3-5 13-15 residential 8137 7731 200
12 6-7 16-17 23-25 28
30-31 37-38
commercial 6714 6378 10
6 8 11 18 26 32-33 industrial 2445 23228 1
10 12 19-22 27 29 34-
36
industrial 1630 15485 1
The days of the year are divided into eight categories spring weekdays spring
weekends summer weekdays summer weekends autumn weekdays autumn
weekends winter weekdays and winter weekends Typical loads profiles for
different consumer types are shown in Fig 6-6-6-8 which are multiplied by the
values of Table 6-1 to obtain the real demand of each node [82] In order to find the
reconfiguration hours for each day type the aggregated load profiles of the main
feeder shown in Fig 6-9 are used
Fig 6-6 Daily load profile of residential consumers
Chapter 6 Distribution Network Reconfiguration amp Transformer Economic
Operation for Network Loss Reduction
Page | 120
Fig 6-7 Daily load profile of commercial consumers
Fig 6-8 Daily load profile of industrial consumers
Fig 6-9 Daily load profile (MW) of the main feeder
Chapter 6 Distribution Network Reconfiguration amp Transformer Economic
Operation for Network Loss Reduction
Page | 121
In this case eight types of day and two time intervals for each of them are
considered As a result the optimisation problem has to be solved 16 times to obtain
a yearly reconfiguration scheme The distribution of load types for a whole year is
shown in Table 6-2
Table 6-2 The distribution of load types for a whole year
Load Types Number of days Total days
Spring
(Mar Apr May)
Weekdays 66 92
Weekends 26
Summer
(Jun Jul Aug)
Weekdays 66 92
Weekends 26
Autumn
(Sep Oct Nov)
Weekdays 65 91
Weekends 26
Winter
(Dec Jan Feb)
Weekdays 64 90
Weekends 26
Year 365 Days
For the purpose of better illustration and comparison three test cases are considered
to analyse the superiority and performance of the proposed method
Test Case 1 The system is optimally reconfigured and has no DGs and EVs
Test Case 2 The system is optimally reconfigured after DGs are placed at certain
buses
Test Case 3 The system is optimally reconfigured after integration of EVs
The proposed ACO algorithm is coded in the MATLAB to obtain the location of tie-
switches and operation modes of transformers for the optimum configuration The
settings of the ACO parameters that provided the optimum solution for these three
cases are presented in Appendix C2 The selection of parameters is a balance
between the convergence rate and the global search ability of the algorithm
Chapter 6 Distribution Network Reconfiguration amp Transformer Economic
Operation for Network Loss Reduction
Page | 122
651 Test Case 1
In this test the tie-switches are relocated and the operation modes of transformers in
all substations are changed to obtain the best network configuration with minimum
network loss
Table 6-3 Results of DNR and TEO with different load types in Test Case 1
As shown in Fig 6-5 the tie-switches are located in L68-71 and each substation has
two transformers operating in parallel for the base network configuration The test
results with different load conditions are presented in Table 6-3 Reconfiguration of
the network and changes in the operation modes of transformers in all substations
using the proposed algorithm result in a reduction of loss for all load conditions As
a result the annual energy loss is reduced from 4337150 kWh to 4117681 kWh
which amounts to a 506 reduction Both transformer loss and feeder loss are
reduced through this optimal planning using DNR and TEO It can be noted that on
winter weekdays the loading of the main feeders is very high from 800 to 2100
Spring
weekday
Spring
weekend
Summer
weekday
Summer
weekend
Autumn
weekday
Autumn
weekend
Winter
weekday
Winter
weekend
Before
Reconfiguration
Whole Day Open branches L68L69
L70L71
L68L69
L70L71
L68L69
L70L71
L68L69
L70L71
L68L69
L70L71
L68L69
L70L71
L68L69
L70L71
L68L69
L70L71
Number of operated
transformers
1st substation 2 2 2 2 2 2 2 2
2nd substation 2 2 2 2 2 2 2 2
3rd substation 2 2 2 2 2 2 2 2
Loss
(kWh)
Cable 9233 3498 8050 3151 9660 3665 11009 4080
Transformer 4301 3410 4109 3350 4372 3437 4597 3507
Total 13534 6908 12159 6501 14032 7102 15606 7587
After
Reconfiguration
1st interval Time (h) 0-7
23-24
0-6 0-7
23
0-7 0-7
22-23
0-6
0-7
22-23
0-6
Open branches L48L68
L69L71
L68L69
L70L71
L17L68
L70L71
L17L68
L70L71
L17L68
L70L71
L68L69
L70L71
L17L68
L70L71
L68L69
L70L71
Number of operated
transformers
1st substation 1 1 1 1 1 1 1 1
2nd substation 1 1 1 1 1 1 1 1
3rd substation 1 1 1 1 1 1 1 1
2nd interval Time (h) 8-22 7-23 8-22 8-23 8-21 7-23 8-21 7-23
Open branches L17L41
L65L70
L68L69
L70L71
L41L48
L65L69
L68L69
L70L71
L17L41
L65L70
L68L69
L70L71
L17L41
L65L70
L68L69
L70L71
Number of operated
transformers
1st substation 2 2 2 2 2 2 2 2
2nd substation 2 1 2 1 2 1 2 1
3rd substation 2 1 2 1 2 1 2 1
Loss
(kWh)
Cable 9043 3516 7851 3169 9519 3685 10845 4103
Transformer 3955 2616 3759 2517 4036 2656 4264 2755
Total 12998 6132 11610 5686 13479 6341 15109 6858
Chapter 6 Distribution Network Reconfiguration amp Transformer Economic
Operation for Network Loss Reduction
Page | 123
0
05
1
15
2
25
3
35
4
45
05 1 15 2 25 3
Before reconfiguration
After reconfiguration
Thus transformers in all substations are operated in parallel However during spring
weekends from 000 to 700 as the loadings supplied by all feeders are lower than
the critical transformer load factor (TCLF) and hence transformers in all substations
are operated in single In addition the loadings supplied by Feeder 4 are much larger
than that of Feeder 3 in summer weekdays between 800 to 2200 Thus the tie-
switch is moved from L71 to L41 and LP24amp25 are moved from Feeder 4 to Feeder
3 This ensures balancing of the loads between the two feeders
652 Test Case 2
In this test the presence of three DG units is taken into consideration The effect of
DGs on assessing the DNR and TEO problems in terms of loss minimisation is
studied The introduction of DGs converts a mono-source distribution network to a
multi-source one [66] The three DGs are located at the end of the feeders ie Bus
17 41 and 65 All the DGs are synchronous generators and considered as PQ models
The capacity of DG is assumed to be 05 1 15 2 25 and 3 MVA respectively
The results are shown in Fig 6-10 and show that the proposed methodology has
successfully reduced the total energy loss for different capacities of DG by
determining the most suitable network topology
Fig 6-10 Annual energy loss with different DG capacities
To
tal
loss
(G
Wh
)
DG Capacity (MW)
Chapter 6 Distribution Network Reconfiguration amp Transformer Economic
Operation for Network Loss Reduction
Page | 124
653 Test Case 3
The objective of this section is to illustrate the behaviour of the proposed
optimisation process when EVs are integrated into the existing distribution network
The impacts of EV penetration levels and charging strategies are studied This
section utilises the optimal planning using DNR and TEO as a technique to decrease
network loss whilst respecting the operation constraints It is assumed that the
battery starts charging once the EV is connected to the charger at home
The charging duration can be calculated according to the following formula [89]
119905119888 =119862119864119881times(1minus119878119874119862)times119863119874119863
120578times119875119862 (6-4)
where 119862119864119881 is the battery capacity In this section EVs are divided into four types
with different market shares and batteries as in Table 6-4 [115] 119863119874119863 and 120578 are
depth of discharge and charger efficiency (assumed to be 80 and 90 separately)
Two types of chargers with different charging rates (119875119862) are commonly used for
consumer EVs at home charging points this study assumes that 80 of EVs are
charged at 3kW (13A) and 20 at 7kW (30A) [92] SOC is state-of-charge and is
defined as the ratio of available energy to maximum battery capacity [89] It is
determined by the distance covered by the EV in terms of number of miles during
the day
Table 6-4 Characteristics of EV
Types 119862119864119881 (kWh) Maximum driving
capability (mile)
Market share ()
Micro car 12 50 20
Economy car 14 53 30
Mid-size car 18 56 30
Light truck SUV 23 60 20
According to [116] the average number of miles covered by a vehicle was reported
to be 2164 milesday in 2014 Then the SOC for an EV is calculated based on
number of miles (m) and the maximum driving capability (MDC) as follows
Chapter 6 Distribution Network Reconfiguration amp Transformer Economic
Operation for Network Loss Reduction
Page | 125
4
42
44
46
48
5
30 60 90
Before reconfiguration
After reconfiguration
119878119874119862 = 0 119898 gt 119872119863119862
119872119863119862minus119898
119872119863119862 119898 le 119872119863119862 (6-5)
As mentioned before the EVs are distributed over all the residential load points The
number of customers of residential loads is given in Table 6-1 It is reported that
each customer has 15 vehicles [92] The problem is solved for three different
penetration levels of EVs in the test network 30 60 and 90 respectively In
addition two charging strategies are introduced (1) uncoordinated charging and (2)
coordinated charging The thermal problems of cables which caused by high
penetration levels of EVs are ignored in this study
1) Uncoordinated Charging Strategy
In this part all EVs are plugged in and immediately start charging when they arrive
home In most cases the EV plug-in time is modelled by normal distribution which
increases uncertainty However in order to simplify the discussion the charging start
time is assumed to be 1800 when most people are back home from work The total
losses in the network for the different penetration levels of EVs are compared in Fig
6-11 It can be seen that as the penetration of EVs is increased the total loss also
increases But the total loss for all penetration levels decreases by implementing the
optimal planning strategy in comparison with the original network
Fig 6-11 Annual energy loss in uncoordinated charging strategy
To
tal
loss
(G
Wh
)
Penetration level ()
Chapter 6 Distribution Network Reconfiguration amp Transformer Economic
Operation for Network Loss Reduction
Page | 126
4
42
44
46
48
5
30 60 90
Before reconfiguration
After reconfiguration
2) Coordinated Charging Strategy
In this case the DNOs tend to charge the EVs during off-peak hours to avoid a clash
with the evening peak hours As a result the charging start time is delayed to 0100
when most people are sleeping The total network loss for different EV penetrations
is compared in Fig 6-12 The results show that the postponement of charging time
and optimal planning strategy has been successful in reducing the total energy loss in
comparison with the uncoordinated charging method
Fig 6-12 Annual energy loss in coordinated charging strategy
66 Summary
This study has presented a new optimal planning strategy using DNR and TEO for
distribution network loss minimisation including transformer loss and feeder loss In
this study the distribution loads experience daily and seasonal variations The day is
divided into two periods The proposed ACO algorithm has been successfully
applied to the modified Bus 4 of the RBTS to find the optimum network
configuration and economic operation mode of transformers in all substations during
each time interval Using the results obtained for reconfiguration the existing tie-
switches are relocated and the transformer operation modes are changed
Furthermore the simulation results obtained with numerical studies further
demonstrate the capability of applying the ACO algorithm to distribution network
planning including networks with DGs and EVs The proposed methodology has
successfully reduced the total network loss for different capacities of DG and
To
tal
loss
(G
Wh
)
Penetration level ()
Chapter 6 Distribution Network Reconfiguration amp Transformer Economic
Operation for Network Loss Reduction
Page | 127
different penetration levels of EVs by determining the most suitable network
topology compared to the original configuration The benefits associated with the
increasing capacity of DGs and increasing penetration levels of EVs are also
presented Comparative results show that coordinated charging of EVs results in less
energy loss compared to uncoordinated charging plan with the same EV penetration
level This is due to the postponement of charging time which avoids a clash with
the peak power demand times
The proposed ACO algorithm is suitable for planning a future network based on the
load estimation results Hence there is no limitation on the calculation time An
additional interesting point about DNR and TEO is that although the opening and
closing of switches and transformers result in the life reduction of plants the
additional costs for utilities is insignificant in comparison with the benefits they
bring All the results have proved that a distribution network can be reconfigured and
the operation modes of transformers can be changed to reduce network power loss
which can increase the profits of the distribution utilities
Page | 128
CHAPTER 7
OPTIMAL PLACEMENT OF
SECTIONALISING SWITCHES FOR
RELIABILITY IMPROVEMENT
71 Introduction
Failures in the distribution network cause the majority of service interruptions [78]
And reliability improvement becomes a motivation for distribution utilities to launch
research and demonstration projects [64] An effective method to reduce customer
minutes lost is the greater and more effective use of automated and remote controlled
sectionalising switches and feeder breaker automation This approach will reduce
customer restoration time and minimise the region of a network affected by a short-
circuit fault The effectiveness depends on the number location and type of
sectionalising switches and feeder breakers
Reliability improvement by reduction of expected customer damaged cost (ECOST)
and system interruption duration index (SAIDI) as well as the minimisation of
switch costs are considered in formulating the objective function used in this study
When there are multiple objectives to be considered a compromise solution has to
be made to obtain the best solution ECOST and switch costs can be converted into a
single objective function by aggregating these objectives in a weighted function
Chapter 7 Optimal Placement of Sectionalising Switches for Reliability
Improvement
Page | 129
However as SAIDI and switch costs have different dimensions and units a single
fuzzy satisfaction objective function is used to transform the two conflicting
objectives into fuzzy memberships and then finally to combine them into a single
objective function Also a fuzzy membership function based on the max-min
principle is presented for optimising ECOST SAIDI and switch costs
simultaneously These are achieved by the optimal installation of new switches and
the relocation of existing switches Therefore identifying the number and location of
switches becomes an optimisation problem The ant colony optimisation (ACO) is
adopted which has the ability to find near optimal solutions close to the global
minimum in a finite number of steps This algorithm is proposed for the assessing
the sectionalising switch placement (SSP) problem based on reliability improvement
and switch costs minimisation using a multi-objective function with fuzzy variables
The impact of benefit-to-cost analysis is then investigated to justify investment
expenses Furthermore the importance of the customer damage function (CDF)
variation in determining the SSP is investigated through sensitivity analysis And the
ACO parameter sensitivity analysis is also provided in this study
The mathematical formulation of the objective function is presented in Section 72
and in Section 73 the applied ACO algorithm used to address the problems of SSP
is discussed Section 74 describes the benefit-cost analysis and the numerical case
studies are presented and discussed in Section 75 The main conclusions of the study
are summarised in Section 76
72 Problem Formulation
The primary objective of this study is to resolve the three conflicting objectives
reduction of unserved energy cost decrease in the average time a customer is
interrupted and minimisation of switch costs Three formulations of objective
functions are presented and the solution is a trade-off between each objective
721 Weighted Aggregation
As ECOST and switch costs have the same units and dimensions they are
transformed into a single objective function by aggregating all the objectives in a
weighted function
Chapter 7 Optimal Placement of Sectionalising Switches for Reliability
Improvement
Page | 130
119872119894119899 119869 = micro1 ∙ 119864119862119874119878119879 + micro2 ∙ 119878119862 (7-1)
where ECOST is the system expected outage cost to customers ($) and SC is the cost
of sectionalising switches ($) micro1and micro2 are the weighting factors given to the
reliability index and the cost of switches
722 Single Fuzzy Satisfaction Objective Function with Two
Parameters
SAIDI and switch costs are associated with a membership function in a fuzzy
domain due to different dimensions The satisfaction level of each objective is
represented by the membership function [66] The higher the membership value is
the better the solution is The two objectives are combined into a fuzzy environment
and a final objective function is formulated as follows
119872119886119909 119870 = 1205961 ∙ 120572119878119860 + 1205962 ∙ 120572119878119862 (7-2)
where 120572119878119860 is the membership function value to distribution reliability improvement
by SAIDI reduction 120572119878119862 is the value of membership function for a decrease in the
switch costs 1205961and 1205962 are the constant weighting factors for each of the parameters
The optimisation process can be changed for different purposes by varying the
values of weighting factors which should satisfy the condition 1205961 + 1205962 = 1 A
higher weighting factor indicates that this parameter is more important [66] In the
fuzzy domain each objective has a membership value varying from zero to unity
[66] The proposed membership function for each objective is described below
Membership function for SAIDI reduction
The basic purpose of this membership function is to improve reliability or obtain the
minimum SAIDI Therefore the placement of sectionalising switches with a lower
SAIDI value obtains a higher membership value The membership function for
reliability improvement is formulated in (7-3) and presented in Fig 7-1 (a) As
SAIDI becomes greater than 119878119860119868119863119868119898119894119899 the degree of satisfaction is decreased This
reduction is continued until SAIDI reaches 119878119860119868119863119868119900119903119894
Chapter 7 Optimal Placement of Sectionalising Switches for Reliability
Improvement
Page | 131
0
1
0
1
120572119878119860 =
1 119878119860119868119863119868 le 119878119860119868119863119868119898119894119899119878119860119868119863119868119900119903119894minus119878119860119868119863119868
119878119860119868119863119868119900119903119894minus119878119860119868119863119868119898119894119899119878119860119868119863119868119898119894119899 lt 119878119860119868119863119868 lt 119878119860119868119863119868119900119903119894
0 119878119860119868119863119868 ge 119878119860119868119863119868119900119903119894
(7-3)
where 119878119860119868119863119868119900119903119894 is the SAIDI of the original network 119878119860119868119863119868119898119894119899 is the minimum
value of SAIDI which is obtained by placing sectionalising switches in all candidate
locations As it is not appropriate for decision makers to obtain a combination of
sectionalising switches which reduces reliability after switch placement the
minimum value of 120572119878119860 is selected as 0 if SAIDI is greater than or equal to 119878119860119868119863119868119900119903119894
(a) SAIDI reduction (b) SC reduction
Fig 7-1 Membership function for SAIDI and switch cost reduction
Membership function for switch cost reduction
The membership function for switch costs reduction is shown in Fig 7-1(b) The
mathematical equation is presented below
120572119878119862 =
1 119878119862 le 119878119862119900119903119894119878119862119898119886119909minus119878119862
119878119862119898119886119909minus119878119862119900119903119894119878119862119900119903119894 lt 119878119862 lt 119878119862119898119886119909
0 119878119862 ge 119878119862119898119886119909
(7-4)
where 119878119862119900119903119894 and 119878119862119898119886119909 are the original and maximum value of switch costs
respectively The maximum switch costs are obtained by installing sectionalising
switches in all candidate sites
723 Single Fuzzy Satisfaction Objective Function with Three
Parameters
When there are more than two objectives with different dimensions and units to be
satisfied simultaneously a single fuzzy satisfaction objective function based on the
120572119878119860
119878119860119868119863119868119898119894119899 119878119860119868119863119868119900119903119894 119878119860119868119863119868
120572119878119862
119878119862119900119903119894 119878119862119898119886119909 119878119862
Chapter 7 Optimal Placement of Sectionalising Switches for Reliability
Improvement
Page | 132
0
1
max-min principle is considered The three conflicting objectives to be optimised are
ECOST SAIDI and switch costs The membership functions for SAIDI and switch
costs are presented in the previous section The function for ECOST is shown in Fig
7-2 and expressed as
120572119864119862 =
1 119864119862119874119878119879 le 119864119862119874119878119879119898119894119899119864119862119874119878119879119900119903119894minus119864119862119874119878119879
119864119862119874119878119879119900119903119894minus119864119862119874119878119879119898119894119899119864119862119874119878119879119898119894119899 lt 119864119862119874119878119879 lt 119864119862119874119878119879119900119903119894
0 119864119862119874119878119879 ge 119864119862119874119878119879119900119903119894
(7-5)
where 119864119862119874119878119879119900119903119894 and 119864119862119874119878119879119898119894119899 are the original and minimum value of ECOST
respectively The minimum ECOST is obtained by installing sectionalising switches
in all candidate locations
Fig 7-2 Membership function for ECOST reduction
The degree of overall satisfaction for these objective functions is the minimum value
of all the membership functions [85] The fuzzy decision for a final compromised
solution is the maximum degree of overall satisfaction and is formulated in (7-6)
Max 119871 = min (120572119878119860 120572119878119862 120572119864119862) (7-6)
724 Evaluation of ECOST
ECOST is an index that combines reliability with economics The best way to
present customer interruption costs is in the form of CDF A CDF provides the
interruption cost versus interruption duration for a various class of customers and
can be aggregated to produce a composite CDF at any particular load point [67] [69]
Generally ECOST is used to represent the customer outage costs since it not only
considers the effects of the system configuration interruption durations load
variations and equipment failure probability but also accounts for the various
customer types and their damage functions [52]
120572119864119862
119864119862119874119878119879119898119894119899 119864119862119874119878119879119900119903119894 119864119862119874119878119879
Chapter 7 Optimal Placement of Sectionalising Switches for Reliability
Improvement
Page | 133
The calculation of ECOST of the total system over T years is based on failure-mode-
and-effect analysis (FMEA) and can be quantified as follows
1 ( 1)
1 1 1 1 1 1
( ) ( ) ( ) ( ) (1 ) (1 )b b b b bN CT NR CT NST
t t
b b k R k s
t b k j k j
ECOST L P k j C d P k j C d IR DR
(7-7)
where T is time period (year) 119873119887 is the total number of branches 120582119887and 119871119887 are the
average failure rate (failurekm-year) and length (km) of branch b 119862119879119887 119873119877119887 and
119873119878119887 are the total number of customer types permanent damaged and temporary
damaged load points when the fault is at branch b P(k j) is the average load of the
kth-type customers at the jth load point (kW) 119862119896(119889) is the CDF for kth-type
customer lasting d hours ($kW) 119889119877 and 119889119878 are the average repair time and the
switch time after failure IR and DR are the annual load increase rate and discount
rate
725 Evaluation of SAIDI
The SAIDI which represents the average outage duration time of each customer
over T years can be expressed as
119878119860119868119863119868 = sum sum 120582119887∙119871119887[sum 119889119877
119873119862119877(119887)119899=1 +sum 119889119878
119873119862119878(119887)119899=1 ]
119873119887119887=1
119873119862119905119900119905119886119897119879
119905=1 (7-8)
where 119873119862119877(119887) and 119873119862119878(119887) are the number of permanent damaged and temporary
damaged customers when the fault is at branch b 119873119862119905119900119905119886119897 is the total number of
served customers SAIDI is measured in hours
726 Evaluation of Switch Costs
In this study reliability is improved by the installation of new sectionalising
switches and relocation of existing switches Thus the total cost of switches can be
determined as following
119878119862 = 119862119868119878 ∙ 119873119899119890119908 + 119862119877119878 ∙ 119873119903119890119897 + sum 119872119862119879119905=1 ∙ (119873119899119890119908 + 119873119890119909119894119904) ∙ (1 + 119863119877)minus(119905minus1) (7-9)
where CIS is the investment and installation cost of a new sectionalising switch ($)
119873119899119890119908 119873119903119890119897 and 119873119890119909119894119904 are the number of newly installed relocated and existing
sectionalising switches respectively CRS is the relocation cost of an existing
Chapter 7 Optimal Placement of Sectionalising Switches for Reliability
Improvement
Page | 134
Home
0
1
0
1
0
1
0
1
Food
Number of candidate locations for sectionalising switches
sectionalising switch ($) and MC is the maintenance and operation cost of a
sectionalising switch ($)
73 Applying ACO to Sectionalising Switch Placement
Problem
This study uses ACO algorithm for distribution automation in terms of the
installation of new sectionalising switches and relocation of existing switches When
the locations of sectionalising switches are changed a new network configuration
will be formed The search method is used for finding the optimal value of objective
functions as presented in Section 721-723
The search space of the automation problem in terms of SSP is modelled as a
directed graph as shown in Fig 7-3 The number of stages is the candidate locations
for all the sectionalising switches 119873119878 For this problem the switch status can be
represented as a binary vector in each stage State 0 ldquono sectionalising switch in this
locationrdquo State 1 is ldquoa sectionalising switch in this locationrdquo The artificial ant
searches for the values of the bits and produces a solution to the problem after it
completes a tour between the home and food source which is similar to the process
described in Section 532
Fig 7-3 Search space of sectionalising switch placement
Chapter 7 Optimal Placement of Sectionalising Switches for Reliability
Improvement
Page | 135
74 Benefit-to-cost Analysis
The benefit-to-cost analysis is a financial term that describes the expected balance of
benefits made from the investment and costs incurred during the production process
It helps predict if an investmentdecision is feasible and whether its benefits
outweigh the costs during a predefined time interval [82]
In this study the benefit-to-cost ratio (BCR) offers a comparison between ECOST
and SC The benefit to the distribution network operator (DNO) is the reduction of
ECOST which is equal to
119887119890119899119890119891119894119905 = sum119864119862119874119878119879119887119886119904119890
119905 minus119864119862119874119878119879119900119901119905119905
(1+119863119877)119905119879119905=1 (7-10)
where 119864119862119874119878119879119887119886119904119890119905 and 119864119862119874119878119879119900119901119905
119905 are the value of ECOST of year t before and after
the placement of switches ($)DR is the annual discount rate
The cost for the DNO is the total switching cost including investment maintenance
and operation cost as presented in (7-9) and BCR is defined as
119861119862119877 =119887119890119899119890119891119894119905
119878119862 (7-11)
A higher value for BCR indicates that the benefits relative to the costs are greater
The investment return time refers to the time when BCR starts to exceed 10 If the
investment return time is less than the lifetime of a switch adding a switch will bring
benefits to the investors
Chapter 7 Optimal Placement of Sectionalising Switches for Reliability
Improvement
Page | 136
LP11 LP12 LP13 LP14 LP15 LP16 LP17
LP8 LP9 LP10
LP1 LP2 LP3 LP4 LP5 LP6 LP7
LP32 LP33 LP34 LP35 LP36 LP37 LP38
LP29 LP30 LP31
LP26 LP27 LP28
LP18 LP19 LP20 LP21 LP22 LP23 LP24 LP25
9 10 11 12 13 33
6 7 8 31
1 2 3 4 5 30
25 26 27 29
22 23 24
19 20 21
32
14 15 16 17 18
28
F3
F2
F1
F7
F6
F5
F4
Normally Open Circuit BreakerNormally Closed Circuit Breaker
Subbus1
Subbus2
Subbus3
T1
T3
T5
Main
feeder
Main
feeder
Main
feeder
T2
T4
T6
75 Application Studies
In this study the proposed methodology is applied to an 11 kV distribution network
developed from Bus 4 of the Roy Billinton Test System (RBTS) The single-line
diagram of the network with 6 existing sectionalising switches is shown in Fig 7-4
Fig 7-4 Distribution feeder connected to RBTS Bus 4 with 6 sectionalising switches
In this study there are 51 locations considered as candidates for switch placement
[114] All the values of the required data ie feeder type and length as well as
component failure rate are available in [114] and summarised in Appendix A4 The
failure rate of the feeders is proportional to their physical length and all other
Chapter 7 Optimal Placement of Sectionalising Switches for Reliability
Improvement
Page | 137
components ie transformers buses and breakers are assumed to be completely
reliable This typical urban distribution network supplies residential commercial and
industrial consumers The average value of active power and the customer type of
each node were also found in [114] and listed in Table 7-1 The power factors of all
the loads are set to 10
Table 7-1 Customer data (Average load)
Number
of load
points
Load points Customer type P
(kW)
Number of
customers
15 1-4 11-13 18-21 32-35 residential 545 220
7 5 14 15 22 23 36 37 residential 500 200
7 8 10 26-30 industrial 1000 1
2 9 31 industrial 1500 1
7 6 7 16 17 24 25 38 commercial 415 10
The relocation cost of a sectionalising switch is US $ 500 The investment and
installation cost of a sectionalising switch is US $ 4700 [64] The annual
maintenance and operation cost is considered to be 2 of the investment cost [64]
All the sectionalising switches and circuit breakers are remotely controlled The
costs of the feeder terminal unit which is used for data acquisition of the switch
status and communication equipment have also been added to the automated
sectionalising switches The overall switching time of sectionalising switch and
circuit breakers for temporary damage load points in other words the time between
the occurrence of a fault and the restoration of energy to unaffected areas is set to 10
minutes [64] And the average repair time of the permanent faulty section is assumed
to be 5 hours The lifetime of a switch depends on various factors such as the
maximum number of allowable switching operations the number of annual
switching operations of the switch etc Based on these factors the life period of the
switches is calculated to be 15 years The load growth rate and the annual interest
rate are set to 3 and 8 respectively The CDF data are extracted from [64] and
summarised in Table 7-2
Chapter 7 Optimal Placement of Sectionalising Switches for Reliability
Improvement
Page | 138
Table 7-2 Sector interruption cost estimation ($kW)
User Sector Interruption Duration
10 min 1 hour 2 hour 4 hour 5 hour 10 hour
Residential 006 11 16 26 316 5
Industrial 288 806 95 124 1387 276
Commercial 205 96 125 185 2151 6306
The proposed ACO algorithm was coded in the MATLAB to obtain the location of
the sectionalising switches In this study three cases with different objective
functions are considered to analyse the superiority and performance of the proposed
method
Test Case 1 Minimisation of ECOST and switch costs
Test Case 2 Minimisation of SAIDI and switch costs
Test Case 3 Minimisation of ECOST SAIDI and switch costs
The final combinations of the ACO control parameters that provide the best results
for all the above tests are given in Appendix C3
751 Test Case 1
In this test the minimisation of ECOST and switch costs are considered in the
formulation of a single objective function this involves aggregating the objective
functions as presented in Section 721 For simplicity both weighting factors micro1
and micro2 are set to 1 ie these two objectives are assumed to be equally important
Three cases are studied as follows
Case 11 Optimal relocation of existing sectionalising switches
Case 12 Optimal installation of new sectionalising switches
Case 13 Optimal installation of new sectionalising switches and relocation of
existing sectionalising switches
Chapter 7 Optimal Placement of Sectionalising Switches for Reliability
Improvement
Page | 139
LP11 LP12 LP13 LP14 LP15 LP16 LP17
LP8 LP9 LP10
LP1 LP2 LP3 LP4 LP5 LP6 LP7
LP32 LP33 LP34 LP35 LP36 LP37 LP38
LP29 LP30 LP31
LP26 LP27 LP28
LP18 LP19 LP20 LP21 LP22 LP23 LP24 LP25
9 10 11 12 13 33
6 7 8 31
1 2 3 4 5 30
25 26 27 29
22 23 24
19 20 21
32
14 15 16 17 18
28
F3
F2
F1
F7
F6
F5
F4
Normally Open Circuit BreakerNormally Closed Circuit Breaker
Subbus1
Subbus2
Subbus3
T1
T3
T5
Main
feeder
Main
feeder
Main
feeder
T2
T4
T6
Case 11 Optimal relocation of existing sectionalising switches
The objective of this case is to investigate the optimum sectionalising switch
relocation problem The optimal locations of sectionalising devices are shown in Fig
7-5 Before relocation the total cost including ECOST operation and maintenance
cost of existing switches over 15 years is US $ 477090 After relocation the total
cost including the addition of relocation cost obtained by the ACO approach is US
$ 343620 which amounts to a reduction of 2798
Fig 7-5 Optimal relocation of sectionalising switches in Test Case 11
Chapter 7 Optimal Placement of Sectionalising Switches for Reliability
Improvement
Page | 140
In comparison with the original configuration 4 switches change their locations The
optimal locations of sectionalising switches and the number and types of loads
adjacent to each switch are presented in Table 7-3 The results indicate that each
feeder attempts to have at least one switch As there are 6 switches and 7 feeders
and the total load level of Feeder 5 is 3000 kW which is the lowest value for all the
feeders no switch is placed on Feeder 5 It should also be noted that the load
density and customer types play an important role in determining the locations of
sectionalising switches For instance the adjacent load of Switch 1 is LP6 and LP7
which has the highest CDF value (commercial load) and relatively high load levels
In addition Switch 2 is placed on 7D whose adjacent load is LP9 and this has the
largest load density
Table 7-3 Results of sectionalising switches relocation in Test Case 11
Switch
No
Feeder Location Total Feeder
Load (kW)
Adjacent Load Adjacent Load Levels (kW) and
Type
1 1 5D 3510 LP6 LP7 415 (commercial) 415 (commercial)
2 2 7D 3500 LP9 1500 (industrial)
3 3 13D 3465 LP16 LP17 415 (commercial) 415 (commercial)
4 4 18D 4010 LP24 LP25 415 (commercial) 415 (commercial)
5 6 23D 3500 LP30 1000 (industrial)
6 7 28D 3595 LP36 500 (commercial)
( Each section has two candidate locations for sectionalising switch placement U means upstream side of the section and D
means downstream side of the section)
Case 12 Optimal installation of new sectionalising switches
In this case the effect of installing new sectionalising switches without relocating
the existing switches is studied As shown in Fig 7-6 there are 11 new
sectionalising switches installed
The detailed results of ECOST capital and installation as well as the operation and
maintenance cost of sectionalising switches over 15 years are shown in Table 7-4
After the installation of sectionalising switches the total system cost is decreased
from US $ 477090 to US $ 286980 ie a reduction of 3984
Chapter 7 Optimal Placement of Sectionalising Switches for Reliability
Improvement
Page | 141
LP11 LP12 LP13 LP14 LP15 LP16 LP17
LP8 LP9 LP10
LP1 LP2 LP3 LP4 LP5 LP6 LP7
LP32 LP33 LP34 LP35 LP36 LP37 LP38
LP29 LP30 LP31
LP26 LP27 LP28
LP18 LP19 LP20 LP21 LP22 LP23 LP24 LP25
9 10 11 12 13 33
6 7 8 31
1 2 3 4 5 30
25 26 27 29
22 23 24
19 20 21
32
14 15 16 17 18
28
F3
F2
F1
F7
F6
F5
F4
Normally Open Circuit BreakerNormally Closed Circuit Breaker
Subbus1
Subbus2
Subbus3
T1
T3
T5
Main
feeder
Main
feeder
Main
feeder
T2
T4
T6
Fig 7-6 Optimal installation of sectionalising switches in Test Case 12
Table 7-4 Results of sectionalising switches installation in Test Case 12
ECOST
($)
Number of
installed
switches
Capital and
installation cost
($)
Maintenance
and operation
cost ($)
Total system
cost ($)
Before switches
installation
472260 0 0 4830 477090
After switches
installation
221610 11 51700 13670 286980
Chapter 7 Optimal Placement of Sectionalising Switches for Reliability
Improvement
Page | 142
LP11 LP12 LP13 LP14 LP15 LP16 LP17
LP8 LP9 LP10
LP1 LP2 LP3 LP4 LP5 LP6 LP7
LP32 LP33 LP34 LP35 LP36 LP37 LP38
LP29 LP30 LP31
LP26 LP27 LP28
LP18 LP19 LP20 LP21 LP22 LP23 LP24 LP25
9 10 11 12 13 33
6 7 8 31
1 2 3 4 5 30
25 26 27 29
22 23 24
19 20 21
32
14 15 16 17 18
28
F3
F2
F1
F7
F6
F5
F4
Normally Open Circuit BreakerNormally Closed Circuit Breaker
Subbus1
Subbus2
Subbus3
T1
T3
T5
Main
feeder
Main
feeder
Main
feeder
T2
T4
T6
Case 13 Optimal relocation and installation of sectionalising switches
A Base case
The main objective of this test is to reduce the total system cost including ECOST
and switch costs by the relocation of existing sectionalising switches and the
installation of new ones The switch locations are presented in Fig 7-7
Fig 7-7 Optimal installation and relocation of sectionalising switches in Test Case 13
In comparison with the original configuration there are 8 new sectionalising
switches installed and 5 existing switches relocated As expected the sectionalising
switches are placed adjacent to the load centres with either the highest load density
Chapter 7 Optimal Placement of Sectionalising Switches for Reliability
Improvement
Page | 143
0
1
2
3
4
5
6
7
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
BC
R
Years
or the highest CDF For example the adjacent load of switch 13D is LP6 and LP7
which has the highest CDF value (commercial loads) In addition switch 7D is
placed adjacent to LP9 which has the largest load density The detailed results for
ECOST and switch costs are shown in Table 7-5 After the installation and relocation
of the switches the total system cost is decreased from US $ 477090 to US
$ 272480 ie a reduction of 4289
Table 7-5 Results of sectionalising switches relocation and installation in Test Case 13
ECOST
($)
Number of
relocated
switches
Relocation
cost ($)
Number of
installed
switches
Capital and
installation
cost ($)
Maintenance
and operation
cost ($)
Total
system
cost ($)
Before switch
placement
472260 0 0 0 0 4830 477090
After switch
placement
221120 5 2500 8 37600 11260 272480
B Benefit-to-Cost analysis
BCR analysis is used to verify the benefits and costs of sectionalising switch
placement for distribution operators The results are presented in Fig 7-8 The
benefits and costs are accumulated during the predefined life period There is no
return on investment for the first year as the BCR for Year 1 is 055 However the
BCR for Year 2 is 108 which means the investors start to get benefits in Year 2 In
addition switch placement proved to be a feasible investment since the BCR is
increased to 620 when the switch achieves its service life 15 years in this study
Fig 7-8 BCR versus years
Chapter 7 Optimal Placement of Sectionalising Switches for Reliability
Improvement
Page | 144
0
20
40
60
80
100
120
140
160
05 1 15 2 25 3 35 4 45 5 55 6 65 7 75 8
Co
st (
th
ou
san
d $
)
CDF multiplier
ECOST
Switch costs
Total costs
C Sensitivity analysis
To demonstrate the impact of changing the values of different parameters on the
corresponding results several sensitivity analysis studies are discussed
CDF variation sensitivity analysis
The main objective of this test is to assess the behaviour of the proposed approach
when the CDF (customer damage function) is varied The CDF is increased from 50
to 800 of its initial value in 50 increments The original value of the CDF
multiplier is 100 The effect of variation in the CDF on the ECOST switching
costs and the total system cost is plotted in Fig 7-9 Switch costs include
sectionalising switch installation relocation operation and maintenance cost The
ECOST and switching costs increase as the CDF is increased However the
difference between ECOST and switching costs is also increased
Fig 7-9 Variation of cost versus change in CDF
Variations of the optimal number of installed sectionalising switches versus the CDF
are presented in Fig 7-10 The optimal number of newly installed switches increases
from 7 to 34 as the CDG multiplier is increased from 05 to 8 This indicates the
network needs to be more automated especially if the consequence of customer
damage becomes more serious However the growth in the optimal number of
sectionalising switches is slowing down As shown in Fig 7-10 when the CDF
multiplier increases above 3 the number of sectionalising switches remains at 32 as
Chapter 7 Optimal Placement of Sectionalising Switches for Reliability
Improvement
Page | 145
0
5
10
15
20
25
30
35
40
05 1 15 2 25 3 35 4 45 5 55 6 65 7 75 8
Nu
mb
er
of
swit
che
s
CDF multiplier
the reduction of ECOST brought by installing a sectionalising switch is small
compared to the increase in switch costs Only when the CDF multiplier reaches 55
does the reduction of ECOST outweigh the installation cost of a switch and hence
acquiring a sectionalising switch is a cost-effective investment This is due to the fact
that the installation of the first sectionalising switch has the largest effect on
reducing the total system cost and the impact of sectionalising switch installation on
ECOST decreases as the network becomes more automated
Fig 7-10 Number of installed sectionalising switches versus change in CDF
ACO parameters sensitivity analysis
The ACO parameter analysis is provided in this section In each test only one
parameter is changed whilst the others remain constant The convergence number is
defined as the number of the iterations when the objective function is convergence
The assessment of the impact of the pheromone evaporation rate ρ on the proposed
algorithm is presented in Table 7-6 The number of ants is 200 and the iteration time
is 400 Parameter ρ is varied from 01 to 06 with an increment of 01 For each ρ the
test is run 100 times Table 7-6 shows the impacts of the ρ variation on the objective
function J It can be seen the evaporation rate ρ has a considerable impact on the
convergence performance of the ACO algorithm When ρ is small the residual
pheromone on the path is dominant and the positive feedback of pheromone is weak
This results in an increment in the stochastic performance and global search ability
Chapter 7 Optimal Placement of Sectionalising Switches for Reliability
Improvement
Page | 146
of the ACO algorithm but a reduction in the convergence rate When ρ is large the
positive feedback of the pheromone is dominant which results in an improvement in
the convergence rate but a reduction in the search ability of the algorithm In other
words the algorithm is more easily trapped into a local optimal solution In summary
the selection of ρ is based on two factors of the algorithm 1) convergence rate 2)
global search ability As shown in the table the best value of ρ for this case is 04
which results in the minimum average value and has a suitable convergence rate
Table 7-6 Impacts of 120588 variation on objective function 119869
120588 Objective function value Average convergence
number Average Maximum Minimum
01 273120 274810 272480 223
02 273400 275960 272480 175
03 273480 274810 272480 132
04 273100 274810 272480 110
05 273550 274810 272480 94
06 273440 274810 272480 81
Table 7-7 presents the impacts of the variation in the number of ants on objective
function J The evaporation rate is 04 and the iteration number is 400 The number
of ants is changed from 100 to 500 with an increment of 100 The greater the
number of ants the more likely the global optimum value is achieved This is due to
the growth in global search capability However the convergence rate decreases To
balance the global search ability and convergence rate the number of ants is set to
400
Table 7-7 Impacts of variation in number of ants on objective function 119869
Number of ants Objective function value Average convergence
number Average Maximum Minimum
100 273865 276120 272480 91
200 273100 274810 272480 110
300 273030 274370 272480 135
400 272820 274230 272480 168
500 273170 274230 272480 245
Chapter 7 Optimal Placement of Sectionalising Switches for Reliability
Improvement
Page | 147
However in this study the proposed approach is used for planning a future network
Thus the computation time is not an issue The number of ants and iteration should
be large enough for the ACO algorithm to find the global optimum solution
752 Test Case 2
The objective of this test is to minimise SAIDI and switch costs by maximising the
fuzzy bi-objective function as presented in Section 722 The results of the
membership values of objectives SAIDI as well as switch costs are listed in Table
7-8 The weighting factors of the system objectives can be changed by the network
operator which make it possible to give preference to one over the other Three
cases are studied in which the weighting factors 1205961and 1205962vary from 01 to 09
As shown in the table as the weighing factor of SAIDI 1205961 is increased more
sectionalising switches are installed and reliability is improved The results show the
algorithm can adapt itself to the variation of the weighting factors For decision
making appropriate weighting factors for each objective are selected and a
compromised switch placement plan is obtained using the proposed approach
Table 7-8 Results of sectionalising switches relocation and installation in Test Case 2
Test Cases 1205961 1205962 120572119878119860 120572119878119862 Objective
Function
SAIDI
(hrscustomer)
Switch costs ($)
Case 21 01 09 04909 09970 09464 1157 68275
Case 22 05 05 08456 09061 08758 556 67378
Case 23 09 01 09384 07761 09221 39936 153950
( Each section has two candidate locations for sectionalising switch placement U means upstream side of the section and D
means downstream side of the section)
753 Test Case 3
In this test the three objective functions of the problem to be optimised are ECOST
SAIDI and switch costs The detailed test results before and after switch placement
are listed in Table 7-9 The placement of sectionalising switches results in a
reduction of 60 in ECOST and 7148 in SAIDI It is observed that the
installation and relocation of sectionalising switches has obtained a compromise
solution of three objectives optimisation
Chapter 7 Optimal Placement of Sectionalising Switches for Reliability
Improvement
Page | 148
Table 7-9 Results of sectionalising switches installation and relocation in Test Case 3
Objective
Function
120572119864119862 120572119878119860 120572119878119862 ECOST
($)
SAIDI
(hrscustomer)
Switch costs
($)
Before
switch
placement
0 0 0 1 472260 1989 4830
After switch
placement
08327 08327 08392 08384 188950 56723 112410
76 Summary
This study has presented an ACO algorithm for assessing the SSP problem in terms
of three conflicting objectives optimisation reduction of unserved energy cost
decrease in the average time that a customer is interrupted and minimisation of
switch costs The proposed model has been successfully applied on Bus 4 of the
RBTS In comparison with the original system the existing sectionalising switches
are relocated and new automatic switches are installed The effectiveness of the
proposed approach has been demonstrated through the results obtained which
indicates switch placement using the ACO algorithm reduces the customer outage
costs and interruption duration times during fault contingencies Furthermore the
importance of the CDF variation in determining the SSP is investigated through
sensitivity analysis The impact of installing sectionalising switches on reducing the
total system costs decreases as the number of sectionalising switches is increased As
the parameters of ACO algorithm affect the performance of the proposed method an
ACO parameter sensitivity analysis is also provided in this study The selection of
pheromone evaporation rate and number of ants is a trade-off between the global
search ability and convergence rate of the algorithm In addition a benefit-to-cost
analysis is implemented and used to prove switch investment is profitable The
procedure is used for system planning and is applied off-line so there is no
limitation in calculation times
The main contribution of this study is the conversion of all the multiple objectives
into a single objective function in two forms weighted aggregation and fuzzy
satisfaction objective function considering ECOST SAIDI and cost of
sectionalising switches simultaneously The selection of each form depends on the
Chapter 7 Optimal Placement of Sectionalising Switches for Reliability
Improvement
Page | 149
number of objectives as well as their units and dimensions Another contribution is
the incorporation of FMEA to evaluate the impact on distribution system reliability
of increased automation
Page | 150
CHAPTER 8
DISTRIBUTION NETWORK
RECONFIGURATION FOR LOSS
REDUCTION amp RELIABILITY
IMPROVEMENT
81 Introduction
Optimal distribution network reconfiguration (DNR) can not only solve a single
objective function such as feeder loss minimisation but can also deal with multiple
objectives The presence of multiple objectives raises the issue of how to consider
them simultaneously [117] In the previous section the multiple objectives are
transformed into a single equation using fuzzy logic based approaches The
optimisation is then formulated either as the weighted sum of the fuzzy membership
functions or with the application of the max-min principle
However the above simple optimisation processes only find a compromise solution
It is no longer acceptable for a system with multiple conflicting objectives if the
distribution network operator (DNO) desires to know all possible optimal solutions
for all the objectives simultaneously [20] Therefore a set of trade-off solutions
using the Pareto optimality concept is now proposed These solutions can be
Chapter 8 Distribution Network Reconfiguration for Loss Reduction amp Reliability
Improvement
Page | 151
compared by using the concept of dominance [88] In this concept a solution is non-
dominated when no other solution exists with better values for all the individual
objectives The Pareto set is the set of all non-dominated solutions and the
corresponding objective values constitute the Pareto front [88] This allows the
DNOs to select the most suitable one for implementation depending on the utilitiesrsquo
priorities Pareto analysis is suitable for addressing problems whose conflicting
solutions cannot be addressed using a single solution [117]
This study formulates the optimal network reconfiguration problem within a Pareto
optimal framework where feeder loss and system reliability indices are
simultaneously optimised Two types of reliability indices are considered system
expected outage costs to customers (ECOST) and system interruption duration index
(SAIDI) The multi-objective ant colony optimisation (MOACO) and artificial
immune systems-ant colony optimisation (AIS-ACO) algorithms are proposed and
compared for the assessment of DNR problems Both algorithms focus on problems
in terms of Pareto optimality where the objective functions are multidimensional In
MOACO each objective function is assigned with a pheromone matrix and all
values from multiple pheromone matrices are aggregated into a single pheromone
value by a weighted sum [96] In AIS-ACO the quality of elements that make up the
solution to the problem is represented by the pheromones developed from the ACO
And the hypermutation from the AIS is used as a random operator to enlarge the
search space [88] To verify the suitability of the proposed algorithms they have
been tested on Bus 4 of the Roy Billinton Test System (RBTS) system and the Pareto
set is obtained
The remaining parts of this chapter are organised as follows Section 82 deals with
the framework of multi-objective optimisation and DNR problem formulation The
implementation details of the MOACO and AIS-ACO algorithms to the problem are
discussed in Section 83 The simulation results and the best compromise solutions
are presented and discussed in Section 84 and 85 Section 86 summarises the main
conclusions
Chapter 8 Distribution Network Reconfiguration for Loss Reduction amp Reliability
Improvement
Page | 152
82 Problem Formulation
This section formulates the DNR problems in the Pareto optimal framework
821 Multi-objective Reconfiguration Problem
In this study three objectives are considered and they are feeder loss unserved
energy cost and the average time that a customer is interrupted Therefore the multi-
objective DNR problem can be defined as the minimisation of the vector
119865(119866) = [1198911(119866)1198912(119866)1198913(119866)]119879 (8-3)
where 1198911(119866) 1198912(119866) and 1198913(119866) are described below for a given network
configuration G
8211 Minimisation of feeder loss
The total feeder loss of the network is formulated as
1198911(119866) = sum 119896119894119877119894(119875119894
2+1198761198942
1198801198942 )
119873119887119894=1 (8-4)
where 119877119894 is the resistance of the ith branch 119875119894 and 119876119894 are the real power (W) and
reactive power (VAr) at the receiving end of branch i 119880119894 represents the rms voltage
at the receiving end of branch i (V) 119896119894 is a binary variable 119896119894 = 0 indicates that
branch 119894 is open and 119896119894 = 1 indicates that branch 119894 is closed The detailed feeder loss
assessment is presented in Section 28
8212 Minimisation of ECOST
The ECOST represents the unserved energy cost and is described as
1 ( 1)
1 1 1 1 1 1
( ) ( ) ( ) ( ) (1 ) (1 )b b b b bN CT NR CT NST
t t
b b k R k s
t b k j k j
ECOST L P k j C d P k j C d IR DR
(8-5)
where T is time period (year) 119873119887 is the total number of branches 120582119887and 119871119887 are the
average failure rate (failurekm-year) and length (km) of branch b 119862119879119887 119873119877119887 and
119873119878119887 are the total number of customer types permanent damaged and temporary
Chapter 8 Distribution Network Reconfiguration for Loss Reduction amp Reliability
Improvement
Page | 153
damaged load points when the fault is at branch b P(k j) is the average load of the
kth-type customers at the jth load point (kW) 119862119896(119889) is the customer damage
function for kth-type customer lasting d hours ($kW) 119889119877 and 119889119878 are the average
repair time and the switch time after failure IR and DR are the annual load increase
rate and discount rate
8213 Minimisation of SAIDI
The average time that a customer is interrupted is represented by a reliability index
SAIDI and is defined as
119878119860119868119863119868 = sum sum 120582119887∙119871119887[sum 119889119877
119873119862119877(119887)119899=1 +sum 119889119878
119873119862119878(119887)119899=1 ]
119873119887119887=1
119873119862119905119900119905119886119897119879
119905=1 (8-6)
where 119873119862119877(119887) and 119873119862119878(119887) are the number of permanent damaged and temporary
damaged customers when the fault is at branch b 119873119862119905119900119905119886119897 is the total number of
served customers SAIDI is measured in hours
8214 Constraints
The computed voltages currents and the power flow at all branches should be kept
in their permissible range and the network should be operated in radial The
configurations that violate any constraint should be disregarded
822 Best Compromise Solution
After obtaining the Pareto set the best compromise solution among the multiple
objectives can be selected by comparing the fitness value of each member in the
Pareto front as follows [45]
119891119901119904(119894) = sum 120596119895max(119900119891119895)minus119900119891119895(119875119878119894)
max(119900119891119895)minusmin (119900119891119895)
119873119900119887119895
119895=1 (8-7)
where 119873119900119887119895 is the number of objectives which is three in this study max(119900119891119895) and
min(119900119891119895) are the maximum and minimum value of the jth objective function
obtained by all the members in the Pareto front respectively 1205961 1205962 and 1205963 are the
weighting factor for feeder loss ECOST and SAIDI respectively
The best compromise solution is varied by changing the values of the weighting
factors based on the tendencies of the decision makers
Chapter 8 Distribution Network Reconfiguration for Loss Reduction amp Reliability
Improvement
Page | 154
83 Solution Methodology
In this study there are two methodologies proposed for generating the Pareto set to
the multi-objective DNR problem which are MOACO and AIS-ACO algorithm
Each solution is represented by a string of integers which indicates the locations of
tie-switches
831 Applying MOACO to Multi-objective DNR Problem
Generally ACO algorithm is developed for the assessment of a single objective
optimisation problem However a MOACO algorithm is proposed for assessing
multiple objective functions in the Pareto optimality framework which can generate
diverse solutions rather than just one The flowchart of the MOACO algorithm is
presented in Fig 8-1 and is divided into six steps
Step 1 Initialisation First of all all the ants are initially located at home The
number of pheromone matrices is equal to the number of objectives Each
pheromone matrix has 33 rowsstates (candidate locations for tie-switches) and 4
columnsstages (number of tie-switches) The pheromone values of the edges in the
search space are all initialised at an equal value which is a small positive constant
number
Step 2 Pheromone matrix generation and ant dispatch As there are multiple
pheromone matrices 1205911 1205912 and 1205913 are associated with feeder loss ECOST and
SAIDI respectively All matrices are aggregated into a single pheromone matrix by
weighted sum as
120591119894119909 = 1199011 ∙ 1205911198941199091 + |1199011 minus 1199012| ∙ 120591119894119909
2 + (1 minus 1199012) ∙ 1205911198941199093 (8-8)
where 1205911198941199091 120591119894119909
2 and 1205911198941199093 are the levels of pheromone deposited on state i of stage x for
feeder loss ECOST and SAIDI respectively where 1199011 and 1199012 are uniform random
numbers between 0 and 1 and 1199011 is less than 1199012 This ensures the selection of the
three pheromone matrices all have the same probability and can be used to build the
new matrix
All the ants begin their tours from the home colony and choose the next node to
move to based on the intensity of pheromones from a new pheromone matrix They
Chapter 8 Distribution Network Reconfiguration for Loss Reduction amp Reliability
Improvement
Page | 155
experience different pheromone matrices according to the random variation of
weights The probability of an ant choosing state i of stage x is
119875119894119909(119873) =120591119894119909(119873)
sum 120591119894119909(119873)ℎisin∆119909
(8-9)
where 120591119894119909(119873) is the level of pheromone deposited on state i of stage x at iteration
N ∆119909 is the set of available states which an ant can choose at stage x
Step 3 Objective Function Evaluation After all the ants have completed their tour
the location list and corresponding objective functions in (8-3) for each ant are
evaluated If any constraint is violated the corresponding solutions are discarded
Step 4 Non-dominated Solutions Extraction and Diversity Measure The non-
dominated solutions extraction extracts solutions from a pool based on the concept
of dominance as presented in Section 821 The crowding distance is used to
measure the extent to which non-dominated solutions are spread over the objective
space [20] As there are three objectives to be optimised the crowding distance of a
solution is equal to the side length of the cuboid which is built by two adjacent
solutions [88] Regarding the boundary solutions (the corner solutions) they are
assigned with an infinite distance The solutions are assigned with a small distance
value if they are located in a crowded area The decision makers tend to choose the
solutions from less crowded regions of the search space (with higher crowding
distance) if the maximum number of non-dominated solutions is restricted to a
certain number [88]
Step 5 Pheromone Updating The aim of this step is to favour transitions towards
states by non-dominated solutions with greater pheromone values There are two
rules of pheromone updating the local rule and global rule
Local rule The pheromones deposited in the search space should be evaporated to
make the paths less attractive The local pheromone update rule is calculated as
follow
120591119894119909119899 (119873) = (1 minus 120588)120591119894119909
119899 (119873 minus 1) + 120591119888 (8-10)
where 120588 is the pheromone evaporation rate which is set between 0 and 1 120591119894119909119899 (119873 minus
1) is pheromone value deposited on state i of stage x of matrix n at iteration N-1 120591119888
Chapter 8 Distribution Network Reconfiguration for Loss Reduction amp Reliability
Improvement
Page | 156
is a small positive constant value Even if the amount of pheromone deposited on an
edge is at the lowest value of 120591119888 there is a slight chance that an ant will still choose
this edge
Global rule The global pheromone updating rule involves ants depositing large
amounts of pheromone to the edges that belong to the corner non-dominated
solutions which are the solutions that have minimum values along each objective
The pheromones of those edges can be updated by
120591119894119909119899 (119873) = 120591119894119909
119899 (119873) + 120588119891119887119890119904119905
119899 (119873)
119891119887119890119904119905119899 (119873minus1)
(8-11)
where 119891119887119890119904119905119899 (119873 minus 1) and 119891119887119890119904119905
119899 (119873) are the minimum values of objective function n
obtained by the non-dominated solutions at iteration N-1 and N respectively
After applying the local and global pheromone updating rules the method Max-Min
ACO algorithm is integrated into the proposed approach
120591119894119909119899 (119873) = 120591119898119886119909 119894119891 120591119894119909
119899 (119873) ge 120591119898119886119909 (8-12)
120591119894119909119899 (119873) = 120591119898119894119899 119894119891 120591119894119909
119899 (119873) le 120591119898119894119899 (8-13)
where 120591119898119886119909and 120591119898119894119899 are the higher and lower bound of pheromone level on each
edge respectively Even if the amount of pheromone deposited to a path is at the
lowest value 120591119898119894119899 there is a slight chance that an ant will still choose this path This
enlarges the search space and prevents convergence from occurring too rapidly
After this the non-dominated solutions with their location lists and corresponding
fitness values in the current iteration are retained and all the ants are free to choose a
new path for the next iteration
Step 6 Termination The computation continues until the predefined maximum
number of iterations is reached The final non-dominated solutions are considered as
the Pareto set to the multi-objective DNR problem
Chapter 8 Distribution Network Reconfiguration for Loss Reduction amp Reliability
Improvement
Page | 157
Start
Iteration N=1
Maximum ant number
reaches
Output Pareto
optimal set and end
No
Yes
Initialise the parameters for MOACO
algorithm search space
Ant number m=1
Random select weights and
aggregate multiple pheromone
matrices into one
Dispatch the ant based on the
amount of pheromone on edges
Calculate the multiple objective functions
for this ant
N=N+1
Read system topology
and load data
Diversity measure and extract non-
dominated solutions
Maximum iteration
reaches
Yes
m=m+1
No
The pheromones are updated according
to local and global rules
Fig 8-1 Flowchart of the MOACO algorithm applied to multi-objective DNR problem
Chapter 8 Distribution Network Reconfiguration for Loss Reduction amp Reliability
Improvement
Page | 158
Start
Cloning
Maximum iteration
reached
Output Pareto
optimal set and end
No
Yes
Initialise and set iteration n=1
Pheromone based hypermutation
Diversity measure and extract non-
dominated solutions
The pheromones are updated according to
local and global rules
n=n+1
832 Applying AIS-ACO to Multi-objective DNR Problem
The general description of AIS-ACO algorithm is presented in Section 34 In this
study the AIS-ACO hybrid approach is used to handle multi-objective formulation
using the Pareto optimality concept The antigen is the multi-objective function and
the antibody is the solution to the problem The affinity between the antibody and the
antigen is the Pareto dominance among solutions which indicates the quality of the
solution [88] The information related to each objective is represented by an
individual pheromone table All the non-dominated solutions experience cloning
hypermutation selection and updating until the maximum number of iterations is
reached The flowchart of the AIS-ACO algorithm for Pareto optimality is presented
in Fig 8-2
Fig 8-2 Flowchart of the AIS-ACO algorithm applied to multi-objective DNR problem
Chapter 8 Distribution Network Reconfiguration for Loss Reduction amp Reliability
Improvement
Page | 159
The key parts of the algorithm are explained as follows
Step 1 Initialisation At the beginning of this algorithm a set of initial solutions is
generated These solutions should satisfy the constraints An individual pheromone
table is also built for each objective Each pheromone table has 33 cells (candidate
locations for tie-switches) The pheromone value of each cell represents the
probability of selecting the corresponding switch to be opened in the network model
The pheromone values of all cells are initially set at the same value
Step 2 Cloning All the non-dominated solutions are subjected to cloning In this
study as there are three objectives to be optimised the number of clones for each
non-dominated solution is three
Step 3 Hypermutation The selection of a cell in each clone for hypermutation is
obtained by applying a roulette wheel on its pheromone table [88] The probability of
selecting a cell is dependent on its pheromone intensity A higher pheromone value
of a cell in the table indicates that the corresponding edge in the network is more
likely to be selected The probability of selection cell i in table n is given by
119901119894119899 =
120591119894119899
sum 120591119895119899
119895 (8-14)
where 120591119894119899 is the pheromone value of cell i in table n sum 120591119895
119899119895 represents the sum of
pheromone values of all cells in table n
Step 4 Non-dominated Solutions Extraction and Diversity Measure This step is
same to the step which has been discussed in Section 831
Step 5 Pheromone Updating The aim of this step is to favour transitions toward
non-dominated solutions with great pheromone values There are two rules of
pheromone updating the local rule and global rule
Local rule Pheromones deposited in the search space should be evaporated to make
the paths less attractive The local pheromone update rule is calculated as follows
120591119894119899(119873) = 119898119886119909 (1 minus 120588)120591119894
119899(119873 minus 1) 120591119898119894119899 (8-15)
where 120588 is the pheromone evaporation rate which is set between 0 and 1 120591119894119899(119873 minus 1)
is pheromone value deposited on cell i of table n at iteration N-1 120591119898119894119899 is the lower
Chapter 8 Distribution Network Reconfiguration for Loss Reduction amp Reliability
Improvement
Page | 160
bound of pheromone level on each edge Even if the amount of pheromone deposited
to a path is at the lowest value 120591119898119894119899 there is a slight chance that an ant will still
choose this path This enlarges the entire search space
Global rule The global pheromone updating rule involves depositing large amounts
of pheromone to the edges that are a part of all the non-dominated solutions in the
current iteration [88] At iteration N the edges of the non-dominated solutions can be
updated as
120591119894119899(119873) = 119898119894119899120591119894
119899(119873) + 120588min (119891119899(119866))
119891119899(119866) 120591119898119886119909 (8-16)
where each 119894 isin edge set of G 119899 isin objective set and 119866 isin non-dominated solutions set
119891119899(119866) is the value of objective function n obtained by the non-dominated solution G
120591119898119886119909 is the higher bound of pheromone level on each edge
After this the non-dominated solutions with their location lists and fitness values in
the current iteration are retained and all the ants are free to choose a new path for the
next iteration
Step 6 Termination The computation continues until the predefined maximum
number iteration is reached The final non-dominated solutions are considered as the
Pareto set to the multi-objective DNR problem
Chapter 8 Distribution Network Reconfiguration for Loss Reduction amp Reliability
Improvement
Page | 161
LP11 LP12 LP13 LP14 LP15 LP16 LP17
LP8 LP9 LP10
LP1 LP2 LP3 LP4 LP5 LP6 LP7
LP32 LP33 LP34 LP35 LP36 LP37 LP38
LP29 LP30 LP31
LP26 LP27 LP28
LP18 LP19 LP20 LP21 LP22 LP23 LP24 LP25
19
20
21
22
23
24
26
25 27
28
29 30
71
13 15
14 16
17
18
69
1 3
2
5
4
7
6 8
10
9
68
11 12
56
57
58 60
59 61 62
65
64 66 67
50 52
51
54
53 55
44
45
46
47
48
49
70
31
32
33
34
36
35
39
37 38 40
41
42 43
63
F3
F2
F1
F7
F6
F5
F4
Normally Open Circuit BreakerNormally Closed Circuit Breaker
Subbus1
Subbus2
Subbus3
T1
T3
T5
Main
feeder
Main
feeder
Main
feeder
T2
T4
T6
84 Application Studies
The proposed MOACO and AIS-ACO algorithms have been tested on an 11 kV
distribution network developed from Bus 4 of the Roy Billinton Test System (RBTS)
a single-line diagram of the network is shown in Fig 8-3 The network consists of 38
load points and 4 tie-switches the associated data can be found in [114] The types
and lengths of 11 kV feeders are listed in Appendix A4 The network built in
OpenDSS incorporates three 3311 kV double transformer substations supplying the
downstream loads
Fig 8-3 Distribution feeder connected to RBTS Bus 4
This typical urban distribution network supplies residential commercial and
industrial consumers The average value of active and reactive power and the
customer type of each node are modified from the original values and the new values
are listed in Table 8-1
Chapter 8 Distribution Network Reconfiguration for Loss Reduction amp Reliability
Improvement
Page | 162
300
350
400
450
4
45
5
55
6
x 104
08
09
1
11
12
13
14
15
Feeder loss (kW)ECOST ($yr)
SA
IDI
(hrs
custo
mer
yr)
Table 8-1 Revised customer data (Average load)
Number
of load
points
Load points Customer type P
(kW)
Q
(kVAr)
Number of
customers
4 1-2 9-10 residential 545 51775 220
6 3-5 13-15 residential 500 475 200
12 6-7 16-17 23-25 28 30-
31 37-38
commercial 415 39425 10
6 8 11 18 26 32-33 industrial 1500 1425 1
10 12 19-22 27 29 34-36 industrial 1000 950 1
The proposed MOACO and AIS-ACO algorithms are coded in the MATLAB to
obtain the location of tie-switches for the optimum configuration The settings of the
algorithm parameters that provided the optimum solution for these two cases are
presented in Appendix C4
The number of Pareto optimal solutions obtained by the two algorithms is 26 and its
Pareto front is presented in Fig 8-4 in three dimensions The Pareto set is listed in
Appendix B3 in detail These solutions provide the network operator with various
configurations for the system to choose from Both algorithms have obtained the
same results However for 100 runs the average computation time of AIS-ACO
algorithm is 402s which is significantly lower than the MOCAO algorithm 1053s
Fig 8-4 Pareto solutions obtained (minimisation of feeder loss ECOST and SAIDI)
Chapter 8 Distribution Network Reconfiguration for Loss Reduction amp Reliability
Improvement
Page | 163
Table 8-2 presents the mean and standard deviation of the Pareto front
Table 8-2 Mean and standard deviation of Pareto Front (loss ECOST and SAIDI)
Feeder loss (kW) ECOST ($yr) SAIDI (hrscustomeryr)
Mean
38074 48139 09975
Standard deviation
3431 5291 01165
The corner non-dominated solutions representing minimum feeder loss minimum
ECOST and minimum SAIDI are marked by the red circle yellow circle and green
circle respectively as shown in Fig 8-4 The objective values of these solutions and
relevant tie-switches locations are presented in Table 8-3 It is obvious that the three
objectives are conflicting with each other and the algorithm is able to find the global
optimal solution for each objective function The minimum loss configuration is the
base configuration of RBTS-Bus4 In minimum ECOST solution the unserved
energy cost is reduced by 1133 in comparison with that in the original network
The minimum SAIDI solution shows a reduction of 3695 in the average time that
a customer is interrupted
Table 8-3 Minimum solutions along each objective (loss ECOST and SAIDI)
Feeder loss (kW) ECOST ($yr) SAIDI
(hrscustomeryr)
Tie-switches location
Minimum Loss
32142 46404 13090 68 69 70 71
Minimum ECOST
35409 41145 10586 10 17 41 70
Minimum SAIDI
43523 57891 08253 7 26 54 69
85 Best Compromise Solution
After obtaining the Pareto set the best compromise solution is the member which
has the largest fitness value as calculated in Eq (8-7) The results are presented in
Table 8-4 The importance of each objective function is represented by its weighting
Chapter 8 Distribution Network Reconfiguration for Loss Reduction amp Reliability
Improvement
Page | 164
factor which ranges from 1 to 10 A higher weighing factor indicates this objective
function is more important It can be seen that the solutions are different if the
weighing factors of each objective function are varied based on the tendencies of
DNO For example as shown in the table Case 2 (1205961 = 10 1205962 = 1 1205963 = 1)
indicates that the importance of feeder loss reduction is higher than the other two
objectives and hence the best compromise solution for this case obtains the
minimum loss among all the solutions which is the same as the results obtained
from Table 8-3 In comparison of Case 5 with Case 2 as the importance of ECOST
reduction is increased the network is reconfigured and its feeder loss increases by
588 to compensate for a 1045 decrease in the ECOST If there is no preferred
objective the best solution is obtained by setting 1205961 = 1205962 = 1205963 (Case 1)
Table 8-4 Best compromise solutions (loss ECOST and SAIDI)
Case No Weighting factors Best
compromise
solution
Feeder
loss
(kW)
ECOST
($yr)
SAIDI
(hrscustomeryr) 1205961 1205962 1205963
1 10 10 10 10 41 69 70 34033 41553 10996
2 10 1 1 68 69 70 71 32142 46404 13090
3 1 10 1 10 17 41 70 35409 41145 10586
4 1 1 10 7 26 54 69 43523 57891 08253
5 10 10 1 10 41 69 70 34033 41553 10996
6 10 1 10 10 54 69 71 34759 46644 10217
7 1 10 10 7 17 41 70 40368 43329 09570
86 Summary
The MOACO and AIS-ACO algorithms have been presented in this study for the
assessment of the multi-objective DNR problem using the Pareto optimality concept
The proposed DNR problem is formulated taking into account three objectives to be
minimised feeder loss ECOST and SAIDI The algorithms have been successfully
tested in an RBTS-Bus 4 network The results illustrate that the proposed algorithm
is able to generate a set of non-dominated solutions with high quality and great
diversity This set of solutions represent different trade-offs among the objective
functions And the corner non-dominated solutions which represent the minimum
Chapter 8 Distribution Network Reconfiguration for Loss Reduction amp Reliability
Improvement
Page | 165
value of each objective function are presented in the Pareto front chart By varying
the weighting factors for the parameters the decision makers can select the best
compromise strategy among the three objectives for implementation depending on
the utilitiesrsquo priorities
According to the obtained results both algorithms have obtained the same Pareto
optimal solutions but the AIS-ACO algorithm performs better in comparison with
the MOACO algorithm in terms of computation time The pheromone tables in AIS-
ACO algorithm are used to guide the search process and improve the solution quality
In addition the hypermutation is used as a random operator to enlarge the search
space and to prevent the algorithm from easily falling into the local optimum Future
work could include the assessment of the DNR problem with other objectives such
as balancing loads on feeders and minimising the maximum node voltage deviation
The AIS-ACO algorithm can also be applied to larger systems
Page | 166
CHAPTER 9
MULTI-OBJECTIVE DISTRIBUTION
NETWORK RECONFIGURATION amp DG
ALLOCATION CONSIDERING LOSS
VOLTAGE DEVIATION AND LOAD
BALANCING
91 Introduction
As discussed in the previous chapters distribution network reconfiguration (DNR)
can not only be used for single objective optimisation but also multi-objective
optimisation The study aims to determine a system topology that simultaneously
minimises feeder loss maximum node voltage deviation and feeder load balancing
This is achieved by optimal DNR and DG allocation
There are two methods presented in this chapter that tackle these objectives a single
fuzzy satisfaction objective function is used to transform the three conflicting
objectives into fuzzy memberships and then finally to combine them into a single
function The ultimate goal is to find a solution that maximises this single objective
while maintaining the constraints of the network [20] In Chapter 7 the degree of
Chapter 9 Multi-objective Distribution Network Reconfiguration amp DG Allocation
Considering Loss Voltage Deviation and Load Balancing
Page | 167
overall fuzzy satisfaction is determined by the max-min principle However there is
no guarantee that if one membership value is weaker than the other membership
values then for the same option the optimised single function will also be weak [86]
Therefore the max-min principle may not predict the best compromise solution In
this study a new operator called lsquomax-geometric meanrsquo has been introduced to
determine the degree of overall fuzzy satisfaction
Another methodology used for assessing the multi-objective DNR and DG allocation
problem is based on the Pareto optimality concept The proposed method provides a
set of non-dominated solutions with high quality and great diversity This constructs
a full Pareto front which represents different trade-offs among the objective
functions It allows the decision makers to select the most suitable one from all the
non-dominated solutions and use this for implementation which depends on the
utilitiesrsquo priorities
The optimisation algorithms for DNR and DG allocation can be classified into two
groups
Ant colony optimisation (ACO) algorithm which is used to solve the
problem in the fuzzy domain
Artificial immune systems-ant colony optimisation (AIS-ACO) algorithm
which is adopted to formulate the optimal network reconfiguration problem
within a multi-objective framework based on the Pareto optimality concept
The effectiveness and the efficiency of the proposed methods are implemented on
two standard IEEE 33-node and 69-node systems as case studies
The remainder of this chapter is organised as follows in Section 92 the
mathematical models of the problem are developed Then the solution procedures
are presented in Section 93 Numerical studies are presented and discussed in
Section 94 and finally Section 95 summarises the main conclusions
Chapter 9 Multi-objective Distribution Network Reconfiguration amp DG Allocation
Considering Loss Voltage Deviation and Load Balancing
Page | 168
0
1
92 Problem Formulation
The primary objective of this study is to minimise the three conflicting objectives
feeder loss maximum node voltage deviation and the feeder load balancing index
Two formulations of objective functions are presented as follow
921 Single Fuzzy Satisfaction Objective Function
In this study the three conflicting objectives are transformed into a single objective
function in the fuzzy domain The best compromise solution is obtained using a
lsquomax-geometric meanrsquo principle and is formulated as follows
Max 119871 = (120572119871 times 120572119881 times 120572119861)1 3frasl (9-1)
where 120572119871 120572119881 120572119861 represents the value of the membership functions for the feeder loss
the maximum node voltage deviation and the feeder load balancing index
respectively
The membership functions used to describe the three objectives of the DNR and DG
allocation problem are presented in the following sections
Membership function for feeder loss reduction
The calculation of feeder loss has been discussed in Section 28 The basic purpose
of this membership function is to reduce feeder loss Therefore the network
topology with a lower loss value obtains a higher membership value The
membership function for loss reduction is formulated in (9-2) and presented in Fig
9-1
Fig 9-1 Membership function for feeder loss reduction
As feeder loss becomes greater than 119871119874119878119878119898119894119899 the degree of satisfaction decreases
This reduction is continued until feeder loss reaches 119871119874119878119878119900119903119894
120572119871
119871119874119878119878119898119894119899 119871119874119878119878119900119903119894 119871119874119878119878
Chapter 9 Multi-objective Distribution Network Reconfiguration amp DG Allocation
Considering Loss Voltage Deviation and Load Balancing
Page | 169
0
1
120572119871 =
1 119871119874119878119878 le 119871119874119878119878119898119894119899119871119874119878119878119900119903119894minus119871119874119878119878
119871119874119878119878119900119903119894minus119871119874119878119878119898119894119899119871119874119878119878119898119894119899 lt 119871119874119878119878 lt 119871119874119878119878119900119903119894
0 119871119874119878119878 ge 119871119874119878119878119900119903119894
(9-2)
where 119871119874119878119878119900119903119894 is the loss of the original network 119871119874119878119878119898119894119899 is the minimum loss that
a network can achieve As it is not appropriate for decision makers to obtain a
network topology which increases loss after DNR and DG allocation the minimum
value of 120572119871 is selected as 0 if the loss is greater than or equal to 119871119874119878119878119900119903119894
Membership function for maximum node voltage deviation reduction
The maximum deviation of bus voltages from their rated values is formulated as
119881119863 = max|119881119903119890119891 minus 119898119894119899(119881119894)| |119881119903119890119891 minus 119898119886119909(119881119894)| 119894 120598 1 2 hellip 119873119887 (9-2)
where 119881119903119890119891 is the reference value for the node voltage which is the substation voltage
it is assumed to be 10 per unit in this study 119881119894 is the voltage at the ith node and 119873119887
is the number of nodes
The membership function for maximum node voltage deviation is shown in Fig 9-2
Fig 9-2 Membership function for maximum node voltage deviation reduction
The mathematical equation is presented below
120572119881 =
1 119881119863 le 119881119863119898119894119899119881119863119900119903119894minus119881119863
119881119863119900119903119894minus119881119863119898119894119899119881119863119898119894119899 lt 119881119863 lt 119881119863119900119903119894
0 119881119863 ge 119881119863119900119903119894
(9-3)
where 119881119863119900119903119894 and 119881119863119898119894119899 are the original and minimum values of the maximum node
voltage deviation respectively
120572119881
119881119863119898119894119899 119881119863119900119903119894 119881119863
Chapter 9 Multi-objective Distribution Network Reconfiguration amp DG Allocation
Considering Loss Voltage Deviation and Load Balancing
Page | 170
0
1
Membership function for feeder load balancing index reduction
The feeder load balancing index is calculated as
119871119861119868 = 119881119886119903[1198681
1198681119898119886119909
1198682
1198682119898119886119909 hellip
119868119894
119868119894119898119886119909 hellip
119868119899
119868119899119898119886119909] (9-4)
where 119868119894 is the current flowing through branch 119894 119868119894119898119886119909 represents the maximum
current limit of branch 119894
The function for feeder load balancing index is shown in Fig 9-3 and expressed as
120572119861 =
1 119871119861119868 le 119871119861119868119898119894119899119871119861119868119900119903119894minus119871119861119868
119871119861119868119900119903119894minus119871119861119868119898119894119899119871119861119868119898119894119899 lt 119871119861119868 lt 119871119861119868119900119903119894
0 119871119861119868 ge 119871119861119868119900119903119894
(9-5)
where 119871119861119868119900119903119894 and 119871119861119868119898119894119899 are the original and minimum values of the feeder load
balancing index respectively
Fig 9-3 Membership function for load balancing index reduction
922 Multi-objective Reconfiguration Problem Using Pareto
Optimality
In this study the multi-objective DNR problem can be defined as the minimisation
of the vector
119865(119866) = [1198911(119866)1198912(119866)1198913(119866)]119879 (9-6)
where 1198911(119866) 1198912(119866) and 1198913(119866) are feeder loss maximum node voltage deviation and
feeder load balancing index respectively The calculation of these three parameters
is discussed in Section 921
120572119861
119871119861119868119898119894119899 119871119861119868119900119903119894 119871119861119868
Chapter 9 Multi-objective Distribution Network Reconfiguration amp DG Allocation
Considering Loss Voltage Deviation and Load Balancing
Page | 171
93 Solution methodology
931 Applying ACO to DNR and DG Allocation in the Fuzzy
Domain
In this study the objective of reconfiguring the network and allocating DGs
simultaneously is to deal with the single fuzzy satisfaction objective function In
order to tackle this optimisation problem an ACO algorithm is adopted to find the
optimum configuration of tie-switches and the location of DGs in the network When
the locations of tie-switches and DGs are changed a new network configuration will
be formed For each network configuration the overall satisfaction of the plan is
calculated using Eq (9-1) The search space of the DNR and DG allocation problems
is modelled as a directed graph as shown in Fig 5-1 The flowchart of the proposed
ACO algorithm is presented in Fig 5-2
932 Applying AIS-ACO to Multi-objective DNR and DG
Allocation Using Pareto Optimality
The application of the AIS-ACO algorithm to the multi-objective DNR and DG
allocation problem using the concept of Pareto optimality is similar to that in Section
832 with an additional process for DG allocation
94 Application Studies
To demonstrate the performance and effectiveness of the proposed techniques in
solving the network reconfiguration and placement of DG problems simultaneously
the proposed ACO and AIS-ACO are implemented on two 1266 kV test systems
consisting of 33 and 69 buses The network models are built in OpenDSS and the
solution algorithms are developed in MATLAB For both test systems the substation
voltage is assumed to be 10 pu and all the sections and buses are considered as
candidate locations for tie-switches and DG placement respectively In this study
for simplicity the number of installed DGs is three All the DGs are synchronous
generators and are represented as PQ models with a 100 kVA and a power factor
Chapter 9 Multi-objective Distribution Network Reconfiguration amp DG Allocation
Considering Loss Voltage Deviation and Load Balancing
Page | 172
equal to 10 However the proposed methodology can be implemented for any
number of DGs For the purpose of better illustration and comparison four cases are
considered to analyse the superiority and performance of the proposed methods
Case I System is without reconfiguration and has no DGs (base case)
Case II System is optimally reconfigured and has no DGs
Case III System is optimally reconfigured after DGs are placed at certain buses
Case IV System is optimally reconfigured and DGs are optimally placed
simultaneously
It is to be noted that the ACO and AIS-ACO control parameters are different for
each test case They are set experimentally using information from several trial runs
The final combinations that provide the best results for all of the above tests are
given in Appendix C5 And the Pareto sets for all test cases are listed in Appendix
B4 in detail
941 33-bus System
In this section the proposed procedure is implemented on a 33-bus 1266 kV radial
distribution system with 37 branches and 5 tie-switches whose single line diagram is
shown in Fig 5-3 The tie-switches are located at L33 to L37 represented by red
dotted lines The data of lines and loads are taken from [108] and summarised in
Appendix A2 The current carrying capacity of all branches is 255A The total real
and reactive power loads of the system are 3715 kW and 2300 kVAr respectively
Case I base case
For the base case without reconfiguration and DGs the initial active feeder loss
maximum node voltage deviation and feeder load balancing index of this system are
20314 kW 00884 pu and 00419 respectively
Chapter 9 Multi-objective Distribution Network Reconfiguration amp DG Allocation
Considering Loss Voltage Deviation and Load Balancing
Page | 173
10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
18 19 20 21
22 23 24
25 26 27 28 29 30 31 32
L1 L2 L3 L4 L5 L6 L7 L8 L9 L10 L11 L12 L13 L14 L15 L16 L17
L18
L19 L20 L21
L22
L23 L24
L25
L26 L27 L28 L29 L30 L31 L32
L33
L34
L35
L36
L37
Case II with reconfiguration only (no DGs)
In this case only reconfiguration is considered and no DGs are installed
After DNR the best compromise solution obtained using ACO algorithm in a single
fuzzy satisfaction objective function is presented in Table 9-1 It can be seen that the
DNR has resulted in a reduction of 2956 in feeder loss 2930 in maximum node
voltage deviation and 3556 in feeder load balancing index compared to the base
case This solution is one of the Pareto optimal solutions which are obtained by
using AIS-ACO algorithm And the network configuration after DNR is shown in
Fig 9-4
Table 9-1 Results of DNR in fuzzy multi-objective formulation for 33-bus system in Case II
Objective function Feeder loss
(kW)
Maximum node
voltage deviation
(pu)
Feeder Load
balancing index
Tie-switches
location
08734 14310 00625 00270 6 9 14 32 37
Fig 9-4 33 bus-system for fuzzy multi-objective optimisation Case II
The number of Pareto optimal solutions obtained using AIS-ACO algorithm is 21
and its Pareto front is presented in Fig 9-5 in three dimensions Table 9-2 presents
the mean and standard deviations of the objective values of the Pareto solutions
Chapter 9 Multi-objective Distribution Network Reconfiguration amp DG Allocation
Considering Loss Voltage Deviation and Load Balancing
Page | 174
120140
160180
200220
006
008
01
012
014
016
0022
0024
0026
0028
003
0032
0034
0036
Feeder loss (kW)Maximum node voltage deviation (pu)
Feeder
load b
ala
ncin
g index
Fig 9-5 Pareto front obtained for 33-bus system in Case II
Table 9-2 Mean and standard deviations of Pareto Front for 33-bus system in Case II
Feeder loss (kW) Maximum node voltage
deviation (pu)
Feeder Load balancing index
Mean
15499 00815 00256
Standard deviation
1549 00194 00023
The corner non-dominated solutions which represent minimum feeder loss
minimum voltage deviation and minimum feeder load balancing index are marked
by the red circle yellow circle and green circle respectively as shown in Fig 9-5
The objective values of these solutions and relevant tie-switches locations are
presented in Table 9-3 In minimum loss solution the feeder loss is reduced by 3118
compared to the initial state If improving voltage profiles is the principle objective
the solution with maximum node voltage deviation of 00604 pu is optimum which
represents a 3167 improvement compared to the base case If balancing feeder
Chapter 9 Multi-objective Distribution Network Reconfiguration amp DG Allocation
Considering Loss Voltage Deviation and Load Balancing
Page | 175
10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
18 19 20 21
22 23 24
25 26 27 28 29 30 31 32
L1 L2 L3 L4 L5 L6 L7 L8 L9 L10 L11 L12 L13 L14 L15 L16 L17
L18
L19 L20 L21
L22
L23 L24
L25
L26 L27 L28 L29 L30 L31 L32
L33
L34
L35
L36
L37
DG2
DG1
DG3
load is the main objective the solution with load balancing index of 00223 is
optimum where the index decreases by 4678 in comparison with the initial case
Table 9-3 Minimum solutions along each objective for 33-bus system in Case II
Feeder loss (kW) Maximum node
voltage deviation (pu)
Feeder Load balancing
index
Tie-switches location
Minimum Loss
13981 00639 00280 7 9 14 32 37
Minimum Voltage Deviation
14026 00604 00310 7 9 14 28 32
Minimum Feeder Load Balancing Index
20248 01309 00223 7 30 34 35 37
Case III with reconfiguration only (with DGs)
In this case the three DGs are located at the end of the feeders ie Bus 17 21 24
The feeder loss maximum node voltage deviation and feeder load balancing of the
original network with DGs are 17831 kW 00823 pu and 00389 pu respectively
After DNR the best compromise solution obtained using ACO algorithm in a single
fuzzy satisfaction objective function is presented in Table 9-4 Compared to the Case
I feeder loss maximum node voltage deviation and feeder load balancing decrease
by 3893 3281 and 4511 respectively This solution belongs to the Pareto
set which are obtained by using AIS-ACO algorithm Fig 9-6 illustrates the optimal
network configuration
Fig 9-6 33 bus-system for fuzzy multi-objective optimisation Case III
Chapter 9 Multi-objective Distribution Network Reconfiguration amp DG Allocation
Considering Loss Voltage Deviation and Load Balancing
Page | 176
110120
130140
150160
170
004
006
008
01
0120018
002
0022
0024
0026
0028
003
Feeder loss (kW)Maximum node voltage deviation (pu)
Feeder
load b
ala
ncin
g index
Table 9-4 Results of DNR in fuzzy multi-objective formulation for 33-bus system in Case III
Objective function Feeder loss
(kW)
Maximum node
voltage deviation
(pu)
Feeder Load
balancing index
Tie-switches
location
08590 12405 00594 00230 6 8 14 32 37
Fig 9-7 shows the Pareto front obtained by the AIS-ACO method and the number
of Pareto optimal solutions for this case is 28 The mean and standard deviations of
the objective values of the Pareto solutions are listed in Table 9-5
Fig 9-7 Pareto front obtained for 33-bus system in Case III
Table 9-5 Mean and standard deviations of Pareto Front for 33-bus system in Case III
Feeder loss (kW) Maximum node voltage
deviation (pu)
Feeder load balancing index
Mean
12850 00711 00231
Standard deviation
1003 00166 00029
Chapter 9 Multi-objective Distribution Network Reconfiguration amp DG Allocation
Considering Loss Voltage Deviation and Load Balancing
Page | 177
The corner non-dominated solutions which represent minimum feeder loss
minimum voltage deviation and minimum feeder load balancing index are marked
by the red circle yellow circle and green circle respectively as shown in Fig 9-7
Table 9-6 presents the objective values of these solutions and relevant tie-switches
locations In minimum loss solution the network reconfiguration results in a
reduction of 4214 in feeder loss compared to the original network and a
reduction of 1594 compared to the reconfigured network without DGs If
improving voltage profiles is the principle objective the solution with maximum
node voltage deviation of 00567 pu is optimum which represents a 3586 and
613 improvement compared to Case I and Case II If balancing feeder load is the
main objective the solution with load balancing index of 00189 is optimum where
the index decreases by 5489 and 1525 in comparison with Case I and Case II
Table 9-6 Minimum solutions along each objective for 33-bus system in Case III
Feeder loss (kW) Maximum node
voltage deviation (pu)
Feeder Load balancing
index
Tie-switches location
Minimum Loss
11753 00643 00241 7 9 14 28 31
Minimum Voltage Deviation
12592 00567 00265 6 8 14 28 32
Minimum Feeder Load Balancing Index
16419 01139 00189 7 21 30 35 37
Case IV with reconfiguration and DG allocation
The network is reconfigured and DGs are allocated simultaneously in this case The
best compromise solution obtained using the proposed algorithm in a single fuzzy
satisfaction objective function after DNR and DG allocation is presented in Table 9-
7 Feeder loss maximum node voltage deviation and feeder load balancing decrease
by 4645 4355 and 4463 respectively in comparison with the base case
This solution is one of the Pareto optimal solutions which are obtained by using
AIS-ACO algorithm Fig 9-8 illustrates the optimal network configuration and DG
locations
Chapter 9 Multi-objective Distribution Network Reconfiguration amp DG Allocation
Considering Loss Voltage Deviation and Load Balancing
Page | 178
10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
18 19 20 21
22 23 24
25 26 27 28 29 30 31 32
L1 L2 L3 L4 L5 L6 L7 L8 L9 L10 L11 L12 L13 L14 L15 L16 L17
L18
L19 L20 L21
L22
L23 L24
L25
L26 L27 L28 L29 L30 L31 L32
L33
L34
L35
L36
L37
DG1
DG3
DG2
100110
120130
140150
160
004
006
008
01
012
0016
0018
002
0022
0024
0026
0028
Feeder loss (kW)Maximum node voltage deviation (pu)
Feeder
load b
ala
ncin
g index
Table 9-7 Results of DNR and DG allocation in fuzzy multi-objective formulation for 33-bus system
in Case IV
Objective
function
Feeder loss
(kW)
Maximum node
voltage
deviation (pu)
Feeder Load
balancing
index
Tie-switches
location
DGs location
08961 10878 00499 00232 7 9 14 36 37 B32 B32 B32
Fig 9-8 33 bus-system for fuzzy multi-objective optimisation Case IV
The number of non-dominated solutions obtained by the AIS-ACO algorithm is 295
However the maximum number for Pareto optimal solutions is restricted to 50
Therefore the solutions with a high value of crowding distance are selected Fig 9-9
shows the Pareto front obtained by the proposed method
Fig 9-9 Pareto front obtained for 33-bus system in Case IV
Chapter 9 Multi-objective Distribution Network Reconfiguration amp DG Allocation
Considering Loss Voltage Deviation and Load Balancing
Page | 179
The mean and standard deviations of the Pareto front are listed in Table 9-8
Table 9-8 Mean and standard deviations of Pareto Front for 33-bus system in Case IV
Feeder loss (kW) Maximum node voltage
deviation (pu)
Feeder Load balancing index
Mean
13295 00873 00194
Standard deviation
1354 00179 00019
The corner non-dominated solutions which represent minimum feeder loss
minimum voltage deviation and minimum feeder load balancing index are marked
by the red circle yellow circle and green circle respectively as shown in Fig 9-9
The objective values of these solutions and relevant tie-switches locations are
presented in Table 9-9 In minimum loss solution the network reconfiguration and
DG allocation result in a reduction of 4662 2244 and 773 in feeder loss
compared to Case I Case II and Case III respectively If improving voltage profiles
is the principle objective the solution with maximum node voltage deviation of
00490 pu is optimum which represents a 4457 1887 and 1358
improvement compared to Case I Case II and Case III respectively If balancing
feeder load is the main objective the solution with load balancing index of 00178 is
optimum where the index decreases by 5752 2018 and 582 in comparison
with Case I Case II and Case III respectively
Table 9-9 Minimum solutions along each objective for 33-bus system in Case IV
Feeder loss (kW) Maximum node
voltage deviation
(pu)
Feeder Load
balancing index
Tie-switches
location
DGs location
Minimum Loss
10844 00538 00228 7 9 14 32 37 B30 B31 B31
Minimum Voltage Deviation
11020 00490 00259 7 9 14 28 36 B31 B31 B32
Minimum Feeder Load Balancing Index
15443 01090 00178 7 30 34 35 37 B8 B9 B12
Chapter 9 Multi-objective Distribution Network Reconfiguration amp DG Allocation
Considering Loss Voltage Deviation and Load Balancing
Page | 180
10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
27
28
29
30
31 32 33 34
35
36
37
38 39 40 41 42 43 44 45
46 47 48 49
50
51
52
53 54 55 56 57 58 59 60 61 62 63 64
65 66
67 68
L1 L2 L3 L4 L5 L6 L7 L8 L9 L10 L11 L12 L13 L14 L15 L16 L17 L18 L19 L20 L21 L22 L23 L24 L25 L26
L27
L28
L29
L30
L31 L32 L33 L34
L35
L36
L37
L38 L39 L40 L41 L42 L43 L44 L45
L46
L47 L48 L49
L50
L51
L52
L53 L54 L55 L56 L57 L58 L59 L60 L61 L62 L63 L64
L65
L66
L67
L68
L69
L70
L71
L72L73
942 69-bus System
This is a large-scale radial distribution system consisting of 73 branches and 5 tie-
switches whose single-line diagram is shown in Fig 5-9 The tie-switches are
located at L69 to L73 represented by red dotted lines The line and load data of the
system are taken from [84] and summarised in Appendix A3 The current carrying
capacity of the branches 1-9 is 400 A 46-49 and 52-64 is 300 A and for all other
branches it is 200 A The total power loads are 379589 kW and 26891 kVAr
respectively
Case I base case
For the base case without reconfiguration and DGs the initial active feeder loss
maximum node voltage deviation and feeder load balancing index of this system are
22562 kW 00928 pu and 00259 respectively
Case II with reconfiguration only (no DGs)
In this case only reconfiguration is considered and no DGs are installed After DNR
the best compromise solution obtained using ACO algorithm in a single fuzzy
satisfaction objective function is presented in Table 9-10 and the network
configuration is shown in Fig 9-10 Reconfiguring the network brings a reduction of
5619 4353 and 2355 in feeder loss maximum node voltage deviation and
feeder load balancing index respectively compared to the base case This solution
belongs to the Pareto set which are obtained by using AIS-ACO algorithm
Fig 9-10 69 bus system for fuzzy multi-objective optimisation Case II
Chapter 9 Multi-objective Distribution Network Reconfiguration amp DG Allocation
Considering Loss Voltage Deviation and Load Balancing
Page | 181
80
100
120
140
160
005
006
007
0080016
0018
002
0022
0024
0026
0028
Feeder loss (kW)Maximum node voltage deviation (pu)
Feeder
load b
ala
ncin
g index
Table 9-10 Results of DNR in fuzzy multi-objective formulation for 69-bus system in Case II
Objective function Feeder loss
(kW)
Maximum node
voltage deviation
(pu)
Feeder Load
balancing index
Tie-switches
location
09676 9885 00524 00195 14 55 61 71 72
The number of Pareto optimal solutions obtained by the AIS-ACO algorithm is 12
and its Pareto front are presented in Fig 9-11 in three dimensions
Fig 9-11 Pareto front obtained for 69-bus system in Case II
The mean and standard deviations of the objective values of the Pareto solutions are
listed in Table 9-11
Table 9-11 Mean and standard deviations of Pareto Front for 69-bus system in Case II
Feeder loss (kW) Maximum node voltage
deviation (pu)
Feeder Load balancing index
Mean
12535 00605 00192
Standard deviation
2458 00085 00028
Chapter 9 Multi-objective Distribution Network Reconfiguration amp DG Allocation
Considering Loss Voltage Deviation and Load Balancing
Page | 182
The corner non-dominated solutions which represent minimum feeder loss
minimum voltage deviation and minimum feeder load balancing index are marked
by the red circle yellow circle and green circle respectively as shown in Fig 9-11
The objective values of these solutions and relevant tie-switches locations are
presented in Table 9-12 In minimum loss solution the feeder loss is reduced by
5619 compared to the initial state If improving voltage profiles is the principle
objective the solution with maximum node voltage deviation of 00523 pu is
optimum which represents a 4364 improvement compared to the base case If
balancing feeder load is the main objective the solution with load balancing index of
00161 is optimum where the index decreases by 3784 in comparison with the
initial case
Table 9-12 Minimum solutions along each objective for 69-bus system in Case II
Feeder loss (kW) Maximum node
voltage deviation (pu)
Feeder load balancing
index
Tie-switches location
Minimum Loss
9885 00524 00195 14 55 61 71 72
Minimum Voltage Deviation
10535 00523 00242 9 14 55 61 71
Minimum Feeder Load Balancing Index
15051 00701 00161 14 61 69 71 72
Case III with reconfiguration only (with DGs)
In this case the three DGs are located at the end of the feeders ie Bus 26 45 64
The feeder loss maximum node voltage deviation and feeder load balancing of the
original network with DGs are 19472 kW 00855 pu and 00234 pu respectively
After DNR Table 9-13 presents the best compromise solution obtained using ACO
algorithm in a single fuzzy satisfaction objective function and the optimal network
configuration is shown in Fig 9-12 Compared to the base case feeder loss
maximum node voltage deviation and feeder load balancing decrease by 6118
4364 and 3282 respectively This solution is one of the Pareto optimal
solutions which are obtained by using AIS-ACO algorithm
Chapter 9 Multi-objective Distribution Network Reconfiguration amp DG Allocation
Considering Loss Voltage Deviation and Load Balancing
Page | 183
10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
27
28
29
30
31 32 33 34
35
36
37
38 39 40 41 42 43 44 45
46 47 48 49
50
51
52
53 54 55 56 57 58 59 60 61 62 63 64
65 66
67 68
L1 L2 L3 L4 L5 L6 L7 L8 L9 L10 L11 L12 L13 L14 L15 L16 L17 L18 L19 L20 L21 L22 L23 L24 L25 L26
L27
L28
L29
L30
L31 L32 L33 L34
L35
L36
L37
L38 L39 L40 L41 L42 L43 L44 L45
L46
L47 L48 L49
L50
L51
L52
L53 L54 L55 L56 L57 L58 L59 L60 L61 L62 L63 L64
L65
L66
L67
L68
L69
L70
L71
L72L73
DG3
DG1
DG2
8090
100110
120130
140
005
006
007
008
0014
0016
0018
002
0022
0024
Feeder loss (kW)Maximum node voltage deviation (pu)
Feeder
load b
ala
ncin
g index
Table 9-13 Results of DNR in fuzzy multi-objective formulation for 69-bus system in Case III
Objective function Feeder loss
(kW)
Maximum node
voltage deviation
(pu)
Feeder Load
balancing index
Tie-switches
location
08829 8758 00523 00174 14 55 61 71 72
Fig 9-12 69-bus system for fuzzy multi-objective optimisation Case III
Fig 9-13 shows the Pareto front obtained by the AIS-ACO method and the number
of Pareto optimal solutions for this case is 19
Fig 9-13 Pareto front obtained for 69-bus system in Case III
Chapter 9 Multi-objective Distribution Network Reconfiguration amp DG Allocation
Considering Loss Voltage Deviation and Load Balancing
Page | 184
The mean and standard deviations of the objective values of the Pareto solutions are
listed in Table 9-14
Table 9-14 Mean and standard deviations of Pareto Front for 69-bus system in Case III
Feeder loss (kW) Maximum node voltage
deviation (pu)
Feeder Load balancing index
Mean
10707 00576 00183
Standard deviation
2042 00071 00029
The corner non-dominated solutions which represent minimum feeder loss
minimum voltage deviation and minimum feeder load balancing index are marked
by the red circle yellow circle and green circle respectively as shown in Fig 9-13
Table 9-15 presents the objective values of these solutions and relevant tie-switches
locations are presented In minimum loss solution the network reconfiguration
results in a reduction of 6118 in feeder loss compared to the original network and
a reduction of 1140 compared to the reconfigured network without DGs If
improving voltage profiles is the principle objective the solution with maximum
node voltage deviation of 00522 pu is optimum which represents a 4375 and
019 improvement compared to Case I and Case II If balancing feeder load is the
main objective the solution with load balancing index of 00147 is optimum where
the index decreases by 4324 and 745 in comparison with Case I and Case II
Table 9-15 Minimum solutions along each objective for 69-bus system in Case III
Feeder loss (kW) Maximum node
voltage deviation (pu)
Feeder Load balancing
index
Tie-switches location
Minimum Loss
8758 00523 00174 13 55 61 71 72
Minimum Voltage Deviation
9729 00522 00226 7 12 55 61 71
Minimum Feeder Load Balancing Index
13686 00681 00147 11 61 69 71 72
Chapter 9 Multi-objective Distribution Network Reconfiguration amp DG Allocation
Considering Loss Voltage Deviation and Load Balancing
Page | 185
10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
27
28
29
30
31 32 33 34
35
36
37
38 39 40 41 42 43 44 45
46 47 48 49
50
51
52
53 54 55 56 57 58 59 60 61 62 63 64
65 66
67 68
L1 L2 L3 L4 L5 L6 L7 L8 L9 L10 L11 L12 L13 L14 L15 L16 L17 L18 L19 L20 L21 L22 L23 L24 L25 L26
L27
L28
L29
L30
L31 L32 L33 L34
L35
L36
L37
L38 L39 L40 L41 L42 L43 L44 L45
L46
L47 L48 L49
L50
L51
L52
L53 L54 L55 L56 L57 L58 L59 L60 L61 L62 L63 L64
L65
L66
L67
L68
L69
L70
L71
L72L73
DG3DG1
DG2
Case IV with reconfiguration and DGs allocation
In this case the network is reconfigured and DGs are allocated simultaneously
Table 9-16 presents the best compromise solution obtained using the ACO algorithm
in a single fuzzy satisfaction objective function after DNR and DGs allocation and
the optimal network configuration and DG locations are shown in Fig 9-14 Feeder
loss maximum node voltage deviation and feeder load balancing decrease by
6721 5377 and 3840 respectively in comparison with the base case This
solution is one of the Pareto optimal solutions which are obtained by using AIS-
ACO algorithm
Table 9-16 Results of DNR and DGs allocation in fuzzy multi-objective formulation for 69-bus
system in Case IV
Objective
function
Feeder loss
(kW)
Maximum
node voltage
deviation (pu)
Feeder Load
balancing
index
Tie-switches
location
DGs location
08882 7397 00429 00158 14 55 61 71 72 B60 B60 B60
Fig 9-14 69-bus system for fuzzy multi-objective optimisation Case IV
The number of non-dominated solutions obtained by the AIS-ACO algorithm is 46
Fig 9-15 shows the Pareto front obtained by the proposed method The mean and
standard deviations of the objective values of the Pareto solutions are listed in Table
9-17
Chapter 9 Multi-objective Distribution Network Reconfiguration amp DG Allocation
Considering Loss Voltage Deviation and Load Balancing
Page | 186
70
80
90
100
110
120
004
0045
005
0055
006
0012
0013
0014
0015
0016
0017
0018
0019
Feeder loss (kW)Maximum node voltage deviation (pu)
Feeder
load b
ala
ncin
g index
Fig 9-15 Pareto front obtained for 69-bus system in Case IV
Table 9-17 Mean and standard deviations of Pareto Front for 69-bus system in Case IV
Feeder loss (kW) Maximum node voltage
deviation (pu)
Feeder Load balancing index
Mean
9872 00520 00147
Standard deviation
1491 00055 00013
The corner non-dominated solutions which represent minimum feeder loss
minimum voltage deviation and minimum feeder load balancing index are marked
by the red circle yellow circle and green circle respectively as shown in Fig 9-15
The objective values of these solutions and relevant tie-switches locations are
presented in Table 9-18 In minimum loss solution the network reconfiguration and
DG allocation result in a reduction of 6721 2517 and 1554 in feeder loss
compared to Case I Case II and Case III respectively If improving voltage profiles
is the principle objective the solution with maximum node voltage deviation of
00428 is optimum which represents a 5388 1816 and 1801 improvement
compared to Case I Case II and Case III respectively If balancing feeder load is the
Chapter 9 Multi-objective Distribution Network Reconfiguration amp DG Allocation
Considering Loss Voltage Deviation and Load Balancing
Page | 187
main objective the solution with load balancing index of 00125 pu is optimum
where the index decreases by 5174 2236 and 1497 in comparison with Case
I Case II and Case III respectively
Table 9-18 Minimum solutions along each objective for 69-bus system in Case IV
Feeder loss (kW) Maximum node
voltage deviation
(pu)
Feeder Load
balancing index
Tie-switches
location
DGs location
Minimum Loss
7397 00429 00158 14 55 61 71 72 B60 B60 B60
Minimum Voltage Deviation
8032 00428 00183 11 55 61 71 72 B60 B60 B60
Minimum Feeder Load Balancing Index
10962 00577 00125 14 63 69 71 72 B62 B62 B62
95 Summary
In this study the DNR and DG allocation problem is formulated either within a
fuzzy satisfaction objective function or within a multi-objective Pareto optimal
framework This formulation incorporates the minimisation of three conflicting
objectives feeder loss maximum node voltage deviation and feeder load balancing
index In the fuzzy multi-objective formulation all three objectives are transformed
into a single fuzzy satisfaction objective function and the ACO algorithm is used to
provide decision support The AIS-ACO algorithm has been presented in this study
for the assessment of the multi-objective DNR problem from a Pareto optimality
point of view The proposed methods have been successfully applied on a 33-bus and
a 69-bus radial distribution system The results illustrate that the proposed algorithm
is able to generate a set of non-dominated solutions with high quality and great
diversity This allows the network operators to choose any one from the non-
dominated solutions for implementation based on utilitiesrsquo priorities And the corner
non-dominated solutions which represent the minimum value of each objective
function are presented in the Pareto front chart
Chapter 9 Multi-objective Distribution Network Reconfiguration amp DG Allocation
Considering Loss Voltage Deviation and Load Balancing
Page | 188
Future work could include the assessment of the DNR and DG allocation problem
with more than three objectives These objectives may include balancing loads on
transformers minimising the number of switching operations etc The proposed
methodologies can be evaluated further by applying them to actual systems
Page | 189
CHAPTER 10
CONCLUSION amp FUTURE WORK
101 Conclusion
The aim of this thesis is to improve service efficiency and quality in distribution
networks Optimal distribution automation (DA) is one of the best solutions to
achieve this goal The multiple objectives are transformed into different forms based
on utilitiesrsquo priorities For this purpose the Monte Carlo method is used to solve
power system issues involving uncertain load values And a set of ant colony
optimisation (ACO)-based algorithms has been developed for objectives
optimisation This section summarises the conclusions drawn from the research
results
A comprehensive review of the network configurations switchgears DA
assessment of loss and reliability indices and different forms of multi-objective
functions was provided in Chapter 2 This has demonstrated the need for DA to
provide a reliable and high efficiency power supply to all customers with a minimum
cost
In Chapter 3 the thesis reviewed the techniques for the assessment of mono-
objectivemulti-objective optimisation problems which were categorised into two
groups simulation methods and analytical methods The Monte Carlo method is a
typical simulation technique and is generally used to deal with power system
calculations involving uncertain parameters It can find the best solution with a high
Chapter 10 Conclusion amp Future Work
Page | 190
degree of accuracy but requires a considerable amount of CPU time and memory
The ant colony optimisation (ACO) algorithm is one of the metaheuristic techniques
designed for assessing the DA problems It can find the global optimum solution in a
reasonable computation time The artificial immune systems (AIS)-ACO hybrid
algorithm was used for assessing the DA problems in order to obtain a set of non-
dominated solutions by using the concept of Pareto dominance
The thesis illustrates why transformer economic operation (TEO) is an economical
solution to reduce transformer loss The TEO mode with minimum loss and
satisfactory voltages is achieved by operating with one or two transformers This
can be summarised as when the transformer load factor is less than the TCLF
transformers should operate separately However when the transformer load factor is
higher than the TCLF it is recommended that transformers operate in parallel In
Chapter 4 a Monte Carlo simulation platform was established to tackle load
uncertainties A methodology based on TEO to reduce transformer loss was then
described This results in a reduction over the conventional transformer loss ie
when two transformers are in parallel operation However simulation studies also
indicate voltage profiles are improved when transformers operate in parallel
Therefore a slight reduction in TCLF results in an increased loss but an
improvement in voltage performance
In Chapter 4 the thesis also demonstrates why distribution network reconfiguration
(DNR) is an effective strategy for transformer loss reduction The presented results
illustrate the optimal locations of tie-switch statuses have successfully reduced the
transformer losses and improved the voltages profiles during a 24 hour operating
period The further away the nodes are from the tie-switch the better the voltage
profiles obtained In addition when the tie-switch moves closer to the middle of the
linked feeder the voltage performance is improved In this case the daily energy
loss in Scenario 5 is 11162 kWh After the introduction of Scenario 9 the annual
saving energy could be 59641 kWh
One conclusion of this thesis is that the network can be reconfigured and DGs can be
relocated simultaneously for feeder loss reduction In Chapter 5 an ACO algorithm
was used for assessing the DNR and DG allocation problems in terms of feeder loss
reduction The numerical results showed that for best performance the existing tie-
Chapter 10 Conclusion amp Future Work
Page | 191
switches were relocated and DGs were optimally placed at the same time The feeder
losses are reduced by 4662 and 6721 for the 33-bus and 69-bus system
respectively The inappropriate network configuration and DG location might result
in loss increment when the size of DG is increased The proposed methodology has
also successfully reduced the total feeder loss and improved the voltage profiles for
different capacities of DG by determining the most suitable network topology and
the DG locations In addition the simulation results have been compared with other
classical methods in literature and it is demonstrated that the proposed ACO is more
efficient and is more likely to obtain the global optimum solution
Another conclusion of this thesis is that the distribution network loss including
transformer loss and feeder loss can be minimised by using a new optimal planning
strategy This strategy is a combination of TEO and network reconfiguration as
presented in Chapter 6 In this chapter the distribution loads experience daily and
seasonal variations and the day is divided into two periods The proposed ACO
algorithm has successfully found the optimum network configuration and economic
operation mode of transformers in all substations during each time interval The
annual energy loss is reduced by 506 compared to the original network Both
transformer loss and feeder loss are reduced through this optimal planning using
DNR and TEO Furthermore simulation results obtained with numerical studies
have demonstrated the capability of applying the ACO algorithm to distribution
network planning including networks with DGs and EVs The proposed
methodology has successfully reduced the total network loss for different capacities
of DG and different penetration levels of EVs by determining the most suitable
network topology compared to the original configuration Comparative results also
show that coordinated charging plan results in less energy loss compared to
uncoordinated charging strategy with the same EV penetration level This is due to
the postponement of charging time which avoids a clash with the peak power
demand times
The thesis develops an effective strategy of sectionalising switch placement (SSP)
for system reliability improvement This is achieved by installing new switches and
relocating existing switches In Chapter 7 an ACO algorithm was proposed for the
assessment of the SSP problem based on reliability improvement and switch costs
minimisation using either a single objective function with weighted aggregation of a
Chapter 10 Conclusion amp Future Work
Page | 192
multi-objective function with fuzzy variables The selection of pheromone
evaporation rate and number of ants is a trade-off between the global search ability
and convergence rate of the ACO algorithm In comparison with the original system
existing sectionalising switches were relocated and new automatic switches were
installed For this practical system the total system costs are reduced by 4289
compared to the original network The impact of installing sectionalising switches on
reducing the total system costs decreases as the number of sectionalising switches is
increased Furthermore a benefit-to-cost analysis which offered a comparison
between ECOST and switch costs was implemented The analysis reveals that the
installing and relocating sectionalising switches is a profitable investment In
addition a set of compromise solutions was obtained by assessing the SSP problem
in terms of ECOST and SAIDI reduction during fault contingencies The placement
of sectionalising switches results in a reduction of 60 in ECOST and 7148 in
SAIDI
The thesis also proposes a strategy for assessing the DNR problems if the
distribution network operator (DNO) desires to know all possible optimal solutions
for all the multiple conflicting objectives simultaneously This formulates the DNR
problem within a multi-objective formulation in the Pareto optimal framework In
Chapter 8 The MOACO and AIS-ACO algorithms were used for assessing this
problem in terms of loss reduction and reliability improvement Both algorithms
have obtained the same Pareto optimal solutions but the AIS-ACO algorithm
performs better in comparison with the MOACO algorithm in terms of computation
time Feeder loss maximum node voltage deviation and feeder load balancing were
simultaneous optimised in Chapter 9 A set of non-dominated solutions with high
quality and great diversity was obtained This set of solutions represent different
trade-offs among the objective functions And the corner non-dominated solutions
which represent the minimum value of each objective function are presented in the
Pareto front chart For IEEE 69-bus system compared to the base case the network
reconfiguration and DG allocation result in a reduction of 6721 in minimum loss
solution If improving the voltage profiles is the principle objective the best solution
represents a 5388 improvement of this index If balancing feeder load is the main
objective this index decreases by 5174 By varying the weighting factors for the
Chapter 10 Conclusion amp Future Work
Page | 193
parameters the decision makers can select the best compromise among the three
objectives for implementation depending on the utilitiesrsquo priorities
102 Future Work
Based on the findings of this project the suggestions for future work are
In this thesis the transformers have the same characteristics In the future as the
cost of replacing an existing transformer with a new one is cheaper than
replacing both transformers the situation that two transformers with different
characteristics in a substation is not uncommon Therefore an optimisation
method for two transformers with different characteristics will be investigated
and four operation modes can occur
1) First transformer operates alone
2) Second transformer operates alone
3) Two transformers operate in parallel
4) Optimisation mode optimum selection of the transformers needed to
supply each feeder
At present in the UK customers pay for losses in the network In this thesis the
losses are analysed as a whole without allocating them to the users in the network
In the future a loss allocation scheme to customers in the distribution network
will be developed However after reconfiguration the total network loss is
reduced but the loss allocation to some customers may increase The customers
with more loss allocated will be dissatisfied with the network reconfiguration It
is therefore important to change the tariff structure for these customers so that
they are not obliged to pay more for the increase in loss allocation as a result of
network reconfiguration
In this thesis the maximum number of objectives to be optimised simultaneously
is three However the work could be extended to solve the DA problem with
more than three objectives These objectives may include balancing load on
transformers minimising the number of switch operations and maximising the
load on feeders
Chapter 10 Conclusion amp Future Work
Page | 194
The optimal DNR DG allocation TEO and SSP will be combined together to
solve the multi-objective optimisation problem The proposed methodologies
could be tested in large-scale practical systems
In this thesis the evaluation of reliability indices only considers the faults in the
line sections And all the feeders are supposed to have the same parameters and
hence the same failure rates However historical data shows the failure rates of a
feeder vary with geographical location and the weather Therefore different
types of feeders and seasonal varying data of feeder section failure rates will be
considered in future work Moreover the impacts of contingencies on the system
such as faults in the transformers and protective devices could also be considered
The integration of large number of electric vehicles (EVs) into the distribution
network places an extra burden on the electricity grid such as increases in energy
loss overloading in feeders decrease in reliability and power quality Therefore
network reconfiguration techniques and smart charging strategies will be
proposed to moderate the charging effects of EVs In addition the vehicle-to-grid
(V2G) technique which returns electricity to the gird will also be studied The
bi-directional of EVs in the network can provide power to improve load
balancing by ldquovalley fillingrdquo (charging) and ldquopeak shavingrdquo (discharging) [118]
The simulation results show ACO-based algorithms could find a set of good
solutions within a reasonable computation time The ACO control parameters are
set experimentally using information from several trial runs More work is
needed to improve the performance of the proposed algorithms by determining
the optimum set of parameter values It is expected that new ACO-based
algorithms will outperform any existing ones or at worst match their results
In the future a multi-objective stochastic optimal flow problem with the
consideration of load DG EV uncertainties will be addressed The load DG
and EV models are obtained by using a Monte Carlo probabilistic power flow
The objectives are then optimised by using a suitable metaheuristic technique
Page | 195
References
[1] L M Faulkenberry Electrical power distribution and transmission Pearson
Education India 1996
[2] Parliamentary Office of Science and Technology ldquoUK Electricity Networksrdquo
2001
[3] R Das et al ldquoDistribution automation strategies evolution of technologies
and the business caserdquo IEEE Trans Smart Grid vol 6 no 4 pp 2166ndash2175
2015
[4] P Balakrishna K Rajagopal and K S Swarup ldquoApplication benefits of
Distribution Automation and AMI systems convergence methodology for
distribution power restoration analysisrdquo Sustain Energy Grids Networks vol
2 pp 15ndash22 2015
[5] ofgem ldquoEnergy Efficiency Directive An assessment of the energy efficiency
potential of Great Britainrsquos gas and electricity infrastructurerdquo 2015
[6] R C Dugan M F McGranaghan and H W Beaty ldquoElectrical power
systems qualityrdquo 1996
[7] British Standards Institution DECC UK Office for National Statistic and
Met Office UK ldquoVoltage characteristics of electricity supplied by public
distribution systemsrdquo Whether and Climate change no December pp 1ndash18
2010
[8] Y F Niu Z Y Gao and W H K Lam ldquoEvaluating the reliability of a
stochastic distribution network in terms of minimal cutsrdquo Transp Res Part E
Logist Transp Rev vol 100 pp 75ndash97 2017
[9] R Billinton and J E Billinton ldquoDistribution system reliability indicesrdquo
IEEE Trans Power Deliv vol 4 no 1 pp 561ndash568 1989
[10] Ofgem ldquoElectricity Distribution Annual Report for 2010-11rdquo 2012
[11] J Hamachi K Eto ldquoUnderstanding the Cost of Power Interruption to US
Electric Consumers LBNL-55718rdquo 2004
[12] R M Vitorino H M Jorge and L P Neves ldquoLoss and reliability
optimization for power distribution system operationrdquo Elsevier BV 2013
[13] E M Carreno R Romero and A Padilha-Feltrin ldquoAn efficient codification
to solve distribution network reconfiguration for loss reduction problemrdquo
IEEE Trans Power Syst vol 23 no 4 pp 1542ndash1551 2008
[14] A Y Abdelaziz R A Osama and S M El-Khodary ldquoReconfiguration of
distribution systems for loss reduction using the hyper-cube ant colony
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2012
[15] European commission ldquoRoadmap for moving to a low-carbon economy in
2050rdquo DG Clim Action portal pp 1ndash2 2011
[16] A Mohamed Imran M Kowsalya and D P Kothari ldquoA novel integration
technique for optimal network reconfiguration and distributed generation
placement in power distribution networksrdquo Int J Electr Power Energy Syst
vol 63 pp 461ndash472 2014
[17] W Guan Y Tan H Zhang and J Song ldquoDistribution system feeder
reconfiguration considering different model of DG sourcesrdquo Int J Electr
Power Energy Syst vol 68 pp 210ndash221 2015
[18] S A Yin and C N Lu ldquoDistribution feeder scheduling considering variable
load profile and outage costsrdquo IEEE Trans Power Syst vol 24 no 2 pp
652ndash660 2009
[19] I Richardson M Thomson D Infield and C Clifford ldquoDomestic electricity
use A high-resolution energy demand modelrdquo Energy Build vol 42 no 10
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[20] K Deb A Pratap S Agarwal and T Meyarivan ldquoA fast and elitist
multiobjective genetic algorithm NSGA-IIrdquo IEEE Trans Evol Comput vol
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[21] M E Elkhatib R El Shatshat and M M A Salama ldquoDecentralized reactive
power control for advanced distribution automation systemsrdquo IEEE Trans
Smart Grid vol 3 no 3 pp 1482ndash1490 2012
[22] C-L Su and J-H Teng ldquoOutage costs quantification for benefitndashcost
analysis of distribution automation systemsrdquo Int J Electr Power Energy
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[23] I Goroohi Sardou M Banejad R Hooshmand and a Dastfan ldquoModified
shuffled frog leaping algorithm for optimal switch placement in distribution
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Transm Distrib vol 6 no 6 p 493 2012
[24] C L Smallwood and J Wennermark ldquoBenefits of distribution automationrdquo
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1994
[28] A Elmitwally E Gouda and S Eladawy ldquoRestoring recloser-fuse
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[30] J M Gers and E J Holmes Protection of electricity distribution networks
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time parameter checkingrdquo in Power Engineering Society General Meeting
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and M Kando ldquoAn analysis and selection of distribution transformer for
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configuration in an urban power distribution systemrdquo in Proc 5th Power
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minimize loss and disruption costs using genetic algorithmsrdquo Electr Power
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distribution systems part 1 A new formulation and a solution methodologyrdquo
IEEE Trans Power Deliv vol 5 no 4 pp 1902ndash1909 1990
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minimum reconfiguration in large-scale distribution systemsrdquo Electr Power
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ldquoDistribution system reconfiguration using a modified Tabu Search algorithmrdquo
Electr Power Syst Res vol 80 no 8 pp 943ndash953 2010
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considering reliability indicesrdquo Ain Shams Eng J 2015
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[61] D Das ldquoA fuzzy multiobjective approach for network reconfiguration of
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[62] J E Mendoza E A Loacutepez M E Loacutepez and C A Coello Coello
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losses and reliability indices for medium voltage distribution networkrdquo IET
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challenges for electric power industries with implementation of distribution
system automation in smart gridsrdquo Renew Sustain Energy Rev vol 46 pp
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method for placement of sectionalizing switches in distribution networks
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[67] M Nematollahi and M Tadayon ldquoOptimal sectionalizing switches and DG
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cost minimizationrdquo IEEE Trans Power Deliv vol 17 no 1 pp 254ndash259
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establishing interconnection and switching location policiesrdquo in CIRED 1991
pp 1ndash6
[71] A Heidari V G Agelidis and M Kia ldquoConsiderations of sectionalizing
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[73] L Li and R Li ldquoStudy on the analysis software of economic operation of
transformerrdquo Adv Mater Res vol 1008ndash1009 pp 497ndash500 2014
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update decision technical and economic analysis modelrdquo in Energy and
Power Engineering 2013 vol 5 no 4 pp 143ndash147
[75] B Amanulla S Chakrabarti and S N Singh ldquoReconfiguration of power
distribution systems considering reliability and power lossrdquo IEEE Trans
Power Deliv vol 27 no 2 pp 918ndash926 2012
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systems using reliability indicesrdquo IEEE Trans Power Syst vol 31 no 2 pp
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[80] B Sultana M W Mustafa U Sultana and A R Bhatti ldquoReview on
reliability improvement and power loss reduction in distribution system via
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[81] K Xie J Zhou and R Billinton ldquoReliability evaluation algorithm for
complex medium voltage electrical distribution networks based on the shortest
pathrdquo IEE Proceedings-Generation Transm Distrib vol 150 no 6 pp
686ndash690 2003
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of radial distribution systemsrdquo IEEE Trans Power Deliv vol 22 no 4 pp
2473ndash2480 2007
[85] T T Nguyen T T Nguyen A V Truong Q T Nguyen and T A Phung
ldquoMulti-objective electric distribution network reconfiguration solution using
runner-root algorithmrdquo Appl Soft Comput J vol 52 pp 93ndash108 2017
[86] N Gupta A Swarnkar R C Bansal and K R Niazi ldquoMulti-objective
reconfiguration of distribution systems using adaptive genetic algorithm in
fuzzy frameworkrdquo IET Gener Transm Distrib vol 4 no 12 pp 1288ndash1298
2010
[87] M R Narimani A Azizi Vahed R Azizipanah-Abarghooee and M
Javidsharifi ldquoEnhanced gravitational search algorithm for multi-objective
distribution feeder reconfiguration considering reliability loss and operational
costrdquo IET Gener Transm Distrib vol 8 no 1 pp 55ndash69 2014
[88] A Ahuja S Das and A Pahwa ldquoAn AIS-ACO hybrid approach for multi-
objective distribution system reconfigurationrdquo IEEE Trans Power Syst vol
22 no 3 pp 1101ndash1111 2007
[89] M Rostami A Kavousi-Fard and T Niknam ldquoExpected cost minimization
of smart grids with plug-in hybrid electric vehicles using optimal distribution
feeder reconfigurationrdquo Ind Informatics IEEE Trans vol 11 no 2 pp
388ndash397 2015
[90] S Oh J Kim S Kwon and S Chung ldquoMonte Carlo simulation of
phytosanitary irradiation treatment for mangosteen using MRI-based
geometryrdquo vol 39 no 3 pp 205ndash214 2014
[91] N HadjSaid and J C Sabonnadiere Electrical Distribution Networks
London ISTE Ltd 2011
[92] Y Li ldquoVoltage balancing on three-phase low voltage feederrdquo The Univerisity
of Manchester 2015
[93] K Bell and P R Allan ldquoComputation of the Value of Securityrdquo 1999
[94] M Dorigo V Maniezzo and A Colorni ldquoThe ant systems optimization by a
colony of cooperative agentsrdquo IEEE Trans Syst Man Cybern B vol 26 no
1 pp 1ndash13 1996
[95] M Dorigo and L M Gambardella ldquoAnt colony system a cooperative
learning approach to the traveling salesman problemrdquo IEEE Trans Evol
Comput vol 1 no 1 pp 53ndash66 1997
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colony optimization algorithmsrdquo IEEE Trans Evol Comput vol 16 no 6
pp 861ndash875 2012
[97] L Charles Daniel and S Ravichandran ldquoDistribution network reconfiguration
for loss reduction using ant colony system algorithmrdquo in IEEE Indicon 2005
Conference 2005 pp 1ndash4
[98] J F Goacutemez et al ldquoAnt colony system algorithm for the planning of primary
distribution circuitsrdquo IEEE Trans Power Syst vol 19 no 2 pp 996ndash1004
2004
[99] J Lu N Wang J Chen and F Su ldquoCooperative path planning for multiple
UCAVs using an AIS-ACO hybrid approachrdquo Proc 2011 Int Conf Electron
Mech Eng Inf Technol EMEIT 2011 vol 8 no 2 pp 4301ndash4305 2011
[100] J E Hunt and D E Cooke ldquoAn adaptive distributed learning system based
on the immune systemrdquo 1995 IEEE Int Conf Syst Man Cybern Intell Syst
21st Century vol 3 pp 2494ndash2499 1995
[101] C A C Coello and N C Cortes ldquoSolving multiobjective optimization
problems using an artificial immune systemrdquo Genet Program Evolvable
Mach vol 6 no 2 pp 163ndash190 2005
[102] L N De Castro and F J Von Zuben ldquoLearning and optimization using the
clonal selection principlerdquo IEEE Trans Evol Comput vol 6 no 3 pp 239ndash
251 2002
[103] Office for National Statistics Population and household estimates for the
United Kingdom UK 2011
[104] S Ingram S Probert and K Jackson ldquoThe impact of small scale embedded
generation on the operating parameters of distribution networksrdquo Department
of Trade and Industry (DTI) 2003 [Online] Available
httpwebarchivenationalarchivesgovuk20100919182407httpwwwensg
govukassets22_01_2004_phase1b_report_v10b_web_site_finalpdf
[105] 63 EDS 02-0027 Engineering design standard EDS 02-007 11 kV Triplex
Cable 2012
[106] TTH ldquo75 MVA-33-11 KV-GTP TTHrdquo 2014 [Online] Available
httpwwwtranstechtransformerscompdf75mva3311kvgtptth24012008pdf
[107] A M Tahboub V R Pandi and H H Zeineldin ldquoDistribution system
reconfiguration for annual energy loss reduction considering variable
distributed generation profilesrdquo IEEE Trans Power Deliv vol 30 no 4 pp
1677ndash1685 2015
[108] M E Baran and F F Wu ldquoNetwork reconfiguration in distribution systems
for loss reduction and load balancingrdquo Power Deliv IEEE Trans vol 4 no
2 pp 1401ndash1407 1989
[109] D Shirmohammadi and H W Hong ldquoReconfiguration of electric distribution
networks for resistive line losses reductionrdquo IEEE Trans Power Deliv vol 4
References
Page | 203
no 2 pp 1492ndash1498 1989
[110] R S Rao K Ravindra K Satish and S V L Narasimham ldquoPower loss
minimization in distribution system using network reconfiguration in the
presence of distributed generationrdquo IEEE Trans Power Syst vol 28 no 1
pp 1ndash9 2012
[111] D Sudha Rani N Subrahmanyam and M Sydulu ldquoMulti-objective invasive
weed optimization - an application to optimal network reconfiguration in
radial distribution systemsrdquo Int J Electr Power Energy Syst vol 73 pp
932ndash942 2015
[112] R L Haupt and S E Haupt Practical genetic algorithms John Wiley amp
Sons 2004
[113] X S Yang and S Deb ldquoCuckoo search via Levy flightsrdquo 2009 World Congr
Nat Biol Inspired Comput NABIC 2009 - Proc pp 210ndash214 2009
[114] R N Allan R Billinton I Sjarief L Goel and K S So ldquoA reliability test
system for educational purposes-basic distribution system data and resultsrdquo
IEEE Trans Power Syst vol 6 no 2 pp 813ndash820 1991
[115] G Li and X-P Zhang ldquoModeling of plug-in hybrid electric vehicle charging
demand in probabilistic power flow calculationsrdquo Smart Grid IEEE Trans
vol 3 no 1 pp 492ndash499 2012
[116] UK Department for Transport ldquoNational Travel Survey England 2013 -
Statistical Releaserdquo no July p 26 2014
[117] A Mazza G Chicco and A Russo ldquoOptimal multi-objective distribution
system reconfiguration with multi criteria decision making-based solution
ranking and enhanced genetic operatorsrdquo Int J Electr Power Energy Syst
vol 54 pp 255ndash267 2014
[118] E Sortomme and M A El-Sharkawi ldquoOptimal charging strategies for
unidirectional vehicle-to-gridrdquo IEEE Trans Smart Grid vol 2 no 1 pp
119ndash126 2011
Page | 204
APPENDIX A Network Model Data
A1 UK generic distribution network
The line parameters given here is related to the single line diagram of the network
shown in Fig 45 which are used in the simulation study in Section 451 and 452
Table A-1 Typical configurations and parameters of 11 kV triplex cables in the UK
11 kV line type Cross
Sectional
Area
(CSA)
Positive sequence
Z
Zero-phase
sequence
Z
Approximate
Capacitance
C
Id Configuration Rph Xph R0 X0 C
(mm2) (Ωkm) (μFkm)
A Nexans
635011000
Volt Triplex
Cable
185 0415 0112 0988 0236 036
B 95 0220 0012 0530 0102 028
Appendix A Network Data
Page | 205
A2 33-bus system
Table A-2 Line and load data of 33-bus system
Branch
number
Sending end
node
Receiving end
node
R
(Ω)
X
(Ω)
P at receiving
end (kW)
Q at receiving
end (kVAr)
1 0 1 00922 0047 100 60
2 1 2 04930 02511 90 40
3 2 3 03660 01864 120 80
4 3 4 03811 01941 60 30
5 4 5 08190 07070 60 20
6 5 6 01872 06188 200 100
7 6 7 07114 02351 200 100
8 7 8 10300 07400 60 20
9 8 9 10440 07400 60 20
10 9 10 01966 00650 45 30
11 10 11 03744 01238 60 35
12 11 12 14680 11550 60 35
13 12 13 05416 07129 120 80
14 13 14 05910 05260 60 10
15 14 15 07463 05450 60 20
16 15 16 12890 17210 60 20
17 16 17 03720 05740 90 40
18 17 18 01640 01565 90 40
19 18 19 15042 13554 90 40
20 19 20 04095 04784 90 40
21 20 21 07089 09373 90 40
22 21 22 04512 03083 90 50
23 22 23 08980 07091 420 200
24 23 24 08960 07011 420 200
25 24 25 02030 01034 60 25
26 25 26 02842 01447 60 25
27 26 27 10590 09337 60 20
28 27 28 08042 07006 120 70
29 28 29 05075 02585 200 600
30 29 30 09744 09630 150 70
31 30 31 03105 03619 210 100
32 31 32 03410 05362 60 40
33 7 20 2 2 -- --
34 11 21 2 2 -- --
35 8 14 2 2 -- --
36 17 32 05 05 -- --
37 24 28 05 05 -- --
Appendix A Network Data
Page | 206
A3 69-bus system
Table A-3 Line and load data of 69-bus system
Branch
number
Sending end
node
Receiving end
node
R
(Ω)
X
(Ω)
P at receiving
end (kW)
Q at receiving
end (kVAr)
1 0 1 00005 00012 0 0
2 1 2 00005 00012 0 0
3 2 3 00015 00036 0 0
4 3 4 00251 00294 0 0
5 4 5 0366 01864 26 22
6 5 6 0381 01941 404 30
7 6 7 00922 0047 75 54
8 7 8 00493 00251 30 22
9 8 9 0819 02707 28 19
10 9 10 01872 00619 145 104
11 10 11 07114 02351 145 104
12 11 12 103 034 8 5
13 12 13 1044 0345 8 55
14 13 14 1058 03496 0 0
15 14 15 01966 0065 455 30
16 15 16 03744 01238 60 35
17 16 17 00047 00016 60 35
18 17 18 03276 01083 0 0
19 18 19 02106 0069 1 06
20 19 20 03416 01129 114 81
21 20 21 0014 00046 5 35
22 21 22 01591 00526 0 0
23 22 23 03463 01145 28 20
24 23 24 07488 02475 0 0
25 24 25 03089 01021 14 10
26 25 26 01732 00572 14 10
27 26 27 00044 00108 26 186
28 27 28 0064 01565 26 186
29 28 29 03978 01315 0 0
30 29 30 00702 00232 0 0
31 30 31 0351 0116 0 0
32 31 32 0839 02816 14 10
33 32 33 1708 05646 195 14
34 33 34 1474 04873 6 4
35 34 35 00044 00108 26 1855
36 35 36 0064 01565 26 1855
37 36 37 01053 0123 0 0
38 37 38 00304 00355 24 17
39 38 39 00018 00021 24 17
40 39 40 07283 08509 12 1
41 40 41 031 03623 0 0
Appendix A Network Data
Page | 207
42 41 42 0041 00478 6 43
43 42 43 00092 00116 0 0
44 43 44 01089 01373 3922 263
45 44 45 00009 00012 3922 263
46 45 46 00034 00084 0 0
47 46 47 00851 02083 79 564
48 47 48 02898 07091 3847 2745
49 48 49 00822 02011 3847 2745
50 49 50 00928 00473 405 283
51 50 51 03319 01114 36 27
52 51 52 0174 00886 435 35
53 52 53 0203 01034 264 19
54 53 54 02842 01447 24 172
55 54 55 02813 01433 0 0
56 55 56 159 05337 0 0
57 56 57 07837 0263 0 0
58 57 58 03042 01006 100 72
59 58 59 03861 01172 0 0
60 59 60 05075 02585 1244 888
61 60 61 00974 00496 32 23
62 61 62 0145 00738 0 0
63 62 63 07105 03619 227 162
64 63 64 1041 05302 59 42
65 64 65 02012 00611 18 13
66 65 66 00047 00014 18 13
67 66 67 07394 02444 28 20
68 67 68 00047 00016 28 20
69 49 58 2 1 -- --
70 26 64 1 05 -- --
71 12 20 05 05 -- --
72 10 42 05 05 -- --
73 14 45 1 05 -- --
A4 RBTS Bus 4 system
Table A-4 Feeder data of RBTS Bus 4
Feeder
Type
Length
(km)
Feeder section number
1 060 2 6 10 14 17 21 25 28 30 34 38 41 43 46 49 51 55 58 61 64 67
68 69 70 71
2 075 1 4 7 9 12 16 19 22 24 27 29 32 3537 40 42 45 48 50 53 56 60
63 65
3 080 3 5 8 11 13 15 18 20 23 26 31 33 36 3944 47 52 54 57 59 62 66
Appendix A Network Data
Page | 208
Table A-5 Reliability Data for RBTS Bus 4
Equipment λA λP λM λt R RM
Lines 004 0 0 0 5 0
Buses 0001 0 1 001 2 8
Switches 0004 0002 1 006 4 72
Distribution Transformers 0015 0 1 0 200 120
λA Active failure rate in (fryrkm) for lines and (fryr) for other components
λP Passive failure rate in (fryrkm) for lines and (fryr) for other components
λM Maintenance outage rate in (fryrkm) for lines and (fryr) for other components
λP Transient failure rate in (fryrkm) for lines and (fryr) for other components
R Repair time of failures in (hr)
RM Maintenance outage time in (hr)
Page | 209
APPENDIX B Simulation Results
B1 Simulation results of Chapter 4
B11Tie-switch location
As discussed in Section 452 the location of tie-switch in Scenario 9 is changeable
and the relevant results are presented in Table B-1 It can be clearly seen that the
NOP is located in lsquoTW1rsquo between 0730 and 1000 1600 and 1630 while in lsquoTW5rsquo
for the rest of the day
Table B-1 The locations of tie-switch in Scenario 9
Time Loc Time Loc Time Loc Time Loc Time Loc Time Loc
0000 TW5 0400 TW5 0800 TW1 1200 TW5 1600 TW1 2000 TW5
0010 TW5 0410 TW5 0810 TW1 1210 TW5 1610 TW1 2010 TW5
0020 TW5 0420 TW5 0820 TW1 1220 TW5 1620 TW1 2020 TW5
0030 TW5 0430 TW5 0830 TW1 1230 TW5 1630 TW1 2030 TW5
0040 TW5 0440 TW5 0840 TW1 1240 TW5 1640 TW5 2040 TW5
0050 TW5 0450 TW5 0850 TW1 1250 TW5 1650 TW5 2050 TW5
0100 TW5 0500 TW5 0900 TW1 1300 TW5 1700 TW5 2100 TW5
0110 TW5 0510 TW5 0910 TW1 1310 TW5 1710 TW5 2110 TW5
0120 TW5 0520 TW5 0920 TW1 1320 TW5 1720 TW5 2120 TW5
0130 TW5 0530 TW5 0930 TW1 1330 TW5 1730 TW5 2130 TW5
0140 TW5 0540 TW5 0940 TW1 1340 TW5 1740 TW5 2140 TW5
0150 TW5 0550 TW5 0950 TW1 1350 TW5 1750 TW5 2150 TW5
0200 TW5 0600 TW5 1000 TW1 1400 TW5 1800 TW5 2200 TW5
0210 TW5 0610 TW5 1010 TW5 1410 TW5 1810 TW5 2210 TW5
0220 TW5 0620 TW5 1020 TW5 1420 TW5 1820 TW5 2220 TW5
0230 TW5 0630 TW5 1030 TW5 1430 TW5 1830 TW5 2230 TW5
0240 TW5 0640 TW5 1040 TW5 1440 TW5 1840 TW5 2240 TW5
0250 TW5 0650 TW5 1050 TW5 1450 TW5 1850 TW5 2250 TW5
0300 TW5 0700 TW5 1100 TW5 1500 TW5 1900 TW5 2300 TW5
0310 TW5 0710 TW5 1110 TW5 1510 TW5 1910 TW5 2310 TW5
0320 TW5 0720 TW5 1120 TW5 1520 TW5 1920 TW5 2320 TW5
0330 TW5 0730 TW1 1130 TW5 1530 TW5 1930 TW5 2330 TW5
0340 TW5 0740 TW1 1140 TW5 1540 TW5 1940 TW5 2340 TW5
0350 TW5 0750 TW1 1150 TW5 1550 TW5 1950 TW5 2350 TW5
Appendix B Simulation Results
Page | 210
B12 Voltage variations
For Test Case 2 in Section 452 the detailed voltage values of the mean and the
corresponding 95th
profiles at each node in the linked feeder are recorded in Table
B-2 and Table B-3
Table B-2 Mean voltage profiles at each node in the linked feeder
Node
No
Scenarios
S1 S2 S3 S4 S5 S6 S7 S8 S9
A4_1 09675 09787 09787 09766 09859 09859 09748 09825 09815
A4_2 09676 09784 09784 09766 09856 09856 09748 09822 09813
A4_3 09677 09782 09782 09767 09854 09854 09749 09819 09811
A4_4 09678 09780 09780 09768 09851 09851 09750 09817 09810
A4_5 09681 09777 09777 09771 09849 09849 09753 09814 09808
A4_6 09685 09775 09775 09775 09846 09846 09757 09812 09807
A4_7 09689 09773 09773 09779 09845 09845 09762 09811 09807
A4_8 09694 09772 09772 09784 09844 09844 09767 09810 09807
B4_8 09700 09772 09772 09790 09844 09844 09773 09810 09808
B4_7 09707 09773 09773 09797 09845 09845 09779 09811 09810
B4_6 09714 09775 09775 09804 09846 09846 09787 09812 09813
B4_5 09722 09777 09777 09813 09849 09849 09795 09814 09816
B4_4 09731 09780 09780 09821 09851 09851 09804 09817 09820
B4_3 09737 09782 09782 09827 09854 09854 09809 09819 09823
B4_2 09743 09784 09784 09833 09856 09856 09815 09822 09826
B4_1 09749 09787 09787 09839 09859 09859 09821 09825 09830
Table B-3 95th
voltage profiles at each node in the linked feeder
Node
No
Scenarios
S1 S2 S3 S4 S5 S6 S7 S8 S9
A4_1 09352 09573 09573 09537 09721 09721 09537 09721 09715
A4_2 09353 09567 09567 09537 09715 09715 09537 09715 09709
A4_3 09355 09562 09562 09539 09711 09711 09539 09711 09704
A4_4 09357 09558 09558 09541 09707 09707 09541 09707 09702
A4_5 09363 09553 09553 09547 09701 09701 09547 09701 09679
A4_6 09370 09548 09548 09555 09697 09697 09555 09697 09694
A4_7 09379 09545 09545 09563 09694 09694 09563 09794 09691
A4_8 09389 09544 09544 09573 09692 09692 09573 09792 09692
B4_8 09400 09544 09544 09585 09692 09692 09585 09792 09692
B4_7 09413 09545 09545 09598 09694 09694 09598 09794 09694
B4_6 09427 09548 09548 09613 09697 09697 09613 09697 09697
B4_5 09443 09553 09553 09628 09701 09701 09628 09701 09701
B4_4 09460 09558 09558 09646 09707 09707 09646 09707 09707
Appendix B Simulation Results
Page | 211
B4_3 09471 09562 09562 09656 09711 09711 09656 09711 09711
B4_2 09482 09567 09567 09668 09715 09715 09668 09715 09715
B4_1 09494 09573 09573 09680 09721 09721 09680 09721 09721
B2 Simulation results of Chapter 5
The network losses in each branch for all test cases of 33-bus system and 69-bus
system are listed in Table B-4 and Table B-5 respectively
Table B-4 Network losses in each branch of 33-bus system
Branch number Feeder loss (kW)
Case I Case II Case III Case IV
1 1227 1189 1010 1003
2 5192 2686 2051 2060
3 1995 756 112 490
4 1874 667 074 415
5 3833 1321 122 807
6 192 006 006 006
7 484 0 0 0
8 418 124 211 124
9 357 0 0 0
10 055 001 001 001
11 088 003 003 003
12 267 045 045 045
13 073 008 008 008
14 036 0 0 0
15 028 045 092 045
16 025 048 115 048
17 003 007 022 007
18 016 226 232 226
19 083 1809 1859 1808
20 01 424 436 423
21 004 118 071 118
22 319 316 914 315
23 516 512 1618 510
24 129 128 869 128
25 26 224 005 124
26 334 285 003 155
27 1133 962 003 510
28 786 664 0 345
29 391 326 199 159
30 160 110 018 003
Appendix B Simulation Results
Page | 212
31 021 012 0 000
32 001 0 013 0
33 0 563 809 563
34 0 215 215 215
35 0 174 320 174
36 0 002 033 002
37 0 0 263 0
Total 20314 13981 11753 10844
Table B-5 Network losses in each branch of 69-bus system
Branch number Feeder loss (kW)
Case I Case II Case III Case IV
1 008 007 006 006
2 008 007 006 006
3 020 012 012 010
4 194 011 011 011
5 2829 159 155 159
6 2939 164 160 164
7 691 035 034 035
8 338 012 012 012
9 477 143 137 142
10 101 029 027 028
11 219 032 030 032
12 128 000 000 000
13 124 000 0 000
14 120 0 000 0
15 022 083 043 083
16 032 138 067 138
17 000 001 001 001
18 010 080 032 080
19 007 052 021 052
20 011 083 033 083
21 000 003 001 002
22 001 022 006 022
23 001 049 013 049
24 001 091 021 091
25 000 037 009 037
26 000 019 004 019
27 000 000 000 000
28 000 000 000 000
29 001 001 001 001
30 000 000 000 000
31 001 001 001 001
Appendix B Simulation Results
Page | 213
32 001 001 001 001
33 001 001 001 001
34 000 000 000 000
35 000 003 001 003
36 001 041 019 041
37 002 064 028 064
38 000 018 008 018
39 000 001 000 001
40 005 391 161 391
41 002 166 068 166
42 000 022 009 022
43 000 005 002 005
44 001 057 023 057
45 000 000 000 000
46 002 017 017 013
47 058 416 416 316
48 164 1321 1321 991
49 012 253 253 178
50 000 000 000 000
51 000 000 000 000
52 580 001 001 001
53 673 001 001 000
54 916 000 000 000
55 882 0 0 0
56 4986 000 000 000
57 2458 000 000 000
58 954 000 000 000
59 1071 627 626 379
60 1408 824 823 498
61 011 0 0 0
62 014 000 000 000
63 066 001 001 001
64 004 071 069 071
65 000 000 000 000
66 000 000 000 000
67 002 002 002 002
68 000 000 000 000
69 0 3783 3782 2384
70 0 102 052 102
71 0 0 0 0
72 0 0 0 0
73 0 423 252 423
Total 22562 9885 8758 7397
Appendix B Simulation Results
Page | 214
B3 Simulation results of Chapter 8
Table B-6 Pareto optimal solutions of multi-objective DNR (loss ECOST and SAIDI)
Tie-switches location Feeder loss (kW) ECOST ($yr) SAIDI
(hrscustomeryr)
70 68 71 69 321415 4640359 130895231648616
70 10 41 54 364131 431068083000 102819629963899
17 10 41 70 354092 411445783000000 105858799638989
17 26 10 70 383269 530285525000000 0968805806257521
7 26 54 69 435225 578907612000000 0825265794223827
7 54 41 69 406035 460067870000000 0915047984356197
7 26 54 70 442913 571756512000000 0836828971119134
17 10 71 70 345231 439663189000000 106361687725632
70 10 71 69 331470 443747189000000 110465057160048
70 10 41 69 340330 415529783000000 109962169073406
70 68 41 69 330274 435818516000000 130392343561974
7 54 71 69 397170 488285276000000 0920076865222623
41 10 54 69 356448 438219183000000 101663312274368
70 10 54 26 393311 549907825000000 0938414109506619
70 7 71 69 381047 465595876000000 100306543321300
70 7 41 17 403678 433294470000000 0957002858002407
70 10 54 71 355269 459285489000000 103322518050542
7 54 71 70 404856 481134176000000 0931640042117930
7 26 17 70 432867 552134212000000 0867220667870036
7 70 41 69 389911 437378470000000 0998036552346570
7 26 69 70 419096 556218212000000 0908254362214200
17 7 71 70 394813 461511876000000 0962031738868833
71 10 54 69 347586 466436589000000 102166200361011
10 26 54 69 385625 557058925000000 0926850932611312
70 26 10 69 369504 534369525000000 100983950060168
7 54 41 70 413721 452916770000000 0926611161251504
Appendix B Simulation Results
Page | 215
B4 Simulation results of Chapter 9
Table B-7 Pareto optimal solutions of multi-objective DNR (loss maximum node voltage deviation
feeder load balancing index) for 33-bus system in Case II
Tie-switches location Feeder loss
(kW)
Maximum node
Voltage deviation
Feeder load
balancing index
7 34 35 31 37 176962 0108696024464801 00228687361961248
7 11 35 32 28 143474 00613272038422790 00305387759787611
7 9 14 31 37 142477 00768537372742428 00252628392269486
6 8 12 36 37 151849 00696765908940439 00259144961258893
7 8 14 31 37 155399 00924077518455773 00239781364880477
6 8 12 31 37 169382 0104485611067200 00236077543160956
6 8 12 32 37 152876 00776641110366926 00250547432924683
33 8 14 30 37 171441 0108063061643879 00230652089068052
7 9 14 32 28 140261 00604355611623940 00310349101268755
7 11 35 32 37 143028 00639069227083702 00273727965037185
6 8 14 31 37 159752 00968913958755809 00236540473688646
6 33 35 32 37 170278 00826562726566354 00249194843739843
6 11 35 32 37 144683 00656445815841987 00261947314082027
6 8 14 32 37 146983 00705648561488426 00256096967694280
7 9 14 32 37 139815 00639015456844128 00280407351785895
6 9 14 32 37 143097 00625183468485540 00270001779728268
7 11 35 31 37 148829 00852978398065017 00245113845932977
7 34 35 30 37 202483 0130888991378581 00223050578905545
6 8 14 36 37 146991 00643933147100736 00266176555168500
6 11 35 31 37 154281 00897759906819439 00242838273201709
6 8 13 32 37 150430 00753226918458818 00253604605496161
Table B-8 Pareto optimal solutions of multi-objective DNR (loss maximum node voltage deviation
feeder load balancing index) for 33-bus system in Case III
Tie-switches location Feeder loss
(kW)
Maximum node
Voltage deviation
Feeder load
balancing index
7 14 8 32 28 121696 00575193535569366 00264544805354717
7 11 35 31 37 123007 00712785797883380 00213250141648472
6 12 8 32 37 128324 00630309398395457 00223824361844486
6 14 8 30 37 145672 0101299721228755 00194921779245086
7 33 35 32 28 130184 00583420082867310 00261406698684195
7 14 8 30 37 140274 00967924815464314 00195001911353607
7 21 35 30 37 164190 0113945920950777 00189031534924873
6 13 8 32 37 126434 00607661484850486 00227035446761735
7 14 9 32 28 117726 00575130414815478 00271215548731366
Appendix B Simulation Results
Page | 216
6 14 8 32 28 125920 00566904604559002 00265195832133384
6 12 8 31 37 137974 00889877482038002 00200083704114662
7 11 35 30 37 133030 00891516445489180 00199682922816912
6 11 35 32 37 123013 00593840879899440 00235298833627789
7 14 9 32 37 121070 00631040005210335 00255168322432724
6 14 9 32 28 123916 00566872316455769 00273594084038335
7 14 9 30 37 126587 00812324184971598 00206873922472966
7 14 9 31 28 117529 00642736861104275 00240537048868074
6 14 9 32 37 122047 00593825021727904 00240927348267257
6 11 35 32 28 124883 00566888115014094 00269082055980326
6 11 35 31 37 126802 00756552348586014 00207586957663036
6 14 8 32 37 124050 00593857418451058 00230337877365745
7 13 8 32 28 124039 00575225874614865 00262247242500743
7 11 35 32 28 119522 00575159230231156 00267430211390231
7 14 9 31 37 118759 00642740886891275 00220228862077971
6 14 8 31 37 130316 00816654599427028 00201908840890301
33 14 8 30 37 140110 00923831702765571 00197570883486903
7 12 8 32 28 125895 00587758838819431 00259864524009700
6 13 8 31 37 134936 00865715938530326 00201790772057552
Table B-9 Pareto optimal solutions of multi-objective DNR (loss maximum node voltage deviation
feeder load balancing index) for 33-bus system in Case IV
Tie-switches location DG location Feeder
loss
(kW)
Maximum node
Voltage deviation
Feeder load
balancing index
7 9 14 30 37 15 17 16 112506 00655990339384582 00207847799664288
6 8 14 31 37 14 11 15 120818 00728143829651942 00199639595336255
7 11 35 30 37 16 16 12 118637 00756705031931788 00198888055963062
6 8 14 31 37 11 29 14 125736 00822955381260978 00194988443664523
6 11 35 32 37 29 11 29 116999 00602917954784902 00213598898907595
7 9 14 31 37 15 14 16 110931 00518306996442978 00223689972435171
7 34 35 30 37 16 13 13 140652 00983575865184194 00182688360250883
7 8 14 30 37 14 11 15 128617 00876913785424229 00190954012999288
7 8 14 30 37 11 16 14 127141 00860397262006276 00191601352391895
7 9 14 36 37 30 30 29 109157 00520335391274761 00229564125698243
7 8 14 30 37 10 14 16 126706 00857230143750372 00192117850059117
7 11 35 30 37 13 16 12 121130 00786215737441328 00196617519208137
7 34 35 30 37 13 10 9 151352 0106960621828031 00178195736666725
7 34 35 30 37 10 12 9 152310 0107688512235453 00178046268710843
6 8 14 30 37 11 15 16 130550 00897068798318073 00189590122249633
6 8 14 30 37 16 14 10 130869 00901533044670202 00189271311922809
7 34 35 30 37 10 13 12 148089 0104837492639545 00178736074180585
Appendix B Simulation Results
Page | 217
7 34 35 30 37 13 11 16 143317 0100615335666250 00181553323058751
6 8 14 30 37 10 14 14 133299 00925968739633617 00188139999335965
7 34 35 30 37 13 9 12 148392 0105013682219175 00178453713901855
6 8 14 30 37 14 11 10 137593 00963962506644021 00186232592604301
6 8 14 30 37 11 8 14 136046 00951731865531927 00187106569470356
6 8 14 30 37 11 11 16 135639 00942616575802945 00187170876179048
7 8 14 30 37 15 16 14 122935 00815907052491111 00195198923102276
7 34 35 30 37 12 14 16 140640 00983915740315128 00182784576692257
6 33 35 31 37 11 11 13 146017 00888852225316270 00188548348595259
7 34 35 30 37 12 16 12 142144 00997534014352579 00181578155086060
6 8 14 30 37 14 11 15 132819 00921338781311946 00188143081376993
6 8 14 30 37 10 15 11 136651 00956093119043262 00186781475357014
7 9 14 31 37 14 14 16 111382 00525319705640723 00222591386298574
7 34 35 30 37 13 14 16 139957 00977014014811679 00183484070331887
7 34 35 30 37 12 15 16 139849 00976123852270839 00183745698300515
7 34 35 30 37 12 16 16 138589 00959671533698319 00184842191427931
7 34 35 30 37 16 13 16 137912 00952795751906571 00185525366651277
6 33 35 31 37 11 11 11 148785 00910856464605774 00187751047204272
7 34 35 30 37 12 16 13 141338 00990484927061306 00181980491991251
7 34 35 30 37 12 13 12 145536 0102926179499332 00179590185768212
6 8 14 30 37 14 10 15 132373 00918145642214576 00188660639598312
6 8 14 30 37 16 11 14 131312 00904718190224125 00188759872087077
7 34 35 30 37 13 15 16 139168 00969230570394858 00184436609617936
7 34 35 30 37 13 9 11 150730 0106620666560267 00178315514588942
6 8 14 30 37 14 11 14 133746 00929165522686308 00187615074100094
7 34 35 30 37 9 9 12 152656 0107867658396772 00178031242058681
6 8 14 30 37 10 11 16 135118 00939381882085281 00187414815201857
7 34 35 30 37 12 12 9 149341 0105739135263959 00178316539838164
7 9 14 36 28 32 32 32 110385 00489797931328652 00256323647901629
7 9 14 36 37 32 31 31 108599 00498935433820196 00235262740306846
7 9 14 32 37 31 30 31 108436 00537552050723257 00227898958267559
7 9 14 36 28 32 31 31 110203 00489682960875768 00259015702487973
7 34 35 30 37 8 12 9 154427 0108962750550623 00178021823053241
Appendix B Simulation Results
Page | 218
Table B-10 Pareto optimal solutions of multi-objective DNR (loss maximum node voltage deviation
feeder load balancing index) for 69-bus system in Case II
Tie-switches location Feeder loss
(kW)
Maximum node
Voltage deviation
Feeder load
balancing index
55 61 71 72 12 99036 00524391619987274 00196366946903149
69 61 71 9 14 145213 00664127006601768 00185315761508749
55 61 71 72 14 98845 00524393494628415 00194882148961848
69 70 71 10 14 145135 00666490251240782 00182871906896542
69 61 71 72 12 150267 00699556148777123 00161708619074924
55 61 71 10 14 104521 00524349487665904 00238104755589364
69 61 71 72 13 150383 00700225094171628 00161512783956020
55 61 71 72 13 98937 00524392488739880 00195710324132613
69 61 71 72 11 150792 00682108082577803 00171029450547815
55 61 71 9 14 105348 00524349082167884 00242117051986541
69 61 71 72 14 150513 00700911373758199 00161129748303495
55 61 71 72 11 105195 00524380932334678 00218572363716938
Table B-11 Pareto optimal solutions of multi-objective DNR (loss maximum node voltage deviation
feeder load balancing index) for 69-bus system in Case III
Tie-switches location Feeder loss
(kW)
Maximum node
Voltage deviation
Feeder load
balancing index
55 61 12 14 9 97461 00523081449765275 00226112450860475
69 61 71 14 9 130761 00662843002557533 00155527078006889
55 61 71 14 7 97263 00523080911134007 00226177446060770
55 61 12 71 72 87588 00523152959484715 00174558059214037
55 61 71 14 8 93176 00523082195004728 00211109499855264
55 61 71 13 72 87581 00523154440245970 00174392153380541
55 61 12 14 72 87755 00523153511186373 00174538759436512
55 61 12 71 7 97289 00523080869366065 00226232791264600
69 61 71 11 9 134009 00662855052002667 00154463391981039
69 61 12 14 9 130989 00662843776081034 00155381836375260
55 61 71 13 7 97273 00523080879708534 00227249951330579
55 61 71 14 9 90907 00523086904216601 00201865894567423
55 61 71 14 10 90291 00523088955157064 00199034032147027
69 61 71 14 10 130894 00665207578684145 00154263271797149
55 61 71 14 72 87582 00523156072908145 00174100597226583
69 61 71 11 10 134197 00665220013747228 00153401360203180
69 61 71 11 72 136858 00680828895070073 00147368269784675
69 61 12 14 10 131126 00665208386694061 00154135530565384
55 61 71 11 72 91274 00523126048676607 00184393848480773
Appendix B Simulation Results
Page | 219
Table B-12 Pareto optimal solutions of multi-objective DNR (loss maximum node voltage deviation
feeder load balancing index) for 69-bus system in Case IV
Tie-switches location DG location Feeder
loss
(kW)
Maximum node
Voltage deviation
Feeder load
balancing index
69 63 71 10 14 60 60 60 105879 00543213716422435 00153740505896722
69 63 12 72 71 60 62 62 109324 00575466375767690 00126779733811642
55 61 71 72 11 60 60 60 80324 00429183191505871 00183159151221229
69 63 12 72 71 61 61 62 109323 00575465740537586 00126842028893447
55 61 71 72 12 60 60 60 74165 00429193759769601 00159264876998350
69 63 14 10 71 62 62 62 106070 00543012249613587 00150279825984642
69 63 11 72 71 60 62 60 110547 00558290844078126 00139841427388105
69 63 14 9 71 62 62 62 106271 00540689205567605 00153025056850459
69 61 71 72 11 60 60 60 108838 00542584369620998 00141625735067141
55 61 71 72 14 60 56 60 75837 00436673338725839 00157367114339890
69 63 14 10 71 62 62 60 105960 00542966739560918 00151430448212008
69 61 71 10 14 60 60 60 104307 00527268149576859 00155323687715422
69 63 11 72 71 61 62 62 110652 00558333983851442 00137892112215884
69 63 13 72 71 62 62 62 109522 00576169823075075 00125440050970194
55 61 71 72 14 60 55 60 75975 00436701836501366 00156758120818947
69 63 71 10 14 60 60 62 105896 00542940500362948 00152768514567046
69 63 14 9 71 62 61 61 106159 00540643102892876 00154245882374843
55 61 71 72 13 60 60 60 74066 00429194617185072 00158554987038681
69 62 71 10 14 61 60 60 105886 00542959390978505 00153513700764165
69 63 14 72 71 62 62 62 109622 00576844280930477 00125002240983144
55 63 71 72 14 62 61 62 74382 00440379610790336 00155858821619573
69 63 71 72 11 60 60 60 110530 00558564471048234 00140822204796308
55 63 71 72 14 60 60 62 74285 00440350644694274 00157371695186626
55 63 14 72 71 62 62 62 74448 00440399072962552 00155438948075735
55 63 71 72 14 60 62 62 74344 00440368353288504 00156312863856681
69 63 71 9 14 60 61 60 105882 00542934725670071 00153515485666183
55 63 71 72 14 60 61 62 74305 00440356668532606 00156816031788752
55 61 20 72 13 60 60 60 80533 00429326269571468 00157463174391893
55 63 71 72 14 61 61 62 74343 00440367927398261 00156346520711234
69 61 71 72 14 60 60 60 107187 00561022028435777 00126909641069497
69 63 71 72 11 60 61 60 110533 00558285040786375 00140595150870697
69 63 12 72 71 62 62 62 109436 00575512407997617 00125707103016452
69 63 14 10 71 61 62 62 106000 00542983427485794 00150838099664421
69 63 11 72 71 60 61 62 110569 00558299818740340 00139149694834405
69 63 14 9 71 61 62 60 106118 00540626433897020 00154840963668230
69 61 71 72 12 60 60 60 107041 00559693311798567 00127785892138089
55 61 71 72 14 60 60 60 73974 00429195606297569 00157682511572302
69 63 14 10 71 61 61 62 105958 00542966109653011 00151492343922130
69 63 12 72 71 62 62 61 109365 00575483243249972 00126225992147273
Appendix B Simulation Results
Page | 220
69 63 11 72 71 62 62 60 110611 00558317226735644 00138490567525274
69 63 14 9 71 62 62 61 106201 00540660395254129 00153587525958041
69 63 14 10 71 61 60 62 105917 00542949434469265 00152083287358888
69 63 14 9 71 62 62 60 106160 00540643732226493 00154184014811756
69 63 11 72 71 61 61 62 110610 00558316590719640 00138552654427231
69 63 71 72 11 62 62 62 110723 00558362979744786 00137328015545176
69 61 71 72 13 60 60 60 107108 00560349171634668 00127435051911921
Page | 221
APPENDIX C Control Parameters of
Algorithms
C1 Control parameters of ACO algorithm in Chapter 5
Table C-1 ACO parameters for distribution network reconfiguration and DG allocation in Test Case
2amp3
Parameter Value
Number of ants 50
Maximum number of iteration 200
Pheromone evaporation rate 120530 03
Higher bound of pheromone level 120533119846119834119857 1
Lower bound of pheromone level 120533119846119842119847 001
Constant accumulation number 120533119836 0002
Table C-2 ACO parameters for distribution network reconfiguration and DG allocation in Test Case 4
Parameter Value
Number of ants 100
Maximum number of iteration 500
Pheromone evaporation rate 120530 03
Higher bound of pheromone level 120533119846119834119857 1
Lower bound of pheromone level 120533119846119842119847 001
Constant accumulation number 120533119836 0002
C2 Control parameters of ACO algorithm in Chapter 6
Table C-3 ACO parameters for distribution network reconfiguration and transformer economic
operation
Parameter Value
Number of ants 150
Maximum number of iteration 500
Pheromone evaporation rate 120530 03
Higher bound of pheromone level 120533119846119834119857 1
Lower bound of pheromone level 120533119846119842119847 001
Constant accumulation number 120533119836 0002
Appendix C Control Parameters of Algorithms
Page | 222
C3 Control parameters of ACO algorithm in Chapter 7
Table C-4 ACO parameters for sectionalising switch placement in Test Case 1
Parameter Value
Number of ants 400
Maximum number of iteration 400
Pheromone evaporation rate 120530 04
Higher bound of pheromone level 120533119846119834119857 1
Lower bound of pheromone level 120533119846119842119847 001
Constant accumulation number 120533119836 0002
Table C-5 ACO parameters for sectionalising switch placement in Test Case 2amp3
Parameter Value
Number of ants 500
Maximum number of iteration 200
Pheromone evaporation rate 120530 01
Higher bound of pheromone level 120533119846119834119857 1
Lower bound of pheromone level 120533119846119842119847 001
Constant accumulation number 120533119836 0002
C4 Control parameters of MOACO and AIS-ACO algorithm in
Chapter 8
Table C-6 MOACO parameters for multi-objective distribution network reconfiguration (loss
ECOST and SAIDI)
Parameter Value
Number of ants 100
Maximum number of iteration 100
Pheromone evaporation rate 120530 01
Higher bound of pheromone level 120533119846119834119857 1
Lower bound of pheromone level 120533119846119842119847 001
Constant accumulation number 120533119836 0002
Appendix C Control Parameters of Algorithms
Page | 223
Table C-7 AIS-ACO parameters for multi-objective distribution network reconfiguration (loss
ECOST and SAIDI)
Parameter Value
Maximum number of iteration 50
Pheromone evaporation rate 120530 01
Higher bound of pheromone level 120533119846119834119857 1
Lower bound of pheromone level 120533119846119842119847 001
Constant accumulation number 120533119836 0002
C5 Control parameters of ACO and AIS-ACO algorithm in
Chapter 9
Table C-8 ACO parameters for multi-objective DNR (loss maximum node voltage deviation feeder
load balancing index)
Parameter Value
Number of ants 200
Maximum number of iteration 800
Pheromone evaporation rate 120530 03
Higher bound of pheromone level 120533119846119834119857 1
Lower bound of pheromone level 120533119846119842119847 001
Constant accumulation number 120533119836 0002
Table C-9 AIS-ACO parameters for multi-objective DNR (loss maximum node voltage deviation
feeder load balancing index)
Parameter Value
Maximum number of iteration 3000
Pheromone evaporation rate 120530 01
Higher bound of pheromone level 120533119846119834119857 1
Lower bound of pheromone level 120533119846119842119847 001
Constant accumulation number 120533119836 0002
Page | 224
APPENDIX D List of Publications
1 B Zhang and P A Crossley ldquoMinimum transformer losses based on transformer
economic operation and optimized tie-switches placementrdquo in Proceedings of the 6th
International Conference on Advanced Power System Automation and Protection
(APAP) pp 1-7 20-25 September 2015
2 B Zhang and P A Crossley ldquoReliability improvement using ant colony
optimization applied to placement of sectionalizing switchesrdquo in Proceedings of the
9th
International Conference on Applied Energy (ICAE) pp 1-7 21-24 August 2017
3 B Zhang and P A Crossley ldquoMinimization of distribution network loss using
ant colony optimization applied to transformer economic operation and relocation of
tie-switchesrdquo to be submitted to IEEE Transactions on Smart Grid
4 B Zhang and PA Crossley ldquoOptimized sectionalising switch placement for
reliability improvement in distribution systemsrdquo to be submitted to IEEE
Transactions on Power Delivery
5 B Zhang and P A Crossley ldquoAn ant colony optimization ndashbased method for
multi-objective distribution system reconfigurationrdquo in Proceedings of the 14th
International Conference on Developments in Power System Protection (DPSP) pp
1-6 12-15 March 2018
Page | 3
27 Transformer Loss Assessment 42
271 Operating Principles 42
272 Transformer Quantities Measurement 43
273 Integrated Transformer Loss 46
28 Feeder Loss Assessment 47
29 Reliability Evaluation 48
291 Reliability Indices 48
292 Reliability Evaluation Methods 50
210 Multi-objective Optimisation 53
2101 Single Objective Function 54
2102 Single Fuzzy Satisfaction Objective Function 54
2103 Multi-objective Formulation in the Pareto Optimality Framework 56
211 Summary 58
CHAPTER 3 60
OPTIMISATION TECHNIQUES 60
31 Introduction 60
32 Monte Carlo Method 61
33 Ant Colony Optimisation 62
34 AIS-ACO Hybrid Algorithm 65
341 Artificial Immune Systems 65
342 Proposed AIS-ACO Hybrid Algorithm 66
35 Summary 68
CHAPTER 4 70
TRANSFORMER ECONOMIC OPERATION amp DISTRIBUTION NETWORK
RECONFIGURATION FOR TRANSFORMER LOSS REDUCTION 70
41 Introduction 70
42 Load Model 72
43 Problem Formulation 73
44 Methodology 73
441 Transformer Economic Operation 73
442 Distribution Network Reconfiguration 76
45 Application Studies 77
451 Test Case 1 77
452 Test Case 2 85
Page | 4
46 Summary 90
CHAPTER 5 92
DISTRIBUTION NETWORK RECONFIGURATION amp DG ALLOCATION FOR
FEEDER LOSS REDUCTION 92
51 Introduction 92
52 Problem Formulation 93
53 Solution Method 94
531 Distribution Network Reconfiguration 94
532 Applying ACO to DNR and DGs Placement 95
54 Application Studies 99
541 33-bus System 99
542 69-bus System 105
55 Summary 109
CHAPTER 6 111
DISTRIBUTION NETWORK RECONFIGURATION amp TRANSFORMER
ECONOMIC OPERATION FOR NETWORK LOSS REDUCTION 111
61 Introduction 111
62 Time-varying Load Model 112
63 Problem Formulation 113
64 Applying ACO to DNR and TEO 114
65 Application Studies 118
651 Test Case 1 122
652 Test Case 2 123
653 Test Case 3 124
66 Summary 126
CHAPTER 7 128
OPTIMAL PLACEMENT OF SECTIONALISING SWITCHES FOR
RELIABILITY IMPROVEMENT 128
71 Introduction 128
72 Problem Formulation 129
721 Weighted Aggregation 129
722 Single Fuzzy Satisfaction Objective Function with Two Parameters 130
723 Single Fuzzy Satisfaction Objective Function with Three Parameters 131
Page | 5
724 Evaluation of ECOST 132
725 Evaluation of SAIDI 133
726 Evaluation of Switch Costs 133
73 Applying ACO to Sectionalising Switch Placement Problem 134
74 Benefit-to-cost Analysis 135
75 Application Studies 136
751 Test Case 1 138
752 Test Case 2 147
753 Test Case 3 147
76 Summary 148
CHAPTER 8 150
DISTRIBUTION NETWORK RECONFIGURATION FOR LOSS REDUCTION amp
RELIABILITY IMPROVEMENT 150
81 Introduction 150
82 Problem Formulation 152
821 Multi-objective Reconfiguration Problem 152
822 Best Compromise Solution 153
83 Solution Methodology 154
831 Applying MOACO to Multi-objective DNR Problem 154
832 Applying AIS-ACO to Multi-objective DNR Problem 158
84 Application Studies 161
85 Best Compromise Solution 163
86 Summary 164
CHAPTER 9 166
MULTI-OBJECTIVE DISTRIBUTION NETWORK RECONFIGURATION amp DG
ALLOCATION CONSIDERING LOSS VOLTAGE DEVIATION AND LOAD
BALANCING 166
91 Introduction 166
92 Problem Formulation 168
921 Single Fuzzy Satisfaction Objective Function 168
922 Multi-objective Reconfiguration Problem Using Pareto Optimality 170
93 Solution methodology 171
931 Applying ACO to DNR and DG Allocation in the Fuzzy Domain 171
932 Applying AIS-ACO to Multi-objective DNR and DG Allocation Using
Pareto Optimality 171
Page | 6
94 Application Studies 171
941 33-bus System 172
942 69-bus System 180
95 Summary 187
CHAPTER 10 189
CONCLUSION amp FUTURE WORK 189
101 Conclusion 189
102 Future Work 193
References 195
APPENDIX A Network Model Data 204
APPENDIX B Simulation Results 209
APPENDIX C Control Parameters of Algorithms 221
APPENDIX D List of Publications 224
Word count 51012
Page | 7
List of Figures
Fig 2-1 Typical Distribution network [27] 29
Fig 2-2 Recloser operation 30
Fig 2-3 Transformer loss versus transformer load 32
Fig 2-4 Daily load curve of a typical substation before and after load smoothing [38]
34
Fig 2-5 Radial test system 35
Fig 2-6 Fully automated distribution feeder 40
Fig 2-7 Partially automated distribution feeder 41
Fig 2-8 Elements of a single phase transformer [33] 43
Fig 2-9 Construction of a three-phase transformer [33] 43
Fig 2-10 The open-circuit test [33] 44
Fig 2-11 The short-circuit test [33] 45
Fig 2-12 Simple two-bus network 47
Fig 2-13 Reliability model for static components 51
Fig 2-14 Procedure for reliability evaluation 52
Fig 2-15 Sample network 53
Fig 2-16 Linear membership function 54
Fig 3-1 Example of ant colony system [69] 63
Fig 3-2 Flowchart of the ant colony algorithm 65
Fig 3-3 Flowchart of the AIS-ACO algorithm 67
Fig 4-1 Procedure of domestic electricity demand profile generation 72
Fig 4-2 Monte Carlo simulation platform for three transformer operation modes
comparison 74
Fig 4-3 Flowchart of transformer loss assessment 75
Fig 4-4 Monte Carlo simulation platform for distribution network reconfiguration 76
Fig 4-5 Generic distribution network topology 78
Fig 4-6 Transformer load factor variation 79
Fig 4-7 Transformer loss variations in different scenarios 80
Fig 4-8 11 kV 4th
feeder voltage profiles in different scenarios 81
Fig 4-9 Voltage profiles of Load 4_1 in different scenarios 82
Fig 4-10 Voltage profiles of Load 4_8 in different scenarios 83
Page | 8
Fig 4-11 11 kV 4th
feeder mean voltage profile of various TCLFs 84
Fig 4-12 Test system 86
Fig 4-13 Daily load variations for different load groups 87
Fig 4-14 Mean voltage profiles in S1 S2 and S3 89
Fig 4-15 Mean voltage profiles in S1 S4 and S7 89
Fig 5-1 Search space of DNR and DGs Placement 95
Fig 5-2 Flowchart of the ACO applied to DNR and DGs placement 98
Fig 5-3 33-bus system 100
Fig 5-4 33-bus system for feeder loss minimisation Case II 101
Fig 5-5 33-bus system for feeder loss minimisation Case III 102
Fig 5-6 33-bus system for feeder loss minimisation Case IV 103
Fig 5-7 Comparison of feeder loss for different DG capacities before and after
simultaneous reconfiguration and DG allocation 104
Fig 5-8 Comparison of voltage profiles in different cases of 33-node system 104
Fig 5-9 69-bus system 105
Fig 5-10 69-bus system for feeder loss minimisation Case II 106
Fig 5-11 69-bus system for feeder loss minimisation Case III 107
Fig 5-12 69-bus system for feeder loss minimisation Case IV 107
Fig 5-13 Comparison of feeder loss for different DG capacities before and after
simultaneous reconfiguration and DG allocation 108
Fig 5-14 Comparison of voltage profiles in different cases of 69-node system 109
Fig 6-1 The reconfiguration hours for a typical day 113
Fig 6-2 Search space of DNR and TEO 115
Fig 6-3 Sample network with three substations 116
Fig 6-4 Flowchart of the ACO applied to DNR and TEO for a specific type of day
117
Fig 6-5 Distribution feeder connected to RBTS Bus 4 118
Fig 6-6 Daily load profile of residential consumers 119
Fig 6-7 Daily load profile of commercial consumers 120
Fig 6-8 Daily load profile of industrial consumers 120
Fig 6-9 Daily load profile (MW) of the main feeder 120
Fig 6-10 Annual energy loss with different DG capacities 123
Fig 6-11 Annual energy loss in uncoordinated charging strategy 125
Fig 6-12 Annual energy loss in coordinated charging strategy 126
Page | 9
Fig 7-1 Membership function for SAIDI and switch cost reduction 131
Fig 7-2 Membership function for ECOST reduction 132
Fig 7-3 Search space of sectionalising switch placement 134
Fig 7-4 Distribution feeder connected to RBTS Bus 4 with 6 sectionalising switches
136
Fig 7-5 Optimal relocation of sectionalising switches in Test Case 11 139
Fig 7-6 Optimal installation of sectionalising switches in Test Case 12 141
Fig 7-7 Optimal installation and relocation of sectionalising switches in Test Case
13 142
Fig 7-8 BCR versus years 143
Fig 7-9 Variation of cost versus change in CDF 144
Fig 7-10 Number of installed sectionalising switches versus change in CDF 145
Fig 8-1 Flowchart of the MOACO algorithm applied to multi-objective DNR
problem 157
Fig 8-2 Flowchart of the AIS-ACO algorithm applied to multi-objective DNR
problem 158
Fig 8-3 Distribution feeder connected to RBTS Bus 4 161
Fig 8-4 Pareto solutions obtained (minimisation of feeder loss ECOST and SAIDI)
162
Fig 9-1 Membership function for feeder loss reduction 168
Fig 9-2 Membership function for maximum node voltage deviation reduction 169
Fig 9-3 Membership function for load balancing index reduction 170
Fig 9-4 33 bus-system for fuzzy multi-objective optimisation Case II 173
Fig 9-5 Pareto front obtained for 33-bus system in Case II 174
Fig 9-6 33 bus-system for fuzzy multi-objective optimisation Case III 175
Fig 9-7 Pareto front obtained for 33-bus system in Case III 176
Fig 9-8 33 bus-system for fuzzy multi-objective optimisation Case IV 178
Fig 9-9 Pareto front obtained for 33-bus system in Case IV 178
Fig 9-10 69 bus system for fuzzy multi-objective optimisation Case II 180
Fig 9-11 Pareto front obtained for 69-bus system in Case II 181
Fig 9-12 69-bus system for fuzzy multi-objective optimisation Case III 183
Fig 9-13 Pareto front obtained for 69-bus system in Case III 183
Fig 9-14 69-bus system for fuzzy multi-objective optimisation Case IV 185
Fig 9-15 Pareto front obtained for 69-bus system in Case IV 186
Page | 10
List of Tables
Table 2-1 Transformer economic operation area 33
Table 2-2 Transformer technical specifications and costs 35
Table 3-1 Relationship of 119911 lowast and 119862 62
Table 4-1 Household size by number of people in household as a proportion [103] 72
Table 4-2 Parameters of a typical 3311 kV two-winding transformer [106] 78
Table 4-3 Daily transformer loss in different scenarios 80
Table 4-4 Transformer loss with different TCLF 85
Table 4-5 Average number of switching operations with different TCLF 85
Table 4-6 Transformer loss in Test Case 2 88
Table 5-1 Results of different cases for the 33-bus system 100
Table 5-2 Comparison of simulation results for 33-bus system in Case II 101
Table 5-3 Comparison of ACO with CGA and CSA for the 33-bus system in Case II
102
Table 5-4 Results of different cases for the 69-bus system 105
Table 5-5 Comparison of simulation results for 69-bus system in Case II 106
Table 6-1 Revised customer data (peak load) 119
Table 6-2 The distribution of load types for a whole year 121
Table 6-3 Results of DNR and TEO with different load types in Test Case 1 122
Table 6-4 Characteristics of EV 124
Table 7-1 Customer data (Average load) 137
Table 7-2 Sector interruption cost estimation ($kW) 138
Table 7-3 Results of sectionalising switches relocation in Test Case 11 140
Table 7-4 Results of sectionalising switches installation in Test Case 12 141
Table 7-5 Results of sectionalising switches relocation and installation in Test Case
13 143
Table 7-6 Impacts of 120588 variation on objective function 119869 146
Table 7-7 Impacts of variation in number of ants on objective function 119869 146
Table 7-8 Results of sectionalising switches relocation and installation in Test Case
2 147
Table 7-9 Results of sectionalising switches installation and relocation in Test Case
3 148
Page | 11
Table 8-1 Revised customer data (Average load) 162
Table 8-2 Mean and standard deviation of Pareto Front (loss ECOST and SAIDI)
163
Table 8-3 Minimum solutions along each objective (loss ECOST and SAIDI) 163
Table 8-4 Best compromise solutions (loss ECOST and SAIDI) 164
Table 9-1 Results of DNR in fuzzy multi-objective formulation for 33-bus system in
Case II 173
Table 9-2 Mean and standard deviations of Pareto Front for 33-bus system in Case II
174
Table 9-3 Minimum solutions along each objective for 33-bus system in Case II 175
Table 9-4 Results of DNR in fuzzy multi-objective formulation for 33-bus system in
Case III 176
Table 9-5 Mean and standard deviations of Pareto Front for 33-bus system in Case
III 176
Table 9-6 Minimum solutions along each objective for 33-bus system in Case III 177
Table 9-7 Results of DNR and DG allocation in fuzzy multi-objective formulation
for 33-bus system in Case IV 178
Table 9-8 Mean and standard deviations of Pareto Front for 33-bus system in Case
IV 179
Table 9-9 Minimum solutions along each objective for 33-bus system in Case IV 179
Table 9-10 Results of DNR in fuzzy multi-objective formulation for 69-bus system
in Case II 181
Table 9-11 Mean and standard deviations of Pareto Front for 69-bus system in Case
II 181
Table 9-12 Minimum solutions along each objective for 69-bus system in Case II 182
Table 9-13 Results of DNR in fuzzy multi-objective formulation for 69-bus system
in Case III 183
Table 9-14 Mean and standard deviations of Pareto Front for 69-bus system in Case
III 184
Table 9-15 Minimum solutions along each objective for 69-bus system in Case III
184
Table 9-16 Results of DNR and DGs allocation in fuzzy multi-objective formulation
for 69-bus system in Case IV 185
Page | 12
Table 9-17 Mean and standard deviations of Pareto Front for 69-bus system in Case
IV 186
Table 9-18 Minimum solutions along each objective for 69-bus system in Case IV
187
Table A-1 Typical configurations and parameters of 11 kV triplex cables in the UK
204
Table A-2 Line and load data of 33-bus system 205
Table A-3 Line and load data of 69-bus system 206
Table A-4 Feeder data of RBTS Bus 4 207
Table A-5 Reliability Data for RBTS Bus 4 208
Table B-1 The locations of tie-switch in Scenario 9 209
Table B-2 Mean voltage profiles at each node in the linked feeder 210
Table B-3 95th
voltage profiles at each node in the linked feeder 210
Table B-4 Network losses in each branch of 33-bus system 211
Table B-5 Network losses in each branch of 69-bus system 212
Table B-6 Pareto optimal solutions of multi-objective DNR (loss ECOST and
SAIDI) 214
Table B-7 Pareto optimal solutions of multi-objective DNR (loss maximum node
voltage deviation feeder load balancing index) for 33-bus system in Case II 215
Table B-8 Pareto optimal solutions of multi-objective DNR (loss maximum node
voltage deviation feeder load balancing index) for 33-bus system in Case III 215
Table B-9 Pareto optimal solutions of multi-objective DNR (loss maximum node
voltage deviation feeder load balancing index) for 33-bus system in Case IV 216
Table B-10 Pareto optimal solutions of multi-objective DNR (loss maximum node
voltage deviation feeder load balancing index) for 69-bus system in Case II 218
Table B-11 Pareto optimal solutions of multi-objective DNR (loss maximum node
voltage deviation feeder load balancing index) for 69-bus system in Case III 218
Table B-12 Pareto optimal solutions of multi-objective DNR (loss maximum node
voltage deviation feeder load balancing index) for 69-bus system in Case IV 219
Table C-1 ACO parameters for distribution network reconfiguration and DG
allocation in Test Case 2amp3 221
Table C-2 ACO parameters for distribution network reconfiguration and DG
allocation in Test Case 4 221
Page | 13
Table C-3 ACO parameters for distribution network reconfiguration and transformer
economic operation 221
Table C-4 ACO parameters for sectionalising switch placement in Test Case 1 222
Table C-5 ACO parameters for sectionalising switch placement in Test Case 2amp3222
Table C-6 MOACO parameters for multi-objective distribution network
reconfiguration (loss ECOST and SAIDI) 222
Table C-7 AIS-ACO parameters for multi-objective distribution network
reconfiguration (loss ECOST and SAIDI) 223
Table C-8 ACO parameters for multi-objective DNR (loss maximum node voltage
deviation feeder load balancing index) 223
Table C-9 AIS-ACO parameters for multi-objective DNR (loss maximum node
voltage deviation feeder load balancing index) 223
Page | 14
List of Abbreviations
Abbreviations Definition
ACO Ant Colony Optimisation
ACS Ant Colony System
AENS Average Energy Not Supplied
AIS Artificial Immune Systems
AIS-ACO Artificial Immune Systems-Ant Colony Optimisation
ANN Artificial Neutral Network
ASP Active Server Pages
BCR Benefit-to-cost Ratio
BEM Branch Exchange Method
BPSO Binary Particle Swarm Optimisation
CDF Customer Damage Function
CGA Continuous Genetic Algorithm
CSA Cuckoo Search Algorithm
DA Distribution Automation
DNO Distribution Network Operator
DNR Distribution Network Reconfiguration
DG Distributed Generation
DPSO Discrete Particle Swarm Optimisation
ECOST Expected Customer Damaged Cost
EDNS Expected Demand Not Supplied
ENS Energy not supplied
EV Electric Vehicle
FMEA Failure-mode-and-effect Analysis
FWA Firework Algorithm
FRTU Feeder Remote Terminal Unit
GA Genetic Algorithm
HC Hyper Cube
HSA Harmony Search Algorithm
HV High Voltage
Page | 15
IWO Invasive Weed Optimisation
LV Low Voltage
MDC Maximum Driving Capability
MILP Mixed Integer Linear Programming
MOACO Multi-objective Ant Colony Optimisation
MV Medium Voltage
PSO Particle Swarm Optimisation
RBTS Roy Billinton Test System
RGA Refined Genetic Algorithm
SA Simulated Annealing
SAIDI System Average Interruption Duration Index
SAIFI System Average Interruption Frequency Index
SCADA Supervisory Control and Data Acquisition
SSP Sectionalising Switch Placement
TS Tabu Search
TCLF Transformer Critical Load Factor
TEO Transformer Economic Operation
TOM Transformer Operation Mode
VML Vector Markup Language
Page | 16
Abstract
The University of Manchester
Submitted by Boyi Zhang
for the degree of Doctor of Philosophy
Distribution Network Automation for Multi-objective Optimisation
December 2017
Asset management and automation are acknowledged by distribution utilities as a
useful strategy to improve service quality and reliability However the major
challenge faced by decision makers in distribution utilities is how to achieve long-
term return on the projects while minimising investment and operation costs
Distribution automation (DA) in terms of transformer economic operation (TEO)
distribution network reconfiguration (DNR) and sectionalising switch placement
(SSP) is recognised as the most effective way for distribution network operators
(DNOs) to increase operation efficiency and reliability Automated tie-switches and
sectionalising switches play a fundamental role in distribution networks
A method based on the Monte Carlo simulation is discussed for transformer loss
reduction which comprises of profile generators of residential demand and a
distribution network model The ant colony optimisation (ACO) algorithm is then
developed for optimal DNR and TEO to minimise network loss An ACO algorithm
based on a fuzzy multi-objective approach is proposed to solve SSP problem which
considers reliability indices and switch costs Finally a multi-objective ant colony
optimisation (MOACO) and an artificial immune systems-ant colony optimisation
(AIS-ACO) algorithm are developed to solve the reconfiguration problem which is
formulated within a multi-objective framework using the concept of Pareto
optimality The performance of the optimisation techniques has been assessed and
illustrated by various case studies on three distribution networks The obtained
optimum network configurations indicate the effectiveness of the proposed methods
for optimal DA
Page | 17
Declaration
No portion of the work referred to in the thesis has been submitted in support of an
application for another degree or qualification of this or any other university or other
institute of learning
Page | 18
Copyright Statement
i The author of this thesis (including any appendices andor schedules to this
thesis) owns certain copyright or related rights in in (the ldquoCopyrightrdquo) she
has given The University of Manchester certain rights to use such Copyright
including for administrative purposes
ii Copies of this thesis either in full or in extracts and whether in hard or
electronic copy may be made only in accordance with the Copyright
Designs and Patents Act 1988 (as amended) and regulations issued under it
or where appropriate in accordance with licensing agreements which the
University has from time to time This page must form part of any such
copies made
iii The ownership of certain Copyright patents designs trademarks and other
intellectual property (the ldquoIntellectual Propertyrdquo) and any reproductions of
copyright works in the thesis for example graphs and tables
(ldquoReproductionsrdquo) which may be described in this thesis may not be owned
by the author and may be owned by third parties Such Intellectual Property
and Reproductions cannot and must not be made available for use without the
prior written permission of the owner(s) of the relevant Intellectual Property
andor Reproductions
iv Further information on the conditions under which disclosure publication
and commercialisation of this thesis the Copyright and any Intellectual
Property andor Reproductions described in it may take place is available in
the University IP Policy (see
httpdocumentsmanchesteracukDocuInfoaspxDocID=24420) in any
relevant Thesis restriction declarations deposited in the University Library
The University Libraryrsquos regulations (see
httpwwwlibrarymanchesteracukaboutregulations) and in The
Universityrsquos policy on Presentation of Theses
Page | 19
Acknowledgements
First and foremost I would like to express my deepest gratitude to my supervisor
Prof Peter Crossley for his invaluable guidance and continuous encouragement
throughout the project
I would like to thank my friends and colleagues in the Ferranti Building at The
University of Manchester Prof Zhongdong Wang and Dr Qiang Liu for the fruitful
research discussions and their encouragement throughout the period of my PhD
I wish to thank North China Electric Power University PR China for the 2+2
course and also to Prof Chunming Duan and Prof Sangao Hu for their help and
encouragement
I also wish to thank Prof Bo Zhang Prof Jianguo Zhao and Prof Li Zhang from
Shandong University PR China who continued to support my research with their
valuable feedback and advice
Finally I would like to express my gratitude to my parents for their encouragement
and support
Page | 20
CHAPTER 1
INTRODUCTION
11 Motivation
The electricity ldquoutilityrdquo distribution network is part of a power system that carries
electricity from a high voltage transmission grid to industrial commercial and
residential customers [1] In England and Wales the voltage level of distribution
networks ranges from 132 kV to 230 V [2] Generally most distribution networks
operating at voltages below 25 kV are designed in closed loop but are operated
radially due to the simplicity of operation the ease of protection coordination and
the minimisation of overall economics [3] [4]
The electric power generation transmission and distribution companies are not only
energy producers but also significant power consumers Power loss occurs when
electricity is supplied to customers In 2013 the total distribution losses of GBrsquos
networks were estimated to be 196 TWh which indicates that about 6 of the total
power generation is wasted in the form of losses at distribution level [5] Utility
statistics also indicate that distribution transformers account for approximately 22
of these losses and the line and cable losses make up the remaining 78 Reduction
in active power loss can help distribution network operators (DNOs) save costs and
increase profits
The expression ldquoPower quality = Voltage qualityrdquo has been widely accepted as the
wave shape and magnitude of voltage that strongly influences the power quality
Chapter 1 Introduction
Page | 21
received by customers [6] According to the EN50160 standard [7] under normal
conditions at least 95 of the mean 10 minutes average rms voltage magnitudes in
an 11 kV electricity distribution network should be within the range 09 pu to 11 pu
during one week
Distribution network reliability has proved to be another fundamental attribute for
the safe operation of any modern power system [8] Data show that about 80 of
customer outages are due to distribution system failures [9] Based on the resource
from [10] in 2011 the average number of minutes of lost supply per customer in GB
is 70 minutes According to [11] electricity breakdowns cost the United States
around $80 billion per year With improved reliability the DNOs can save expenses
that are spent on networkrsquos maintenances after a failure [12]
The major challenge faced by DNOs is how to distribute the power in a low-cost
reliable and efficient way Distribution automation (DA) is recognised as the most
effective method for DNOs to increase operation efficiency and reliability The three
main parts of DA are transformer economic operation (TEO) distribution network
reconfiguration (DNR) and sectionalising switch placement (SSP) TEO refers to the
optimum selection of the transformers needed to supply each feeder This is related
to the economic evaluation of network performance and the resilience of the
network DNR is a process that involves changing the network topology by altering
the openclose status of sectionalising (normally closed) and tie (normally open)
switches [13] [14] Installation of new sectionalising switches and relocation of
existing sectionalising switches are defined as SSP
Mathematically DA is a discrete non-linear constrained combinational optimisation
problem that is subject to operating constraints As it is not a practical solution to
investigate all possible network configurations ant colony optimisation (ACO)-
based heuristic search algorithms have been developed
To build a cleaner climate-friendly community the European Union has set a target
on carbon emissions for a 40 60 and 80 below 1990 levels by 2030 2040
and 2050 respectively [15] Therefore a large number of renewable distributed
generations (DGs) are deployed DG is a small electric generation unit that is
connected directly to the distribution network or appears on side of the meter
accessed by the customer [16] Since the number of DGs has increased in recent
Chapter 1 Introduction
Page | 22
years this has resulted in bidirectional power flows and locally looped networks [17]
The integration of high numbers of DGs strongly affects network operation and
planning Therefore optimal placement and sizing of DGs strongly improve
distribution network performance
12 Objectives
The aim of this research is to improve service quality and efficiency based on the
results of DA To achieve this aim the objectives of this thesis are as follows
To review distribution networks DA loss and reliability assessment and
optimisation functions
To propose three optimisation techniques namely the Monte Carlo Method the
ACO algorithm and the artificial immune systems-ant colony optimisation (AIS-
ACO) algorithm
To develop an optimal strategy consisting of TEO and DNR for transformer loss
reduction Statistic models of customer electrical demands should be established
to evaluate their impact from the perspective of probability
To assess the DNR and DG placement problems simultaneously in terms of
distribution feeder loss minimisation
To assess the TEO and DNR problem simultaneously in terms of distribution
network loss minimisation including transformer loss and feeder loss under
different load scenarios
To assess the SSP problem simultaneously based on three objectives namely
reduction of unserved energy cost decrease in the average time that a customer is
interrupted and minimisation of switch costs and using the fuzzy set theory
To propose a benefit-to-cost analysis to justify whether the benefits of installing
and relocating sectionalising switches can justify the cost or not
To formulate the optimal network reconfiguration problem within a multi-
objective framework using the Pareto optimality concept where network loss
and reliability indices are simultaneously optimised
Chapter 1 Introduction
Page | 23
To assess the DNR and DG allocation problem in terms of three conflicting
objectives optimisation network loss maximum node voltage deviation and
load balancing index in order to obtain a set of non-dominated solutions
13 Contribution of the work
This thesis has presented three methodologies of DA All of them are designed to
achieve service quality and efficiency improvement
The contributions of this thesis are summarised below
Load profiles In most literatures the load variations are ignored in their studies
which could underestimate the total energy loss for the utility [18] The
stochastic nature associated with load variety is considered in Chapter 4 In this
chapter the value of the load associated with domestic demand profiles are
obtained from the research described in [19] this can produce a random 1-min
resolution model for UK households A pool of load profiles is randomly
generated by this model in MATLAB Following this each node in the feeders
from the system is assigned with residential demand profiles from the pool based
on the Monte Carlo methodology
In Chapter 6 the distribution loads experience daily and seasonal variations The
study considers the daily load curves of different types of consumers (residential
commercial and industrial) In addition the days are divided into eight types
spring weekdays spring weekends summer weekdays summer weekends
autumn weekdays autumn weekends winter weekdays and winter weekends
Optimisation problems Previously it was observed that sufficient work has
been completed in terms of examining the TEO and the DNR problems
separately In Chapter 4 and 6 both the TEO and network reconfiguration
problems are integrated to benefit the whole distribution network effectively
Different combinations of locations of tie-switches in the network and operation
modes of all transformers in the substations represent different network
configurations Network reconfiguration and transformer operation modes
variation are dealt simultaneously using the ACO algorithm with an objective of
network loss minimisation as presented in Chapter 6
Chapter 1 Introduction
Page | 24
Most research projects have focused only on the optimisation of either the DNR
or the DG allocation problem An ACO algorithm is proposed in Chapter 5 to
deal with the DNR and DG allocation problems simultaneously in terms of
feeder loss minimisation In Chapter 9 the study aims to determine the optimum
network configurations and DG locations that minimise the active power loss
maximum node voltage deviation and feeder load balancing simultaneously
Multi-objective optimisation framework When there are multiple and
conflicting objectives that need to be satisfied all objective can be converted into
a single objective function which reflects a compromise among all objectives
The single objective function has two forms weighted aggregation and fuzzy
satisfaction objective function The selection of the form depends on the number
of objectives as well as their units and dimensions In Chapter 7 the system
expected outage cost to customers (ECOST) and switch costs can be converted
into a single objective function by aggregating these objectives in a weighted
function However as system interruption duration index (SAIDI) and switch
costs have different dimensions and units the two conflicting objectives are
modelled with fuzzy sets and then combined into a single objective function
Also a fuzzy membership function based on max-min principle is presented for
optimising ECOST SAIDI and switch costs simultaneously In Chapter 9 a new
operator called lsquomax-geometric meanrsquo has been introduced to determine the
degree of overall fuzzy satisfaction
However the above simple optimisation processes only obtain a compromise
solution It is no longer suitable if the DNO wishes to obtain all possible optimal
solutions for all the conflicting objectives at the same time [20] Therefore a set
of Pareto optimal solutions is introduced in this study And the corresponding
objective values constitute the Pareto front It allows decision makers to select
the most suitable topology from the Pareto optimal solutions for implementation
depending on the utilitiesrsquo priorities In Chapter 8 the study formulates the
optimal network reconfiguration problem within a multi-objective framework
using the concept of Pareto optimality where network loss and reliability indices
are simultaneously optimised In Chapter 9 active power loss maximum node
voltage deviation and feeder load balancing are optimised simultaneously
After obtaining the Pareto optimal solutions the best compromise solution
among the multiple objectives can be selected by comparing the fitness value of
Chapter 1 Introduction
Page | 25
each member in the Pareto front The best compromise solution is varied by
changing the values of weighting factors based on the tendencies of the network
decision makers A set of best compromise solutions can be obtained by varying
the weighing factors of each objective function and this is presented in Chapter 8
Proposal of ACO-based algorithms for assessment of optimisation problems
The ACO algorithm is a population-based approach based on the behaviour of
real ants [14] The proposed algorithm is not only used for assessment of the
TEO problem but also with DNR DG allocation and SSP problems The ACO
control parameters are different for each test case The selection of parameters is
a balance between the convergence rate and the global search ability of the
algorithm They are set experimentally using information from several trial runs
The results obtained by the ACO algorithm have been compared to those from
other algorithms in Chapter 5 and the ACO parameter sensitivity analysis is
provided in Chapter 7
In Chapter 8 the multi-objective ant colony optimisation (MOACO) and AIS-
ACO algorithms have been proposed and compared for assessment of multi-
objective DNR problems Both algorithms focus on problems in terms of Pareto
optimality where the objective functions are multidimensional and not scalar
A full list of publications resulting from this thesis is included in Appendix D
14 Structure of the thesis
The thesis is organised as follows
Chapter 2 introduces the distribution network configurations and associated
equipment It also gives a comprehensive literature survey which reviews the
existing knowledge and research activities in the distribution automation (DA)
including transformer economic operation (TEO) distribution network
reconfiguration (DNR) and sectionalising switch placement (SSP) The assessment
of transformer loss feeder loss and reliability indices as well as the multi-objective
optimisation functions are also described in this chapter
Chapter 3 summarises the optimisation techniques for assessment of the multi-
objective problem The Monte Carlo Method ACO algorithm and AIS-ACO hybrid
algorithm are described in detail
Chapter 1 Introduction
Page | 26
Chapter 4 proposes two methodologies for transformer loss reduction whilst
maintaining satisfactory voltages which are TEO and DNR The demand profiles are
randomly generated by the profile generators in MATLAB Following this each
node in the feeders from the system is assigned with demand profiles based on the
Monte Carlo Method The effectiveness of the two investigated methods
implemented either alone or together are presented and discussed
Chapter 5 describes an ACO algorithm to assess the network reconfiguration and
DG placement problems simultaneously in terms of distribution feeder loss
minimisation The results of four scenarios carried out on two standard IEEE 33-
node and 69-node systems are presented to show the effectiveness of the proposed
approach The effect of DG capacities on DNR for feeder loss reduction is also
discussed Moreover the results obtained by ACO algorithm have been compared to
those from other algorithms in the literature
Chapter 6 presents the ACO algorithm for minimisation of the losses associated
with a network loss including transformer loss and feeder loss under different load
scenarios This is achieved by the optimum selection of which transformers need to
supply each feeder and by determining the optimal locations of the tie-switches The
performance of this approach to minimise power loss is assessed and illustrated by
various case studies on a typical UK distribution network The impact of DGs and
electrical vehicles (EVs) in reducing the loss is also discussed
Chapter 7 explores an ACO-based methodology for the placement of sectionalising
switches in distribution networks The objectives of the proposed sectionalising
switch placement problem are reduction of unserved energy costs decrease in the
average time that a customer is interrupted and minimisation of switch costs These
objectives are formulated in either a single objective function or a fuzzy satisfaction
objective function The performance of the proposed methodology is assessed and
illustrated by various test cases on a well-known reliability test system
Chapter 8 formulates the optimal network reconfiguration problem within a multi-
objective framework using the Pareto optimality concept where network loss and
reliability indices are simultaneously optimised The MOACO algorithm and AIS-
ACO algorithm are proposed and compared for assessment of DNR problems The
Chapter 1 Introduction
Page | 27
proposed approaches are tested on Bus 4 of the RBTS and a set of high quality non-
dominated solutions are obtained
Chapter 9 addresses two algorithms to assess the DNR and DG allocation problems
in terms of the three conflicting objectives minimisation network loss maximum
node voltage deviation and load balancing index The ACO algorithm is used to
solve the problem in the fuzzy domain and the AIS-ACO algorithm is adopted to
obtain a set of non-dominated solutions using the concept of Pareto optimality The
effectiveness and the efficiency of the proposed methods are implemented on two
standard test systems as case studies
Chapter 10 concludes the thesis by summarising the main findings of the work
Finally possible future research ideas associated with this thesis are proposed
All the network models are built in OpenDSS and all the algorithms are coded in
MATLAB They are carried on a 340-GHz processor with 16 GBs of RAM memory
for all studies
Page | 28
CHAPTER 2
DISTRIBUTION AUTOMATION
21 Introduction
Distribution automation (DA) is an important part of a Smart Grid [21] It enables a
distribution network operator (DNO) to monitor coordinate and operate distribution
components in real-time from a remote control centre [22] [23] This improves the
reliability performance and operational efficiency of the electrical distribution
system and helps increase the market penetration of distributed generations (DGs)
and electrical vehicles (EVs) [24]ndash[26]
The remainder of this chapter is structured as follows Sections 22-23 introduce the
network configurations and associated equipment Sections 24-26 present the three
main parts of DA namely transformer economic operation (TEO) distribution
network reconfiguration (DNR) and sectionalising switch placement (SSP)
Transformer loss feeder loss and reliability indices assessments are described in
Sections 27-29 Three methods for assessment of multi-objective optimisation
problems are reviewed in Section 210 A summary of the main conclusions in this
chapter is given in Section 211
Chapter 2 Distribution Automation
Page | 29
Tie-switch
Sectionalising switch
22 Distribution Network Configurations
In England and Wales the voltage level of distribution networks ranges from 132 kV
to 230 V [2] Generally most distribution networks are designed in closed loop but
are operated radially due to the simplicity of operation the ease of protection
coordination and the minimisation of overall economics [3] [4]
There are three typical system configurations shown in Fig 2-1 [27] The radial
system in Fig 2-1 (a) is common in rural areas but does not include any backup
supplies Consequently the lack of feeder interconnections means a short-circuit
fault will interrupt power to all the downstream customers and power will not be
restored until the faulted equipment is repaired The tie-switches (normally open) in
Fig 2-1 (b) connect two feeders and make the system radial in a primary loop There
are multiple tie-switches between multiple feeders in distribution systems Fig 2-1 (c)
describes a link arrangement and during normal conditions the systems are operated
radially However when a fault occurs the part affected by the fault is isolated by
tripping the breakers The unaffected areas can then be restored from a different
busbar by closing the tie-switches and feeding the supply
(a) Radial system (b) Primary loop (c) Link Arrangement
Fig 2-1 Typical Distribution network [27]
Chapter 2 Distribution Automation
Page | 30
23 Switchgear for Distribution Network
There is a large variety of switchgears used in distribution networks this includes
reclosers sectionalising switches tie-switches fuses and circuit breakers This
section mainly focuses on reclosers sectionalising switches and tie-switches
231 Reclosers
Reclosers are automatic self-contained protection devices installed on main feeders
and operate as a part of the protection schemes [28] [29] They are a type of circuit
breakers with control measurement and automatic re-closing functions Most faults
on distribution feeders are temporary ie they last from a few cycles to a few
seconds and are cleared by protection tripping a circuit breaker [1] Reclosers
normally count the number of overcurrent pulses followed by the line de-
energisation sequences [1] They always coordinate with other types of protection
equipment These include such as fuses and sectionalising switches for the purpose
of fault isolation and system restoration The process of recloser operation is shown
in Fig 2-2 The time between reclosures and the time of the reclose can be
programmed If the fault is transient the recloser will operate 1-3 times and then
restore service quickly If the fault is permanent after a pre-set number of trip-
reclose operations the recloser is locked and the recloser interrupter triggers a final
trip
Fig 2-2 Recloser operation
Time between reclosures
Time of the reclose Fault current
Recloser locks
out on 2nd
reclose
as programmed
Recloser opens
Recloser recloses
fault still present
Recloser recloses
fault still present
Recloser re-opens
fault still present
Load current
Chapter 2 Distribution Automation
Page | 31
232 Sectionalising Switches
Sectionalising switches are the protective devices that operate in conjunction with
backup circuit breakers or reclosers [25] They are isolating devices that
automatically isolate the faulted sections from a distribution network after a
permanent fault has occurred and after the line is de-energised by the feeder breaker
[1] This is because sectionalising switches are not designed to interrupt the fault
current and must be used with the feeder breaker that can break and reclose a circuit
under all conditions ie normal or faulty operating conditions [25] [30] A detailed
operation of sectionalising switches is presented in Section 26
233 Tie-switches
Tie-switches refer to the normally open switches of the network By closing the
opened tie-switch the load is transferred from one feeder to another but this requires
an appropriate sectionalising switch to be opened to restore the radial topology [31]
The tie-switch placement should follow certain principles ie all the loads are
energised and the network is operated in radial configurations The tie-switches are
designed to operate in normal condition but are not suitable for the interruption of
fault currents They are designed to operate after a switching device (circuit breaker
of fuse) has interrupted the fault current
24 Transformer Economic Operation
241 Basic Concepts
Power transformers are the interface between the generators and the transmission
lines and between lines operating at different voltage levels [32] They are a critical
part of an electric power system and transform the ac voltage based on the principle
of electromagnetic induction A step-up transformer ensures the efficient
transmission of power ie high voltage-low current and a step-down transformer
permits the transmitted power to be used at a lower and safer voltage [33]
Distribution transformers are used to reduce the primary system voltages to the
Chapter 2 Distribution Automation
Page | 32
Tran
sfo
rme
r Lo
ss
Transformer Load Factor
1 Transformer
2 Transformers
utilisation voltages [25] normally 132 kV for high voltage (HV) 11 kV-33 kV for
medium voltage (MV) and 400 V for low voltage (LV) in UK distribution networks
For transformers currently in operation developing a new strategy for transformer
loss reduction is required rather than replacing them with high efficiency
transformers [34] Transformer economic operation refers to the optimum selection
of transformers needed to supply each feeder This is related to the economic
evaluation of network performance and the resilience of the network
In order to meet reliability requirements the load factor of each transformer should
not go beyond 50 when two transformers are operated in parallel In other words
the transformer load factor must be within 100 in separate operation modes
The integrated power loss curves of onetwo transformers in operations are shown in
Fig 2-3 The intersection of the two curves is 119878119871 which is called the transformer
critical load factor (TCLF) Therefore it can be concluded that
When the total load 119878 lt 119878119871 a single transformer produces less integrated
power loss than parallel transformers
When 119878 gt 119878119871 parallel operation of transformer is more economical
When 119878 = 119878119871 the losses in single or parallel operation modes are identical
Fig 2-3 Transformer loss versus transformer load
119878119871
Core loss for 2 transformers
Core loss for 1 transformer
Chapter 2 Distribution Automation
Page | 33
As a result Table 2-1 presents the transformer commercial operation area
Table 2-1 Transformer economic operation area
Operation modes Single Transformer Two Parallel Transformers
Economic operation area 0 ~ 119878119871 119878119871 ~ 119878
242 Literatures on Transformer Economic Operation
Several papers that discuss research on transformer economic operation not only
focuse on transformer loss reduction but also discuss cost reduction and reliability
improvement
The papers concerned with transformer economic operation based on loss reduction
were presented in [35]ndash[37] Wang and Liu [35] used the ASP (Active Server Pages)
language as a foundation to analyse transformer economic operation on-line The
operation curves and interval graph of commercial operation were achieved from the
VML (Vector Markup Language) and the simulation results In the interest of the
economical and profitable operation of transformer real-time data was obtained
using the SCADA (Supervisory Control and Data Acquisition) and this included the
measurement of active power load and voltage [36] [37] Then the transformers
were monitored in real-time and the methods used to ensure their economical and
profitable operation were suggested online
However if the active power loss of transformers was measured based on the real-
time load data transformers would frequently be switched to a new state associated
with instantaneous economical and profitable operation As the number of switching
operations increases the lifetime of the transformers decreases As a result Song and
Zhang [38] developed a load smoothing algorithm to reduce the number of switching
operations of the transformer effectively The curves of transformer loads before and
after smoothing are presented in Fig 2-4 Table 2-2 and 2-3 illustrate the transformer
operation mode variation before and after smoothing respectively The results show
that the active loss achieved when using the load smoothing algorithm was a little
higher than when smoothing was not used However the total number of switching
operations of transformers with load smoothing was reduced from 6 to 2 which
would expand the transformer life cycle
Chapter 2 Distribution Automation
Page | 34
(a) Before load smoothing (b) After load smoothing
Fig 2-4 Daily load curve of a typical substation before and after load smoothing [38]
Table 2-2 Transformer operation mode variation before load smoothing
Time Transformer operation mode The sum of active power loss
(Kw)
000-300 1 transformer in operation 12363
300-1600 2 transformer in operation
1600-2100 Parallel operation
2100-2400 2 transformer in operation
Table 2-3 Transformer operation mode variation before load smoothing
Time Transformer operation mode The sum of active power loss
(Kw)
000-600 2 transformer in operation 12768
600-2100 Parallel operation
2100-2400 2 transformer in operation
Generally the cost of the energy loss of a transformer over its service life is much
higher than its initial capital price As a result the transformer selection decision is
based not only on the purchase price but also includes the cost of installation
maintenance and loss over the lifetime of the equipment [39]
Amoiralis etc [40] have investigated the cost of two transformers that have the same
capacity but different specifications The transformers were loaded at 50 of full
load and with an increase of 37 for each year The technical characteristics and the
costs associated with the two transformers are presented in Table 2-4 The total cost
is the summation of loss and capital cost of a transformer over 30 years Purchasing a
Chapter 2 Distribution Automation
Page | 35
transformer with low efficiency (Transformer A) reduced the initial cost but resulted
in higher energy costs during the transformer lifetime in comparison with
Transformer B The economic approach in [41] and [42] were used to determine the
suitable size of transformers in Thailand The choice of a high capacity transformer
could improve voltage profiles and provide extra room for emergency conditions and
load increments in the future
Table 2-4 Transformer technical specifications and costs [40]
Transformer Size
(kVA)
No load loss
(kW)
Load loss
(kW)
Capital
price (euro)
Cost of loss
(euro)
Total cost
(euro)
A 1000 11 9 9074 34211 43285
B 1000 094 76 11362 28986 40348
25 Distribution Network Reconfiguration
251 Basic Concepts
DNR refers to a process that involves changing the network topology at normal and
abnormal operating conditions by altering the openclose status of sectionalising
(normally closed) and tie (normally open) switches [13] [14] In fact DNR can be
used as a tool for distribution network planning and real-time operation [14]
As presented in Fig 2-5 the openclosed status of the tie switches and sectionalising
switches determines the structure of the system To achieve a new system
configuration the tie-switch 3 is closed which will create a new loop In order to
restore the network back to a radial structure a switch from 1 2 4 and 5 is selected
and opened
Fig 2-5 Radial test system
Chapter 2 Distribution Automation
Page | 36
Since there are various combinations of switching DNR is treated as a discrete and
constrained optimisation problem Recently optimal DNR strategies discussed in
many literatures have been implemented to achieve active power loss reduction and
system reliability improvement
252 Literatures on Distribution Network Reconfiguration
Network reconfiguration was first introduced by Merlin and Back [43] using a
discrete branch and bound optimisation method to reduce network loss Firstly all
the switches were closed to build a meshed network and then in each step one
branch was removed until the radial configuration was found
Another early study on loss reduction through network reconfiguration was
presented in [44] which discussed how to achieve minimum power loss in
distribution feeders through feeder reconfiguration It is possible to determine loss
variation by analysing the load flow results This involved simulating the system
configuration before and after the feeder was reconfigured [44] It was based on a
single pair switch operation per iteration The relevant results showed that the loss
was reduced only if the voltage across the tie-switch was significant and if the loads
connected at the lower voltage side were transferred to the other side [44] This
criterion was developed to eliminate undesirable switching options The best
switching option was then obtained from the results of load flow studies simulating
all feasible feeder configurations
Zehra etc [31] have proposed a branch exchange algorithm based on two stages of
the solution methodology It started with a feasible network operating in a radial
configuration The first step determined the loop that achieved maximum loss
reduction by comparing the circle sizes for each loop The largest circle indicated the
maximum loss reduction The second phase determined the switching options to be
operated in that loop to provide maximum loss reduction The smallest circle was
identified for the best solution In comparison with [44] the introduction of the
branch exchange method allowed the number of load flow solutions related to the
computation time to be greatly reduced However the results were strongly related to
the initial configuration of the electrical network [45] The above methodologies [31]
[43] [44] were able to obtain the global optimal solution but were only applied to
simplified network models
Chapter 2 Distribution Automation
Page | 37
Later on the artificial intelligent and modern heuristic optimisation algorithms such
as genetic algorithm (GA) [46]ndash[49] simulated annealing (SA) [50] [51] tabu
search (TS) [52]ndash[54] and particle swarm optimisation (PSO) [55] etc were
developed with minor computational effort These intelligent techniques which are
affected by the selection of parameters are able to obtain the optimum solution of
good quality The GA based network reconfiguration method was presented and
tested in a real 136-bus distribution network in [13] Various radial topologies were
generated after the implementation of the genetic operators and the search space was
enlarged by a local improvement method The results show that after network
reconfiguration the power loss is reduced from 3203 kW to 2801 kW which
amounts to a 1255 reduction
Other important objectives including reliability improvement and service restoration
by DNR were mentioned in [56]ndash[58] An intelligent binary particle swarm
optimisation (BPSO) based search method was presented in [57] for assessment of
the DNR problem in terms of reliability improvement The failure of all distribution
equipment such as transformers feeders breakers etc was considered In this paper
the reliability index was in the form of expected demand not supplied (EDNS) The
EDNS of the original configuration is 1008 kW and after reconfiguration the best
result is reached with 849 kW
Network reconfiguration can be formulated not only as a single objective problem
but also as a multi-objective problem that considers various parameters
simultaneously [45] [59]ndash[62] In [59] the objective function was to minimise the
combination of loss cost and consumer interruption cost thus the multiple objectives
were aggregated into an single objective function In order to achieve optimal DNR
a new method was proposed in [60] using a fuzzy multi-objective function to
balance feeder loads and reduce power loss of the distribution systems Depending
on the operatorrsquos preferences the weighting factors of each of the variables could be
varied Das [61] introduced another fuzzy membership formulation to handle the
multiple objectives In this work the degree of overall satisfaction was the minimum
of all the above membership values and the final optimal solution was the maximum
of all such overall degrees of satisfaction [61] Mendoza etc [62] introduced a
micro-genetic algorithm to deal with the trade-offs between the power loss and
reliability indices in order to obtain a set of optimal network configurations using
Chapter 2 Distribution Automation
Page | 38
the concept of Pareto optimality Andervazh etc [45] have presented another Pareto-
based multi-objective DNR method using discrete PSO The objectives were the
minimisation of power loss bus voltage deviations and number of switching
operations
In addition an optimal planning strategy based on network reconfiguration and DGs
placement was presented in [16] The primary objective was power loss reduction
and voltage stability improvement The performance of the methodology was tested
on a 33-bus network and three DGs were installed The power loss was reduced by
3093 by DNR 5624 by DG installation and 6689 by employing
reconfiguration and DG installation simultaneously
26 Placement of Sectionalising Switches
261 Basic Concepts
The implementation of DA requires the installation of various new devices [63]
Among other things DA involves the placement of sectionalising switches ie the
installation of new switches and relocation of existing switches DA in terms of
automatic and remote controlled sectionalising switch placement brings major
benefits to distribution network operators (DNOs) [64] [65] The duration and
number of outages per year determines the annual interruption time of customers
[66] It is possible to shorten outage duration by decreasing the restoration time and
to reduce the number of outages by improving failure rates [67] SSP is useful for the
reduction of the time required to detect and locate a fault and the improvement of
the speed of isolating the faulty sections in the primary distribution network [64]
The effectiveness of these objectives depends on the number and location of
sectionalising switches
In a distribution feeder the section is defined as a group of line segments between
adjacent sectionalising switches [68] And the equivalent load of the section is the
sum of the individual load points in this section [69] When a permanent fault occurs
the switch actions need to respond as follows
Chapter 2 Distribution Automation
Page | 39
1 Detect and locate the fault and initiate tripping to clear the fault A transient
fault is normally cleared by two or three trips and reclose cycles
2 However if the fault persists beyond the predefined cycles reclosure will be
inhibited and the protection will initiate a final trip The load breaker will open and
all the downstream loads will be de-energised
3 The faulty section is then isolated by opening the upstream and downstream
sectionalising switches located next to the fault
4 Restore the loads in the healthy area by closing the upstream and downstream
circuit breakers automatically
5 Repair the faulty section of the feeder and manually restore the loads (ie
reconnect loads to the supply)
A fully and a partially automated distribution feeder are shown in Fig 2-6 and Fig
2-7 respectively The fault occurs on line section 4 It can be clearly seen in Fig 2-6
that all loads are restored after the faulty area is isolated and the total outage time is
the same as the switching time of circuit breakers and sectionalising switches [64]
However as shown in Fig 2-7 only Loads LP1 LP5 LP6 are restored after the
isolation of the faulty section the outage duration of other loads is equal to the repair
time ie significantly longer than the switching time As a result the installation of
sectionalising switches could increase the network reliability as well as the
investment and operation cost of automation [64]
Chapter 2 Distribution Automation
Page | 40
LP1 LP2 LP3 LP4 LP5 LP6
1 2 3 4 5 6 7
LP1 LP2 LP3 LP4 LP5 LP6
1 2 3 4 5 6 7
LP1 LP2 LP3 LP4 LP5 LP6
1 2 3 4 5 6 7
LP1 LP2 LP3 LP4 LP5 LP6
1 2 3 4 5 6 7
Fault occurred on line section 4
CB1 opened
Sectionalising switches adjacent to the faulted area are opened
Energy restored to un-faulted area by closing CB1 and CB2
CB1 CB2
CB1CB2
CB1 CB2
CB1 CB2
Normally closed circuit breaker
Normally open circuit breaker
Closed sectionalising switch
Open sectionalising switch
Interrupted
load
Fig 2-6 Fully automated distribution feeder
Chapter 2 Distribution Automation
Page | 41
LP1 LP2 LP3 LP4 LP5 LP6
1 2 3 4 5 6 7
LP1 LP2 LP3 LP4 LP5 LP6
1 2 3 4 5 6 7
LP1 LP2 LP3 LP4 LP5 LP6
1 2 3 4 5 6 7
LP1 LP2 LP3 LP4 LP5 LP6
1 2 3 4 5 6 7
Fault occurred on line section 4
CB1 opened
Sectionalising switches adjacent to the faulted area are opened
Energy restored to un-faulted area by closing CB1 and CB2
CB1 CB2
CB1CB2
CB1 CB2
CB1 CB2
Normally closed circuit breaker
Normally open circuit breaker
Closed sectionalising switch
Open sectionalising switch
Interrupted
load
Fig 2-7 Partially automated distribution feeder
262 Literatures on Sectionalising Switch Placement
The earliest work that discussed SSP in distribution networks was presented by
Miranda [70] A fuzzy-logic-based optimisation technique has been used to
determine the location of sectionalising switches
In [69] the optimum sectionalising switch relocation problem has been solved by
using the ant colony system (ACS) based method to reduce feeder interruption costs
Chapter 2 Distribution Automation
Page | 42
after a fault In this work it is assumed that there were no additional capital
investments brought by switch relocation However the investment and operation
cost of a sectionalising switch is an important issue which cannot be ignored when
considering the problem of unsupplied energy costs minimisation since they conflict
with each other Therefore the information provided by the multi-objective model is
more valuable than the traditional mono-objective model Abiri-Jahromi etc [64]
have developed a mixed-integer linear programming (MILP) to deal with the new
sectionalising switch installation problem which considers customer outage costs as
well as switch capital operation and maintenance costs After the placement of
sectionalising switches the total system cost over the life period of the switches was
greatly reduced [64] In addition the impacts of customer damage function and load
density variations on SSP were also investigated through sensitivity analysis
The impacts of DG on the optimal number and location of sectionalising switches
were discussed in [71] The introduction of DGs connects a mono-source distribution
network to a multi-source one [66] This potentially improves network reliability
since it reduces the duration and restoration time of interruptions Many loads can be
restored through DGs when operating in islanding mode A mathematical
optimisation methodology has been proposed to minimise the reliability cost when
operating with a minimum number of sectionalising switches The results indicate
the reliability indices of distribution networks are affected by the number and
location of sectionalising switches
27 Transformer Loss Assessment
271 Operating Principles
A transformer has three essential elements a primary winding a secondary winding
and a core [33] As shown in Fig 2-8 the winding connected to the electrical source
is called the primary winding and the secondary winding is linked with the loads All
the windings are connected by the common magnetic flux in the core
Chapter 2 Distribution Automation
Page | 43
Fig 2-8 Elements of a single phase transformer [33]
Usually the power is generated and distributed in a three-phase system Therefore it
is necessary to use a three-phase transformer to increasedecrease the voltage The
structure of the three-phase transformer is presented in Fig 2-9
Fig 2-9 Construction of a three-phase transformer [33]
272 Transformer Quantities Measurement
The transformer quantities present the self-loss during power transmission which
consists of active power loss together with increase in the reactive power of the
network unit [72]
Open-circuit test
The equivalent circuit for the open-circuit test is shown in Fig 2-10 The test is made
on the low-voltage side by applying rated voltage at rated frequency with the high-
voltage winding open [33] The input power and current are measured which are
named no-load loss 119875119874119862 and no-load current 119868119874119862
Chapter 2 Distribution Automation
Page | 44
(a) Test circuit
(b) Equivalent circuit
Fig 2-10 The open-circuit test [33]
As the secondary is open the primary current is equal to the no-load current The no-
load current is used to produce the primary magnetic flux when the transformer is in
no-load operation which is also called the exciting current The voltage drops in the
primary winding can be ignored so the no-load loss is the summation of hysteresis
and eddy current losses [33] The input power is practically equal to the no-load loss
at rated voltage and frequency
119875119874119862 = 119875ℎ+119890 =119880119874119862
2
119877119888119871119881= 119880119874119862119868ℎ+119890 (2-1)
where 119877119888119871119881 is the resistance referred to the low-voltage side 119868ℎ+119890 is the core loss
current
Short-circuit test
The short-circuit test is used to measure the equivalent resistance and reactance of
the winding [6] As shown in Fig 2-11 the low-voltage terminal is shorted together
and the high-voltage side of the transformer is connected to a low-voltage high-
119880119900119888
119868ℎ+119890 119868120601
119868119900119888 119885119890119902 119871119881
119877119888 119871119881 119883119898 119871119881
Chapter 2 Distribution Automation
Page | 45
current source at rated frequency [33] The source voltage is increased until the short
circuit current reaches the rated value At this time value of the source voltage is
known as the short-circuit source voltage 119880119878119862
(a) Test circuit
(b) Equivalent circuit
Fig 2-11 The short-circuit test [33]
As the secondary side is shorted the voltage applied to the full load current is low
compared to the rated voltage and the exciting current 119868119890119909 is negligible during this
test [33] Since the rated current is used the input power is equal to the full-load loss
and expressed as
119875119878119862 = 1198681198781198622 119877119890119902119867119881 (2-2)
where 119877119890119902119867119881 is the winding resistance referred to the high voltage side
As the full-load loss depends on the value of the full load current the loss in the
winding resistance is varied under different loading conditions
119880119904119888
119868119890119909
119868119904119888 119877119890119902 119867119881 119883119890119902 119867119881
(119899119890119892119897119890119888119905)
Chapter 2 Distribution Automation
Page | 46
Active power loss
The active power loss ∆119875 of a two-winding transformer is decided by the no-load
loss 119875119874119862 full-load loss 119875119878119862 and the transformer load factor [73]
∆119875 = 119875119874119862 + 1205732119875119878119862 (2-3)
where 120573 =119878119871
119878119873 represents the transformer load factor 119878119871 is the transformer actual
loading (kVA) 119878119873 is the transformer rated capacity (kVA) Assuming the voltages
are held constant at 10 pu
Reactive power loss
The no-load current 119868119900119888 and short-circuit source voltage 119880119878119862 represent the change of
reactive power ∆119876 in other words the reactive power loss which can be simplified
as
∆119876 = 119876119874119862 + 1205732119876119878119862 (2-4)
119876119874119862 = 119878119874119862 =119868119874119862
119868119873∙ 119878119873 (2-5)
119876119878119862 = 119878119878119862 = 119880119878119862
119880119873∙ 119878119873 (2-6)
273 Integrated Transformer Loss
In general the power loss of a transformer is related to the active power [74]
However if a transformer draws reactive power (it takes current) this causes real
power loss in the network The integrated power loss refers to the sum of active
power loss of the transformer and the increased active power loss contributed by the
reactive power of the transformer [72]
The integrated power loss of a two-winding transformer is calculated by
1198791198711 = 11988002119875119885119874119862 +
1205732
11988002 119875119885119878119862 (2-7)
119875119885119874119862 = 119875119874119862 + 119870119876119876119874119862 (2-8)
Chapter 2 Distribution Automation
Page | 47
119875119885119878119862 = 119875119878119862 + 119870119876119876119878119862 (2-9)
where 119875119885119874119862 and 119875119885119878119862 are the integrated no-load loss (kW) and the full-load loss (kW)
120573 =119878119871
119878119873 represents the transformer load factor 119878119871 is the transformer actual loading
(kVA) 119878119873 is the rated capacity of the transformer (kVA) 119875119874119862 and 119876119874119862 are the no-
load active power loss (kW) and no-load reactive power loss (kVAr) 119875119878119862 and 119876119878119862
are the full load active power loss (kW) and full load reactive power loss (kVAr) 119870119876
represents the reactive equivalent which is the ratio of increased active power loss to
the change of the node reactive power (kWkVAr) [72] 1198800 is the operational voltage
of the transformer low voltage side in per unit
The no-load and full-load power losses are obtained from the open-circuit and short-
circuit test separately
For two transformers operating in parallel with the same capacity the current
flowing through each transformer is reduced by half Thus the full-load loss of each
transformer becomes a quarter of the previous case The total integrated power loss
is twice the no-load loss and half (2 times1
4) of the full-load loss of one transformer
1198791198712 = 211988002119875119885119874119862 +
1
2
1205732
11988002 119875119885119878119862 (2-10)
28 Feeder Loss Assessment
The distribution network power loss is mainly due to resistive loss in distribution
feeders which is obtained through a power flow study [75] The calculation of
power loss is explained using a two-bus network as shown in Fig 2-12
Fig 2-12 Simple two-bus network
Chapter 2 Distribution Automation
Page | 48
Assume there is no capacitance on either the sending or receiving bus and 119868119887119904 =
119868119887119903 = 119868119887 As a result the current flowing through branch b and the real power loss
are derived using the following equations
119875119887119877 + 119895119876119887119877 = 119887119877 times 119868lowast (2-11)
119875119887 = 1198681198872 times 119877119887 (2-12)
From (2-11) and (2-12) it is calculated as
119875119887 =119875119887119877
2 +1198761198871198772
1198811198871198772 times 119877119887 (2-13)
where 119875119887 is the real power loss of branch b (W) 119875119887119877 and 119876119887119877 are the real power (W)
and reactive power (VAr) at the receiving end of branch b 119881119887119877 represents the rms
voltage at the receiving end of branch b (V) 119868119887 is the rms current through branch b
(A) and 119877119887 is the resistance of branch b (Ω)
The real power losses in the other branches are evaluated similarly and the network
real loss is the sum of the power losses in all branches as presented in (2-14)
119864119871 = sum 119875119887119899119873119887119899 (2-14)
where 119873119887 is the set of all the distribution network branches
29 Reliability Evaluation
291 Reliability Indices
Reliability is a fundamental attribute for the safe operation of any modern power
system [8] A distribution network which is directly connected to customers has a
large impact on power reliability Distribution reliability primarily relates to
equipment outages and customer interruptions [76] The reliability indices of
distribution network can be classified into two groups ie load point reliability
indices and system reliability indices [77]
Chapter 2 Distribution Automation
Page | 49
The three primary load point reliability indices average failure rate (120582) average
annual outage time (119880) and average outage time (119903) are calculated by [73]
120582 = sum 120582119895119895 (2-15)
119880 = sum 120582119895119895 119903119895 (2-16)
119903 =119880
120582 (2-17)
where 120582119895 and 119903119895 are the failure rate and outage time of contingency j for this load
point
The system reliability indices mainly include system average interruption frequency
index (SAIFI) system average interruption duration index (SAIDI) average energy
not supplied (AENS) and expected customer damaged cost (ECOST) [78] The
Formulae for these reliability indicators are presented in (2-18) to (2-21) [78]
119878119860119868119865119868 =sum 120582119894119873119894119894
sum 119873119894119894 (2-18)
119878119860119868119863119868 =sum 119880119894119873119894119894
sum 119873119894119894 (2-19)
119860119864119873119878 =sum 119880119894119871119894119894
sum 119873119894119894 (2-20)
119864119862119874119878119879 = sum 119888119898(119889119898)119891119898119871119898119872119898=1 (2-21)
where 119873119894 is the total number of customers of load point 119894 120582119894 119880119894 and 119871119894is the failure
rate outage time and average load connected to load point i 119872 is quantity of load
outage events 119871119898 is load curtailed (kW) due to outage event m 119891119898 and 119889119898 are the
frequency and duration of outage event m 119888119898(119889119898) is the outage cost (poundkW) of
outage duration 119889119898 using the customer damage function (CDF)
SAIFI is a measure of the number of outages an average customer will experience
SAIDI states the average interruption hours for a customer in the system AENS
presents the effect of interruptions on the energy that is not supplied to the customers
during failures [79] ECOST is the index that connects reliability with economics
Chapter 2 Distribution Automation
Page | 50
292 Reliability Evaluation Methods
The methods used to calculate reliability indicators for distribution network are
classified into two groups namely the simulation method and analytical method
Simulation method
The simulation method has better scalability and flexibility when incorporating
complex considerations in comparison with the analytical technique And it is more
capable of dealing with large-scale power systems and the variation of load points
[77] The Monte Carlo method is a typical example of a simulation method and
takes into account the time varying and stochastic nature of load models in
evaluating the power system reliability [80] Vitorino etc [12] proposed a non-
sequential Monte Carlo method based on branch reliability to estimate energy not
supplied (ENS) index Contingencies were simulated by randomly selecting a faulty
branch from a candidate network pool based on failure probabilities [12] However
although the Monte Carlo method can simulate the behaviour of a complex system
with a high degree of accuracy it requires a considerable amount of CPU time and
memory
Analytical method
The first step of an analytical technique is to build a reliability probabilistic model
for the system according to network topology as well as the relationships between
the system and components [77] The model is then solved by calculating the
reliability indices in iterations [77] The most common analytical methods are
minimal path method minimal cutset method and failure-mode-and-effect analysis
(FMEA)
In [81] the minimal path method which identifies the shortest paths from a node to
a source and between any two nodes was described The minimal path of the source
node to the load points was obtained by searching for the upstream node from the
load points [82] As the distribution network was radial each node had only one
upstream node The sections out of service after a fault occurred were identified and
separate subsystems were formed The nodes were classified in terms of the effect of
a failure on them Using the node class and amount of load shedding data the
reliability indexes could then be evaluated [81]
Chapter 2 Distribution Automation
Page | 51
FMEA is a classical analytical algorithm for distribution network reliability
evaluation based on the analysis of all the failure modes of each static component
[82] As shown in Fig 2-13 there are four failure modes which are 1) active failure
2) transient failure 3) passive failure and 4) maintenance The active and transient
failures can cause the operation of breakers and hence the healthy components can
be removed from service [75] The passive failures are similar to maintenance outage
and have no effect on the protection system and remaining heathy zone [82]
Fig 2-13 Reliability model for static components
The proposed reliability evaluation method is based on the N-1 criterion and its
computation procedure is demonstrated in Fig 2-14
Normal operation
Active
failure
Transient
failure
Passive
failure
Maintenance
120582119860 120582119879 120582119875 120582119872
120583119860 120583119879 120583119875
120583119872
Chapter 2 Distribution Automation
Page | 52
Start
Read system topology load
data and reliability parameters
Initialise failure number i=1
All failures are considered
Search for the upstream feeder breaker
Search for the upstream and downstream
sectionalising switches and tie-switch
The load points are classified into three categories
Evaluate the reliability of load points
and whole system when fault at line i
Next failure i=i+1
Calculate the reliability of the whole system
End
No
Yes
Fig 2-14 Procedure for reliability evaluation
The system failure events are enumerated first For a failure event the scope of the
failure is determined by searching for the adjacent circuit breaker or tie switch The
isolation zone is then confirmed by the location of the upstream and downstream
sectionalising switches and the appropriate tie-switch Subsequently all the load
points are classified based on their interruption times Finally the consequence of
each contingency and a value for total system reliability are evaluated
When a fault occurs all the load points can be categorised as follows
Healthy points are load points not affected by the fault and refer to upstream
nodes of the upstream circuit breaker or downstream nodes of the
Chapter 2 Distribution Automation
Page | 53
downstream circuit breaker or tie-switch For example when a fault occurs at
L2 in Fig 2-15 LP1 and LP5 are healthy points
Temporary damaged points when the protection systems are in operation
they cause the load points to be interrupted but the load points can be
restored by isolating the faulty area and by using a supply through another
path When a fault occurs at L2 in Fig 2-15 LP2 and LP4 are isolated by
opening the sectionalising switches S1 and S2 LP2 is restored by closing B1
and LP4 is supplied by closing the tie-switch As a result LP2 and LP4 are
temporary damaged points The interruption time is 119879119878 which is the average
switching time after failure
Permanent damaged points are load points that are interrupted by the
operation of protection devices and cannot be restored until the fault is
cleared [82] When a fault occurs at L2 in Fig 2-15 LP3 is the permanent
damaged point The interruption time is 119879119877 which is the average repair time
after failure
Fig 2-15 Sample network
Overall the analytical method which is based on a reliability model of each
component evaluates system reliability by enumeration of all failure states However
the increasing number of devices in a complex system results in an increase in the
quantity of failure states and the complexity of calculation As such the scale of the
network might be limited
210 Multi-objective Optimisation
The aim of this section is to provide fundamental information in order to assess
multi-objective optimisation problems The objectives are conflicting and can be
Chapter 2 Distribution Automation
Page | 54
0
1
converted into three forms which are 1) single objective function 2) single fuzzy
satisfaction objective function and 3) Pareto front
2101 Single Objective Function
The single objective function is generally done by simply aggregating the objectives
with the same dimension and transforming others into constraints [83] It can be
solved by traditionally scalar-valued optimisation techniques However this function
has several limits 1) it results in only one solution 2) the analysis of the objectives
that are converted into constraints is limited
In [64] a sectionalising switch placement strategy was proposed to minimise the
sum of ECOST and sectionalising switch costs The above mentioned objectives
were simply aggregated and calculated in US dollars Other objectives such as the
number of available switches were converted into constraints
2102 Single Fuzzy Satisfaction Objective Function
In the fuzzy domain each variable is associated with a membership function varying
from zero to unity which indicates the satisfaction level of the objective [84] The
higher the membership value is the better the solution is Generally the linear
membership function is formulated as given in (2-22) and is presented in Fig 2-16
120572 =
1 119883 le 119883119898119894119899119883119898119886119909minus119883
119883119898119886119909minus119883119898119894119899119883119898119894119899 lt 119883 lt 119883119898119886119909
0 119883 ge 119883119898119886119909
(2-22)
Fig 2-16 Linear membership function
If 119883 is equal or less than 119883119898119894119899 the membership value is one As 119883 becomes greater
than 119883119898119894119899 the degree of satisfaction decreases This decrease is continued until 119883
reaches 119883119898119886119909 and the membership function becomes zero
120572
119883119898119894119899 119883119898119886119909 119883
Chapter 2 Distribution Automation
Page | 55
The fuzzy-based optimisation procedure is used for handling multiple conflicting
objectives with different dimensions and units [66] The degrees of satisfaction level
can be formulated into a single objective function in three methods which are 1)
weighted aggregation 2) max-min method 3) max-geometric-mean method The
objective is to maximise such degree of satisfaction
Weighted aggregation
In this method the degree of satisfaction level is the weighted aggregation of the
membership values of all objectives [85] Thus the final compromise solution for
multi-objective functions is described as follows
119872119886119909 119869 = 12059611205721 + 12059621205722 + ⋯ + 120596119899120572119899 (2-23)
where 120596119894 is the constant weighting factor for each of the membership values and
they should meet the condition sum 120596119894119894 = 1
The weighting factors are decided by the decision makers and a higher weighting
factor indicates that this parameter is more important However the disadvantage of
this technique is that DNOs may have difficulty in obtaining enough information
about the relative importance of each objective to determine the trade-offs among the
selected objectives
Saffar etc [60] have developed a network reconfiguration technique to reduce power
loss and equal load balancing of feeders As these objectives had different
dimensions and units they were transformed into a single objective function with
fuzzy variables A set of compromised solutions was obtained by varying the
weighting factors of each element
Max-min method
In this technique the degree of overall satisfaction is the minimal value among the
membership values of all objectives [85] Thus the final compromise solution for
multi-objective functions is described as follows
119872119886119909 119869 = min 1205721 1205722 hellip 120572119899 (2-24)
The solution is optimised by maximising the overall satisfaction of all objectives
However the max-min method might not predict the best compromise solution
Chapter 2 Distribution Automation
Page | 56
because even if one membership value is weak it does not necessarily mean that
other membership values are also weak [86]
The max-min principle was adopted in [84] for the multi-objective optimisation with
fuzzy sets The aim was to minimise real power loss and the absolute value of branch
current as well as to minimise nodes voltage deviation Finally an optimal solution
was obtained which indicated a concession among all the objectives The results also
revealed that although network reconfiguration resulted in a significant reduction in
total system loss the loss allocated to a certain number of customers increased [84]
It is important to change the tariff structure for these consumers so that they are not
obliged to pay more for the increase in loss allocation as a result of network
reconfiguration
Max-geometric-mean method
Like the above max-min method the geometric-mean function is also used to
evaluate the degree of overall fuzzy satisfaction but in different forms The objective
is computed as follows
119872119886119909 119869 = (1205721 ∙ 1205722 ∙ hellip ∙ 120572119873)1 119899frasl (2-25)
In [86] firstly all the variables (real power loss branch current loading maximum
voltage deviation and switching numbers) were assigned by truncated sinusoidal
fuzzy membership functions The overall degree of satisfaction was the geometric
mean of all fuzzy membership values [86] The best compromise solution was then
obtained by maximising this satisfaction level
2103 Multi-objective Formulation in the Pareto Optimality
Framework
All the studies mentioned above are solved by a single-objective optimisation
technique In contrast a Pareto optimal solution is provided for the treatment of
multi-objective problems This produces a range of solutions rather than just one
which represents a compromise that goes some way to optimise objective functions
[87] [88] The Pareto optimal solution is based on a dominance concept The
solution 119883 dominates 119884 means that 119865(119883) is no worse than 119865(119884) for all objectives
Chapter 2 Distribution Automation
Page | 57
and there is at least one objective for which 119865(119883) is better than 119865(119884) as expressed in
(2-26) and (2-27) The following conditions should be satisfied concurrently
forall 119894 = 12 hellip 119873119900119887119895 119865119894(119883) le 119865119894(119884) (2-26)
exist 119894 = 12 hellip 119873119900119887119895 119865119894(119883) lt 119865119894(119884) (2-27)
where 119873119900119887119895 is the number of objective functions
If a solution 119883 and solution 119884 do not dominate each other these two solutions are
incomparable For example the objective is to minimise 1198911 and 1198912 and there are
three solutions whose objective function values are 119865(119883) = (24) 119865(119884) = (44)
119865(119885) = (52) It can be seen that 119883 dominates 119884 as 1198911(119883) lt 1198911(119884) and 1198912(119883) le
1198912(119884) And the solution 119883 and 119885 are incomparable because 1198911(119883) lt 1198911(119885) and
1198912(119883) gt 1198912(119885) Similarly solutions 119884 and 119885 are also incomparable
A solution belongs to Pareto optimal solutions if there is no other solution that can
improve at least one objective without degradation of any other objectives [83] In
other words there is no another solution that dominates it The Pareto set is the set of
all non-dominated solutions and its corresponding objective values constitute the
Pareto front [88] The goal of the multi-objective optimisation is to select the most
suitable one from the Pareto set for implementation according to decision makersrsquo
preferences
In [45] the study proposed a Pareto-based multi-objective DNR method using a
discrete PSO algorithm It aims to reduce power loss voltage deviations and the
number of switching operations Firstly each objective function was optimised
separately and the best results were found All objectives were then optimised
simultaneously and the Pareto optimal set was obtained The best results for each
objective were included in the Pareto front and the corresponding solutions were
stored in the Pareto optimal set Finally the best compromise solutions among the
multiple objectives were derived Different scenarios were modelled by assigning
different weighting factors based on the preferences of the decision makers
Chapter 2 Distribution Automation
Page | 58
211 Summary
Generally most distribution networks are designed in closed loop but are operated
radially There are three typical distribution network topologies which are the radial
system primary loop and link arrangement The descriptions of three switchgears ie
recloser sectionalising switch and tie-switch are also included in this chapter
TEO DNR and SSP are the three main parts of DA In this chapter there are several
reviews of these techniques TEO which refers to optimum selection of which
transformers need to supply each feeder can not only reduce loss but also reduce
total costs and improve network reliability DNR is defined as a process that
involves changing the network topology under normal and abnormal operating
conditions by relocation of tie-switches [13] [14] The methodologies from a branch
and bound optimisation method to modern heuristic optimisation algorithms
designed for loss reduction are reviewed In addition DNR is also able to improve
service quality and efficiency at the same time The placement of sectionalising
switches refers to the installation of new switches and relocation of existing switches
It is used for distribution network reliability improvement and service restoration
However so far few studies have been carried out that consider the combination of
the above three techniques
The major challenge facing DNOs is how to distribute the power in a low-cost
reliable and efficient way Thus the assessments of transformer loss feeder loss and
reliability indices are proposed in Section 27-29 The integrated transformer loss
consists of not only real power loss but also reactive power loss The transformer
quantities such as no-load loss and full-load loss are obtained from open-circuit test
and short-circuit test The distribution network power loss is achieved through power
flow study The reliability indices can be calculated through reliability evaluation
methods namely simulation methods and analytical methods The most common one
is FMEA which is also used for reliability evaluation in this thesis Although there
are many research projects that consider feeder loss and reliability simultaneously
few consider transformer loss and feeder loss at the same time
Three objective functions for optimising multiple conflicting objectives are 1) single
objective function 2) single fuzzy satisfaction objective function and 3) Pareto front
Chapter 2 Distribution Automation
Page | 59
The single objective function is generally done by simply aggregating some
objectives and transforming others into constraints In the fuzzy objective function
each variable is associated with a membership function and then aggregated into a
single objective function [84] The first two functions only obtain a single solution
However Pareto optimal solutions can obtain a set of non-dominated solutions
rather than one which represents a compromise that goes some way to optimising
objective functions In this thesis all three objectives functions will be studied and
results will be presented in the following chapters
This thesis will deal with single objective and multiple objectives through different
methods of DA based on various algorithms The next chapter will introduce the
Monte Carlo method and modern heuristic optimisation algorithms such as ant
colony optimisation (ACO) and artificial immune systems (AIS)
Page | 60
CHAPTER 3
OPTIMISATION TECHNIQUES
31 Introduction
Mathematically distribution automation (DA) is categorised as a discrete non-linear
constrained and combinational optimisation problem since the problem is to
determine the status of all transformers and switches In general the optimisation
techniques for assessment of this problem can be divided into two large groups 1)
simulation methods and 2) analytical methods
The Monte Carlo method is a typical example of a simulation method which will be
discussed in Section 32 in detail It can handle uncertainties and solve the
probabilistic optimal power flow [89] In a complex system with hundreds of
switches although the Monte Carlo method can find the best solution with a high
degree of accuracy it is generally not practical to carry out an extensive search of all
possible configurations as it consumes a great deal of CPU time and memory [88]
Therefore most DA problems are solved by analytical methods
The analytical methods can obtain a solution of good quality or even the global
optimal solution of the problem [13] It can be classified into four types 1) branch
and bound 2) optimal flow pattern 3) branch exchange and 4) metaheuristic
techniques Recently the last type has become the most popular
Chapter 3 Optimisation Techniques
Page | 61
The metaheuristic method is a process that attempts to find a solution to the problem
beginning from a starting point or a set of starting points and exploring all the search
space [13] It also includes a strategy to explore the search space and provide an
escape from the local optimal This process does not guarantee a globally optimal
solution but can offer near optimal solutions with a reasonable computational effort
This includes genetic algorithm (GA) ant colony optimisation (ACO) particle
swarm optimisation (PSO) and artificial immune systems (AIS) Different
metaheuristic techniques use different strategies that pass through and explore the
search space [13]
As for the remainder of the chapter the Monte Carlo method is discussed in Section
32 Section 33 presents the proposed ACO algorithm Section 34 discusses a new
hybrid AIS-ACO framework and the summary of this chapter is provided in Section
35
32 Monte Carlo Method
The Monte Carlo method is a simulation algorithm that can be carried out many
times to produce numerical samples that accurately reflect the probability
distribution of the real results [90] [91] This method is always used to solve power
system issues involving uncertain parameters [92] The uncertainties are allocated
randomly and each simulation is operated numerous times In theory the more
simulations are running the less deviation error between actual mean value and
sample mean value Therefore it is important to determine the overall running times
of the Monte Carlo simulation The convergence or stopping criteria is used to
determine the simulation times required to obtain acceptable accurate results
The confidence interval acts as a good estimate of the unknown parameters The
probability that the true parameter remains in the confidence interval is calculated as
follows [93]
119862 = 119875(119883 minus 119871 le 120583 le 119883 + 119871) = int 119866(119883)119889119909119883+119871
119883minus119871 (3-1)
119871 = 119911lowast 120590
radic119899 (3-2)
Chapter 3 Optimisation Techniques
Page | 62
where 119862 is the degree of confidence is the estimated mean value 119871 is the
confidence interval which provides an estimate range of values which probably
contains an unknown population parameter 120583 is the true population mean value
119866(119883) is the Gaussian distribution 120590 is the sample standard deviation and 119899 is the
number of samples the estimation of 119911lowast is based on the degree of confidence 119862 as
presented in Table 3-1 The most common 119911lowast is 196 and the corresponding 119862 is
095
Table 3-1 Relationship of 119911lowast and 119862
119862 09 095 099 0999
119911lowast 1645 1960 2576 3291
The required number of samples could be expressed as
119899 = (119911lowast120590
119871)2 (3-3)
There are several methods used to determine the sample size and to obtain results
with acceptable accuracy One is by predefining the maximum sample size 119873 when
119899 reaches 119873 the simulation is stopped Another one is by using the degree of
confidence 119862 The confidence interval 119871 is calculated and compared with the
predefined 119871 for each sample and the simulation reaches the stopping criteria when
the confidence interval is less than the critical value
33 Ant Colony Optimisation
The ant colony optimisation method is one of the metaheuristic techniques that has
been employed for the solution of combinational optimisation problems in recent
years [60] The ant colony system (ACS) simulates the behaviour of real ants [94]
[95] The moving paths of artificial ants construct the candidate solutions to a
problem [96] The ants communicate with other ants by a chemical substance called
pheromones [97] Originally all the ants start from their nest and search for their
food in a random manner When the food source is found the ants leave a chemical
Chapter 3 Optimisation Techniques
Page | 63
substance trail on the way home The pheromone deposited by the ants is used as the
primary guide function for the other ants The pheromones will then evaporate after a
period of time As all of the ants travel approximately at the same speed the shortest
path has the largest probability to contain more pheromones because more ants
choose this one The ants tend to follow the path that has more pheromones than
others After a brief period the shortest path with the most intensity of pheromones
could attract more and more ants providing feedback to the system that promotes the
use of best paths [98] Fig 3-1 represents the behaviours of real ants [69]
Fig 3-1 Example of ant colony system [69]
As shown in Fig 3-1 (a) all the ants are travelling in the same path which connects
point A and point B by a straight line The environment is changed due to the
occurrence of an obstacle in Fig 3-1 (b) and (c) At first all the ants choose the left
or right path randomly because they have no guide It is assumed that they move
through path C or D with the same probability Later on the ants that choose path C
will move faster than that choose path D As a result the pheromones deposited on
path C accumulate faster than those on the path D and this attracts more ants to
choose path C Finally all the ants tend to choose the shortest path (path C) as this
contains the most pheromones
The flowchart of ACO algorithm is shown in Fig 3-2 and the main stages of the
algorithm are presented as follows [69] [94] [95] [97] [98]
Initialisation In this stage the trail intensity on each edge in the search
space is initialised to a constant positive value and all the ants are located in
Chapter 3 Optimisation Techniques
Page | 64
the nest
Ant Dispatch In this step each ant begins its tour at the starting point and
chooses the next node to move to according to a probabilistic selection rule
which involves the intensity of pheromones deposited on each node by other
ants [88] [99] The ants prefer to choose the path with a higher pheromones
This process is repeated until all the ants have reached the food source
Quality Function Evaluation After all the ants have completed a tour the
relevant quality function of the optimisation problem is calculated to evaluate
the performance of each ant If any constraint is violated the configuration is
discarded Otherwise the objective function is evaluated
Trail Intensity Update There are two pheromone updating rules applied in
this step One is called the global pheromone update It accumulates the
pheromone values on the high-quality solution path to improve convergence
However the pheromone intensity of each edge evaporates over time due to
another rule called the local pheromone update This update is used to
enlarge the search space and to avoid premature convergence for local
minima Ants travelling between two nodes update the relevant pheromone
intensity in the corresponding edge
Convergence Determination This process is operated until the maximum
iteration number is reached or all the ants choose the same path between their
home colony and food source
Chapter 3 Optimisation Techniques
Page | 65
Start
Set Iteration n=1
Maximum iteration
reached
End
No
Yes
Initialise the parameters for ACO algorithm
searching space and build graph of the tours
Dispatch ants based on the
amount of pheromones on edges
Quality function evaluation
Trail intensity update
Record the high quality solutions of this
iteration and empty all location lists
n=n+1
Fig 3-2 Flowchart of the ant colony algorithm
The above procedure should be modified to a computational procedure to solve
different optimisation problems and this is discussed in the following chapters
Several factors need to be taken into account when designing an ACO algorithm
such as search space transition probability etc
34 AIS-ACO Hybrid Algorithm
341 Artificial Immune Systems
The immune system acts as a defensive barrier to recognise and eliminate foreign
antigens ie bacteria virus etc B lymphocytes are the main immune cells in the
biological immune system and originate in the bone marrow Being exposed to an
Chapter 3 Optimisation Techniques
Page | 66
antigen a specific antibody is produced on the surfaces of B cells and an immune
response is elicited to make antibodies recognise and bind the antigen [88] [100]
Those B cells whose antibodies best match the antigen are activated and cloned
several times [88] This process is called cloning To identify the most suitable
antibodies for the antigen it is necessary to cause the antibody and the antigen to
interact more closely with each other This is achieved through a process call
hypermutation in which random changes are introduced into the genes of the cloned
B cells [88] One such change might lead to an increase or decrease in the closeness
between antibody and antigen [88] The new B cells can only survive if they are
closely related to the antigen and therefore the B cells that are closely related are
then chosen to enter the pool of memory cells [100] These cloning hypermutation
and selection processes are called the clonal selection principle [101] By repeating
this principle a number of times the immune system learns to respond more
efficiently for the same antigen
Several computational models of the AIS have been developed recently as the
immune system is an adaptive learning system that has the following specifications
learning memory recognition of foreigners and pattern recognition [102]
342 Proposed AIS-ACO Hybrid Algorithm
The proposed AIS-ACO hybrid algorithm combines the advantages of AIS and ACO
The hypermutation developed from the AIS is used as a random operator by
adopting random changes to perturb a solution and hence to enlarge the search space
However the pheromones provided by the ACO can store information about the
quality of solution components for improving the objective functions [88] In
addition the information obtained from pheromone updating guides the algorithm in
its search and improves the convergence rate [88]
The limitation of ACO is that the algorithm can easily fall into a local optimum
which might be due to an insufficient range of candidate solutions This can be made
up by the random changes of solutions in AIS through hypermutation Also the
weakness of the global searching ability in AIS is improved by the pheromone tables
in ACO Thus the new hybrid AIS-ACO framework based on the pheromone-based
hypermutation method has better diversity and convergence in comparison with
either the AIS or ACO algorithms
Chapter 3 Optimisation Techniques
Page | 67
Start
Cloning
Maximum iteration
reached
End
No
Yes
Initialise and set iteration number n=1
Hypermutation
Fitness evaluation
Non-dominated solutions extraction
Pheromone updating
n=n+1
Record the Pareto front and
Pareto optimal solutions
In this thesis the AIS-ACO hybrid approach is used to generate a set of non-
dominated solutions The antigen is the multi-objective function and the antibody is
the solution to the problem The affinity between the antibody and the antigen is the
Pareto dominance among solutions which indicates the quality of the solution [88]
All the non-dominated solutions experience cloning hypermutation and selection
until the maximum number of iterations is reached The flowchart of the AIS-ACO
algorithm for Pareto optimality is presented in Fig 3-3
Fig 3-3 Flowchart of the AIS-ACO algorithm
Chapter 3 Optimisation Techniques
Page | 68
The key parts of the algorithm are explained as follows
Initialisation At the beginning of this algorithm a set of initial solutions is
generated These solutions should meet the condition of constraints The
information related to each objective is represented by an individual
pheromone table Each pheromone value represents the probability of
selection of the corresponding edge in the network model [88] All
pheromone values are initially set as the same value
Cloning The number of clones for each non-dominated solution should be
the same as the number of objectives and also as the number of pheromone
tables [88]
Hypermutation The selection of an edge in each cloned solution for
hypermutation is dependent on its pheromone values [88] A higher
pheromone value of a cell in the table indicates that the corresponding edge
in the network is more likely to be selected
Non-dominated solutions extraction This is the process of selecting non-
dominated solutions according to their affinity value [99] All the solutions
are compared as presented in Section 2103 and all the non-dominated
solutions are then extracted for the next iteration
Pheromone updating The aim of this stage is to accumulate the pheromone
values on the edges that belong to a part of the non-dominated solutions and
this is called the global pheromone update However the pheromone
intensity of all edges will evaporate over time by the local pheromone update
This update is used to explore the entire search space
Termination This process is operated until the maximum iteration number
is reached The set of final non-dominated solutions is called the Pareto set
which is used to solve the problem [88]
35 Summary
This chapter introduces the techniques for assessment of mono-objectivemulti-
objective optimisation problems The optimisation techniques are categorised into
two groups simulation methods and analytical methods
Chapter 3 Optimisation Techniques
Page | 69
The Monte Carlo method is a typical simulation technique and is generally used to
handle uncertain parameters It can find the best solution with a high degree of
accuracy but requires a considerable amount of CPU time and memory The
application of this methodology is discussed in Chapter 4 In that chapter an
efficient methodology based on the Monte Carlo Method is proposed for finding
transformer economic operation modes and optimal tie-switch placement strategies
to minimise transformer loss
The ACO algorithm is one of the metaheuristic techniques designed for assessment
of distribution automation (DA) problems It simulates the behaviour of artificial
ants with positive feedback and distributed computation The positive feedback
enhances the search speed in order to find the global solution and the distributed
computation explores the search space The ACO algorithm is able to find the global
solution in a reasonable computation time It is used for either loss reduction or
reliability improvement as discussed in Chapter 5-7 In addition a new multi-
objective ACO (MOACO) algorithm for assessment of multi-objective DNR
problems in terms of Pareto optimality is provided in Chapter 8
The AIS-ACO hybrid algorithm is a combination of AIS and ACO Hypermutation
is used in AIS as a random operator by using random changes to perturb a solution to
maintain the diversity of the solutions avoiding premature convergence for local
minima The pheromone tables used in the ACO are used to direct the algorithm
towards high quality solutions [88] The AIS-ACO hybrid algorithm is always used
for assessing the DA problem in terms of multiple objectives optimisation in order
to obtain a set of non-dominated solutions In addition the advantages of the AIS-
ACO algorithm over the MOACO algorithm for the assessment of multi-objective
optimisation problems are also discussed in Chapter 8
Page | 70
CHAPTER 4
TRANSFORMER ECONOMIC
OPERATION amp DISTRIBUTION
NETWORK RECONFIGURATION FOR
TRANSFORMER LOSS REDUCTION
41 Introduction
The electrical power generation transmission and distribution companies are not
only energy producers but also significant power consumers Energy loss occurs in
the process of power transfer and takes place in all electrical equipment including
generators power lines and transformers The large number and power capacity of
transformers used in a transformer and distribution network means transformer loss
is a significant component in energy loss The lifetime cost of energy loss in a
transformer is significant especially when one considers rising electricity demand
and the cost of the energy supplied For this reason it is important to tackle the
causes of transformer loss and the problems which then ensue so that energy
consumption can be reduced To support this statement several research projects
that have focused on transformer loss reduction are discussed in Section 242
Chapter 4 Transformer Economic Operation amp Distribution Network
Reconfiguration for Transformer Loss Reduction
Page | 71
An efficient methodology based on the Monte Carlo Method for the 3311 kV
transformer loss reduction with consideration of the voltage issues observed on a
distribution network is proposed in this chapter For a substation with two
transformers there are three operation modes that can occur 1) single transformer in
separate operation 2) two transformers in parallel operation 3) transformer
economic operation (TEO) as mentioned in Section 24 With regard to the load
models which are also discussed in this chapter a database containing numerous
domestic electricity demand profiles is imported into MATLAB to work as the
profile generators A Monte Carlo simulation platform is established by combining
the residential demand profiles with a 3311 kV distribution network model built in
OpenDSS Based on this platform the impacts of three operation modes of
transformers on transformer loss minimisation are investigated and compared
In addition an enumeration approach used for the optimum relocation of tie-switches
in a linked 11 kV distribution network is also suggested The process that involves
changing the distribution network topology by relocation of tie-switches is called
distribution network reconfiguration (DNR) [13] [14] The control centre can
change the location of tie-switches and the transformer operation modes (TOMs) in
each substation based on load data and simulated power loss from the test system at
each time interval The proposed approach is applied to the test system and the
effectiveness of an optimal planning strategy using TEO and DNR to achieve
minimum transformer loss is demonstrated through the results obtained
The remainder of this chapter is structured as follows Section 42 explains the load
models Section 43 describes the mathematical formulation of transformer loss
Section 44 analyses the methodology used to minimise transformer loss whilst
maintaining satisfactory voltages and the case studies and the results are presented
and discussed in Section 45 Finally the main conclusions are summarised in
Section 46
Chapter 4 Transformer Economic Operation amp Distribution Network
Reconfiguration for Transformer Loss Reduction
Page | 72
42 Load Model
In order to access the performance of the distribution feeders with different operation
modes of transformers in the substation the time-series behaviour of loads has to be
modelled
The value of the load associated with domestic electricity demand customers has
been obtained from the research described in [19] this can produce a random 1-min
resolution model for UK households There are six steps for creating a domestic
electricity demand model as shown in Fig 4-1 Table 4-1 presents the proportion of
household sizes based on UK statistics [103]
Fig 4-1 Procedure of domestic electricity demand profile generation
Table 4-1 Household size by number of people in household as a proportion [103]
Number of people
in household
1 2 3 4 ge5
Percentage () 3058 341 1557 1288 686
A pool of 10000 different load profiles covering 24 hours in a typical February
weekday are generated by this model For computation reasons the 1440 1-min
time-step load profiles are integrated as 144 10-min resolution profiles in this study
Specify the number of residents in the house from 1 to 5
Specify either a weekday or
weekend
Select the month of the year from 1 to
12
Random allocate appliances to the
dwelling
Run the active occupancy model
Run the electricity demand simulation
Chapter 4 Transformer Economic Operation amp Distribution Network
Reconfiguration for Transformer Loss Reduction
Page | 73
(active power is recorded for each minute and then averaged at intervals of 10
minutes) The power factors of all the loads are set to 095
43 Problem Formulation
The objective of this study is to minimise transformer loss through TEO and optimal
DNR The energy loss of the transformer is related to active power However as a
transformer draws reactive power (it takes current) it causes real power loss in the
network The integrated power loss refers to the sum of active power loss of the
transformer itself and the increased active power loss contributed by reactive power
loss of the transformer [73] The mathematical formulation can be expressed as
follows
Minimise 119891 = 1198800
2119875119885119874119862 +1205732
11988002 119875119885119878119862 119905119903119886119899119904119891119900119903119898119890119903 119894119899 119904119894119899119892119897119890 119900119901119890119903119886119905119894119900119899
211988002119875119885119874119862 +
1
2
1205732
11988002 119875119885119878119862 119905119903119886119899119904119891119900119903119898119890119903119904 119894119899 119901119886119903119886119897119897119890119897 119900119901119890119903119886119905119894119900119899
(4-1)
where 119875119885119874119862 and 119875119885119878119862 are the integrated no-load loss (kW) and the full-load loss (kW)
120573 =119878119871
119878119873 represents the transformer load factor S is the transformer actual loading
(kVA) 119878119873 is the transformer rated capacity (kVA) 1198800 is the operational voltage of
the transformer secondary side in per unit
44 Methodology
In this study there are two methodologies used for transformer loss reduction which
are called TEO and DNR
441 Transformer Economic Operation
In this section a Monte Carlo simulation platform for three TOMs comparison is
established as shown in Fig 4-2 and the flowchart of the transformer loss assessment
is presented in Fig 4-3
Chapter 4 Transformer Economic Operation amp Distribution Network
Reconfiguration for Transformer Loss Reduction
Page | 74
Fig 4-2 Monte Carlo simulation platform for three transformer operation modes comparison
Firstly a pool of 10000 10-min daily domestic electricity demand profiles is
randomly generated by the profile generators in MATLAB Following this each
node in the feeders from the system is assigned with residential demand profiles
from the pool using the Monte Carlo Method Theses profiles and one of the TOMs
are then imported into the distribution network model built in OpenDSS After this a
sequential load flow calculation is performed and the simulation results are returned
including voltage profiles and transformer losses to MATLAB The obtained
results are then analysed and compared with the system constraints for each time
step In this study for each TOM the calculation is set to be repeated 10000 times
in order to satisfy the convergence criteria When the losses of all TOMs are
calculated the minimum transformer loss and its associated operation mode are
obtained
Profile
generator of
domestic
electricity
demand profiles
Transformer
operation
modes
MATLAB
Distribution
network
model built
in OpenDSS
Analyse and
compare
simulation
results in
MATLAB
Load flow calculation
Chapter 4 Transformer Economic Operation amp Distribution Network
Reconfiguration for Transformer Loss Reduction
Page | 75
Start
Monte Carlo trail number N=1
All transformer operation
modes considered
End
No
Yes
Select demand profiles to each
customer randomly
Select transformer operation
mode
Sequentially run power flow
calculation for 144 10-minute time step
Record results
Change
transformer
operation
mode
N=N+1
Maximum iteration reached
Minimum transformer loss and its associated
transformer operation mode are obtained
No
Yes
Load and aggregate the domestic
electricity demand profiles pool
(144 10-minute time steps)
Fig 4-3 Flowchart of transformer loss assessment
Chapter 4 Transformer Economic Operation amp Distribution Network
Reconfiguration for Transformer Loss Reduction
Page | 76
442 Distribution Network Reconfiguration
Reconfiguration of radial distribution system is achieved by local control of tie-
switches located in linked feeders The Monte Carlo simulation platform through
DNR is presented in Fig 4-4
Fig 4-4 Monte Carlo simulation platform for distribution network reconfiguration
In the proposed strategy the tie-switch status is modified by the control centre and
the detailed control algorithm is discussed below
Step 1 Random load profiles are first selected
Step 2 When the load profiles have been imported into the network model a
sequential load flow calculation is performed to calculate and compare the
transformer loss under different network configurations (different tie-switches
location) at each time interval
Step 3 Minimum transformer loss and its associated network configuration are
obtained
Step 4 Location of tie-switches based on minimum transformer loss over a whole
day is recorded
Step 5 Optimal DNR strategy is obtained
Profile
generator of
domestic
electricity
demand profiles
Tie-switch
status
MATLAB
Distribution
network
model built
in OpenDSS
Analyse and
compare
simulation
results in
MATLAB
Load flow calculation
Chapter 4 Transformer Economic Operation amp Distribution Network
Reconfiguration for Transformer Loss Reduction
Page | 77
45 Application Studies
To demonstrate the impact of TOMs and DNR on transformer loss the proposed
methodologies are applied to two test networks Several scenarios are tested and the
results are analysed and reported
451 Test Case 1
The single line diagram of the network shown in Fig 4-5 is developed from the UK
generic distribution network [104] The network model is built to incorporate a 3311
kV substation supplying the downstream loads in the OpenDSS software
environment The two transformers have the same specifications and their
characteristics are presented in Table 4-2 The corresponding TCLF is calculated as
5244 The 11 kV network is represented by four outgoing feeders from a single
busbar For computation reasons three of the feeders are simplified lumped loads
whilst the 4th
feeder is modelled in detail The 4th
11 kV feeder consists of eight
nodes which represents a small system with a total of 252 domestic single phase
house loads connected on each node A Monte Carlo simulation approach is
implemented to select these load profiles randomly from a pool of domestic
electricity demand profiles Each house in the 4th
feeder is then assigned with a
residential demand profile The loads in the other three feeders are then lumped with
the same daily profile of the 4th
feeder All the values of the network components are
based on a broad collection from [104] [105] and are recorded in Appendix A1
In this test a comparison of the three TOM methods for transformer loss
minimisation is provided A time-series load flow algorithm is implemented to
quantify the changes in feeder voltage and transformer loss in the previous described
3311 kV UK distribution network for different TOMs In this test three scenarios
are studied and summarised as follows
Scenario 1 Single transformer in separate operation
Scenario 2 Two transformers in parallel operation
Scenario 3 Transformer economic operation in this mode if the transformer load
factor is less than TCLF only one transformer remains in service if the transformer
load factor is higher than TCLF two transformers are operated in parallel
Chapter 4 Transformer Economic Operation amp Distribution Network
Reconfiguration for Transformer Loss Reduction
Page | 78
A
A
A
A
B
B
B
B
Load1Load2Load3Load4_1
Load4_2
Load4_3
Load4_4
Load4_5
Load4_6
Load4_7
Load4_8
75 MVA
33 kV
11 kV
33 kV
Voltage
Source
75 MVA
Fig 4-5 Generic distribution network topology
Table 4-2 Parameters of a typical 3311 kV two-winding transformer [106]
Sub-
sector
Transf
Rating
(kVA)
Conn Tapping
Range
Load
Losses
at
75
(kW)
No-
Load
Losses
(kW)
Impedance voltage
at rated current for
the principle
tapping
()
Reference
standard
Urban 7500 YY0 plusmn75
6 steps of 25
Each
50
75
835 BS 171 amp
IEC 60076
1) Test 1-1 Base Case
The simulation results of transformer load factor variation are shown in Fig 4-6 and
the transformer loss variation curves are presented in Fig 4-7 It is observed that the
transformer loss in Scenario 3 is the same as in Scenario 1 between 000 to 630 and
Chapter 4 Transformer Economic Operation amp Distribution Network
Reconfiguration for Transformer Loss Reduction
Page | 79
0
10
20
30
40
50
60
70
80
90
100
0 2 4 6 8 10 12 14 16 18 20 22
Tran
sfo
rme
r Lo
ad F
acto
r
Time (h)
0
10
20
30
40
50
60
70
0 2 4 6 8 10 12 14 16 18 20 22
Tran
sfo
rme
r Lo
sse
s (k
W)
Time (h)
0
10
20
30
40
50
60
70
0 2 4 6 8 10 12 14 16 18 20 22
Tran
sfo
rme
r Lo
sse
s (k
W)
Time (h)
the same in Scenario 2 from 1800 to 2200 With the introduction of Scenario 3 the
minimum loss is around 9 kW at 000 which is below the 18 kW of Scenario 2 The
maximum loss of Scenario 3 is nearly 40 kW at 1900 which is far below the 60 kW
of Scenario 1
Fig 4-6 Transformer load factor variation
(a) Scenario 1
(b) Scenario 2
Chapter 4 Transformer Economic Operation amp Distribution Network
Reconfiguration for Transformer Loss Reduction
Page | 80
0
10
20
30
40
50
60
70
0 2 4 6 8 10 12 14 16 18 20 22
Tran
sfo
rme
r Lo
sse
s (k
W)
Time (h)
(c) Scenario 3
Fig 4-7 Transformer loss variations in different scenarios
The mean values of 3311 kV transformer energy loss during one day under different
scenarios are presented in Table 4-3 As shown in Fig 4-6 the average transformer
load factor during a whole day is slightly below the TCLF (5244 in this test) This
situation is more suitable for a single transformer than two transformers The loss in
Scenario 3 reaches the lowest value and results in a reduction of 1133 and 1441
in comparison with Scenario 1 and Scenario 2
Table 4-3 Daily transformer loss in different scenarios
Scenario 1 Scenario 2 Scenario 3
Transformer losses (kWh) 53982 55922 47865
According to the EN50160 standard [7] under normal conditions at least 95 of the
10-min average mean rms voltage magnitude in the 11 kV electricity distribution
network should be within the range 09 pu to 11 pu over one week In other words
the 95th
percentile voltage profile is compared with the allowed voltage range to
check the networkrsquos reliability
The mean and 95th
percentile voltage profiles at each node in the fourth feeder are
presented in Fig 4-8 It can be seen that the voltage level at each node can change
considerably after the scenario changes It also appears that the nodes in Scenario 1
experience the most severe voltage drop in comparison with the other two scenarios
The worst 95 voltage value of the node lsquoLoad4_8rsquo at the end of the studied feeder
in Scenario 1 is around 098 pu which is not as satisfactory as the results of 0987 pu
and 0984 pu observed in Scenario 2 and Scenario 3
Chapter 4 Transformer Economic Operation amp Distribution Network
Reconfiguration for Transformer Loss Reduction
Page | 81
0976
0978
098
0982
0984
0986
0988
099
0992
Load4_1 Load4_2 Load4_3 Load4_4 Load4_5 Load4_6 Load4_7 Load4_8
Vo
ltag
e (
pu
)
Scenario1
Scenario2
Scenario3
0974
0976
0978
098
0982
0984
0986
0988
099
Load4_1 Load4_2 Load4_3 Load4_4 Load4_5 Load4_6 Load4_7 Load4_8
Vo
ltag
e (
pu
)
Scenario1
Scenario2
Scenario3
(a) Mean value
(b) 95th
value
Fig 4-8 11 kV 4th
feeder voltage profiles in different scenarios
To show in detail the voltage profiles affected by different TOMs the load at the
start of the 4th
feeder lsquoLoad4_1rsquo and the end one lsquoLoad4_8rsquo have been selected
Since the Monte Carlo method produces many loss and voltage values it is
preferable to present the averages of all these values and their deviations
As shown in the charts from Fig 4-9 and Fig 4-10 the voltage drops severely from
1800 to 2000 which is also the maximum daily demand period It also appears that
the voltage profile in Scenario 3 is the same as in Scenario 1 between 000 to 630
and the same as in Scenario 2 from 1800 to 2200 With the introduction of Scenario
Chapter 4 Transformer Economic Operation amp Distribution Network
Reconfiguration for Transformer Loss Reduction
Page | 82
088
09
092
094
096
098
1
0 2 4 6 8 10 12 14 16 18 20 22
Bu
s V
olt
age
(p
u)
Time (h)
088
09
092
094
096
098
1
0 2 4 6 8 10 12 14 16 18 20 22
Bu
s V
olt
age
(p
u)
Time (h)
088
09
092
094
096
098
1
0 2 4 6 8 10 12 14 16 18 20 22
Bu
s V
olt
age
(p
u)
Time (h)
3 the lowest voltage of lsquoLoad4_8rsquo is around 097 pu which is significantly above
the lower limit 090 pu
(a) Scenario 1
(b) Scenario 2
(c) Scenario 3
Fig 4-9 Voltage profiles of Load 4_1 in different scenarios
Lower Limit
Lower Limit
Lower Limit
Chapter 4 Transformer Economic Operation amp Distribution Network
Reconfiguration for Transformer Loss Reduction
Page | 83
088
09
092
094
096
098
1
0 2 4 6 8 10 12 14 16 18 20 22
Bu
s V
olt
age
(p
u)
Time (h)
088
09
092
094
096
098
1
0 2 4 6 8 10 12 14 16 18 20 22
Bu
s V
olt
age
(p
u)
Time (h)
088
09
092
094
096
098
1
0 2 4 6 8 10 12 14 16 18 20 22
Bu
s V
olt
age
(p
u)
Time (h)
(a) Scenario 1
(b) Scenario 2
(c) Scenario 3
Fig 4-10 Voltage profiles of Load 4_8 in different scenarios
Lower Limit
Lower Limit
Lower Limit
Chapter 4 Transformer Economic Operation amp Distribution Network
Reconfiguration for Transformer Loss Reduction
Page | 84
0976
0978
098
0982
0984
0986
0988
099
0992
Load4_1 Load4_2 Load4_3 Load4_4 Load4_5 Load4_6 Load4_7 Load4_8
0 25
5244 75
100
As most people are sleeping late at night and the transformer load factor is less than
the TCLF transformers are in individual operation mode When most people are at
home again from 1800 the transformer load factor increases beyond the TCLF As a
result the voltage profiles are improved when transformers are operated in parallel
In conclusion when the transformer load factor is less than the TCLF transformers
in a separate service result in less loss but more voltage dips however transformers
operating in parallel cause lower voltage drops but more loss When the transformer
load factor is higher than the TCLF transformers in parallel operation cause less loss
and lower voltage drops As a result based on the economic operation theory the
transformer in Scenario 3 significantly reduces transformer loss and maintains the
voltages at a satisfactory level
2) Test 1-2 TCLF Sensitivity Analysis
In this test the value of TCLF used to distinguish whether the transformer should be
in separate or parallel operation is discussed The complete process presented
previously is carried out again but takes into account the effect of different critical
values 0 25 5244 75 and 100
Fig 4-11 shows the effect on the mean voltage magnitudes of various TCLFs The
results indicate that the voltage profile is closely related to the TCLF and the TCLF
should be decreased to increase the region in which transformers operate in parallel
This will improve the voltage profiles
Fig 4-11 11 kV 4th
feeder mean voltage profile of various TCLFs
Chapter 4 Transformer Economic Operation amp Distribution Network
Reconfiguration for Transformer Loss Reduction
Page | 85
Table 4-4 describes the effect on the transformer loss when TCLF is changed It
reaches the lowest value when TCLF is 5244 If the TCLF is decreased or
increased above this value the loss increases Overall the TCLF should be set to
5244 in order to minimise transformer loss
Table 4-4 Transformer loss with different TCLF
TCLF () 0 25 5244 75 100
Transformer loss
(kWh)
55922 50783 47865 49414 53982
As presented in Table 4-5 the average number of switching operations is increased
as the TCLF is approached to its optimum value
Table 4-5 Average number of switching operations with different TCLF
TCLF () 0 25 5244 75 100
Average number of
switching operations
0 2 4 2 0
452 Test Case 2
The impacts of TOMs and DNR on transformer loss are evaluated in this section As
presented in Fig 4-12 the model of the test system is developed from the
duplication of the generic distribution network shown in Fig 4-5 All the values of
the network parameters are obtained from [104]ndash[106] The system is supplied by
two 3311 kV substations and each bus has four feeders There is one linked feeder
with nine tie-switches Tie-switches refer to the switches of the network that are
normally open The function of the tie-switches is to alter the network topology to
provide various routes for supplying loads In order to feed all loads and keep the
systemrsquos radial topology only one tie-switch is open and all the others are closed
Chapter 4 Transformer Economic Operation amp Distribution Network
Reconfiguration for Transformer Loss Reduction
Page | 86
0
02
04
06
08
1
12
14
16
0 2 4 6 8 10 12 14 16 18 20 22
Act
ive
Po
we
r (k
W)
Time (h)
TW1 TW2 TW3 TW4 TW5
A1
A2
A3
A4_1 A4_2 A4_3 A4_4 A4_5 A4_6 A4_7 A4_8 B4_8 B4_7 B4_6 B4_5 B4_4 B4_3 B4_2 B4_1
B1
B2
B3
EndA EndB
TW9TW8TW7TW6
Tie-Switch (close) Tie-Switch (open)
Fig 4-12 Test system
For simplicity the daily load variations in each feeder are the same and the load
profiles of each node in the linked feeder are also the same Therefore the loads
could be categorised into two groups
Group 1 A1 A2 A3 B1 B2 B3
Group 2 A4_1 A4_2 A4_3 A4_4 A4_5 A4_6 A4_7 A4_8 B4_1 B4_2
B4_3 B4_4 B4_5 B4_6 B4_7 B4_8
On the basis of transformer load factor variation shown in Fig 4-6 the relevant 10-
min resolution load models of the two groups are presented in Fig 4-13 The power
factors of all the loads are set to 095
(a) Group 1
Chapter 4 Transformer Economic Operation amp Distribution Network
Reconfiguration for Transformer Loss Reduction
Page | 87
0
002
004
006
008
01
012
014
016
018
02
0 2 4 6 8 10 12 14 16 18 20 22
Act
ive
Po
we
r (k
W)
Time (h)
(b) Group 2
Fig 4-13 Daily load variations for different load groups
As this test system is developed from the duplication of the generic distribution
network and all the loads have the same profiles the position of the tie-switch is
selected from lsquoTW1rsquo to lsquoTW5rsquo For example the tie-switch located in lsquoTW1rsquo has the
same effect as lsquoTW9rsquo The control strategy is used to quantify the changes in feeder
voltage and transformer loss in the previously described test system under different
scenarios which could be categorised as
Scenario 1 each end has one transformer in operation and the tie-switch is located
at TW1 ie entire feeder supplied from end B
Scenario 2 each end has one transformer in operation and the tie-switch is located
in TW5 ie feeder split at mid-point
Scenario 3 each end has one transformer in operation and the location of the tie-
switch is based on minimum transformer loss operation
Scenario 4 each end has two transformers in operation and the tie-switch is located
at TW1
Scenario 5 each end has two transformers in operation and the tie-switch is located
at TW5
Scenario 6 each end has two transformers in operation and the location of the tie-
switch is based on minimum transformer loss operation
Chapter 4 Transformer Economic Operation amp Distribution Network
Reconfiguration for Transformer Loss Reduction
Page | 88
Scenario 7 each end has onetwo transformers in operation based on the transformer
load factor and the tie-switch is located at TW1
Scenario 8 each end has onetwo transformers in operation based on the transformer
load factor and the tie-switch is located at TW5
Scenario 9 each end has onetwo transformers in operation based on the transformer
load factor and the location of the tie-switch is based on minimum transformer loss
operation
Table 4-6 indicates the mean value of 3311 kV transformer loss during one day
under different scenarios As can be seen from the table when the tie-switches have
the same location TW1 transformer loss in Scenario 7 results in a reduction of
1396 and 1456 in comparison with Scenario 1 and Scenario 4 In conclusion
the mode introducing a flexible number of transformers in operation based on TCLF
reduces the loss In addition the transformer loss in Scenario 9 is 9528 kWh per day
which is 217 and 014 lower than Scenario 7 and Scenario 8 As a result the
variation of tie-switch locations could reduce transformer loss The detailed location
of the tie-switch in Scenario 9 is included in Appendix B1
Table 4-6 Transformer loss in Test Case 2
Scenarios S1 S2 S3 S4 S5 S6 S7 S8 S9
Loss
(kWhday)
11319 10848 10848 11399 11162 11162 9739 9572 9528
The graph presented in Fig 4-14 illustrates the voltage variation caused by the tie-
switch relocation The node voltages in Scenario 1 experience the worst profile
which increases to a peak of 09749 pu from 09675 pu along the linked feeder In
order to reduce the loss the tie-switch is always located in the middle of the feeder
TW5 in Scenario 3 As a result the voltage profiles of Scenario 2 and Scenario 3 are
the same It should be noted that Scenario 2 experiences a slight drop from 09787 pu
to 0972 pu and then climbs back to 09827 pu It can also be clearly seen that the
voltage reaches the lowest value where the tie-switch is located The further away
the nodes are from the tie-switch the better the voltage profiles that can be obtained
In addition when the tie-switch moves closer to the middle of the linked feeder the
Chapter 4 Transformer Economic Operation amp Distribution Network
Reconfiguration for Transformer Loss Reduction
Page | 89
096
0962
0964
0966
0968
097
0972
0974
0976
0978
098
A4_1A4_2A4_3A4_4A4_5A4_6A4_7A4_8B4_8B4_7B4_6B4_5B4_4B4_3B4_2B4_1
Vo
ltag
e (
pu
)
Scenario1
Scenario2
Scenario3
0955
096
0965
097
0975
098
0985
099
A4_1A4_2A4_3A4_4A4_5A4_6A4_7A4_8B4_8B4_7B4_6B4_5B4_4B4_3B4_2B4_1
Vo
ltag
e (
pu
)
Scenario1
Scenario4
Scenario7
voltage performance is improved And the detailed voltage values at each node in the
linked feeder for different scenarios are presented in Appendix B1
Fig 4-14 Mean voltage profiles in S1 S2 and S3
As shown in Fig 4-15 the voltage variation is due to a change in TOMs
Fig 4-15 Mean voltage profiles in S1 S4 and S7
As in the case of the tie-switch located in lsquoTW1rsquo all the node voltages experience a
rise along the linked feeder from lsquoEndArsquo to lsquoEndBrsquo It should be noted that the node
voltages in Scenario 4 achieve the best profile which increase to a peak of 0984 pu
from 0976 pu As discussed in Test Case 1 the transformers in parallel operation
could improve the voltage profiles In addition the flexible number of transformers
Chapter 4 Transformer Economic Operation amp Distribution Network
Reconfiguration for Transformer Loss Reduction
Page | 90
in operation based on TCLF (Scenario 7) shows a slight difference in voltage from
that in Scenario 4
As discussed above the location of the tie-switch and the change of TOMs have an
impact on the feeder voltage variation The tie-switch located in the middle of the
feeder and transformers with parallel operation defines the best voltage profiles
46 Summary
This chapter illustrates why transformer economic operation (TEO) is an economical
solution to reduce transformer loss The substation composed of two transformers
with the same characteristics has been used as an example to introduce the general
approach of determining the TCLF and TEO area A Monte Carlo simulation
platform was established to tackle load uncertainties A methodology to prove that
the TOM variation affects the performance of the 11kV distribution network is
discussed and analysed The TEO mode with minimum loss and satisfactory voltages
is achieved depending on the the transformer load factors by operating with either
one or two transformers and can be summarised as when the transformer load factor
is less than the TCLF transformers should be in separate operation when the
transformer load factor is higher than the TCLF transformers are recommended to
operate in parallel This results in a reduction of 1441 over the conventional
transformer loss ie when two transformers are in parallel operation However
simulation studies also indicate voltage profiles are improved when transformers
operate in parallel Therefore a slight reduction in TCLF results in an increased loss
but an improvement in voltage performance
The effectiveness of a DNR strategy has also been proposed through the results
obtained The presented results illustrate the impact of different TOMs in each
substation and tie-switch statuses on transformer loss and the voltages measured
along the feeder during a 24 hour operating period The optimal economic operation
strategy with TEO and DNR have successfully reduced the transformer loss and
improved the voltage profiles The further away the nodes are from the tie-switch
the better the voltage profiles obtained In addition when the tie-switch moves closer
to the middle of the linked feeder the voltage performance is improved
Chapter 4 Transformer Economic Operation amp Distribution Network
Reconfiguration for Transformer Loss Reduction
Page | 91
In normal operating conditions transformers operate in parallel and the tie-switch is
located in the middle of the linked feeder As indicated by Table 46 the daily
energy loss in Scenario 5 is 11162 kWh After the introduction of Scenario 9 the
annual saving energy could be 59641 kWh
Page | 92
CHAPTER 5
DISTRIBUTION NETWORK
RECONFIGURATION amp DG ALLOCATION
FOR FEEDER LOSS REDUCTION
51 Introduction
Distribution networks generally operate in radial configuration to ease protection
coordination and to reduce short circuit current [107] Distribution feeders can be
reconfigured to alter the network topology at normal and abnormal operating
conditions by changing the openclose status of switches to satisfy the operatorrsquos
objectives [13] [14]
DG is a small electric generation unit that is connected directly to the distribution
network or appears on side of the meter accessed by the customer [16] With the
increasing number of DGs bidirectional power flows have appeared and locally
looped networks have become inevitable [17] Therefore the type size and location
of DGs in the distribution networks strongly affect power system operation and
planning
The studies in [5] indicate that about 5 of the total power generation is wasted in
the form of feeder loss at the distribution level Reduction in active power loss can
help distribution network operators (DNOs) save costs and increase profits The
Chapter 5 Distribution Network Reconfiguration amp DG Allocation for Feeder Loss
Reduction
Page | 93
optimal distribution network reconfiguration (DNR) placement and sizing of DGs
strategies should be used to reduce feeder loss while satisfying the operating
constraints
The ant colony optimisation (ACO) developed by M Dorigo is a metaheuristic
algorithm for the assessment of optimisation problems [94] It is based on the
pheromones deposited by ants as a guide for finding the shortest path between a food
source and their home colony The detailed description of ACO algorithm has been
presented in Section 33 In this chapter an ACO algorithm is proposed to solve the
network reconfiguration and DG placement problems simultaneously based on
distribution feeder loss minimisation The proposed technique is tested on two
standard IEEE 33-node and 69-node systems and the simulation results show the
performance and effectiveness of the proposed method Four scenarios are
considered during network reconfiguration and DG allocation The impacts of DG
capacity on assessing the DNR and DG allocation problems in terms of feeder loss
reduction are also studied Moreover the results obtained by ACO algorithm have
been compared to those from other algorithms in the literature
As for the remainder of this chapter the mathematical formulation of the objective
function and its constraints are explained in Section 52 Section 53 discusses the
application of ACO algorithms in order to solve the problem Section 54 provides a
detailed analysis of the numerical results and Section 55 provides the final
conclusions
52 Problem Formulation
The proposed objective function (F) of the problem is formulated to minimise the
feeder loss of a distribution network which is described as follows
119872119894119899119894119898119894119904119890 119891 = sum 119896119894119877119894(119875119894
2+1198761198942
1198801198942 )
119873119887119894=1 (5-1)
where 119877119894 is the resistance of the ith branch 119875119894 and 119876119894 are the real power (W) and
reactive power (VAr) at the receiving end of branch i 119880119894 represents the rms voltage
at the receiving end of branch i (V) 119896119894 is a binary variable 119896119894 = 0 indicates that
Chapter 5 Distribution Network Reconfiguration amp DG Allocation for Feeder Loss
Reduction
Page | 94
branch 119894 is open and 119896119894 = 1 indicates that branch 119894 is closed The detailed feeder loss
assessment has been given in Section 28
Subject to
∆119881119899 le ∆119881119898119886119909 for all load points (5-2)
119868119887 le 119868119898119886119909 for all branches (5-3)
119875119894 le 119875119894119898119886119909 (5-4)
det(119860) = 1 119900119903 minus 1 (5-5)
Constraints (5-2) ndash (5-3) represent the computed voltages and currents and should be
in their permissible range Constraint (5-4) indicates that the power flow at all
branches should be within the limits defined for each branch Constraint (5-5)
ensures the radial topology of the network [32] The branch to node incidence matrix
Arsquo has one row for each branch and one column for each node 119886119894119895 represents the
coefficient in row i and column j 119886119894119895 = 0 if branch i is not connected with node j
119886119894119895 = 1 if branch i is directed away from node j and 119886119894119895 = minus1 if branch i is directed
towards node j When the column corresponding to the reference node and the rows
of open branches are deleted from matrix Arsquo a new square branch-to-node matrix A
is obtained Then the determinant of A is calculated If det(A) is 1 or -1 the system is
radial Otherwise the system is not radial
53 Solution Method
531 Distribution Network Reconfiguration
With regard to the DNR problem each solution is represented by a string of integers
which indicates the location of tie-switches As the number of tie-switches that keep
the network radial is always constant the number of the solutionrsquos elements is equal
to the number of tie-switches in the network
Chapter 5 Distribution Network Reconfiguration amp DG Allocation for Feeder Loss
Reduction
Page | 95
Home
1 2 NP1NP1-1
1 2 NP1-1 NP1
1 2 NP1NP1-1
1 2 NP2-1 NP2
1 2 NP2NP2-1
1 2 NP2-1 NP2
1 2 NP2NP2-1
1 2 NP2-1 NP2
Food
Stage
1
2
NT-1
NT
NT+1
NT+2
NT+NDG-1
NT+NDG
Part 1 Number of
existing tie-switches
Part 2 Number
of DGs
532 Applying ACO to DNR and DGs Placement
In this chapter an ACO algorithm is adopted to find the optimum locations of tie-
switches and sites of DGs placement in the network in terms of feeder loss
minimisation When the locations of tie-switches and DGs are changed a new
network configuration will be formed For each network configuration the feeder
loss is evaluated by using the approach presented in Section 52
Fig 5-1 Search space of DNR and DGs Placement
Chapter 5 Distribution Network Reconfiguration amp DG Allocation for Feeder Loss
Reduction
Page | 96
The search space of the DNR and DG allocation problems is modelled as a directed
graph as shown in Fig 5-1 In Part I the states signify the location of tie switches
and the sites for DGs installation are represented by states in Part II The number of
stages in this graph is the sum of the amount of existing tie-switches 119873119905 and the
number of installed DGs 119873119863119866 1198731199011is the number of possible locations for the tie-
switches relocation and 1198731199012 is the number of candidate buses for DGs installation
Artificial ants start their tours at home moving along the paths in the graph and end
at the food source Each location list consists of a string of integers and represents a
solution to the problem Different orders of the solutionrsquos elements indicate different
routes However several routes might indicate a certain solution as the order of the
solutionrsquos elements makes no difference to the network configuration For example
the solution vector (1 2 3) represents the same network configuration as the solution
vector (3 2 1) And the objective functions of these two routes are the same In this
study the first route that the ants found will be chosen as the feasible solution The
flowchart of the proposed ACO algorithm is presented in Fig 5-2 and is expressed in
five steps
Step 1 Initialisation First of all all the ants are initially located at home The
pheromone values of the edges in the search space are all set to a small positive
constant value
Step 2 Ant Dispatch All the ants are sent in parallel from the home colony and one
of the states is chosen in the next stage according to a probabilistic selection rule
which involves the intensity of pheromones deposited on the states [66] The
locations of the tie-switches are determined first and the sites for the DGs
installation are then selected The probability of an ant choosing state j of the next
stage y is
119875119895119910(119873) =
120591119895119910
(119873)
sum 120591119895119910
(119873)ℎisin∆119910
(5-6)
where 120591119895119910
(119873) is the pheromone value of state j of stage y at iteration N ∆119910 is the set
of available states which an ant can choose at stage y
Chapter 5 Distribution Network Reconfiguration amp DG Allocation for Feeder Loss
Reduction
Page | 97
Step 3 Objective Function Evaluation After all the ants have completed their tour
the location list and corresponding objective function in (5-1) for each ant are
evaluated If any constraint in (5-2) - (5-5) is violated the corresponding solution is
assigned with a huge value and is discarded If not all the objective functions are
assessed and the best configuration of the Nth iteration with minimum objective
function 119891119887119890119904119905(119873) is recorded This should be compared to the best configuration
obtained so far 119891119887119890119904119905 if 119891119887119890119904119905(119873) lt 119891119887119890119904119905 the best solution should be updated such
that 119891119887119890119904119905 = 119891119887119890119904119905(119873) [14] If not the best configuration found in the previous
iteration is retained After this the location list is emptied and all the ants are free to
choose a new trail
Step 4 Pheromone Updating The aim of this step is to favour transitions towards
states involving high quality solutions with greater pheromones There are two rules
of pheromone updating the local rule and global rule
Local rule The amount of pheromone deposited in the search space should be
evaporated to make paths less attractive The local pheromone update rule is
calculated as following
120591119895119910
(119873) = (1 minus 120588)120591119895119910
(119873 minus 1) + 120591119888 (5-7)
where 120588 is the pheromone evaporation rate which is set between 0 and 1 120591119888 is a
small positive constant value Even if the amount of pheromone deposited on an
edge is at the lowest value of 120591119888 there is a slight chance that an ant will still choose
this edge
Global rule The global pheromone updating rule involves ants depositing large
amounts of pheromone to the edges that belong to the highest quality solution per
iteration This rule is to guide the search to find the global optimal solution The
pheromones of those edges can be modified by
120591119895119910(119873) = 120591119895
119910(119873) + 120588119891119887119890119904119905
119891119887119890119904119905(119873) (5-8)
After applying the local and global pheromone updating rules the method Max-Min
ACO algorithm is integrated into the proposed approach
120591119895119910(119873) = 120591119898119886119909 119894119891 120591119895
119910(119873) ge 120591119898119886119909 (5-9)
120591119895119910(119873) = 120591119898119894119899 119894119891 120591119895
119910(119873) le 120591119898119894119899 (5-10)
Chapter 5 Distribution Network Reconfiguration amp DG Allocation for Feeder Loss
Reduction
Page | 98
Start
Set Iteration n=1
Maximum iteration
reached
Output best
configuration and end
No
Yes
Initialise the parameters for ACO algorithm
searching space and build graph of the tours
Dispatch ants based on the
amount of pheromones on edges
Relocate tie-switches and DGs by location lists
Calculate the objective function for each ant
The pheromones are updated according
to local and global rules
n=n+1
Record the best solution so far and empty
all location lists
Read system topology
and load data
where 120591119898119886119909and 120591119898119894119899 are the higher and lower bound of the pheromone level on each
edge respectively The trail limit of the pheromone ensures the probabilities of all
the edges are greater than zero which maintains the diversity of the solutions and
avoids premature convergence for local minima
Step 5 Termination The computation continues until the predefined maximum
number iterations is reached The best tour selected among all iterations implies the
optimal solution
Fig 5-2 Flowchart of the ACO applied to DNR and DGs placement
Chapter 5 Distribution Network Reconfiguration amp DG Allocation for Feeder Loss
Reduction
Page | 99
54 Application Studies
To demonstrate the performance and effectiveness of the proposed technique in
assessing the network reconfiguration and placement of DG problems
simultaneously the proposed ACO is implemented on two 1266 kV test systems
consisting of 33 and 69 buses The network models are built in OpenDSS and the
solution algorithm is developed in MATLAB For both test systems the substation
voltage is assumed to be 10 pu and all the branches and buses are considered as
candidate locations for tie-switches and DG placement respectively In this study
for simplicity the number of installed DGs is three All the DGs are synchronous
generators and are represented as PQ models with a 100 kVA capability and a
power factor equal to 10 For the purpose of better illustration and comparison four
cases are considered to analyse the superiority and performance of the proposed
method
Case I System is without reconfiguration and has no DGs (base case)
Case II System is optimally reconfigured and has no DGs
Case III System is optimally reconfigured after DGs are placed at certain buses
Case IV System is optimally reconfigured and DGs are optimally placed
simultaneously
It is to be noted that the ACO control parameters are different for each test case
They are set experimentally using information from several trial runs The final
combinations that provide the best results for all of the above tests are given in
Appendix C1
541 33-bus System
In this section the proposed procedure is implemented on a 33-bus 1266 kV radial
distribution system with 37 branches and 5 tie-switches whose single-line diagram
is shown in Fig 5-3 The tie-switches are located at L33 to L37 represented by red
dotted lines The data of line and load are taken from [108] and summarised in
Appendix A2 The total real and reactive power loads of the system are 3715 kW
and 2300 kVAr respectively The performance of the presented method for the four
Chapter 5 Distribution Network Reconfiguration amp DG Allocation for Feeder Loss
Reduction
Page | 100
10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
18 19 20 21
22 23 24
25 26 27 28 29 30 31 32
L1 L2 L3 L4 L5 L6 L7 L8 L9 L10 L11 L12 L13 L14 L15 L16 L17
L18
L19 L20 L21
L22
L23 L24
L25
L26 L27 L28 L29 L30 L31 L32
L33
L34
L35
L36
L37
cases is given in Table 5-1 The network losses in each branch for all test cases are
listed in Appendix B2
Fig 5-3 33-bus system
Table 5-1 Results of different cases for the 33-bus system
Case Active feeder
loss (kW)
Minimum voltage
(pu)
(Bus No)
Location of tie-switches
on Fig 53
DG location
Case I 20314 09116 (B17) L33 L34 L35 L36 L37 NA
Case II 13981 09361 (B31) L7 L9 L14 L32 L37 NA
Case III 11753 09357 (B31) L7 L9 L14 L28 L31 B17 B21 B24
Case IV 10844 09462 (B32) L7 L9 L14 L32 L37 B30 B31 B31
Case I base case
For the base case without reconfiguration and DGs the initial active feeder loss of
this system is 20314 kW The lowest bus voltage is 09116 pu and this occurs at
Bus 17
Case II with reconfiguration only (no DGs)
In this case only reconfiguration is considered and no DGs are installed The
network configuration after DNR is shown in Fig 5-4 The number of the solutionrsquos
elements for this case is 5 which is the number of tie-switches After DNR the total
feeder loss is 13981 kW which corresponds to a 3118 reduction in loss In
addition the minimum voltage also increases from 09116 pu to 09361 pu
Chapter 5 Distribution Network Reconfiguration amp DG Allocation for Feeder Loss
Reduction
Page | 101
10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
18 19 20 21
22 23 24
25 26 27 28 29 30 31 32
L1 L2 L3 L4 L5 L6 L7 L8 L9 L10 L11 L12 L13 L14 L15 L16 L17
L18
L19 L20 L21
L22
L23 L24
L25
L26 L27 L28 L29 L30 L31 L32
L33
L34
L35
L36
L37
Fig 5-4 33-bus system for feeder loss minimisation Case II
To illustrate the performance of the proposed ACO the results are compared with
the results obtained using the branch exchange method (BEM) [109] harmony
search algorithm (HSA) [110] fireworks algorithm (FWA) [16] particle swarm
optimisation (PSO) [55] and invasive weed optimisation (IWO) [111] these are all
described in the literature and are presented in Table 5-2 It is observed that the
results obtained from the ACO are identical to those from the HAS PSO and IWO
but better than the results from the BEM and FWA This is because that BEM and
FWA have plunged into a local optimal solution and they lack the ability to escape
from it
Table 5-2 Comparison of simulation results for 33-bus system in Case II
Method Feeder loss
(kW)
Loss reduction
()
Tie-switches location Minimum
voltage (pu)
The proposed ACO 13981 3118 L7 L9 L14 L32 L37 09361
BEM [109] 14054 3082 L7 L10 L14 L32 L37 09361
HSA [110] 13981 3118 L7 L9 L14 L32 L37 09361
FWA [16] 14026 3095 L7 L9 L14 L28 L32 09396
PSO [55] 13981 3118 L7 L9 L14 L32 L37 09361
IWO [111] 13981 3118 L7 L9 L14 L32 L37 09361
Moreover both the continuous genetic algorithm (CGA) [112] and cuckoo search
algorithm (CSA) [113] are implemented to further investigate the performance of the
proposed ACO It is important to note that the performance of the ACO CGA and
CSA depends on the selection of their control parameters All three algorithms are
solved 100 times The average maximum minimum and standard deviation of the
100 runs are compared and shown in Table 5-3 The convergence number is defined
Chapter 5 Distribution Network Reconfiguration amp DG Allocation for Feeder Loss
Reduction
Page | 102
10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
18 19 20 21
22 23 24
25 26 27 28 29 30 31 32
L1 L2 L3 L4 L5 L6 L7 L8 L9 L10 L11 L12 L13 L14 L15 L16 L17
L18
L19 L20 L21
L22
L23 L24
L25
L26 L27 L28 L29 L30 L31 L32
L33
L34
L35
L36
L37
DG2
DG1
DG3
as the number of the iterations when the objective function is convergence It can be
seen that all three algorithms have obtained the same minimum loss However the
proposed ACO method has a higher probability in finding the global optimum
solution as the mean and standard deviation of the fitness values of the ACO
algorithm are less than those obtained by the other algorithms Furthermore as the
average value of convergence number of the ACO is less than that of the other two
algorithms this means the proposed algorithm has a higher convergence rate In
terms of the computation times the proposed ACO runs faster when compared with
CGA and CSA
Table 5-3 Comparison of ACO with CGA and CSA for the 33-bus system in Case II
Method Feeder loss (kW) Convergence number Average
computation
times
(second)
AVG MAX MIN STD AVG STD
ACO 13981 13981 13981 0 228 821 1448
CGA [112] 14002 14619 13981 12121 5463 2986 3926
CSA [113] 13986 14028 13981 01328 8363 3425 7258
AVG MAX MIN and STD mean the average maximum minimum and standard deviation of the 100 runs
Case III with reconfiguration only (with DGs)
In this case the three DGs are located at the end of the feeders ie Bus 17 21 24
The network configuration after DNR is illustrated in Fig 5-5 As shown in Table 5-
1 the network reconfiguration results in a reduction of 4214 in feeder loss in
comparison with the original network without DGs and a reduction of 1594 in
comparison with the reconfigured system without DGs
Fig 5-5 33-bus system for feeder loss minimisation Case III
Chapter 5 Distribution Network Reconfiguration amp DG Allocation for Feeder Loss
Reduction
Page | 103
10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
18 19 20 21
22 23 24
25 26 27 28 29 30 31 32
L1 L2 L3 L4 L5 L6 L7 L8 L9 L10 L11 L12 L13 L14 L15 L16 L17
L18
L19 L20 L21
L22
L23 L24
L25
L26 L27 L28 L29 L30 L31 L32
L33
L34
L35
L36
L37
DG2DG1
DG3
Case IV with reconfiguration and DG allocation
Fig 5-6 illustrates the optimal network configuration and DG locations The network
is reconfigured and DGs are allocated simultaneously in this case Therefore the
number of the solutionrsquos elements for this case becomes 8 which is the sum of the
number of tie-switches and DGs The results show the final configuration with a
feeder loss of 10844 kW with 4662 2244 and 773 reduction in comparison
with that in Case I Case II and Case III respectively
Fig 5-6 33-bus system for feeder loss minimisation Case IV
In this case the impacts of DG capacity on assessing the DNR and DG allocation
problems in terms of feeder loss reduction are also studied The capacity of each DG
is set as 100 400 700 and 1000 kVA respectively The feeder losses for different
DG capacities are shown in Fig 5-7 Before simultaneous reconfiguration and DG
allocation the feeder loss decreases from 1783 kW to 1023 kW when the capacity
of DG is increased from 100 kVA to 700 kVA However the feeder loss increases to
1042 kW if the capacity of DG continuously grows to 1000 kVA The inappropriate
network configuration and DG location might result in loss increment when the size
of the DG is increased However with the introduction of network reconfiguration
and DG allocation feeder loss is reduced no matter what the capacity of DG is This
proves that the proposed methodology can reduce the total feeder loss by
determining the most suitable network topology and DG locations in comparison
with the original configuration
Chapter 5 Distribution Network Reconfiguration amp DG Allocation for Feeder Loss
Reduction
Page | 104
086
088
09
092
094
096
098
1
102
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32
Vo
ltag
e (
pu
)
Bus No
Case I
Case II
Case III
Case IV
0
20
40
60
80
100
120
140
160
180
200
100 400 700 1000
Fee
de
r lo
ss (
kW)
DG Capacity (kVA)
Before simultaneousreconfiguration and DG allocation
After simultaneous reconfigurationand DG allocation
Fig 5-7 Comparison of feeder loss for different DG capacities before and after simultaneous
reconfiguration and DG allocation
The voltage profiles of four cases are compared and shown in Fig 5-8 It can be seen
that the voltage profiles at most buses in Case IV have been improved in comparison
with the other three cases In terms of Case III and Case IV the buses which inject
DGs show the improvement in voltage profiles ie the voltage of Bus 31 is
improved from 09357 pu in Case III to 09537 pu in Case IV In Case IV as Bus 32
is the furthest bus being supplied its voltage is the lowest value among all buses In
conclusion the systemrsquos voltage profiles are improved by optimal DNR and DG
allocation
Fig 5-8 Comparison of voltage profiles in different cases of 33-node system
Chapter 5 Distribution Network Reconfiguration amp DG Allocation for Feeder Loss
Reduction
Page | 105
10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
27
28
29
30
31 32 33 34
35
36
37
38 39 40 41 42 43 44 45
46 47 48 49
50
51
52
53 54 55 56 57 58 59 60 61 62 63 64
65 66
67 68
L1 L2 L3 L4 L5 L6 L7 L8 L9 L10 L11 L12 L13 L14 L15 L16 L17 L18 L19 L20 L21 L22 L23 L24 L25 L26
L27
L28
L29
L30
L31 L32 L33 L34
L35
L36
L37
L38 L39 L40 L41 L42 L43 L44 L45
L46
L47 L48 L49
L50
L51
L52
L53 L54 L55 L56 L57 L58 L59 L60 L61 L62 L63 L64
L65
L66
L67
L68
L69
L70
L71
L72L73
542 69-bus System
This is a large-scale radial distribution system consisting of 73 branches and 5 tie-
switches whose single-line diagram is shown in Fig 5-9 The tie-switches are
located at L69 to L73 represented by red dotted lines The line and load data of the
system are taken from [84] and summarised in Appendix A3 The total power loads
are 379589 kW and 26891 kVAr respectively Similar to 33-bus system this
system is also simulated for four cases and the results are given in Table 5-4 The
network losses in each branch for all test cases are listed in Appendix B2
Fig 5-9 69-bus system
Table 5-4 Results of different cases for the 69-bus system
Case Active feeder
loss (kW)
Minimum voltage
(pu)
(Bus No)
Tie-switches location DG location
Case I 22562 09072 (B64) L69 L70 L71 L72 L73 NA
Case II 9885 09476 (B60) L14 L55 L61 L71 L72 NA
Case III 8758 09477 (B60) L13 L55 L61 L71 L72 B26 B45 B64
Case IV 7397 09571 (B60) L14 L55 L61 L71 L72 B60 B60 B60
Case I base case
Base case active feeder loss in the system is 22562 kW The lowest bus voltage is
09072 pu and occurs at bus 64
Chapter 5 Distribution Network Reconfiguration amp DG Allocation for Feeder Loss
Reduction
Page | 106
10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
27
28
29
30
31 32 33 34
35
36
37
38 39 40 41 42 43 44 45
46 47 48 49
50
51
52
53 54 55 56 57 58 59 60 61 62 63 64
65 66
67 68
L1 L2 L3 L4 L5 L6 L7 L8 L9 L10 L11 L12 L13 L14 L15 L16 L17 L18 L19 L20 L21 L22 L23 L24 L25 L26
L27
L28
L29
L30
L31 L32 L33 L34
L35
L36
L37
L38 L39 L40 L41 L42 L43 L44 L45
L46
L47 L48 L49
L50
L51
L52
L53 L54 L55 L56 L57 L58 L59 L60 L61 L62 L63 L64
L65
L66
L67
L68
L69
L70
L71
L72L73
Case II with reconfiguration only (no DGs)
After DNR switches at L14 L55 L61 L71 and L72 are opened as shown in Fig 5-
10 The total feeder loss is reduced by 5619 and the minimum voltage is
increased to 09476 pu in comparison with the base case
Fig 5-10 69-bus system for feeder loss minimisation Case II
The comparisons of results among the proposed ACO with FWA [16] HSA [110]
and genetic algorithm (GA) [110] are presented in Table 5-5 It is observed that the
results obtained from the ACO are better than those from the FWA HSA and GA
as these algorithms are trapped into the local optimal solution
Table 5-5 Comparison of simulation results for 69-bus system in Case II
Method Feeder loss
(kW)
Loss reduction
()
Tie-switches location Minimum
voltage (pu)
The proposed ACO 9885 5619 L14 L55 L61 L71 L72 09476
FWA [16] 9886 5618 L14 L56 L61 L71 L72 09476
HSA [110] 10546 5326 L13 L18 L56 L61 L72 09475
GA [110] 10242 5461 L14 L53 L61 L71 L72 09462
Case III with reconfiguration only (with DGs)
In this case the three DGs are located at the end of the feeders ie Bus 26 45 64
The network configuration after DNR is illustrated in Fig 5-11 As shown in Table
Chapter 5 Distribution Network Reconfiguration amp DG Allocation for Feeder Loss
Reduction
Page | 107
10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
27
28
29
30
31 32 33 34
35
36
37
38 39 40 41 42 43 44 45
46 47 48 49
50
51
52
53 54 55 56 57 58 59 60 61 62 63 64
65 66
67 68
L1 L2 L3 L4 L5 L6 L7 L8 L9 L10 L11 L12 L13 L14 L15 L16 L17 L18 L19 L20 L21 L22 L23 L24 L25 L26
L27
L28
L29
L30
L31 L32 L33 L34
L35
L36
L37
L38 L39 L40 L41 L42 L43 L44 L45
L46
L47 L48 L49
L50
L51
L52
L53 L54 L55 L56 L57 L58 L59 L60 L61 L62 L63 L64
L65
L66
L67
L68
L69
L70
L71
L72L73
DG3
DG1
DG2
10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
27
28
29
30
31 32 33 34
35
36
37
38 39 40 41 42 43 44 45
46 47 48 49
50
51
52
53 54 55 56 57 58 59 60 61 62 63 64
65 66
67 68
L1 L2 L3 L4 L5 L6 L7 L8 L9 L10 L11 L12 L13 L14 L15 L16 L17 L18 L19 L20 L21 L22 L23 L24 L25 L26
L27
L28
L29
L30
L31 L32 L33 L34
L35
L36
L37
L38 L39 L40 L41 L42 L43 L44 L45
L46
L47 L48 L49
L50
L51
L52
L53 L54 L55 L56 L57 L58 L59 L60 L61 L62 L63 L64
L65
L66
L67
L68
L69
L70
L71
L72L73
DG3DG1
DG2
5-5 the network reconfiguration results in a reduction of 6118 in feeder losses as
compared with the original network without DGs and a reduction of 1140 in
comparison with the reconfigured system without DGs
Fig 5-11 69-bus system for feeder loss minimisation Case III
Case IV with reconfiguration and DG allocation
Fig 5-12 illustrates the optimal network configuration and DG locations In this case
the results show the final configuration with a feeder loss of 7397 kW with 6721
2517 and 1554 reduction in comparison with that in Case I Case II and Case
III respectively
Fig 5-12 69-bus system for feeder loss minimisation Case IV
Chapter 5 Distribution Network Reconfiguration amp DG Allocation for Feeder Loss
Reduction
Page | 108
0
50
100
150
200
250
100 400 700 1000
Fee
de
r lo
ss (
kW)
DG Capacity (kVA)
Before simultaneousreconfiguration and DG allocation
After simultaneous reconfigurationand DG allocation
In this case the impacts of DG capacity on assessing the DNR and DG allocation
problems in terms of feeder loss reduction are also studied The capacity of each DG
is set as 100 500 900 and 1300 kVA respectively The feeder loss curves for
different DG capacities are shown in Fig 5-13 After simultaneous reconfiguration
and DG allocation the feeder loss decreases from 7397 kW to 873 kW when the
DG capacity is increased from 100 kVA to 900 kVA However the loss bounces
back to 114 kW if the DG capacity continues to increase to 1300 kVA This means
that the capability of network reconfiguration and DG allocation on feeder loss
reduction is limited when the size of DGs is large But the proposed methodology
can still reduce the total feeder loss for all DG capacities by determining the most
suitable network topology and DG locations in comparison with the original
configuration
Fig 5-13 Comparison of feeder loss for different DG capacities before and after simultaneous
reconfiguration and DG allocation
Fig 5-14 shows the voltage profile of the 69-bus system It can be seen that the
voltage profiles at most buses in Case IV have been improved in comparison with
the other three cases Compared with Case III and Case IV the buses which inject
DGs show improvement in voltage profiles ie the voltage of Bus 60 is improved
from 09477 pu in Case III to 09571 pu in Case IV In Case IV although there are
three DGs connected as Bus 60 as the value of load connected at this bus is the
largest (1244 kW) this bus voltage is the lowest among all buses In conclusion the
systemrsquos voltage profiles are improved by optimal DNR and DG allocation
Chapter 5 Distribution Network Reconfiguration amp DG Allocation for Feeder Loss
Reduction
Page | 109
086
088
09
092
094
096
098
1
102
0 5 10 15 20 25 30 35 40 45 50 55 60 65
Vo
ltag
e (
pu
)
Bus No
Case I
Case II
Case III
Case IV
Fig 5-14 Comparison of voltage profiles in different cases of 69-node system
55 Summary
In this chapter the application of optimal planning using DNR and DG allocation for
the problem of distribution feeder loss minimisation has been implemented The
method based on ACO has been successfully applied to the 1266 kV 33-bus and 69-
bus systems to find the optimum system configuration and DG locations
There are four cases used to analyse the superiority and performance of the proposed
method The proposed ACO is capable of finding the optimal solutions in all cases
In Case IV the feeder losses are reduced by 4662 and 6721 for the 33-bus and
69-bus system respectively in comparison with the base case Therefore Case IV is
found to be more effective in minimising the total loss and improving voltage
profiles compared to the other cases The numerical results show that for best
performance the existing tie-switches are relocated and the DGs are optimally
placed in comparison with the original network In addition the impacts of DG
capacity on assessing the DNR and DG allocation problems in terms of feeder loss
reduction are also studied The inappropriate network configuration and DG location
might result in loss increment when the size of DG is increased The proposed
methodology has successfully reduced the total feeder loss for different capacities of
DG by determining the most suitable network topology and the DG locations
Chapter 5 Distribution Network Reconfiguration amp DG Allocation for Feeder Loss
Reduction
Page | 110
compared to the original configuration The minimum loss obtained by DNR and DG
allocation decreases as the capacities of DGs are increased However this decrease
stops when DGs can supply all the loads without the main supply After that the
minimum loss increases as the capacities of DGs are increased
Moreover the simulation results have been compared with other classical methods in
literature and the proposed ACO is more efficient and is more likely to obtain the
global optimum solution
Page | 111
CHAPTER 6
DISTRIBUTION NETWORK
RECONFIGURATION amp TRANSFORMER
ECONOMIC OPERATION FOR NETWORK
LOSS REDUCTION
61 Introduction
Rapid increases in electricity demand have forced electric power utilities throughout
the world into major reconstructing processes As a significant proportion of electric
energy is dissipated in the operation of a distribution network the reduction of loss
should be considered an important problem for the economic operation of the overall
system [82]
Load variations have been disregarded in most studies on distribution automation
(DA) problems ie average loads were used in their reconfiguration schemes In this
chapter distribution loads experience daily and seasonal variations The study
considers the daily load curves of different types of consumers (residential
commercial and industrial) and in addition the days are divided into eight types
spring weekdays spring weekends summer weekdays summer weekends autumn
Chapter 6 Distribution Network Reconfiguration amp Transformer Economic
Operation for Network Loss Reduction
Page | 112
weekdays autumn weekends winter weekdays and winter weekends The best
reconfiguration hours during each of these typical days are then selected
The objective function for finding the best configuration of the network when
considering feeder loss and transformer loss will be studied in this chapter Different
combinations of locations of tie-switches in the network and operation modes of all
transformers in the substations represent different network configurations An Ant
colony optimisation (ACO) algorithm is adopted on an 11 kV distribution network
developed from Bus 4 of the Roy Billinton Test System (RBTS) to determine the
optimal network configuration during each type of day Furthermore the effects of
DGs and EVs in solving distribution network reconfiguration (DNR) and
transformer economic operation (TEO) based on network loss reduction are also
investigated
This chapter is organised as follows the next section discusses the variation of loads
and the reconfiguration hours Section 63 presents the objective function and
constraints for DNR Section 64 describes the application of ACO algorithms to the
problem Numerical studies are presented and discussed in Section 65 and finally
Section 66 summarises the main conclusions
62 Time-varying Load Model
As distribution loads experience daily and seasonal variations the optimum network
configuration constantly changes [82] However it is not reasonable to reconfigure a
network frequently ie based on hourly schedule since each switch has a maximum
number of allowable switching operations during its lifetime and frequent switching
actions will increase its maintenance costs [82]
However infrequent actions cause the system to work well below its optimum state
In order to determine the best reconfiguration time during a day the daily load
profiles should be smoothed In other words the daily load curves are divided into a
number of periods As the maintenance cost of a switch increases with the increasing
number of switching actions the number of intervals is a trade-off between the
optimum reconfiguration and switch cost As there is a peak and a valley of network
Chapter 6 Distribution Network Reconfiguration amp Transformer Economic
Operation for Network Loss Reduction
Page | 113
Actual daily load curve
Smoothed daily load curve
load variations during a day it is appropriate to divide the 24 hours daily load curves
into two periods Increasing the number of intervals will not change the nature of the
problem but will increase its complexity
Fig 6-1 The reconfiguration hours for a typical day
As the difference between 1198751 and 1198752 is increased the effect of DNR on loss
reduction increases where 1198751 and 1198752 are the average active power of the loads
during the first and second time periods respectively As shown in Fig 6-1 hours
1199051and 1199052 are calculated to maximise |1198751 minus 1198752| It should also be noted that the above
load smoothing methodology is only used to determine the reconfiguration intervals
and the active power loss during each interval is calculated based on the actual daily
load curve [82]
63 Problem Formulation
In this study the 24 hours of a typical day is divided into two periods The first time
period is 0000 to 1199051 and 1199052 to 2400 and the second time period is between 1199051 and 1199052
The following objective function is calculated for all possible network configurations
during each time interval and the one that minimises the total power loss and
satisfies all constraints is selected The energy losses of the distribution network over
the first and second time interval are presented in (6-1) and (6-2) the objective
function (6-3) is to minimise f the sum of f1 and f2
P1
P2
1199051 1199052 Time (h)
Chapter 6 Distribution Network Reconfiguration amp Transformer Economic
Operation for Network Loss Reduction
Page | 114
1198911 = sum (119864119871119905 + 119879119871119905)1199051minus1119905=1 + sum (119864119871119905 + 119879119871119905) 1199051
24119905=1199052 isin 1 2 hellip 24 (6-1)
1198912 = sum (119864119871119905 + 119879119871119905)1199052minus1119905=1199051 1199052 isin 1 2 hellip 24 (6-2)
Min 119891 = 1198911 + 1198912 (6-3)
where 119864119871119905 is the feeder loss of the distribution network during hour t (kWh) 119879119871119905
represents the transformer loss during hour t (kWh) The detailed calculation of
transformer loss and feeder loss are presented in Section 27 and 28 respectively
The computed voltages currents and the power flow at all branches should be kept
in their permissible range and the network should be operated in radial The
configurations that violate any constraint are assigned with huge objective functions
and are disregarded
64 Applying ACO to DNR and TEO
In this chapter the objective of simultaneous reconfiguring network and changing
transformer operation modes is to deal with energy loss minimisation including
transformer loss and feeder loss To implement the optimisation problem the
developed ACO algorithm is adopted to find the optimum location of tie-switches
and transformer operation modes in the network When the location of tie-switches
and operation modes of transformers are changed a new network configuration will
be formed For each network configuration the objective function is evaluated by
using the approach presented in Section 63
The search space of the DNR and TEO problems is modelled as a directed graph as
shown in Fig 6-2 Each solution is represented by a string of integers which
indicates the transformer operation modes and the location of tie-switches The
number of the solutionrsquos elements is equal to the number of stages in this graph
which is the sum of the amount of main feeders (the number of transformer pairs 119873119904)
and the number of existing tie-switches 119873119905
Chapter 6 Distribution Network Reconfiguration amp Transformer Economic
Operation for Network Loss Reduction
Page | 115
Home
0 1
0 1
0 1
0 1
1 2 NPNP-1
1 2 NP-1 NP
1 2 NPNP-1
1 2 NP-1 NP
Food
Stage
1
2
Ns-1
Ns
Ns+1
Ns+2
Ns+Nt-1
Ns+Nt
Part 1
Number of
substations
Ns
Part 2 Number
of existing tie-
switches Nt
Number of candidate locations for the tie-switches NP
Fig 6-2 Search space of DNR and TEO
As shown in Fig 6-3 the number of transformer pairs is 3 and the number of
existing tie-switches is 4 Therefore the number of the solutionrsquos elements for this
system is 7 In addition the possible branches for tie-switch placement are 4
Chapter 6 Distribution Network Reconfiguration amp Transformer Economic
Operation for Network Loss Reduction
Page | 116
Tie-switch
Transformer
Fig 6-3 Sample network with three substations
For transformer operation mode selection in Part I the ACO algorithm is applied to
assign each bit of the front part of the solution vector to the status of substations and
hence the number of transformers in operation in each substation can be represented
as a binary vector
State 0 this substation has one transformer in operation
State 1 this substation has two transformers in operation
However for the relocation of existing tie-switches in Part II the states indicate the
location of switches Artificial ants will start their tours at home move along the
paths in the graph and end at the food source
The 24 hour load curve is divided into two time intervals for all load types in terms
of the principle presented in Section 62 Fig 6-4 demonstrates the computation
procedure for the transformer operation mode selection and tie-switches relocation
problem at each of the time interval The application of the ACO algorithm to the
TEO and DNR problem is similar to that in Section 532 For each time interval the
operation modes of the transformers are selected first and the locations of tie-
switches are then determined
Chapter 6 Distribution Network Reconfiguration amp Transformer Economic
Operation for Network Loss Reduction
Page | 117
Start
Set time interval T=1
Maximum iteration
reached
Output best
configuration and end
No
Yes
Divide the 24-h daily load curve into two
intervals using the technique in Section 62
Iteration N=1
Initialise the parameters for ACO
algorithm searching space
Dispatch ants based on the amount
of pheromone on edges
Relocate tie-switches and select the
number of transformers to be operated in
all substations by location lists
N=N+1
Calculate the objective function
for each ant at this time interval
Read system topology
and load data
The pheromones are updates
according to local and global rules
Record the best solution so far
and empty all location lists
T=T+1
Tgt2
Yes
t=t+1
No
Fig 6-4 Flowchart of the ACO applied to DNR and TEO for a specific type of day
Chapter 6 Distribution Network Reconfiguration amp Transformer Economic
Operation for Network Loss Reduction
Page | 118
LP11 LP12 LP13 LP14 LP15 LP16 LP17
LP8 LP9 LP10
LP1 LP2 LP3 LP4 LP5 LP6 LP7
LP32 LP33 LP34 LP35 LP36 LP37 LP38
LP29 LP30 LP31
LP26 LP27 LP28
LP18 LP19 LP20 LP21 LP22 LP23 LP24 LP25
19
20
21
22
23
24
26
25 27
28
29 30
71
13 15
14 16
17
18
69
1 3
2
5
4
7
6 8
10
9
68
11 12
56
57
58 60
59 61 62
65
64 66 67
50 52
51
54
53 55
44
45
46
47
48
49
70
31
32
33
34
36
35
39
37 38 40
41
42 43
63
F3
F2
F1
F7
F6
F5
F4
Normally Open Circuit BreakerNormally Closed Circuit Breaker
Subbus1
Subbus2
Subbus3
T1
T3
T5
Main
feeder
Main
feeder
Main
feeder
T2
T4
T6
65 Application Studies
In this study the proposed methodology is applied to an 11 kV distribution network
developed from Bus 4 of the RBTS a single-line diagram of the network is shown in
Fig 6-5 The network consists of 38 load points and 4 tie-switches the associated
data can be found in [114] The types and lengths of 11 kV feeders are listed in
Appendix A4 The network built in OpenDSS incorporates three 3311 kV double
transformer substations supplying the downstream loads
Fig 6-5 Distribution feeder connected to RBTS Bus 4
This typical urban distribution network supplies residential commercial and
industrial consumers The maximum value of active and reactive power and the
Chapter 6 Distribution Network Reconfiguration amp Transformer Economic
Operation for Network Loss Reduction
Page | 119
customer type of each node are modified from the original values and the new values
are listed in Table 6-1
Table 6-1 Revised customer data (peak load)
Number
of load
points
Load points Customer type P
(kW)
Q
(kVAr)
Number of
customers
4 1-2 9-10 residential 8869 8426 220
6 3-5 13-15 residential 8137 7731 200
12 6-7 16-17 23-25 28
30-31 37-38
commercial 6714 6378 10
6 8 11 18 26 32-33 industrial 2445 23228 1
10 12 19-22 27 29 34-
36
industrial 1630 15485 1
The days of the year are divided into eight categories spring weekdays spring
weekends summer weekdays summer weekends autumn weekdays autumn
weekends winter weekdays and winter weekends Typical loads profiles for
different consumer types are shown in Fig 6-6-6-8 which are multiplied by the
values of Table 6-1 to obtain the real demand of each node [82] In order to find the
reconfiguration hours for each day type the aggregated load profiles of the main
feeder shown in Fig 6-9 are used
Fig 6-6 Daily load profile of residential consumers
Chapter 6 Distribution Network Reconfiguration amp Transformer Economic
Operation for Network Loss Reduction
Page | 120
Fig 6-7 Daily load profile of commercial consumers
Fig 6-8 Daily load profile of industrial consumers
Fig 6-9 Daily load profile (MW) of the main feeder
Chapter 6 Distribution Network Reconfiguration amp Transformer Economic
Operation for Network Loss Reduction
Page | 121
In this case eight types of day and two time intervals for each of them are
considered As a result the optimisation problem has to be solved 16 times to obtain
a yearly reconfiguration scheme The distribution of load types for a whole year is
shown in Table 6-2
Table 6-2 The distribution of load types for a whole year
Load Types Number of days Total days
Spring
(Mar Apr May)
Weekdays 66 92
Weekends 26
Summer
(Jun Jul Aug)
Weekdays 66 92
Weekends 26
Autumn
(Sep Oct Nov)
Weekdays 65 91
Weekends 26
Winter
(Dec Jan Feb)
Weekdays 64 90
Weekends 26
Year 365 Days
For the purpose of better illustration and comparison three test cases are considered
to analyse the superiority and performance of the proposed method
Test Case 1 The system is optimally reconfigured and has no DGs and EVs
Test Case 2 The system is optimally reconfigured after DGs are placed at certain
buses
Test Case 3 The system is optimally reconfigured after integration of EVs
The proposed ACO algorithm is coded in the MATLAB to obtain the location of tie-
switches and operation modes of transformers for the optimum configuration The
settings of the ACO parameters that provided the optimum solution for these three
cases are presented in Appendix C2 The selection of parameters is a balance
between the convergence rate and the global search ability of the algorithm
Chapter 6 Distribution Network Reconfiguration amp Transformer Economic
Operation for Network Loss Reduction
Page | 122
651 Test Case 1
In this test the tie-switches are relocated and the operation modes of transformers in
all substations are changed to obtain the best network configuration with minimum
network loss
Table 6-3 Results of DNR and TEO with different load types in Test Case 1
As shown in Fig 6-5 the tie-switches are located in L68-71 and each substation has
two transformers operating in parallel for the base network configuration The test
results with different load conditions are presented in Table 6-3 Reconfiguration of
the network and changes in the operation modes of transformers in all substations
using the proposed algorithm result in a reduction of loss for all load conditions As
a result the annual energy loss is reduced from 4337150 kWh to 4117681 kWh
which amounts to a 506 reduction Both transformer loss and feeder loss are
reduced through this optimal planning using DNR and TEO It can be noted that on
winter weekdays the loading of the main feeders is very high from 800 to 2100
Spring
weekday
Spring
weekend
Summer
weekday
Summer
weekend
Autumn
weekday
Autumn
weekend
Winter
weekday
Winter
weekend
Before
Reconfiguration
Whole Day Open branches L68L69
L70L71
L68L69
L70L71
L68L69
L70L71
L68L69
L70L71
L68L69
L70L71
L68L69
L70L71
L68L69
L70L71
L68L69
L70L71
Number of operated
transformers
1st substation 2 2 2 2 2 2 2 2
2nd substation 2 2 2 2 2 2 2 2
3rd substation 2 2 2 2 2 2 2 2
Loss
(kWh)
Cable 9233 3498 8050 3151 9660 3665 11009 4080
Transformer 4301 3410 4109 3350 4372 3437 4597 3507
Total 13534 6908 12159 6501 14032 7102 15606 7587
After
Reconfiguration
1st interval Time (h) 0-7
23-24
0-6 0-7
23
0-7 0-7
22-23
0-6
0-7
22-23
0-6
Open branches L48L68
L69L71
L68L69
L70L71
L17L68
L70L71
L17L68
L70L71
L17L68
L70L71
L68L69
L70L71
L17L68
L70L71
L68L69
L70L71
Number of operated
transformers
1st substation 1 1 1 1 1 1 1 1
2nd substation 1 1 1 1 1 1 1 1
3rd substation 1 1 1 1 1 1 1 1
2nd interval Time (h) 8-22 7-23 8-22 8-23 8-21 7-23 8-21 7-23
Open branches L17L41
L65L70
L68L69
L70L71
L41L48
L65L69
L68L69
L70L71
L17L41
L65L70
L68L69
L70L71
L17L41
L65L70
L68L69
L70L71
Number of operated
transformers
1st substation 2 2 2 2 2 2 2 2
2nd substation 2 1 2 1 2 1 2 1
3rd substation 2 1 2 1 2 1 2 1
Loss
(kWh)
Cable 9043 3516 7851 3169 9519 3685 10845 4103
Transformer 3955 2616 3759 2517 4036 2656 4264 2755
Total 12998 6132 11610 5686 13479 6341 15109 6858
Chapter 6 Distribution Network Reconfiguration amp Transformer Economic
Operation for Network Loss Reduction
Page | 123
0
05
1
15
2
25
3
35
4
45
05 1 15 2 25 3
Before reconfiguration
After reconfiguration
Thus transformers in all substations are operated in parallel However during spring
weekends from 000 to 700 as the loadings supplied by all feeders are lower than
the critical transformer load factor (TCLF) and hence transformers in all substations
are operated in single In addition the loadings supplied by Feeder 4 are much larger
than that of Feeder 3 in summer weekdays between 800 to 2200 Thus the tie-
switch is moved from L71 to L41 and LP24amp25 are moved from Feeder 4 to Feeder
3 This ensures balancing of the loads between the two feeders
652 Test Case 2
In this test the presence of three DG units is taken into consideration The effect of
DGs on assessing the DNR and TEO problems in terms of loss minimisation is
studied The introduction of DGs converts a mono-source distribution network to a
multi-source one [66] The three DGs are located at the end of the feeders ie Bus
17 41 and 65 All the DGs are synchronous generators and considered as PQ models
The capacity of DG is assumed to be 05 1 15 2 25 and 3 MVA respectively
The results are shown in Fig 6-10 and show that the proposed methodology has
successfully reduced the total energy loss for different capacities of DG by
determining the most suitable network topology
Fig 6-10 Annual energy loss with different DG capacities
To
tal
loss
(G
Wh
)
DG Capacity (MW)
Chapter 6 Distribution Network Reconfiguration amp Transformer Economic
Operation for Network Loss Reduction
Page | 124
653 Test Case 3
The objective of this section is to illustrate the behaviour of the proposed
optimisation process when EVs are integrated into the existing distribution network
The impacts of EV penetration levels and charging strategies are studied This
section utilises the optimal planning using DNR and TEO as a technique to decrease
network loss whilst respecting the operation constraints It is assumed that the
battery starts charging once the EV is connected to the charger at home
The charging duration can be calculated according to the following formula [89]
119905119888 =119862119864119881times(1minus119878119874119862)times119863119874119863
120578times119875119862 (6-4)
where 119862119864119881 is the battery capacity In this section EVs are divided into four types
with different market shares and batteries as in Table 6-4 [115] 119863119874119863 and 120578 are
depth of discharge and charger efficiency (assumed to be 80 and 90 separately)
Two types of chargers with different charging rates (119875119862) are commonly used for
consumer EVs at home charging points this study assumes that 80 of EVs are
charged at 3kW (13A) and 20 at 7kW (30A) [92] SOC is state-of-charge and is
defined as the ratio of available energy to maximum battery capacity [89] It is
determined by the distance covered by the EV in terms of number of miles during
the day
Table 6-4 Characteristics of EV
Types 119862119864119881 (kWh) Maximum driving
capability (mile)
Market share ()
Micro car 12 50 20
Economy car 14 53 30
Mid-size car 18 56 30
Light truck SUV 23 60 20
According to [116] the average number of miles covered by a vehicle was reported
to be 2164 milesday in 2014 Then the SOC for an EV is calculated based on
number of miles (m) and the maximum driving capability (MDC) as follows
Chapter 6 Distribution Network Reconfiguration amp Transformer Economic
Operation for Network Loss Reduction
Page | 125
4
42
44
46
48
5
30 60 90
Before reconfiguration
After reconfiguration
119878119874119862 = 0 119898 gt 119872119863119862
119872119863119862minus119898
119872119863119862 119898 le 119872119863119862 (6-5)
As mentioned before the EVs are distributed over all the residential load points The
number of customers of residential loads is given in Table 6-1 It is reported that
each customer has 15 vehicles [92] The problem is solved for three different
penetration levels of EVs in the test network 30 60 and 90 respectively In
addition two charging strategies are introduced (1) uncoordinated charging and (2)
coordinated charging The thermal problems of cables which caused by high
penetration levels of EVs are ignored in this study
1) Uncoordinated Charging Strategy
In this part all EVs are plugged in and immediately start charging when they arrive
home In most cases the EV plug-in time is modelled by normal distribution which
increases uncertainty However in order to simplify the discussion the charging start
time is assumed to be 1800 when most people are back home from work The total
losses in the network for the different penetration levels of EVs are compared in Fig
6-11 It can be seen that as the penetration of EVs is increased the total loss also
increases But the total loss for all penetration levels decreases by implementing the
optimal planning strategy in comparison with the original network
Fig 6-11 Annual energy loss in uncoordinated charging strategy
To
tal
loss
(G
Wh
)
Penetration level ()
Chapter 6 Distribution Network Reconfiguration amp Transformer Economic
Operation for Network Loss Reduction
Page | 126
4
42
44
46
48
5
30 60 90
Before reconfiguration
After reconfiguration
2) Coordinated Charging Strategy
In this case the DNOs tend to charge the EVs during off-peak hours to avoid a clash
with the evening peak hours As a result the charging start time is delayed to 0100
when most people are sleeping The total network loss for different EV penetrations
is compared in Fig 6-12 The results show that the postponement of charging time
and optimal planning strategy has been successful in reducing the total energy loss in
comparison with the uncoordinated charging method
Fig 6-12 Annual energy loss in coordinated charging strategy
66 Summary
This study has presented a new optimal planning strategy using DNR and TEO for
distribution network loss minimisation including transformer loss and feeder loss In
this study the distribution loads experience daily and seasonal variations The day is
divided into two periods The proposed ACO algorithm has been successfully
applied to the modified Bus 4 of the RBTS to find the optimum network
configuration and economic operation mode of transformers in all substations during
each time interval Using the results obtained for reconfiguration the existing tie-
switches are relocated and the transformer operation modes are changed
Furthermore the simulation results obtained with numerical studies further
demonstrate the capability of applying the ACO algorithm to distribution network
planning including networks with DGs and EVs The proposed methodology has
successfully reduced the total network loss for different capacities of DG and
To
tal
loss
(G
Wh
)
Penetration level ()
Chapter 6 Distribution Network Reconfiguration amp Transformer Economic
Operation for Network Loss Reduction
Page | 127
different penetration levels of EVs by determining the most suitable network
topology compared to the original configuration The benefits associated with the
increasing capacity of DGs and increasing penetration levels of EVs are also
presented Comparative results show that coordinated charging of EVs results in less
energy loss compared to uncoordinated charging plan with the same EV penetration
level This is due to the postponement of charging time which avoids a clash with
the peak power demand times
The proposed ACO algorithm is suitable for planning a future network based on the
load estimation results Hence there is no limitation on the calculation time An
additional interesting point about DNR and TEO is that although the opening and
closing of switches and transformers result in the life reduction of plants the
additional costs for utilities is insignificant in comparison with the benefits they
bring All the results have proved that a distribution network can be reconfigured and
the operation modes of transformers can be changed to reduce network power loss
which can increase the profits of the distribution utilities
Page | 128
CHAPTER 7
OPTIMAL PLACEMENT OF
SECTIONALISING SWITCHES FOR
RELIABILITY IMPROVEMENT
71 Introduction
Failures in the distribution network cause the majority of service interruptions [78]
And reliability improvement becomes a motivation for distribution utilities to launch
research and demonstration projects [64] An effective method to reduce customer
minutes lost is the greater and more effective use of automated and remote controlled
sectionalising switches and feeder breaker automation This approach will reduce
customer restoration time and minimise the region of a network affected by a short-
circuit fault The effectiveness depends on the number location and type of
sectionalising switches and feeder breakers
Reliability improvement by reduction of expected customer damaged cost (ECOST)
and system interruption duration index (SAIDI) as well as the minimisation of
switch costs are considered in formulating the objective function used in this study
When there are multiple objectives to be considered a compromise solution has to
be made to obtain the best solution ECOST and switch costs can be converted into a
single objective function by aggregating these objectives in a weighted function
Chapter 7 Optimal Placement of Sectionalising Switches for Reliability
Improvement
Page | 129
However as SAIDI and switch costs have different dimensions and units a single
fuzzy satisfaction objective function is used to transform the two conflicting
objectives into fuzzy memberships and then finally to combine them into a single
objective function Also a fuzzy membership function based on the max-min
principle is presented for optimising ECOST SAIDI and switch costs
simultaneously These are achieved by the optimal installation of new switches and
the relocation of existing switches Therefore identifying the number and location of
switches becomes an optimisation problem The ant colony optimisation (ACO) is
adopted which has the ability to find near optimal solutions close to the global
minimum in a finite number of steps This algorithm is proposed for the assessing
the sectionalising switch placement (SSP) problem based on reliability improvement
and switch costs minimisation using a multi-objective function with fuzzy variables
The impact of benefit-to-cost analysis is then investigated to justify investment
expenses Furthermore the importance of the customer damage function (CDF)
variation in determining the SSP is investigated through sensitivity analysis And the
ACO parameter sensitivity analysis is also provided in this study
The mathematical formulation of the objective function is presented in Section 72
and in Section 73 the applied ACO algorithm used to address the problems of SSP
is discussed Section 74 describes the benefit-cost analysis and the numerical case
studies are presented and discussed in Section 75 The main conclusions of the study
are summarised in Section 76
72 Problem Formulation
The primary objective of this study is to resolve the three conflicting objectives
reduction of unserved energy cost decrease in the average time a customer is
interrupted and minimisation of switch costs Three formulations of objective
functions are presented and the solution is a trade-off between each objective
721 Weighted Aggregation
As ECOST and switch costs have the same units and dimensions they are
transformed into a single objective function by aggregating all the objectives in a
weighted function
Chapter 7 Optimal Placement of Sectionalising Switches for Reliability
Improvement
Page | 130
119872119894119899 119869 = micro1 ∙ 119864119862119874119878119879 + micro2 ∙ 119878119862 (7-1)
where ECOST is the system expected outage cost to customers ($) and SC is the cost
of sectionalising switches ($) micro1and micro2 are the weighting factors given to the
reliability index and the cost of switches
722 Single Fuzzy Satisfaction Objective Function with Two
Parameters
SAIDI and switch costs are associated with a membership function in a fuzzy
domain due to different dimensions The satisfaction level of each objective is
represented by the membership function [66] The higher the membership value is
the better the solution is The two objectives are combined into a fuzzy environment
and a final objective function is formulated as follows
119872119886119909 119870 = 1205961 ∙ 120572119878119860 + 1205962 ∙ 120572119878119862 (7-2)
where 120572119878119860 is the membership function value to distribution reliability improvement
by SAIDI reduction 120572119878119862 is the value of membership function for a decrease in the
switch costs 1205961and 1205962 are the constant weighting factors for each of the parameters
The optimisation process can be changed for different purposes by varying the
values of weighting factors which should satisfy the condition 1205961 + 1205962 = 1 A
higher weighting factor indicates that this parameter is more important [66] In the
fuzzy domain each objective has a membership value varying from zero to unity
[66] The proposed membership function for each objective is described below
Membership function for SAIDI reduction
The basic purpose of this membership function is to improve reliability or obtain the
minimum SAIDI Therefore the placement of sectionalising switches with a lower
SAIDI value obtains a higher membership value The membership function for
reliability improvement is formulated in (7-3) and presented in Fig 7-1 (a) As
SAIDI becomes greater than 119878119860119868119863119868119898119894119899 the degree of satisfaction is decreased This
reduction is continued until SAIDI reaches 119878119860119868119863119868119900119903119894
Chapter 7 Optimal Placement of Sectionalising Switches for Reliability
Improvement
Page | 131
0
1
0
1
120572119878119860 =
1 119878119860119868119863119868 le 119878119860119868119863119868119898119894119899119878119860119868119863119868119900119903119894minus119878119860119868119863119868
119878119860119868119863119868119900119903119894minus119878119860119868119863119868119898119894119899119878119860119868119863119868119898119894119899 lt 119878119860119868119863119868 lt 119878119860119868119863119868119900119903119894
0 119878119860119868119863119868 ge 119878119860119868119863119868119900119903119894
(7-3)
where 119878119860119868119863119868119900119903119894 is the SAIDI of the original network 119878119860119868119863119868119898119894119899 is the minimum
value of SAIDI which is obtained by placing sectionalising switches in all candidate
locations As it is not appropriate for decision makers to obtain a combination of
sectionalising switches which reduces reliability after switch placement the
minimum value of 120572119878119860 is selected as 0 if SAIDI is greater than or equal to 119878119860119868119863119868119900119903119894
(a) SAIDI reduction (b) SC reduction
Fig 7-1 Membership function for SAIDI and switch cost reduction
Membership function for switch cost reduction
The membership function for switch costs reduction is shown in Fig 7-1(b) The
mathematical equation is presented below
120572119878119862 =
1 119878119862 le 119878119862119900119903119894119878119862119898119886119909minus119878119862
119878119862119898119886119909minus119878119862119900119903119894119878119862119900119903119894 lt 119878119862 lt 119878119862119898119886119909
0 119878119862 ge 119878119862119898119886119909
(7-4)
where 119878119862119900119903119894 and 119878119862119898119886119909 are the original and maximum value of switch costs
respectively The maximum switch costs are obtained by installing sectionalising
switches in all candidate sites
723 Single Fuzzy Satisfaction Objective Function with Three
Parameters
When there are more than two objectives with different dimensions and units to be
satisfied simultaneously a single fuzzy satisfaction objective function based on the
120572119878119860
119878119860119868119863119868119898119894119899 119878119860119868119863119868119900119903119894 119878119860119868119863119868
120572119878119862
119878119862119900119903119894 119878119862119898119886119909 119878119862
Chapter 7 Optimal Placement of Sectionalising Switches for Reliability
Improvement
Page | 132
0
1
max-min principle is considered The three conflicting objectives to be optimised are
ECOST SAIDI and switch costs The membership functions for SAIDI and switch
costs are presented in the previous section The function for ECOST is shown in Fig
7-2 and expressed as
120572119864119862 =
1 119864119862119874119878119879 le 119864119862119874119878119879119898119894119899119864119862119874119878119879119900119903119894minus119864119862119874119878119879
119864119862119874119878119879119900119903119894minus119864119862119874119878119879119898119894119899119864119862119874119878119879119898119894119899 lt 119864119862119874119878119879 lt 119864119862119874119878119879119900119903119894
0 119864119862119874119878119879 ge 119864119862119874119878119879119900119903119894
(7-5)
where 119864119862119874119878119879119900119903119894 and 119864119862119874119878119879119898119894119899 are the original and minimum value of ECOST
respectively The minimum ECOST is obtained by installing sectionalising switches
in all candidate locations
Fig 7-2 Membership function for ECOST reduction
The degree of overall satisfaction for these objective functions is the minimum value
of all the membership functions [85] The fuzzy decision for a final compromised
solution is the maximum degree of overall satisfaction and is formulated in (7-6)
Max 119871 = min (120572119878119860 120572119878119862 120572119864119862) (7-6)
724 Evaluation of ECOST
ECOST is an index that combines reliability with economics The best way to
present customer interruption costs is in the form of CDF A CDF provides the
interruption cost versus interruption duration for a various class of customers and
can be aggregated to produce a composite CDF at any particular load point [67] [69]
Generally ECOST is used to represent the customer outage costs since it not only
considers the effects of the system configuration interruption durations load
variations and equipment failure probability but also accounts for the various
customer types and their damage functions [52]
120572119864119862
119864119862119874119878119879119898119894119899 119864119862119874119878119879119900119903119894 119864119862119874119878119879
Chapter 7 Optimal Placement of Sectionalising Switches for Reliability
Improvement
Page | 133
The calculation of ECOST of the total system over T years is based on failure-mode-
and-effect analysis (FMEA) and can be quantified as follows
1 ( 1)
1 1 1 1 1 1
( ) ( ) ( ) ( ) (1 ) (1 )b b b b bN CT NR CT NST
t t
b b k R k s
t b k j k j
ECOST L P k j C d P k j C d IR DR
(7-7)
where T is time period (year) 119873119887 is the total number of branches 120582119887and 119871119887 are the
average failure rate (failurekm-year) and length (km) of branch b 119862119879119887 119873119877119887 and
119873119878119887 are the total number of customer types permanent damaged and temporary
damaged load points when the fault is at branch b P(k j) is the average load of the
kth-type customers at the jth load point (kW) 119862119896(119889) is the CDF for kth-type
customer lasting d hours ($kW) 119889119877 and 119889119878 are the average repair time and the
switch time after failure IR and DR are the annual load increase rate and discount
rate
725 Evaluation of SAIDI
The SAIDI which represents the average outage duration time of each customer
over T years can be expressed as
119878119860119868119863119868 = sum sum 120582119887∙119871119887[sum 119889119877
119873119862119877(119887)119899=1 +sum 119889119878
119873119862119878(119887)119899=1 ]
119873119887119887=1
119873119862119905119900119905119886119897119879
119905=1 (7-8)
where 119873119862119877(119887) and 119873119862119878(119887) are the number of permanent damaged and temporary
damaged customers when the fault is at branch b 119873119862119905119900119905119886119897 is the total number of
served customers SAIDI is measured in hours
726 Evaluation of Switch Costs
In this study reliability is improved by the installation of new sectionalising
switches and relocation of existing switches Thus the total cost of switches can be
determined as following
119878119862 = 119862119868119878 ∙ 119873119899119890119908 + 119862119877119878 ∙ 119873119903119890119897 + sum 119872119862119879119905=1 ∙ (119873119899119890119908 + 119873119890119909119894119904) ∙ (1 + 119863119877)minus(119905minus1) (7-9)
where CIS is the investment and installation cost of a new sectionalising switch ($)
119873119899119890119908 119873119903119890119897 and 119873119890119909119894119904 are the number of newly installed relocated and existing
sectionalising switches respectively CRS is the relocation cost of an existing
Chapter 7 Optimal Placement of Sectionalising Switches for Reliability
Improvement
Page | 134
Home
0
1
0
1
0
1
0
1
Food
Number of candidate locations for sectionalising switches
sectionalising switch ($) and MC is the maintenance and operation cost of a
sectionalising switch ($)
73 Applying ACO to Sectionalising Switch Placement
Problem
This study uses ACO algorithm for distribution automation in terms of the
installation of new sectionalising switches and relocation of existing switches When
the locations of sectionalising switches are changed a new network configuration
will be formed The search method is used for finding the optimal value of objective
functions as presented in Section 721-723
The search space of the automation problem in terms of SSP is modelled as a
directed graph as shown in Fig 7-3 The number of stages is the candidate locations
for all the sectionalising switches 119873119878 For this problem the switch status can be
represented as a binary vector in each stage State 0 ldquono sectionalising switch in this
locationrdquo State 1 is ldquoa sectionalising switch in this locationrdquo The artificial ant
searches for the values of the bits and produces a solution to the problem after it
completes a tour between the home and food source which is similar to the process
described in Section 532
Fig 7-3 Search space of sectionalising switch placement
Chapter 7 Optimal Placement of Sectionalising Switches for Reliability
Improvement
Page | 135
74 Benefit-to-cost Analysis
The benefit-to-cost analysis is a financial term that describes the expected balance of
benefits made from the investment and costs incurred during the production process
It helps predict if an investmentdecision is feasible and whether its benefits
outweigh the costs during a predefined time interval [82]
In this study the benefit-to-cost ratio (BCR) offers a comparison between ECOST
and SC The benefit to the distribution network operator (DNO) is the reduction of
ECOST which is equal to
119887119890119899119890119891119894119905 = sum119864119862119874119878119879119887119886119904119890
119905 minus119864119862119874119878119879119900119901119905119905
(1+119863119877)119905119879119905=1 (7-10)
where 119864119862119874119878119879119887119886119904119890119905 and 119864119862119874119878119879119900119901119905
119905 are the value of ECOST of year t before and after
the placement of switches ($)DR is the annual discount rate
The cost for the DNO is the total switching cost including investment maintenance
and operation cost as presented in (7-9) and BCR is defined as
119861119862119877 =119887119890119899119890119891119894119905
119878119862 (7-11)
A higher value for BCR indicates that the benefits relative to the costs are greater
The investment return time refers to the time when BCR starts to exceed 10 If the
investment return time is less than the lifetime of a switch adding a switch will bring
benefits to the investors
Chapter 7 Optimal Placement of Sectionalising Switches for Reliability
Improvement
Page | 136
LP11 LP12 LP13 LP14 LP15 LP16 LP17
LP8 LP9 LP10
LP1 LP2 LP3 LP4 LP5 LP6 LP7
LP32 LP33 LP34 LP35 LP36 LP37 LP38
LP29 LP30 LP31
LP26 LP27 LP28
LP18 LP19 LP20 LP21 LP22 LP23 LP24 LP25
9 10 11 12 13 33
6 7 8 31
1 2 3 4 5 30
25 26 27 29
22 23 24
19 20 21
32
14 15 16 17 18
28
F3
F2
F1
F7
F6
F5
F4
Normally Open Circuit BreakerNormally Closed Circuit Breaker
Subbus1
Subbus2
Subbus3
T1
T3
T5
Main
feeder
Main
feeder
Main
feeder
T2
T4
T6
75 Application Studies
In this study the proposed methodology is applied to an 11 kV distribution network
developed from Bus 4 of the Roy Billinton Test System (RBTS) The single-line
diagram of the network with 6 existing sectionalising switches is shown in Fig 7-4
Fig 7-4 Distribution feeder connected to RBTS Bus 4 with 6 sectionalising switches
In this study there are 51 locations considered as candidates for switch placement
[114] All the values of the required data ie feeder type and length as well as
component failure rate are available in [114] and summarised in Appendix A4 The
failure rate of the feeders is proportional to their physical length and all other
Chapter 7 Optimal Placement of Sectionalising Switches for Reliability
Improvement
Page | 137
components ie transformers buses and breakers are assumed to be completely
reliable This typical urban distribution network supplies residential commercial and
industrial consumers The average value of active power and the customer type of
each node were also found in [114] and listed in Table 7-1 The power factors of all
the loads are set to 10
Table 7-1 Customer data (Average load)
Number
of load
points
Load points Customer type P
(kW)
Number of
customers
15 1-4 11-13 18-21 32-35 residential 545 220
7 5 14 15 22 23 36 37 residential 500 200
7 8 10 26-30 industrial 1000 1
2 9 31 industrial 1500 1
7 6 7 16 17 24 25 38 commercial 415 10
The relocation cost of a sectionalising switch is US $ 500 The investment and
installation cost of a sectionalising switch is US $ 4700 [64] The annual
maintenance and operation cost is considered to be 2 of the investment cost [64]
All the sectionalising switches and circuit breakers are remotely controlled The
costs of the feeder terminal unit which is used for data acquisition of the switch
status and communication equipment have also been added to the automated
sectionalising switches The overall switching time of sectionalising switch and
circuit breakers for temporary damage load points in other words the time between
the occurrence of a fault and the restoration of energy to unaffected areas is set to 10
minutes [64] And the average repair time of the permanent faulty section is assumed
to be 5 hours The lifetime of a switch depends on various factors such as the
maximum number of allowable switching operations the number of annual
switching operations of the switch etc Based on these factors the life period of the
switches is calculated to be 15 years The load growth rate and the annual interest
rate are set to 3 and 8 respectively The CDF data are extracted from [64] and
summarised in Table 7-2
Chapter 7 Optimal Placement of Sectionalising Switches for Reliability
Improvement
Page | 138
Table 7-2 Sector interruption cost estimation ($kW)
User Sector Interruption Duration
10 min 1 hour 2 hour 4 hour 5 hour 10 hour
Residential 006 11 16 26 316 5
Industrial 288 806 95 124 1387 276
Commercial 205 96 125 185 2151 6306
The proposed ACO algorithm was coded in the MATLAB to obtain the location of
the sectionalising switches In this study three cases with different objective
functions are considered to analyse the superiority and performance of the proposed
method
Test Case 1 Minimisation of ECOST and switch costs
Test Case 2 Minimisation of SAIDI and switch costs
Test Case 3 Minimisation of ECOST SAIDI and switch costs
The final combinations of the ACO control parameters that provide the best results
for all the above tests are given in Appendix C3
751 Test Case 1
In this test the minimisation of ECOST and switch costs are considered in the
formulation of a single objective function this involves aggregating the objective
functions as presented in Section 721 For simplicity both weighting factors micro1
and micro2 are set to 1 ie these two objectives are assumed to be equally important
Three cases are studied as follows
Case 11 Optimal relocation of existing sectionalising switches
Case 12 Optimal installation of new sectionalising switches
Case 13 Optimal installation of new sectionalising switches and relocation of
existing sectionalising switches
Chapter 7 Optimal Placement of Sectionalising Switches for Reliability
Improvement
Page | 139
LP11 LP12 LP13 LP14 LP15 LP16 LP17
LP8 LP9 LP10
LP1 LP2 LP3 LP4 LP5 LP6 LP7
LP32 LP33 LP34 LP35 LP36 LP37 LP38
LP29 LP30 LP31
LP26 LP27 LP28
LP18 LP19 LP20 LP21 LP22 LP23 LP24 LP25
9 10 11 12 13 33
6 7 8 31
1 2 3 4 5 30
25 26 27 29
22 23 24
19 20 21
32
14 15 16 17 18
28
F3
F2
F1
F7
F6
F5
F4
Normally Open Circuit BreakerNormally Closed Circuit Breaker
Subbus1
Subbus2
Subbus3
T1
T3
T5
Main
feeder
Main
feeder
Main
feeder
T2
T4
T6
Case 11 Optimal relocation of existing sectionalising switches
The objective of this case is to investigate the optimum sectionalising switch
relocation problem The optimal locations of sectionalising devices are shown in Fig
7-5 Before relocation the total cost including ECOST operation and maintenance
cost of existing switches over 15 years is US $ 477090 After relocation the total
cost including the addition of relocation cost obtained by the ACO approach is US
$ 343620 which amounts to a reduction of 2798
Fig 7-5 Optimal relocation of sectionalising switches in Test Case 11
Chapter 7 Optimal Placement of Sectionalising Switches for Reliability
Improvement
Page | 140
In comparison with the original configuration 4 switches change their locations The
optimal locations of sectionalising switches and the number and types of loads
adjacent to each switch are presented in Table 7-3 The results indicate that each
feeder attempts to have at least one switch As there are 6 switches and 7 feeders
and the total load level of Feeder 5 is 3000 kW which is the lowest value for all the
feeders no switch is placed on Feeder 5 It should also be noted that the load
density and customer types play an important role in determining the locations of
sectionalising switches For instance the adjacent load of Switch 1 is LP6 and LP7
which has the highest CDF value (commercial load) and relatively high load levels
In addition Switch 2 is placed on 7D whose adjacent load is LP9 and this has the
largest load density
Table 7-3 Results of sectionalising switches relocation in Test Case 11
Switch
No
Feeder Location Total Feeder
Load (kW)
Adjacent Load Adjacent Load Levels (kW) and
Type
1 1 5D 3510 LP6 LP7 415 (commercial) 415 (commercial)
2 2 7D 3500 LP9 1500 (industrial)
3 3 13D 3465 LP16 LP17 415 (commercial) 415 (commercial)
4 4 18D 4010 LP24 LP25 415 (commercial) 415 (commercial)
5 6 23D 3500 LP30 1000 (industrial)
6 7 28D 3595 LP36 500 (commercial)
( Each section has two candidate locations for sectionalising switch placement U means upstream side of the section and D
means downstream side of the section)
Case 12 Optimal installation of new sectionalising switches
In this case the effect of installing new sectionalising switches without relocating
the existing switches is studied As shown in Fig 7-6 there are 11 new
sectionalising switches installed
The detailed results of ECOST capital and installation as well as the operation and
maintenance cost of sectionalising switches over 15 years are shown in Table 7-4
After the installation of sectionalising switches the total system cost is decreased
from US $ 477090 to US $ 286980 ie a reduction of 3984
Chapter 7 Optimal Placement of Sectionalising Switches for Reliability
Improvement
Page | 141
LP11 LP12 LP13 LP14 LP15 LP16 LP17
LP8 LP9 LP10
LP1 LP2 LP3 LP4 LP5 LP6 LP7
LP32 LP33 LP34 LP35 LP36 LP37 LP38
LP29 LP30 LP31
LP26 LP27 LP28
LP18 LP19 LP20 LP21 LP22 LP23 LP24 LP25
9 10 11 12 13 33
6 7 8 31
1 2 3 4 5 30
25 26 27 29
22 23 24
19 20 21
32
14 15 16 17 18
28
F3
F2
F1
F7
F6
F5
F4
Normally Open Circuit BreakerNormally Closed Circuit Breaker
Subbus1
Subbus2
Subbus3
T1
T3
T5
Main
feeder
Main
feeder
Main
feeder
T2
T4
T6
Fig 7-6 Optimal installation of sectionalising switches in Test Case 12
Table 7-4 Results of sectionalising switches installation in Test Case 12
ECOST
($)
Number of
installed
switches
Capital and
installation cost
($)
Maintenance
and operation
cost ($)
Total system
cost ($)
Before switches
installation
472260 0 0 4830 477090
After switches
installation
221610 11 51700 13670 286980
Chapter 7 Optimal Placement of Sectionalising Switches for Reliability
Improvement
Page | 142
LP11 LP12 LP13 LP14 LP15 LP16 LP17
LP8 LP9 LP10
LP1 LP2 LP3 LP4 LP5 LP6 LP7
LP32 LP33 LP34 LP35 LP36 LP37 LP38
LP29 LP30 LP31
LP26 LP27 LP28
LP18 LP19 LP20 LP21 LP22 LP23 LP24 LP25
9 10 11 12 13 33
6 7 8 31
1 2 3 4 5 30
25 26 27 29
22 23 24
19 20 21
32
14 15 16 17 18
28
F3
F2
F1
F7
F6
F5
F4
Normally Open Circuit BreakerNormally Closed Circuit Breaker
Subbus1
Subbus2
Subbus3
T1
T3
T5
Main
feeder
Main
feeder
Main
feeder
T2
T4
T6
Case 13 Optimal relocation and installation of sectionalising switches
A Base case
The main objective of this test is to reduce the total system cost including ECOST
and switch costs by the relocation of existing sectionalising switches and the
installation of new ones The switch locations are presented in Fig 7-7
Fig 7-7 Optimal installation and relocation of sectionalising switches in Test Case 13
In comparison with the original configuration there are 8 new sectionalising
switches installed and 5 existing switches relocated As expected the sectionalising
switches are placed adjacent to the load centres with either the highest load density
Chapter 7 Optimal Placement of Sectionalising Switches for Reliability
Improvement
Page | 143
0
1
2
3
4
5
6
7
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
BC
R
Years
or the highest CDF For example the adjacent load of switch 13D is LP6 and LP7
which has the highest CDF value (commercial loads) In addition switch 7D is
placed adjacent to LP9 which has the largest load density The detailed results for
ECOST and switch costs are shown in Table 7-5 After the installation and relocation
of the switches the total system cost is decreased from US $ 477090 to US
$ 272480 ie a reduction of 4289
Table 7-5 Results of sectionalising switches relocation and installation in Test Case 13
ECOST
($)
Number of
relocated
switches
Relocation
cost ($)
Number of
installed
switches
Capital and
installation
cost ($)
Maintenance
and operation
cost ($)
Total
system
cost ($)
Before switch
placement
472260 0 0 0 0 4830 477090
After switch
placement
221120 5 2500 8 37600 11260 272480
B Benefit-to-Cost analysis
BCR analysis is used to verify the benefits and costs of sectionalising switch
placement for distribution operators The results are presented in Fig 7-8 The
benefits and costs are accumulated during the predefined life period There is no
return on investment for the first year as the BCR for Year 1 is 055 However the
BCR for Year 2 is 108 which means the investors start to get benefits in Year 2 In
addition switch placement proved to be a feasible investment since the BCR is
increased to 620 when the switch achieves its service life 15 years in this study
Fig 7-8 BCR versus years
Chapter 7 Optimal Placement of Sectionalising Switches for Reliability
Improvement
Page | 144
0
20
40
60
80
100
120
140
160
05 1 15 2 25 3 35 4 45 5 55 6 65 7 75 8
Co
st (
th
ou
san
d $
)
CDF multiplier
ECOST
Switch costs
Total costs
C Sensitivity analysis
To demonstrate the impact of changing the values of different parameters on the
corresponding results several sensitivity analysis studies are discussed
CDF variation sensitivity analysis
The main objective of this test is to assess the behaviour of the proposed approach
when the CDF (customer damage function) is varied The CDF is increased from 50
to 800 of its initial value in 50 increments The original value of the CDF
multiplier is 100 The effect of variation in the CDF on the ECOST switching
costs and the total system cost is plotted in Fig 7-9 Switch costs include
sectionalising switch installation relocation operation and maintenance cost The
ECOST and switching costs increase as the CDF is increased However the
difference between ECOST and switching costs is also increased
Fig 7-9 Variation of cost versus change in CDF
Variations of the optimal number of installed sectionalising switches versus the CDF
are presented in Fig 7-10 The optimal number of newly installed switches increases
from 7 to 34 as the CDG multiplier is increased from 05 to 8 This indicates the
network needs to be more automated especially if the consequence of customer
damage becomes more serious However the growth in the optimal number of
sectionalising switches is slowing down As shown in Fig 7-10 when the CDF
multiplier increases above 3 the number of sectionalising switches remains at 32 as
Chapter 7 Optimal Placement of Sectionalising Switches for Reliability
Improvement
Page | 145
0
5
10
15
20
25
30
35
40
05 1 15 2 25 3 35 4 45 5 55 6 65 7 75 8
Nu
mb
er
of
swit
che
s
CDF multiplier
the reduction of ECOST brought by installing a sectionalising switch is small
compared to the increase in switch costs Only when the CDF multiplier reaches 55
does the reduction of ECOST outweigh the installation cost of a switch and hence
acquiring a sectionalising switch is a cost-effective investment This is due to the fact
that the installation of the first sectionalising switch has the largest effect on
reducing the total system cost and the impact of sectionalising switch installation on
ECOST decreases as the network becomes more automated
Fig 7-10 Number of installed sectionalising switches versus change in CDF
ACO parameters sensitivity analysis
The ACO parameter analysis is provided in this section In each test only one
parameter is changed whilst the others remain constant The convergence number is
defined as the number of the iterations when the objective function is convergence
The assessment of the impact of the pheromone evaporation rate ρ on the proposed
algorithm is presented in Table 7-6 The number of ants is 200 and the iteration time
is 400 Parameter ρ is varied from 01 to 06 with an increment of 01 For each ρ the
test is run 100 times Table 7-6 shows the impacts of the ρ variation on the objective
function J It can be seen the evaporation rate ρ has a considerable impact on the
convergence performance of the ACO algorithm When ρ is small the residual
pheromone on the path is dominant and the positive feedback of pheromone is weak
This results in an increment in the stochastic performance and global search ability
Chapter 7 Optimal Placement of Sectionalising Switches for Reliability
Improvement
Page | 146
of the ACO algorithm but a reduction in the convergence rate When ρ is large the
positive feedback of the pheromone is dominant which results in an improvement in
the convergence rate but a reduction in the search ability of the algorithm In other
words the algorithm is more easily trapped into a local optimal solution In summary
the selection of ρ is based on two factors of the algorithm 1) convergence rate 2)
global search ability As shown in the table the best value of ρ for this case is 04
which results in the minimum average value and has a suitable convergence rate
Table 7-6 Impacts of 120588 variation on objective function 119869
120588 Objective function value Average convergence
number Average Maximum Minimum
01 273120 274810 272480 223
02 273400 275960 272480 175
03 273480 274810 272480 132
04 273100 274810 272480 110
05 273550 274810 272480 94
06 273440 274810 272480 81
Table 7-7 presents the impacts of the variation in the number of ants on objective
function J The evaporation rate is 04 and the iteration number is 400 The number
of ants is changed from 100 to 500 with an increment of 100 The greater the
number of ants the more likely the global optimum value is achieved This is due to
the growth in global search capability However the convergence rate decreases To
balance the global search ability and convergence rate the number of ants is set to
400
Table 7-7 Impacts of variation in number of ants on objective function 119869
Number of ants Objective function value Average convergence
number Average Maximum Minimum
100 273865 276120 272480 91
200 273100 274810 272480 110
300 273030 274370 272480 135
400 272820 274230 272480 168
500 273170 274230 272480 245
Chapter 7 Optimal Placement of Sectionalising Switches for Reliability
Improvement
Page | 147
However in this study the proposed approach is used for planning a future network
Thus the computation time is not an issue The number of ants and iteration should
be large enough for the ACO algorithm to find the global optimum solution
752 Test Case 2
The objective of this test is to minimise SAIDI and switch costs by maximising the
fuzzy bi-objective function as presented in Section 722 The results of the
membership values of objectives SAIDI as well as switch costs are listed in Table
7-8 The weighting factors of the system objectives can be changed by the network
operator which make it possible to give preference to one over the other Three
cases are studied in which the weighting factors 1205961and 1205962vary from 01 to 09
As shown in the table as the weighing factor of SAIDI 1205961 is increased more
sectionalising switches are installed and reliability is improved The results show the
algorithm can adapt itself to the variation of the weighting factors For decision
making appropriate weighting factors for each objective are selected and a
compromised switch placement plan is obtained using the proposed approach
Table 7-8 Results of sectionalising switches relocation and installation in Test Case 2
Test Cases 1205961 1205962 120572119878119860 120572119878119862 Objective
Function
SAIDI
(hrscustomer)
Switch costs ($)
Case 21 01 09 04909 09970 09464 1157 68275
Case 22 05 05 08456 09061 08758 556 67378
Case 23 09 01 09384 07761 09221 39936 153950
( Each section has two candidate locations for sectionalising switch placement U means upstream side of the section and D
means downstream side of the section)
753 Test Case 3
In this test the three objective functions of the problem to be optimised are ECOST
SAIDI and switch costs The detailed test results before and after switch placement
are listed in Table 7-9 The placement of sectionalising switches results in a
reduction of 60 in ECOST and 7148 in SAIDI It is observed that the
installation and relocation of sectionalising switches has obtained a compromise
solution of three objectives optimisation
Chapter 7 Optimal Placement of Sectionalising Switches for Reliability
Improvement
Page | 148
Table 7-9 Results of sectionalising switches installation and relocation in Test Case 3
Objective
Function
120572119864119862 120572119878119860 120572119878119862 ECOST
($)
SAIDI
(hrscustomer)
Switch costs
($)
Before
switch
placement
0 0 0 1 472260 1989 4830
After switch
placement
08327 08327 08392 08384 188950 56723 112410
76 Summary
This study has presented an ACO algorithm for assessing the SSP problem in terms
of three conflicting objectives optimisation reduction of unserved energy cost
decrease in the average time that a customer is interrupted and minimisation of
switch costs The proposed model has been successfully applied on Bus 4 of the
RBTS In comparison with the original system the existing sectionalising switches
are relocated and new automatic switches are installed The effectiveness of the
proposed approach has been demonstrated through the results obtained which
indicates switch placement using the ACO algorithm reduces the customer outage
costs and interruption duration times during fault contingencies Furthermore the
importance of the CDF variation in determining the SSP is investigated through
sensitivity analysis The impact of installing sectionalising switches on reducing the
total system costs decreases as the number of sectionalising switches is increased As
the parameters of ACO algorithm affect the performance of the proposed method an
ACO parameter sensitivity analysis is also provided in this study The selection of
pheromone evaporation rate and number of ants is a trade-off between the global
search ability and convergence rate of the algorithm In addition a benefit-to-cost
analysis is implemented and used to prove switch investment is profitable The
procedure is used for system planning and is applied off-line so there is no
limitation in calculation times
The main contribution of this study is the conversion of all the multiple objectives
into a single objective function in two forms weighted aggregation and fuzzy
satisfaction objective function considering ECOST SAIDI and cost of
sectionalising switches simultaneously The selection of each form depends on the
Chapter 7 Optimal Placement of Sectionalising Switches for Reliability
Improvement
Page | 149
number of objectives as well as their units and dimensions Another contribution is
the incorporation of FMEA to evaluate the impact on distribution system reliability
of increased automation
Page | 150
CHAPTER 8
DISTRIBUTION NETWORK
RECONFIGURATION FOR LOSS
REDUCTION amp RELIABILITY
IMPROVEMENT
81 Introduction
Optimal distribution network reconfiguration (DNR) can not only solve a single
objective function such as feeder loss minimisation but can also deal with multiple
objectives The presence of multiple objectives raises the issue of how to consider
them simultaneously [117] In the previous section the multiple objectives are
transformed into a single equation using fuzzy logic based approaches The
optimisation is then formulated either as the weighted sum of the fuzzy membership
functions or with the application of the max-min principle
However the above simple optimisation processes only find a compromise solution
It is no longer acceptable for a system with multiple conflicting objectives if the
distribution network operator (DNO) desires to know all possible optimal solutions
for all the objectives simultaneously [20] Therefore a set of trade-off solutions
using the Pareto optimality concept is now proposed These solutions can be
Chapter 8 Distribution Network Reconfiguration for Loss Reduction amp Reliability
Improvement
Page | 151
compared by using the concept of dominance [88] In this concept a solution is non-
dominated when no other solution exists with better values for all the individual
objectives The Pareto set is the set of all non-dominated solutions and the
corresponding objective values constitute the Pareto front [88] This allows the
DNOs to select the most suitable one for implementation depending on the utilitiesrsquo
priorities Pareto analysis is suitable for addressing problems whose conflicting
solutions cannot be addressed using a single solution [117]
This study formulates the optimal network reconfiguration problem within a Pareto
optimal framework where feeder loss and system reliability indices are
simultaneously optimised Two types of reliability indices are considered system
expected outage costs to customers (ECOST) and system interruption duration index
(SAIDI) The multi-objective ant colony optimisation (MOACO) and artificial
immune systems-ant colony optimisation (AIS-ACO) algorithms are proposed and
compared for the assessment of DNR problems Both algorithms focus on problems
in terms of Pareto optimality where the objective functions are multidimensional In
MOACO each objective function is assigned with a pheromone matrix and all
values from multiple pheromone matrices are aggregated into a single pheromone
value by a weighted sum [96] In AIS-ACO the quality of elements that make up the
solution to the problem is represented by the pheromones developed from the ACO
And the hypermutation from the AIS is used as a random operator to enlarge the
search space [88] To verify the suitability of the proposed algorithms they have
been tested on Bus 4 of the Roy Billinton Test System (RBTS) system and the Pareto
set is obtained
The remaining parts of this chapter are organised as follows Section 82 deals with
the framework of multi-objective optimisation and DNR problem formulation The
implementation details of the MOACO and AIS-ACO algorithms to the problem are
discussed in Section 83 The simulation results and the best compromise solutions
are presented and discussed in Section 84 and 85 Section 86 summarises the main
conclusions
Chapter 8 Distribution Network Reconfiguration for Loss Reduction amp Reliability
Improvement
Page | 152
82 Problem Formulation
This section formulates the DNR problems in the Pareto optimal framework
821 Multi-objective Reconfiguration Problem
In this study three objectives are considered and they are feeder loss unserved
energy cost and the average time that a customer is interrupted Therefore the multi-
objective DNR problem can be defined as the minimisation of the vector
119865(119866) = [1198911(119866)1198912(119866)1198913(119866)]119879 (8-3)
where 1198911(119866) 1198912(119866) and 1198913(119866) are described below for a given network
configuration G
8211 Minimisation of feeder loss
The total feeder loss of the network is formulated as
1198911(119866) = sum 119896119894119877119894(119875119894
2+1198761198942
1198801198942 )
119873119887119894=1 (8-4)
where 119877119894 is the resistance of the ith branch 119875119894 and 119876119894 are the real power (W) and
reactive power (VAr) at the receiving end of branch i 119880119894 represents the rms voltage
at the receiving end of branch i (V) 119896119894 is a binary variable 119896119894 = 0 indicates that
branch 119894 is open and 119896119894 = 1 indicates that branch 119894 is closed The detailed feeder loss
assessment is presented in Section 28
8212 Minimisation of ECOST
The ECOST represents the unserved energy cost and is described as
1 ( 1)
1 1 1 1 1 1
( ) ( ) ( ) ( ) (1 ) (1 )b b b b bN CT NR CT NST
t t
b b k R k s
t b k j k j
ECOST L P k j C d P k j C d IR DR
(8-5)
where T is time period (year) 119873119887 is the total number of branches 120582119887and 119871119887 are the
average failure rate (failurekm-year) and length (km) of branch b 119862119879119887 119873119877119887 and
119873119878119887 are the total number of customer types permanent damaged and temporary
Chapter 8 Distribution Network Reconfiguration for Loss Reduction amp Reliability
Improvement
Page | 153
damaged load points when the fault is at branch b P(k j) is the average load of the
kth-type customers at the jth load point (kW) 119862119896(119889) is the customer damage
function for kth-type customer lasting d hours ($kW) 119889119877 and 119889119878 are the average
repair time and the switch time after failure IR and DR are the annual load increase
rate and discount rate
8213 Minimisation of SAIDI
The average time that a customer is interrupted is represented by a reliability index
SAIDI and is defined as
119878119860119868119863119868 = sum sum 120582119887∙119871119887[sum 119889119877
119873119862119877(119887)119899=1 +sum 119889119878
119873119862119878(119887)119899=1 ]
119873119887119887=1
119873119862119905119900119905119886119897119879
119905=1 (8-6)
where 119873119862119877(119887) and 119873119862119878(119887) are the number of permanent damaged and temporary
damaged customers when the fault is at branch b 119873119862119905119900119905119886119897 is the total number of
served customers SAIDI is measured in hours
8214 Constraints
The computed voltages currents and the power flow at all branches should be kept
in their permissible range and the network should be operated in radial The
configurations that violate any constraint should be disregarded
822 Best Compromise Solution
After obtaining the Pareto set the best compromise solution among the multiple
objectives can be selected by comparing the fitness value of each member in the
Pareto front as follows [45]
119891119901119904(119894) = sum 120596119895max(119900119891119895)minus119900119891119895(119875119878119894)
max(119900119891119895)minusmin (119900119891119895)
119873119900119887119895
119895=1 (8-7)
where 119873119900119887119895 is the number of objectives which is three in this study max(119900119891119895) and
min(119900119891119895) are the maximum and minimum value of the jth objective function
obtained by all the members in the Pareto front respectively 1205961 1205962 and 1205963 are the
weighting factor for feeder loss ECOST and SAIDI respectively
The best compromise solution is varied by changing the values of the weighting
factors based on the tendencies of the decision makers
Chapter 8 Distribution Network Reconfiguration for Loss Reduction amp Reliability
Improvement
Page | 154
83 Solution Methodology
In this study there are two methodologies proposed for generating the Pareto set to
the multi-objective DNR problem which are MOACO and AIS-ACO algorithm
Each solution is represented by a string of integers which indicates the locations of
tie-switches
831 Applying MOACO to Multi-objective DNR Problem
Generally ACO algorithm is developed for the assessment of a single objective
optimisation problem However a MOACO algorithm is proposed for assessing
multiple objective functions in the Pareto optimality framework which can generate
diverse solutions rather than just one The flowchart of the MOACO algorithm is
presented in Fig 8-1 and is divided into six steps
Step 1 Initialisation First of all all the ants are initially located at home The
number of pheromone matrices is equal to the number of objectives Each
pheromone matrix has 33 rowsstates (candidate locations for tie-switches) and 4
columnsstages (number of tie-switches) The pheromone values of the edges in the
search space are all initialised at an equal value which is a small positive constant
number
Step 2 Pheromone matrix generation and ant dispatch As there are multiple
pheromone matrices 1205911 1205912 and 1205913 are associated with feeder loss ECOST and
SAIDI respectively All matrices are aggregated into a single pheromone matrix by
weighted sum as
120591119894119909 = 1199011 ∙ 1205911198941199091 + |1199011 minus 1199012| ∙ 120591119894119909
2 + (1 minus 1199012) ∙ 1205911198941199093 (8-8)
where 1205911198941199091 120591119894119909
2 and 1205911198941199093 are the levels of pheromone deposited on state i of stage x for
feeder loss ECOST and SAIDI respectively where 1199011 and 1199012 are uniform random
numbers between 0 and 1 and 1199011 is less than 1199012 This ensures the selection of the
three pheromone matrices all have the same probability and can be used to build the
new matrix
All the ants begin their tours from the home colony and choose the next node to
move to based on the intensity of pheromones from a new pheromone matrix They
Chapter 8 Distribution Network Reconfiguration for Loss Reduction amp Reliability
Improvement
Page | 155
experience different pheromone matrices according to the random variation of
weights The probability of an ant choosing state i of stage x is
119875119894119909(119873) =120591119894119909(119873)
sum 120591119894119909(119873)ℎisin∆119909
(8-9)
where 120591119894119909(119873) is the level of pheromone deposited on state i of stage x at iteration
N ∆119909 is the set of available states which an ant can choose at stage x
Step 3 Objective Function Evaluation After all the ants have completed their tour
the location list and corresponding objective functions in (8-3) for each ant are
evaluated If any constraint is violated the corresponding solutions are discarded
Step 4 Non-dominated Solutions Extraction and Diversity Measure The non-
dominated solutions extraction extracts solutions from a pool based on the concept
of dominance as presented in Section 821 The crowding distance is used to
measure the extent to which non-dominated solutions are spread over the objective
space [20] As there are three objectives to be optimised the crowding distance of a
solution is equal to the side length of the cuboid which is built by two adjacent
solutions [88] Regarding the boundary solutions (the corner solutions) they are
assigned with an infinite distance The solutions are assigned with a small distance
value if they are located in a crowded area The decision makers tend to choose the
solutions from less crowded regions of the search space (with higher crowding
distance) if the maximum number of non-dominated solutions is restricted to a
certain number [88]
Step 5 Pheromone Updating The aim of this step is to favour transitions towards
states by non-dominated solutions with greater pheromone values There are two
rules of pheromone updating the local rule and global rule
Local rule The pheromones deposited in the search space should be evaporated to
make the paths less attractive The local pheromone update rule is calculated as
follow
120591119894119909119899 (119873) = (1 minus 120588)120591119894119909
119899 (119873 minus 1) + 120591119888 (8-10)
where 120588 is the pheromone evaporation rate which is set between 0 and 1 120591119894119909119899 (119873 minus
1) is pheromone value deposited on state i of stage x of matrix n at iteration N-1 120591119888
Chapter 8 Distribution Network Reconfiguration for Loss Reduction amp Reliability
Improvement
Page | 156
is a small positive constant value Even if the amount of pheromone deposited on an
edge is at the lowest value of 120591119888 there is a slight chance that an ant will still choose
this edge
Global rule The global pheromone updating rule involves ants depositing large
amounts of pheromone to the edges that belong to the corner non-dominated
solutions which are the solutions that have minimum values along each objective
The pheromones of those edges can be updated by
120591119894119909119899 (119873) = 120591119894119909
119899 (119873) + 120588119891119887119890119904119905
119899 (119873)
119891119887119890119904119905119899 (119873minus1)
(8-11)
where 119891119887119890119904119905119899 (119873 minus 1) and 119891119887119890119904119905
119899 (119873) are the minimum values of objective function n
obtained by the non-dominated solutions at iteration N-1 and N respectively
After applying the local and global pheromone updating rules the method Max-Min
ACO algorithm is integrated into the proposed approach
120591119894119909119899 (119873) = 120591119898119886119909 119894119891 120591119894119909
119899 (119873) ge 120591119898119886119909 (8-12)
120591119894119909119899 (119873) = 120591119898119894119899 119894119891 120591119894119909
119899 (119873) le 120591119898119894119899 (8-13)
where 120591119898119886119909and 120591119898119894119899 are the higher and lower bound of pheromone level on each
edge respectively Even if the amount of pheromone deposited to a path is at the
lowest value 120591119898119894119899 there is a slight chance that an ant will still choose this path This
enlarges the search space and prevents convergence from occurring too rapidly
After this the non-dominated solutions with their location lists and corresponding
fitness values in the current iteration are retained and all the ants are free to choose a
new path for the next iteration
Step 6 Termination The computation continues until the predefined maximum
number of iterations is reached The final non-dominated solutions are considered as
the Pareto set to the multi-objective DNR problem
Chapter 8 Distribution Network Reconfiguration for Loss Reduction amp Reliability
Improvement
Page | 157
Start
Iteration N=1
Maximum ant number
reaches
Output Pareto
optimal set and end
No
Yes
Initialise the parameters for MOACO
algorithm search space
Ant number m=1
Random select weights and
aggregate multiple pheromone
matrices into one
Dispatch the ant based on the
amount of pheromone on edges
Calculate the multiple objective functions
for this ant
N=N+1
Read system topology
and load data
Diversity measure and extract non-
dominated solutions
Maximum iteration
reaches
Yes
m=m+1
No
The pheromones are updated according
to local and global rules
Fig 8-1 Flowchart of the MOACO algorithm applied to multi-objective DNR problem
Chapter 8 Distribution Network Reconfiguration for Loss Reduction amp Reliability
Improvement
Page | 158
Start
Cloning
Maximum iteration
reached
Output Pareto
optimal set and end
No
Yes
Initialise and set iteration n=1
Pheromone based hypermutation
Diversity measure and extract non-
dominated solutions
The pheromones are updated according to
local and global rules
n=n+1
832 Applying AIS-ACO to Multi-objective DNR Problem
The general description of AIS-ACO algorithm is presented in Section 34 In this
study the AIS-ACO hybrid approach is used to handle multi-objective formulation
using the Pareto optimality concept The antigen is the multi-objective function and
the antibody is the solution to the problem The affinity between the antibody and the
antigen is the Pareto dominance among solutions which indicates the quality of the
solution [88] The information related to each objective is represented by an
individual pheromone table All the non-dominated solutions experience cloning
hypermutation selection and updating until the maximum number of iterations is
reached The flowchart of the AIS-ACO algorithm for Pareto optimality is presented
in Fig 8-2
Fig 8-2 Flowchart of the AIS-ACO algorithm applied to multi-objective DNR problem
Chapter 8 Distribution Network Reconfiguration for Loss Reduction amp Reliability
Improvement
Page | 159
The key parts of the algorithm are explained as follows
Step 1 Initialisation At the beginning of this algorithm a set of initial solutions is
generated These solutions should satisfy the constraints An individual pheromone
table is also built for each objective Each pheromone table has 33 cells (candidate
locations for tie-switches) The pheromone value of each cell represents the
probability of selecting the corresponding switch to be opened in the network model
The pheromone values of all cells are initially set at the same value
Step 2 Cloning All the non-dominated solutions are subjected to cloning In this
study as there are three objectives to be optimised the number of clones for each
non-dominated solution is three
Step 3 Hypermutation The selection of a cell in each clone for hypermutation is
obtained by applying a roulette wheel on its pheromone table [88] The probability of
selecting a cell is dependent on its pheromone intensity A higher pheromone value
of a cell in the table indicates that the corresponding edge in the network is more
likely to be selected The probability of selection cell i in table n is given by
119901119894119899 =
120591119894119899
sum 120591119895119899
119895 (8-14)
where 120591119894119899 is the pheromone value of cell i in table n sum 120591119895
119899119895 represents the sum of
pheromone values of all cells in table n
Step 4 Non-dominated Solutions Extraction and Diversity Measure This step is
same to the step which has been discussed in Section 831
Step 5 Pheromone Updating The aim of this step is to favour transitions toward
non-dominated solutions with great pheromone values There are two rules of
pheromone updating the local rule and global rule
Local rule Pheromones deposited in the search space should be evaporated to make
the paths less attractive The local pheromone update rule is calculated as follows
120591119894119899(119873) = 119898119886119909 (1 minus 120588)120591119894
119899(119873 minus 1) 120591119898119894119899 (8-15)
where 120588 is the pheromone evaporation rate which is set between 0 and 1 120591119894119899(119873 minus 1)
is pheromone value deposited on cell i of table n at iteration N-1 120591119898119894119899 is the lower
Chapter 8 Distribution Network Reconfiguration for Loss Reduction amp Reliability
Improvement
Page | 160
bound of pheromone level on each edge Even if the amount of pheromone deposited
to a path is at the lowest value 120591119898119894119899 there is a slight chance that an ant will still
choose this path This enlarges the entire search space
Global rule The global pheromone updating rule involves depositing large amounts
of pheromone to the edges that are a part of all the non-dominated solutions in the
current iteration [88] At iteration N the edges of the non-dominated solutions can be
updated as
120591119894119899(119873) = 119898119894119899120591119894
119899(119873) + 120588min (119891119899(119866))
119891119899(119866) 120591119898119886119909 (8-16)
where each 119894 isin edge set of G 119899 isin objective set and 119866 isin non-dominated solutions set
119891119899(119866) is the value of objective function n obtained by the non-dominated solution G
120591119898119886119909 is the higher bound of pheromone level on each edge
After this the non-dominated solutions with their location lists and fitness values in
the current iteration are retained and all the ants are free to choose a new path for the
next iteration
Step 6 Termination The computation continues until the predefined maximum
number iteration is reached The final non-dominated solutions are considered as the
Pareto set to the multi-objective DNR problem
Chapter 8 Distribution Network Reconfiguration for Loss Reduction amp Reliability
Improvement
Page | 161
LP11 LP12 LP13 LP14 LP15 LP16 LP17
LP8 LP9 LP10
LP1 LP2 LP3 LP4 LP5 LP6 LP7
LP32 LP33 LP34 LP35 LP36 LP37 LP38
LP29 LP30 LP31
LP26 LP27 LP28
LP18 LP19 LP20 LP21 LP22 LP23 LP24 LP25
19
20
21
22
23
24
26
25 27
28
29 30
71
13 15
14 16
17
18
69
1 3
2
5
4
7
6 8
10
9
68
11 12
56
57
58 60
59 61 62
65
64 66 67
50 52
51
54
53 55
44
45
46
47
48
49
70
31
32
33
34
36
35
39
37 38 40
41
42 43
63
F3
F2
F1
F7
F6
F5
F4
Normally Open Circuit BreakerNormally Closed Circuit Breaker
Subbus1
Subbus2
Subbus3
T1
T3
T5
Main
feeder
Main
feeder
Main
feeder
T2
T4
T6
84 Application Studies
The proposed MOACO and AIS-ACO algorithms have been tested on an 11 kV
distribution network developed from Bus 4 of the Roy Billinton Test System (RBTS)
a single-line diagram of the network is shown in Fig 8-3 The network consists of 38
load points and 4 tie-switches the associated data can be found in [114] The types
and lengths of 11 kV feeders are listed in Appendix A4 The network built in
OpenDSS incorporates three 3311 kV double transformer substations supplying the
downstream loads
Fig 8-3 Distribution feeder connected to RBTS Bus 4
This typical urban distribution network supplies residential commercial and
industrial consumers The average value of active and reactive power and the
customer type of each node are modified from the original values and the new values
are listed in Table 8-1
Chapter 8 Distribution Network Reconfiguration for Loss Reduction amp Reliability
Improvement
Page | 162
300
350
400
450
4
45
5
55
6
x 104
08
09
1
11
12
13
14
15
Feeder loss (kW)ECOST ($yr)
SA
IDI
(hrs
custo
mer
yr)
Table 8-1 Revised customer data (Average load)
Number
of load
points
Load points Customer type P
(kW)
Q
(kVAr)
Number of
customers
4 1-2 9-10 residential 545 51775 220
6 3-5 13-15 residential 500 475 200
12 6-7 16-17 23-25 28 30-
31 37-38
commercial 415 39425 10
6 8 11 18 26 32-33 industrial 1500 1425 1
10 12 19-22 27 29 34-36 industrial 1000 950 1
The proposed MOACO and AIS-ACO algorithms are coded in the MATLAB to
obtain the location of tie-switches for the optimum configuration The settings of the
algorithm parameters that provided the optimum solution for these two cases are
presented in Appendix C4
The number of Pareto optimal solutions obtained by the two algorithms is 26 and its
Pareto front is presented in Fig 8-4 in three dimensions The Pareto set is listed in
Appendix B3 in detail These solutions provide the network operator with various
configurations for the system to choose from Both algorithms have obtained the
same results However for 100 runs the average computation time of AIS-ACO
algorithm is 402s which is significantly lower than the MOCAO algorithm 1053s
Fig 8-4 Pareto solutions obtained (minimisation of feeder loss ECOST and SAIDI)
Chapter 8 Distribution Network Reconfiguration for Loss Reduction amp Reliability
Improvement
Page | 163
Table 8-2 presents the mean and standard deviation of the Pareto front
Table 8-2 Mean and standard deviation of Pareto Front (loss ECOST and SAIDI)
Feeder loss (kW) ECOST ($yr) SAIDI (hrscustomeryr)
Mean
38074 48139 09975
Standard deviation
3431 5291 01165
The corner non-dominated solutions representing minimum feeder loss minimum
ECOST and minimum SAIDI are marked by the red circle yellow circle and green
circle respectively as shown in Fig 8-4 The objective values of these solutions and
relevant tie-switches locations are presented in Table 8-3 It is obvious that the three
objectives are conflicting with each other and the algorithm is able to find the global
optimal solution for each objective function The minimum loss configuration is the
base configuration of RBTS-Bus4 In minimum ECOST solution the unserved
energy cost is reduced by 1133 in comparison with that in the original network
The minimum SAIDI solution shows a reduction of 3695 in the average time that
a customer is interrupted
Table 8-3 Minimum solutions along each objective (loss ECOST and SAIDI)
Feeder loss (kW) ECOST ($yr) SAIDI
(hrscustomeryr)
Tie-switches location
Minimum Loss
32142 46404 13090 68 69 70 71
Minimum ECOST
35409 41145 10586 10 17 41 70
Minimum SAIDI
43523 57891 08253 7 26 54 69
85 Best Compromise Solution
After obtaining the Pareto set the best compromise solution is the member which
has the largest fitness value as calculated in Eq (8-7) The results are presented in
Table 8-4 The importance of each objective function is represented by its weighting
Chapter 8 Distribution Network Reconfiguration for Loss Reduction amp Reliability
Improvement
Page | 164
factor which ranges from 1 to 10 A higher weighing factor indicates this objective
function is more important It can be seen that the solutions are different if the
weighing factors of each objective function are varied based on the tendencies of
DNO For example as shown in the table Case 2 (1205961 = 10 1205962 = 1 1205963 = 1)
indicates that the importance of feeder loss reduction is higher than the other two
objectives and hence the best compromise solution for this case obtains the
minimum loss among all the solutions which is the same as the results obtained
from Table 8-3 In comparison of Case 5 with Case 2 as the importance of ECOST
reduction is increased the network is reconfigured and its feeder loss increases by
588 to compensate for a 1045 decrease in the ECOST If there is no preferred
objective the best solution is obtained by setting 1205961 = 1205962 = 1205963 (Case 1)
Table 8-4 Best compromise solutions (loss ECOST and SAIDI)
Case No Weighting factors Best
compromise
solution
Feeder
loss
(kW)
ECOST
($yr)
SAIDI
(hrscustomeryr) 1205961 1205962 1205963
1 10 10 10 10 41 69 70 34033 41553 10996
2 10 1 1 68 69 70 71 32142 46404 13090
3 1 10 1 10 17 41 70 35409 41145 10586
4 1 1 10 7 26 54 69 43523 57891 08253
5 10 10 1 10 41 69 70 34033 41553 10996
6 10 1 10 10 54 69 71 34759 46644 10217
7 1 10 10 7 17 41 70 40368 43329 09570
86 Summary
The MOACO and AIS-ACO algorithms have been presented in this study for the
assessment of the multi-objective DNR problem using the Pareto optimality concept
The proposed DNR problem is formulated taking into account three objectives to be
minimised feeder loss ECOST and SAIDI The algorithms have been successfully
tested in an RBTS-Bus 4 network The results illustrate that the proposed algorithm
is able to generate a set of non-dominated solutions with high quality and great
diversity This set of solutions represent different trade-offs among the objective
functions And the corner non-dominated solutions which represent the minimum
Chapter 8 Distribution Network Reconfiguration for Loss Reduction amp Reliability
Improvement
Page | 165
value of each objective function are presented in the Pareto front chart By varying
the weighting factors for the parameters the decision makers can select the best
compromise strategy among the three objectives for implementation depending on
the utilitiesrsquo priorities
According to the obtained results both algorithms have obtained the same Pareto
optimal solutions but the AIS-ACO algorithm performs better in comparison with
the MOACO algorithm in terms of computation time The pheromone tables in AIS-
ACO algorithm are used to guide the search process and improve the solution quality
In addition the hypermutation is used as a random operator to enlarge the search
space and to prevent the algorithm from easily falling into the local optimum Future
work could include the assessment of the DNR problem with other objectives such
as balancing loads on feeders and minimising the maximum node voltage deviation
The AIS-ACO algorithm can also be applied to larger systems
Page | 166
CHAPTER 9
MULTI-OBJECTIVE DISTRIBUTION
NETWORK RECONFIGURATION amp DG
ALLOCATION CONSIDERING LOSS
VOLTAGE DEVIATION AND LOAD
BALANCING
91 Introduction
As discussed in the previous chapters distribution network reconfiguration (DNR)
can not only be used for single objective optimisation but also multi-objective
optimisation The study aims to determine a system topology that simultaneously
minimises feeder loss maximum node voltage deviation and feeder load balancing
This is achieved by optimal DNR and DG allocation
There are two methods presented in this chapter that tackle these objectives a single
fuzzy satisfaction objective function is used to transform the three conflicting
objectives into fuzzy memberships and then finally to combine them into a single
function The ultimate goal is to find a solution that maximises this single objective
while maintaining the constraints of the network [20] In Chapter 7 the degree of
Chapter 9 Multi-objective Distribution Network Reconfiguration amp DG Allocation
Considering Loss Voltage Deviation and Load Balancing
Page | 167
overall fuzzy satisfaction is determined by the max-min principle However there is
no guarantee that if one membership value is weaker than the other membership
values then for the same option the optimised single function will also be weak [86]
Therefore the max-min principle may not predict the best compromise solution In
this study a new operator called lsquomax-geometric meanrsquo has been introduced to
determine the degree of overall fuzzy satisfaction
Another methodology used for assessing the multi-objective DNR and DG allocation
problem is based on the Pareto optimality concept The proposed method provides a
set of non-dominated solutions with high quality and great diversity This constructs
a full Pareto front which represents different trade-offs among the objective
functions It allows the decision makers to select the most suitable one from all the
non-dominated solutions and use this for implementation which depends on the
utilitiesrsquo priorities
The optimisation algorithms for DNR and DG allocation can be classified into two
groups
Ant colony optimisation (ACO) algorithm which is used to solve the
problem in the fuzzy domain
Artificial immune systems-ant colony optimisation (AIS-ACO) algorithm
which is adopted to formulate the optimal network reconfiguration problem
within a multi-objective framework based on the Pareto optimality concept
The effectiveness and the efficiency of the proposed methods are implemented on
two standard IEEE 33-node and 69-node systems as case studies
The remainder of this chapter is organised as follows in Section 92 the
mathematical models of the problem are developed Then the solution procedures
are presented in Section 93 Numerical studies are presented and discussed in
Section 94 and finally Section 95 summarises the main conclusions
Chapter 9 Multi-objective Distribution Network Reconfiguration amp DG Allocation
Considering Loss Voltage Deviation and Load Balancing
Page | 168
0
1
92 Problem Formulation
The primary objective of this study is to minimise the three conflicting objectives
feeder loss maximum node voltage deviation and the feeder load balancing index
Two formulations of objective functions are presented as follow
921 Single Fuzzy Satisfaction Objective Function
In this study the three conflicting objectives are transformed into a single objective
function in the fuzzy domain The best compromise solution is obtained using a
lsquomax-geometric meanrsquo principle and is formulated as follows
Max 119871 = (120572119871 times 120572119881 times 120572119861)1 3frasl (9-1)
where 120572119871 120572119881 120572119861 represents the value of the membership functions for the feeder loss
the maximum node voltage deviation and the feeder load balancing index
respectively
The membership functions used to describe the three objectives of the DNR and DG
allocation problem are presented in the following sections
Membership function for feeder loss reduction
The calculation of feeder loss has been discussed in Section 28 The basic purpose
of this membership function is to reduce feeder loss Therefore the network
topology with a lower loss value obtains a higher membership value The
membership function for loss reduction is formulated in (9-2) and presented in Fig
9-1
Fig 9-1 Membership function for feeder loss reduction
As feeder loss becomes greater than 119871119874119878119878119898119894119899 the degree of satisfaction decreases
This reduction is continued until feeder loss reaches 119871119874119878119878119900119903119894
120572119871
119871119874119878119878119898119894119899 119871119874119878119878119900119903119894 119871119874119878119878
Chapter 9 Multi-objective Distribution Network Reconfiguration amp DG Allocation
Considering Loss Voltage Deviation and Load Balancing
Page | 169
0
1
120572119871 =
1 119871119874119878119878 le 119871119874119878119878119898119894119899119871119874119878119878119900119903119894minus119871119874119878119878
119871119874119878119878119900119903119894minus119871119874119878119878119898119894119899119871119874119878119878119898119894119899 lt 119871119874119878119878 lt 119871119874119878119878119900119903119894
0 119871119874119878119878 ge 119871119874119878119878119900119903119894
(9-2)
where 119871119874119878119878119900119903119894 is the loss of the original network 119871119874119878119878119898119894119899 is the minimum loss that
a network can achieve As it is not appropriate for decision makers to obtain a
network topology which increases loss after DNR and DG allocation the minimum
value of 120572119871 is selected as 0 if the loss is greater than or equal to 119871119874119878119878119900119903119894
Membership function for maximum node voltage deviation reduction
The maximum deviation of bus voltages from their rated values is formulated as
119881119863 = max|119881119903119890119891 minus 119898119894119899(119881119894)| |119881119903119890119891 minus 119898119886119909(119881119894)| 119894 120598 1 2 hellip 119873119887 (9-2)
where 119881119903119890119891 is the reference value for the node voltage which is the substation voltage
it is assumed to be 10 per unit in this study 119881119894 is the voltage at the ith node and 119873119887
is the number of nodes
The membership function for maximum node voltage deviation is shown in Fig 9-2
Fig 9-2 Membership function for maximum node voltage deviation reduction
The mathematical equation is presented below
120572119881 =
1 119881119863 le 119881119863119898119894119899119881119863119900119903119894minus119881119863
119881119863119900119903119894minus119881119863119898119894119899119881119863119898119894119899 lt 119881119863 lt 119881119863119900119903119894
0 119881119863 ge 119881119863119900119903119894
(9-3)
where 119881119863119900119903119894 and 119881119863119898119894119899 are the original and minimum values of the maximum node
voltage deviation respectively
120572119881
119881119863119898119894119899 119881119863119900119903119894 119881119863
Chapter 9 Multi-objective Distribution Network Reconfiguration amp DG Allocation
Considering Loss Voltage Deviation and Load Balancing
Page | 170
0
1
Membership function for feeder load balancing index reduction
The feeder load balancing index is calculated as
119871119861119868 = 119881119886119903[1198681
1198681119898119886119909
1198682
1198682119898119886119909 hellip
119868119894
119868119894119898119886119909 hellip
119868119899
119868119899119898119886119909] (9-4)
where 119868119894 is the current flowing through branch 119894 119868119894119898119886119909 represents the maximum
current limit of branch 119894
The function for feeder load balancing index is shown in Fig 9-3 and expressed as
120572119861 =
1 119871119861119868 le 119871119861119868119898119894119899119871119861119868119900119903119894minus119871119861119868
119871119861119868119900119903119894minus119871119861119868119898119894119899119871119861119868119898119894119899 lt 119871119861119868 lt 119871119861119868119900119903119894
0 119871119861119868 ge 119871119861119868119900119903119894
(9-5)
where 119871119861119868119900119903119894 and 119871119861119868119898119894119899 are the original and minimum values of the feeder load
balancing index respectively
Fig 9-3 Membership function for load balancing index reduction
922 Multi-objective Reconfiguration Problem Using Pareto
Optimality
In this study the multi-objective DNR problem can be defined as the minimisation
of the vector
119865(119866) = [1198911(119866)1198912(119866)1198913(119866)]119879 (9-6)
where 1198911(119866) 1198912(119866) and 1198913(119866) are feeder loss maximum node voltage deviation and
feeder load balancing index respectively The calculation of these three parameters
is discussed in Section 921
120572119861
119871119861119868119898119894119899 119871119861119868119900119903119894 119871119861119868
Chapter 9 Multi-objective Distribution Network Reconfiguration amp DG Allocation
Considering Loss Voltage Deviation and Load Balancing
Page | 171
93 Solution methodology
931 Applying ACO to DNR and DG Allocation in the Fuzzy
Domain
In this study the objective of reconfiguring the network and allocating DGs
simultaneously is to deal with the single fuzzy satisfaction objective function In
order to tackle this optimisation problem an ACO algorithm is adopted to find the
optimum configuration of tie-switches and the location of DGs in the network When
the locations of tie-switches and DGs are changed a new network configuration will
be formed For each network configuration the overall satisfaction of the plan is
calculated using Eq (9-1) The search space of the DNR and DG allocation problems
is modelled as a directed graph as shown in Fig 5-1 The flowchart of the proposed
ACO algorithm is presented in Fig 5-2
932 Applying AIS-ACO to Multi-objective DNR and DG
Allocation Using Pareto Optimality
The application of the AIS-ACO algorithm to the multi-objective DNR and DG
allocation problem using the concept of Pareto optimality is similar to that in Section
832 with an additional process for DG allocation
94 Application Studies
To demonstrate the performance and effectiveness of the proposed techniques in
solving the network reconfiguration and placement of DG problems simultaneously
the proposed ACO and AIS-ACO are implemented on two 1266 kV test systems
consisting of 33 and 69 buses The network models are built in OpenDSS and the
solution algorithms are developed in MATLAB For both test systems the substation
voltage is assumed to be 10 pu and all the sections and buses are considered as
candidate locations for tie-switches and DG placement respectively In this study
for simplicity the number of installed DGs is three All the DGs are synchronous
generators and are represented as PQ models with a 100 kVA and a power factor
Chapter 9 Multi-objective Distribution Network Reconfiguration amp DG Allocation
Considering Loss Voltage Deviation and Load Balancing
Page | 172
equal to 10 However the proposed methodology can be implemented for any
number of DGs For the purpose of better illustration and comparison four cases are
considered to analyse the superiority and performance of the proposed methods
Case I System is without reconfiguration and has no DGs (base case)
Case II System is optimally reconfigured and has no DGs
Case III System is optimally reconfigured after DGs are placed at certain buses
Case IV System is optimally reconfigured and DGs are optimally placed
simultaneously
It is to be noted that the ACO and AIS-ACO control parameters are different for
each test case They are set experimentally using information from several trial runs
The final combinations that provide the best results for all of the above tests are
given in Appendix C5 And the Pareto sets for all test cases are listed in Appendix
B4 in detail
941 33-bus System
In this section the proposed procedure is implemented on a 33-bus 1266 kV radial
distribution system with 37 branches and 5 tie-switches whose single line diagram is
shown in Fig 5-3 The tie-switches are located at L33 to L37 represented by red
dotted lines The data of lines and loads are taken from [108] and summarised in
Appendix A2 The current carrying capacity of all branches is 255A The total real
and reactive power loads of the system are 3715 kW and 2300 kVAr respectively
Case I base case
For the base case without reconfiguration and DGs the initial active feeder loss
maximum node voltage deviation and feeder load balancing index of this system are
20314 kW 00884 pu and 00419 respectively
Chapter 9 Multi-objective Distribution Network Reconfiguration amp DG Allocation
Considering Loss Voltage Deviation and Load Balancing
Page | 173
10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
18 19 20 21
22 23 24
25 26 27 28 29 30 31 32
L1 L2 L3 L4 L5 L6 L7 L8 L9 L10 L11 L12 L13 L14 L15 L16 L17
L18
L19 L20 L21
L22
L23 L24
L25
L26 L27 L28 L29 L30 L31 L32
L33
L34
L35
L36
L37
Case II with reconfiguration only (no DGs)
In this case only reconfiguration is considered and no DGs are installed
After DNR the best compromise solution obtained using ACO algorithm in a single
fuzzy satisfaction objective function is presented in Table 9-1 It can be seen that the
DNR has resulted in a reduction of 2956 in feeder loss 2930 in maximum node
voltage deviation and 3556 in feeder load balancing index compared to the base
case This solution is one of the Pareto optimal solutions which are obtained by
using AIS-ACO algorithm And the network configuration after DNR is shown in
Fig 9-4
Table 9-1 Results of DNR in fuzzy multi-objective formulation for 33-bus system in Case II
Objective function Feeder loss
(kW)
Maximum node
voltage deviation
(pu)
Feeder Load
balancing index
Tie-switches
location
08734 14310 00625 00270 6 9 14 32 37
Fig 9-4 33 bus-system for fuzzy multi-objective optimisation Case II
The number of Pareto optimal solutions obtained using AIS-ACO algorithm is 21
and its Pareto front is presented in Fig 9-5 in three dimensions Table 9-2 presents
the mean and standard deviations of the objective values of the Pareto solutions
Chapter 9 Multi-objective Distribution Network Reconfiguration amp DG Allocation
Considering Loss Voltage Deviation and Load Balancing
Page | 174
120140
160180
200220
006
008
01
012
014
016
0022
0024
0026
0028
003
0032
0034
0036
Feeder loss (kW)Maximum node voltage deviation (pu)
Feeder
load b
ala
ncin
g index
Fig 9-5 Pareto front obtained for 33-bus system in Case II
Table 9-2 Mean and standard deviations of Pareto Front for 33-bus system in Case II
Feeder loss (kW) Maximum node voltage
deviation (pu)
Feeder Load balancing index
Mean
15499 00815 00256
Standard deviation
1549 00194 00023
The corner non-dominated solutions which represent minimum feeder loss
minimum voltage deviation and minimum feeder load balancing index are marked
by the red circle yellow circle and green circle respectively as shown in Fig 9-5
The objective values of these solutions and relevant tie-switches locations are
presented in Table 9-3 In minimum loss solution the feeder loss is reduced by 3118
compared to the initial state If improving voltage profiles is the principle objective
the solution with maximum node voltage deviation of 00604 pu is optimum which
represents a 3167 improvement compared to the base case If balancing feeder
Chapter 9 Multi-objective Distribution Network Reconfiguration amp DG Allocation
Considering Loss Voltage Deviation and Load Balancing
Page | 175
10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
18 19 20 21
22 23 24
25 26 27 28 29 30 31 32
L1 L2 L3 L4 L5 L6 L7 L8 L9 L10 L11 L12 L13 L14 L15 L16 L17
L18
L19 L20 L21
L22
L23 L24
L25
L26 L27 L28 L29 L30 L31 L32
L33
L34
L35
L36
L37
DG2
DG1
DG3
load is the main objective the solution with load balancing index of 00223 is
optimum where the index decreases by 4678 in comparison with the initial case
Table 9-3 Minimum solutions along each objective for 33-bus system in Case II
Feeder loss (kW) Maximum node
voltage deviation (pu)
Feeder Load balancing
index
Tie-switches location
Minimum Loss
13981 00639 00280 7 9 14 32 37
Minimum Voltage Deviation
14026 00604 00310 7 9 14 28 32
Minimum Feeder Load Balancing Index
20248 01309 00223 7 30 34 35 37
Case III with reconfiguration only (with DGs)
In this case the three DGs are located at the end of the feeders ie Bus 17 21 24
The feeder loss maximum node voltage deviation and feeder load balancing of the
original network with DGs are 17831 kW 00823 pu and 00389 pu respectively
After DNR the best compromise solution obtained using ACO algorithm in a single
fuzzy satisfaction objective function is presented in Table 9-4 Compared to the Case
I feeder loss maximum node voltage deviation and feeder load balancing decrease
by 3893 3281 and 4511 respectively This solution belongs to the Pareto
set which are obtained by using AIS-ACO algorithm Fig 9-6 illustrates the optimal
network configuration
Fig 9-6 33 bus-system for fuzzy multi-objective optimisation Case III
Chapter 9 Multi-objective Distribution Network Reconfiguration amp DG Allocation
Considering Loss Voltage Deviation and Load Balancing
Page | 176
110120
130140
150160
170
004
006
008
01
0120018
002
0022
0024
0026
0028
003
Feeder loss (kW)Maximum node voltage deviation (pu)
Feeder
load b
ala
ncin
g index
Table 9-4 Results of DNR in fuzzy multi-objective formulation for 33-bus system in Case III
Objective function Feeder loss
(kW)
Maximum node
voltage deviation
(pu)
Feeder Load
balancing index
Tie-switches
location
08590 12405 00594 00230 6 8 14 32 37
Fig 9-7 shows the Pareto front obtained by the AIS-ACO method and the number
of Pareto optimal solutions for this case is 28 The mean and standard deviations of
the objective values of the Pareto solutions are listed in Table 9-5
Fig 9-7 Pareto front obtained for 33-bus system in Case III
Table 9-5 Mean and standard deviations of Pareto Front for 33-bus system in Case III
Feeder loss (kW) Maximum node voltage
deviation (pu)
Feeder load balancing index
Mean
12850 00711 00231
Standard deviation
1003 00166 00029
Chapter 9 Multi-objective Distribution Network Reconfiguration amp DG Allocation
Considering Loss Voltage Deviation and Load Balancing
Page | 177
The corner non-dominated solutions which represent minimum feeder loss
minimum voltage deviation and minimum feeder load balancing index are marked
by the red circle yellow circle and green circle respectively as shown in Fig 9-7
Table 9-6 presents the objective values of these solutions and relevant tie-switches
locations In minimum loss solution the network reconfiguration results in a
reduction of 4214 in feeder loss compared to the original network and a
reduction of 1594 compared to the reconfigured network without DGs If
improving voltage profiles is the principle objective the solution with maximum
node voltage deviation of 00567 pu is optimum which represents a 3586 and
613 improvement compared to Case I and Case II If balancing feeder load is the
main objective the solution with load balancing index of 00189 is optimum where
the index decreases by 5489 and 1525 in comparison with Case I and Case II
Table 9-6 Minimum solutions along each objective for 33-bus system in Case III
Feeder loss (kW) Maximum node
voltage deviation (pu)
Feeder Load balancing
index
Tie-switches location
Minimum Loss
11753 00643 00241 7 9 14 28 31
Minimum Voltage Deviation
12592 00567 00265 6 8 14 28 32
Minimum Feeder Load Balancing Index
16419 01139 00189 7 21 30 35 37
Case IV with reconfiguration and DG allocation
The network is reconfigured and DGs are allocated simultaneously in this case The
best compromise solution obtained using the proposed algorithm in a single fuzzy
satisfaction objective function after DNR and DG allocation is presented in Table 9-
7 Feeder loss maximum node voltage deviation and feeder load balancing decrease
by 4645 4355 and 4463 respectively in comparison with the base case
This solution is one of the Pareto optimal solutions which are obtained by using
AIS-ACO algorithm Fig 9-8 illustrates the optimal network configuration and DG
locations
Chapter 9 Multi-objective Distribution Network Reconfiguration amp DG Allocation
Considering Loss Voltage Deviation and Load Balancing
Page | 178
10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
18 19 20 21
22 23 24
25 26 27 28 29 30 31 32
L1 L2 L3 L4 L5 L6 L7 L8 L9 L10 L11 L12 L13 L14 L15 L16 L17
L18
L19 L20 L21
L22
L23 L24
L25
L26 L27 L28 L29 L30 L31 L32
L33
L34
L35
L36
L37
DG1
DG3
DG2
100110
120130
140150
160
004
006
008
01
012
0016
0018
002
0022
0024
0026
0028
Feeder loss (kW)Maximum node voltage deviation (pu)
Feeder
load b
ala
ncin
g index
Table 9-7 Results of DNR and DG allocation in fuzzy multi-objective formulation for 33-bus system
in Case IV
Objective
function
Feeder loss
(kW)
Maximum node
voltage
deviation (pu)
Feeder Load
balancing
index
Tie-switches
location
DGs location
08961 10878 00499 00232 7 9 14 36 37 B32 B32 B32
Fig 9-8 33 bus-system for fuzzy multi-objective optimisation Case IV
The number of non-dominated solutions obtained by the AIS-ACO algorithm is 295
However the maximum number for Pareto optimal solutions is restricted to 50
Therefore the solutions with a high value of crowding distance are selected Fig 9-9
shows the Pareto front obtained by the proposed method
Fig 9-9 Pareto front obtained for 33-bus system in Case IV
Chapter 9 Multi-objective Distribution Network Reconfiguration amp DG Allocation
Considering Loss Voltage Deviation and Load Balancing
Page | 179
The mean and standard deviations of the Pareto front are listed in Table 9-8
Table 9-8 Mean and standard deviations of Pareto Front for 33-bus system in Case IV
Feeder loss (kW) Maximum node voltage
deviation (pu)
Feeder Load balancing index
Mean
13295 00873 00194
Standard deviation
1354 00179 00019
The corner non-dominated solutions which represent minimum feeder loss
minimum voltage deviation and minimum feeder load balancing index are marked
by the red circle yellow circle and green circle respectively as shown in Fig 9-9
The objective values of these solutions and relevant tie-switches locations are
presented in Table 9-9 In minimum loss solution the network reconfiguration and
DG allocation result in a reduction of 4662 2244 and 773 in feeder loss
compared to Case I Case II and Case III respectively If improving voltage profiles
is the principle objective the solution with maximum node voltage deviation of
00490 pu is optimum which represents a 4457 1887 and 1358
improvement compared to Case I Case II and Case III respectively If balancing
feeder load is the main objective the solution with load balancing index of 00178 is
optimum where the index decreases by 5752 2018 and 582 in comparison
with Case I Case II and Case III respectively
Table 9-9 Minimum solutions along each objective for 33-bus system in Case IV
Feeder loss (kW) Maximum node
voltage deviation
(pu)
Feeder Load
balancing index
Tie-switches
location
DGs location
Minimum Loss
10844 00538 00228 7 9 14 32 37 B30 B31 B31
Minimum Voltage Deviation
11020 00490 00259 7 9 14 28 36 B31 B31 B32
Minimum Feeder Load Balancing Index
15443 01090 00178 7 30 34 35 37 B8 B9 B12
Chapter 9 Multi-objective Distribution Network Reconfiguration amp DG Allocation
Considering Loss Voltage Deviation and Load Balancing
Page | 180
10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
27
28
29
30
31 32 33 34
35
36
37
38 39 40 41 42 43 44 45
46 47 48 49
50
51
52
53 54 55 56 57 58 59 60 61 62 63 64
65 66
67 68
L1 L2 L3 L4 L5 L6 L7 L8 L9 L10 L11 L12 L13 L14 L15 L16 L17 L18 L19 L20 L21 L22 L23 L24 L25 L26
L27
L28
L29
L30
L31 L32 L33 L34
L35
L36
L37
L38 L39 L40 L41 L42 L43 L44 L45
L46
L47 L48 L49
L50
L51
L52
L53 L54 L55 L56 L57 L58 L59 L60 L61 L62 L63 L64
L65
L66
L67
L68
L69
L70
L71
L72L73
942 69-bus System
This is a large-scale radial distribution system consisting of 73 branches and 5 tie-
switches whose single-line diagram is shown in Fig 5-9 The tie-switches are
located at L69 to L73 represented by red dotted lines The line and load data of the
system are taken from [84] and summarised in Appendix A3 The current carrying
capacity of the branches 1-9 is 400 A 46-49 and 52-64 is 300 A and for all other
branches it is 200 A The total power loads are 379589 kW and 26891 kVAr
respectively
Case I base case
For the base case without reconfiguration and DGs the initial active feeder loss
maximum node voltage deviation and feeder load balancing index of this system are
22562 kW 00928 pu and 00259 respectively
Case II with reconfiguration only (no DGs)
In this case only reconfiguration is considered and no DGs are installed After DNR
the best compromise solution obtained using ACO algorithm in a single fuzzy
satisfaction objective function is presented in Table 9-10 and the network
configuration is shown in Fig 9-10 Reconfiguring the network brings a reduction of
5619 4353 and 2355 in feeder loss maximum node voltage deviation and
feeder load balancing index respectively compared to the base case This solution
belongs to the Pareto set which are obtained by using AIS-ACO algorithm
Fig 9-10 69 bus system for fuzzy multi-objective optimisation Case II
Chapter 9 Multi-objective Distribution Network Reconfiguration amp DG Allocation
Considering Loss Voltage Deviation and Load Balancing
Page | 181
80
100
120
140
160
005
006
007
0080016
0018
002
0022
0024
0026
0028
Feeder loss (kW)Maximum node voltage deviation (pu)
Feeder
load b
ala
ncin
g index
Table 9-10 Results of DNR in fuzzy multi-objective formulation for 69-bus system in Case II
Objective function Feeder loss
(kW)
Maximum node
voltage deviation
(pu)
Feeder Load
balancing index
Tie-switches
location
09676 9885 00524 00195 14 55 61 71 72
The number of Pareto optimal solutions obtained by the AIS-ACO algorithm is 12
and its Pareto front are presented in Fig 9-11 in three dimensions
Fig 9-11 Pareto front obtained for 69-bus system in Case II
The mean and standard deviations of the objective values of the Pareto solutions are
listed in Table 9-11
Table 9-11 Mean and standard deviations of Pareto Front for 69-bus system in Case II
Feeder loss (kW) Maximum node voltage
deviation (pu)
Feeder Load balancing index
Mean
12535 00605 00192
Standard deviation
2458 00085 00028
Chapter 9 Multi-objective Distribution Network Reconfiguration amp DG Allocation
Considering Loss Voltage Deviation and Load Balancing
Page | 182
The corner non-dominated solutions which represent minimum feeder loss
minimum voltage deviation and minimum feeder load balancing index are marked
by the red circle yellow circle and green circle respectively as shown in Fig 9-11
The objective values of these solutions and relevant tie-switches locations are
presented in Table 9-12 In minimum loss solution the feeder loss is reduced by
5619 compared to the initial state If improving voltage profiles is the principle
objective the solution with maximum node voltage deviation of 00523 pu is
optimum which represents a 4364 improvement compared to the base case If
balancing feeder load is the main objective the solution with load balancing index of
00161 is optimum where the index decreases by 3784 in comparison with the
initial case
Table 9-12 Minimum solutions along each objective for 69-bus system in Case II
Feeder loss (kW) Maximum node
voltage deviation (pu)
Feeder load balancing
index
Tie-switches location
Minimum Loss
9885 00524 00195 14 55 61 71 72
Minimum Voltage Deviation
10535 00523 00242 9 14 55 61 71
Minimum Feeder Load Balancing Index
15051 00701 00161 14 61 69 71 72
Case III with reconfiguration only (with DGs)
In this case the three DGs are located at the end of the feeders ie Bus 26 45 64
The feeder loss maximum node voltage deviation and feeder load balancing of the
original network with DGs are 19472 kW 00855 pu and 00234 pu respectively
After DNR Table 9-13 presents the best compromise solution obtained using ACO
algorithm in a single fuzzy satisfaction objective function and the optimal network
configuration is shown in Fig 9-12 Compared to the base case feeder loss
maximum node voltage deviation and feeder load balancing decrease by 6118
4364 and 3282 respectively This solution is one of the Pareto optimal
solutions which are obtained by using AIS-ACO algorithm
Chapter 9 Multi-objective Distribution Network Reconfiguration amp DG Allocation
Considering Loss Voltage Deviation and Load Balancing
Page | 183
10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
27
28
29
30
31 32 33 34
35
36
37
38 39 40 41 42 43 44 45
46 47 48 49
50
51
52
53 54 55 56 57 58 59 60 61 62 63 64
65 66
67 68
L1 L2 L3 L4 L5 L6 L7 L8 L9 L10 L11 L12 L13 L14 L15 L16 L17 L18 L19 L20 L21 L22 L23 L24 L25 L26
L27
L28
L29
L30
L31 L32 L33 L34
L35
L36
L37
L38 L39 L40 L41 L42 L43 L44 L45
L46
L47 L48 L49
L50
L51
L52
L53 L54 L55 L56 L57 L58 L59 L60 L61 L62 L63 L64
L65
L66
L67
L68
L69
L70
L71
L72L73
DG3
DG1
DG2
8090
100110
120130
140
005
006
007
008
0014
0016
0018
002
0022
0024
Feeder loss (kW)Maximum node voltage deviation (pu)
Feeder
load b
ala
ncin
g index
Table 9-13 Results of DNR in fuzzy multi-objective formulation for 69-bus system in Case III
Objective function Feeder loss
(kW)
Maximum node
voltage deviation
(pu)
Feeder Load
balancing index
Tie-switches
location
08829 8758 00523 00174 14 55 61 71 72
Fig 9-12 69-bus system for fuzzy multi-objective optimisation Case III
Fig 9-13 shows the Pareto front obtained by the AIS-ACO method and the number
of Pareto optimal solutions for this case is 19
Fig 9-13 Pareto front obtained for 69-bus system in Case III
Chapter 9 Multi-objective Distribution Network Reconfiguration amp DG Allocation
Considering Loss Voltage Deviation and Load Balancing
Page | 184
The mean and standard deviations of the objective values of the Pareto solutions are
listed in Table 9-14
Table 9-14 Mean and standard deviations of Pareto Front for 69-bus system in Case III
Feeder loss (kW) Maximum node voltage
deviation (pu)
Feeder Load balancing index
Mean
10707 00576 00183
Standard deviation
2042 00071 00029
The corner non-dominated solutions which represent minimum feeder loss
minimum voltage deviation and minimum feeder load balancing index are marked
by the red circle yellow circle and green circle respectively as shown in Fig 9-13
Table 9-15 presents the objective values of these solutions and relevant tie-switches
locations are presented In minimum loss solution the network reconfiguration
results in a reduction of 6118 in feeder loss compared to the original network and
a reduction of 1140 compared to the reconfigured network without DGs If
improving voltage profiles is the principle objective the solution with maximum
node voltage deviation of 00522 pu is optimum which represents a 4375 and
019 improvement compared to Case I and Case II If balancing feeder load is the
main objective the solution with load balancing index of 00147 is optimum where
the index decreases by 4324 and 745 in comparison with Case I and Case II
Table 9-15 Minimum solutions along each objective for 69-bus system in Case III
Feeder loss (kW) Maximum node
voltage deviation (pu)
Feeder Load balancing
index
Tie-switches location
Minimum Loss
8758 00523 00174 13 55 61 71 72
Minimum Voltage Deviation
9729 00522 00226 7 12 55 61 71
Minimum Feeder Load Balancing Index
13686 00681 00147 11 61 69 71 72
Chapter 9 Multi-objective Distribution Network Reconfiguration amp DG Allocation
Considering Loss Voltage Deviation and Load Balancing
Page | 185
10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
27
28
29
30
31 32 33 34
35
36
37
38 39 40 41 42 43 44 45
46 47 48 49
50
51
52
53 54 55 56 57 58 59 60 61 62 63 64
65 66
67 68
L1 L2 L3 L4 L5 L6 L7 L8 L9 L10 L11 L12 L13 L14 L15 L16 L17 L18 L19 L20 L21 L22 L23 L24 L25 L26
L27
L28
L29
L30
L31 L32 L33 L34
L35
L36
L37
L38 L39 L40 L41 L42 L43 L44 L45
L46
L47 L48 L49
L50
L51
L52
L53 L54 L55 L56 L57 L58 L59 L60 L61 L62 L63 L64
L65
L66
L67
L68
L69
L70
L71
L72L73
DG3DG1
DG2
Case IV with reconfiguration and DGs allocation
In this case the network is reconfigured and DGs are allocated simultaneously
Table 9-16 presents the best compromise solution obtained using the ACO algorithm
in a single fuzzy satisfaction objective function after DNR and DGs allocation and
the optimal network configuration and DG locations are shown in Fig 9-14 Feeder
loss maximum node voltage deviation and feeder load balancing decrease by
6721 5377 and 3840 respectively in comparison with the base case This
solution is one of the Pareto optimal solutions which are obtained by using AIS-
ACO algorithm
Table 9-16 Results of DNR and DGs allocation in fuzzy multi-objective formulation for 69-bus
system in Case IV
Objective
function
Feeder loss
(kW)
Maximum
node voltage
deviation (pu)
Feeder Load
balancing
index
Tie-switches
location
DGs location
08882 7397 00429 00158 14 55 61 71 72 B60 B60 B60
Fig 9-14 69-bus system for fuzzy multi-objective optimisation Case IV
The number of non-dominated solutions obtained by the AIS-ACO algorithm is 46
Fig 9-15 shows the Pareto front obtained by the proposed method The mean and
standard deviations of the objective values of the Pareto solutions are listed in Table
9-17
Chapter 9 Multi-objective Distribution Network Reconfiguration amp DG Allocation
Considering Loss Voltage Deviation and Load Balancing
Page | 186
70
80
90
100
110
120
004
0045
005
0055
006
0012
0013
0014
0015
0016
0017
0018
0019
Feeder loss (kW)Maximum node voltage deviation (pu)
Feeder
load b
ala
ncin
g index
Fig 9-15 Pareto front obtained for 69-bus system in Case IV
Table 9-17 Mean and standard deviations of Pareto Front for 69-bus system in Case IV
Feeder loss (kW) Maximum node voltage
deviation (pu)
Feeder Load balancing index
Mean
9872 00520 00147
Standard deviation
1491 00055 00013
The corner non-dominated solutions which represent minimum feeder loss
minimum voltage deviation and minimum feeder load balancing index are marked
by the red circle yellow circle and green circle respectively as shown in Fig 9-15
The objective values of these solutions and relevant tie-switches locations are
presented in Table 9-18 In minimum loss solution the network reconfiguration and
DG allocation result in a reduction of 6721 2517 and 1554 in feeder loss
compared to Case I Case II and Case III respectively If improving voltage profiles
is the principle objective the solution with maximum node voltage deviation of
00428 is optimum which represents a 5388 1816 and 1801 improvement
compared to Case I Case II and Case III respectively If balancing feeder load is the
Chapter 9 Multi-objective Distribution Network Reconfiguration amp DG Allocation
Considering Loss Voltage Deviation and Load Balancing
Page | 187
main objective the solution with load balancing index of 00125 pu is optimum
where the index decreases by 5174 2236 and 1497 in comparison with Case
I Case II and Case III respectively
Table 9-18 Minimum solutions along each objective for 69-bus system in Case IV
Feeder loss (kW) Maximum node
voltage deviation
(pu)
Feeder Load
balancing index
Tie-switches
location
DGs location
Minimum Loss
7397 00429 00158 14 55 61 71 72 B60 B60 B60
Minimum Voltage Deviation
8032 00428 00183 11 55 61 71 72 B60 B60 B60
Minimum Feeder Load Balancing Index
10962 00577 00125 14 63 69 71 72 B62 B62 B62
95 Summary
In this study the DNR and DG allocation problem is formulated either within a
fuzzy satisfaction objective function or within a multi-objective Pareto optimal
framework This formulation incorporates the minimisation of three conflicting
objectives feeder loss maximum node voltage deviation and feeder load balancing
index In the fuzzy multi-objective formulation all three objectives are transformed
into a single fuzzy satisfaction objective function and the ACO algorithm is used to
provide decision support The AIS-ACO algorithm has been presented in this study
for the assessment of the multi-objective DNR problem from a Pareto optimality
point of view The proposed methods have been successfully applied on a 33-bus and
a 69-bus radial distribution system The results illustrate that the proposed algorithm
is able to generate a set of non-dominated solutions with high quality and great
diversity This allows the network operators to choose any one from the non-
dominated solutions for implementation based on utilitiesrsquo priorities And the corner
non-dominated solutions which represent the minimum value of each objective
function are presented in the Pareto front chart
Chapter 9 Multi-objective Distribution Network Reconfiguration amp DG Allocation
Considering Loss Voltage Deviation and Load Balancing
Page | 188
Future work could include the assessment of the DNR and DG allocation problem
with more than three objectives These objectives may include balancing loads on
transformers minimising the number of switching operations etc The proposed
methodologies can be evaluated further by applying them to actual systems
Page | 189
CHAPTER 10
CONCLUSION amp FUTURE WORK
101 Conclusion
The aim of this thesis is to improve service efficiency and quality in distribution
networks Optimal distribution automation (DA) is one of the best solutions to
achieve this goal The multiple objectives are transformed into different forms based
on utilitiesrsquo priorities For this purpose the Monte Carlo method is used to solve
power system issues involving uncertain load values And a set of ant colony
optimisation (ACO)-based algorithms has been developed for objectives
optimisation This section summarises the conclusions drawn from the research
results
A comprehensive review of the network configurations switchgears DA
assessment of loss and reliability indices and different forms of multi-objective
functions was provided in Chapter 2 This has demonstrated the need for DA to
provide a reliable and high efficiency power supply to all customers with a minimum
cost
In Chapter 3 the thesis reviewed the techniques for the assessment of mono-
objectivemulti-objective optimisation problems which were categorised into two
groups simulation methods and analytical methods The Monte Carlo method is a
typical simulation technique and is generally used to deal with power system
calculations involving uncertain parameters It can find the best solution with a high
Chapter 10 Conclusion amp Future Work
Page | 190
degree of accuracy but requires a considerable amount of CPU time and memory
The ant colony optimisation (ACO) algorithm is one of the metaheuristic techniques
designed for assessing the DA problems It can find the global optimum solution in a
reasonable computation time The artificial immune systems (AIS)-ACO hybrid
algorithm was used for assessing the DA problems in order to obtain a set of non-
dominated solutions by using the concept of Pareto dominance
The thesis illustrates why transformer economic operation (TEO) is an economical
solution to reduce transformer loss The TEO mode with minimum loss and
satisfactory voltages is achieved by operating with one or two transformers This
can be summarised as when the transformer load factor is less than the TCLF
transformers should operate separately However when the transformer load factor is
higher than the TCLF it is recommended that transformers operate in parallel In
Chapter 4 a Monte Carlo simulation platform was established to tackle load
uncertainties A methodology based on TEO to reduce transformer loss was then
described This results in a reduction over the conventional transformer loss ie
when two transformers are in parallel operation However simulation studies also
indicate voltage profiles are improved when transformers operate in parallel
Therefore a slight reduction in TCLF results in an increased loss but an
improvement in voltage performance
In Chapter 4 the thesis also demonstrates why distribution network reconfiguration
(DNR) is an effective strategy for transformer loss reduction The presented results
illustrate the optimal locations of tie-switch statuses have successfully reduced the
transformer losses and improved the voltages profiles during a 24 hour operating
period The further away the nodes are from the tie-switch the better the voltage
profiles obtained In addition when the tie-switch moves closer to the middle of the
linked feeder the voltage performance is improved In this case the daily energy
loss in Scenario 5 is 11162 kWh After the introduction of Scenario 9 the annual
saving energy could be 59641 kWh
One conclusion of this thesis is that the network can be reconfigured and DGs can be
relocated simultaneously for feeder loss reduction In Chapter 5 an ACO algorithm
was used for assessing the DNR and DG allocation problems in terms of feeder loss
reduction The numerical results showed that for best performance the existing tie-
Chapter 10 Conclusion amp Future Work
Page | 191
switches were relocated and DGs were optimally placed at the same time The feeder
losses are reduced by 4662 and 6721 for the 33-bus and 69-bus system
respectively The inappropriate network configuration and DG location might result
in loss increment when the size of DG is increased The proposed methodology has
also successfully reduced the total feeder loss and improved the voltage profiles for
different capacities of DG by determining the most suitable network topology and
the DG locations In addition the simulation results have been compared with other
classical methods in literature and it is demonstrated that the proposed ACO is more
efficient and is more likely to obtain the global optimum solution
Another conclusion of this thesis is that the distribution network loss including
transformer loss and feeder loss can be minimised by using a new optimal planning
strategy This strategy is a combination of TEO and network reconfiguration as
presented in Chapter 6 In this chapter the distribution loads experience daily and
seasonal variations and the day is divided into two periods The proposed ACO
algorithm has successfully found the optimum network configuration and economic
operation mode of transformers in all substations during each time interval The
annual energy loss is reduced by 506 compared to the original network Both
transformer loss and feeder loss are reduced through this optimal planning using
DNR and TEO Furthermore simulation results obtained with numerical studies
have demonstrated the capability of applying the ACO algorithm to distribution
network planning including networks with DGs and EVs The proposed
methodology has successfully reduced the total network loss for different capacities
of DG and different penetration levels of EVs by determining the most suitable
network topology compared to the original configuration Comparative results also
show that coordinated charging plan results in less energy loss compared to
uncoordinated charging strategy with the same EV penetration level This is due to
the postponement of charging time which avoids a clash with the peak power
demand times
The thesis develops an effective strategy of sectionalising switch placement (SSP)
for system reliability improvement This is achieved by installing new switches and
relocating existing switches In Chapter 7 an ACO algorithm was proposed for the
assessment of the SSP problem based on reliability improvement and switch costs
minimisation using either a single objective function with weighted aggregation of a
Chapter 10 Conclusion amp Future Work
Page | 192
multi-objective function with fuzzy variables The selection of pheromone
evaporation rate and number of ants is a trade-off between the global search ability
and convergence rate of the ACO algorithm In comparison with the original system
existing sectionalising switches were relocated and new automatic switches were
installed For this practical system the total system costs are reduced by 4289
compared to the original network The impact of installing sectionalising switches on
reducing the total system costs decreases as the number of sectionalising switches is
increased Furthermore a benefit-to-cost analysis which offered a comparison
between ECOST and switch costs was implemented The analysis reveals that the
installing and relocating sectionalising switches is a profitable investment In
addition a set of compromise solutions was obtained by assessing the SSP problem
in terms of ECOST and SAIDI reduction during fault contingencies The placement
of sectionalising switches results in a reduction of 60 in ECOST and 7148 in
SAIDI
The thesis also proposes a strategy for assessing the DNR problems if the
distribution network operator (DNO) desires to know all possible optimal solutions
for all the multiple conflicting objectives simultaneously This formulates the DNR
problem within a multi-objective formulation in the Pareto optimal framework In
Chapter 8 The MOACO and AIS-ACO algorithms were used for assessing this
problem in terms of loss reduction and reliability improvement Both algorithms
have obtained the same Pareto optimal solutions but the AIS-ACO algorithm
performs better in comparison with the MOACO algorithm in terms of computation
time Feeder loss maximum node voltage deviation and feeder load balancing were
simultaneous optimised in Chapter 9 A set of non-dominated solutions with high
quality and great diversity was obtained This set of solutions represent different
trade-offs among the objective functions And the corner non-dominated solutions
which represent the minimum value of each objective function are presented in the
Pareto front chart For IEEE 69-bus system compared to the base case the network
reconfiguration and DG allocation result in a reduction of 6721 in minimum loss
solution If improving the voltage profiles is the principle objective the best solution
represents a 5388 improvement of this index If balancing feeder load is the main
objective this index decreases by 5174 By varying the weighting factors for the
Chapter 10 Conclusion amp Future Work
Page | 193
parameters the decision makers can select the best compromise among the three
objectives for implementation depending on the utilitiesrsquo priorities
102 Future Work
Based on the findings of this project the suggestions for future work are
In this thesis the transformers have the same characteristics In the future as the
cost of replacing an existing transformer with a new one is cheaper than
replacing both transformers the situation that two transformers with different
characteristics in a substation is not uncommon Therefore an optimisation
method for two transformers with different characteristics will be investigated
and four operation modes can occur
1) First transformer operates alone
2) Second transformer operates alone
3) Two transformers operate in parallel
4) Optimisation mode optimum selection of the transformers needed to
supply each feeder
At present in the UK customers pay for losses in the network In this thesis the
losses are analysed as a whole without allocating them to the users in the network
In the future a loss allocation scheme to customers in the distribution network
will be developed However after reconfiguration the total network loss is
reduced but the loss allocation to some customers may increase The customers
with more loss allocated will be dissatisfied with the network reconfiguration It
is therefore important to change the tariff structure for these customers so that
they are not obliged to pay more for the increase in loss allocation as a result of
network reconfiguration
In this thesis the maximum number of objectives to be optimised simultaneously
is three However the work could be extended to solve the DA problem with
more than three objectives These objectives may include balancing load on
transformers minimising the number of switch operations and maximising the
load on feeders
Chapter 10 Conclusion amp Future Work
Page | 194
The optimal DNR DG allocation TEO and SSP will be combined together to
solve the multi-objective optimisation problem The proposed methodologies
could be tested in large-scale practical systems
In this thesis the evaluation of reliability indices only considers the faults in the
line sections And all the feeders are supposed to have the same parameters and
hence the same failure rates However historical data shows the failure rates of a
feeder vary with geographical location and the weather Therefore different
types of feeders and seasonal varying data of feeder section failure rates will be
considered in future work Moreover the impacts of contingencies on the system
such as faults in the transformers and protective devices could also be considered
The integration of large number of electric vehicles (EVs) into the distribution
network places an extra burden on the electricity grid such as increases in energy
loss overloading in feeders decrease in reliability and power quality Therefore
network reconfiguration techniques and smart charging strategies will be
proposed to moderate the charging effects of EVs In addition the vehicle-to-grid
(V2G) technique which returns electricity to the gird will also be studied The
bi-directional of EVs in the network can provide power to improve load
balancing by ldquovalley fillingrdquo (charging) and ldquopeak shavingrdquo (discharging) [118]
The simulation results show ACO-based algorithms could find a set of good
solutions within a reasonable computation time The ACO control parameters are
set experimentally using information from several trial runs More work is
needed to improve the performance of the proposed algorithms by determining
the optimum set of parameter values It is expected that new ACO-based
algorithms will outperform any existing ones or at worst match their results
In the future a multi-objective stochastic optimal flow problem with the
consideration of load DG EV uncertainties will be addressed The load DG
and EV models are obtained by using a Monte Carlo probabilistic power flow
The objectives are then optimised by using a suitable metaheuristic technique
Page | 195
References
[1] L M Faulkenberry Electrical power distribution and transmission Pearson
Education India 1996
[2] Parliamentary Office of Science and Technology ldquoUK Electricity Networksrdquo
2001
[3] R Das et al ldquoDistribution automation strategies evolution of technologies
and the business caserdquo IEEE Trans Smart Grid vol 6 no 4 pp 2166ndash2175
2015
[4] P Balakrishna K Rajagopal and K S Swarup ldquoApplication benefits of
Distribution Automation and AMI systems convergence methodology for
distribution power restoration analysisrdquo Sustain Energy Grids Networks vol
2 pp 15ndash22 2015
[5] ofgem ldquoEnergy Efficiency Directive An assessment of the energy efficiency
potential of Great Britainrsquos gas and electricity infrastructurerdquo 2015
[6] R C Dugan M F McGranaghan and H W Beaty ldquoElectrical power
systems qualityrdquo 1996
[7] British Standards Institution DECC UK Office for National Statistic and
Met Office UK ldquoVoltage characteristics of electricity supplied by public
distribution systemsrdquo Whether and Climate change no December pp 1ndash18
2010
[8] Y F Niu Z Y Gao and W H K Lam ldquoEvaluating the reliability of a
stochastic distribution network in terms of minimal cutsrdquo Transp Res Part E
Logist Transp Rev vol 100 pp 75ndash97 2017
[9] R Billinton and J E Billinton ldquoDistribution system reliability indicesrdquo
IEEE Trans Power Deliv vol 4 no 1 pp 561ndash568 1989
[10] Ofgem ldquoElectricity Distribution Annual Report for 2010-11rdquo 2012
[11] J Hamachi K Eto ldquoUnderstanding the Cost of Power Interruption to US
Electric Consumers LBNL-55718rdquo 2004
[12] R M Vitorino H M Jorge and L P Neves ldquoLoss and reliability
optimization for power distribution system operationrdquo Elsevier BV 2013
[13] E M Carreno R Romero and A Padilha-Feltrin ldquoAn efficient codification
to solve distribution network reconfiguration for loss reduction problemrdquo
IEEE Trans Power Syst vol 23 no 4 pp 1542ndash1551 2008
[14] A Y Abdelaziz R A Osama and S M El-Khodary ldquoReconfiguration of
distribution systems for loss reduction using the hyper-cube ant colony
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2012
[15] European commission ldquoRoadmap for moving to a low-carbon economy in
2050rdquo DG Clim Action portal pp 1ndash2 2011
[16] A Mohamed Imran M Kowsalya and D P Kothari ldquoA novel integration
technique for optimal network reconfiguration and distributed generation
placement in power distribution networksrdquo Int J Electr Power Energy Syst
vol 63 pp 461ndash472 2014
[17] W Guan Y Tan H Zhang and J Song ldquoDistribution system feeder
reconfiguration considering different model of DG sourcesrdquo Int J Electr
Power Energy Syst vol 68 pp 210ndash221 2015
[18] S A Yin and C N Lu ldquoDistribution feeder scheduling considering variable
load profile and outage costsrdquo IEEE Trans Power Syst vol 24 no 2 pp
652ndash660 2009
[19] I Richardson M Thomson D Infield and C Clifford ldquoDomestic electricity
use A high-resolution energy demand modelrdquo Energy Build vol 42 no 10
pp 1878ndash1887 2010
[20] K Deb A Pratap S Agarwal and T Meyarivan ldquoA fast and elitist
multiobjective genetic algorithm NSGA-IIrdquo IEEE Trans Evol Comput vol
6 no 2 pp 182ndash197 2002
[21] M E Elkhatib R El Shatshat and M M A Salama ldquoDecentralized reactive
power control for advanced distribution automation systemsrdquo IEEE Trans
Smart Grid vol 3 no 3 pp 1482ndash1490 2012
[22] C-L Su and J-H Teng ldquoOutage costs quantification for benefitndashcost
analysis of distribution automation systemsrdquo Int J Electr Power Energy
Syst vol 29 no 10 pp 767ndash774 2007
[23] I Goroohi Sardou M Banejad R Hooshmand and a Dastfan ldquoModified
shuffled frog leaping algorithm for optimal switch placement in distribution
automation system using a multi-objective fuzzy approachrdquo IET Gener
Transm Distrib vol 6 no 6 p 493 2012
[24] C L Smallwood and J Wennermark ldquoBenefits of distribution automationrdquo
IEEE Ind Appl Mag vol 16 no 1 pp 65ndash73 2010
[25] T Goumlnen Electric power distribution system engineering McGraw-Hill New
York 1986
[26] V Madani et al ldquoDistribution automation strategies challenges and
opportunities in a changing landscaperdquo IEEE Trans Smart Grid vol 6 no 4
pp 2157ndash2165 2015
[27] J J Burke ldquoPower distribution engineering fundamentals and applicationsrdquo
1994
[28] A Elmitwally E Gouda and S Eladawy ldquoRestoring recloser-fuse
coordination by optimal fault current limiters planning in DG-integrated
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[29] L He J R Mayor R G Harley H Liles G Zhang and Y Deng ldquoMulti-
physics modeling of the dynamic response of a circuit breaker recloser
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[30] J M Gers and E J Holmes Protection of electricity distribution networks
vol 47 The Institution of Electrical Engineers 2004
[31] E-J-A Zehra M Moghavvemi M M I Hashim and M Kashem ldquoNetwork
reconfiguration using PSAT for loss reduction in distribution systemsrdquo in 1st
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[32] J J S Grainger W D J J Grainger and W D Stevenson Power system
analysis McGraw-Hill New York 1994
[33] R D Laramore An introduction to electrical machines and transformers
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[34] D Borge-Diez A Colmenar-Santos M Castro-Gil and J Carpio-Ibaacutentildeez
ldquoParallel distribution transformer loss reductions A proposed method and
experimental validationrdquo Int J Electr Power Energy Syst vol 49 no 1 pp
170ndash180 2013
[35] Y Wang and hui chao Liu ldquoThe information system for economic operation
of transformer based on ASPrdquo in Intertational Power Engineering
Conference 2007 pp 1914ndash1917
[36] X Chen and Z Guo ldquoEconomic operation of power transformer based on real
time parameter checkingrdquo in Power Engineering Society General Meeting
2006 pp 4ndash6
[37] W Yuan and Y Zhang ldquoEconomic operation of transformers in the area
power network based on real-time analysis and controlrdquo in China
International Conference on Electricity Distribution 2008 pp 1ndash5
[38] R Song and X Zhang ldquoThe application research of load smoothing algorithm
in the transformer economic operationrdquo in International Conference on
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[39] C Mamane ldquoTransformer loss evaluation user-manufacturer
communicationsrdquo IEEE Trans Ind Appl vol IA-20 no 1 pp 11ndash15 1984
[40] E I Amoiralis M A Tsili and A G Kladas ldquoEconomic evaluation of
transformer selection in electrical power systemsrdquo in 19th International
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[41] B Suechoey J Ekburanawat N Kraisnachinda S Banjongjit C Chompoo
and M Kando ldquoAn analysis and selection of distribution transformer for
losses reductionrdquo in IEEE Power Engineering Society Winter Meeting 2000
pp 2290ndash2293
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[42] B Suechoey S Bunjongjit and M Kando ldquoThe result analysis of economic
distribution transformer design in Thailandrdquo in Transmission and Distribution
Conference and Exhibition 2002 pp 1820ndash1823
[43] A Merlin and H Back ldquoSearch for a minimal-loss operating spanning tree
configuration in an urban power distribution systemrdquo in Proc 5th Power
System Computation Conf 1975 pp 1ndash18
[44] S Civanlar J J Grainger H Yin and S S H Lee ldquoDistribution feeder
reconfiguration for loss reductionrdquo IEEE Trans Power Deliv vol 3 no 3
pp 1217ndash1223 1988
[45] M-R Andervazh J Olamaei and M-R Haghifam ldquoAdaptive multi-
objective distribution network reconfiguration using multi-objective discrete
particles swarm optimisation algorithm and graph theoryrdquo IET Gener Transm
Distrib vol 7 no 12 pp 1367ndash1382 2013
[46] K Nara A Shiose M Kitagawa and T Ishihara ldquoImplementation of genetic
algorithm for distribution systems loss minimum re-configurationrdquo IEEE
Trans Power Syst vol 7 no 3 pp 1044ndash1051 1992
[47] J Z Zhu ldquoOptimal reconfiguration of electrical distribution network using
the refined genetic algorithmrdquo Electr Power Syst Res vol 62 no 1 pp 37ndash
42 2002
[48] B Enacheanu B Raison R Caire O Devaux W Bienia and N HadjSaid
ldquoRadial network reconfiguration using genetic algorithm based on the matroid
theoryrdquo IEEE Trans Power Syst vol 23 no 1 pp 186ndash195 2008
[49] J C Cebrian and N Kagan ldquoReconfiguration of distribution networks to
minimize loss and disruption costs using genetic algorithmsrdquo Electr Power
Syst Res vol 80 no 1 pp 53ndash62 2010
[50] H D Chiang and R Jean-Jumeau ldquoOptimal network reconfigurations in
distribution systems part 1 A new formulation and a solution methodologyrdquo
IEEE Trans Power Deliv vol 5 no 4 pp 1902ndash1909 1990
[51] Y J Jeon J C Kim and J O Kim ldquoAn efficient simulted annealing
algorithm for network reconfiguration in large-scale distribution systemsrdquo
IEEE Trans Power Deliv vol 17 no 4 pp 1070ndash1078 2002
[52] H Mori and Y Ogita ldquoA parallel tabu search based method for
reconfigurations of distribution systemsrdquo in Power Engineering Society
Summer Meeting 2000 pp 73ndash78
[53] D Zhang Z Fu and L Zhang ldquoAn improved TS algorithm for loss-
minimum reconfiguration in large-scale distribution systemsrdquo Electr Power
Syst Res vol 77 no 5ndash6 pp 685ndash694 2007
[54] A Y Abdelaziz F M Mohamed S F Mekhamer and M A L Badr
ldquoDistribution system reconfiguration using a modified Tabu Search algorithmrdquo
Electr Power Syst Res vol 80 no 8 pp 943ndash953 2010
[55] A Y Abdelaziz F M Mohammed S F Mekhamer and M A L Badr
References
Page | 199
ldquoDistribution systems reconfiguration using a modified particle swarm
optimization algorithmrdquo Electr Power Syst Res vol 79 no 11 pp 1521ndash
1530 2009
[56] A Skoonpong and S Sirisumrannukul ldquoNetwork reconfiguration for
reliability worth enhancement in distribution systems by simulated annealingrdquo
5th Int Conf Electr Eng Comput Telecommun Inf Technol ECTI-CON pp
937ndash940 2008
[57] S Elsaiah M Benidris and J Mitra ldquoReliability improvement of power
distribution system through feeder reconfigurationrdquo in 13th International
Conference on Probabilistic Methods Applied to Power Systems 2014
[58] A Kavousi-Fard and T Niknam ldquoOptimal distribution feeder reconfiguration
for reliability improvement considering uncertaintyrdquo IEEE Trans Power
Deliv vol 29 no 3 pp 1344ndash1353 2014
[59] S Ghasemi ldquoBalanced and unbalanced distribution networks reconfiguration
considering reliability indicesrdquo Ain Shams Eng J 2015
[60] A Saffar R Hooshmand and A Khodabakhshian ldquoA new fuzzy optimal
reconfiguration of distribution systems for loss reduction and load balancing
using ant colony search-based algorithmrdquo Appl Soft Comput J vol 11 no 5
pp 4021ndash4028 2011
[61] D Das ldquoA fuzzy multiobjective approach for network reconfiguration of
distribution systemsrdquo IEEE Trans Power Deliv vol 21 no 1 pp 202ndash209
2006
[62] J E Mendoza E A Loacutepez M E Loacutepez and C A Coello Coello
ldquoMicrogenetic multiobjective reconfiguration algorithm considering power
losses and reliability indices for medium voltage distribution networkrdquo IET
Gener Transm Distrib vol 3 no 9 pp 825ndash840 2009
[63] K M Muttaqi J Aghaei V Ganapathy and A E Nezhad ldquoTechnical
challenges for electric power industries with implementation of distribution
system automation in smart gridsrdquo Renew Sustain Energy Rev vol 46 pp
129ndash142 2015
[64] A Abiri-Jahromi M Fotuhi-Firuzabad M Parvania and M Mosleh
ldquoOptimized sectionalizing switch placement strategy in distribution systemsrdquo
IEEE Trans Power Deliv vol 27 no 1 pp 362ndash370 2012
[65] J Northcote-Green and R G Wilson Control and automation of electrical
power distribution systems vol 28 CRC Press 2006
[66] H Falaghi M R Haghifam and C Singh ldquoAnt colony optimization-based
method for placement of sectionalizing switches in distribution networks
using a fuzzy multiobjective approachrdquo IEEE Trans Power Deliv vol 24
no 1 pp 268ndash276 2009
[67] M Nematollahi and M Tadayon ldquoOptimal sectionalizing switches and DG
placement considering critical system conditionrdquo in 21st Iranian Conference
References
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on Electrical Engineering 2013 pp 1ndash6
[68] J H Teng and C N Lu ldquoFeeder-switch relocation for customer interruption
cost minimizationrdquo IEEE Trans Power Deliv vol 17 no 1 pp 254ndash259
2002
[69] J H Teng and Y H Liu ldquoA novel ACS-based optimum switch relocation
methodrdquo IEEE Trans Power Syst vol 18 no 1 pp 113ndash120 2003
[70] V Miranda ldquoUsing fuzzy reliability in a decision aid environment for
establishing interconnection and switching location policiesrdquo in CIRED 1991
pp 1ndash6
[71] A Heidari V G Agelidis and M Kia ldquoConsiderations of sectionalizing
switches in distribution networks with distributed generationrdquo IEEE Trans
Power Deliv vol 30 no 3 pp 1401ndash1409 2015
[72] I v Zhezhelenko Y Papaika and others ldquoEstimating economic equivalent of
reactive power in the systems of enterprise electric power supplyrdquo Sci Bull
Natl Min Univ no 5 2016
[73] L Li and R Li ldquoStudy on the analysis software of economic operation of
transformerrdquo Adv Mater Res vol 1008ndash1009 pp 497ndash500 2014
[74] J Shang Z Tan C Zhang and L Ju ldquoThe transformer equipment selectionrsquos
update decision technical and economic analysis modelrdquo in Energy and
Power Engineering 2013 vol 5 no 4 pp 143ndash147
[75] B Amanulla S Chakrabarti and S N Singh ldquoReconfiguration of power
distribution systems considering reliability and power lossrdquo IEEE Trans
Power Deliv vol 27 no 2 pp 918ndash926 2012
[76] R E Brown Electric power distribution reliability CRC press 2008
[77] P Zhou R Y Jin and L W Fan ldquoReliability and economic evaluation of
power system with renewables A reviewrdquo Renew Sustain Energy Rev vol
58 pp 537ndash547 2016
[78] R Billington and R N Allan Reliability evaluation of power systems
Plenum Publishing Corp New York NY 1996
[79] N G Paterakis et al ldquoMulti-objective reconfiguration of radial distribution
systems using reliability indicesrdquo IEEE Trans Power Syst vol 31 no 2 pp
1048ndash1062 2016
[80] B Sultana M W Mustafa U Sultana and A R Bhatti ldquoReview on
reliability improvement and power loss reduction in distribution system via
network reconfigurationrdquo Renew Sustain Energy Rev vol 66 pp 297ndash310
2016
[81] K Xie J Zhou and R Billinton ldquoReliability evaluation algorithm for
complex medium voltage electrical distribution networks based on the shortest
pathrdquo IEE Proceedings-Generation Transm Distrib vol 150 no 6 pp
686ndash690 2003
References
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[82] Z Ghofrani-Jahromi M Kazemi and M Ehsan ldquoDistribution switches
upgrade for loss reduction and reliability improvementrdquo IEEE Trans Power
Deliv vol 30 no 2 pp 684ndash692 2015
[83] P Ngatchou A Zarei and A El-Sharkawi ldquoPareto multi objective
optimizationrdquo in Proceedings of the 13th International Conference on
Intelligent Systems Application to Power Systems 2005 pp 84ndash91
[84] J S Savier and D Das ldquoImpact of network reconfiguration on loss allocation
of radial distribution systemsrdquo IEEE Trans Power Deliv vol 22 no 4 pp
2473ndash2480 2007
[85] T T Nguyen T T Nguyen A V Truong Q T Nguyen and T A Phung
ldquoMulti-objective electric distribution network reconfiguration solution using
runner-root algorithmrdquo Appl Soft Comput J vol 52 pp 93ndash108 2017
[86] N Gupta A Swarnkar R C Bansal and K R Niazi ldquoMulti-objective
reconfiguration of distribution systems using adaptive genetic algorithm in
fuzzy frameworkrdquo IET Gener Transm Distrib vol 4 no 12 pp 1288ndash1298
2010
[87] M R Narimani A Azizi Vahed R Azizipanah-Abarghooee and M
Javidsharifi ldquoEnhanced gravitational search algorithm for multi-objective
distribution feeder reconfiguration considering reliability loss and operational
costrdquo IET Gener Transm Distrib vol 8 no 1 pp 55ndash69 2014
[88] A Ahuja S Das and A Pahwa ldquoAn AIS-ACO hybrid approach for multi-
objective distribution system reconfigurationrdquo IEEE Trans Power Syst vol
22 no 3 pp 1101ndash1111 2007
[89] M Rostami A Kavousi-Fard and T Niknam ldquoExpected cost minimization
of smart grids with plug-in hybrid electric vehicles using optimal distribution
feeder reconfigurationrdquo Ind Informatics IEEE Trans vol 11 no 2 pp
388ndash397 2015
[90] S Oh J Kim S Kwon and S Chung ldquoMonte Carlo simulation of
phytosanitary irradiation treatment for mangosteen using MRI-based
geometryrdquo vol 39 no 3 pp 205ndash214 2014
[91] N HadjSaid and J C Sabonnadiere Electrical Distribution Networks
London ISTE Ltd 2011
[92] Y Li ldquoVoltage balancing on three-phase low voltage feederrdquo The Univerisity
of Manchester 2015
[93] K Bell and P R Allan ldquoComputation of the Value of Securityrdquo 1999
[94] M Dorigo V Maniezzo and A Colorni ldquoThe ant systems optimization by a
colony of cooperative agentsrdquo IEEE Trans Syst Man Cybern B vol 26 no
1 pp 1ndash13 1996
[95] M Dorigo and L M Gambardella ldquoAnt colony system a cooperative
learning approach to the traveling salesman problemrdquo IEEE Trans Evol
Comput vol 1 no 1 pp 53ndash66 1997
References
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[96] M Lopez-Ibanez and T Stuetzle ldquoThe automatic design of multiobjective ant
colony optimization algorithmsrdquo IEEE Trans Evol Comput vol 16 no 6
pp 861ndash875 2012
[97] L Charles Daniel and S Ravichandran ldquoDistribution network reconfiguration
for loss reduction using ant colony system algorithmrdquo in IEEE Indicon 2005
Conference 2005 pp 1ndash4
[98] J F Goacutemez et al ldquoAnt colony system algorithm for the planning of primary
distribution circuitsrdquo IEEE Trans Power Syst vol 19 no 2 pp 996ndash1004
2004
[99] J Lu N Wang J Chen and F Su ldquoCooperative path planning for multiple
UCAVs using an AIS-ACO hybrid approachrdquo Proc 2011 Int Conf Electron
Mech Eng Inf Technol EMEIT 2011 vol 8 no 2 pp 4301ndash4305 2011
[100] J E Hunt and D E Cooke ldquoAn adaptive distributed learning system based
on the immune systemrdquo 1995 IEEE Int Conf Syst Man Cybern Intell Syst
21st Century vol 3 pp 2494ndash2499 1995
[101] C A C Coello and N C Cortes ldquoSolving multiobjective optimization
problems using an artificial immune systemrdquo Genet Program Evolvable
Mach vol 6 no 2 pp 163ndash190 2005
[102] L N De Castro and F J Von Zuben ldquoLearning and optimization using the
clonal selection principlerdquo IEEE Trans Evol Comput vol 6 no 3 pp 239ndash
251 2002
[103] Office for National Statistics Population and household estimates for the
United Kingdom UK 2011
[104] S Ingram S Probert and K Jackson ldquoThe impact of small scale embedded
generation on the operating parameters of distribution networksrdquo Department
of Trade and Industry (DTI) 2003 [Online] Available
httpwebarchivenationalarchivesgovuk20100919182407httpwwwensg
govukassets22_01_2004_phase1b_report_v10b_web_site_finalpdf
[105] 63 EDS 02-0027 Engineering design standard EDS 02-007 11 kV Triplex
Cable 2012
[106] TTH ldquo75 MVA-33-11 KV-GTP TTHrdquo 2014 [Online] Available
httpwwwtranstechtransformerscompdf75mva3311kvgtptth24012008pdf
[107] A M Tahboub V R Pandi and H H Zeineldin ldquoDistribution system
reconfiguration for annual energy loss reduction considering variable
distributed generation profilesrdquo IEEE Trans Power Deliv vol 30 no 4 pp
1677ndash1685 2015
[108] M E Baran and F F Wu ldquoNetwork reconfiguration in distribution systems
for loss reduction and load balancingrdquo Power Deliv IEEE Trans vol 4 no
2 pp 1401ndash1407 1989
[109] D Shirmohammadi and H W Hong ldquoReconfiguration of electric distribution
networks for resistive line losses reductionrdquo IEEE Trans Power Deliv vol 4
References
Page | 203
no 2 pp 1492ndash1498 1989
[110] R S Rao K Ravindra K Satish and S V L Narasimham ldquoPower loss
minimization in distribution system using network reconfiguration in the
presence of distributed generationrdquo IEEE Trans Power Syst vol 28 no 1
pp 1ndash9 2012
[111] D Sudha Rani N Subrahmanyam and M Sydulu ldquoMulti-objective invasive
weed optimization - an application to optimal network reconfiguration in
radial distribution systemsrdquo Int J Electr Power Energy Syst vol 73 pp
932ndash942 2015
[112] R L Haupt and S E Haupt Practical genetic algorithms John Wiley amp
Sons 2004
[113] X S Yang and S Deb ldquoCuckoo search via Levy flightsrdquo 2009 World Congr
Nat Biol Inspired Comput NABIC 2009 - Proc pp 210ndash214 2009
[114] R N Allan R Billinton I Sjarief L Goel and K S So ldquoA reliability test
system for educational purposes-basic distribution system data and resultsrdquo
IEEE Trans Power Syst vol 6 no 2 pp 813ndash820 1991
[115] G Li and X-P Zhang ldquoModeling of plug-in hybrid electric vehicle charging
demand in probabilistic power flow calculationsrdquo Smart Grid IEEE Trans
vol 3 no 1 pp 492ndash499 2012
[116] UK Department for Transport ldquoNational Travel Survey England 2013 -
Statistical Releaserdquo no July p 26 2014
[117] A Mazza G Chicco and A Russo ldquoOptimal multi-objective distribution
system reconfiguration with multi criteria decision making-based solution
ranking and enhanced genetic operatorsrdquo Int J Electr Power Energy Syst
vol 54 pp 255ndash267 2014
[118] E Sortomme and M A El-Sharkawi ldquoOptimal charging strategies for
unidirectional vehicle-to-gridrdquo IEEE Trans Smart Grid vol 2 no 1 pp
119ndash126 2011
Page | 204
APPENDIX A Network Model Data
A1 UK generic distribution network
The line parameters given here is related to the single line diagram of the network
shown in Fig 45 which are used in the simulation study in Section 451 and 452
Table A-1 Typical configurations and parameters of 11 kV triplex cables in the UK
11 kV line type Cross
Sectional
Area
(CSA)
Positive sequence
Z
Zero-phase
sequence
Z
Approximate
Capacitance
C
Id Configuration Rph Xph R0 X0 C
(mm2) (Ωkm) (μFkm)
A Nexans
635011000
Volt Triplex
Cable
185 0415 0112 0988 0236 036
B 95 0220 0012 0530 0102 028
Appendix A Network Data
Page | 205
A2 33-bus system
Table A-2 Line and load data of 33-bus system
Branch
number
Sending end
node
Receiving end
node
R
(Ω)
X
(Ω)
P at receiving
end (kW)
Q at receiving
end (kVAr)
1 0 1 00922 0047 100 60
2 1 2 04930 02511 90 40
3 2 3 03660 01864 120 80
4 3 4 03811 01941 60 30
5 4 5 08190 07070 60 20
6 5 6 01872 06188 200 100
7 6 7 07114 02351 200 100
8 7 8 10300 07400 60 20
9 8 9 10440 07400 60 20
10 9 10 01966 00650 45 30
11 10 11 03744 01238 60 35
12 11 12 14680 11550 60 35
13 12 13 05416 07129 120 80
14 13 14 05910 05260 60 10
15 14 15 07463 05450 60 20
16 15 16 12890 17210 60 20
17 16 17 03720 05740 90 40
18 17 18 01640 01565 90 40
19 18 19 15042 13554 90 40
20 19 20 04095 04784 90 40
21 20 21 07089 09373 90 40
22 21 22 04512 03083 90 50
23 22 23 08980 07091 420 200
24 23 24 08960 07011 420 200
25 24 25 02030 01034 60 25
26 25 26 02842 01447 60 25
27 26 27 10590 09337 60 20
28 27 28 08042 07006 120 70
29 28 29 05075 02585 200 600
30 29 30 09744 09630 150 70
31 30 31 03105 03619 210 100
32 31 32 03410 05362 60 40
33 7 20 2 2 -- --
34 11 21 2 2 -- --
35 8 14 2 2 -- --
36 17 32 05 05 -- --
37 24 28 05 05 -- --
Appendix A Network Data
Page | 206
A3 69-bus system
Table A-3 Line and load data of 69-bus system
Branch
number
Sending end
node
Receiving end
node
R
(Ω)
X
(Ω)
P at receiving
end (kW)
Q at receiving
end (kVAr)
1 0 1 00005 00012 0 0
2 1 2 00005 00012 0 0
3 2 3 00015 00036 0 0
4 3 4 00251 00294 0 0
5 4 5 0366 01864 26 22
6 5 6 0381 01941 404 30
7 6 7 00922 0047 75 54
8 7 8 00493 00251 30 22
9 8 9 0819 02707 28 19
10 9 10 01872 00619 145 104
11 10 11 07114 02351 145 104
12 11 12 103 034 8 5
13 12 13 1044 0345 8 55
14 13 14 1058 03496 0 0
15 14 15 01966 0065 455 30
16 15 16 03744 01238 60 35
17 16 17 00047 00016 60 35
18 17 18 03276 01083 0 0
19 18 19 02106 0069 1 06
20 19 20 03416 01129 114 81
21 20 21 0014 00046 5 35
22 21 22 01591 00526 0 0
23 22 23 03463 01145 28 20
24 23 24 07488 02475 0 0
25 24 25 03089 01021 14 10
26 25 26 01732 00572 14 10
27 26 27 00044 00108 26 186
28 27 28 0064 01565 26 186
29 28 29 03978 01315 0 0
30 29 30 00702 00232 0 0
31 30 31 0351 0116 0 0
32 31 32 0839 02816 14 10
33 32 33 1708 05646 195 14
34 33 34 1474 04873 6 4
35 34 35 00044 00108 26 1855
36 35 36 0064 01565 26 1855
37 36 37 01053 0123 0 0
38 37 38 00304 00355 24 17
39 38 39 00018 00021 24 17
40 39 40 07283 08509 12 1
41 40 41 031 03623 0 0
Appendix A Network Data
Page | 207
42 41 42 0041 00478 6 43
43 42 43 00092 00116 0 0
44 43 44 01089 01373 3922 263
45 44 45 00009 00012 3922 263
46 45 46 00034 00084 0 0
47 46 47 00851 02083 79 564
48 47 48 02898 07091 3847 2745
49 48 49 00822 02011 3847 2745
50 49 50 00928 00473 405 283
51 50 51 03319 01114 36 27
52 51 52 0174 00886 435 35
53 52 53 0203 01034 264 19
54 53 54 02842 01447 24 172
55 54 55 02813 01433 0 0
56 55 56 159 05337 0 0
57 56 57 07837 0263 0 0
58 57 58 03042 01006 100 72
59 58 59 03861 01172 0 0
60 59 60 05075 02585 1244 888
61 60 61 00974 00496 32 23
62 61 62 0145 00738 0 0
63 62 63 07105 03619 227 162
64 63 64 1041 05302 59 42
65 64 65 02012 00611 18 13
66 65 66 00047 00014 18 13
67 66 67 07394 02444 28 20
68 67 68 00047 00016 28 20
69 49 58 2 1 -- --
70 26 64 1 05 -- --
71 12 20 05 05 -- --
72 10 42 05 05 -- --
73 14 45 1 05 -- --
A4 RBTS Bus 4 system
Table A-4 Feeder data of RBTS Bus 4
Feeder
Type
Length
(km)
Feeder section number
1 060 2 6 10 14 17 21 25 28 30 34 38 41 43 46 49 51 55 58 61 64 67
68 69 70 71
2 075 1 4 7 9 12 16 19 22 24 27 29 32 3537 40 42 45 48 50 53 56 60
63 65
3 080 3 5 8 11 13 15 18 20 23 26 31 33 36 3944 47 52 54 57 59 62 66
Appendix A Network Data
Page | 208
Table A-5 Reliability Data for RBTS Bus 4
Equipment λA λP λM λt R RM
Lines 004 0 0 0 5 0
Buses 0001 0 1 001 2 8
Switches 0004 0002 1 006 4 72
Distribution Transformers 0015 0 1 0 200 120
λA Active failure rate in (fryrkm) for lines and (fryr) for other components
λP Passive failure rate in (fryrkm) for lines and (fryr) for other components
λM Maintenance outage rate in (fryrkm) for lines and (fryr) for other components
λP Transient failure rate in (fryrkm) for lines and (fryr) for other components
R Repair time of failures in (hr)
RM Maintenance outage time in (hr)
Page | 209
APPENDIX B Simulation Results
B1 Simulation results of Chapter 4
B11Tie-switch location
As discussed in Section 452 the location of tie-switch in Scenario 9 is changeable
and the relevant results are presented in Table B-1 It can be clearly seen that the
NOP is located in lsquoTW1rsquo between 0730 and 1000 1600 and 1630 while in lsquoTW5rsquo
for the rest of the day
Table B-1 The locations of tie-switch in Scenario 9
Time Loc Time Loc Time Loc Time Loc Time Loc Time Loc
0000 TW5 0400 TW5 0800 TW1 1200 TW5 1600 TW1 2000 TW5
0010 TW5 0410 TW5 0810 TW1 1210 TW5 1610 TW1 2010 TW5
0020 TW5 0420 TW5 0820 TW1 1220 TW5 1620 TW1 2020 TW5
0030 TW5 0430 TW5 0830 TW1 1230 TW5 1630 TW1 2030 TW5
0040 TW5 0440 TW5 0840 TW1 1240 TW5 1640 TW5 2040 TW5
0050 TW5 0450 TW5 0850 TW1 1250 TW5 1650 TW5 2050 TW5
0100 TW5 0500 TW5 0900 TW1 1300 TW5 1700 TW5 2100 TW5
0110 TW5 0510 TW5 0910 TW1 1310 TW5 1710 TW5 2110 TW5
0120 TW5 0520 TW5 0920 TW1 1320 TW5 1720 TW5 2120 TW5
0130 TW5 0530 TW5 0930 TW1 1330 TW5 1730 TW5 2130 TW5
0140 TW5 0540 TW5 0940 TW1 1340 TW5 1740 TW5 2140 TW5
0150 TW5 0550 TW5 0950 TW1 1350 TW5 1750 TW5 2150 TW5
0200 TW5 0600 TW5 1000 TW1 1400 TW5 1800 TW5 2200 TW5
0210 TW5 0610 TW5 1010 TW5 1410 TW5 1810 TW5 2210 TW5
0220 TW5 0620 TW5 1020 TW5 1420 TW5 1820 TW5 2220 TW5
0230 TW5 0630 TW5 1030 TW5 1430 TW5 1830 TW5 2230 TW5
0240 TW5 0640 TW5 1040 TW5 1440 TW5 1840 TW5 2240 TW5
0250 TW5 0650 TW5 1050 TW5 1450 TW5 1850 TW5 2250 TW5
0300 TW5 0700 TW5 1100 TW5 1500 TW5 1900 TW5 2300 TW5
0310 TW5 0710 TW5 1110 TW5 1510 TW5 1910 TW5 2310 TW5
0320 TW5 0720 TW5 1120 TW5 1520 TW5 1920 TW5 2320 TW5
0330 TW5 0730 TW1 1130 TW5 1530 TW5 1930 TW5 2330 TW5
0340 TW5 0740 TW1 1140 TW5 1540 TW5 1940 TW5 2340 TW5
0350 TW5 0750 TW1 1150 TW5 1550 TW5 1950 TW5 2350 TW5
Appendix B Simulation Results
Page | 210
B12 Voltage variations
For Test Case 2 in Section 452 the detailed voltage values of the mean and the
corresponding 95th
profiles at each node in the linked feeder are recorded in Table
B-2 and Table B-3
Table B-2 Mean voltage profiles at each node in the linked feeder
Node
No
Scenarios
S1 S2 S3 S4 S5 S6 S7 S8 S9
A4_1 09675 09787 09787 09766 09859 09859 09748 09825 09815
A4_2 09676 09784 09784 09766 09856 09856 09748 09822 09813
A4_3 09677 09782 09782 09767 09854 09854 09749 09819 09811
A4_4 09678 09780 09780 09768 09851 09851 09750 09817 09810
A4_5 09681 09777 09777 09771 09849 09849 09753 09814 09808
A4_6 09685 09775 09775 09775 09846 09846 09757 09812 09807
A4_7 09689 09773 09773 09779 09845 09845 09762 09811 09807
A4_8 09694 09772 09772 09784 09844 09844 09767 09810 09807
B4_8 09700 09772 09772 09790 09844 09844 09773 09810 09808
B4_7 09707 09773 09773 09797 09845 09845 09779 09811 09810
B4_6 09714 09775 09775 09804 09846 09846 09787 09812 09813
B4_5 09722 09777 09777 09813 09849 09849 09795 09814 09816
B4_4 09731 09780 09780 09821 09851 09851 09804 09817 09820
B4_3 09737 09782 09782 09827 09854 09854 09809 09819 09823
B4_2 09743 09784 09784 09833 09856 09856 09815 09822 09826
B4_1 09749 09787 09787 09839 09859 09859 09821 09825 09830
Table B-3 95th
voltage profiles at each node in the linked feeder
Node
No
Scenarios
S1 S2 S3 S4 S5 S6 S7 S8 S9
A4_1 09352 09573 09573 09537 09721 09721 09537 09721 09715
A4_2 09353 09567 09567 09537 09715 09715 09537 09715 09709
A4_3 09355 09562 09562 09539 09711 09711 09539 09711 09704
A4_4 09357 09558 09558 09541 09707 09707 09541 09707 09702
A4_5 09363 09553 09553 09547 09701 09701 09547 09701 09679
A4_6 09370 09548 09548 09555 09697 09697 09555 09697 09694
A4_7 09379 09545 09545 09563 09694 09694 09563 09794 09691
A4_8 09389 09544 09544 09573 09692 09692 09573 09792 09692
B4_8 09400 09544 09544 09585 09692 09692 09585 09792 09692
B4_7 09413 09545 09545 09598 09694 09694 09598 09794 09694
B4_6 09427 09548 09548 09613 09697 09697 09613 09697 09697
B4_5 09443 09553 09553 09628 09701 09701 09628 09701 09701
B4_4 09460 09558 09558 09646 09707 09707 09646 09707 09707
Appendix B Simulation Results
Page | 211
B4_3 09471 09562 09562 09656 09711 09711 09656 09711 09711
B4_2 09482 09567 09567 09668 09715 09715 09668 09715 09715
B4_1 09494 09573 09573 09680 09721 09721 09680 09721 09721
B2 Simulation results of Chapter 5
The network losses in each branch for all test cases of 33-bus system and 69-bus
system are listed in Table B-4 and Table B-5 respectively
Table B-4 Network losses in each branch of 33-bus system
Branch number Feeder loss (kW)
Case I Case II Case III Case IV
1 1227 1189 1010 1003
2 5192 2686 2051 2060
3 1995 756 112 490
4 1874 667 074 415
5 3833 1321 122 807
6 192 006 006 006
7 484 0 0 0
8 418 124 211 124
9 357 0 0 0
10 055 001 001 001
11 088 003 003 003
12 267 045 045 045
13 073 008 008 008
14 036 0 0 0
15 028 045 092 045
16 025 048 115 048
17 003 007 022 007
18 016 226 232 226
19 083 1809 1859 1808
20 01 424 436 423
21 004 118 071 118
22 319 316 914 315
23 516 512 1618 510
24 129 128 869 128
25 26 224 005 124
26 334 285 003 155
27 1133 962 003 510
28 786 664 0 345
29 391 326 199 159
30 160 110 018 003
Appendix B Simulation Results
Page | 212
31 021 012 0 000
32 001 0 013 0
33 0 563 809 563
34 0 215 215 215
35 0 174 320 174
36 0 002 033 002
37 0 0 263 0
Total 20314 13981 11753 10844
Table B-5 Network losses in each branch of 69-bus system
Branch number Feeder loss (kW)
Case I Case II Case III Case IV
1 008 007 006 006
2 008 007 006 006
3 020 012 012 010
4 194 011 011 011
5 2829 159 155 159
6 2939 164 160 164
7 691 035 034 035
8 338 012 012 012
9 477 143 137 142
10 101 029 027 028
11 219 032 030 032
12 128 000 000 000
13 124 000 0 000
14 120 0 000 0
15 022 083 043 083
16 032 138 067 138
17 000 001 001 001
18 010 080 032 080
19 007 052 021 052
20 011 083 033 083
21 000 003 001 002
22 001 022 006 022
23 001 049 013 049
24 001 091 021 091
25 000 037 009 037
26 000 019 004 019
27 000 000 000 000
28 000 000 000 000
29 001 001 001 001
30 000 000 000 000
31 001 001 001 001
Appendix B Simulation Results
Page | 213
32 001 001 001 001
33 001 001 001 001
34 000 000 000 000
35 000 003 001 003
36 001 041 019 041
37 002 064 028 064
38 000 018 008 018
39 000 001 000 001
40 005 391 161 391
41 002 166 068 166
42 000 022 009 022
43 000 005 002 005
44 001 057 023 057
45 000 000 000 000
46 002 017 017 013
47 058 416 416 316
48 164 1321 1321 991
49 012 253 253 178
50 000 000 000 000
51 000 000 000 000
52 580 001 001 001
53 673 001 001 000
54 916 000 000 000
55 882 0 0 0
56 4986 000 000 000
57 2458 000 000 000
58 954 000 000 000
59 1071 627 626 379
60 1408 824 823 498
61 011 0 0 0
62 014 000 000 000
63 066 001 001 001
64 004 071 069 071
65 000 000 000 000
66 000 000 000 000
67 002 002 002 002
68 000 000 000 000
69 0 3783 3782 2384
70 0 102 052 102
71 0 0 0 0
72 0 0 0 0
73 0 423 252 423
Total 22562 9885 8758 7397
Appendix B Simulation Results
Page | 214
B3 Simulation results of Chapter 8
Table B-6 Pareto optimal solutions of multi-objective DNR (loss ECOST and SAIDI)
Tie-switches location Feeder loss (kW) ECOST ($yr) SAIDI
(hrscustomeryr)
70 68 71 69 321415 4640359 130895231648616
70 10 41 54 364131 431068083000 102819629963899
17 10 41 70 354092 411445783000000 105858799638989
17 26 10 70 383269 530285525000000 0968805806257521
7 26 54 69 435225 578907612000000 0825265794223827
7 54 41 69 406035 460067870000000 0915047984356197
7 26 54 70 442913 571756512000000 0836828971119134
17 10 71 70 345231 439663189000000 106361687725632
70 10 71 69 331470 443747189000000 110465057160048
70 10 41 69 340330 415529783000000 109962169073406
70 68 41 69 330274 435818516000000 130392343561974
7 54 71 69 397170 488285276000000 0920076865222623
41 10 54 69 356448 438219183000000 101663312274368
70 10 54 26 393311 549907825000000 0938414109506619
70 7 71 69 381047 465595876000000 100306543321300
70 7 41 17 403678 433294470000000 0957002858002407
70 10 54 71 355269 459285489000000 103322518050542
7 54 71 70 404856 481134176000000 0931640042117930
7 26 17 70 432867 552134212000000 0867220667870036
7 70 41 69 389911 437378470000000 0998036552346570
7 26 69 70 419096 556218212000000 0908254362214200
17 7 71 70 394813 461511876000000 0962031738868833
71 10 54 69 347586 466436589000000 102166200361011
10 26 54 69 385625 557058925000000 0926850932611312
70 26 10 69 369504 534369525000000 100983950060168
7 54 41 70 413721 452916770000000 0926611161251504
Appendix B Simulation Results
Page | 215
B4 Simulation results of Chapter 9
Table B-7 Pareto optimal solutions of multi-objective DNR (loss maximum node voltage deviation
feeder load balancing index) for 33-bus system in Case II
Tie-switches location Feeder loss
(kW)
Maximum node
Voltage deviation
Feeder load
balancing index
7 34 35 31 37 176962 0108696024464801 00228687361961248
7 11 35 32 28 143474 00613272038422790 00305387759787611
7 9 14 31 37 142477 00768537372742428 00252628392269486
6 8 12 36 37 151849 00696765908940439 00259144961258893
7 8 14 31 37 155399 00924077518455773 00239781364880477
6 8 12 31 37 169382 0104485611067200 00236077543160956
6 8 12 32 37 152876 00776641110366926 00250547432924683
33 8 14 30 37 171441 0108063061643879 00230652089068052
7 9 14 32 28 140261 00604355611623940 00310349101268755
7 11 35 32 37 143028 00639069227083702 00273727965037185
6 8 14 31 37 159752 00968913958755809 00236540473688646
6 33 35 32 37 170278 00826562726566354 00249194843739843
6 11 35 32 37 144683 00656445815841987 00261947314082027
6 8 14 32 37 146983 00705648561488426 00256096967694280
7 9 14 32 37 139815 00639015456844128 00280407351785895
6 9 14 32 37 143097 00625183468485540 00270001779728268
7 11 35 31 37 148829 00852978398065017 00245113845932977
7 34 35 30 37 202483 0130888991378581 00223050578905545
6 8 14 36 37 146991 00643933147100736 00266176555168500
6 11 35 31 37 154281 00897759906819439 00242838273201709
6 8 13 32 37 150430 00753226918458818 00253604605496161
Table B-8 Pareto optimal solutions of multi-objective DNR (loss maximum node voltage deviation
feeder load balancing index) for 33-bus system in Case III
Tie-switches location Feeder loss
(kW)
Maximum node
Voltage deviation
Feeder load
balancing index
7 14 8 32 28 121696 00575193535569366 00264544805354717
7 11 35 31 37 123007 00712785797883380 00213250141648472
6 12 8 32 37 128324 00630309398395457 00223824361844486
6 14 8 30 37 145672 0101299721228755 00194921779245086
7 33 35 32 28 130184 00583420082867310 00261406698684195
7 14 8 30 37 140274 00967924815464314 00195001911353607
7 21 35 30 37 164190 0113945920950777 00189031534924873
6 13 8 32 37 126434 00607661484850486 00227035446761735
7 14 9 32 28 117726 00575130414815478 00271215548731366
Appendix B Simulation Results
Page | 216
6 14 8 32 28 125920 00566904604559002 00265195832133384
6 12 8 31 37 137974 00889877482038002 00200083704114662
7 11 35 30 37 133030 00891516445489180 00199682922816912
6 11 35 32 37 123013 00593840879899440 00235298833627789
7 14 9 32 37 121070 00631040005210335 00255168322432724
6 14 9 32 28 123916 00566872316455769 00273594084038335
7 14 9 30 37 126587 00812324184971598 00206873922472966
7 14 9 31 28 117529 00642736861104275 00240537048868074
6 14 9 32 37 122047 00593825021727904 00240927348267257
6 11 35 32 28 124883 00566888115014094 00269082055980326
6 11 35 31 37 126802 00756552348586014 00207586957663036
6 14 8 32 37 124050 00593857418451058 00230337877365745
7 13 8 32 28 124039 00575225874614865 00262247242500743
7 11 35 32 28 119522 00575159230231156 00267430211390231
7 14 9 31 37 118759 00642740886891275 00220228862077971
6 14 8 31 37 130316 00816654599427028 00201908840890301
33 14 8 30 37 140110 00923831702765571 00197570883486903
7 12 8 32 28 125895 00587758838819431 00259864524009700
6 13 8 31 37 134936 00865715938530326 00201790772057552
Table B-9 Pareto optimal solutions of multi-objective DNR (loss maximum node voltage deviation
feeder load balancing index) for 33-bus system in Case IV
Tie-switches location DG location Feeder
loss
(kW)
Maximum node
Voltage deviation
Feeder load
balancing index
7 9 14 30 37 15 17 16 112506 00655990339384582 00207847799664288
6 8 14 31 37 14 11 15 120818 00728143829651942 00199639595336255
7 11 35 30 37 16 16 12 118637 00756705031931788 00198888055963062
6 8 14 31 37 11 29 14 125736 00822955381260978 00194988443664523
6 11 35 32 37 29 11 29 116999 00602917954784902 00213598898907595
7 9 14 31 37 15 14 16 110931 00518306996442978 00223689972435171
7 34 35 30 37 16 13 13 140652 00983575865184194 00182688360250883
7 8 14 30 37 14 11 15 128617 00876913785424229 00190954012999288
7 8 14 30 37 11 16 14 127141 00860397262006276 00191601352391895
7 9 14 36 37 30 30 29 109157 00520335391274761 00229564125698243
7 8 14 30 37 10 14 16 126706 00857230143750372 00192117850059117
7 11 35 30 37 13 16 12 121130 00786215737441328 00196617519208137
7 34 35 30 37 13 10 9 151352 0106960621828031 00178195736666725
7 34 35 30 37 10 12 9 152310 0107688512235453 00178046268710843
6 8 14 30 37 11 15 16 130550 00897068798318073 00189590122249633
6 8 14 30 37 16 14 10 130869 00901533044670202 00189271311922809
7 34 35 30 37 10 13 12 148089 0104837492639545 00178736074180585
Appendix B Simulation Results
Page | 217
7 34 35 30 37 13 11 16 143317 0100615335666250 00181553323058751
6 8 14 30 37 10 14 14 133299 00925968739633617 00188139999335965
7 34 35 30 37 13 9 12 148392 0105013682219175 00178453713901855
6 8 14 30 37 14 11 10 137593 00963962506644021 00186232592604301
6 8 14 30 37 11 8 14 136046 00951731865531927 00187106569470356
6 8 14 30 37 11 11 16 135639 00942616575802945 00187170876179048
7 8 14 30 37 15 16 14 122935 00815907052491111 00195198923102276
7 34 35 30 37 12 14 16 140640 00983915740315128 00182784576692257
6 33 35 31 37 11 11 13 146017 00888852225316270 00188548348595259
7 34 35 30 37 12 16 12 142144 00997534014352579 00181578155086060
6 8 14 30 37 14 11 15 132819 00921338781311946 00188143081376993
6 8 14 30 37 10 15 11 136651 00956093119043262 00186781475357014
7 9 14 31 37 14 14 16 111382 00525319705640723 00222591386298574
7 34 35 30 37 13 14 16 139957 00977014014811679 00183484070331887
7 34 35 30 37 12 15 16 139849 00976123852270839 00183745698300515
7 34 35 30 37 12 16 16 138589 00959671533698319 00184842191427931
7 34 35 30 37 16 13 16 137912 00952795751906571 00185525366651277
6 33 35 31 37 11 11 11 148785 00910856464605774 00187751047204272
7 34 35 30 37 12 16 13 141338 00990484927061306 00181980491991251
7 34 35 30 37 12 13 12 145536 0102926179499332 00179590185768212
6 8 14 30 37 14 10 15 132373 00918145642214576 00188660639598312
6 8 14 30 37 16 11 14 131312 00904718190224125 00188759872087077
7 34 35 30 37 13 15 16 139168 00969230570394858 00184436609617936
7 34 35 30 37 13 9 11 150730 0106620666560267 00178315514588942
6 8 14 30 37 14 11 14 133746 00929165522686308 00187615074100094
7 34 35 30 37 9 9 12 152656 0107867658396772 00178031242058681
6 8 14 30 37 10 11 16 135118 00939381882085281 00187414815201857
7 34 35 30 37 12 12 9 149341 0105739135263959 00178316539838164
7 9 14 36 28 32 32 32 110385 00489797931328652 00256323647901629
7 9 14 36 37 32 31 31 108599 00498935433820196 00235262740306846
7 9 14 32 37 31 30 31 108436 00537552050723257 00227898958267559
7 9 14 36 28 32 31 31 110203 00489682960875768 00259015702487973
7 34 35 30 37 8 12 9 154427 0108962750550623 00178021823053241
Appendix B Simulation Results
Page | 218
Table B-10 Pareto optimal solutions of multi-objective DNR (loss maximum node voltage deviation
feeder load balancing index) for 69-bus system in Case II
Tie-switches location Feeder loss
(kW)
Maximum node
Voltage deviation
Feeder load
balancing index
55 61 71 72 12 99036 00524391619987274 00196366946903149
69 61 71 9 14 145213 00664127006601768 00185315761508749
55 61 71 72 14 98845 00524393494628415 00194882148961848
69 70 71 10 14 145135 00666490251240782 00182871906896542
69 61 71 72 12 150267 00699556148777123 00161708619074924
55 61 71 10 14 104521 00524349487665904 00238104755589364
69 61 71 72 13 150383 00700225094171628 00161512783956020
55 61 71 72 13 98937 00524392488739880 00195710324132613
69 61 71 72 11 150792 00682108082577803 00171029450547815
55 61 71 9 14 105348 00524349082167884 00242117051986541
69 61 71 72 14 150513 00700911373758199 00161129748303495
55 61 71 72 11 105195 00524380932334678 00218572363716938
Table B-11 Pareto optimal solutions of multi-objective DNR (loss maximum node voltage deviation
feeder load balancing index) for 69-bus system in Case III
Tie-switches location Feeder loss
(kW)
Maximum node
Voltage deviation
Feeder load
balancing index
55 61 12 14 9 97461 00523081449765275 00226112450860475
69 61 71 14 9 130761 00662843002557533 00155527078006889
55 61 71 14 7 97263 00523080911134007 00226177446060770
55 61 12 71 72 87588 00523152959484715 00174558059214037
55 61 71 14 8 93176 00523082195004728 00211109499855264
55 61 71 13 72 87581 00523154440245970 00174392153380541
55 61 12 14 72 87755 00523153511186373 00174538759436512
55 61 12 71 7 97289 00523080869366065 00226232791264600
69 61 71 11 9 134009 00662855052002667 00154463391981039
69 61 12 14 9 130989 00662843776081034 00155381836375260
55 61 71 13 7 97273 00523080879708534 00227249951330579
55 61 71 14 9 90907 00523086904216601 00201865894567423
55 61 71 14 10 90291 00523088955157064 00199034032147027
69 61 71 14 10 130894 00665207578684145 00154263271797149
55 61 71 14 72 87582 00523156072908145 00174100597226583
69 61 71 11 10 134197 00665220013747228 00153401360203180
69 61 71 11 72 136858 00680828895070073 00147368269784675
69 61 12 14 10 131126 00665208386694061 00154135530565384
55 61 71 11 72 91274 00523126048676607 00184393848480773
Appendix B Simulation Results
Page | 219
Table B-12 Pareto optimal solutions of multi-objective DNR (loss maximum node voltage deviation
feeder load balancing index) for 69-bus system in Case IV
Tie-switches location DG location Feeder
loss
(kW)
Maximum node
Voltage deviation
Feeder load
balancing index
69 63 71 10 14 60 60 60 105879 00543213716422435 00153740505896722
69 63 12 72 71 60 62 62 109324 00575466375767690 00126779733811642
55 61 71 72 11 60 60 60 80324 00429183191505871 00183159151221229
69 63 12 72 71 61 61 62 109323 00575465740537586 00126842028893447
55 61 71 72 12 60 60 60 74165 00429193759769601 00159264876998350
69 63 14 10 71 62 62 62 106070 00543012249613587 00150279825984642
69 63 11 72 71 60 62 60 110547 00558290844078126 00139841427388105
69 63 14 9 71 62 62 62 106271 00540689205567605 00153025056850459
69 61 71 72 11 60 60 60 108838 00542584369620998 00141625735067141
55 61 71 72 14 60 56 60 75837 00436673338725839 00157367114339890
69 63 14 10 71 62 62 60 105960 00542966739560918 00151430448212008
69 61 71 10 14 60 60 60 104307 00527268149576859 00155323687715422
69 63 11 72 71 61 62 62 110652 00558333983851442 00137892112215884
69 63 13 72 71 62 62 62 109522 00576169823075075 00125440050970194
55 61 71 72 14 60 55 60 75975 00436701836501366 00156758120818947
69 63 71 10 14 60 60 62 105896 00542940500362948 00152768514567046
69 63 14 9 71 62 61 61 106159 00540643102892876 00154245882374843
55 61 71 72 13 60 60 60 74066 00429194617185072 00158554987038681
69 62 71 10 14 61 60 60 105886 00542959390978505 00153513700764165
69 63 14 72 71 62 62 62 109622 00576844280930477 00125002240983144
55 63 71 72 14 62 61 62 74382 00440379610790336 00155858821619573
69 63 71 72 11 60 60 60 110530 00558564471048234 00140822204796308
55 63 71 72 14 60 60 62 74285 00440350644694274 00157371695186626
55 63 14 72 71 62 62 62 74448 00440399072962552 00155438948075735
55 63 71 72 14 60 62 62 74344 00440368353288504 00156312863856681
69 63 71 9 14 60 61 60 105882 00542934725670071 00153515485666183
55 63 71 72 14 60 61 62 74305 00440356668532606 00156816031788752
55 61 20 72 13 60 60 60 80533 00429326269571468 00157463174391893
55 63 71 72 14 61 61 62 74343 00440367927398261 00156346520711234
69 61 71 72 14 60 60 60 107187 00561022028435777 00126909641069497
69 63 71 72 11 60 61 60 110533 00558285040786375 00140595150870697
69 63 12 72 71 62 62 62 109436 00575512407997617 00125707103016452
69 63 14 10 71 61 62 62 106000 00542983427485794 00150838099664421
69 63 11 72 71 60 61 62 110569 00558299818740340 00139149694834405
69 63 14 9 71 61 62 60 106118 00540626433897020 00154840963668230
69 61 71 72 12 60 60 60 107041 00559693311798567 00127785892138089
55 61 71 72 14 60 60 60 73974 00429195606297569 00157682511572302
69 63 14 10 71 61 61 62 105958 00542966109653011 00151492343922130
69 63 12 72 71 62 62 61 109365 00575483243249972 00126225992147273
Appendix B Simulation Results
Page | 220
69 63 11 72 71 62 62 60 110611 00558317226735644 00138490567525274
69 63 14 9 71 62 62 61 106201 00540660395254129 00153587525958041
69 63 14 10 71 61 60 62 105917 00542949434469265 00152083287358888
69 63 14 9 71 62 62 60 106160 00540643732226493 00154184014811756
69 63 11 72 71 61 61 62 110610 00558316590719640 00138552654427231
69 63 71 72 11 62 62 62 110723 00558362979744786 00137328015545176
69 61 71 72 13 60 60 60 107108 00560349171634668 00127435051911921
Page | 221
APPENDIX C Control Parameters of
Algorithms
C1 Control parameters of ACO algorithm in Chapter 5
Table C-1 ACO parameters for distribution network reconfiguration and DG allocation in Test Case
2amp3
Parameter Value
Number of ants 50
Maximum number of iteration 200
Pheromone evaporation rate 120530 03
Higher bound of pheromone level 120533119846119834119857 1
Lower bound of pheromone level 120533119846119842119847 001
Constant accumulation number 120533119836 0002
Table C-2 ACO parameters for distribution network reconfiguration and DG allocation in Test Case 4
Parameter Value
Number of ants 100
Maximum number of iteration 500
Pheromone evaporation rate 120530 03
Higher bound of pheromone level 120533119846119834119857 1
Lower bound of pheromone level 120533119846119842119847 001
Constant accumulation number 120533119836 0002
C2 Control parameters of ACO algorithm in Chapter 6
Table C-3 ACO parameters for distribution network reconfiguration and transformer economic
operation
Parameter Value
Number of ants 150
Maximum number of iteration 500
Pheromone evaporation rate 120530 03
Higher bound of pheromone level 120533119846119834119857 1
Lower bound of pheromone level 120533119846119842119847 001
Constant accumulation number 120533119836 0002
Appendix C Control Parameters of Algorithms
Page | 222
C3 Control parameters of ACO algorithm in Chapter 7
Table C-4 ACO parameters for sectionalising switch placement in Test Case 1
Parameter Value
Number of ants 400
Maximum number of iteration 400
Pheromone evaporation rate 120530 04
Higher bound of pheromone level 120533119846119834119857 1
Lower bound of pheromone level 120533119846119842119847 001
Constant accumulation number 120533119836 0002
Table C-5 ACO parameters for sectionalising switch placement in Test Case 2amp3
Parameter Value
Number of ants 500
Maximum number of iteration 200
Pheromone evaporation rate 120530 01
Higher bound of pheromone level 120533119846119834119857 1
Lower bound of pheromone level 120533119846119842119847 001
Constant accumulation number 120533119836 0002
C4 Control parameters of MOACO and AIS-ACO algorithm in
Chapter 8
Table C-6 MOACO parameters for multi-objective distribution network reconfiguration (loss
ECOST and SAIDI)
Parameter Value
Number of ants 100
Maximum number of iteration 100
Pheromone evaporation rate 120530 01
Higher bound of pheromone level 120533119846119834119857 1
Lower bound of pheromone level 120533119846119842119847 001
Constant accumulation number 120533119836 0002
Appendix C Control Parameters of Algorithms
Page | 223
Table C-7 AIS-ACO parameters for multi-objective distribution network reconfiguration (loss
ECOST and SAIDI)
Parameter Value
Maximum number of iteration 50
Pheromone evaporation rate 120530 01
Higher bound of pheromone level 120533119846119834119857 1
Lower bound of pheromone level 120533119846119842119847 001
Constant accumulation number 120533119836 0002
C5 Control parameters of ACO and AIS-ACO algorithm in
Chapter 9
Table C-8 ACO parameters for multi-objective DNR (loss maximum node voltage deviation feeder
load balancing index)
Parameter Value
Number of ants 200
Maximum number of iteration 800
Pheromone evaporation rate 120530 03
Higher bound of pheromone level 120533119846119834119857 1
Lower bound of pheromone level 120533119846119842119847 001
Constant accumulation number 120533119836 0002
Table C-9 AIS-ACO parameters for multi-objective DNR (loss maximum node voltage deviation
feeder load balancing index)
Parameter Value
Maximum number of iteration 3000
Pheromone evaporation rate 120530 01
Higher bound of pheromone level 120533119846119834119857 1
Lower bound of pheromone level 120533119846119842119847 001
Constant accumulation number 120533119836 0002
Page | 224
APPENDIX D List of Publications
1 B Zhang and P A Crossley ldquoMinimum transformer losses based on transformer
economic operation and optimized tie-switches placementrdquo in Proceedings of the 6th
International Conference on Advanced Power System Automation and Protection
(APAP) pp 1-7 20-25 September 2015
2 B Zhang and P A Crossley ldquoReliability improvement using ant colony
optimization applied to placement of sectionalizing switchesrdquo in Proceedings of the
9th
International Conference on Applied Energy (ICAE) pp 1-7 21-24 August 2017
3 B Zhang and P A Crossley ldquoMinimization of distribution network loss using
ant colony optimization applied to transformer economic operation and relocation of
tie-switchesrdquo to be submitted to IEEE Transactions on Smart Grid
4 B Zhang and PA Crossley ldquoOptimized sectionalising switch placement for
reliability improvement in distribution systemsrdquo to be submitted to IEEE
Transactions on Power Delivery
5 B Zhang and P A Crossley ldquoAn ant colony optimization ndashbased method for
multi-objective distribution system reconfigurationrdquo in Proceedings of the 14th
International Conference on Developments in Power System Protection (DPSP) pp
1-6 12-15 March 2018
Page | 4
46 Summary 90
CHAPTER 5 92
DISTRIBUTION NETWORK RECONFIGURATION amp DG ALLOCATION FOR
FEEDER LOSS REDUCTION 92
51 Introduction 92
52 Problem Formulation 93
53 Solution Method 94
531 Distribution Network Reconfiguration 94
532 Applying ACO to DNR and DGs Placement 95
54 Application Studies 99
541 33-bus System 99
542 69-bus System 105
55 Summary 109
CHAPTER 6 111
DISTRIBUTION NETWORK RECONFIGURATION amp TRANSFORMER
ECONOMIC OPERATION FOR NETWORK LOSS REDUCTION 111
61 Introduction 111
62 Time-varying Load Model 112
63 Problem Formulation 113
64 Applying ACO to DNR and TEO 114
65 Application Studies 118
651 Test Case 1 122
652 Test Case 2 123
653 Test Case 3 124
66 Summary 126
CHAPTER 7 128
OPTIMAL PLACEMENT OF SECTIONALISING SWITCHES FOR
RELIABILITY IMPROVEMENT 128
71 Introduction 128
72 Problem Formulation 129
721 Weighted Aggregation 129
722 Single Fuzzy Satisfaction Objective Function with Two Parameters 130
723 Single Fuzzy Satisfaction Objective Function with Three Parameters 131
Page | 5
724 Evaluation of ECOST 132
725 Evaluation of SAIDI 133
726 Evaluation of Switch Costs 133
73 Applying ACO to Sectionalising Switch Placement Problem 134
74 Benefit-to-cost Analysis 135
75 Application Studies 136
751 Test Case 1 138
752 Test Case 2 147
753 Test Case 3 147
76 Summary 148
CHAPTER 8 150
DISTRIBUTION NETWORK RECONFIGURATION FOR LOSS REDUCTION amp
RELIABILITY IMPROVEMENT 150
81 Introduction 150
82 Problem Formulation 152
821 Multi-objective Reconfiguration Problem 152
822 Best Compromise Solution 153
83 Solution Methodology 154
831 Applying MOACO to Multi-objective DNR Problem 154
832 Applying AIS-ACO to Multi-objective DNR Problem 158
84 Application Studies 161
85 Best Compromise Solution 163
86 Summary 164
CHAPTER 9 166
MULTI-OBJECTIVE DISTRIBUTION NETWORK RECONFIGURATION amp DG
ALLOCATION CONSIDERING LOSS VOLTAGE DEVIATION AND LOAD
BALANCING 166
91 Introduction 166
92 Problem Formulation 168
921 Single Fuzzy Satisfaction Objective Function 168
922 Multi-objective Reconfiguration Problem Using Pareto Optimality 170
93 Solution methodology 171
931 Applying ACO to DNR and DG Allocation in the Fuzzy Domain 171
932 Applying AIS-ACO to Multi-objective DNR and DG Allocation Using
Pareto Optimality 171
Page | 6
94 Application Studies 171
941 33-bus System 172
942 69-bus System 180
95 Summary 187
CHAPTER 10 189
CONCLUSION amp FUTURE WORK 189
101 Conclusion 189
102 Future Work 193
References 195
APPENDIX A Network Model Data 204
APPENDIX B Simulation Results 209
APPENDIX C Control Parameters of Algorithms 221
APPENDIX D List of Publications 224
Word count 51012
Page | 7
List of Figures
Fig 2-1 Typical Distribution network [27] 29
Fig 2-2 Recloser operation 30
Fig 2-3 Transformer loss versus transformer load 32
Fig 2-4 Daily load curve of a typical substation before and after load smoothing [38]
34
Fig 2-5 Radial test system 35
Fig 2-6 Fully automated distribution feeder 40
Fig 2-7 Partially automated distribution feeder 41
Fig 2-8 Elements of a single phase transformer [33] 43
Fig 2-9 Construction of a three-phase transformer [33] 43
Fig 2-10 The open-circuit test [33] 44
Fig 2-11 The short-circuit test [33] 45
Fig 2-12 Simple two-bus network 47
Fig 2-13 Reliability model for static components 51
Fig 2-14 Procedure for reliability evaluation 52
Fig 2-15 Sample network 53
Fig 2-16 Linear membership function 54
Fig 3-1 Example of ant colony system [69] 63
Fig 3-2 Flowchart of the ant colony algorithm 65
Fig 3-3 Flowchart of the AIS-ACO algorithm 67
Fig 4-1 Procedure of domestic electricity demand profile generation 72
Fig 4-2 Monte Carlo simulation platform for three transformer operation modes
comparison 74
Fig 4-3 Flowchart of transformer loss assessment 75
Fig 4-4 Monte Carlo simulation platform for distribution network reconfiguration 76
Fig 4-5 Generic distribution network topology 78
Fig 4-6 Transformer load factor variation 79
Fig 4-7 Transformer loss variations in different scenarios 80
Fig 4-8 11 kV 4th
feeder voltage profiles in different scenarios 81
Fig 4-9 Voltage profiles of Load 4_1 in different scenarios 82
Fig 4-10 Voltage profiles of Load 4_8 in different scenarios 83
Page | 8
Fig 4-11 11 kV 4th
feeder mean voltage profile of various TCLFs 84
Fig 4-12 Test system 86
Fig 4-13 Daily load variations for different load groups 87
Fig 4-14 Mean voltage profiles in S1 S2 and S3 89
Fig 4-15 Mean voltage profiles in S1 S4 and S7 89
Fig 5-1 Search space of DNR and DGs Placement 95
Fig 5-2 Flowchart of the ACO applied to DNR and DGs placement 98
Fig 5-3 33-bus system 100
Fig 5-4 33-bus system for feeder loss minimisation Case II 101
Fig 5-5 33-bus system for feeder loss minimisation Case III 102
Fig 5-6 33-bus system for feeder loss minimisation Case IV 103
Fig 5-7 Comparison of feeder loss for different DG capacities before and after
simultaneous reconfiguration and DG allocation 104
Fig 5-8 Comparison of voltage profiles in different cases of 33-node system 104
Fig 5-9 69-bus system 105
Fig 5-10 69-bus system for feeder loss minimisation Case II 106
Fig 5-11 69-bus system for feeder loss minimisation Case III 107
Fig 5-12 69-bus system for feeder loss minimisation Case IV 107
Fig 5-13 Comparison of feeder loss for different DG capacities before and after
simultaneous reconfiguration and DG allocation 108
Fig 5-14 Comparison of voltage profiles in different cases of 69-node system 109
Fig 6-1 The reconfiguration hours for a typical day 113
Fig 6-2 Search space of DNR and TEO 115
Fig 6-3 Sample network with three substations 116
Fig 6-4 Flowchart of the ACO applied to DNR and TEO for a specific type of day
117
Fig 6-5 Distribution feeder connected to RBTS Bus 4 118
Fig 6-6 Daily load profile of residential consumers 119
Fig 6-7 Daily load profile of commercial consumers 120
Fig 6-8 Daily load profile of industrial consumers 120
Fig 6-9 Daily load profile (MW) of the main feeder 120
Fig 6-10 Annual energy loss with different DG capacities 123
Fig 6-11 Annual energy loss in uncoordinated charging strategy 125
Fig 6-12 Annual energy loss in coordinated charging strategy 126
Page | 9
Fig 7-1 Membership function for SAIDI and switch cost reduction 131
Fig 7-2 Membership function for ECOST reduction 132
Fig 7-3 Search space of sectionalising switch placement 134
Fig 7-4 Distribution feeder connected to RBTS Bus 4 with 6 sectionalising switches
136
Fig 7-5 Optimal relocation of sectionalising switches in Test Case 11 139
Fig 7-6 Optimal installation of sectionalising switches in Test Case 12 141
Fig 7-7 Optimal installation and relocation of sectionalising switches in Test Case
13 142
Fig 7-8 BCR versus years 143
Fig 7-9 Variation of cost versus change in CDF 144
Fig 7-10 Number of installed sectionalising switches versus change in CDF 145
Fig 8-1 Flowchart of the MOACO algorithm applied to multi-objective DNR
problem 157
Fig 8-2 Flowchart of the AIS-ACO algorithm applied to multi-objective DNR
problem 158
Fig 8-3 Distribution feeder connected to RBTS Bus 4 161
Fig 8-4 Pareto solutions obtained (minimisation of feeder loss ECOST and SAIDI)
162
Fig 9-1 Membership function for feeder loss reduction 168
Fig 9-2 Membership function for maximum node voltage deviation reduction 169
Fig 9-3 Membership function for load balancing index reduction 170
Fig 9-4 33 bus-system for fuzzy multi-objective optimisation Case II 173
Fig 9-5 Pareto front obtained for 33-bus system in Case II 174
Fig 9-6 33 bus-system for fuzzy multi-objective optimisation Case III 175
Fig 9-7 Pareto front obtained for 33-bus system in Case III 176
Fig 9-8 33 bus-system for fuzzy multi-objective optimisation Case IV 178
Fig 9-9 Pareto front obtained for 33-bus system in Case IV 178
Fig 9-10 69 bus system for fuzzy multi-objective optimisation Case II 180
Fig 9-11 Pareto front obtained for 69-bus system in Case II 181
Fig 9-12 69-bus system for fuzzy multi-objective optimisation Case III 183
Fig 9-13 Pareto front obtained for 69-bus system in Case III 183
Fig 9-14 69-bus system for fuzzy multi-objective optimisation Case IV 185
Fig 9-15 Pareto front obtained for 69-bus system in Case IV 186
Page | 10
List of Tables
Table 2-1 Transformer economic operation area 33
Table 2-2 Transformer technical specifications and costs 35
Table 3-1 Relationship of 119911 lowast and 119862 62
Table 4-1 Household size by number of people in household as a proportion [103] 72
Table 4-2 Parameters of a typical 3311 kV two-winding transformer [106] 78
Table 4-3 Daily transformer loss in different scenarios 80
Table 4-4 Transformer loss with different TCLF 85
Table 4-5 Average number of switching operations with different TCLF 85
Table 4-6 Transformer loss in Test Case 2 88
Table 5-1 Results of different cases for the 33-bus system 100
Table 5-2 Comparison of simulation results for 33-bus system in Case II 101
Table 5-3 Comparison of ACO with CGA and CSA for the 33-bus system in Case II
102
Table 5-4 Results of different cases for the 69-bus system 105
Table 5-5 Comparison of simulation results for 69-bus system in Case II 106
Table 6-1 Revised customer data (peak load) 119
Table 6-2 The distribution of load types for a whole year 121
Table 6-3 Results of DNR and TEO with different load types in Test Case 1 122
Table 6-4 Characteristics of EV 124
Table 7-1 Customer data (Average load) 137
Table 7-2 Sector interruption cost estimation ($kW) 138
Table 7-3 Results of sectionalising switches relocation in Test Case 11 140
Table 7-4 Results of sectionalising switches installation in Test Case 12 141
Table 7-5 Results of sectionalising switches relocation and installation in Test Case
13 143
Table 7-6 Impacts of 120588 variation on objective function 119869 146
Table 7-7 Impacts of variation in number of ants on objective function 119869 146
Table 7-8 Results of sectionalising switches relocation and installation in Test Case
2 147
Table 7-9 Results of sectionalising switches installation and relocation in Test Case
3 148
Page | 11
Table 8-1 Revised customer data (Average load) 162
Table 8-2 Mean and standard deviation of Pareto Front (loss ECOST and SAIDI)
163
Table 8-3 Minimum solutions along each objective (loss ECOST and SAIDI) 163
Table 8-4 Best compromise solutions (loss ECOST and SAIDI) 164
Table 9-1 Results of DNR in fuzzy multi-objective formulation for 33-bus system in
Case II 173
Table 9-2 Mean and standard deviations of Pareto Front for 33-bus system in Case II
174
Table 9-3 Minimum solutions along each objective for 33-bus system in Case II 175
Table 9-4 Results of DNR in fuzzy multi-objective formulation for 33-bus system in
Case III 176
Table 9-5 Mean and standard deviations of Pareto Front for 33-bus system in Case
III 176
Table 9-6 Minimum solutions along each objective for 33-bus system in Case III 177
Table 9-7 Results of DNR and DG allocation in fuzzy multi-objective formulation
for 33-bus system in Case IV 178
Table 9-8 Mean and standard deviations of Pareto Front for 33-bus system in Case
IV 179
Table 9-9 Minimum solutions along each objective for 33-bus system in Case IV 179
Table 9-10 Results of DNR in fuzzy multi-objective formulation for 69-bus system
in Case II 181
Table 9-11 Mean and standard deviations of Pareto Front for 69-bus system in Case
II 181
Table 9-12 Minimum solutions along each objective for 69-bus system in Case II 182
Table 9-13 Results of DNR in fuzzy multi-objective formulation for 69-bus system
in Case III 183
Table 9-14 Mean and standard deviations of Pareto Front for 69-bus system in Case
III 184
Table 9-15 Minimum solutions along each objective for 69-bus system in Case III
184
Table 9-16 Results of DNR and DGs allocation in fuzzy multi-objective formulation
for 69-bus system in Case IV 185
Page | 12
Table 9-17 Mean and standard deviations of Pareto Front for 69-bus system in Case
IV 186
Table 9-18 Minimum solutions along each objective for 69-bus system in Case IV
187
Table A-1 Typical configurations and parameters of 11 kV triplex cables in the UK
204
Table A-2 Line and load data of 33-bus system 205
Table A-3 Line and load data of 69-bus system 206
Table A-4 Feeder data of RBTS Bus 4 207
Table A-5 Reliability Data for RBTS Bus 4 208
Table B-1 The locations of tie-switch in Scenario 9 209
Table B-2 Mean voltage profiles at each node in the linked feeder 210
Table B-3 95th
voltage profiles at each node in the linked feeder 210
Table B-4 Network losses in each branch of 33-bus system 211
Table B-5 Network losses in each branch of 69-bus system 212
Table B-6 Pareto optimal solutions of multi-objective DNR (loss ECOST and
SAIDI) 214
Table B-7 Pareto optimal solutions of multi-objective DNR (loss maximum node
voltage deviation feeder load balancing index) for 33-bus system in Case II 215
Table B-8 Pareto optimal solutions of multi-objective DNR (loss maximum node
voltage deviation feeder load balancing index) for 33-bus system in Case III 215
Table B-9 Pareto optimal solutions of multi-objective DNR (loss maximum node
voltage deviation feeder load balancing index) for 33-bus system in Case IV 216
Table B-10 Pareto optimal solutions of multi-objective DNR (loss maximum node
voltage deviation feeder load balancing index) for 69-bus system in Case II 218
Table B-11 Pareto optimal solutions of multi-objective DNR (loss maximum node
voltage deviation feeder load balancing index) for 69-bus system in Case III 218
Table B-12 Pareto optimal solutions of multi-objective DNR (loss maximum node
voltage deviation feeder load balancing index) for 69-bus system in Case IV 219
Table C-1 ACO parameters for distribution network reconfiguration and DG
allocation in Test Case 2amp3 221
Table C-2 ACO parameters for distribution network reconfiguration and DG
allocation in Test Case 4 221
Page | 13
Table C-3 ACO parameters for distribution network reconfiguration and transformer
economic operation 221
Table C-4 ACO parameters for sectionalising switch placement in Test Case 1 222
Table C-5 ACO parameters for sectionalising switch placement in Test Case 2amp3222
Table C-6 MOACO parameters for multi-objective distribution network
reconfiguration (loss ECOST and SAIDI) 222
Table C-7 AIS-ACO parameters for multi-objective distribution network
reconfiguration (loss ECOST and SAIDI) 223
Table C-8 ACO parameters for multi-objective DNR (loss maximum node voltage
deviation feeder load balancing index) 223
Table C-9 AIS-ACO parameters for multi-objective DNR (loss maximum node
voltage deviation feeder load balancing index) 223
Page | 14
List of Abbreviations
Abbreviations Definition
ACO Ant Colony Optimisation
ACS Ant Colony System
AENS Average Energy Not Supplied
AIS Artificial Immune Systems
AIS-ACO Artificial Immune Systems-Ant Colony Optimisation
ANN Artificial Neutral Network
ASP Active Server Pages
BCR Benefit-to-cost Ratio
BEM Branch Exchange Method
BPSO Binary Particle Swarm Optimisation
CDF Customer Damage Function
CGA Continuous Genetic Algorithm
CSA Cuckoo Search Algorithm
DA Distribution Automation
DNO Distribution Network Operator
DNR Distribution Network Reconfiguration
DG Distributed Generation
DPSO Discrete Particle Swarm Optimisation
ECOST Expected Customer Damaged Cost
EDNS Expected Demand Not Supplied
ENS Energy not supplied
EV Electric Vehicle
FMEA Failure-mode-and-effect Analysis
FWA Firework Algorithm
FRTU Feeder Remote Terminal Unit
GA Genetic Algorithm
HC Hyper Cube
HSA Harmony Search Algorithm
HV High Voltage
Page | 15
IWO Invasive Weed Optimisation
LV Low Voltage
MDC Maximum Driving Capability
MILP Mixed Integer Linear Programming
MOACO Multi-objective Ant Colony Optimisation
MV Medium Voltage
PSO Particle Swarm Optimisation
RBTS Roy Billinton Test System
RGA Refined Genetic Algorithm
SA Simulated Annealing
SAIDI System Average Interruption Duration Index
SAIFI System Average Interruption Frequency Index
SCADA Supervisory Control and Data Acquisition
SSP Sectionalising Switch Placement
TS Tabu Search
TCLF Transformer Critical Load Factor
TEO Transformer Economic Operation
TOM Transformer Operation Mode
VML Vector Markup Language
Page | 16
Abstract
The University of Manchester
Submitted by Boyi Zhang
for the degree of Doctor of Philosophy
Distribution Network Automation for Multi-objective Optimisation
December 2017
Asset management and automation are acknowledged by distribution utilities as a
useful strategy to improve service quality and reliability However the major
challenge faced by decision makers in distribution utilities is how to achieve long-
term return on the projects while minimising investment and operation costs
Distribution automation (DA) in terms of transformer economic operation (TEO)
distribution network reconfiguration (DNR) and sectionalising switch placement
(SSP) is recognised as the most effective way for distribution network operators
(DNOs) to increase operation efficiency and reliability Automated tie-switches and
sectionalising switches play a fundamental role in distribution networks
A method based on the Monte Carlo simulation is discussed for transformer loss
reduction which comprises of profile generators of residential demand and a
distribution network model The ant colony optimisation (ACO) algorithm is then
developed for optimal DNR and TEO to minimise network loss An ACO algorithm
based on a fuzzy multi-objective approach is proposed to solve SSP problem which
considers reliability indices and switch costs Finally a multi-objective ant colony
optimisation (MOACO) and an artificial immune systems-ant colony optimisation
(AIS-ACO) algorithm are developed to solve the reconfiguration problem which is
formulated within a multi-objective framework using the concept of Pareto
optimality The performance of the optimisation techniques has been assessed and
illustrated by various case studies on three distribution networks The obtained
optimum network configurations indicate the effectiveness of the proposed methods
for optimal DA
Page | 17
Declaration
No portion of the work referred to in the thesis has been submitted in support of an
application for another degree or qualification of this or any other university or other
institute of learning
Page | 18
Copyright Statement
i The author of this thesis (including any appendices andor schedules to this
thesis) owns certain copyright or related rights in in (the ldquoCopyrightrdquo) she
has given The University of Manchester certain rights to use such Copyright
including for administrative purposes
ii Copies of this thesis either in full or in extracts and whether in hard or
electronic copy may be made only in accordance with the Copyright
Designs and Patents Act 1988 (as amended) and regulations issued under it
or where appropriate in accordance with licensing agreements which the
University has from time to time This page must form part of any such
copies made
iii The ownership of certain Copyright patents designs trademarks and other
intellectual property (the ldquoIntellectual Propertyrdquo) and any reproductions of
copyright works in the thesis for example graphs and tables
(ldquoReproductionsrdquo) which may be described in this thesis may not be owned
by the author and may be owned by third parties Such Intellectual Property
and Reproductions cannot and must not be made available for use without the
prior written permission of the owner(s) of the relevant Intellectual Property
andor Reproductions
iv Further information on the conditions under which disclosure publication
and commercialisation of this thesis the Copyright and any Intellectual
Property andor Reproductions described in it may take place is available in
the University IP Policy (see
httpdocumentsmanchesteracukDocuInfoaspxDocID=24420) in any
relevant Thesis restriction declarations deposited in the University Library
The University Libraryrsquos regulations (see
httpwwwlibrarymanchesteracukaboutregulations) and in The
Universityrsquos policy on Presentation of Theses
Page | 19
Acknowledgements
First and foremost I would like to express my deepest gratitude to my supervisor
Prof Peter Crossley for his invaluable guidance and continuous encouragement
throughout the project
I would like to thank my friends and colleagues in the Ferranti Building at The
University of Manchester Prof Zhongdong Wang and Dr Qiang Liu for the fruitful
research discussions and their encouragement throughout the period of my PhD
I wish to thank North China Electric Power University PR China for the 2+2
course and also to Prof Chunming Duan and Prof Sangao Hu for their help and
encouragement
I also wish to thank Prof Bo Zhang Prof Jianguo Zhao and Prof Li Zhang from
Shandong University PR China who continued to support my research with their
valuable feedback and advice
Finally I would like to express my gratitude to my parents for their encouragement
and support
Page | 20
CHAPTER 1
INTRODUCTION
11 Motivation
The electricity ldquoutilityrdquo distribution network is part of a power system that carries
electricity from a high voltage transmission grid to industrial commercial and
residential customers [1] In England and Wales the voltage level of distribution
networks ranges from 132 kV to 230 V [2] Generally most distribution networks
operating at voltages below 25 kV are designed in closed loop but are operated
radially due to the simplicity of operation the ease of protection coordination and
the minimisation of overall economics [3] [4]
The electric power generation transmission and distribution companies are not only
energy producers but also significant power consumers Power loss occurs when
electricity is supplied to customers In 2013 the total distribution losses of GBrsquos
networks were estimated to be 196 TWh which indicates that about 6 of the total
power generation is wasted in the form of losses at distribution level [5] Utility
statistics also indicate that distribution transformers account for approximately 22
of these losses and the line and cable losses make up the remaining 78 Reduction
in active power loss can help distribution network operators (DNOs) save costs and
increase profits
The expression ldquoPower quality = Voltage qualityrdquo has been widely accepted as the
wave shape and magnitude of voltage that strongly influences the power quality
Chapter 1 Introduction
Page | 21
received by customers [6] According to the EN50160 standard [7] under normal
conditions at least 95 of the mean 10 minutes average rms voltage magnitudes in
an 11 kV electricity distribution network should be within the range 09 pu to 11 pu
during one week
Distribution network reliability has proved to be another fundamental attribute for
the safe operation of any modern power system [8] Data show that about 80 of
customer outages are due to distribution system failures [9] Based on the resource
from [10] in 2011 the average number of minutes of lost supply per customer in GB
is 70 minutes According to [11] electricity breakdowns cost the United States
around $80 billion per year With improved reliability the DNOs can save expenses
that are spent on networkrsquos maintenances after a failure [12]
The major challenge faced by DNOs is how to distribute the power in a low-cost
reliable and efficient way Distribution automation (DA) is recognised as the most
effective method for DNOs to increase operation efficiency and reliability The three
main parts of DA are transformer economic operation (TEO) distribution network
reconfiguration (DNR) and sectionalising switch placement (SSP) TEO refers to the
optimum selection of the transformers needed to supply each feeder This is related
to the economic evaluation of network performance and the resilience of the
network DNR is a process that involves changing the network topology by altering
the openclose status of sectionalising (normally closed) and tie (normally open)
switches [13] [14] Installation of new sectionalising switches and relocation of
existing sectionalising switches are defined as SSP
Mathematically DA is a discrete non-linear constrained combinational optimisation
problem that is subject to operating constraints As it is not a practical solution to
investigate all possible network configurations ant colony optimisation (ACO)-
based heuristic search algorithms have been developed
To build a cleaner climate-friendly community the European Union has set a target
on carbon emissions for a 40 60 and 80 below 1990 levels by 2030 2040
and 2050 respectively [15] Therefore a large number of renewable distributed
generations (DGs) are deployed DG is a small electric generation unit that is
connected directly to the distribution network or appears on side of the meter
accessed by the customer [16] Since the number of DGs has increased in recent
Chapter 1 Introduction
Page | 22
years this has resulted in bidirectional power flows and locally looped networks [17]
The integration of high numbers of DGs strongly affects network operation and
planning Therefore optimal placement and sizing of DGs strongly improve
distribution network performance
12 Objectives
The aim of this research is to improve service quality and efficiency based on the
results of DA To achieve this aim the objectives of this thesis are as follows
To review distribution networks DA loss and reliability assessment and
optimisation functions
To propose three optimisation techniques namely the Monte Carlo Method the
ACO algorithm and the artificial immune systems-ant colony optimisation (AIS-
ACO) algorithm
To develop an optimal strategy consisting of TEO and DNR for transformer loss
reduction Statistic models of customer electrical demands should be established
to evaluate their impact from the perspective of probability
To assess the DNR and DG placement problems simultaneously in terms of
distribution feeder loss minimisation
To assess the TEO and DNR problem simultaneously in terms of distribution
network loss minimisation including transformer loss and feeder loss under
different load scenarios
To assess the SSP problem simultaneously based on three objectives namely
reduction of unserved energy cost decrease in the average time that a customer is
interrupted and minimisation of switch costs and using the fuzzy set theory
To propose a benefit-to-cost analysis to justify whether the benefits of installing
and relocating sectionalising switches can justify the cost or not
To formulate the optimal network reconfiguration problem within a multi-
objective framework using the Pareto optimality concept where network loss
and reliability indices are simultaneously optimised
Chapter 1 Introduction
Page | 23
To assess the DNR and DG allocation problem in terms of three conflicting
objectives optimisation network loss maximum node voltage deviation and
load balancing index in order to obtain a set of non-dominated solutions
13 Contribution of the work
This thesis has presented three methodologies of DA All of them are designed to
achieve service quality and efficiency improvement
The contributions of this thesis are summarised below
Load profiles In most literatures the load variations are ignored in their studies
which could underestimate the total energy loss for the utility [18] The
stochastic nature associated with load variety is considered in Chapter 4 In this
chapter the value of the load associated with domestic demand profiles are
obtained from the research described in [19] this can produce a random 1-min
resolution model for UK households A pool of load profiles is randomly
generated by this model in MATLAB Following this each node in the feeders
from the system is assigned with residential demand profiles from the pool based
on the Monte Carlo methodology
In Chapter 6 the distribution loads experience daily and seasonal variations The
study considers the daily load curves of different types of consumers (residential
commercial and industrial) In addition the days are divided into eight types
spring weekdays spring weekends summer weekdays summer weekends
autumn weekdays autumn weekends winter weekdays and winter weekends
Optimisation problems Previously it was observed that sufficient work has
been completed in terms of examining the TEO and the DNR problems
separately In Chapter 4 and 6 both the TEO and network reconfiguration
problems are integrated to benefit the whole distribution network effectively
Different combinations of locations of tie-switches in the network and operation
modes of all transformers in the substations represent different network
configurations Network reconfiguration and transformer operation modes
variation are dealt simultaneously using the ACO algorithm with an objective of
network loss minimisation as presented in Chapter 6
Chapter 1 Introduction
Page | 24
Most research projects have focused only on the optimisation of either the DNR
or the DG allocation problem An ACO algorithm is proposed in Chapter 5 to
deal with the DNR and DG allocation problems simultaneously in terms of
feeder loss minimisation In Chapter 9 the study aims to determine the optimum
network configurations and DG locations that minimise the active power loss
maximum node voltage deviation and feeder load balancing simultaneously
Multi-objective optimisation framework When there are multiple and
conflicting objectives that need to be satisfied all objective can be converted into
a single objective function which reflects a compromise among all objectives
The single objective function has two forms weighted aggregation and fuzzy
satisfaction objective function The selection of the form depends on the number
of objectives as well as their units and dimensions In Chapter 7 the system
expected outage cost to customers (ECOST) and switch costs can be converted
into a single objective function by aggregating these objectives in a weighted
function However as system interruption duration index (SAIDI) and switch
costs have different dimensions and units the two conflicting objectives are
modelled with fuzzy sets and then combined into a single objective function
Also a fuzzy membership function based on max-min principle is presented for
optimising ECOST SAIDI and switch costs simultaneously In Chapter 9 a new
operator called lsquomax-geometric meanrsquo has been introduced to determine the
degree of overall fuzzy satisfaction
However the above simple optimisation processes only obtain a compromise
solution It is no longer suitable if the DNO wishes to obtain all possible optimal
solutions for all the conflicting objectives at the same time [20] Therefore a set
of Pareto optimal solutions is introduced in this study And the corresponding
objective values constitute the Pareto front It allows decision makers to select
the most suitable topology from the Pareto optimal solutions for implementation
depending on the utilitiesrsquo priorities In Chapter 8 the study formulates the
optimal network reconfiguration problem within a multi-objective framework
using the concept of Pareto optimality where network loss and reliability indices
are simultaneously optimised In Chapter 9 active power loss maximum node
voltage deviation and feeder load balancing are optimised simultaneously
After obtaining the Pareto optimal solutions the best compromise solution
among the multiple objectives can be selected by comparing the fitness value of
Chapter 1 Introduction
Page | 25
each member in the Pareto front The best compromise solution is varied by
changing the values of weighting factors based on the tendencies of the network
decision makers A set of best compromise solutions can be obtained by varying
the weighing factors of each objective function and this is presented in Chapter 8
Proposal of ACO-based algorithms for assessment of optimisation problems
The ACO algorithm is a population-based approach based on the behaviour of
real ants [14] The proposed algorithm is not only used for assessment of the
TEO problem but also with DNR DG allocation and SSP problems The ACO
control parameters are different for each test case The selection of parameters is
a balance between the convergence rate and the global search ability of the
algorithm They are set experimentally using information from several trial runs
The results obtained by the ACO algorithm have been compared to those from
other algorithms in Chapter 5 and the ACO parameter sensitivity analysis is
provided in Chapter 7
In Chapter 8 the multi-objective ant colony optimisation (MOACO) and AIS-
ACO algorithms have been proposed and compared for assessment of multi-
objective DNR problems Both algorithms focus on problems in terms of Pareto
optimality where the objective functions are multidimensional and not scalar
A full list of publications resulting from this thesis is included in Appendix D
14 Structure of the thesis
The thesis is organised as follows
Chapter 2 introduces the distribution network configurations and associated
equipment It also gives a comprehensive literature survey which reviews the
existing knowledge and research activities in the distribution automation (DA)
including transformer economic operation (TEO) distribution network
reconfiguration (DNR) and sectionalising switch placement (SSP) The assessment
of transformer loss feeder loss and reliability indices as well as the multi-objective
optimisation functions are also described in this chapter
Chapter 3 summarises the optimisation techniques for assessment of the multi-
objective problem The Monte Carlo Method ACO algorithm and AIS-ACO hybrid
algorithm are described in detail
Chapter 1 Introduction
Page | 26
Chapter 4 proposes two methodologies for transformer loss reduction whilst
maintaining satisfactory voltages which are TEO and DNR The demand profiles are
randomly generated by the profile generators in MATLAB Following this each
node in the feeders from the system is assigned with demand profiles based on the
Monte Carlo Method The effectiveness of the two investigated methods
implemented either alone or together are presented and discussed
Chapter 5 describes an ACO algorithm to assess the network reconfiguration and
DG placement problems simultaneously in terms of distribution feeder loss
minimisation The results of four scenarios carried out on two standard IEEE 33-
node and 69-node systems are presented to show the effectiveness of the proposed
approach The effect of DG capacities on DNR for feeder loss reduction is also
discussed Moreover the results obtained by ACO algorithm have been compared to
those from other algorithms in the literature
Chapter 6 presents the ACO algorithm for minimisation of the losses associated
with a network loss including transformer loss and feeder loss under different load
scenarios This is achieved by the optimum selection of which transformers need to
supply each feeder and by determining the optimal locations of the tie-switches The
performance of this approach to minimise power loss is assessed and illustrated by
various case studies on a typical UK distribution network The impact of DGs and
electrical vehicles (EVs) in reducing the loss is also discussed
Chapter 7 explores an ACO-based methodology for the placement of sectionalising
switches in distribution networks The objectives of the proposed sectionalising
switch placement problem are reduction of unserved energy costs decrease in the
average time that a customer is interrupted and minimisation of switch costs These
objectives are formulated in either a single objective function or a fuzzy satisfaction
objective function The performance of the proposed methodology is assessed and
illustrated by various test cases on a well-known reliability test system
Chapter 8 formulates the optimal network reconfiguration problem within a multi-
objective framework using the Pareto optimality concept where network loss and
reliability indices are simultaneously optimised The MOACO algorithm and AIS-
ACO algorithm are proposed and compared for assessment of DNR problems The
Chapter 1 Introduction
Page | 27
proposed approaches are tested on Bus 4 of the RBTS and a set of high quality non-
dominated solutions are obtained
Chapter 9 addresses two algorithms to assess the DNR and DG allocation problems
in terms of the three conflicting objectives minimisation network loss maximum
node voltage deviation and load balancing index The ACO algorithm is used to
solve the problem in the fuzzy domain and the AIS-ACO algorithm is adopted to
obtain a set of non-dominated solutions using the concept of Pareto optimality The
effectiveness and the efficiency of the proposed methods are implemented on two
standard test systems as case studies
Chapter 10 concludes the thesis by summarising the main findings of the work
Finally possible future research ideas associated with this thesis are proposed
All the network models are built in OpenDSS and all the algorithms are coded in
MATLAB They are carried on a 340-GHz processor with 16 GBs of RAM memory
for all studies
Page | 28
CHAPTER 2
DISTRIBUTION AUTOMATION
21 Introduction
Distribution automation (DA) is an important part of a Smart Grid [21] It enables a
distribution network operator (DNO) to monitor coordinate and operate distribution
components in real-time from a remote control centre [22] [23] This improves the
reliability performance and operational efficiency of the electrical distribution
system and helps increase the market penetration of distributed generations (DGs)
and electrical vehicles (EVs) [24]ndash[26]
The remainder of this chapter is structured as follows Sections 22-23 introduce the
network configurations and associated equipment Sections 24-26 present the three
main parts of DA namely transformer economic operation (TEO) distribution
network reconfiguration (DNR) and sectionalising switch placement (SSP)
Transformer loss feeder loss and reliability indices assessments are described in
Sections 27-29 Three methods for assessment of multi-objective optimisation
problems are reviewed in Section 210 A summary of the main conclusions in this
chapter is given in Section 211
Chapter 2 Distribution Automation
Page | 29
Tie-switch
Sectionalising switch
22 Distribution Network Configurations
In England and Wales the voltage level of distribution networks ranges from 132 kV
to 230 V [2] Generally most distribution networks are designed in closed loop but
are operated radially due to the simplicity of operation the ease of protection
coordination and the minimisation of overall economics [3] [4]
There are three typical system configurations shown in Fig 2-1 [27] The radial
system in Fig 2-1 (a) is common in rural areas but does not include any backup
supplies Consequently the lack of feeder interconnections means a short-circuit
fault will interrupt power to all the downstream customers and power will not be
restored until the faulted equipment is repaired The tie-switches (normally open) in
Fig 2-1 (b) connect two feeders and make the system radial in a primary loop There
are multiple tie-switches between multiple feeders in distribution systems Fig 2-1 (c)
describes a link arrangement and during normal conditions the systems are operated
radially However when a fault occurs the part affected by the fault is isolated by
tripping the breakers The unaffected areas can then be restored from a different
busbar by closing the tie-switches and feeding the supply
(a) Radial system (b) Primary loop (c) Link Arrangement
Fig 2-1 Typical Distribution network [27]
Chapter 2 Distribution Automation
Page | 30
23 Switchgear for Distribution Network
There is a large variety of switchgears used in distribution networks this includes
reclosers sectionalising switches tie-switches fuses and circuit breakers This
section mainly focuses on reclosers sectionalising switches and tie-switches
231 Reclosers
Reclosers are automatic self-contained protection devices installed on main feeders
and operate as a part of the protection schemes [28] [29] They are a type of circuit
breakers with control measurement and automatic re-closing functions Most faults
on distribution feeders are temporary ie they last from a few cycles to a few
seconds and are cleared by protection tripping a circuit breaker [1] Reclosers
normally count the number of overcurrent pulses followed by the line de-
energisation sequences [1] They always coordinate with other types of protection
equipment These include such as fuses and sectionalising switches for the purpose
of fault isolation and system restoration The process of recloser operation is shown
in Fig 2-2 The time between reclosures and the time of the reclose can be
programmed If the fault is transient the recloser will operate 1-3 times and then
restore service quickly If the fault is permanent after a pre-set number of trip-
reclose operations the recloser is locked and the recloser interrupter triggers a final
trip
Fig 2-2 Recloser operation
Time between reclosures
Time of the reclose Fault current
Recloser locks
out on 2nd
reclose
as programmed
Recloser opens
Recloser recloses
fault still present
Recloser recloses
fault still present
Recloser re-opens
fault still present
Load current
Chapter 2 Distribution Automation
Page | 31
232 Sectionalising Switches
Sectionalising switches are the protective devices that operate in conjunction with
backup circuit breakers or reclosers [25] They are isolating devices that
automatically isolate the faulted sections from a distribution network after a
permanent fault has occurred and after the line is de-energised by the feeder breaker
[1] This is because sectionalising switches are not designed to interrupt the fault
current and must be used with the feeder breaker that can break and reclose a circuit
under all conditions ie normal or faulty operating conditions [25] [30] A detailed
operation of sectionalising switches is presented in Section 26
233 Tie-switches
Tie-switches refer to the normally open switches of the network By closing the
opened tie-switch the load is transferred from one feeder to another but this requires
an appropriate sectionalising switch to be opened to restore the radial topology [31]
The tie-switch placement should follow certain principles ie all the loads are
energised and the network is operated in radial configurations The tie-switches are
designed to operate in normal condition but are not suitable for the interruption of
fault currents They are designed to operate after a switching device (circuit breaker
of fuse) has interrupted the fault current
24 Transformer Economic Operation
241 Basic Concepts
Power transformers are the interface between the generators and the transmission
lines and between lines operating at different voltage levels [32] They are a critical
part of an electric power system and transform the ac voltage based on the principle
of electromagnetic induction A step-up transformer ensures the efficient
transmission of power ie high voltage-low current and a step-down transformer
permits the transmitted power to be used at a lower and safer voltage [33]
Distribution transformers are used to reduce the primary system voltages to the
Chapter 2 Distribution Automation
Page | 32
Tran
sfo
rme
r Lo
ss
Transformer Load Factor
1 Transformer
2 Transformers
utilisation voltages [25] normally 132 kV for high voltage (HV) 11 kV-33 kV for
medium voltage (MV) and 400 V for low voltage (LV) in UK distribution networks
For transformers currently in operation developing a new strategy for transformer
loss reduction is required rather than replacing them with high efficiency
transformers [34] Transformer economic operation refers to the optimum selection
of transformers needed to supply each feeder This is related to the economic
evaluation of network performance and the resilience of the network
In order to meet reliability requirements the load factor of each transformer should
not go beyond 50 when two transformers are operated in parallel In other words
the transformer load factor must be within 100 in separate operation modes
The integrated power loss curves of onetwo transformers in operations are shown in
Fig 2-3 The intersection of the two curves is 119878119871 which is called the transformer
critical load factor (TCLF) Therefore it can be concluded that
When the total load 119878 lt 119878119871 a single transformer produces less integrated
power loss than parallel transformers
When 119878 gt 119878119871 parallel operation of transformer is more economical
When 119878 = 119878119871 the losses in single or parallel operation modes are identical
Fig 2-3 Transformer loss versus transformer load
119878119871
Core loss for 2 transformers
Core loss for 1 transformer
Chapter 2 Distribution Automation
Page | 33
As a result Table 2-1 presents the transformer commercial operation area
Table 2-1 Transformer economic operation area
Operation modes Single Transformer Two Parallel Transformers
Economic operation area 0 ~ 119878119871 119878119871 ~ 119878
242 Literatures on Transformer Economic Operation
Several papers that discuss research on transformer economic operation not only
focuse on transformer loss reduction but also discuss cost reduction and reliability
improvement
The papers concerned with transformer economic operation based on loss reduction
were presented in [35]ndash[37] Wang and Liu [35] used the ASP (Active Server Pages)
language as a foundation to analyse transformer economic operation on-line The
operation curves and interval graph of commercial operation were achieved from the
VML (Vector Markup Language) and the simulation results In the interest of the
economical and profitable operation of transformer real-time data was obtained
using the SCADA (Supervisory Control and Data Acquisition) and this included the
measurement of active power load and voltage [36] [37] Then the transformers
were monitored in real-time and the methods used to ensure their economical and
profitable operation were suggested online
However if the active power loss of transformers was measured based on the real-
time load data transformers would frequently be switched to a new state associated
with instantaneous economical and profitable operation As the number of switching
operations increases the lifetime of the transformers decreases As a result Song and
Zhang [38] developed a load smoothing algorithm to reduce the number of switching
operations of the transformer effectively The curves of transformer loads before and
after smoothing are presented in Fig 2-4 Table 2-2 and 2-3 illustrate the transformer
operation mode variation before and after smoothing respectively The results show
that the active loss achieved when using the load smoothing algorithm was a little
higher than when smoothing was not used However the total number of switching
operations of transformers with load smoothing was reduced from 6 to 2 which
would expand the transformer life cycle
Chapter 2 Distribution Automation
Page | 34
(a) Before load smoothing (b) After load smoothing
Fig 2-4 Daily load curve of a typical substation before and after load smoothing [38]
Table 2-2 Transformer operation mode variation before load smoothing
Time Transformer operation mode The sum of active power loss
(Kw)
000-300 1 transformer in operation 12363
300-1600 2 transformer in operation
1600-2100 Parallel operation
2100-2400 2 transformer in operation
Table 2-3 Transformer operation mode variation before load smoothing
Time Transformer operation mode The sum of active power loss
(Kw)
000-600 2 transformer in operation 12768
600-2100 Parallel operation
2100-2400 2 transformer in operation
Generally the cost of the energy loss of a transformer over its service life is much
higher than its initial capital price As a result the transformer selection decision is
based not only on the purchase price but also includes the cost of installation
maintenance and loss over the lifetime of the equipment [39]
Amoiralis etc [40] have investigated the cost of two transformers that have the same
capacity but different specifications The transformers were loaded at 50 of full
load and with an increase of 37 for each year The technical characteristics and the
costs associated with the two transformers are presented in Table 2-4 The total cost
is the summation of loss and capital cost of a transformer over 30 years Purchasing a
Chapter 2 Distribution Automation
Page | 35
transformer with low efficiency (Transformer A) reduced the initial cost but resulted
in higher energy costs during the transformer lifetime in comparison with
Transformer B The economic approach in [41] and [42] were used to determine the
suitable size of transformers in Thailand The choice of a high capacity transformer
could improve voltage profiles and provide extra room for emergency conditions and
load increments in the future
Table 2-4 Transformer technical specifications and costs [40]
Transformer Size
(kVA)
No load loss
(kW)
Load loss
(kW)
Capital
price (euro)
Cost of loss
(euro)
Total cost
(euro)
A 1000 11 9 9074 34211 43285
B 1000 094 76 11362 28986 40348
25 Distribution Network Reconfiguration
251 Basic Concepts
DNR refers to a process that involves changing the network topology at normal and
abnormal operating conditions by altering the openclose status of sectionalising
(normally closed) and tie (normally open) switches [13] [14] In fact DNR can be
used as a tool for distribution network planning and real-time operation [14]
As presented in Fig 2-5 the openclosed status of the tie switches and sectionalising
switches determines the structure of the system To achieve a new system
configuration the tie-switch 3 is closed which will create a new loop In order to
restore the network back to a radial structure a switch from 1 2 4 and 5 is selected
and opened
Fig 2-5 Radial test system
Chapter 2 Distribution Automation
Page | 36
Since there are various combinations of switching DNR is treated as a discrete and
constrained optimisation problem Recently optimal DNR strategies discussed in
many literatures have been implemented to achieve active power loss reduction and
system reliability improvement
252 Literatures on Distribution Network Reconfiguration
Network reconfiguration was first introduced by Merlin and Back [43] using a
discrete branch and bound optimisation method to reduce network loss Firstly all
the switches were closed to build a meshed network and then in each step one
branch was removed until the radial configuration was found
Another early study on loss reduction through network reconfiguration was
presented in [44] which discussed how to achieve minimum power loss in
distribution feeders through feeder reconfiguration It is possible to determine loss
variation by analysing the load flow results This involved simulating the system
configuration before and after the feeder was reconfigured [44] It was based on a
single pair switch operation per iteration The relevant results showed that the loss
was reduced only if the voltage across the tie-switch was significant and if the loads
connected at the lower voltage side were transferred to the other side [44] This
criterion was developed to eliminate undesirable switching options The best
switching option was then obtained from the results of load flow studies simulating
all feasible feeder configurations
Zehra etc [31] have proposed a branch exchange algorithm based on two stages of
the solution methodology It started with a feasible network operating in a radial
configuration The first step determined the loop that achieved maximum loss
reduction by comparing the circle sizes for each loop The largest circle indicated the
maximum loss reduction The second phase determined the switching options to be
operated in that loop to provide maximum loss reduction The smallest circle was
identified for the best solution In comparison with [44] the introduction of the
branch exchange method allowed the number of load flow solutions related to the
computation time to be greatly reduced However the results were strongly related to
the initial configuration of the electrical network [45] The above methodologies [31]
[43] [44] were able to obtain the global optimal solution but were only applied to
simplified network models
Chapter 2 Distribution Automation
Page | 37
Later on the artificial intelligent and modern heuristic optimisation algorithms such
as genetic algorithm (GA) [46]ndash[49] simulated annealing (SA) [50] [51] tabu
search (TS) [52]ndash[54] and particle swarm optimisation (PSO) [55] etc were
developed with minor computational effort These intelligent techniques which are
affected by the selection of parameters are able to obtain the optimum solution of
good quality The GA based network reconfiguration method was presented and
tested in a real 136-bus distribution network in [13] Various radial topologies were
generated after the implementation of the genetic operators and the search space was
enlarged by a local improvement method The results show that after network
reconfiguration the power loss is reduced from 3203 kW to 2801 kW which
amounts to a 1255 reduction
Other important objectives including reliability improvement and service restoration
by DNR were mentioned in [56]ndash[58] An intelligent binary particle swarm
optimisation (BPSO) based search method was presented in [57] for assessment of
the DNR problem in terms of reliability improvement The failure of all distribution
equipment such as transformers feeders breakers etc was considered In this paper
the reliability index was in the form of expected demand not supplied (EDNS) The
EDNS of the original configuration is 1008 kW and after reconfiguration the best
result is reached with 849 kW
Network reconfiguration can be formulated not only as a single objective problem
but also as a multi-objective problem that considers various parameters
simultaneously [45] [59]ndash[62] In [59] the objective function was to minimise the
combination of loss cost and consumer interruption cost thus the multiple objectives
were aggregated into an single objective function In order to achieve optimal DNR
a new method was proposed in [60] using a fuzzy multi-objective function to
balance feeder loads and reduce power loss of the distribution systems Depending
on the operatorrsquos preferences the weighting factors of each of the variables could be
varied Das [61] introduced another fuzzy membership formulation to handle the
multiple objectives In this work the degree of overall satisfaction was the minimum
of all the above membership values and the final optimal solution was the maximum
of all such overall degrees of satisfaction [61] Mendoza etc [62] introduced a
micro-genetic algorithm to deal with the trade-offs between the power loss and
reliability indices in order to obtain a set of optimal network configurations using
Chapter 2 Distribution Automation
Page | 38
the concept of Pareto optimality Andervazh etc [45] have presented another Pareto-
based multi-objective DNR method using discrete PSO The objectives were the
minimisation of power loss bus voltage deviations and number of switching
operations
In addition an optimal planning strategy based on network reconfiguration and DGs
placement was presented in [16] The primary objective was power loss reduction
and voltage stability improvement The performance of the methodology was tested
on a 33-bus network and three DGs were installed The power loss was reduced by
3093 by DNR 5624 by DG installation and 6689 by employing
reconfiguration and DG installation simultaneously
26 Placement of Sectionalising Switches
261 Basic Concepts
The implementation of DA requires the installation of various new devices [63]
Among other things DA involves the placement of sectionalising switches ie the
installation of new switches and relocation of existing switches DA in terms of
automatic and remote controlled sectionalising switch placement brings major
benefits to distribution network operators (DNOs) [64] [65] The duration and
number of outages per year determines the annual interruption time of customers
[66] It is possible to shorten outage duration by decreasing the restoration time and
to reduce the number of outages by improving failure rates [67] SSP is useful for the
reduction of the time required to detect and locate a fault and the improvement of
the speed of isolating the faulty sections in the primary distribution network [64]
The effectiveness of these objectives depends on the number and location of
sectionalising switches
In a distribution feeder the section is defined as a group of line segments between
adjacent sectionalising switches [68] And the equivalent load of the section is the
sum of the individual load points in this section [69] When a permanent fault occurs
the switch actions need to respond as follows
Chapter 2 Distribution Automation
Page | 39
1 Detect and locate the fault and initiate tripping to clear the fault A transient
fault is normally cleared by two or three trips and reclose cycles
2 However if the fault persists beyond the predefined cycles reclosure will be
inhibited and the protection will initiate a final trip The load breaker will open and
all the downstream loads will be de-energised
3 The faulty section is then isolated by opening the upstream and downstream
sectionalising switches located next to the fault
4 Restore the loads in the healthy area by closing the upstream and downstream
circuit breakers automatically
5 Repair the faulty section of the feeder and manually restore the loads (ie
reconnect loads to the supply)
A fully and a partially automated distribution feeder are shown in Fig 2-6 and Fig
2-7 respectively The fault occurs on line section 4 It can be clearly seen in Fig 2-6
that all loads are restored after the faulty area is isolated and the total outage time is
the same as the switching time of circuit breakers and sectionalising switches [64]
However as shown in Fig 2-7 only Loads LP1 LP5 LP6 are restored after the
isolation of the faulty section the outage duration of other loads is equal to the repair
time ie significantly longer than the switching time As a result the installation of
sectionalising switches could increase the network reliability as well as the
investment and operation cost of automation [64]
Chapter 2 Distribution Automation
Page | 40
LP1 LP2 LP3 LP4 LP5 LP6
1 2 3 4 5 6 7
LP1 LP2 LP3 LP4 LP5 LP6
1 2 3 4 5 6 7
LP1 LP2 LP3 LP4 LP5 LP6
1 2 3 4 5 6 7
LP1 LP2 LP3 LP4 LP5 LP6
1 2 3 4 5 6 7
Fault occurred on line section 4
CB1 opened
Sectionalising switches adjacent to the faulted area are opened
Energy restored to un-faulted area by closing CB1 and CB2
CB1 CB2
CB1CB2
CB1 CB2
CB1 CB2
Normally closed circuit breaker
Normally open circuit breaker
Closed sectionalising switch
Open sectionalising switch
Interrupted
load
Fig 2-6 Fully automated distribution feeder
Chapter 2 Distribution Automation
Page | 41
LP1 LP2 LP3 LP4 LP5 LP6
1 2 3 4 5 6 7
LP1 LP2 LP3 LP4 LP5 LP6
1 2 3 4 5 6 7
LP1 LP2 LP3 LP4 LP5 LP6
1 2 3 4 5 6 7
LP1 LP2 LP3 LP4 LP5 LP6
1 2 3 4 5 6 7
Fault occurred on line section 4
CB1 opened
Sectionalising switches adjacent to the faulted area are opened
Energy restored to un-faulted area by closing CB1 and CB2
CB1 CB2
CB1CB2
CB1 CB2
CB1 CB2
Normally closed circuit breaker
Normally open circuit breaker
Closed sectionalising switch
Open sectionalising switch
Interrupted
load
Fig 2-7 Partially automated distribution feeder
262 Literatures on Sectionalising Switch Placement
The earliest work that discussed SSP in distribution networks was presented by
Miranda [70] A fuzzy-logic-based optimisation technique has been used to
determine the location of sectionalising switches
In [69] the optimum sectionalising switch relocation problem has been solved by
using the ant colony system (ACS) based method to reduce feeder interruption costs
Chapter 2 Distribution Automation
Page | 42
after a fault In this work it is assumed that there were no additional capital
investments brought by switch relocation However the investment and operation
cost of a sectionalising switch is an important issue which cannot be ignored when
considering the problem of unsupplied energy costs minimisation since they conflict
with each other Therefore the information provided by the multi-objective model is
more valuable than the traditional mono-objective model Abiri-Jahromi etc [64]
have developed a mixed-integer linear programming (MILP) to deal with the new
sectionalising switch installation problem which considers customer outage costs as
well as switch capital operation and maintenance costs After the placement of
sectionalising switches the total system cost over the life period of the switches was
greatly reduced [64] In addition the impacts of customer damage function and load
density variations on SSP were also investigated through sensitivity analysis
The impacts of DG on the optimal number and location of sectionalising switches
were discussed in [71] The introduction of DGs connects a mono-source distribution
network to a multi-source one [66] This potentially improves network reliability
since it reduces the duration and restoration time of interruptions Many loads can be
restored through DGs when operating in islanding mode A mathematical
optimisation methodology has been proposed to minimise the reliability cost when
operating with a minimum number of sectionalising switches The results indicate
the reliability indices of distribution networks are affected by the number and
location of sectionalising switches
27 Transformer Loss Assessment
271 Operating Principles
A transformer has three essential elements a primary winding a secondary winding
and a core [33] As shown in Fig 2-8 the winding connected to the electrical source
is called the primary winding and the secondary winding is linked with the loads All
the windings are connected by the common magnetic flux in the core
Chapter 2 Distribution Automation
Page | 43
Fig 2-8 Elements of a single phase transformer [33]
Usually the power is generated and distributed in a three-phase system Therefore it
is necessary to use a three-phase transformer to increasedecrease the voltage The
structure of the three-phase transformer is presented in Fig 2-9
Fig 2-9 Construction of a three-phase transformer [33]
272 Transformer Quantities Measurement
The transformer quantities present the self-loss during power transmission which
consists of active power loss together with increase in the reactive power of the
network unit [72]
Open-circuit test
The equivalent circuit for the open-circuit test is shown in Fig 2-10 The test is made
on the low-voltage side by applying rated voltage at rated frequency with the high-
voltage winding open [33] The input power and current are measured which are
named no-load loss 119875119874119862 and no-load current 119868119874119862
Chapter 2 Distribution Automation
Page | 44
(a) Test circuit
(b) Equivalent circuit
Fig 2-10 The open-circuit test [33]
As the secondary is open the primary current is equal to the no-load current The no-
load current is used to produce the primary magnetic flux when the transformer is in
no-load operation which is also called the exciting current The voltage drops in the
primary winding can be ignored so the no-load loss is the summation of hysteresis
and eddy current losses [33] The input power is practically equal to the no-load loss
at rated voltage and frequency
119875119874119862 = 119875ℎ+119890 =119880119874119862
2
119877119888119871119881= 119880119874119862119868ℎ+119890 (2-1)
where 119877119888119871119881 is the resistance referred to the low-voltage side 119868ℎ+119890 is the core loss
current
Short-circuit test
The short-circuit test is used to measure the equivalent resistance and reactance of
the winding [6] As shown in Fig 2-11 the low-voltage terminal is shorted together
and the high-voltage side of the transformer is connected to a low-voltage high-
119880119900119888
119868ℎ+119890 119868120601
119868119900119888 119885119890119902 119871119881
119877119888 119871119881 119883119898 119871119881
Chapter 2 Distribution Automation
Page | 45
current source at rated frequency [33] The source voltage is increased until the short
circuit current reaches the rated value At this time value of the source voltage is
known as the short-circuit source voltage 119880119878119862
(a) Test circuit
(b) Equivalent circuit
Fig 2-11 The short-circuit test [33]
As the secondary side is shorted the voltage applied to the full load current is low
compared to the rated voltage and the exciting current 119868119890119909 is negligible during this
test [33] Since the rated current is used the input power is equal to the full-load loss
and expressed as
119875119878119862 = 1198681198781198622 119877119890119902119867119881 (2-2)
where 119877119890119902119867119881 is the winding resistance referred to the high voltage side
As the full-load loss depends on the value of the full load current the loss in the
winding resistance is varied under different loading conditions
119880119904119888
119868119890119909
119868119904119888 119877119890119902 119867119881 119883119890119902 119867119881
(119899119890119892119897119890119888119905)
Chapter 2 Distribution Automation
Page | 46
Active power loss
The active power loss ∆119875 of a two-winding transformer is decided by the no-load
loss 119875119874119862 full-load loss 119875119878119862 and the transformer load factor [73]
∆119875 = 119875119874119862 + 1205732119875119878119862 (2-3)
where 120573 =119878119871
119878119873 represents the transformer load factor 119878119871 is the transformer actual
loading (kVA) 119878119873 is the transformer rated capacity (kVA) Assuming the voltages
are held constant at 10 pu
Reactive power loss
The no-load current 119868119900119888 and short-circuit source voltage 119880119878119862 represent the change of
reactive power ∆119876 in other words the reactive power loss which can be simplified
as
∆119876 = 119876119874119862 + 1205732119876119878119862 (2-4)
119876119874119862 = 119878119874119862 =119868119874119862
119868119873∙ 119878119873 (2-5)
119876119878119862 = 119878119878119862 = 119880119878119862
119880119873∙ 119878119873 (2-6)
273 Integrated Transformer Loss
In general the power loss of a transformer is related to the active power [74]
However if a transformer draws reactive power (it takes current) this causes real
power loss in the network The integrated power loss refers to the sum of active
power loss of the transformer and the increased active power loss contributed by the
reactive power of the transformer [72]
The integrated power loss of a two-winding transformer is calculated by
1198791198711 = 11988002119875119885119874119862 +
1205732
11988002 119875119885119878119862 (2-7)
119875119885119874119862 = 119875119874119862 + 119870119876119876119874119862 (2-8)
Chapter 2 Distribution Automation
Page | 47
119875119885119878119862 = 119875119878119862 + 119870119876119876119878119862 (2-9)
where 119875119885119874119862 and 119875119885119878119862 are the integrated no-load loss (kW) and the full-load loss (kW)
120573 =119878119871
119878119873 represents the transformer load factor 119878119871 is the transformer actual loading
(kVA) 119878119873 is the rated capacity of the transformer (kVA) 119875119874119862 and 119876119874119862 are the no-
load active power loss (kW) and no-load reactive power loss (kVAr) 119875119878119862 and 119876119878119862
are the full load active power loss (kW) and full load reactive power loss (kVAr) 119870119876
represents the reactive equivalent which is the ratio of increased active power loss to
the change of the node reactive power (kWkVAr) [72] 1198800 is the operational voltage
of the transformer low voltage side in per unit
The no-load and full-load power losses are obtained from the open-circuit and short-
circuit test separately
For two transformers operating in parallel with the same capacity the current
flowing through each transformer is reduced by half Thus the full-load loss of each
transformer becomes a quarter of the previous case The total integrated power loss
is twice the no-load loss and half (2 times1
4) of the full-load loss of one transformer
1198791198712 = 211988002119875119885119874119862 +
1
2
1205732
11988002 119875119885119878119862 (2-10)
28 Feeder Loss Assessment
The distribution network power loss is mainly due to resistive loss in distribution
feeders which is obtained through a power flow study [75] The calculation of
power loss is explained using a two-bus network as shown in Fig 2-12
Fig 2-12 Simple two-bus network
Chapter 2 Distribution Automation
Page | 48
Assume there is no capacitance on either the sending or receiving bus and 119868119887119904 =
119868119887119903 = 119868119887 As a result the current flowing through branch b and the real power loss
are derived using the following equations
119875119887119877 + 119895119876119887119877 = 119887119877 times 119868lowast (2-11)
119875119887 = 1198681198872 times 119877119887 (2-12)
From (2-11) and (2-12) it is calculated as
119875119887 =119875119887119877
2 +1198761198871198772
1198811198871198772 times 119877119887 (2-13)
where 119875119887 is the real power loss of branch b (W) 119875119887119877 and 119876119887119877 are the real power (W)
and reactive power (VAr) at the receiving end of branch b 119881119887119877 represents the rms
voltage at the receiving end of branch b (V) 119868119887 is the rms current through branch b
(A) and 119877119887 is the resistance of branch b (Ω)
The real power losses in the other branches are evaluated similarly and the network
real loss is the sum of the power losses in all branches as presented in (2-14)
119864119871 = sum 119875119887119899119873119887119899 (2-14)
where 119873119887 is the set of all the distribution network branches
29 Reliability Evaluation
291 Reliability Indices
Reliability is a fundamental attribute for the safe operation of any modern power
system [8] A distribution network which is directly connected to customers has a
large impact on power reliability Distribution reliability primarily relates to
equipment outages and customer interruptions [76] The reliability indices of
distribution network can be classified into two groups ie load point reliability
indices and system reliability indices [77]
Chapter 2 Distribution Automation
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The three primary load point reliability indices average failure rate (120582) average
annual outage time (119880) and average outage time (119903) are calculated by [73]
120582 = sum 120582119895119895 (2-15)
119880 = sum 120582119895119895 119903119895 (2-16)
119903 =119880
120582 (2-17)
where 120582119895 and 119903119895 are the failure rate and outage time of contingency j for this load
point
The system reliability indices mainly include system average interruption frequency
index (SAIFI) system average interruption duration index (SAIDI) average energy
not supplied (AENS) and expected customer damaged cost (ECOST) [78] The
Formulae for these reliability indicators are presented in (2-18) to (2-21) [78]
119878119860119868119865119868 =sum 120582119894119873119894119894
sum 119873119894119894 (2-18)
119878119860119868119863119868 =sum 119880119894119873119894119894
sum 119873119894119894 (2-19)
119860119864119873119878 =sum 119880119894119871119894119894
sum 119873119894119894 (2-20)
119864119862119874119878119879 = sum 119888119898(119889119898)119891119898119871119898119872119898=1 (2-21)
where 119873119894 is the total number of customers of load point 119894 120582119894 119880119894 and 119871119894is the failure
rate outage time and average load connected to load point i 119872 is quantity of load
outage events 119871119898 is load curtailed (kW) due to outage event m 119891119898 and 119889119898 are the
frequency and duration of outage event m 119888119898(119889119898) is the outage cost (poundkW) of
outage duration 119889119898 using the customer damage function (CDF)
SAIFI is a measure of the number of outages an average customer will experience
SAIDI states the average interruption hours for a customer in the system AENS
presents the effect of interruptions on the energy that is not supplied to the customers
during failures [79] ECOST is the index that connects reliability with economics
Chapter 2 Distribution Automation
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292 Reliability Evaluation Methods
The methods used to calculate reliability indicators for distribution network are
classified into two groups namely the simulation method and analytical method
Simulation method
The simulation method has better scalability and flexibility when incorporating
complex considerations in comparison with the analytical technique And it is more
capable of dealing with large-scale power systems and the variation of load points
[77] The Monte Carlo method is a typical example of a simulation method and
takes into account the time varying and stochastic nature of load models in
evaluating the power system reliability [80] Vitorino etc [12] proposed a non-
sequential Monte Carlo method based on branch reliability to estimate energy not
supplied (ENS) index Contingencies were simulated by randomly selecting a faulty
branch from a candidate network pool based on failure probabilities [12] However
although the Monte Carlo method can simulate the behaviour of a complex system
with a high degree of accuracy it requires a considerable amount of CPU time and
memory
Analytical method
The first step of an analytical technique is to build a reliability probabilistic model
for the system according to network topology as well as the relationships between
the system and components [77] The model is then solved by calculating the
reliability indices in iterations [77] The most common analytical methods are
minimal path method minimal cutset method and failure-mode-and-effect analysis
(FMEA)
In [81] the minimal path method which identifies the shortest paths from a node to
a source and between any two nodes was described The minimal path of the source
node to the load points was obtained by searching for the upstream node from the
load points [82] As the distribution network was radial each node had only one
upstream node The sections out of service after a fault occurred were identified and
separate subsystems were formed The nodes were classified in terms of the effect of
a failure on them Using the node class and amount of load shedding data the
reliability indexes could then be evaluated [81]
Chapter 2 Distribution Automation
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FMEA is a classical analytical algorithm for distribution network reliability
evaluation based on the analysis of all the failure modes of each static component
[82] As shown in Fig 2-13 there are four failure modes which are 1) active failure
2) transient failure 3) passive failure and 4) maintenance The active and transient
failures can cause the operation of breakers and hence the healthy components can
be removed from service [75] The passive failures are similar to maintenance outage
and have no effect on the protection system and remaining heathy zone [82]
Fig 2-13 Reliability model for static components
The proposed reliability evaluation method is based on the N-1 criterion and its
computation procedure is demonstrated in Fig 2-14
Normal operation
Active
failure
Transient
failure
Passive
failure
Maintenance
120582119860 120582119879 120582119875 120582119872
120583119860 120583119879 120583119875
120583119872
Chapter 2 Distribution Automation
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Start
Read system topology load
data and reliability parameters
Initialise failure number i=1
All failures are considered
Search for the upstream feeder breaker
Search for the upstream and downstream
sectionalising switches and tie-switch
The load points are classified into three categories
Evaluate the reliability of load points
and whole system when fault at line i
Next failure i=i+1
Calculate the reliability of the whole system
End
No
Yes
Fig 2-14 Procedure for reliability evaluation
The system failure events are enumerated first For a failure event the scope of the
failure is determined by searching for the adjacent circuit breaker or tie switch The
isolation zone is then confirmed by the location of the upstream and downstream
sectionalising switches and the appropriate tie-switch Subsequently all the load
points are classified based on their interruption times Finally the consequence of
each contingency and a value for total system reliability are evaluated
When a fault occurs all the load points can be categorised as follows
Healthy points are load points not affected by the fault and refer to upstream
nodes of the upstream circuit breaker or downstream nodes of the
Chapter 2 Distribution Automation
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downstream circuit breaker or tie-switch For example when a fault occurs at
L2 in Fig 2-15 LP1 and LP5 are healthy points
Temporary damaged points when the protection systems are in operation
they cause the load points to be interrupted but the load points can be
restored by isolating the faulty area and by using a supply through another
path When a fault occurs at L2 in Fig 2-15 LP2 and LP4 are isolated by
opening the sectionalising switches S1 and S2 LP2 is restored by closing B1
and LP4 is supplied by closing the tie-switch As a result LP2 and LP4 are
temporary damaged points The interruption time is 119879119878 which is the average
switching time after failure
Permanent damaged points are load points that are interrupted by the
operation of protection devices and cannot be restored until the fault is
cleared [82] When a fault occurs at L2 in Fig 2-15 LP3 is the permanent
damaged point The interruption time is 119879119877 which is the average repair time
after failure
Fig 2-15 Sample network
Overall the analytical method which is based on a reliability model of each
component evaluates system reliability by enumeration of all failure states However
the increasing number of devices in a complex system results in an increase in the
quantity of failure states and the complexity of calculation As such the scale of the
network might be limited
210 Multi-objective Optimisation
The aim of this section is to provide fundamental information in order to assess
multi-objective optimisation problems The objectives are conflicting and can be
Chapter 2 Distribution Automation
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0
1
converted into three forms which are 1) single objective function 2) single fuzzy
satisfaction objective function and 3) Pareto front
2101 Single Objective Function
The single objective function is generally done by simply aggregating the objectives
with the same dimension and transforming others into constraints [83] It can be
solved by traditionally scalar-valued optimisation techniques However this function
has several limits 1) it results in only one solution 2) the analysis of the objectives
that are converted into constraints is limited
In [64] a sectionalising switch placement strategy was proposed to minimise the
sum of ECOST and sectionalising switch costs The above mentioned objectives
were simply aggregated and calculated in US dollars Other objectives such as the
number of available switches were converted into constraints
2102 Single Fuzzy Satisfaction Objective Function
In the fuzzy domain each variable is associated with a membership function varying
from zero to unity which indicates the satisfaction level of the objective [84] The
higher the membership value is the better the solution is Generally the linear
membership function is formulated as given in (2-22) and is presented in Fig 2-16
120572 =
1 119883 le 119883119898119894119899119883119898119886119909minus119883
119883119898119886119909minus119883119898119894119899119883119898119894119899 lt 119883 lt 119883119898119886119909
0 119883 ge 119883119898119886119909
(2-22)
Fig 2-16 Linear membership function
If 119883 is equal or less than 119883119898119894119899 the membership value is one As 119883 becomes greater
than 119883119898119894119899 the degree of satisfaction decreases This decrease is continued until 119883
reaches 119883119898119886119909 and the membership function becomes zero
120572
119883119898119894119899 119883119898119886119909 119883
Chapter 2 Distribution Automation
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The fuzzy-based optimisation procedure is used for handling multiple conflicting
objectives with different dimensions and units [66] The degrees of satisfaction level
can be formulated into a single objective function in three methods which are 1)
weighted aggregation 2) max-min method 3) max-geometric-mean method The
objective is to maximise such degree of satisfaction
Weighted aggregation
In this method the degree of satisfaction level is the weighted aggregation of the
membership values of all objectives [85] Thus the final compromise solution for
multi-objective functions is described as follows
119872119886119909 119869 = 12059611205721 + 12059621205722 + ⋯ + 120596119899120572119899 (2-23)
where 120596119894 is the constant weighting factor for each of the membership values and
they should meet the condition sum 120596119894119894 = 1
The weighting factors are decided by the decision makers and a higher weighting
factor indicates that this parameter is more important However the disadvantage of
this technique is that DNOs may have difficulty in obtaining enough information
about the relative importance of each objective to determine the trade-offs among the
selected objectives
Saffar etc [60] have developed a network reconfiguration technique to reduce power
loss and equal load balancing of feeders As these objectives had different
dimensions and units they were transformed into a single objective function with
fuzzy variables A set of compromised solutions was obtained by varying the
weighting factors of each element
Max-min method
In this technique the degree of overall satisfaction is the minimal value among the
membership values of all objectives [85] Thus the final compromise solution for
multi-objective functions is described as follows
119872119886119909 119869 = min 1205721 1205722 hellip 120572119899 (2-24)
The solution is optimised by maximising the overall satisfaction of all objectives
However the max-min method might not predict the best compromise solution
Chapter 2 Distribution Automation
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because even if one membership value is weak it does not necessarily mean that
other membership values are also weak [86]
The max-min principle was adopted in [84] for the multi-objective optimisation with
fuzzy sets The aim was to minimise real power loss and the absolute value of branch
current as well as to minimise nodes voltage deviation Finally an optimal solution
was obtained which indicated a concession among all the objectives The results also
revealed that although network reconfiguration resulted in a significant reduction in
total system loss the loss allocated to a certain number of customers increased [84]
It is important to change the tariff structure for these consumers so that they are not
obliged to pay more for the increase in loss allocation as a result of network
reconfiguration
Max-geometric-mean method
Like the above max-min method the geometric-mean function is also used to
evaluate the degree of overall fuzzy satisfaction but in different forms The objective
is computed as follows
119872119886119909 119869 = (1205721 ∙ 1205722 ∙ hellip ∙ 120572119873)1 119899frasl (2-25)
In [86] firstly all the variables (real power loss branch current loading maximum
voltage deviation and switching numbers) were assigned by truncated sinusoidal
fuzzy membership functions The overall degree of satisfaction was the geometric
mean of all fuzzy membership values [86] The best compromise solution was then
obtained by maximising this satisfaction level
2103 Multi-objective Formulation in the Pareto Optimality
Framework
All the studies mentioned above are solved by a single-objective optimisation
technique In contrast a Pareto optimal solution is provided for the treatment of
multi-objective problems This produces a range of solutions rather than just one
which represents a compromise that goes some way to optimise objective functions
[87] [88] The Pareto optimal solution is based on a dominance concept The
solution 119883 dominates 119884 means that 119865(119883) is no worse than 119865(119884) for all objectives
Chapter 2 Distribution Automation
Page | 57
and there is at least one objective for which 119865(119883) is better than 119865(119884) as expressed in
(2-26) and (2-27) The following conditions should be satisfied concurrently
forall 119894 = 12 hellip 119873119900119887119895 119865119894(119883) le 119865119894(119884) (2-26)
exist 119894 = 12 hellip 119873119900119887119895 119865119894(119883) lt 119865119894(119884) (2-27)
where 119873119900119887119895 is the number of objective functions
If a solution 119883 and solution 119884 do not dominate each other these two solutions are
incomparable For example the objective is to minimise 1198911 and 1198912 and there are
three solutions whose objective function values are 119865(119883) = (24) 119865(119884) = (44)
119865(119885) = (52) It can be seen that 119883 dominates 119884 as 1198911(119883) lt 1198911(119884) and 1198912(119883) le
1198912(119884) And the solution 119883 and 119885 are incomparable because 1198911(119883) lt 1198911(119885) and
1198912(119883) gt 1198912(119885) Similarly solutions 119884 and 119885 are also incomparable
A solution belongs to Pareto optimal solutions if there is no other solution that can
improve at least one objective without degradation of any other objectives [83] In
other words there is no another solution that dominates it The Pareto set is the set of
all non-dominated solutions and its corresponding objective values constitute the
Pareto front [88] The goal of the multi-objective optimisation is to select the most
suitable one from the Pareto set for implementation according to decision makersrsquo
preferences
In [45] the study proposed a Pareto-based multi-objective DNR method using a
discrete PSO algorithm It aims to reduce power loss voltage deviations and the
number of switching operations Firstly each objective function was optimised
separately and the best results were found All objectives were then optimised
simultaneously and the Pareto optimal set was obtained The best results for each
objective were included in the Pareto front and the corresponding solutions were
stored in the Pareto optimal set Finally the best compromise solutions among the
multiple objectives were derived Different scenarios were modelled by assigning
different weighting factors based on the preferences of the decision makers
Chapter 2 Distribution Automation
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211 Summary
Generally most distribution networks are designed in closed loop but are operated
radially There are three typical distribution network topologies which are the radial
system primary loop and link arrangement The descriptions of three switchgears ie
recloser sectionalising switch and tie-switch are also included in this chapter
TEO DNR and SSP are the three main parts of DA In this chapter there are several
reviews of these techniques TEO which refers to optimum selection of which
transformers need to supply each feeder can not only reduce loss but also reduce
total costs and improve network reliability DNR is defined as a process that
involves changing the network topology under normal and abnormal operating
conditions by relocation of tie-switches [13] [14] The methodologies from a branch
and bound optimisation method to modern heuristic optimisation algorithms
designed for loss reduction are reviewed In addition DNR is also able to improve
service quality and efficiency at the same time The placement of sectionalising
switches refers to the installation of new switches and relocation of existing switches
It is used for distribution network reliability improvement and service restoration
However so far few studies have been carried out that consider the combination of
the above three techniques
The major challenge facing DNOs is how to distribute the power in a low-cost
reliable and efficient way Thus the assessments of transformer loss feeder loss and
reliability indices are proposed in Section 27-29 The integrated transformer loss
consists of not only real power loss but also reactive power loss The transformer
quantities such as no-load loss and full-load loss are obtained from open-circuit test
and short-circuit test The distribution network power loss is achieved through power
flow study The reliability indices can be calculated through reliability evaluation
methods namely simulation methods and analytical methods The most common one
is FMEA which is also used for reliability evaluation in this thesis Although there
are many research projects that consider feeder loss and reliability simultaneously
few consider transformer loss and feeder loss at the same time
Three objective functions for optimising multiple conflicting objectives are 1) single
objective function 2) single fuzzy satisfaction objective function and 3) Pareto front
Chapter 2 Distribution Automation
Page | 59
The single objective function is generally done by simply aggregating some
objectives and transforming others into constraints In the fuzzy objective function
each variable is associated with a membership function and then aggregated into a
single objective function [84] The first two functions only obtain a single solution
However Pareto optimal solutions can obtain a set of non-dominated solutions
rather than one which represents a compromise that goes some way to optimising
objective functions In this thesis all three objectives functions will be studied and
results will be presented in the following chapters
This thesis will deal with single objective and multiple objectives through different
methods of DA based on various algorithms The next chapter will introduce the
Monte Carlo method and modern heuristic optimisation algorithms such as ant
colony optimisation (ACO) and artificial immune systems (AIS)
Page | 60
CHAPTER 3
OPTIMISATION TECHNIQUES
31 Introduction
Mathematically distribution automation (DA) is categorised as a discrete non-linear
constrained and combinational optimisation problem since the problem is to
determine the status of all transformers and switches In general the optimisation
techniques for assessment of this problem can be divided into two large groups 1)
simulation methods and 2) analytical methods
The Monte Carlo method is a typical example of a simulation method which will be
discussed in Section 32 in detail It can handle uncertainties and solve the
probabilistic optimal power flow [89] In a complex system with hundreds of
switches although the Monte Carlo method can find the best solution with a high
degree of accuracy it is generally not practical to carry out an extensive search of all
possible configurations as it consumes a great deal of CPU time and memory [88]
Therefore most DA problems are solved by analytical methods
The analytical methods can obtain a solution of good quality or even the global
optimal solution of the problem [13] It can be classified into four types 1) branch
and bound 2) optimal flow pattern 3) branch exchange and 4) metaheuristic
techniques Recently the last type has become the most popular
Chapter 3 Optimisation Techniques
Page | 61
The metaheuristic method is a process that attempts to find a solution to the problem
beginning from a starting point or a set of starting points and exploring all the search
space [13] It also includes a strategy to explore the search space and provide an
escape from the local optimal This process does not guarantee a globally optimal
solution but can offer near optimal solutions with a reasonable computational effort
This includes genetic algorithm (GA) ant colony optimisation (ACO) particle
swarm optimisation (PSO) and artificial immune systems (AIS) Different
metaheuristic techniques use different strategies that pass through and explore the
search space [13]
As for the remainder of the chapter the Monte Carlo method is discussed in Section
32 Section 33 presents the proposed ACO algorithm Section 34 discusses a new
hybrid AIS-ACO framework and the summary of this chapter is provided in Section
35
32 Monte Carlo Method
The Monte Carlo method is a simulation algorithm that can be carried out many
times to produce numerical samples that accurately reflect the probability
distribution of the real results [90] [91] This method is always used to solve power
system issues involving uncertain parameters [92] The uncertainties are allocated
randomly and each simulation is operated numerous times In theory the more
simulations are running the less deviation error between actual mean value and
sample mean value Therefore it is important to determine the overall running times
of the Monte Carlo simulation The convergence or stopping criteria is used to
determine the simulation times required to obtain acceptable accurate results
The confidence interval acts as a good estimate of the unknown parameters The
probability that the true parameter remains in the confidence interval is calculated as
follows [93]
119862 = 119875(119883 minus 119871 le 120583 le 119883 + 119871) = int 119866(119883)119889119909119883+119871
119883minus119871 (3-1)
119871 = 119911lowast 120590
radic119899 (3-2)
Chapter 3 Optimisation Techniques
Page | 62
where 119862 is the degree of confidence is the estimated mean value 119871 is the
confidence interval which provides an estimate range of values which probably
contains an unknown population parameter 120583 is the true population mean value
119866(119883) is the Gaussian distribution 120590 is the sample standard deviation and 119899 is the
number of samples the estimation of 119911lowast is based on the degree of confidence 119862 as
presented in Table 3-1 The most common 119911lowast is 196 and the corresponding 119862 is
095
Table 3-1 Relationship of 119911lowast and 119862
119862 09 095 099 0999
119911lowast 1645 1960 2576 3291
The required number of samples could be expressed as
119899 = (119911lowast120590
119871)2 (3-3)
There are several methods used to determine the sample size and to obtain results
with acceptable accuracy One is by predefining the maximum sample size 119873 when
119899 reaches 119873 the simulation is stopped Another one is by using the degree of
confidence 119862 The confidence interval 119871 is calculated and compared with the
predefined 119871 for each sample and the simulation reaches the stopping criteria when
the confidence interval is less than the critical value
33 Ant Colony Optimisation
The ant colony optimisation method is one of the metaheuristic techniques that has
been employed for the solution of combinational optimisation problems in recent
years [60] The ant colony system (ACS) simulates the behaviour of real ants [94]
[95] The moving paths of artificial ants construct the candidate solutions to a
problem [96] The ants communicate with other ants by a chemical substance called
pheromones [97] Originally all the ants start from their nest and search for their
food in a random manner When the food source is found the ants leave a chemical
Chapter 3 Optimisation Techniques
Page | 63
substance trail on the way home The pheromone deposited by the ants is used as the
primary guide function for the other ants The pheromones will then evaporate after a
period of time As all of the ants travel approximately at the same speed the shortest
path has the largest probability to contain more pheromones because more ants
choose this one The ants tend to follow the path that has more pheromones than
others After a brief period the shortest path with the most intensity of pheromones
could attract more and more ants providing feedback to the system that promotes the
use of best paths [98] Fig 3-1 represents the behaviours of real ants [69]
Fig 3-1 Example of ant colony system [69]
As shown in Fig 3-1 (a) all the ants are travelling in the same path which connects
point A and point B by a straight line The environment is changed due to the
occurrence of an obstacle in Fig 3-1 (b) and (c) At first all the ants choose the left
or right path randomly because they have no guide It is assumed that they move
through path C or D with the same probability Later on the ants that choose path C
will move faster than that choose path D As a result the pheromones deposited on
path C accumulate faster than those on the path D and this attracts more ants to
choose path C Finally all the ants tend to choose the shortest path (path C) as this
contains the most pheromones
The flowchart of ACO algorithm is shown in Fig 3-2 and the main stages of the
algorithm are presented as follows [69] [94] [95] [97] [98]
Initialisation In this stage the trail intensity on each edge in the search
space is initialised to a constant positive value and all the ants are located in
Chapter 3 Optimisation Techniques
Page | 64
the nest
Ant Dispatch In this step each ant begins its tour at the starting point and
chooses the next node to move to according to a probabilistic selection rule
which involves the intensity of pheromones deposited on each node by other
ants [88] [99] The ants prefer to choose the path with a higher pheromones
This process is repeated until all the ants have reached the food source
Quality Function Evaluation After all the ants have completed a tour the
relevant quality function of the optimisation problem is calculated to evaluate
the performance of each ant If any constraint is violated the configuration is
discarded Otherwise the objective function is evaluated
Trail Intensity Update There are two pheromone updating rules applied in
this step One is called the global pheromone update It accumulates the
pheromone values on the high-quality solution path to improve convergence
However the pheromone intensity of each edge evaporates over time due to
another rule called the local pheromone update This update is used to
enlarge the search space and to avoid premature convergence for local
minima Ants travelling between two nodes update the relevant pheromone
intensity in the corresponding edge
Convergence Determination This process is operated until the maximum
iteration number is reached or all the ants choose the same path between their
home colony and food source
Chapter 3 Optimisation Techniques
Page | 65
Start
Set Iteration n=1
Maximum iteration
reached
End
No
Yes
Initialise the parameters for ACO algorithm
searching space and build graph of the tours
Dispatch ants based on the
amount of pheromones on edges
Quality function evaluation
Trail intensity update
Record the high quality solutions of this
iteration and empty all location lists
n=n+1
Fig 3-2 Flowchart of the ant colony algorithm
The above procedure should be modified to a computational procedure to solve
different optimisation problems and this is discussed in the following chapters
Several factors need to be taken into account when designing an ACO algorithm
such as search space transition probability etc
34 AIS-ACO Hybrid Algorithm
341 Artificial Immune Systems
The immune system acts as a defensive barrier to recognise and eliminate foreign
antigens ie bacteria virus etc B lymphocytes are the main immune cells in the
biological immune system and originate in the bone marrow Being exposed to an
Chapter 3 Optimisation Techniques
Page | 66
antigen a specific antibody is produced on the surfaces of B cells and an immune
response is elicited to make antibodies recognise and bind the antigen [88] [100]
Those B cells whose antibodies best match the antigen are activated and cloned
several times [88] This process is called cloning To identify the most suitable
antibodies for the antigen it is necessary to cause the antibody and the antigen to
interact more closely with each other This is achieved through a process call
hypermutation in which random changes are introduced into the genes of the cloned
B cells [88] One such change might lead to an increase or decrease in the closeness
between antibody and antigen [88] The new B cells can only survive if they are
closely related to the antigen and therefore the B cells that are closely related are
then chosen to enter the pool of memory cells [100] These cloning hypermutation
and selection processes are called the clonal selection principle [101] By repeating
this principle a number of times the immune system learns to respond more
efficiently for the same antigen
Several computational models of the AIS have been developed recently as the
immune system is an adaptive learning system that has the following specifications
learning memory recognition of foreigners and pattern recognition [102]
342 Proposed AIS-ACO Hybrid Algorithm
The proposed AIS-ACO hybrid algorithm combines the advantages of AIS and ACO
The hypermutation developed from the AIS is used as a random operator by
adopting random changes to perturb a solution and hence to enlarge the search space
However the pheromones provided by the ACO can store information about the
quality of solution components for improving the objective functions [88] In
addition the information obtained from pheromone updating guides the algorithm in
its search and improves the convergence rate [88]
The limitation of ACO is that the algorithm can easily fall into a local optimum
which might be due to an insufficient range of candidate solutions This can be made
up by the random changes of solutions in AIS through hypermutation Also the
weakness of the global searching ability in AIS is improved by the pheromone tables
in ACO Thus the new hybrid AIS-ACO framework based on the pheromone-based
hypermutation method has better diversity and convergence in comparison with
either the AIS or ACO algorithms
Chapter 3 Optimisation Techniques
Page | 67
Start
Cloning
Maximum iteration
reached
End
No
Yes
Initialise and set iteration number n=1
Hypermutation
Fitness evaluation
Non-dominated solutions extraction
Pheromone updating
n=n+1
Record the Pareto front and
Pareto optimal solutions
In this thesis the AIS-ACO hybrid approach is used to generate a set of non-
dominated solutions The antigen is the multi-objective function and the antibody is
the solution to the problem The affinity between the antibody and the antigen is the
Pareto dominance among solutions which indicates the quality of the solution [88]
All the non-dominated solutions experience cloning hypermutation and selection
until the maximum number of iterations is reached The flowchart of the AIS-ACO
algorithm for Pareto optimality is presented in Fig 3-3
Fig 3-3 Flowchart of the AIS-ACO algorithm
Chapter 3 Optimisation Techniques
Page | 68
The key parts of the algorithm are explained as follows
Initialisation At the beginning of this algorithm a set of initial solutions is
generated These solutions should meet the condition of constraints The
information related to each objective is represented by an individual
pheromone table Each pheromone value represents the probability of
selection of the corresponding edge in the network model [88] All
pheromone values are initially set as the same value
Cloning The number of clones for each non-dominated solution should be
the same as the number of objectives and also as the number of pheromone
tables [88]
Hypermutation The selection of an edge in each cloned solution for
hypermutation is dependent on its pheromone values [88] A higher
pheromone value of a cell in the table indicates that the corresponding edge
in the network is more likely to be selected
Non-dominated solutions extraction This is the process of selecting non-
dominated solutions according to their affinity value [99] All the solutions
are compared as presented in Section 2103 and all the non-dominated
solutions are then extracted for the next iteration
Pheromone updating The aim of this stage is to accumulate the pheromone
values on the edges that belong to a part of the non-dominated solutions and
this is called the global pheromone update However the pheromone
intensity of all edges will evaporate over time by the local pheromone update
This update is used to explore the entire search space
Termination This process is operated until the maximum iteration number
is reached The set of final non-dominated solutions is called the Pareto set
which is used to solve the problem [88]
35 Summary
This chapter introduces the techniques for assessment of mono-objectivemulti-
objective optimisation problems The optimisation techniques are categorised into
two groups simulation methods and analytical methods
Chapter 3 Optimisation Techniques
Page | 69
The Monte Carlo method is a typical simulation technique and is generally used to
handle uncertain parameters It can find the best solution with a high degree of
accuracy but requires a considerable amount of CPU time and memory The
application of this methodology is discussed in Chapter 4 In that chapter an
efficient methodology based on the Monte Carlo Method is proposed for finding
transformer economic operation modes and optimal tie-switch placement strategies
to minimise transformer loss
The ACO algorithm is one of the metaheuristic techniques designed for assessment
of distribution automation (DA) problems It simulates the behaviour of artificial
ants with positive feedback and distributed computation The positive feedback
enhances the search speed in order to find the global solution and the distributed
computation explores the search space The ACO algorithm is able to find the global
solution in a reasonable computation time It is used for either loss reduction or
reliability improvement as discussed in Chapter 5-7 In addition a new multi-
objective ACO (MOACO) algorithm for assessment of multi-objective DNR
problems in terms of Pareto optimality is provided in Chapter 8
The AIS-ACO hybrid algorithm is a combination of AIS and ACO Hypermutation
is used in AIS as a random operator by using random changes to perturb a solution to
maintain the diversity of the solutions avoiding premature convergence for local
minima The pheromone tables used in the ACO are used to direct the algorithm
towards high quality solutions [88] The AIS-ACO hybrid algorithm is always used
for assessing the DA problem in terms of multiple objectives optimisation in order
to obtain a set of non-dominated solutions In addition the advantages of the AIS-
ACO algorithm over the MOACO algorithm for the assessment of multi-objective
optimisation problems are also discussed in Chapter 8
Page | 70
CHAPTER 4
TRANSFORMER ECONOMIC
OPERATION amp DISTRIBUTION
NETWORK RECONFIGURATION FOR
TRANSFORMER LOSS REDUCTION
41 Introduction
The electrical power generation transmission and distribution companies are not
only energy producers but also significant power consumers Energy loss occurs in
the process of power transfer and takes place in all electrical equipment including
generators power lines and transformers The large number and power capacity of
transformers used in a transformer and distribution network means transformer loss
is a significant component in energy loss The lifetime cost of energy loss in a
transformer is significant especially when one considers rising electricity demand
and the cost of the energy supplied For this reason it is important to tackle the
causes of transformer loss and the problems which then ensue so that energy
consumption can be reduced To support this statement several research projects
that have focused on transformer loss reduction are discussed in Section 242
Chapter 4 Transformer Economic Operation amp Distribution Network
Reconfiguration for Transformer Loss Reduction
Page | 71
An efficient methodology based on the Monte Carlo Method for the 3311 kV
transformer loss reduction with consideration of the voltage issues observed on a
distribution network is proposed in this chapter For a substation with two
transformers there are three operation modes that can occur 1) single transformer in
separate operation 2) two transformers in parallel operation 3) transformer
economic operation (TEO) as mentioned in Section 24 With regard to the load
models which are also discussed in this chapter a database containing numerous
domestic electricity demand profiles is imported into MATLAB to work as the
profile generators A Monte Carlo simulation platform is established by combining
the residential demand profiles with a 3311 kV distribution network model built in
OpenDSS Based on this platform the impacts of three operation modes of
transformers on transformer loss minimisation are investigated and compared
In addition an enumeration approach used for the optimum relocation of tie-switches
in a linked 11 kV distribution network is also suggested The process that involves
changing the distribution network topology by relocation of tie-switches is called
distribution network reconfiguration (DNR) [13] [14] The control centre can
change the location of tie-switches and the transformer operation modes (TOMs) in
each substation based on load data and simulated power loss from the test system at
each time interval The proposed approach is applied to the test system and the
effectiveness of an optimal planning strategy using TEO and DNR to achieve
minimum transformer loss is demonstrated through the results obtained
The remainder of this chapter is structured as follows Section 42 explains the load
models Section 43 describes the mathematical formulation of transformer loss
Section 44 analyses the methodology used to minimise transformer loss whilst
maintaining satisfactory voltages and the case studies and the results are presented
and discussed in Section 45 Finally the main conclusions are summarised in
Section 46
Chapter 4 Transformer Economic Operation amp Distribution Network
Reconfiguration for Transformer Loss Reduction
Page | 72
42 Load Model
In order to access the performance of the distribution feeders with different operation
modes of transformers in the substation the time-series behaviour of loads has to be
modelled
The value of the load associated with domestic electricity demand customers has
been obtained from the research described in [19] this can produce a random 1-min
resolution model for UK households There are six steps for creating a domestic
electricity demand model as shown in Fig 4-1 Table 4-1 presents the proportion of
household sizes based on UK statistics [103]
Fig 4-1 Procedure of domestic electricity demand profile generation
Table 4-1 Household size by number of people in household as a proportion [103]
Number of people
in household
1 2 3 4 ge5
Percentage () 3058 341 1557 1288 686
A pool of 10000 different load profiles covering 24 hours in a typical February
weekday are generated by this model For computation reasons the 1440 1-min
time-step load profiles are integrated as 144 10-min resolution profiles in this study
Specify the number of residents in the house from 1 to 5
Specify either a weekday or
weekend
Select the month of the year from 1 to
12
Random allocate appliances to the
dwelling
Run the active occupancy model
Run the electricity demand simulation
Chapter 4 Transformer Economic Operation amp Distribution Network
Reconfiguration for Transformer Loss Reduction
Page | 73
(active power is recorded for each minute and then averaged at intervals of 10
minutes) The power factors of all the loads are set to 095
43 Problem Formulation
The objective of this study is to minimise transformer loss through TEO and optimal
DNR The energy loss of the transformer is related to active power However as a
transformer draws reactive power (it takes current) it causes real power loss in the
network The integrated power loss refers to the sum of active power loss of the
transformer itself and the increased active power loss contributed by reactive power
loss of the transformer [73] The mathematical formulation can be expressed as
follows
Minimise 119891 = 1198800
2119875119885119874119862 +1205732
11988002 119875119885119878119862 119905119903119886119899119904119891119900119903119898119890119903 119894119899 119904119894119899119892119897119890 119900119901119890119903119886119905119894119900119899
211988002119875119885119874119862 +
1
2
1205732
11988002 119875119885119878119862 119905119903119886119899119904119891119900119903119898119890119903119904 119894119899 119901119886119903119886119897119897119890119897 119900119901119890119903119886119905119894119900119899
(4-1)
where 119875119885119874119862 and 119875119885119878119862 are the integrated no-load loss (kW) and the full-load loss (kW)
120573 =119878119871
119878119873 represents the transformer load factor S is the transformer actual loading
(kVA) 119878119873 is the transformer rated capacity (kVA) 1198800 is the operational voltage of
the transformer secondary side in per unit
44 Methodology
In this study there are two methodologies used for transformer loss reduction which
are called TEO and DNR
441 Transformer Economic Operation
In this section a Monte Carlo simulation platform for three TOMs comparison is
established as shown in Fig 4-2 and the flowchart of the transformer loss assessment
is presented in Fig 4-3
Chapter 4 Transformer Economic Operation amp Distribution Network
Reconfiguration for Transformer Loss Reduction
Page | 74
Fig 4-2 Monte Carlo simulation platform for three transformer operation modes comparison
Firstly a pool of 10000 10-min daily domestic electricity demand profiles is
randomly generated by the profile generators in MATLAB Following this each
node in the feeders from the system is assigned with residential demand profiles
from the pool using the Monte Carlo Method Theses profiles and one of the TOMs
are then imported into the distribution network model built in OpenDSS After this a
sequential load flow calculation is performed and the simulation results are returned
including voltage profiles and transformer losses to MATLAB The obtained
results are then analysed and compared with the system constraints for each time
step In this study for each TOM the calculation is set to be repeated 10000 times
in order to satisfy the convergence criteria When the losses of all TOMs are
calculated the minimum transformer loss and its associated operation mode are
obtained
Profile
generator of
domestic
electricity
demand profiles
Transformer
operation
modes
MATLAB
Distribution
network
model built
in OpenDSS
Analyse and
compare
simulation
results in
MATLAB
Load flow calculation
Chapter 4 Transformer Economic Operation amp Distribution Network
Reconfiguration for Transformer Loss Reduction
Page | 75
Start
Monte Carlo trail number N=1
All transformer operation
modes considered
End
No
Yes
Select demand profiles to each
customer randomly
Select transformer operation
mode
Sequentially run power flow
calculation for 144 10-minute time step
Record results
Change
transformer
operation
mode
N=N+1
Maximum iteration reached
Minimum transformer loss and its associated
transformer operation mode are obtained
No
Yes
Load and aggregate the domestic
electricity demand profiles pool
(144 10-minute time steps)
Fig 4-3 Flowchart of transformer loss assessment
Chapter 4 Transformer Economic Operation amp Distribution Network
Reconfiguration for Transformer Loss Reduction
Page | 76
442 Distribution Network Reconfiguration
Reconfiguration of radial distribution system is achieved by local control of tie-
switches located in linked feeders The Monte Carlo simulation platform through
DNR is presented in Fig 4-4
Fig 4-4 Monte Carlo simulation platform for distribution network reconfiguration
In the proposed strategy the tie-switch status is modified by the control centre and
the detailed control algorithm is discussed below
Step 1 Random load profiles are first selected
Step 2 When the load profiles have been imported into the network model a
sequential load flow calculation is performed to calculate and compare the
transformer loss under different network configurations (different tie-switches
location) at each time interval
Step 3 Minimum transformer loss and its associated network configuration are
obtained
Step 4 Location of tie-switches based on minimum transformer loss over a whole
day is recorded
Step 5 Optimal DNR strategy is obtained
Profile
generator of
domestic
electricity
demand profiles
Tie-switch
status
MATLAB
Distribution
network
model built
in OpenDSS
Analyse and
compare
simulation
results in
MATLAB
Load flow calculation
Chapter 4 Transformer Economic Operation amp Distribution Network
Reconfiguration for Transformer Loss Reduction
Page | 77
45 Application Studies
To demonstrate the impact of TOMs and DNR on transformer loss the proposed
methodologies are applied to two test networks Several scenarios are tested and the
results are analysed and reported
451 Test Case 1
The single line diagram of the network shown in Fig 4-5 is developed from the UK
generic distribution network [104] The network model is built to incorporate a 3311
kV substation supplying the downstream loads in the OpenDSS software
environment The two transformers have the same specifications and their
characteristics are presented in Table 4-2 The corresponding TCLF is calculated as
5244 The 11 kV network is represented by four outgoing feeders from a single
busbar For computation reasons three of the feeders are simplified lumped loads
whilst the 4th
feeder is modelled in detail The 4th
11 kV feeder consists of eight
nodes which represents a small system with a total of 252 domestic single phase
house loads connected on each node A Monte Carlo simulation approach is
implemented to select these load profiles randomly from a pool of domestic
electricity demand profiles Each house in the 4th
feeder is then assigned with a
residential demand profile The loads in the other three feeders are then lumped with
the same daily profile of the 4th
feeder All the values of the network components are
based on a broad collection from [104] [105] and are recorded in Appendix A1
In this test a comparison of the three TOM methods for transformer loss
minimisation is provided A time-series load flow algorithm is implemented to
quantify the changes in feeder voltage and transformer loss in the previous described
3311 kV UK distribution network for different TOMs In this test three scenarios
are studied and summarised as follows
Scenario 1 Single transformer in separate operation
Scenario 2 Two transformers in parallel operation
Scenario 3 Transformer economic operation in this mode if the transformer load
factor is less than TCLF only one transformer remains in service if the transformer
load factor is higher than TCLF two transformers are operated in parallel
Chapter 4 Transformer Economic Operation amp Distribution Network
Reconfiguration for Transformer Loss Reduction
Page | 78
A
A
A
A
B
B
B
B
Load1Load2Load3Load4_1
Load4_2
Load4_3
Load4_4
Load4_5
Load4_6
Load4_7
Load4_8
75 MVA
33 kV
11 kV
33 kV
Voltage
Source
75 MVA
Fig 4-5 Generic distribution network topology
Table 4-2 Parameters of a typical 3311 kV two-winding transformer [106]
Sub-
sector
Transf
Rating
(kVA)
Conn Tapping
Range
Load
Losses
at
75
(kW)
No-
Load
Losses
(kW)
Impedance voltage
at rated current for
the principle
tapping
()
Reference
standard
Urban 7500 YY0 plusmn75
6 steps of 25
Each
50
75
835 BS 171 amp
IEC 60076
1) Test 1-1 Base Case
The simulation results of transformer load factor variation are shown in Fig 4-6 and
the transformer loss variation curves are presented in Fig 4-7 It is observed that the
transformer loss in Scenario 3 is the same as in Scenario 1 between 000 to 630 and
Chapter 4 Transformer Economic Operation amp Distribution Network
Reconfiguration for Transformer Loss Reduction
Page | 79
0
10
20
30
40
50
60
70
80
90
100
0 2 4 6 8 10 12 14 16 18 20 22
Tran
sfo
rme
r Lo
ad F
acto
r
Time (h)
0
10
20
30
40
50
60
70
0 2 4 6 8 10 12 14 16 18 20 22
Tran
sfo
rme
r Lo
sse
s (k
W)
Time (h)
0
10
20
30
40
50
60
70
0 2 4 6 8 10 12 14 16 18 20 22
Tran
sfo
rme
r Lo
sse
s (k
W)
Time (h)
the same in Scenario 2 from 1800 to 2200 With the introduction of Scenario 3 the
minimum loss is around 9 kW at 000 which is below the 18 kW of Scenario 2 The
maximum loss of Scenario 3 is nearly 40 kW at 1900 which is far below the 60 kW
of Scenario 1
Fig 4-6 Transformer load factor variation
(a) Scenario 1
(b) Scenario 2
Chapter 4 Transformer Economic Operation amp Distribution Network
Reconfiguration for Transformer Loss Reduction
Page | 80
0
10
20
30
40
50
60
70
0 2 4 6 8 10 12 14 16 18 20 22
Tran
sfo
rme
r Lo
sse
s (k
W)
Time (h)
(c) Scenario 3
Fig 4-7 Transformer loss variations in different scenarios
The mean values of 3311 kV transformer energy loss during one day under different
scenarios are presented in Table 4-3 As shown in Fig 4-6 the average transformer
load factor during a whole day is slightly below the TCLF (5244 in this test) This
situation is more suitable for a single transformer than two transformers The loss in
Scenario 3 reaches the lowest value and results in a reduction of 1133 and 1441
in comparison with Scenario 1 and Scenario 2
Table 4-3 Daily transformer loss in different scenarios
Scenario 1 Scenario 2 Scenario 3
Transformer losses (kWh) 53982 55922 47865
According to the EN50160 standard [7] under normal conditions at least 95 of the
10-min average mean rms voltage magnitude in the 11 kV electricity distribution
network should be within the range 09 pu to 11 pu over one week In other words
the 95th
percentile voltage profile is compared with the allowed voltage range to
check the networkrsquos reliability
The mean and 95th
percentile voltage profiles at each node in the fourth feeder are
presented in Fig 4-8 It can be seen that the voltage level at each node can change
considerably after the scenario changes It also appears that the nodes in Scenario 1
experience the most severe voltage drop in comparison with the other two scenarios
The worst 95 voltage value of the node lsquoLoad4_8rsquo at the end of the studied feeder
in Scenario 1 is around 098 pu which is not as satisfactory as the results of 0987 pu
and 0984 pu observed in Scenario 2 and Scenario 3
Chapter 4 Transformer Economic Operation amp Distribution Network
Reconfiguration for Transformer Loss Reduction
Page | 81
0976
0978
098
0982
0984
0986
0988
099
0992
Load4_1 Load4_2 Load4_3 Load4_4 Load4_5 Load4_6 Load4_7 Load4_8
Vo
ltag
e (
pu
)
Scenario1
Scenario2
Scenario3
0974
0976
0978
098
0982
0984
0986
0988
099
Load4_1 Load4_2 Load4_3 Load4_4 Load4_5 Load4_6 Load4_7 Load4_8
Vo
ltag
e (
pu
)
Scenario1
Scenario2
Scenario3
(a) Mean value
(b) 95th
value
Fig 4-8 11 kV 4th
feeder voltage profiles in different scenarios
To show in detail the voltage profiles affected by different TOMs the load at the
start of the 4th
feeder lsquoLoad4_1rsquo and the end one lsquoLoad4_8rsquo have been selected
Since the Monte Carlo method produces many loss and voltage values it is
preferable to present the averages of all these values and their deviations
As shown in the charts from Fig 4-9 and Fig 4-10 the voltage drops severely from
1800 to 2000 which is also the maximum daily demand period It also appears that
the voltage profile in Scenario 3 is the same as in Scenario 1 between 000 to 630
and the same as in Scenario 2 from 1800 to 2200 With the introduction of Scenario
Chapter 4 Transformer Economic Operation amp Distribution Network
Reconfiguration for Transformer Loss Reduction
Page | 82
088
09
092
094
096
098
1
0 2 4 6 8 10 12 14 16 18 20 22
Bu
s V
olt
age
(p
u)
Time (h)
088
09
092
094
096
098
1
0 2 4 6 8 10 12 14 16 18 20 22
Bu
s V
olt
age
(p
u)
Time (h)
088
09
092
094
096
098
1
0 2 4 6 8 10 12 14 16 18 20 22
Bu
s V
olt
age
(p
u)
Time (h)
3 the lowest voltage of lsquoLoad4_8rsquo is around 097 pu which is significantly above
the lower limit 090 pu
(a) Scenario 1
(b) Scenario 2
(c) Scenario 3
Fig 4-9 Voltage profiles of Load 4_1 in different scenarios
Lower Limit
Lower Limit
Lower Limit
Chapter 4 Transformer Economic Operation amp Distribution Network
Reconfiguration for Transformer Loss Reduction
Page | 83
088
09
092
094
096
098
1
0 2 4 6 8 10 12 14 16 18 20 22
Bu
s V
olt
age
(p
u)
Time (h)
088
09
092
094
096
098
1
0 2 4 6 8 10 12 14 16 18 20 22
Bu
s V
olt
age
(p
u)
Time (h)
088
09
092
094
096
098
1
0 2 4 6 8 10 12 14 16 18 20 22
Bu
s V
olt
age
(p
u)
Time (h)
(a) Scenario 1
(b) Scenario 2
(c) Scenario 3
Fig 4-10 Voltage profiles of Load 4_8 in different scenarios
Lower Limit
Lower Limit
Lower Limit
Chapter 4 Transformer Economic Operation amp Distribution Network
Reconfiguration for Transformer Loss Reduction
Page | 84
0976
0978
098
0982
0984
0986
0988
099
0992
Load4_1 Load4_2 Load4_3 Load4_4 Load4_5 Load4_6 Load4_7 Load4_8
0 25
5244 75
100
As most people are sleeping late at night and the transformer load factor is less than
the TCLF transformers are in individual operation mode When most people are at
home again from 1800 the transformer load factor increases beyond the TCLF As a
result the voltage profiles are improved when transformers are operated in parallel
In conclusion when the transformer load factor is less than the TCLF transformers
in a separate service result in less loss but more voltage dips however transformers
operating in parallel cause lower voltage drops but more loss When the transformer
load factor is higher than the TCLF transformers in parallel operation cause less loss
and lower voltage drops As a result based on the economic operation theory the
transformer in Scenario 3 significantly reduces transformer loss and maintains the
voltages at a satisfactory level
2) Test 1-2 TCLF Sensitivity Analysis
In this test the value of TCLF used to distinguish whether the transformer should be
in separate or parallel operation is discussed The complete process presented
previously is carried out again but takes into account the effect of different critical
values 0 25 5244 75 and 100
Fig 4-11 shows the effect on the mean voltage magnitudes of various TCLFs The
results indicate that the voltage profile is closely related to the TCLF and the TCLF
should be decreased to increase the region in which transformers operate in parallel
This will improve the voltage profiles
Fig 4-11 11 kV 4th
feeder mean voltage profile of various TCLFs
Chapter 4 Transformer Economic Operation amp Distribution Network
Reconfiguration for Transformer Loss Reduction
Page | 85
Table 4-4 describes the effect on the transformer loss when TCLF is changed It
reaches the lowest value when TCLF is 5244 If the TCLF is decreased or
increased above this value the loss increases Overall the TCLF should be set to
5244 in order to minimise transformer loss
Table 4-4 Transformer loss with different TCLF
TCLF () 0 25 5244 75 100
Transformer loss
(kWh)
55922 50783 47865 49414 53982
As presented in Table 4-5 the average number of switching operations is increased
as the TCLF is approached to its optimum value
Table 4-5 Average number of switching operations with different TCLF
TCLF () 0 25 5244 75 100
Average number of
switching operations
0 2 4 2 0
452 Test Case 2
The impacts of TOMs and DNR on transformer loss are evaluated in this section As
presented in Fig 4-12 the model of the test system is developed from the
duplication of the generic distribution network shown in Fig 4-5 All the values of
the network parameters are obtained from [104]ndash[106] The system is supplied by
two 3311 kV substations and each bus has four feeders There is one linked feeder
with nine tie-switches Tie-switches refer to the switches of the network that are
normally open The function of the tie-switches is to alter the network topology to
provide various routes for supplying loads In order to feed all loads and keep the
systemrsquos radial topology only one tie-switch is open and all the others are closed
Chapter 4 Transformer Economic Operation amp Distribution Network
Reconfiguration for Transformer Loss Reduction
Page | 86
0
02
04
06
08
1
12
14
16
0 2 4 6 8 10 12 14 16 18 20 22
Act
ive
Po
we
r (k
W)
Time (h)
TW1 TW2 TW3 TW4 TW5
A1
A2
A3
A4_1 A4_2 A4_3 A4_4 A4_5 A4_6 A4_7 A4_8 B4_8 B4_7 B4_6 B4_5 B4_4 B4_3 B4_2 B4_1
B1
B2
B3
EndA EndB
TW9TW8TW7TW6
Tie-Switch (close) Tie-Switch (open)
Fig 4-12 Test system
For simplicity the daily load variations in each feeder are the same and the load
profiles of each node in the linked feeder are also the same Therefore the loads
could be categorised into two groups
Group 1 A1 A2 A3 B1 B2 B3
Group 2 A4_1 A4_2 A4_3 A4_4 A4_5 A4_6 A4_7 A4_8 B4_1 B4_2
B4_3 B4_4 B4_5 B4_6 B4_7 B4_8
On the basis of transformer load factor variation shown in Fig 4-6 the relevant 10-
min resolution load models of the two groups are presented in Fig 4-13 The power
factors of all the loads are set to 095
(a) Group 1
Chapter 4 Transformer Economic Operation amp Distribution Network
Reconfiguration for Transformer Loss Reduction
Page | 87
0
002
004
006
008
01
012
014
016
018
02
0 2 4 6 8 10 12 14 16 18 20 22
Act
ive
Po
we
r (k
W)
Time (h)
(b) Group 2
Fig 4-13 Daily load variations for different load groups
As this test system is developed from the duplication of the generic distribution
network and all the loads have the same profiles the position of the tie-switch is
selected from lsquoTW1rsquo to lsquoTW5rsquo For example the tie-switch located in lsquoTW1rsquo has the
same effect as lsquoTW9rsquo The control strategy is used to quantify the changes in feeder
voltage and transformer loss in the previously described test system under different
scenarios which could be categorised as
Scenario 1 each end has one transformer in operation and the tie-switch is located
at TW1 ie entire feeder supplied from end B
Scenario 2 each end has one transformer in operation and the tie-switch is located
in TW5 ie feeder split at mid-point
Scenario 3 each end has one transformer in operation and the location of the tie-
switch is based on minimum transformer loss operation
Scenario 4 each end has two transformers in operation and the tie-switch is located
at TW1
Scenario 5 each end has two transformers in operation and the tie-switch is located
at TW5
Scenario 6 each end has two transformers in operation and the location of the tie-
switch is based on minimum transformer loss operation
Chapter 4 Transformer Economic Operation amp Distribution Network
Reconfiguration for Transformer Loss Reduction
Page | 88
Scenario 7 each end has onetwo transformers in operation based on the transformer
load factor and the tie-switch is located at TW1
Scenario 8 each end has onetwo transformers in operation based on the transformer
load factor and the tie-switch is located at TW5
Scenario 9 each end has onetwo transformers in operation based on the transformer
load factor and the location of the tie-switch is based on minimum transformer loss
operation
Table 4-6 indicates the mean value of 3311 kV transformer loss during one day
under different scenarios As can be seen from the table when the tie-switches have
the same location TW1 transformer loss in Scenario 7 results in a reduction of
1396 and 1456 in comparison with Scenario 1 and Scenario 4 In conclusion
the mode introducing a flexible number of transformers in operation based on TCLF
reduces the loss In addition the transformer loss in Scenario 9 is 9528 kWh per day
which is 217 and 014 lower than Scenario 7 and Scenario 8 As a result the
variation of tie-switch locations could reduce transformer loss The detailed location
of the tie-switch in Scenario 9 is included in Appendix B1
Table 4-6 Transformer loss in Test Case 2
Scenarios S1 S2 S3 S4 S5 S6 S7 S8 S9
Loss
(kWhday)
11319 10848 10848 11399 11162 11162 9739 9572 9528
The graph presented in Fig 4-14 illustrates the voltage variation caused by the tie-
switch relocation The node voltages in Scenario 1 experience the worst profile
which increases to a peak of 09749 pu from 09675 pu along the linked feeder In
order to reduce the loss the tie-switch is always located in the middle of the feeder
TW5 in Scenario 3 As a result the voltage profiles of Scenario 2 and Scenario 3 are
the same It should be noted that Scenario 2 experiences a slight drop from 09787 pu
to 0972 pu and then climbs back to 09827 pu It can also be clearly seen that the
voltage reaches the lowest value where the tie-switch is located The further away
the nodes are from the tie-switch the better the voltage profiles that can be obtained
In addition when the tie-switch moves closer to the middle of the linked feeder the
Chapter 4 Transformer Economic Operation amp Distribution Network
Reconfiguration for Transformer Loss Reduction
Page | 89
096
0962
0964
0966
0968
097
0972
0974
0976
0978
098
A4_1A4_2A4_3A4_4A4_5A4_6A4_7A4_8B4_8B4_7B4_6B4_5B4_4B4_3B4_2B4_1
Vo
ltag
e (
pu
)
Scenario1
Scenario2
Scenario3
0955
096
0965
097
0975
098
0985
099
A4_1A4_2A4_3A4_4A4_5A4_6A4_7A4_8B4_8B4_7B4_6B4_5B4_4B4_3B4_2B4_1
Vo
ltag
e (
pu
)
Scenario1
Scenario4
Scenario7
voltage performance is improved And the detailed voltage values at each node in the
linked feeder for different scenarios are presented in Appendix B1
Fig 4-14 Mean voltage profiles in S1 S2 and S3
As shown in Fig 4-15 the voltage variation is due to a change in TOMs
Fig 4-15 Mean voltage profiles in S1 S4 and S7
As in the case of the tie-switch located in lsquoTW1rsquo all the node voltages experience a
rise along the linked feeder from lsquoEndArsquo to lsquoEndBrsquo It should be noted that the node
voltages in Scenario 4 achieve the best profile which increase to a peak of 0984 pu
from 0976 pu As discussed in Test Case 1 the transformers in parallel operation
could improve the voltage profiles In addition the flexible number of transformers
Chapter 4 Transformer Economic Operation amp Distribution Network
Reconfiguration for Transformer Loss Reduction
Page | 90
in operation based on TCLF (Scenario 7) shows a slight difference in voltage from
that in Scenario 4
As discussed above the location of the tie-switch and the change of TOMs have an
impact on the feeder voltage variation The tie-switch located in the middle of the
feeder and transformers with parallel operation defines the best voltage profiles
46 Summary
This chapter illustrates why transformer economic operation (TEO) is an economical
solution to reduce transformer loss The substation composed of two transformers
with the same characteristics has been used as an example to introduce the general
approach of determining the TCLF and TEO area A Monte Carlo simulation
platform was established to tackle load uncertainties A methodology to prove that
the TOM variation affects the performance of the 11kV distribution network is
discussed and analysed The TEO mode with minimum loss and satisfactory voltages
is achieved depending on the the transformer load factors by operating with either
one or two transformers and can be summarised as when the transformer load factor
is less than the TCLF transformers should be in separate operation when the
transformer load factor is higher than the TCLF transformers are recommended to
operate in parallel This results in a reduction of 1441 over the conventional
transformer loss ie when two transformers are in parallel operation However
simulation studies also indicate voltage profiles are improved when transformers
operate in parallel Therefore a slight reduction in TCLF results in an increased loss
but an improvement in voltage performance
The effectiveness of a DNR strategy has also been proposed through the results
obtained The presented results illustrate the impact of different TOMs in each
substation and tie-switch statuses on transformer loss and the voltages measured
along the feeder during a 24 hour operating period The optimal economic operation
strategy with TEO and DNR have successfully reduced the transformer loss and
improved the voltage profiles The further away the nodes are from the tie-switch
the better the voltage profiles obtained In addition when the tie-switch moves closer
to the middle of the linked feeder the voltage performance is improved
Chapter 4 Transformer Economic Operation amp Distribution Network
Reconfiguration for Transformer Loss Reduction
Page | 91
In normal operating conditions transformers operate in parallel and the tie-switch is
located in the middle of the linked feeder As indicated by Table 46 the daily
energy loss in Scenario 5 is 11162 kWh After the introduction of Scenario 9 the
annual saving energy could be 59641 kWh
Page | 92
CHAPTER 5
DISTRIBUTION NETWORK
RECONFIGURATION amp DG ALLOCATION
FOR FEEDER LOSS REDUCTION
51 Introduction
Distribution networks generally operate in radial configuration to ease protection
coordination and to reduce short circuit current [107] Distribution feeders can be
reconfigured to alter the network topology at normal and abnormal operating
conditions by changing the openclose status of switches to satisfy the operatorrsquos
objectives [13] [14]
DG is a small electric generation unit that is connected directly to the distribution
network or appears on side of the meter accessed by the customer [16] With the
increasing number of DGs bidirectional power flows have appeared and locally
looped networks have become inevitable [17] Therefore the type size and location
of DGs in the distribution networks strongly affect power system operation and
planning
The studies in [5] indicate that about 5 of the total power generation is wasted in
the form of feeder loss at the distribution level Reduction in active power loss can
help distribution network operators (DNOs) save costs and increase profits The
Chapter 5 Distribution Network Reconfiguration amp DG Allocation for Feeder Loss
Reduction
Page | 93
optimal distribution network reconfiguration (DNR) placement and sizing of DGs
strategies should be used to reduce feeder loss while satisfying the operating
constraints
The ant colony optimisation (ACO) developed by M Dorigo is a metaheuristic
algorithm for the assessment of optimisation problems [94] It is based on the
pheromones deposited by ants as a guide for finding the shortest path between a food
source and their home colony The detailed description of ACO algorithm has been
presented in Section 33 In this chapter an ACO algorithm is proposed to solve the
network reconfiguration and DG placement problems simultaneously based on
distribution feeder loss minimisation The proposed technique is tested on two
standard IEEE 33-node and 69-node systems and the simulation results show the
performance and effectiveness of the proposed method Four scenarios are
considered during network reconfiguration and DG allocation The impacts of DG
capacity on assessing the DNR and DG allocation problems in terms of feeder loss
reduction are also studied Moreover the results obtained by ACO algorithm have
been compared to those from other algorithms in the literature
As for the remainder of this chapter the mathematical formulation of the objective
function and its constraints are explained in Section 52 Section 53 discusses the
application of ACO algorithms in order to solve the problem Section 54 provides a
detailed analysis of the numerical results and Section 55 provides the final
conclusions
52 Problem Formulation
The proposed objective function (F) of the problem is formulated to minimise the
feeder loss of a distribution network which is described as follows
119872119894119899119894119898119894119904119890 119891 = sum 119896119894119877119894(119875119894
2+1198761198942
1198801198942 )
119873119887119894=1 (5-1)
where 119877119894 is the resistance of the ith branch 119875119894 and 119876119894 are the real power (W) and
reactive power (VAr) at the receiving end of branch i 119880119894 represents the rms voltage
at the receiving end of branch i (V) 119896119894 is a binary variable 119896119894 = 0 indicates that
Chapter 5 Distribution Network Reconfiguration amp DG Allocation for Feeder Loss
Reduction
Page | 94
branch 119894 is open and 119896119894 = 1 indicates that branch 119894 is closed The detailed feeder loss
assessment has been given in Section 28
Subject to
∆119881119899 le ∆119881119898119886119909 for all load points (5-2)
119868119887 le 119868119898119886119909 for all branches (5-3)
119875119894 le 119875119894119898119886119909 (5-4)
det(119860) = 1 119900119903 minus 1 (5-5)
Constraints (5-2) ndash (5-3) represent the computed voltages and currents and should be
in their permissible range Constraint (5-4) indicates that the power flow at all
branches should be within the limits defined for each branch Constraint (5-5)
ensures the radial topology of the network [32] The branch to node incidence matrix
Arsquo has one row for each branch and one column for each node 119886119894119895 represents the
coefficient in row i and column j 119886119894119895 = 0 if branch i is not connected with node j
119886119894119895 = 1 if branch i is directed away from node j and 119886119894119895 = minus1 if branch i is directed
towards node j When the column corresponding to the reference node and the rows
of open branches are deleted from matrix Arsquo a new square branch-to-node matrix A
is obtained Then the determinant of A is calculated If det(A) is 1 or -1 the system is
radial Otherwise the system is not radial
53 Solution Method
531 Distribution Network Reconfiguration
With regard to the DNR problem each solution is represented by a string of integers
which indicates the location of tie-switches As the number of tie-switches that keep
the network radial is always constant the number of the solutionrsquos elements is equal
to the number of tie-switches in the network
Chapter 5 Distribution Network Reconfiguration amp DG Allocation for Feeder Loss
Reduction
Page | 95
Home
1 2 NP1NP1-1
1 2 NP1-1 NP1
1 2 NP1NP1-1
1 2 NP2-1 NP2
1 2 NP2NP2-1
1 2 NP2-1 NP2
1 2 NP2NP2-1
1 2 NP2-1 NP2
Food
Stage
1
2
NT-1
NT
NT+1
NT+2
NT+NDG-1
NT+NDG
Part 1 Number of
existing tie-switches
Part 2 Number
of DGs
532 Applying ACO to DNR and DGs Placement
In this chapter an ACO algorithm is adopted to find the optimum locations of tie-
switches and sites of DGs placement in the network in terms of feeder loss
minimisation When the locations of tie-switches and DGs are changed a new
network configuration will be formed For each network configuration the feeder
loss is evaluated by using the approach presented in Section 52
Fig 5-1 Search space of DNR and DGs Placement
Chapter 5 Distribution Network Reconfiguration amp DG Allocation for Feeder Loss
Reduction
Page | 96
The search space of the DNR and DG allocation problems is modelled as a directed
graph as shown in Fig 5-1 In Part I the states signify the location of tie switches
and the sites for DGs installation are represented by states in Part II The number of
stages in this graph is the sum of the amount of existing tie-switches 119873119905 and the
number of installed DGs 119873119863119866 1198731199011is the number of possible locations for the tie-
switches relocation and 1198731199012 is the number of candidate buses for DGs installation
Artificial ants start their tours at home moving along the paths in the graph and end
at the food source Each location list consists of a string of integers and represents a
solution to the problem Different orders of the solutionrsquos elements indicate different
routes However several routes might indicate a certain solution as the order of the
solutionrsquos elements makes no difference to the network configuration For example
the solution vector (1 2 3) represents the same network configuration as the solution
vector (3 2 1) And the objective functions of these two routes are the same In this
study the first route that the ants found will be chosen as the feasible solution The
flowchart of the proposed ACO algorithm is presented in Fig 5-2 and is expressed in
five steps
Step 1 Initialisation First of all all the ants are initially located at home The
pheromone values of the edges in the search space are all set to a small positive
constant value
Step 2 Ant Dispatch All the ants are sent in parallel from the home colony and one
of the states is chosen in the next stage according to a probabilistic selection rule
which involves the intensity of pheromones deposited on the states [66] The
locations of the tie-switches are determined first and the sites for the DGs
installation are then selected The probability of an ant choosing state j of the next
stage y is
119875119895119910(119873) =
120591119895119910
(119873)
sum 120591119895119910
(119873)ℎisin∆119910
(5-6)
where 120591119895119910
(119873) is the pheromone value of state j of stage y at iteration N ∆119910 is the set
of available states which an ant can choose at stage y
Chapter 5 Distribution Network Reconfiguration amp DG Allocation for Feeder Loss
Reduction
Page | 97
Step 3 Objective Function Evaluation After all the ants have completed their tour
the location list and corresponding objective function in (5-1) for each ant are
evaluated If any constraint in (5-2) - (5-5) is violated the corresponding solution is
assigned with a huge value and is discarded If not all the objective functions are
assessed and the best configuration of the Nth iteration with minimum objective
function 119891119887119890119904119905(119873) is recorded This should be compared to the best configuration
obtained so far 119891119887119890119904119905 if 119891119887119890119904119905(119873) lt 119891119887119890119904119905 the best solution should be updated such
that 119891119887119890119904119905 = 119891119887119890119904119905(119873) [14] If not the best configuration found in the previous
iteration is retained After this the location list is emptied and all the ants are free to
choose a new trail
Step 4 Pheromone Updating The aim of this step is to favour transitions towards
states involving high quality solutions with greater pheromones There are two rules
of pheromone updating the local rule and global rule
Local rule The amount of pheromone deposited in the search space should be
evaporated to make paths less attractive The local pheromone update rule is
calculated as following
120591119895119910
(119873) = (1 minus 120588)120591119895119910
(119873 minus 1) + 120591119888 (5-7)
where 120588 is the pheromone evaporation rate which is set between 0 and 1 120591119888 is a
small positive constant value Even if the amount of pheromone deposited on an
edge is at the lowest value of 120591119888 there is a slight chance that an ant will still choose
this edge
Global rule The global pheromone updating rule involves ants depositing large
amounts of pheromone to the edges that belong to the highest quality solution per
iteration This rule is to guide the search to find the global optimal solution The
pheromones of those edges can be modified by
120591119895119910(119873) = 120591119895
119910(119873) + 120588119891119887119890119904119905
119891119887119890119904119905(119873) (5-8)
After applying the local and global pheromone updating rules the method Max-Min
ACO algorithm is integrated into the proposed approach
120591119895119910(119873) = 120591119898119886119909 119894119891 120591119895
119910(119873) ge 120591119898119886119909 (5-9)
120591119895119910(119873) = 120591119898119894119899 119894119891 120591119895
119910(119873) le 120591119898119894119899 (5-10)
Chapter 5 Distribution Network Reconfiguration amp DG Allocation for Feeder Loss
Reduction
Page | 98
Start
Set Iteration n=1
Maximum iteration
reached
Output best
configuration and end
No
Yes
Initialise the parameters for ACO algorithm
searching space and build graph of the tours
Dispatch ants based on the
amount of pheromones on edges
Relocate tie-switches and DGs by location lists
Calculate the objective function for each ant
The pheromones are updated according
to local and global rules
n=n+1
Record the best solution so far and empty
all location lists
Read system topology
and load data
where 120591119898119886119909and 120591119898119894119899 are the higher and lower bound of the pheromone level on each
edge respectively The trail limit of the pheromone ensures the probabilities of all
the edges are greater than zero which maintains the diversity of the solutions and
avoids premature convergence for local minima
Step 5 Termination The computation continues until the predefined maximum
number iterations is reached The best tour selected among all iterations implies the
optimal solution
Fig 5-2 Flowchart of the ACO applied to DNR and DGs placement
Chapter 5 Distribution Network Reconfiguration amp DG Allocation for Feeder Loss
Reduction
Page | 99
54 Application Studies
To demonstrate the performance and effectiveness of the proposed technique in
assessing the network reconfiguration and placement of DG problems
simultaneously the proposed ACO is implemented on two 1266 kV test systems
consisting of 33 and 69 buses The network models are built in OpenDSS and the
solution algorithm is developed in MATLAB For both test systems the substation
voltage is assumed to be 10 pu and all the branches and buses are considered as
candidate locations for tie-switches and DG placement respectively In this study
for simplicity the number of installed DGs is three All the DGs are synchronous
generators and are represented as PQ models with a 100 kVA capability and a
power factor equal to 10 For the purpose of better illustration and comparison four
cases are considered to analyse the superiority and performance of the proposed
method
Case I System is without reconfiguration and has no DGs (base case)
Case II System is optimally reconfigured and has no DGs
Case III System is optimally reconfigured after DGs are placed at certain buses
Case IV System is optimally reconfigured and DGs are optimally placed
simultaneously
It is to be noted that the ACO control parameters are different for each test case
They are set experimentally using information from several trial runs The final
combinations that provide the best results for all of the above tests are given in
Appendix C1
541 33-bus System
In this section the proposed procedure is implemented on a 33-bus 1266 kV radial
distribution system with 37 branches and 5 tie-switches whose single-line diagram
is shown in Fig 5-3 The tie-switches are located at L33 to L37 represented by red
dotted lines The data of line and load are taken from [108] and summarised in
Appendix A2 The total real and reactive power loads of the system are 3715 kW
and 2300 kVAr respectively The performance of the presented method for the four
Chapter 5 Distribution Network Reconfiguration amp DG Allocation for Feeder Loss
Reduction
Page | 100
10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
18 19 20 21
22 23 24
25 26 27 28 29 30 31 32
L1 L2 L3 L4 L5 L6 L7 L8 L9 L10 L11 L12 L13 L14 L15 L16 L17
L18
L19 L20 L21
L22
L23 L24
L25
L26 L27 L28 L29 L30 L31 L32
L33
L34
L35
L36
L37
cases is given in Table 5-1 The network losses in each branch for all test cases are
listed in Appendix B2
Fig 5-3 33-bus system
Table 5-1 Results of different cases for the 33-bus system
Case Active feeder
loss (kW)
Minimum voltage
(pu)
(Bus No)
Location of tie-switches
on Fig 53
DG location
Case I 20314 09116 (B17) L33 L34 L35 L36 L37 NA
Case II 13981 09361 (B31) L7 L9 L14 L32 L37 NA
Case III 11753 09357 (B31) L7 L9 L14 L28 L31 B17 B21 B24
Case IV 10844 09462 (B32) L7 L9 L14 L32 L37 B30 B31 B31
Case I base case
For the base case without reconfiguration and DGs the initial active feeder loss of
this system is 20314 kW The lowest bus voltage is 09116 pu and this occurs at
Bus 17
Case II with reconfiguration only (no DGs)
In this case only reconfiguration is considered and no DGs are installed The
network configuration after DNR is shown in Fig 5-4 The number of the solutionrsquos
elements for this case is 5 which is the number of tie-switches After DNR the total
feeder loss is 13981 kW which corresponds to a 3118 reduction in loss In
addition the minimum voltage also increases from 09116 pu to 09361 pu
Chapter 5 Distribution Network Reconfiguration amp DG Allocation for Feeder Loss
Reduction
Page | 101
10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
18 19 20 21
22 23 24
25 26 27 28 29 30 31 32
L1 L2 L3 L4 L5 L6 L7 L8 L9 L10 L11 L12 L13 L14 L15 L16 L17
L18
L19 L20 L21
L22
L23 L24
L25
L26 L27 L28 L29 L30 L31 L32
L33
L34
L35
L36
L37
Fig 5-4 33-bus system for feeder loss minimisation Case II
To illustrate the performance of the proposed ACO the results are compared with
the results obtained using the branch exchange method (BEM) [109] harmony
search algorithm (HSA) [110] fireworks algorithm (FWA) [16] particle swarm
optimisation (PSO) [55] and invasive weed optimisation (IWO) [111] these are all
described in the literature and are presented in Table 5-2 It is observed that the
results obtained from the ACO are identical to those from the HAS PSO and IWO
but better than the results from the BEM and FWA This is because that BEM and
FWA have plunged into a local optimal solution and they lack the ability to escape
from it
Table 5-2 Comparison of simulation results for 33-bus system in Case II
Method Feeder loss
(kW)
Loss reduction
()
Tie-switches location Minimum
voltage (pu)
The proposed ACO 13981 3118 L7 L9 L14 L32 L37 09361
BEM [109] 14054 3082 L7 L10 L14 L32 L37 09361
HSA [110] 13981 3118 L7 L9 L14 L32 L37 09361
FWA [16] 14026 3095 L7 L9 L14 L28 L32 09396
PSO [55] 13981 3118 L7 L9 L14 L32 L37 09361
IWO [111] 13981 3118 L7 L9 L14 L32 L37 09361
Moreover both the continuous genetic algorithm (CGA) [112] and cuckoo search
algorithm (CSA) [113] are implemented to further investigate the performance of the
proposed ACO It is important to note that the performance of the ACO CGA and
CSA depends on the selection of their control parameters All three algorithms are
solved 100 times The average maximum minimum and standard deviation of the
100 runs are compared and shown in Table 5-3 The convergence number is defined
Chapter 5 Distribution Network Reconfiguration amp DG Allocation for Feeder Loss
Reduction
Page | 102
10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
18 19 20 21
22 23 24
25 26 27 28 29 30 31 32
L1 L2 L3 L4 L5 L6 L7 L8 L9 L10 L11 L12 L13 L14 L15 L16 L17
L18
L19 L20 L21
L22
L23 L24
L25
L26 L27 L28 L29 L30 L31 L32
L33
L34
L35
L36
L37
DG2
DG1
DG3
as the number of the iterations when the objective function is convergence It can be
seen that all three algorithms have obtained the same minimum loss However the
proposed ACO method has a higher probability in finding the global optimum
solution as the mean and standard deviation of the fitness values of the ACO
algorithm are less than those obtained by the other algorithms Furthermore as the
average value of convergence number of the ACO is less than that of the other two
algorithms this means the proposed algorithm has a higher convergence rate In
terms of the computation times the proposed ACO runs faster when compared with
CGA and CSA
Table 5-3 Comparison of ACO with CGA and CSA for the 33-bus system in Case II
Method Feeder loss (kW) Convergence number Average
computation
times
(second)
AVG MAX MIN STD AVG STD
ACO 13981 13981 13981 0 228 821 1448
CGA [112] 14002 14619 13981 12121 5463 2986 3926
CSA [113] 13986 14028 13981 01328 8363 3425 7258
AVG MAX MIN and STD mean the average maximum minimum and standard deviation of the 100 runs
Case III with reconfiguration only (with DGs)
In this case the three DGs are located at the end of the feeders ie Bus 17 21 24
The network configuration after DNR is illustrated in Fig 5-5 As shown in Table 5-
1 the network reconfiguration results in a reduction of 4214 in feeder loss in
comparison with the original network without DGs and a reduction of 1594 in
comparison with the reconfigured system without DGs
Fig 5-5 33-bus system for feeder loss minimisation Case III
Chapter 5 Distribution Network Reconfiguration amp DG Allocation for Feeder Loss
Reduction
Page | 103
10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
18 19 20 21
22 23 24
25 26 27 28 29 30 31 32
L1 L2 L3 L4 L5 L6 L7 L8 L9 L10 L11 L12 L13 L14 L15 L16 L17
L18
L19 L20 L21
L22
L23 L24
L25
L26 L27 L28 L29 L30 L31 L32
L33
L34
L35
L36
L37
DG2DG1
DG3
Case IV with reconfiguration and DG allocation
Fig 5-6 illustrates the optimal network configuration and DG locations The network
is reconfigured and DGs are allocated simultaneously in this case Therefore the
number of the solutionrsquos elements for this case becomes 8 which is the sum of the
number of tie-switches and DGs The results show the final configuration with a
feeder loss of 10844 kW with 4662 2244 and 773 reduction in comparison
with that in Case I Case II and Case III respectively
Fig 5-6 33-bus system for feeder loss minimisation Case IV
In this case the impacts of DG capacity on assessing the DNR and DG allocation
problems in terms of feeder loss reduction are also studied The capacity of each DG
is set as 100 400 700 and 1000 kVA respectively The feeder losses for different
DG capacities are shown in Fig 5-7 Before simultaneous reconfiguration and DG
allocation the feeder loss decreases from 1783 kW to 1023 kW when the capacity
of DG is increased from 100 kVA to 700 kVA However the feeder loss increases to
1042 kW if the capacity of DG continuously grows to 1000 kVA The inappropriate
network configuration and DG location might result in loss increment when the size
of the DG is increased However with the introduction of network reconfiguration
and DG allocation feeder loss is reduced no matter what the capacity of DG is This
proves that the proposed methodology can reduce the total feeder loss by
determining the most suitable network topology and DG locations in comparison
with the original configuration
Chapter 5 Distribution Network Reconfiguration amp DG Allocation for Feeder Loss
Reduction
Page | 104
086
088
09
092
094
096
098
1
102
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32
Vo
ltag
e (
pu
)
Bus No
Case I
Case II
Case III
Case IV
0
20
40
60
80
100
120
140
160
180
200
100 400 700 1000
Fee
de
r lo
ss (
kW)
DG Capacity (kVA)
Before simultaneousreconfiguration and DG allocation
After simultaneous reconfigurationand DG allocation
Fig 5-7 Comparison of feeder loss for different DG capacities before and after simultaneous
reconfiguration and DG allocation
The voltage profiles of four cases are compared and shown in Fig 5-8 It can be seen
that the voltage profiles at most buses in Case IV have been improved in comparison
with the other three cases In terms of Case III and Case IV the buses which inject
DGs show the improvement in voltage profiles ie the voltage of Bus 31 is
improved from 09357 pu in Case III to 09537 pu in Case IV In Case IV as Bus 32
is the furthest bus being supplied its voltage is the lowest value among all buses In
conclusion the systemrsquos voltage profiles are improved by optimal DNR and DG
allocation
Fig 5-8 Comparison of voltage profiles in different cases of 33-node system
Chapter 5 Distribution Network Reconfiguration amp DG Allocation for Feeder Loss
Reduction
Page | 105
10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
27
28
29
30
31 32 33 34
35
36
37
38 39 40 41 42 43 44 45
46 47 48 49
50
51
52
53 54 55 56 57 58 59 60 61 62 63 64
65 66
67 68
L1 L2 L3 L4 L5 L6 L7 L8 L9 L10 L11 L12 L13 L14 L15 L16 L17 L18 L19 L20 L21 L22 L23 L24 L25 L26
L27
L28
L29
L30
L31 L32 L33 L34
L35
L36
L37
L38 L39 L40 L41 L42 L43 L44 L45
L46
L47 L48 L49
L50
L51
L52
L53 L54 L55 L56 L57 L58 L59 L60 L61 L62 L63 L64
L65
L66
L67
L68
L69
L70
L71
L72L73
542 69-bus System
This is a large-scale radial distribution system consisting of 73 branches and 5 tie-
switches whose single-line diagram is shown in Fig 5-9 The tie-switches are
located at L69 to L73 represented by red dotted lines The line and load data of the
system are taken from [84] and summarised in Appendix A3 The total power loads
are 379589 kW and 26891 kVAr respectively Similar to 33-bus system this
system is also simulated for four cases and the results are given in Table 5-4 The
network losses in each branch for all test cases are listed in Appendix B2
Fig 5-9 69-bus system
Table 5-4 Results of different cases for the 69-bus system
Case Active feeder
loss (kW)
Minimum voltage
(pu)
(Bus No)
Tie-switches location DG location
Case I 22562 09072 (B64) L69 L70 L71 L72 L73 NA
Case II 9885 09476 (B60) L14 L55 L61 L71 L72 NA
Case III 8758 09477 (B60) L13 L55 L61 L71 L72 B26 B45 B64
Case IV 7397 09571 (B60) L14 L55 L61 L71 L72 B60 B60 B60
Case I base case
Base case active feeder loss in the system is 22562 kW The lowest bus voltage is
09072 pu and occurs at bus 64
Chapter 5 Distribution Network Reconfiguration amp DG Allocation for Feeder Loss
Reduction
Page | 106
10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
27
28
29
30
31 32 33 34
35
36
37
38 39 40 41 42 43 44 45
46 47 48 49
50
51
52
53 54 55 56 57 58 59 60 61 62 63 64
65 66
67 68
L1 L2 L3 L4 L5 L6 L7 L8 L9 L10 L11 L12 L13 L14 L15 L16 L17 L18 L19 L20 L21 L22 L23 L24 L25 L26
L27
L28
L29
L30
L31 L32 L33 L34
L35
L36
L37
L38 L39 L40 L41 L42 L43 L44 L45
L46
L47 L48 L49
L50
L51
L52
L53 L54 L55 L56 L57 L58 L59 L60 L61 L62 L63 L64
L65
L66
L67
L68
L69
L70
L71
L72L73
Case II with reconfiguration only (no DGs)
After DNR switches at L14 L55 L61 L71 and L72 are opened as shown in Fig 5-
10 The total feeder loss is reduced by 5619 and the minimum voltage is
increased to 09476 pu in comparison with the base case
Fig 5-10 69-bus system for feeder loss minimisation Case II
The comparisons of results among the proposed ACO with FWA [16] HSA [110]
and genetic algorithm (GA) [110] are presented in Table 5-5 It is observed that the
results obtained from the ACO are better than those from the FWA HSA and GA
as these algorithms are trapped into the local optimal solution
Table 5-5 Comparison of simulation results for 69-bus system in Case II
Method Feeder loss
(kW)
Loss reduction
()
Tie-switches location Minimum
voltage (pu)
The proposed ACO 9885 5619 L14 L55 L61 L71 L72 09476
FWA [16] 9886 5618 L14 L56 L61 L71 L72 09476
HSA [110] 10546 5326 L13 L18 L56 L61 L72 09475
GA [110] 10242 5461 L14 L53 L61 L71 L72 09462
Case III with reconfiguration only (with DGs)
In this case the three DGs are located at the end of the feeders ie Bus 26 45 64
The network configuration after DNR is illustrated in Fig 5-11 As shown in Table
Chapter 5 Distribution Network Reconfiguration amp DG Allocation for Feeder Loss
Reduction
Page | 107
10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
27
28
29
30
31 32 33 34
35
36
37
38 39 40 41 42 43 44 45
46 47 48 49
50
51
52
53 54 55 56 57 58 59 60 61 62 63 64
65 66
67 68
L1 L2 L3 L4 L5 L6 L7 L8 L9 L10 L11 L12 L13 L14 L15 L16 L17 L18 L19 L20 L21 L22 L23 L24 L25 L26
L27
L28
L29
L30
L31 L32 L33 L34
L35
L36
L37
L38 L39 L40 L41 L42 L43 L44 L45
L46
L47 L48 L49
L50
L51
L52
L53 L54 L55 L56 L57 L58 L59 L60 L61 L62 L63 L64
L65
L66
L67
L68
L69
L70
L71
L72L73
DG3
DG1
DG2
10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
27
28
29
30
31 32 33 34
35
36
37
38 39 40 41 42 43 44 45
46 47 48 49
50
51
52
53 54 55 56 57 58 59 60 61 62 63 64
65 66
67 68
L1 L2 L3 L4 L5 L6 L7 L8 L9 L10 L11 L12 L13 L14 L15 L16 L17 L18 L19 L20 L21 L22 L23 L24 L25 L26
L27
L28
L29
L30
L31 L32 L33 L34
L35
L36
L37
L38 L39 L40 L41 L42 L43 L44 L45
L46
L47 L48 L49
L50
L51
L52
L53 L54 L55 L56 L57 L58 L59 L60 L61 L62 L63 L64
L65
L66
L67
L68
L69
L70
L71
L72L73
DG3DG1
DG2
5-5 the network reconfiguration results in a reduction of 6118 in feeder losses as
compared with the original network without DGs and a reduction of 1140 in
comparison with the reconfigured system without DGs
Fig 5-11 69-bus system for feeder loss minimisation Case III
Case IV with reconfiguration and DG allocation
Fig 5-12 illustrates the optimal network configuration and DG locations In this case
the results show the final configuration with a feeder loss of 7397 kW with 6721
2517 and 1554 reduction in comparison with that in Case I Case II and Case
III respectively
Fig 5-12 69-bus system for feeder loss minimisation Case IV
Chapter 5 Distribution Network Reconfiguration amp DG Allocation for Feeder Loss
Reduction
Page | 108
0
50
100
150
200
250
100 400 700 1000
Fee
de
r lo
ss (
kW)
DG Capacity (kVA)
Before simultaneousreconfiguration and DG allocation
After simultaneous reconfigurationand DG allocation
In this case the impacts of DG capacity on assessing the DNR and DG allocation
problems in terms of feeder loss reduction are also studied The capacity of each DG
is set as 100 500 900 and 1300 kVA respectively The feeder loss curves for
different DG capacities are shown in Fig 5-13 After simultaneous reconfiguration
and DG allocation the feeder loss decreases from 7397 kW to 873 kW when the
DG capacity is increased from 100 kVA to 900 kVA However the loss bounces
back to 114 kW if the DG capacity continues to increase to 1300 kVA This means
that the capability of network reconfiguration and DG allocation on feeder loss
reduction is limited when the size of DGs is large But the proposed methodology
can still reduce the total feeder loss for all DG capacities by determining the most
suitable network topology and DG locations in comparison with the original
configuration
Fig 5-13 Comparison of feeder loss for different DG capacities before and after simultaneous
reconfiguration and DG allocation
Fig 5-14 shows the voltage profile of the 69-bus system It can be seen that the
voltage profiles at most buses in Case IV have been improved in comparison with
the other three cases Compared with Case III and Case IV the buses which inject
DGs show improvement in voltage profiles ie the voltage of Bus 60 is improved
from 09477 pu in Case III to 09571 pu in Case IV In Case IV although there are
three DGs connected as Bus 60 as the value of load connected at this bus is the
largest (1244 kW) this bus voltage is the lowest among all buses In conclusion the
systemrsquos voltage profiles are improved by optimal DNR and DG allocation
Chapter 5 Distribution Network Reconfiguration amp DG Allocation for Feeder Loss
Reduction
Page | 109
086
088
09
092
094
096
098
1
102
0 5 10 15 20 25 30 35 40 45 50 55 60 65
Vo
ltag
e (
pu
)
Bus No
Case I
Case II
Case III
Case IV
Fig 5-14 Comparison of voltage profiles in different cases of 69-node system
55 Summary
In this chapter the application of optimal planning using DNR and DG allocation for
the problem of distribution feeder loss minimisation has been implemented The
method based on ACO has been successfully applied to the 1266 kV 33-bus and 69-
bus systems to find the optimum system configuration and DG locations
There are four cases used to analyse the superiority and performance of the proposed
method The proposed ACO is capable of finding the optimal solutions in all cases
In Case IV the feeder losses are reduced by 4662 and 6721 for the 33-bus and
69-bus system respectively in comparison with the base case Therefore Case IV is
found to be more effective in minimising the total loss and improving voltage
profiles compared to the other cases The numerical results show that for best
performance the existing tie-switches are relocated and the DGs are optimally
placed in comparison with the original network In addition the impacts of DG
capacity on assessing the DNR and DG allocation problems in terms of feeder loss
reduction are also studied The inappropriate network configuration and DG location
might result in loss increment when the size of DG is increased The proposed
methodology has successfully reduced the total feeder loss for different capacities of
DG by determining the most suitable network topology and the DG locations
Chapter 5 Distribution Network Reconfiguration amp DG Allocation for Feeder Loss
Reduction
Page | 110
compared to the original configuration The minimum loss obtained by DNR and DG
allocation decreases as the capacities of DGs are increased However this decrease
stops when DGs can supply all the loads without the main supply After that the
minimum loss increases as the capacities of DGs are increased
Moreover the simulation results have been compared with other classical methods in
literature and the proposed ACO is more efficient and is more likely to obtain the
global optimum solution
Page | 111
CHAPTER 6
DISTRIBUTION NETWORK
RECONFIGURATION amp TRANSFORMER
ECONOMIC OPERATION FOR NETWORK
LOSS REDUCTION
61 Introduction
Rapid increases in electricity demand have forced electric power utilities throughout
the world into major reconstructing processes As a significant proportion of electric
energy is dissipated in the operation of a distribution network the reduction of loss
should be considered an important problem for the economic operation of the overall
system [82]
Load variations have been disregarded in most studies on distribution automation
(DA) problems ie average loads were used in their reconfiguration schemes In this
chapter distribution loads experience daily and seasonal variations The study
considers the daily load curves of different types of consumers (residential
commercial and industrial) and in addition the days are divided into eight types
spring weekdays spring weekends summer weekdays summer weekends autumn
Chapter 6 Distribution Network Reconfiguration amp Transformer Economic
Operation for Network Loss Reduction
Page | 112
weekdays autumn weekends winter weekdays and winter weekends The best
reconfiguration hours during each of these typical days are then selected
The objective function for finding the best configuration of the network when
considering feeder loss and transformer loss will be studied in this chapter Different
combinations of locations of tie-switches in the network and operation modes of all
transformers in the substations represent different network configurations An Ant
colony optimisation (ACO) algorithm is adopted on an 11 kV distribution network
developed from Bus 4 of the Roy Billinton Test System (RBTS) to determine the
optimal network configuration during each type of day Furthermore the effects of
DGs and EVs in solving distribution network reconfiguration (DNR) and
transformer economic operation (TEO) based on network loss reduction are also
investigated
This chapter is organised as follows the next section discusses the variation of loads
and the reconfiguration hours Section 63 presents the objective function and
constraints for DNR Section 64 describes the application of ACO algorithms to the
problem Numerical studies are presented and discussed in Section 65 and finally
Section 66 summarises the main conclusions
62 Time-varying Load Model
As distribution loads experience daily and seasonal variations the optimum network
configuration constantly changes [82] However it is not reasonable to reconfigure a
network frequently ie based on hourly schedule since each switch has a maximum
number of allowable switching operations during its lifetime and frequent switching
actions will increase its maintenance costs [82]
However infrequent actions cause the system to work well below its optimum state
In order to determine the best reconfiguration time during a day the daily load
profiles should be smoothed In other words the daily load curves are divided into a
number of periods As the maintenance cost of a switch increases with the increasing
number of switching actions the number of intervals is a trade-off between the
optimum reconfiguration and switch cost As there is a peak and a valley of network
Chapter 6 Distribution Network Reconfiguration amp Transformer Economic
Operation for Network Loss Reduction
Page | 113
Actual daily load curve
Smoothed daily load curve
load variations during a day it is appropriate to divide the 24 hours daily load curves
into two periods Increasing the number of intervals will not change the nature of the
problem but will increase its complexity
Fig 6-1 The reconfiguration hours for a typical day
As the difference between 1198751 and 1198752 is increased the effect of DNR on loss
reduction increases where 1198751 and 1198752 are the average active power of the loads
during the first and second time periods respectively As shown in Fig 6-1 hours
1199051and 1199052 are calculated to maximise |1198751 minus 1198752| It should also be noted that the above
load smoothing methodology is only used to determine the reconfiguration intervals
and the active power loss during each interval is calculated based on the actual daily
load curve [82]
63 Problem Formulation
In this study the 24 hours of a typical day is divided into two periods The first time
period is 0000 to 1199051 and 1199052 to 2400 and the second time period is between 1199051 and 1199052
The following objective function is calculated for all possible network configurations
during each time interval and the one that minimises the total power loss and
satisfies all constraints is selected The energy losses of the distribution network over
the first and second time interval are presented in (6-1) and (6-2) the objective
function (6-3) is to minimise f the sum of f1 and f2
P1
P2
1199051 1199052 Time (h)
Chapter 6 Distribution Network Reconfiguration amp Transformer Economic
Operation for Network Loss Reduction
Page | 114
1198911 = sum (119864119871119905 + 119879119871119905)1199051minus1119905=1 + sum (119864119871119905 + 119879119871119905) 1199051
24119905=1199052 isin 1 2 hellip 24 (6-1)
1198912 = sum (119864119871119905 + 119879119871119905)1199052minus1119905=1199051 1199052 isin 1 2 hellip 24 (6-2)
Min 119891 = 1198911 + 1198912 (6-3)
where 119864119871119905 is the feeder loss of the distribution network during hour t (kWh) 119879119871119905
represents the transformer loss during hour t (kWh) The detailed calculation of
transformer loss and feeder loss are presented in Section 27 and 28 respectively
The computed voltages currents and the power flow at all branches should be kept
in their permissible range and the network should be operated in radial The
configurations that violate any constraint are assigned with huge objective functions
and are disregarded
64 Applying ACO to DNR and TEO
In this chapter the objective of simultaneous reconfiguring network and changing
transformer operation modes is to deal with energy loss minimisation including
transformer loss and feeder loss To implement the optimisation problem the
developed ACO algorithm is adopted to find the optimum location of tie-switches
and transformer operation modes in the network When the location of tie-switches
and operation modes of transformers are changed a new network configuration will
be formed For each network configuration the objective function is evaluated by
using the approach presented in Section 63
The search space of the DNR and TEO problems is modelled as a directed graph as
shown in Fig 6-2 Each solution is represented by a string of integers which
indicates the transformer operation modes and the location of tie-switches The
number of the solutionrsquos elements is equal to the number of stages in this graph
which is the sum of the amount of main feeders (the number of transformer pairs 119873119904)
and the number of existing tie-switches 119873119905
Chapter 6 Distribution Network Reconfiguration amp Transformer Economic
Operation for Network Loss Reduction
Page | 115
Home
0 1
0 1
0 1
0 1
1 2 NPNP-1
1 2 NP-1 NP
1 2 NPNP-1
1 2 NP-1 NP
Food
Stage
1
2
Ns-1
Ns
Ns+1
Ns+2
Ns+Nt-1
Ns+Nt
Part 1
Number of
substations
Ns
Part 2 Number
of existing tie-
switches Nt
Number of candidate locations for the tie-switches NP
Fig 6-2 Search space of DNR and TEO
As shown in Fig 6-3 the number of transformer pairs is 3 and the number of
existing tie-switches is 4 Therefore the number of the solutionrsquos elements for this
system is 7 In addition the possible branches for tie-switch placement are 4
Chapter 6 Distribution Network Reconfiguration amp Transformer Economic
Operation for Network Loss Reduction
Page | 116
Tie-switch
Transformer
Fig 6-3 Sample network with three substations
For transformer operation mode selection in Part I the ACO algorithm is applied to
assign each bit of the front part of the solution vector to the status of substations and
hence the number of transformers in operation in each substation can be represented
as a binary vector
State 0 this substation has one transformer in operation
State 1 this substation has two transformers in operation
However for the relocation of existing tie-switches in Part II the states indicate the
location of switches Artificial ants will start their tours at home move along the
paths in the graph and end at the food source
The 24 hour load curve is divided into two time intervals for all load types in terms
of the principle presented in Section 62 Fig 6-4 demonstrates the computation
procedure for the transformer operation mode selection and tie-switches relocation
problem at each of the time interval The application of the ACO algorithm to the
TEO and DNR problem is similar to that in Section 532 For each time interval the
operation modes of the transformers are selected first and the locations of tie-
switches are then determined
Chapter 6 Distribution Network Reconfiguration amp Transformer Economic
Operation for Network Loss Reduction
Page | 117
Start
Set time interval T=1
Maximum iteration
reached
Output best
configuration and end
No
Yes
Divide the 24-h daily load curve into two
intervals using the technique in Section 62
Iteration N=1
Initialise the parameters for ACO
algorithm searching space
Dispatch ants based on the amount
of pheromone on edges
Relocate tie-switches and select the
number of transformers to be operated in
all substations by location lists
N=N+1
Calculate the objective function
for each ant at this time interval
Read system topology
and load data
The pheromones are updates
according to local and global rules
Record the best solution so far
and empty all location lists
T=T+1
Tgt2
Yes
t=t+1
No
Fig 6-4 Flowchart of the ACO applied to DNR and TEO for a specific type of day
Chapter 6 Distribution Network Reconfiguration amp Transformer Economic
Operation for Network Loss Reduction
Page | 118
LP11 LP12 LP13 LP14 LP15 LP16 LP17
LP8 LP9 LP10
LP1 LP2 LP3 LP4 LP5 LP6 LP7
LP32 LP33 LP34 LP35 LP36 LP37 LP38
LP29 LP30 LP31
LP26 LP27 LP28
LP18 LP19 LP20 LP21 LP22 LP23 LP24 LP25
19
20
21
22
23
24
26
25 27
28
29 30
71
13 15
14 16
17
18
69
1 3
2
5
4
7
6 8
10
9
68
11 12
56
57
58 60
59 61 62
65
64 66 67
50 52
51
54
53 55
44
45
46
47
48
49
70
31
32
33
34
36
35
39
37 38 40
41
42 43
63
F3
F2
F1
F7
F6
F5
F4
Normally Open Circuit BreakerNormally Closed Circuit Breaker
Subbus1
Subbus2
Subbus3
T1
T3
T5
Main
feeder
Main
feeder
Main
feeder
T2
T4
T6
65 Application Studies
In this study the proposed methodology is applied to an 11 kV distribution network
developed from Bus 4 of the RBTS a single-line diagram of the network is shown in
Fig 6-5 The network consists of 38 load points and 4 tie-switches the associated
data can be found in [114] The types and lengths of 11 kV feeders are listed in
Appendix A4 The network built in OpenDSS incorporates three 3311 kV double
transformer substations supplying the downstream loads
Fig 6-5 Distribution feeder connected to RBTS Bus 4
This typical urban distribution network supplies residential commercial and
industrial consumers The maximum value of active and reactive power and the
Chapter 6 Distribution Network Reconfiguration amp Transformer Economic
Operation for Network Loss Reduction
Page | 119
customer type of each node are modified from the original values and the new values
are listed in Table 6-1
Table 6-1 Revised customer data (peak load)
Number
of load
points
Load points Customer type P
(kW)
Q
(kVAr)
Number of
customers
4 1-2 9-10 residential 8869 8426 220
6 3-5 13-15 residential 8137 7731 200
12 6-7 16-17 23-25 28
30-31 37-38
commercial 6714 6378 10
6 8 11 18 26 32-33 industrial 2445 23228 1
10 12 19-22 27 29 34-
36
industrial 1630 15485 1
The days of the year are divided into eight categories spring weekdays spring
weekends summer weekdays summer weekends autumn weekdays autumn
weekends winter weekdays and winter weekends Typical loads profiles for
different consumer types are shown in Fig 6-6-6-8 which are multiplied by the
values of Table 6-1 to obtain the real demand of each node [82] In order to find the
reconfiguration hours for each day type the aggregated load profiles of the main
feeder shown in Fig 6-9 are used
Fig 6-6 Daily load profile of residential consumers
Chapter 6 Distribution Network Reconfiguration amp Transformer Economic
Operation for Network Loss Reduction
Page | 120
Fig 6-7 Daily load profile of commercial consumers
Fig 6-8 Daily load profile of industrial consumers
Fig 6-9 Daily load profile (MW) of the main feeder
Chapter 6 Distribution Network Reconfiguration amp Transformer Economic
Operation for Network Loss Reduction
Page | 121
In this case eight types of day and two time intervals for each of them are
considered As a result the optimisation problem has to be solved 16 times to obtain
a yearly reconfiguration scheme The distribution of load types for a whole year is
shown in Table 6-2
Table 6-2 The distribution of load types for a whole year
Load Types Number of days Total days
Spring
(Mar Apr May)
Weekdays 66 92
Weekends 26
Summer
(Jun Jul Aug)
Weekdays 66 92
Weekends 26
Autumn
(Sep Oct Nov)
Weekdays 65 91
Weekends 26
Winter
(Dec Jan Feb)
Weekdays 64 90
Weekends 26
Year 365 Days
For the purpose of better illustration and comparison three test cases are considered
to analyse the superiority and performance of the proposed method
Test Case 1 The system is optimally reconfigured and has no DGs and EVs
Test Case 2 The system is optimally reconfigured after DGs are placed at certain
buses
Test Case 3 The system is optimally reconfigured after integration of EVs
The proposed ACO algorithm is coded in the MATLAB to obtain the location of tie-
switches and operation modes of transformers for the optimum configuration The
settings of the ACO parameters that provided the optimum solution for these three
cases are presented in Appendix C2 The selection of parameters is a balance
between the convergence rate and the global search ability of the algorithm
Chapter 6 Distribution Network Reconfiguration amp Transformer Economic
Operation for Network Loss Reduction
Page | 122
651 Test Case 1
In this test the tie-switches are relocated and the operation modes of transformers in
all substations are changed to obtain the best network configuration with minimum
network loss
Table 6-3 Results of DNR and TEO with different load types in Test Case 1
As shown in Fig 6-5 the tie-switches are located in L68-71 and each substation has
two transformers operating in parallel for the base network configuration The test
results with different load conditions are presented in Table 6-3 Reconfiguration of
the network and changes in the operation modes of transformers in all substations
using the proposed algorithm result in a reduction of loss for all load conditions As
a result the annual energy loss is reduced from 4337150 kWh to 4117681 kWh
which amounts to a 506 reduction Both transformer loss and feeder loss are
reduced through this optimal planning using DNR and TEO It can be noted that on
winter weekdays the loading of the main feeders is very high from 800 to 2100
Spring
weekday
Spring
weekend
Summer
weekday
Summer
weekend
Autumn
weekday
Autumn
weekend
Winter
weekday
Winter
weekend
Before
Reconfiguration
Whole Day Open branches L68L69
L70L71
L68L69
L70L71
L68L69
L70L71
L68L69
L70L71
L68L69
L70L71
L68L69
L70L71
L68L69
L70L71
L68L69
L70L71
Number of operated
transformers
1st substation 2 2 2 2 2 2 2 2
2nd substation 2 2 2 2 2 2 2 2
3rd substation 2 2 2 2 2 2 2 2
Loss
(kWh)
Cable 9233 3498 8050 3151 9660 3665 11009 4080
Transformer 4301 3410 4109 3350 4372 3437 4597 3507
Total 13534 6908 12159 6501 14032 7102 15606 7587
After
Reconfiguration
1st interval Time (h) 0-7
23-24
0-6 0-7
23
0-7 0-7
22-23
0-6
0-7
22-23
0-6
Open branches L48L68
L69L71
L68L69
L70L71
L17L68
L70L71
L17L68
L70L71
L17L68
L70L71
L68L69
L70L71
L17L68
L70L71
L68L69
L70L71
Number of operated
transformers
1st substation 1 1 1 1 1 1 1 1
2nd substation 1 1 1 1 1 1 1 1
3rd substation 1 1 1 1 1 1 1 1
2nd interval Time (h) 8-22 7-23 8-22 8-23 8-21 7-23 8-21 7-23
Open branches L17L41
L65L70
L68L69
L70L71
L41L48
L65L69
L68L69
L70L71
L17L41
L65L70
L68L69
L70L71
L17L41
L65L70
L68L69
L70L71
Number of operated
transformers
1st substation 2 2 2 2 2 2 2 2
2nd substation 2 1 2 1 2 1 2 1
3rd substation 2 1 2 1 2 1 2 1
Loss
(kWh)
Cable 9043 3516 7851 3169 9519 3685 10845 4103
Transformer 3955 2616 3759 2517 4036 2656 4264 2755
Total 12998 6132 11610 5686 13479 6341 15109 6858
Chapter 6 Distribution Network Reconfiguration amp Transformer Economic
Operation for Network Loss Reduction
Page | 123
0
05
1
15
2
25
3
35
4
45
05 1 15 2 25 3
Before reconfiguration
After reconfiguration
Thus transformers in all substations are operated in parallel However during spring
weekends from 000 to 700 as the loadings supplied by all feeders are lower than
the critical transformer load factor (TCLF) and hence transformers in all substations
are operated in single In addition the loadings supplied by Feeder 4 are much larger
than that of Feeder 3 in summer weekdays between 800 to 2200 Thus the tie-
switch is moved from L71 to L41 and LP24amp25 are moved from Feeder 4 to Feeder
3 This ensures balancing of the loads between the two feeders
652 Test Case 2
In this test the presence of three DG units is taken into consideration The effect of
DGs on assessing the DNR and TEO problems in terms of loss minimisation is
studied The introduction of DGs converts a mono-source distribution network to a
multi-source one [66] The three DGs are located at the end of the feeders ie Bus
17 41 and 65 All the DGs are synchronous generators and considered as PQ models
The capacity of DG is assumed to be 05 1 15 2 25 and 3 MVA respectively
The results are shown in Fig 6-10 and show that the proposed methodology has
successfully reduced the total energy loss for different capacities of DG by
determining the most suitable network topology
Fig 6-10 Annual energy loss with different DG capacities
To
tal
loss
(G
Wh
)
DG Capacity (MW)
Chapter 6 Distribution Network Reconfiguration amp Transformer Economic
Operation for Network Loss Reduction
Page | 124
653 Test Case 3
The objective of this section is to illustrate the behaviour of the proposed
optimisation process when EVs are integrated into the existing distribution network
The impacts of EV penetration levels and charging strategies are studied This
section utilises the optimal planning using DNR and TEO as a technique to decrease
network loss whilst respecting the operation constraints It is assumed that the
battery starts charging once the EV is connected to the charger at home
The charging duration can be calculated according to the following formula [89]
119905119888 =119862119864119881times(1minus119878119874119862)times119863119874119863
120578times119875119862 (6-4)
where 119862119864119881 is the battery capacity In this section EVs are divided into four types
with different market shares and batteries as in Table 6-4 [115] 119863119874119863 and 120578 are
depth of discharge and charger efficiency (assumed to be 80 and 90 separately)
Two types of chargers with different charging rates (119875119862) are commonly used for
consumer EVs at home charging points this study assumes that 80 of EVs are
charged at 3kW (13A) and 20 at 7kW (30A) [92] SOC is state-of-charge and is
defined as the ratio of available energy to maximum battery capacity [89] It is
determined by the distance covered by the EV in terms of number of miles during
the day
Table 6-4 Characteristics of EV
Types 119862119864119881 (kWh) Maximum driving
capability (mile)
Market share ()
Micro car 12 50 20
Economy car 14 53 30
Mid-size car 18 56 30
Light truck SUV 23 60 20
According to [116] the average number of miles covered by a vehicle was reported
to be 2164 milesday in 2014 Then the SOC for an EV is calculated based on
number of miles (m) and the maximum driving capability (MDC) as follows
Chapter 6 Distribution Network Reconfiguration amp Transformer Economic
Operation for Network Loss Reduction
Page | 125
4
42
44
46
48
5
30 60 90
Before reconfiguration
After reconfiguration
119878119874119862 = 0 119898 gt 119872119863119862
119872119863119862minus119898
119872119863119862 119898 le 119872119863119862 (6-5)
As mentioned before the EVs are distributed over all the residential load points The
number of customers of residential loads is given in Table 6-1 It is reported that
each customer has 15 vehicles [92] The problem is solved for three different
penetration levels of EVs in the test network 30 60 and 90 respectively In
addition two charging strategies are introduced (1) uncoordinated charging and (2)
coordinated charging The thermal problems of cables which caused by high
penetration levels of EVs are ignored in this study
1) Uncoordinated Charging Strategy
In this part all EVs are plugged in and immediately start charging when they arrive
home In most cases the EV plug-in time is modelled by normal distribution which
increases uncertainty However in order to simplify the discussion the charging start
time is assumed to be 1800 when most people are back home from work The total
losses in the network for the different penetration levels of EVs are compared in Fig
6-11 It can be seen that as the penetration of EVs is increased the total loss also
increases But the total loss for all penetration levels decreases by implementing the
optimal planning strategy in comparison with the original network
Fig 6-11 Annual energy loss in uncoordinated charging strategy
To
tal
loss
(G
Wh
)
Penetration level ()
Chapter 6 Distribution Network Reconfiguration amp Transformer Economic
Operation for Network Loss Reduction
Page | 126
4
42
44
46
48
5
30 60 90
Before reconfiguration
After reconfiguration
2) Coordinated Charging Strategy
In this case the DNOs tend to charge the EVs during off-peak hours to avoid a clash
with the evening peak hours As a result the charging start time is delayed to 0100
when most people are sleeping The total network loss for different EV penetrations
is compared in Fig 6-12 The results show that the postponement of charging time
and optimal planning strategy has been successful in reducing the total energy loss in
comparison with the uncoordinated charging method
Fig 6-12 Annual energy loss in coordinated charging strategy
66 Summary
This study has presented a new optimal planning strategy using DNR and TEO for
distribution network loss minimisation including transformer loss and feeder loss In
this study the distribution loads experience daily and seasonal variations The day is
divided into two periods The proposed ACO algorithm has been successfully
applied to the modified Bus 4 of the RBTS to find the optimum network
configuration and economic operation mode of transformers in all substations during
each time interval Using the results obtained for reconfiguration the existing tie-
switches are relocated and the transformer operation modes are changed
Furthermore the simulation results obtained with numerical studies further
demonstrate the capability of applying the ACO algorithm to distribution network
planning including networks with DGs and EVs The proposed methodology has
successfully reduced the total network loss for different capacities of DG and
To
tal
loss
(G
Wh
)
Penetration level ()
Chapter 6 Distribution Network Reconfiguration amp Transformer Economic
Operation for Network Loss Reduction
Page | 127
different penetration levels of EVs by determining the most suitable network
topology compared to the original configuration The benefits associated with the
increasing capacity of DGs and increasing penetration levels of EVs are also
presented Comparative results show that coordinated charging of EVs results in less
energy loss compared to uncoordinated charging plan with the same EV penetration
level This is due to the postponement of charging time which avoids a clash with
the peak power demand times
The proposed ACO algorithm is suitable for planning a future network based on the
load estimation results Hence there is no limitation on the calculation time An
additional interesting point about DNR and TEO is that although the opening and
closing of switches and transformers result in the life reduction of plants the
additional costs for utilities is insignificant in comparison with the benefits they
bring All the results have proved that a distribution network can be reconfigured and
the operation modes of transformers can be changed to reduce network power loss
which can increase the profits of the distribution utilities
Page | 128
CHAPTER 7
OPTIMAL PLACEMENT OF
SECTIONALISING SWITCHES FOR
RELIABILITY IMPROVEMENT
71 Introduction
Failures in the distribution network cause the majority of service interruptions [78]
And reliability improvement becomes a motivation for distribution utilities to launch
research and demonstration projects [64] An effective method to reduce customer
minutes lost is the greater and more effective use of automated and remote controlled
sectionalising switches and feeder breaker automation This approach will reduce
customer restoration time and minimise the region of a network affected by a short-
circuit fault The effectiveness depends on the number location and type of
sectionalising switches and feeder breakers
Reliability improvement by reduction of expected customer damaged cost (ECOST)
and system interruption duration index (SAIDI) as well as the minimisation of
switch costs are considered in formulating the objective function used in this study
When there are multiple objectives to be considered a compromise solution has to
be made to obtain the best solution ECOST and switch costs can be converted into a
single objective function by aggregating these objectives in a weighted function
Chapter 7 Optimal Placement of Sectionalising Switches for Reliability
Improvement
Page | 129
However as SAIDI and switch costs have different dimensions and units a single
fuzzy satisfaction objective function is used to transform the two conflicting
objectives into fuzzy memberships and then finally to combine them into a single
objective function Also a fuzzy membership function based on the max-min
principle is presented for optimising ECOST SAIDI and switch costs
simultaneously These are achieved by the optimal installation of new switches and
the relocation of existing switches Therefore identifying the number and location of
switches becomes an optimisation problem The ant colony optimisation (ACO) is
adopted which has the ability to find near optimal solutions close to the global
minimum in a finite number of steps This algorithm is proposed for the assessing
the sectionalising switch placement (SSP) problem based on reliability improvement
and switch costs minimisation using a multi-objective function with fuzzy variables
The impact of benefit-to-cost analysis is then investigated to justify investment
expenses Furthermore the importance of the customer damage function (CDF)
variation in determining the SSP is investigated through sensitivity analysis And the
ACO parameter sensitivity analysis is also provided in this study
The mathematical formulation of the objective function is presented in Section 72
and in Section 73 the applied ACO algorithm used to address the problems of SSP
is discussed Section 74 describes the benefit-cost analysis and the numerical case
studies are presented and discussed in Section 75 The main conclusions of the study
are summarised in Section 76
72 Problem Formulation
The primary objective of this study is to resolve the three conflicting objectives
reduction of unserved energy cost decrease in the average time a customer is
interrupted and minimisation of switch costs Three formulations of objective
functions are presented and the solution is a trade-off between each objective
721 Weighted Aggregation
As ECOST and switch costs have the same units and dimensions they are
transformed into a single objective function by aggregating all the objectives in a
weighted function
Chapter 7 Optimal Placement of Sectionalising Switches for Reliability
Improvement
Page | 130
119872119894119899 119869 = micro1 ∙ 119864119862119874119878119879 + micro2 ∙ 119878119862 (7-1)
where ECOST is the system expected outage cost to customers ($) and SC is the cost
of sectionalising switches ($) micro1and micro2 are the weighting factors given to the
reliability index and the cost of switches
722 Single Fuzzy Satisfaction Objective Function with Two
Parameters
SAIDI and switch costs are associated with a membership function in a fuzzy
domain due to different dimensions The satisfaction level of each objective is
represented by the membership function [66] The higher the membership value is
the better the solution is The two objectives are combined into a fuzzy environment
and a final objective function is formulated as follows
119872119886119909 119870 = 1205961 ∙ 120572119878119860 + 1205962 ∙ 120572119878119862 (7-2)
where 120572119878119860 is the membership function value to distribution reliability improvement
by SAIDI reduction 120572119878119862 is the value of membership function for a decrease in the
switch costs 1205961and 1205962 are the constant weighting factors for each of the parameters
The optimisation process can be changed for different purposes by varying the
values of weighting factors which should satisfy the condition 1205961 + 1205962 = 1 A
higher weighting factor indicates that this parameter is more important [66] In the
fuzzy domain each objective has a membership value varying from zero to unity
[66] The proposed membership function for each objective is described below
Membership function for SAIDI reduction
The basic purpose of this membership function is to improve reliability or obtain the
minimum SAIDI Therefore the placement of sectionalising switches with a lower
SAIDI value obtains a higher membership value The membership function for
reliability improvement is formulated in (7-3) and presented in Fig 7-1 (a) As
SAIDI becomes greater than 119878119860119868119863119868119898119894119899 the degree of satisfaction is decreased This
reduction is continued until SAIDI reaches 119878119860119868119863119868119900119903119894
Chapter 7 Optimal Placement of Sectionalising Switches for Reliability
Improvement
Page | 131
0
1
0
1
120572119878119860 =
1 119878119860119868119863119868 le 119878119860119868119863119868119898119894119899119878119860119868119863119868119900119903119894minus119878119860119868119863119868
119878119860119868119863119868119900119903119894minus119878119860119868119863119868119898119894119899119878119860119868119863119868119898119894119899 lt 119878119860119868119863119868 lt 119878119860119868119863119868119900119903119894
0 119878119860119868119863119868 ge 119878119860119868119863119868119900119903119894
(7-3)
where 119878119860119868119863119868119900119903119894 is the SAIDI of the original network 119878119860119868119863119868119898119894119899 is the minimum
value of SAIDI which is obtained by placing sectionalising switches in all candidate
locations As it is not appropriate for decision makers to obtain a combination of
sectionalising switches which reduces reliability after switch placement the
minimum value of 120572119878119860 is selected as 0 if SAIDI is greater than or equal to 119878119860119868119863119868119900119903119894
(a) SAIDI reduction (b) SC reduction
Fig 7-1 Membership function for SAIDI and switch cost reduction
Membership function for switch cost reduction
The membership function for switch costs reduction is shown in Fig 7-1(b) The
mathematical equation is presented below
120572119878119862 =
1 119878119862 le 119878119862119900119903119894119878119862119898119886119909minus119878119862
119878119862119898119886119909minus119878119862119900119903119894119878119862119900119903119894 lt 119878119862 lt 119878119862119898119886119909
0 119878119862 ge 119878119862119898119886119909
(7-4)
where 119878119862119900119903119894 and 119878119862119898119886119909 are the original and maximum value of switch costs
respectively The maximum switch costs are obtained by installing sectionalising
switches in all candidate sites
723 Single Fuzzy Satisfaction Objective Function with Three
Parameters
When there are more than two objectives with different dimensions and units to be
satisfied simultaneously a single fuzzy satisfaction objective function based on the
120572119878119860
119878119860119868119863119868119898119894119899 119878119860119868119863119868119900119903119894 119878119860119868119863119868
120572119878119862
119878119862119900119903119894 119878119862119898119886119909 119878119862
Chapter 7 Optimal Placement of Sectionalising Switches for Reliability
Improvement
Page | 132
0
1
max-min principle is considered The three conflicting objectives to be optimised are
ECOST SAIDI and switch costs The membership functions for SAIDI and switch
costs are presented in the previous section The function for ECOST is shown in Fig
7-2 and expressed as
120572119864119862 =
1 119864119862119874119878119879 le 119864119862119874119878119879119898119894119899119864119862119874119878119879119900119903119894minus119864119862119874119878119879
119864119862119874119878119879119900119903119894minus119864119862119874119878119879119898119894119899119864119862119874119878119879119898119894119899 lt 119864119862119874119878119879 lt 119864119862119874119878119879119900119903119894
0 119864119862119874119878119879 ge 119864119862119874119878119879119900119903119894
(7-5)
where 119864119862119874119878119879119900119903119894 and 119864119862119874119878119879119898119894119899 are the original and minimum value of ECOST
respectively The minimum ECOST is obtained by installing sectionalising switches
in all candidate locations
Fig 7-2 Membership function for ECOST reduction
The degree of overall satisfaction for these objective functions is the minimum value
of all the membership functions [85] The fuzzy decision for a final compromised
solution is the maximum degree of overall satisfaction and is formulated in (7-6)
Max 119871 = min (120572119878119860 120572119878119862 120572119864119862) (7-6)
724 Evaluation of ECOST
ECOST is an index that combines reliability with economics The best way to
present customer interruption costs is in the form of CDF A CDF provides the
interruption cost versus interruption duration for a various class of customers and
can be aggregated to produce a composite CDF at any particular load point [67] [69]
Generally ECOST is used to represent the customer outage costs since it not only
considers the effects of the system configuration interruption durations load
variations and equipment failure probability but also accounts for the various
customer types and their damage functions [52]
120572119864119862
119864119862119874119878119879119898119894119899 119864119862119874119878119879119900119903119894 119864119862119874119878119879
Chapter 7 Optimal Placement of Sectionalising Switches for Reliability
Improvement
Page | 133
The calculation of ECOST of the total system over T years is based on failure-mode-
and-effect analysis (FMEA) and can be quantified as follows
1 ( 1)
1 1 1 1 1 1
( ) ( ) ( ) ( ) (1 ) (1 )b b b b bN CT NR CT NST
t t
b b k R k s
t b k j k j
ECOST L P k j C d P k j C d IR DR
(7-7)
where T is time period (year) 119873119887 is the total number of branches 120582119887and 119871119887 are the
average failure rate (failurekm-year) and length (km) of branch b 119862119879119887 119873119877119887 and
119873119878119887 are the total number of customer types permanent damaged and temporary
damaged load points when the fault is at branch b P(k j) is the average load of the
kth-type customers at the jth load point (kW) 119862119896(119889) is the CDF for kth-type
customer lasting d hours ($kW) 119889119877 and 119889119878 are the average repair time and the
switch time after failure IR and DR are the annual load increase rate and discount
rate
725 Evaluation of SAIDI
The SAIDI which represents the average outage duration time of each customer
over T years can be expressed as
119878119860119868119863119868 = sum sum 120582119887∙119871119887[sum 119889119877
119873119862119877(119887)119899=1 +sum 119889119878
119873119862119878(119887)119899=1 ]
119873119887119887=1
119873119862119905119900119905119886119897119879
119905=1 (7-8)
where 119873119862119877(119887) and 119873119862119878(119887) are the number of permanent damaged and temporary
damaged customers when the fault is at branch b 119873119862119905119900119905119886119897 is the total number of
served customers SAIDI is measured in hours
726 Evaluation of Switch Costs
In this study reliability is improved by the installation of new sectionalising
switches and relocation of existing switches Thus the total cost of switches can be
determined as following
119878119862 = 119862119868119878 ∙ 119873119899119890119908 + 119862119877119878 ∙ 119873119903119890119897 + sum 119872119862119879119905=1 ∙ (119873119899119890119908 + 119873119890119909119894119904) ∙ (1 + 119863119877)minus(119905minus1) (7-9)
where CIS is the investment and installation cost of a new sectionalising switch ($)
119873119899119890119908 119873119903119890119897 and 119873119890119909119894119904 are the number of newly installed relocated and existing
sectionalising switches respectively CRS is the relocation cost of an existing
Chapter 7 Optimal Placement of Sectionalising Switches for Reliability
Improvement
Page | 134
Home
0
1
0
1
0
1
0
1
Food
Number of candidate locations for sectionalising switches
sectionalising switch ($) and MC is the maintenance and operation cost of a
sectionalising switch ($)
73 Applying ACO to Sectionalising Switch Placement
Problem
This study uses ACO algorithm for distribution automation in terms of the
installation of new sectionalising switches and relocation of existing switches When
the locations of sectionalising switches are changed a new network configuration
will be formed The search method is used for finding the optimal value of objective
functions as presented in Section 721-723
The search space of the automation problem in terms of SSP is modelled as a
directed graph as shown in Fig 7-3 The number of stages is the candidate locations
for all the sectionalising switches 119873119878 For this problem the switch status can be
represented as a binary vector in each stage State 0 ldquono sectionalising switch in this
locationrdquo State 1 is ldquoa sectionalising switch in this locationrdquo The artificial ant
searches for the values of the bits and produces a solution to the problem after it
completes a tour between the home and food source which is similar to the process
described in Section 532
Fig 7-3 Search space of sectionalising switch placement
Chapter 7 Optimal Placement of Sectionalising Switches for Reliability
Improvement
Page | 135
74 Benefit-to-cost Analysis
The benefit-to-cost analysis is a financial term that describes the expected balance of
benefits made from the investment and costs incurred during the production process
It helps predict if an investmentdecision is feasible and whether its benefits
outweigh the costs during a predefined time interval [82]
In this study the benefit-to-cost ratio (BCR) offers a comparison between ECOST
and SC The benefit to the distribution network operator (DNO) is the reduction of
ECOST which is equal to
119887119890119899119890119891119894119905 = sum119864119862119874119878119879119887119886119904119890
119905 minus119864119862119874119878119879119900119901119905119905
(1+119863119877)119905119879119905=1 (7-10)
where 119864119862119874119878119879119887119886119904119890119905 and 119864119862119874119878119879119900119901119905
119905 are the value of ECOST of year t before and after
the placement of switches ($)DR is the annual discount rate
The cost for the DNO is the total switching cost including investment maintenance
and operation cost as presented in (7-9) and BCR is defined as
119861119862119877 =119887119890119899119890119891119894119905
119878119862 (7-11)
A higher value for BCR indicates that the benefits relative to the costs are greater
The investment return time refers to the time when BCR starts to exceed 10 If the
investment return time is less than the lifetime of a switch adding a switch will bring
benefits to the investors
Chapter 7 Optimal Placement of Sectionalising Switches for Reliability
Improvement
Page | 136
LP11 LP12 LP13 LP14 LP15 LP16 LP17
LP8 LP9 LP10
LP1 LP2 LP3 LP4 LP5 LP6 LP7
LP32 LP33 LP34 LP35 LP36 LP37 LP38
LP29 LP30 LP31
LP26 LP27 LP28
LP18 LP19 LP20 LP21 LP22 LP23 LP24 LP25
9 10 11 12 13 33
6 7 8 31
1 2 3 4 5 30
25 26 27 29
22 23 24
19 20 21
32
14 15 16 17 18
28
F3
F2
F1
F7
F6
F5
F4
Normally Open Circuit BreakerNormally Closed Circuit Breaker
Subbus1
Subbus2
Subbus3
T1
T3
T5
Main
feeder
Main
feeder
Main
feeder
T2
T4
T6
75 Application Studies
In this study the proposed methodology is applied to an 11 kV distribution network
developed from Bus 4 of the Roy Billinton Test System (RBTS) The single-line
diagram of the network with 6 existing sectionalising switches is shown in Fig 7-4
Fig 7-4 Distribution feeder connected to RBTS Bus 4 with 6 sectionalising switches
In this study there are 51 locations considered as candidates for switch placement
[114] All the values of the required data ie feeder type and length as well as
component failure rate are available in [114] and summarised in Appendix A4 The
failure rate of the feeders is proportional to their physical length and all other
Chapter 7 Optimal Placement of Sectionalising Switches for Reliability
Improvement
Page | 137
components ie transformers buses and breakers are assumed to be completely
reliable This typical urban distribution network supplies residential commercial and
industrial consumers The average value of active power and the customer type of
each node were also found in [114] and listed in Table 7-1 The power factors of all
the loads are set to 10
Table 7-1 Customer data (Average load)
Number
of load
points
Load points Customer type P
(kW)
Number of
customers
15 1-4 11-13 18-21 32-35 residential 545 220
7 5 14 15 22 23 36 37 residential 500 200
7 8 10 26-30 industrial 1000 1
2 9 31 industrial 1500 1
7 6 7 16 17 24 25 38 commercial 415 10
The relocation cost of a sectionalising switch is US $ 500 The investment and
installation cost of a sectionalising switch is US $ 4700 [64] The annual
maintenance and operation cost is considered to be 2 of the investment cost [64]
All the sectionalising switches and circuit breakers are remotely controlled The
costs of the feeder terminal unit which is used for data acquisition of the switch
status and communication equipment have also been added to the automated
sectionalising switches The overall switching time of sectionalising switch and
circuit breakers for temporary damage load points in other words the time between
the occurrence of a fault and the restoration of energy to unaffected areas is set to 10
minutes [64] And the average repair time of the permanent faulty section is assumed
to be 5 hours The lifetime of a switch depends on various factors such as the
maximum number of allowable switching operations the number of annual
switching operations of the switch etc Based on these factors the life period of the
switches is calculated to be 15 years The load growth rate and the annual interest
rate are set to 3 and 8 respectively The CDF data are extracted from [64] and
summarised in Table 7-2
Chapter 7 Optimal Placement of Sectionalising Switches for Reliability
Improvement
Page | 138
Table 7-2 Sector interruption cost estimation ($kW)
User Sector Interruption Duration
10 min 1 hour 2 hour 4 hour 5 hour 10 hour
Residential 006 11 16 26 316 5
Industrial 288 806 95 124 1387 276
Commercial 205 96 125 185 2151 6306
The proposed ACO algorithm was coded in the MATLAB to obtain the location of
the sectionalising switches In this study three cases with different objective
functions are considered to analyse the superiority and performance of the proposed
method
Test Case 1 Minimisation of ECOST and switch costs
Test Case 2 Minimisation of SAIDI and switch costs
Test Case 3 Minimisation of ECOST SAIDI and switch costs
The final combinations of the ACO control parameters that provide the best results
for all the above tests are given in Appendix C3
751 Test Case 1
In this test the minimisation of ECOST and switch costs are considered in the
formulation of a single objective function this involves aggregating the objective
functions as presented in Section 721 For simplicity both weighting factors micro1
and micro2 are set to 1 ie these two objectives are assumed to be equally important
Three cases are studied as follows
Case 11 Optimal relocation of existing sectionalising switches
Case 12 Optimal installation of new sectionalising switches
Case 13 Optimal installation of new sectionalising switches and relocation of
existing sectionalising switches
Chapter 7 Optimal Placement of Sectionalising Switches for Reliability
Improvement
Page | 139
LP11 LP12 LP13 LP14 LP15 LP16 LP17
LP8 LP9 LP10
LP1 LP2 LP3 LP4 LP5 LP6 LP7
LP32 LP33 LP34 LP35 LP36 LP37 LP38
LP29 LP30 LP31
LP26 LP27 LP28
LP18 LP19 LP20 LP21 LP22 LP23 LP24 LP25
9 10 11 12 13 33
6 7 8 31
1 2 3 4 5 30
25 26 27 29
22 23 24
19 20 21
32
14 15 16 17 18
28
F3
F2
F1
F7
F6
F5
F4
Normally Open Circuit BreakerNormally Closed Circuit Breaker
Subbus1
Subbus2
Subbus3
T1
T3
T5
Main
feeder
Main
feeder
Main
feeder
T2
T4
T6
Case 11 Optimal relocation of existing sectionalising switches
The objective of this case is to investigate the optimum sectionalising switch
relocation problem The optimal locations of sectionalising devices are shown in Fig
7-5 Before relocation the total cost including ECOST operation and maintenance
cost of existing switches over 15 years is US $ 477090 After relocation the total
cost including the addition of relocation cost obtained by the ACO approach is US
$ 343620 which amounts to a reduction of 2798
Fig 7-5 Optimal relocation of sectionalising switches in Test Case 11
Chapter 7 Optimal Placement of Sectionalising Switches for Reliability
Improvement
Page | 140
In comparison with the original configuration 4 switches change their locations The
optimal locations of sectionalising switches and the number and types of loads
adjacent to each switch are presented in Table 7-3 The results indicate that each
feeder attempts to have at least one switch As there are 6 switches and 7 feeders
and the total load level of Feeder 5 is 3000 kW which is the lowest value for all the
feeders no switch is placed on Feeder 5 It should also be noted that the load
density and customer types play an important role in determining the locations of
sectionalising switches For instance the adjacent load of Switch 1 is LP6 and LP7
which has the highest CDF value (commercial load) and relatively high load levels
In addition Switch 2 is placed on 7D whose adjacent load is LP9 and this has the
largest load density
Table 7-3 Results of sectionalising switches relocation in Test Case 11
Switch
No
Feeder Location Total Feeder
Load (kW)
Adjacent Load Adjacent Load Levels (kW) and
Type
1 1 5D 3510 LP6 LP7 415 (commercial) 415 (commercial)
2 2 7D 3500 LP9 1500 (industrial)
3 3 13D 3465 LP16 LP17 415 (commercial) 415 (commercial)
4 4 18D 4010 LP24 LP25 415 (commercial) 415 (commercial)
5 6 23D 3500 LP30 1000 (industrial)
6 7 28D 3595 LP36 500 (commercial)
( Each section has two candidate locations for sectionalising switch placement U means upstream side of the section and D
means downstream side of the section)
Case 12 Optimal installation of new sectionalising switches
In this case the effect of installing new sectionalising switches without relocating
the existing switches is studied As shown in Fig 7-6 there are 11 new
sectionalising switches installed
The detailed results of ECOST capital and installation as well as the operation and
maintenance cost of sectionalising switches over 15 years are shown in Table 7-4
After the installation of sectionalising switches the total system cost is decreased
from US $ 477090 to US $ 286980 ie a reduction of 3984
Chapter 7 Optimal Placement of Sectionalising Switches for Reliability
Improvement
Page | 141
LP11 LP12 LP13 LP14 LP15 LP16 LP17
LP8 LP9 LP10
LP1 LP2 LP3 LP4 LP5 LP6 LP7
LP32 LP33 LP34 LP35 LP36 LP37 LP38
LP29 LP30 LP31
LP26 LP27 LP28
LP18 LP19 LP20 LP21 LP22 LP23 LP24 LP25
9 10 11 12 13 33
6 7 8 31
1 2 3 4 5 30
25 26 27 29
22 23 24
19 20 21
32
14 15 16 17 18
28
F3
F2
F1
F7
F6
F5
F4
Normally Open Circuit BreakerNormally Closed Circuit Breaker
Subbus1
Subbus2
Subbus3
T1
T3
T5
Main
feeder
Main
feeder
Main
feeder
T2
T4
T6
Fig 7-6 Optimal installation of sectionalising switches in Test Case 12
Table 7-4 Results of sectionalising switches installation in Test Case 12
ECOST
($)
Number of
installed
switches
Capital and
installation cost
($)
Maintenance
and operation
cost ($)
Total system
cost ($)
Before switches
installation
472260 0 0 4830 477090
After switches
installation
221610 11 51700 13670 286980
Chapter 7 Optimal Placement of Sectionalising Switches for Reliability
Improvement
Page | 142
LP11 LP12 LP13 LP14 LP15 LP16 LP17
LP8 LP9 LP10
LP1 LP2 LP3 LP4 LP5 LP6 LP7
LP32 LP33 LP34 LP35 LP36 LP37 LP38
LP29 LP30 LP31
LP26 LP27 LP28
LP18 LP19 LP20 LP21 LP22 LP23 LP24 LP25
9 10 11 12 13 33
6 7 8 31
1 2 3 4 5 30
25 26 27 29
22 23 24
19 20 21
32
14 15 16 17 18
28
F3
F2
F1
F7
F6
F5
F4
Normally Open Circuit BreakerNormally Closed Circuit Breaker
Subbus1
Subbus2
Subbus3
T1
T3
T5
Main
feeder
Main
feeder
Main
feeder
T2
T4
T6
Case 13 Optimal relocation and installation of sectionalising switches
A Base case
The main objective of this test is to reduce the total system cost including ECOST
and switch costs by the relocation of existing sectionalising switches and the
installation of new ones The switch locations are presented in Fig 7-7
Fig 7-7 Optimal installation and relocation of sectionalising switches in Test Case 13
In comparison with the original configuration there are 8 new sectionalising
switches installed and 5 existing switches relocated As expected the sectionalising
switches are placed adjacent to the load centres with either the highest load density
Chapter 7 Optimal Placement of Sectionalising Switches for Reliability
Improvement
Page | 143
0
1
2
3
4
5
6
7
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
BC
R
Years
or the highest CDF For example the adjacent load of switch 13D is LP6 and LP7
which has the highest CDF value (commercial loads) In addition switch 7D is
placed adjacent to LP9 which has the largest load density The detailed results for
ECOST and switch costs are shown in Table 7-5 After the installation and relocation
of the switches the total system cost is decreased from US $ 477090 to US
$ 272480 ie a reduction of 4289
Table 7-5 Results of sectionalising switches relocation and installation in Test Case 13
ECOST
($)
Number of
relocated
switches
Relocation
cost ($)
Number of
installed
switches
Capital and
installation
cost ($)
Maintenance
and operation
cost ($)
Total
system
cost ($)
Before switch
placement
472260 0 0 0 0 4830 477090
After switch
placement
221120 5 2500 8 37600 11260 272480
B Benefit-to-Cost analysis
BCR analysis is used to verify the benefits and costs of sectionalising switch
placement for distribution operators The results are presented in Fig 7-8 The
benefits and costs are accumulated during the predefined life period There is no
return on investment for the first year as the BCR for Year 1 is 055 However the
BCR for Year 2 is 108 which means the investors start to get benefits in Year 2 In
addition switch placement proved to be a feasible investment since the BCR is
increased to 620 when the switch achieves its service life 15 years in this study
Fig 7-8 BCR versus years
Chapter 7 Optimal Placement of Sectionalising Switches for Reliability
Improvement
Page | 144
0
20
40
60
80
100
120
140
160
05 1 15 2 25 3 35 4 45 5 55 6 65 7 75 8
Co
st (
th
ou
san
d $
)
CDF multiplier
ECOST
Switch costs
Total costs
C Sensitivity analysis
To demonstrate the impact of changing the values of different parameters on the
corresponding results several sensitivity analysis studies are discussed
CDF variation sensitivity analysis
The main objective of this test is to assess the behaviour of the proposed approach
when the CDF (customer damage function) is varied The CDF is increased from 50
to 800 of its initial value in 50 increments The original value of the CDF
multiplier is 100 The effect of variation in the CDF on the ECOST switching
costs and the total system cost is plotted in Fig 7-9 Switch costs include
sectionalising switch installation relocation operation and maintenance cost The
ECOST and switching costs increase as the CDF is increased However the
difference between ECOST and switching costs is also increased
Fig 7-9 Variation of cost versus change in CDF
Variations of the optimal number of installed sectionalising switches versus the CDF
are presented in Fig 7-10 The optimal number of newly installed switches increases
from 7 to 34 as the CDG multiplier is increased from 05 to 8 This indicates the
network needs to be more automated especially if the consequence of customer
damage becomes more serious However the growth in the optimal number of
sectionalising switches is slowing down As shown in Fig 7-10 when the CDF
multiplier increases above 3 the number of sectionalising switches remains at 32 as
Chapter 7 Optimal Placement of Sectionalising Switches for Reliability
Improvement
Page | 145
0
5
10
15
20
25
30
35
40
05 1 15 2 25 3 35 4 45 5 55 6 65 7 75 8
Nu
mb
er
of
swit
che
s
CDF multiplier
the reduction of ECOST brought by installing a sectionalising switch is small
compared to the increase in switch costs Only when the CDF multiplier reaches 55
does the reduction of ECOST outweigh the installation cost of a switch and hence
acquiring a sectionalising switch is a cost-effective investment This is due to the fact
that the installation of the first sectionalising switch has the largest effect on
reducing the total system cost and the impact of sectionalising switch installation on
ECOST decreases as the network becomes more automated
Fig 7-10 Number of installed sectionalising switches versus change in CDF
ACO parameters sensitivity analysis
The ACO parameter analysis is provided in this section In each test only one
parameter is changed whilst the others remain constant The convergence number is
defined as the number of the iterations when the objective function is convergence
The assessment of the impact of the pheromone evaporation rate ρ on the proposed
algorithm is presented in Table 7-6 The number of ants is 200 and the iteration time
is 400 Parameter ρ is varied from 01 to 06 with an increment of 01 For each ρ the
test is run 100 times Table 7-6 shows the impacts of the ρ variation on the objective
function J It can be seen the evaporation rate ρ has a considerable impact on the
convergence performance of the ACO algorithm When ρ is small the residual
pheromone on the path is dominant and the positive feedback of pheromone is weak
This results in an increment in the stochastic performance and global search ability
Chapter 7 Optimal Placement of Sectionalising Switches for Reliability
Improvement
Page | 146
of the ACO algorithm but a reduction in the convergence rate When ρ is large the
positive feedback of the pheromone is dominant which results in an improvement in
the convergence rate but a reduction in the search ability of the algorithm In other
words the algorithm is more easily trapped into a local optimal solution In summary
the selection of ρ is based on two factors of the algorithm 1) convergence rate 2)
global search ability As shown in the table the best value of ρ for this case is 04
which results in the minimum average value and has a suitable convergence rate
Table 7-6 Impacts of 120588 variation on objective function 119869
120588 Objective function value Average convergence
number Average Maximum Minimum
01 273120 274810 272480 223
02 273400 275960 272480 175
03 273480 274810 272480 132
04 273100 274810 272480 110
05 273550 274810 272480 94
06 273440 274810 272480 81
Table 7-7 presents the impacts of the variation in the number of ants on objective
function J The evaporation rate is 04 and the iteration number is 400 The number
of ants is changed from 100 to 500 with an increment of 100 The greater the
number of ants the more likely the global optimum value is achieved This is due to
the growth in global search capability However the convergence rate decreases To
balance the global search ability and convergence rate the number of ants is set to
400
Table 7-7 Impacts of variation in number of ants on objective function 119869
Number of ants Objective function value Average convergence
number Average Maximum Minimum
100 273865 276120 272480 91
200 273100 274810 272480 110
300 273030 274370 272480 135
400 272820 274230 272480 168
500 273170 274230 272480 245
Chapter 7 Optimal Placement of Sectionalising Switches for Reliability
Improvement
Page | 147
However in this study the proposed approach is used for planning a future network
Thus the computation time is not an issue The number of ants and iteration should
be large enough for the ACO algorithm to find the global optimum solution
752 Test Case 2
The objective of this test is to minimise SAIDI and switch costs by maximising the
fuzzy bi-objective function as presented in Section 722 The results of the
membership values of objectives SAIDI as well as switch costs are listed in Table
7-8 The weighting factors of the system objectives can be changed by the network
operator which make it possible to give preference to one over the other Three
cases are studied in which the weighting factors 1205961and 1205962vary from 01 to 09
As shown in the table as the weighing factor of SAIDI 1205961 is increased more
sectionalising switches are installed and reliability is improved The results show the
algorithm can adapt itself to the variation of the weighting factors For decision
making appropriate weighting factors for each objective are selected and a
compromised switch placement plan is obtained using the proposed approach
Table 7-8 Results of sectionalising switches relocation and installation in Test Case 2
Test Cases 1205961 1205962 120572119878119860 120572119878119862 Objective
Function
SAIDI
(hrscustomer)
Switch costs ($)
Case 21 01 09 04909 09970 09464 1157 68275
Case 22 05 05 08456 09061 08758 556 67378
Case 23 09 01 09384 07761 09221 39936 153950
( Each section has two candidate locations for sectionalising switch placement U means upstream side of the section and D
means downstream side of the section)
753 Test Case 3
In this test the three objective functions of the problem to be optimised are ECOST
SAIDI and switch costs The detailed test results before and after switch placement
are listed in Table 7-9 The placement of sectionalising switches results in a
reduction of 60 in ECOST and 7148 in SAIDI It is observed that the
installation and relocation of sectionalising switches has obtained a compromise
solution of three objectives optimisation
Chapter 7 Optimal Placement of Sectionalising Switches for Reliability
Improvement
Page | 148
Table 7-9 Results of sectionalising switches installation and relocation in Test Case 3
Objective
Function
120572119864119862 120572119878119860 120572119878119862 ECOST
($)
SAIDI
(hrscustomer)
Switch costs
($)
Before
switch
placement
0 0 0 1 472260 1989 4830
After switch
placement
08327 08327 08392 08384 188950 56723 112410
76 Summary
This study has presented an ACO algorithm for assessing the SSP problem in terms
of three conflicting objectives optimisation reduction of unserved energy cost
decrease in the average time that a customer is interrupted and minimisation of
switch costs The proposed model has been successfully applied on Bus 4 of the
RBTS In comparison with the original system the existing sectionalising switches
are relocated and new automatic switches are installed The effectiveness of the
proposed approach has been demonstrated through the results obtained which
indicates switch placement using the ACO algorithm reduces the customer outage
costs and interruption duration times during fault contingencies Furthermore the
importance of the CDF variation in determining the SSP is investigated through
sensitivity analysis The impact of installing sectionalising switches on reducing the
total system costs decreases as the number of sectionalising switches is increased As
the parameters of ACO algorithm affect the performance of the proposed method an
ACO parameter sensitivity analysis is also provided in this study The selection of
pheromone evaporation rate and number of ants is a trade-off between the global
search ability and convergence rate of the algorithm In addition a benefit-to-cost
analysis is implemented and used to prove switch investment is profitable The
procedure is used for system planning and is applied off-line so there is no
limitation in calculation times
The main contribution of this study is the conversion of all the multiple objectives
into a single objective function in two forms weighted aggregation and fuzzy
satisfaction objective function considering ECOST SAIDI and cost of
sectionalising switches simultaneously The selection of each form depends on the
Chapter 7 Optimal Placement of Sectionalising Switches for Reliability
Improvement
Page | 149
number of objectives as well as their units and dimensions Another contribution is
the incorporation of FMEA to evaluate the impact on distribution system reliability
of increased automation
Page | 150
CHAPTER 8
DISTRIBUTION NETWORK
RECONFIGURATION FOR LOSS
REDUCTION amp RELIABILITY
IMPROVEMENT
81 Introduction
Optimal distribution network reconfiguration (DNR) can not only solve a single
objective function such as feeder loss minimisation but can also deal with multiple
objectives The presence of multiple objectives raises the issue of how to consider
them simultaneously [117] In the previous section the multiple objectives are
transformed into a single equation using fuzzy logic based approaches The
optimisation is then formulated either as the weighted sum of the fuzzy membership
functions or with the application of the max-min principle
However the above simple optimisation processes only find a compromise solution
It is no longer acceptable for a system with multiple conflicting objectives if the
distribution network operator (DNO) desires to know all possible optimal solutions
for all the objectives simultaneously [20] Therefore a set of trade-off solutions
using the Pareto optimality concept is now proposed These solutions can be
Chapter 8 Distribution Network Reconfiguration for Loss Reduction amp Reliability
Improvement
Page | 151
compared by using the concept of dominance [88] In this concept a solution is non-
dominated when no other solution exists with better values for all the individual
objectives The Pareto set is the set of all non-dominated solutions and the
corresponding objective values constitute the Pareto front [88] This allows the
DNOs to select the most suitable one for implementation depending on the utilitiesrsquo
priorities Pareto analysis is suitable for addressing problems whose conflicting
solutions cannot be addressed using a single solution [117]
This study formulates the optimal network reconfiguration problem within a Pareto
optimal framework where feeder loss and system reliability indices are
simultaneously optimised Two types of reliability indices are considered system
expected outage costs to customers (ECOST) and system interruption duration index
(SAIDI) The multi-objective ant colony optimisation (MOACO) and artificial
immune systems-ant colony optimisation (AIS-ACO) algorithms are proposed and
compared for the assessment of DNR problems Both algorithms focus on problems
in terms of Pareto optimality where the objective functions are multidimensional In
MOACO each objective function is assigned with a pheromone matrix and all
values from multiple pheromone matrices are aggregated into a single pheromone
value by a weighted sum [96] In AIS-ACO the quality of elements that make up the
solution to the problem is represented by the pheromones developed from the ACO
And the hypermutation from the AIS is used as a random operator to enlarge the
search space [88] To verify the suitability of the proposed algorithms they have
been tested on Bus 4 of the Roy Billinton Test System (RBTS) system and the Pareto
set is obtained
The remaining parts of this chapter are organised as follows Section 82 deals with
the framework of multi-objective optimisation and DNR problem formulation The
implementation details of the MOACO and AIS-ACO algorithms to the problem are
discussed in Section 83 The simulation results and the best compromise solutions
are presented and discussed in Section 84 and 85 Section 86 summarises the main
conclusions
Chapter 8 Distribution Network Reconfiguration for Loss Reduction amp Reliability
Improvement
Page | 152
82 Problem Formulation
This section formulates the DNR problems in the Pareto optimal framework
821 Multi-objective Reconfiguration Problem
In this study three objectives are considered and they are feeder loss unserved
energy cost and the average time that a customer is interrupted Therefore the multi-
objective DNR problem can be defined as the minimisation of the vector
119865(119866) = [1198911(119866)1198912(119866)1198913(119866)]119879 (8-3)
where 1198911(119866) 1198912(119866) and 1198913(119866) are described below for a given network
configuration G
8211 Minimisation of feeder loss
The total feeder loss of the network is formulated as
1198911(119866) = sum 119896119894119877119894(119875119894
2+1198761198942
1198801198942 )
119873119887119894=1 (8-4)
where 119877119894 is the resistance of the ith branch 119875119894 and 119876119894 are the real power (W) and
reactive power (VAr) at the receiving end of branch i 119880119894 represents the rms voltage
at the receiving end of branch i (V) 119896119894 is a binary variable 119896119894 = 0 indicates that
branch 119894 is open and 119896119894 = 1 indicates that branch 119894 is closed The detailed feeder loss
assessment is presented in Section 28
8212 Minimisation of ECOST
The ECOST represents the unserved energy cost and is described as
1 ( 1)
1 1 1 1 1 1
( ) ( ) ( ) ( ) (1 ) (1 )b b b b bN CT NR CT NST
t t
b b k R k s
t b k j k j
ECOST L P k j C d P k j C d IR DR
(8-5)
where T is time period (year) 119873119887 is the total number of branches 120582119887and 119871119887 are the
average failure rate (failurekm-year) and length (km) of branch b 119862119879119887 119873119877119887 and
119873119878119887 are the total number of customer types permanent damaged and temporary
Chapter 8 Distribution Network Reconfiguration for Loss Reduction amp Reliability
Improvement
Page | 153
damaged load points when the fault is at branch b P(k j) is the average load of the
kth-type customers at the jth load point (kW) 119862119896(119889) is the customer damage
function for kth-type customer lasting d hours ($kW) 119889119877 and 119889119878 are the average
repair time and the switch time after failure IR and DR are the annual load increase
rate and discount rate
8213 Minimisation of SAIDI
The average time that a customer is interrupted is represented by a reliability index
SAIDI and is defined as
119878119860119868119863119868 = sum sum 120582119887∙119871119887[sum 119889119877
119873119862119877(119887)119899=1 +sum 119889119878
119873119862119878(119887)119899=1 ]
119873119887119887=1
119873119862119905119900119905119886119897119879
119905=1 (8-6)
where 119873119862119877(119887) and 119873119862119878(119887) are the number of permanent damaged and temporary
damaged customers when the fault is at branch b 119873119862119905119900119905119886119897 is the total number of
served customers SAIDI is measured in hours
8214 Constraints
The computed voltages currents and the power flow at all branches should be kept
in their permissible range and the network should be operated in radial The
configurations that violate any constraint should be disregarded
822 Best Compromise Solution
After obtaining the Pareto set the best compromise solution among the multiple
objectives can be selected by comparing the fitness value of each member in the
Pareto front as follows [45]
119891119901119904(119894) = sum 120596119895max(119900119891119895)minus119900119891119895(119875119878119894)
max(119900119891119895)minusmin (119900119891119895)
119873119900119887119895
119895=1 (8-7)
where 119873119900119887119895 is the number of objectives which is three in this study max(119900119891119895) and
min(119900119891119895) are the maximum and minimum value of the jth objective function
obtained by all the members in the Pareto front respectively 1205961 1205962 and 1205963 are the
weighting factor for feeder loss ECOST and SAIDI respectively
The best compromise solution is varied by changing the values of the weighting
factors based on the tendencies of the decision makers
Chapter 8 Distribution Network Reconfiguration for Loss Reduction amp Reliability
Improvement
Page | 154
83 Solution Methodology
In this study there are two methodologies proposed for generating the Pareto set to
the multi-objective DNR problem which are MOACO and AIS-ACO algorithm
Each solution is represented by a string of integers which indicates the locations of
tie-switches
831 Applying MOACO to Multi-objective DNR Problem
Generally ACO algorithm is developed for the assessment of a single objective
optimisation problem However a MOACO algorithm is proposed for assessing
multiple objective functions in the Pareto optimality framework which can generate
diverse solutions rather than just one The flowchart of the MOACO algorithm is
presented in Fig 8-1 and is divided into six steps
Step 1 Initialisation First of all all the ants are initially located at home The
number of pheromone matrices is equal to the number of objectives Each
pheromone matrix has 33 rowsstates (candidate locations for tie-switches) and 4
columnsstages (number of tie-switches) The pheromone values of the edges in the
search space are all initialised at an equal value which is a small positive constant
number
Step 2 Pheromone matrix generation and ant dispatch As there are multiple
pheromone matrices 1205911 1205912 and 1205913 are associated with feeder loss ECOST and
SAIDI respectively All matrices are aggregated into a single pheromone matrix by
weighted sum as
120591119894119909 = 1199011 ∙ 1205911198941199091 + |1199011 minus 1199012| ∙ 120591119894119909
2 + (1 minus 1199012) ∙ 1205911198941199093 (8-8)
where 1205911198941199091 120591119894119909
2 and 1205911198941199093 are the levels of pheromone deposited on state i of stage x for
feeder loss ECOST and SAIDI respectively where 1199011 and 1199012 are uniform random
numbers between 0 and 1 and 1199011 is less than 1199012 This ensures the selection of the
three pheromone matrices all have the same probability and can be used to build the
new matrix
All the ants begin their tours from the home colony and choose the next node to
move to based on the intensity of pheromones from a new pheromone matrix They
Chapter 8 Distribution Network Reconfiguration for Loss Reduction amp Reliability
Improvement
Page | 155
experience different pheromone matrices according to the random variation of
weights The probability of an ant choosing state i of stage x is
119875119894119909(119873) =120591119894119909(119873)
sum 120591119894119909(119873)ℎisin∆119909
(8-9)
where 120591119894119909(119873) is the level of pheromone deposited on state i of stage x at iteration
N ∆119909 is the set of available states which an ant can choose at stage x
Step 3 Objective Function Evaluation After all the ants have completed their tour
the location list and corresponding objective functions in (8-3) for each ant are
evaluated If any constraint is violated the corresponding solutions are discarded
Step 4 Non-dominated Solutions Extraction and Diversity Measure The non-
dominated solutions extraction extracts solutions from a pool based on the concept
of dominance as presented in Section 821 The crowding distance is used to
measure the extent to which non-dominated solutions are spread over the objective
space [20] As there are three objectives to be optimised the crowding distance of a
solution is equal to the side length of the cuboid which is built by two adjacent
solutions [88] Regarding the boundary solutions (the corner solutions) they are
assigned with an infinite distance The solutions are assigned with a small distance
value if they are located in a crowded area The decision makers tend to choose the
solutions from less crowded regions of the search space (with higher crowding
distance) if the maximum number of non-dominated solutions is restricted to a
certain number [88]
Step 5 Pheromone Updating The aim of this step is to favour transitions towards
states by non-dominated solutions with greater pheromone values There are two
rules of pheromone updating the local rule and global rule
Local rule The pheromones deposited in the search space should be evaporated to
make the paths less attractive The local pheromone update rule is calculated as
follow
120591119894119909119899 (119873) = (1 minus 120588)120591119894119909
119899 (119873 minus 1) + 120591119888 (8-10)
where 120588 is the pheromone evaporation rate which is set between 0 and 1 120591119894119909119899 (119873 minus
1) is pheromone value deposited on state i of stage x of matrix n at iteration N-1 120591119888
Chapter 8 Distribution Network Reconfiguration for Loss Reduction amp Reliability
Improvement
Page | 156
is a small positive constant value Even if the amount of pheromone deposited on an
edge is at the lowest value of 120591119888 there is a slight chance that an ant will still choose
this edge
Global rule The global pheromone updating rule involves ants depositing large
amounts of pheromone to the edges that belong to the corner non-dominated
solutions which are the solutions that have minimum values along each objective
The pheromones of those edges can be updated by
120591119894119909119899 (119873) = 120591119894119909
119899 (119873) + 120588119891119887119890119904119905
119899 (119873)
119891119887119890119904119905119899 (119873minus1)
(8-11)
where 119891119887119890119904119905119899 (119873 minus 1) and 119891119887119890119904119905
119899 (119873) are the minimum values of objective function n
obtained by the non-dominated solutions at iteration N-1 and N respectively
After applying the local and global pheromone updating rules the method Max-Min
ACO algorithm is integrated into the proposed approach
120591119894119909119899 (119873) = 120591119898119886119909 119894119891 120591119894119909
119899 (119873) ge 120591119898119886119909 (8-12)
120591119894119909119899 (119873) = 120591119898119894119899 119894119891 120591119894119909
119899 (119873) le 120591119898119894119899 (8-13)
where 120591119898119886119909and 120591119898119894119899 are the higher and lower bound of pheromone level on each
edge respectively Even if the amount of pheromone deposited to a path is at the
lowest value 120591119898119894119899 there is a slight chance that an ant will still choose this path This
enlarges the search space and prevents convergence from occurring too rapidly
After this the non-dominated solutions with their location lists and corresponding
fitness values in the current iteration are retained and all the ants are free to choose a
new path for the next iteration
Step 6 Termination The computation continues until the predefined maximum
number of iterations is reached The final non-dominated solutions are considered as
the Pareto set to the multi-objective DNR problem
Chapter 8 Distribution Network Reconfiguration for Loss Reduction amp Reliability
Improvement
Page | 157
Start
Iteration N=1
Maximum ant number
reaches
Output Pareto
optimal set and end
No
Yes
Initialise the parameters for MOACO
algorithm search space
Ant number m=1
Random select weights and
aggregate multiple pheromone
matrices into one
Dispatch the ant based on the
amount of pheromone on edges
Calculate the multiple objective functions
for this ant
N=N+1
Read system topology
and load data
Diversity measure and extract non-
dominated solutions
Maximum iteration
reaches
Yes
m=m+1
No
The pheromones are updated according
to local and global rules
Fig 8-1 Flowchart of the MOACO algorithm applied to multi-objective DNR problem
Chapter 8 Distribution Network Reconfiguration for Loss Reduction amp Reliability
Improvement
Page | 158
Start
Cloning
Maximum iteration
reached
Output Pareto
optimal set and end
No
Yes
Initialise and set iteration n=1
Pheromone based hypermutation
Diversity measure and extract non-
dominated solutions
The pheromones are updated according to
local and global rules
n=n+1
832 Applying AIS-ACO to Multi-objective DNR Problem
The general description of AIS-ACO algorithm is presented in Section 34 In this
study the AIS-ACO hybrid approach is used to handle multi-objective formulation
using the Pareto optimality concept The antigen is the multi-objective function and
the antibody is the solution to the problem The affinity between the antibody and the
antigen is the Pareto dominance among solutions which indicates the quality of the
solution [88] The information related to each objective is represented by an
individual pheromone table All the non-dominated solutions experience cloning
hypermutation selection and updating until the maximum number of iterations is
reached The flowchart of the AIS-ACO algorithm for Pareto optimality is presented
in Fig 8-2
Fig 8-2 Flowchart of the AIS-ACO algorithm applied to multi-objective DNR problem
Chapter 8 Distribution Network Reconfiguration for Loss Reduction amp Reliability
Improvement
Page | 159
The key parts of the algorithm are explained as follows
Step 1 Initialisation At the beginning of this algorithm a set of initial solutions is
generated These solutions should satisfy the constraints An individual pheromone
table is also built for each objective Each pheromone table has 33 cells (candidate
locations for tie-switches) The pheromone value of each cell represents the
probability of selecting the corresponding switch to be opened in the network model
The pheromone values of all cells are initially set at the same value
Step 2 Cloning All the non-dominated solutions are subjected to cloning In this
study as there are three objectives to be optimised the number of clones for each
non-dominated solution is three
Step 3 Hypermutation The selection of a cell in each clone for hypermutation is
obtained by applying a roulette wheel on its pheromone table [88] The probability of
selecting a cell is dependent on its pheromone intensity A higher pheromone value
of a cell in the table indicates that the corresponding edge in the network is more
likely to be selected The probability of selection cell i in table n is given by
119901119894119899 =
120591119894119899
sum 120591119895119899
119895 (8-14)
where 120591119894119899 is the pheromone value of cell i in table n sum 120591119895
119899119895 represents the sum of
pheromone values of all cells in table n
Step 4 Non-dominated Solutions Extraction and Diversity Measure This step is
same to the step which has been discussed in Section 831
Step 5 Pheromone Updating The aim of this step is to favour transitions toward
non-dominated solutions with great pheromone values There are two rules of
pheromone updating the local rule and global rule
Local rule Pheromones deposited in the search space should be evaporated to make
the paths less attractive The local pheromone update rule is calculated as follows
120591119894119899(119873) = 119898119886119909 (1 minus 120588)120591119894
119899(119873 minus 1) 120591119898119894119899 (8-15)
where 120588 is the pheromone evaporation rate which is set between 0 and 1 120591119894119899(119873 minus 1)
is pheromone value deposited on cell i of table n at iteration N-1 120591119898119894119899 is the lower
Chapter 8 Distribution Network Reconfiguration for Loss Reduction amp Reliability
Improvement
Page | 160
bound of pheromone level on each edge Even if the amount of pheromone deposited
to a path is at the lowest value 120591119898119894119899 there is a slight chance that an ant will still
choose this path This enlarges the entire search space
Global rule The global pheromone updating rule involves depositing large amounts
of pheromone to the edges that are a part of all the non-dominated solutions in the
current iteration [88] At iteration N the edges of the non-dominated solutions can be
updated as
120591119894119899(119873) = 119898119894119899120591119894
119899(119873) + 120588min (119891119899(119866))
119891119899(119866) 120591119898119886119909 (8-16)
where each 119894 isin edge set of G 119899 isin objective set and 119866 isin non-dominated solutions set
119891119899(119866) is the value of objective function n obtained by the non-dominated solution G
120591119898119886119909 is the higher bound of pheromone level on each edge
After this the non-dominated solutions with their location lists and fitness values in
the current iteration are retained and all the ants are free to choose a new path for the
next iteration
Step 6 Termination The computation continues until the predefined maximum
number iteration is reached The final non-dominated solutions are considered as the
Pareto set to the multi-objective DNR problem
Chapter 8 Distribution Network Reconfiguration for Loss Reduction amp Reliability
Improvement
Page | 161
LP11 LP12 LP13 LP14 LP15 LP16 LP17
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LP26 LP27 LP28
LP18 LP19 LP20 LP21 LP22 LP23 LP24 LP25
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6 8
10
9
68
11 12
56
57
58 60
59 61 62
65
64 66 67
50 52
51
54
53 55
44
45
46
47
48
49
70
31
32
33
34
36
35
39
37 38 40
41
42 43
63
F3
F2
F1
F7
F6
F5
F4
Normally Open Circuit BreakerNormally Closed Circuit Breaker
Subbus1
Subbus2
Subbus3
T1
T3
T5
Main
feeder
Main
feeder
Main
feeder
T2
T4
T6
84 Application Studies
The proposed MOACO and AIS-ACO algorithms have been tested on an 11 kV
distribution network developed from Bus 4 of the Roy Billinton Test System (RBTS)
a single-line diagram of the network is shown in Fig 8-3 The network consists of 38
load points and 4 tie-switches the associated data can be found in [114] The types
and lengths of 11 kV feeders are listed in Appendix A4 The network built in
OpenDSS incorporates three 3311 kV double transformer substations supplying the
downstream loads
Fig 8-3 Distribution feeder connected to RBTS Bus 4
This typical urban distribution network supplies residential commercial and
industrial consumers The average value of active and reactive power and the
customer type of each node are modified from the original values and the new values
are listed in Table 8-1
Chapter 8 Distribution Network Reconfiguration for Loss Reduction amp Reliability
Improvement
Page | 162
300
350
400
450
4
45
5
55
6
x 104
08
09
1
11
12
13
14
15
Feeder loss (kW)ECOST ($yr)
SA
IDI
(hrs
custo
mer
yr)
Table 8-1 Revised customer data (Average load)
Number
of load
points
Load points Customer type P
(kW)
Q
(kVAr)
Number of
customers
4 1-2 9-10 residential 545 51775 220
6 3-5 13-15 residential 500 475 200
12 6-7 16-17 23-25 28 30-
31 37-38
commercial 415 39425 10
6 8 11 18 26 32-33 industrial 1500 1425 1
10 12 19-22 27 29 34-36 industrial 1000 950 1
The proposed MOACO and AIS-ACO algorithms are coded in the MATLAB to
obtain the location of tie-switches for the optimum configuration The settings of the
algorithm parameters that provided the optimum solution for these two cases are
presented in Appendix C4
The number of Pareto optimal solutions obtained by the two algorithms is 26 and its
Pareto front is presented in Fig 8-4 in three dimensions The Pareto set is listed in
Appendix B3 in detail These solutions provide the network operator with various
configurations for the system to choose from Both algorithms have obtained the
same results However for 100 runs the average computation time of AIS-ACO
algorithm is 402s which is significantly lower than the MOCAO algorithm 1053s
Fig 8-4 Pareto solutions obtained (minimisation of feeder loss ECOST and SAIDI)
Chapter 8 Distribution Network Reconfiguration for Loss Reduction amp Reliability
Improvement
Page | 163
Table 8-2 presents the mean and standard deviation of the Pareto front
Table 8-2 Mean and standard deviation of Pareto Front (loss ECOST and SAIDI)
Feeder loss (kW) ECOST ($yr) SAIDI (hrscustomeryr)
Mean
38074 48139 09975
Standard deviation
3431 5291 01165
The corner non-dominated solutions representing minimum feeder loss minimum
ECOST and minimum SAIDI are marked by the red circle yellow circle and green
circle respectively as shown in Fig 8-4 The objective values of these solutions and
relevant tie-switches locations are presented in Table 8-3 It is obvious that the three
objectives are conflicting with each other and the algorithm is able to find the global
optimal solution for each objective function The minimum loss configuration is the
base configuration of RBTS-Bus4 In minimum ECOST solution the unserved
energy cost is reduced by 1133 in comparison with that in the original network
The minimum SAIDI solution shows a reduction of 3695 in the average time that
a customer is interrupted
Table 8-3 Minimum solutions along each objective (loss ECOST and SAIDI)
Feeder loss (kW) ECOST ($yr) SAIDI
(hrscustomeryr)
Tie-switches location
Minimum Loss
32142 46404 13090 68 69 70 71
Minimum ECOST
35409 41145 10586 10 17 41 70
Minimum SAIDI
43523 57891 08253 7 26 54 69
85 Best Compromise Solution
After obtaining the Pareto set the best compromise solution is the member which
has the largest fitness value as calculated in Eq (8-7) The results are presented in
Table 8-4 The importance of each objective function is represented by its weighting
Chapter 8 Distribution Network Reconfiguration for Loss Reduction amp Reliability
Improvement
Page | 164
factor which ranges from 1 to 10 A higher weighing factor indicates this objective
function is more important It can be seen that the solutions are different if the
weighing factors of each objective function are varied based on the tendencies of
DNO For example as shown in the table Case 2 (1205961 = 10 1205962 = 1 1205963 = 1)
indicates that the importance of feeder loss reduction is higher than the other two
objectives and hence the best compromise solution for this case obtains the
minimum loss among all the solutions which is the same as the results obtained
from Table 8-3 In comparison of Case 5 with Case 2 as the importance of ECOST
reduction is increased the network is reconfigured and its feeder loss increases by
588 to compensate for a 1045 decrease in the ECOST If there is no preferred
objective the best solution is obtained by setting 1205961 = 1205962 = 1205963 (Case 1)
Table 8-4 Best compromise solutions (loss ECOST and SAIDI)
Case No Weighting factors Best
compromise
solution
Feeder
loss
(kW)
ECOST
($yr)
SAIDI
(hrscustomeryr) 1205961 1205962 1205963
1 10 10 10 10 41 69 70 34033 41553 10996
2 10 1 1 68 69 70 71 32142 46404 13090
3 1 10 1 10 17 41 70 35409 41145 10586
4 1 1 10 7 26 54 69 43523 57891 08253
5 10 10 1 10 41 69 70 34033 41553 10996
6 10 1 10 10 54 69 71 34759 46644 10217
7 1 10 10 7 17 41 70 40368 43329 09570
86 Summary
The MOACO and AIS-ACO algorithms have been presented in this study for the
assessment of the multi-objective DNR problem using the Pareto optimality concept
The proposed DNR problem is formulated taking into account three objectives to be
minimised feeder loss ECOST and SAIDI The algorithms have been successfully
tested in an RBTS-Bus 4 network The results illustrate that the proposed algorithm
is able to generate a set of non-dominated solutions with high quality and great
diversity This set of solutions represent different trade-offs among the objective
functions And the corner non-dominated solutions which represent the minimum
Chapter 8 Distribution Network Reconfiguration for Loss Reduction amp Reliability
Improvement
Page | 165
value of each objective function are presented in the Pareto front chart By varying
the weighting factors for the parameters the decision makers can select the best
compromise strategy among the three objectives for implementation depending on
the utilitiesrsquo priorities
According to the obtained results both algorithms have obtained the same Pareto
optimal solutions but the AIS-ACO algorithm performs better in comparison with
the MOACO algorithm in terms of computation time The pheromone tables in AIS-
ACO algorithm are used to guide the search process and improve the solution quality
In addition the hypermutation is used as a random operator to enlarge the search
space and to prevent the algorithm from easily falling into the local optimum Future
work could include the assessment of the DNR problem with other objectives such
as balancing loads on feeders and minimising the maximum node voltage deviation
The AIS-ACO algorithm can also be applied to larger systems
Page | 166
CHAPTER 9
MULTI-OBJECTIVE DISTRIBUTION
NETWORK RECONFIGURATION amp DG
ALLOCATION CONSIDERING LOSS
VOLTAGE DEVIATION AND LOAD
BALANCING
91 Introduction
As discussed in the previous chapters distribution network reconfiguration (DNR)
can not only be used for single objective optimisation but also multi-objective
optimisation The study aims to determine a system topology that simultaneously
minimises feeder loss maximum node voltage deviation and feeder load balancing
This is achieved by optimal DNR and DG allocation
There are two methods presented in this chapter that tackle these objectives a single
fuzzy satisfaction objective function is used to transform the three conflicting
objectives into fuzzy memberships and then finally to combine them into a single
function The ultimate goal is to find a solution that maximises this single objective
while maintaining the constraints of the network [20] In Chapter 7 the degree of
Chapter 9 Multi-objective Distribution Network Reconfiguration amp DG Allocation
Considering Loss Voltage Deviation and Load Balancing
Page | 167
overall fuzzy satisfaction is determined by the max-min principle However there is
no guarantee that if one membership value is weaker than the other membership
values then for the same option the optimised single function will also be weak [86]
Therefore the max-min principle may not predict the best compromise solution In
this study a new operator called lsquomax-geometric meanrsquo has been introduced to
determine the degree of overall fuzzy satisfaction
Another methodology used for assessing the multi-objective DNR and DG allocation
problem is based on the Pareto optimality concept The proposed method provides a
set of non-dominated solutions with high quality and great diversity This constructs
a full Pareto front which represents different trade-offs among the objective
functions It allows the decision makers to select the most suitable one from all the
non-dominated solutions and use this for implementation which depends on the
utilitiesrsquo priorities
The optimisation algorithms for DNR and DG allocation can be classified into two
groups
Ant colony optimisation (ACO) algorithm which is used to solve the
problem in the fuzzy domain
Artificial immune systems-ant colony optimisation (AIS-ACO) algorithm
which is adopted to formulate the optimal network reconfiguration problem
within a multi-objective framework based on the Pareto optimality concept
The effectiveness and the efficiency of the proposed methods are implemented on
two standard IEEE 33-node and 69-node systems as case studies
The remainder of this chapter is organised as follows in Section 92 the
mathematical models of the problem are developed Then the solution procedures
are presented in Section 93 Numerical studies are presented and discussed in
Section 94 and finally Section 95 summarises the main conclusions
Chapter 9 Multi-objective Distribution Network Reconfiguration amp DG Allocation
Considering Loss Voltage Deviation and Load Balancing
Page | 168
0
1
92 Problem Formulation
The primary objective of this study is to minimise the three conflicting objectives
feeder loss maximum node voltage deviation and the feeder load balancing index
Two formulations of objective functions are presented as follow
921 Single Fuzzy Satisfaction Objective Function
In this study the three conflicting objectives are transformed into a single objective
function in the fuzzy domain The best compromise solution is obtained using a
lsquomax-geometric meanrsquo principle and is formulated as follows
Max 119871 = (120572119871 times 120572119881 times 120572119861)1 3frasl (9-1)
where 120572119871 120572119881 120572119861 represents the value of the membership functions for the feeder loss
the maximum node voltage deviation and the feeder load balancing index
respectively
The membership functions used to describe the three objectives of the DNR and DG
allocation problem are presented in the following sections
Membership function for feeder loss reduction
The calculation of feeder loss has been discussed in Section 28 The basic purpose
of this membership function is to reduce feeder loss Therefore the network
topology with a lower loss value obtains a higher membership value The
membership function for loss reduction is formulated in (9-2) and presented in Fig
9-1
Fig 9-1 Membership function for feeder loss reduction
As feeder loss becomes greater than 119871119874119878119878119898119894119899 the degree of satisfaction decreases
This reduction is continued until feeder loss reaches 119871119874119878119878119900119903119894
120572119871
119871119874119878119878119898119894119899 119871119874119878119878119900119903119894 119871119874119878119878
Chapter 9 Multi-objective Distribution Network Reconfiguration amp DG Allocation
Considering Loss Voltage Deviation and Load Balancing
Page | 169
0
1
120572119871 =
1 119871119874119878119878 le 119871119874119878119878119898119894119899119871119874119878119878119900119903119894minus119871119874119878119878
119871119874119878119878119900119903119894minus119871119874119878119878119898119894119899119871119874119878119878119898119894119899 lt 119871119874119878119878 lt 119871119874119878119878119900119903119894
0 119871119874119878119878 ge 119871119874119878119878119900119903119894
(9-2)
where 119871119874119878119878119900119903119894 is the loss of the original network 119871119874119878119878119898119894119899 is the minimum loss that
a network can achieve As it is not appropriate for decision makers to obtain a
network topology which increases loss after DNR and DG allocation the minimum
value of 120572119871 is selected as 0 if the loss is greater than or equal to 119871119874119878119878119900119903119894
Membership function for maximum node voltage deviation reduction
The maximum deviation of bus voltages from their rated values is formulated as
119881119863 = max|119881119903119890119891 minus 119898119894119899(119881119894)| |119881119903119890119891 minus 119898119886119909(119881119894)| 119894 120598 1 2 hellip 119873119887 (9-2)
where 119881119903119890119891 is the reference value for the node voltage which is the substation voltage
it is assumed to be 10 per unit in this study 119881119894 is the voltage at the ith node and 119873119887
is the number of nodes
The membership function for maximum node voltage deviation is shown in Fig 9-2
Fig 9-2 Membership function for maximum node voltage deviation reduction
The mathematical equation is presented below
120572119881 =
1 119881119863 le 119881119863119898119894119899119881119863119900119903119894minus119881119863
119881119863119900119903119894minus119881119863119898119894119899119881119863119898119894119899 lt 119881119863 lt 119881119863119900119903119894
0 119881119863 ge 119881119863119900119903119894
(9-3)
where 119881119863119900119903119894 and 119881119863119898119894119899 are the original and minimum values of the maximum node
voltage deviation respectively
120572119881
119881119863119898119894119899 119881119863119900119903119894 119881119863
Chapter 9 Multi-objective Distribution Network Reconfiguration amp DG Allocation
Considering Loss Voltage Deviation and Load Balancing
Page | 170
0
1
Membership function for feeder load balancing index reduction
The feeder load balancing index is calculated as
119871119861119868 = 119881119886119903[1198681
1198681119898119886119909
1198682
1198682119898119886119909 hellip
119868119894
119868119894119898119886119909 hellip
119868119899
119868119899119898119886119909] (9-4)
where 119868119894 is the current flowing through branch 119894 119868119894119898119886119909 represents the maximum
current limit of branch 119894
The function for feeder load balancing index is shown in Fig 9-3 and expressed as
120572119861 =
1 119871119861119868 le 119871119861119868119898119894119899119871119861119868119900119903119894minus119871119861119868
119871119861119868119900119903119894minus119871119861119868119898119894119899119871119861119868119898119894119899 lt 119871119861119868 lt 119871119861119868119900119903119894
0 119871119861119868 ge 119871119861119868119900119903119894
(9-5)
where 119871119861119868119900119903119894 and 119871119861119868119898119894119899 are the original and minimum values of the feeder load
balancing index respectively
Fig 9-3 Membership function for load balancing index reduction
922 Multi-objective Reconfiguration Problem Using Pareto
Optimality
In this study the multi-objective DNR problem can be defined as the minimisation
of the vector
119865(119866) = [1198911(119866)1198912(119866)1198913(119866)]119879 (9-6)
where 1198911(119866) 1198912(119866) and 1198913(119866) are feeder loss maximum node voltage deviation and
feeder load balancing index respectively The calculation of these three parameters
is discussed in Section 921
120572119861
119871119861119868119898119894119899 119871119861119868119900119903119894 119871119861119868
Chapter 9 Multi-objective Distribution Network Reconfiguration amp DG Allocation
Considering Loss Voltage Deviation and Load Balancing
Page | 171
93 Solution methodology
931 Applying ACO to DNR and DG Allocation in the Fuzzy
Domain
In this study the objective of reconfiguring the network and allocating DGs
simultaneously is to deal with the single fuzzy satisfaction objective function In
order to tackle this optimisation problem an ACO algorithm is adopted to find the
optimum configuration of tie-switches and the location of DGs in the network When
the locations of tie-switches and DGs are changed a new network configuration will
be formed For each network configuration the overall satisfaction of the plan is
calculated using Eq (9-1) The search space of the DNR and DG allocation problems
is modelled as a directed graph as shown in Fig 5-1 The flowchart of the proposed
ACO algorithm is presented in Fig 5-2
932 Applying AIS-ACO to Multi-objective DNR and DG
Allocation Using Pareto Optimality
The application of the AIS-ACO algorithm to the multi-objective DNR and DG
allocation problem using the concept of Pareto optimality is similar to that in Section
832 with an additional process for DG allocation
94 Application Studies
To demonstrate the performance and effectiveness of the proposed techniques in
solving the network reconfiguration and placement of DG problems simultaneously
the proposed ACO and AIS-ACO are implemented on two 1266 kV test systems
consisting of 33 and 69 buses The network models are built in OpenDSS and the
solution algorithms are developed in MATLAB For both test systems the substation
voltage is assumed to be 10 pu and all the sections and buses are considered as
candidate locations for tie-switches and DG placement respectively In this study
for simplicity the number of installed DGs is three All the DGs are synchronous
generators and are represented as PQ models with a 100 kVA and a power factor
Chapter 9 Multi-objective Distribution Network Reconfiguration amp DG Allocation
Considering Loss Voltage Deviation and Load Balancing
Page | 172
equal to 10 However the proposed methodology can be implemented for any
number of DGs For the purpose of better illustration and comparison four cases are
considered to analyse the superiority and performance of the proposed methods
Case I System is without reconfiguration and has no DGs (base case)
Case II System is optimally reconfigured and has no DGs
Case III System is optimally reconfigured after DGs are placed at certain buses
Case IV System is optimally reconfigured and DGs are optimally placed
simultaneously
It is to be noted that the ACO and AIS-ACO control parameters are different for
each test case They are set experimentally using information from several trial runs
The final combinations that provide the best results for all of the above tests are
given in Appendix C5 And the Pareto sets for all test cases are listed in Appendix
B4 in detail
941 33-bus System
In this section the proposed procedure is implemented on a 33-bus 1266 kV radial
distribution system with 37 branches and 5 tie-switches whose single line diagram is
shown in Fig 5-3 The tie-switches are located at L33 to L37 represented by red
dotted lines The data of lines and loads are taken from [108] and summarised in
Appendix A2 The current carrying capacity of all branches is 255A The total real
and reactive power loads of the system are 3715 kW and 2300 kVAr respectively
Case I base case
For the base case without reconfiguration and DGs the initial active feeder loss
maximum node voltage deviation and feeder load balancing index of this system are
20314 kW 00884 pu and 00419 respectively
Chapter 9 Multi-objective Distribution Network Reconfiguration amp DG Allocation
Considering Loss Voltage Deviation and Load Balancing
Page | 173
10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
18 19 20 21
22 23 24
25 26 27 28 29 30 31 32
L1 L2 L3 L4 L5 L6 L7 L8 L9 L10 L11 L12 L13 L14 L15 L16 L17
L18
L19 L20 L21
L22
L23 L24
L25
L26 L27 L28 L29 L30 L31 L32
L33
L34
L35
L36
L37
Case II with reconfiguration only (no DGs)
In this case only reconfiguration is considered and no DGs are installed
After DNR the best compromise solution obtained using ACO algorithm in a single
fuzzy satisfaction objective function is presented in Table 9-1 It can be seen that the
DNR has resulted in a reduction of 2956 in feeder loss 2930 in maximum node
voltage deviation and 3556 in feeder load balancing index compared to the base
case This solution is one of the Pareto optimal solutions which are obtained by
using AIS-ACO algorithm And the network configuration after DNR is shown in
Fig 9-4
Table 9-1 Results of DNR in fuzzy multi-objective formulation for 33-bus system in Case II
Objective function Feeder loss
(kW)
Maximum node
voltage deviation
(pu)
Feeder Load
balancing index
Tie-switches
location
08734 14310 00625 00270 6 9 14 32 37
Fig 9-4 33 bus-system for fuzzy multi-objective optimisation Case II
The number of Pareto optimal solutions obtained using AIS-ACO algorithm is 21
and its Pareto front is presented in Fig 9-5 in three dimensions Table 9-2 presents
the mean and standard deviations of the objective values of the Pareto solutions
Chapter 9 Multi-objective Distribution Network Reconfiguration amp DG Allocation
Considering Loss Voltage Deviation and Load Balancing
Page | 174
120140
160180
200220
006
008
01
012
014
016
0022
0024
0026
0028
003
0032
0034
0036
Feeder loss (kW)Maximum node voltage deviation (pu)
Feeder
load b
ala
ncin
g index
Fig 9-5 Pareto front obtained for 33-bus system in Case II
Table 9-2 Mean and standard deviations of Pareto Front for 33-bus system in Case II
Feeder loss (kW) Maximum node voltage
deviation (pu)
Feeder Load balancing index
Mean
15499 00815 00256
Standard deviation
1549 00194 00023
The corner non-dominated solutions which represent minimum feeder loss
minimum voltage deviation and minimum feeder load balancing index are marked
by the red circle yellow circle and green circle respectively as shown in Fig 9-5
The objective values of these solutions and relevant tie-switches locations are
presented in Table 9-3 In minimum loss solution the feeder loss is reduced by 3118
compared to the initial state If improving voltage profiles is the principle objective
the solution with maximum node voltage deviation of 00604 pu is optimum which
represents a 3167 improvement compared to the base case If balancing feeder
Chapter 9 Multi-objective Distribution Network Reconfiguration amp DG Allocation
Considering Loss Voltage Deviation and Load Balancing
Page | 175
10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
18 19 20 21
22 23 24
25 26 27 28 29 30 31 32
L1 L2 L3 L4 L5 L6 L7 L8 L9 L10 L11 L12 L13 L14 L15 L16 L17
L18
L19 L20 L21
L22
L23 L24
L25
L26 L27 L28 L29 L30 L31 L32
L33
L34
L35
L36
L37
DG2
DG1
DG3
load is the main objective the solution with load balancing index of 00223 is
optimum where the index decreases by 4678 in comparison with the initial case
Table 9-3 Minimum solutions along each objective for 33-bus system in Case II
Feeder loss (kW) Maximum node
voltage deviation (pu)
Feeder Load balancing
index
Tie-switches location
Minimum Loss
13981 00639 00280 7 9 14 32 37
Minimum Voltage Deviation
14026 00604 00310 7 9 14 28 32
Minimum Feeder Load Balancing Index
20248 01309 00223 7 30 34 35 37
Case III with reconfiguration only (with DGs)
In this case the three DGs are located at the end of the feeders ie Bus 17 21 24
The feeder loss maximum node voltage deviation and feeder load balancing of the
original network with DGs are 17831 kW 00823 pu and 00389 pu respectively
After DNR the best compromise solution obtained using ACO algorithm in a single
fuzzy satisfaction objective function is presented in Table 9-4 Compared to the Case
I feeder loss maximum node voltage deviation and feeder load balancing decrease
by 3893 3281 and 4511 respectively This solution belongs to the Pareto
set which are obtained by using AIS-ACO algorithm Fig 9-6 illustrates the optimal
network configuration
Fig 9-6 33 bus-system for fuzzy multi-objective optimisation Case III
Chapter 9 Multi-objective Distribution Network Reconfiguration amp DG Allocation
Considering Loss Voltage Deviation and Load Balancing
Page | 176
110120
130140
150160
170
004
006
008
01
0120018
002
0022
0024
0026
0028
003
Feeder loss (kW)Maximum node voltage deviation (pu)
Feeder
load b
ala
ncin
g index
Table 9-4 Results of DNR in fuzzy multi-objective formulation for 33-bus system in Case III
Objective function Feeder loss
(kW)
Maximum node
voltage deviation
(pu)
Feeder Load
balancing index
Tie-switches
location
08590 12405 00594 00230 6 8 14 32 37
Fig 9-7 shows the Pareto front obtained by the AIS-ACO method and the number
of Pareto optimal solutions for this case is 28 The mean and standard deviations of
the objective values of the Pareto solutions are listed in Table 9-5
Fig 9-7 Pareto front obtained for 33-bus system in Case III
Table 9-5 Mean and standard deviations of Pareto Front for 33-bus system in Case III
Feeder loss (kW) Maximum node voltage
deviation (pu)
Feeder load balancing index
Mean
12850 00711 00231
Standard deviation
1003 00166 00029
Chapter 9 Multi-objective Distribution Network Reconfiguration amp DG Allocation
Considering Loss Voltage Deviation and Load Balancing
Page | 177
The corner non-dominated solutions which represent minimum feeder loss
minimum voltage deviation and minimum feeder load balancing index are marked
by the red circle yellow circle and green circle respectively as shown in Fig 9-7
Table 9-6 presents the objective values of these solutions and relevant tie-switches
locations In minimum loss solution the network reconfiguration results in a
reduction of 4214 in feeder loss compared to the original network and a
reduction of 1594 compared to the reconfigured network without DGs If
improving voltage profiles is the principle objective the solution with maximum
node voltage deviation of 00567 pu is optimum which represents a 3586 and
613 improvement compared to Case I and Case II If balancing feeder load is the
main objective the solution with load balancing index of 00189 is optimum where
the index decreases by 5489 and 1525 in comparison with Case I and Case II
Table 9-6 Minimum solutions along each objective for 33-bus system in Case III
Feeder loss (kW) Maximum node
voltage deviation (pu)
Feeder Load balancing
index
Tie-switches location
Minimum Loss
11753 00643 00241 7 9 14 28 31
Minimum Voltage Deviation
12592 00567 00265 6 8 14 28 32
Minimum Feeder Load Balancing Index
16419 01139 00189 7 21 30 35 37
Case IV with reconfiguration and DG allocation
The network is reconfigured and DGs are allocated simultaneously in this case The
best compromise solution obtained using the proposed algorithm in a single fuzzy
satisfaction objective function after DNR and DG allocation is presented in Table 9-
7 Feeder loss maximum node voltage deviation and feeder load balancing decrease
by 4645 4355 and 4463 respectively in comparison with the base case
This solution is one of the Pareto optimal solutions which are obtained by using
AIS-ACO algorithm Fig 9-8 illustrates the optimal network configuration and DG
locations
Chapter 9 Multi-objective Distribution Network Reconfiguration amp DG Allocation
Considering Loss Voltage Deviation and Load Balancing
Page | 178
10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
18 19 20 21
22 23 24
25 26 27 28 29 30 31 32
L1 L2 L3 L4 L5 L6 L7 L8 L9 L10 L11 L12 L13 L14 L15 L16 L17
L18
L19 L20 L21
L22
L23 L24
L25
L26 L27 L28 L29 L30 L31 L32
L33
L34
L35
L36
L37
DG1
DG3
DG2
100110
120130
140150
160
004
006
008
01
012
0016
0018
002
0022
0024
0026
0028
Feeder loss (kW)Maximum node voltage deviation (pu)
Feeder
load b
ala
ncin
g index
Table 9-7 Results of DNR and DG allocation in fuzzy multi-objective formulation for 33-bus system
in Case IV
Objective
function
Feeder loss
(kW)
Maximum node
voltage
deviation (pu)
Feeder Load
balancing
index
Tie-switches
location
DGs location
08961 10878 00499 00232 7 9 14 36 37 B32 B32 B32
Fig 9-8 33 bus-system for fuzzy multi-objective optimisation Case IV
The number of non-dominated solutions obtained by the AIS-ACO algorithm is 295
However the maximum number for Pareto optimal solutions is restricted to 50
Therefore the solutions with a high value of crowding distance are selected Fig 9-9
shows the Pareto front obtained by the proposed method
Fig 9-9 Pareto front obtained for 33-bus system in Case IV
Chapter 9 Multi-objective Distribution Network Reconfiguration amp DG Allocation
Considering Loss Voltage Deviation and Load Balancing
Page | 179
The mean and standard deviations of the Pareto front are listed in Table 9-8
Table 9-8 Mean and standard deviations of Pareto Front for 33-bus system in Case IV
Feeder loss (kW) Maximum node voltage
deviation (pu)
Feeder Load balancing index
Mean
13295 00873 00194
Standard deviation
1354 00179 00019
The corner non-dominated solutions which represent minimum feeder loss
minimum voltage deviation and minimum feeder load balancing index are marked
by the red circle yellow circle and green circle respectively as shown in Fig 9-9
The objective values of these solutions and relevant tie-switches locations are
presented in Table 9-9 In minimum loss solution the network reconfiguration and
DG allocation result in a reduction of 4662 2244 and 773 in feeder loss
compared to Case I Case II and Case III respectively If improving voltage profiles
is the principle objective the solution with maximum node voltage deviation of
00490 pu is optimum which represents a 4457 1887 and 1358
improvement compared to Case I Case II and Case III respectively If balancing
feeder load is the main objective the solution with load balancing index of 00178 is
optimum where the index decreases by 5752 2018 and 582 in comparison
with Case I Case II and Case III respectively
Table 9-9 Minimum solutions along each objective for 33-bus system in Case IV
Feeder loss (kW) Maximum node
voltage deviation
(pu)
Feeder Load
balancing index
Tie-switches
location
DGs location
Minimum Loss
10844 00538 00228 7 9 14 32 37 B30 B31 B31
Minimum Voltage Deviation
11020 00490 00259 7 9 14 28 36 B31 B31 B32
Minimum Feeder Load Balancing Index
15443 01090 00178 7 30 34 35 37 B8 B9 B12
Chapter 9 Multi-objective Distribution Network Reconfiguration amp DG Allocation
Considering Loss Voltage Deviation and Load Balancing
Page | 180
10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
27
28
29
30
31 32 33 34
35
36
37
38 39 40 41 42 43 44 45
46 47 48 49
50
51
52
53 54 55 56 57 58 59 60 61 62 63 64
65 66
67 68
L1 L2 L3 L4 L5 L6 L7 L8 L9 L10 L11 L12 L13 L14 L15 L16 L17 L18 L19 L20 L21 L22 L23 L24 L25 L26
L27
L28
L29
L30
L31 L32 L33 L34
L35
L36
L37
L38 L39 L40 L41 L42 L43 L44 L45
L46
L47 L48 L49
L50
L51
L52
L53 L54 L55 L56 L57 L58 L59 L60 L61 L62 L63 L64
L65
L66
L67
L68
L69
L70
L71
L72L73
942 69-bus System
This is a large-scale radial distribution system consisting of 73 branches and 5 tie-
switches whose single-line diagram is shown in Fig 5-9 The tie-switches are
located at L69 to L73 represented by red dotted lines The line and load data of the
system are taken from [84] and summarised in Appendix A3 The current carrying
capacity of the branches 1-9 is 400 A 46-49 and 52-64 is 300 A and for all other
branches it is 200 A The total power loads are 379589 kW and 26891 kVAr
respectively
Case I base case
For the base case without reconfiguration and DGs the initial active feeder loss
maximum node voltage deviation and feeder load balancing index of this system are
22562 kW 00928 pu and 00259 respectively
Case II with reconfiguration only (no DGs)
In this case only reconfiguration is considered and no DGs are installed After DNR
the best compromise solution obtained using ACO algorithm in a single fuzzy
satisfaction objective function is presented in Table 9-10 and the network
configuration is shown in Fig 9-10 Reconfiguring the network brings a reduction of
5619 4353 and 2355 in feeder loss maximum node voltage deviation and
feeder load balancing index respectively compared to the base case This solution
belongs to the Pareto set which are obtained by using AIS-ACO algorithm
Fig 9-10 69 bus system for fuzzy multi-objective optimisation Case II
Chapter 9 Multi-objective Distribution Network Reconfiguration amp DG Allocation
Considering Loss Voltage Deviation and Load Balancing
Page | 181
80
100
120
140
160
005
006
007
0080016
0018
002
0022
0024
0026
0028
Feeder loss (kW)Maximum node voltage deviation (pu)
Feeder
load b
ala
ncin
g index
Table 9-10 Results of DNR in fuzzy multi-objective formulation for 69-bus system in Case II
Objective function Feeder loss
(kW)
Maximum node
voltage deviation
(pu)
Feeder Load
balancing index
Tie-switches
location
09676 9885 00524 00195 14 55 61 71 72
The number of Pareto optimal solutions obtained by the AIS-ACO algorithm is 12
and its Pareto front are presented in Fig 9-11 in three dimensions
Fig 9-11 Pareto front obtained for 69-bus system in Case II
The mean and standard deviations of the objective values of the Pareto solutions are
listed in Table 9-11
Table 9-11 Mean and standard deviations of Pareto Front for 69-bus system in Case II
Feeder loss (kW) Maximum node voltage
deviation (pu)
Feeder Load balancing index
Mean
12535 00605 00192
Standard deviation
2458 00085 00028
Chapter 9 Multi-objective Distribution Network Reconfiguration amp DG Allocation
Considering Loss Voltage Deviation and Load Balancing
Page | 182
The corner non-dominated solutions which represent minimum feeder loss
minimum voltage deviation and minimum feeder load balancing index are marked
by the red circle yellow circle and green circle respectively as shown in Fig 9-11
The objective values of these solutions and relevant tie-switches locations are
presented in Table 9-12 In minimum loss solution the feeder loss is reduced by
5619 compared to the initial state If improving voltage profiles is the principle
objective the solution with maximum node voltage deviation of 00523 pu is
optimum which represents a 4364 improvement compared to the base case If
balancing feeder load is the main objective the solution with load balancing index of
00161 is optimum where the index decreases by 3784 in comparison with the
initial case
Table 9-12 Minimum solutions along each objective for 69-bus system in Case II
Feeder loss (kW) Maximum node
voltage deviation (pu)
Feeder load balancing
index
Tie-switches location
Minimum Loss
9885 00524 00195 14 55 61 71 72
Minimum Voltage Deviation
10535 00523 00242 9 14 55 61 71
Minimum Feeder Load Balancing Index
15051 00701 00161 14 61 69 71 72
Case III with reconfiguration only (with DGs)
In this case the three DGs are located at the end of the feeders ie Bus 26 45 64
The feeder loss maximum node voltage deviation and feeder load balancing of the
original network with DGs are 19472 kW 00855 pu and 00234 pu respectively
After DNR Table 9-13 presents the best compromise solution obtained using ACO
algorithm in a single fuzzy satisfaction objective function and the optimal network
configuration is shown in Fig 9-12 Compared to the base case feeder loss
maximum node voltage deviation and feeder load balancing decrease by 6118
4364 and 3282 respectively This solution is one of the Pareto optimal
solutions which are obtained by using AIS-ACO algorithm
Chapter 9 Multi-objective Distribution Network Reconfiguration amp DG Allocation
Considering Loss Voltage Deviation and Load Balancing
Page | 183
10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
27
28
29
30
31 32 33 34
35
36
37
38 39 40 41 42 43 44 45
46 47 48 49
50
51
52
53 54 55 56 57 58 59 60 61 62 63 64
65 66
67 68
L1 L2 L3 L4 L5 L6 L7 L8 L9 L10 L11 L12 L13 L14 L15 L16 L17 L18 L19 L20 L21 L22 L23 L24 L25 L26
L27
L28
L29
L30
L31 L32 L33 L34
L35
L36
L37
L38 L39 L40 L41 L42 L43 L44 L45
L46
L47 L48 L49
L50
L51
L52
L53 L54 L55 L56 L57 L58 L59 L60 L61 L62 L63 L64
L65
L66
L67
L68
L69
L70
L71
L72L73
DG3
DG1
DG2
8090
100110
120130
140
005
006
007
008
0014
0016
0018
002
0022
0024
Feeder loss (kW)Maximum node voltage deviation (pu)
Feeder
load b
ala
ncin
g index
Table 9-13 Results of DNR in fuzzy multi-objective formulation for 69-bus system in Case III
Objective function Feeder loss
(kW)
Maximum node
voltage deviation
(pu)
Feeder Load
balancing index
Tie-switches
location
08829 8758 00523 00174 14 55 61 71 72
Fig 9-12 69-bus system for fuzzy multi-objective optimisation Case III
Fig 9-13 shows the Pareto front obtained by the AIS-ACO method and the number
of Pareto optimal solutions for this case is 19
Fig 9-13 Pareto front obtained for 69-bus system in Case III
Chapter 9 Multi-objective Distribution Network Reconfiguration amp DG Allocation
Considering Loss Voltage Deviation and Load Balancing
Page | 184
The mean and standard deviations of the objective values of the Pareto solutions are
listed in Table 9-14
Table 9-14 Mean and standard deviations of Pareto Front for 69-bus system in Case III
Feeder loss (kW) Maximum node voltage
deviation (pu)
Feeder Load balancing index
Mean
10707 00576 00183
Standard deviation
2042 00071 00029
The corner non-dominated solutions which represent minimum feeder loss
minimum voltage deviation and minimum feeder load balancing index are marked
by the red circle yellow circle and green circle respectively as shown in Fig 9-13
Table 9-15 presents the objective values of these solutions and relevant tie-switches
locations are presented In minimum loss solution the network reconfiguration
results in a reduction of 6118 in feeder loss compared to the original network and
a reduction of 1140 compared to the reconfigured network without DGs If
improving voltage profiles is the principle objective the solution with maximum
node voltage deviation of 00522 pu is optimum which represents a 4375 and
019 improvement compared to Case I and Case II If balancing feeder load is the
main objective the solution with load balancing index of 00147 is optimum where
the index decreases by 4324 and 745 in comparison with Case I and Case II
Table 9-15 Minimum solutions along each objective for 69-bus system in Case III
Feeder loss (kW) Maximum node
voltage deviation (pu)
Feeder Load balancing
index
Tie-switches location
Minimum Loss
8758 00523 00174 13 55 61 71 72
Minimum Voltage Deviation
9729 00522 00226 7 12 55 61 71
Minimum Feeder Load Balancing Index
13686 00681 00147 11 61 69 71 72
Chapter 9 Multi-objective Distribution Network Reconfiguration amp DG Allocation
Considering Loss Voltage Deviation and Load Balancing
Page | 185
10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
27
28
29
30
31 32 33 34
35
36
37
38 39 40 41 42 43 44 45
46 47 48 49
50
51
52
53 54 55 56 57 58 59 60 61 62 63 64
65 66
67 68
L1 L2 L3 L4 L5 L6 L7 L8 L9 L10 L11 L12 L13 L14 L15 L16 L17 L18 L19 L20 L21 L22 L23 L24 L25 L26
L27
L28
L29
L30
L31 L32 L33 L34
L35
L36
L37
L38 L39 L40 L41 L42 L43 L44 L45
L46
L47 L48 L49
L50
L51
L52
L53 L54 L55 L56 L57 L58 L59 L60 L61 L62 L63 L64
L65
L66
L67
L68
L69
L70
L71
L72L73
DG3DG1
DG2
Case IV with reconfiguration and DGs allocation
In this case the network is reconfigured and DGs are allocated simultaneously
Table 9-16 presents the best compromise solution obtained using the ACO algorithm
in a single fuzzy satisfaction objective function after DNR and DGs allocation and
the optimal network configuration and DG locations are shown in Fig 9-14 Feeder
loss maximum node voltage deviation and feeder load balancing decrease by
6721 5377 and 3840 respectively in comparison with the base case This
solution is one of the Pareto optimal solutions which are obtained by using AIS-
ACO algorithm
Table 9-16 Results of DNR and DGs allocation in fuzzy multi-objective formulation for 69-bus
system in Case IV
Objective
function
Feeder loss
(kW)
Maximum
node voltage
deviation (pu)
Feeder Load
balancing
index
Tie-switches
location
DGs location
08882 7397 00429 00158 14 55 61 71 72 B60 B60 B60
Fig 9-14 69-bus system for fuzzy multi-objective optimisation Case IV
The number of non-dominated solutions obtained by the AIS-ACO algorithm is 46
Fig 9-15 shows the Pareto front obtained by the proposed method The mean and
standard deviations of the objective values of the Pareto solutions are listed in Table
9-17
Chapter 9 Multi-objective Distribution Network Reconfiguration amp DG Allocation
Considering Loss Voltage Deviation and Load Balancing
Page | 186
70
80
90
100
110
120
004
0045
005
0055
006
0012
0013
0014
0015
0016
0017
0018
0019
Feeder loss (kW)Maximum node voltage deviation (pu)
Feeder
load b
ala
ncin
g index
Fig 9-15 Pareto front obtained for 69-bus system in Case IV
Table 9-17 Mean and standard deviations of Pareto Front for 69-bus system in Case IV
Feeder loss (kW) Maximum node voltage
deviation (pu)
Feeder Load balancing index
Mean
9872 00520 00147
Standard deviation
1491 00055 00013
The corner non-dominated solutions which represent minimum feeder loss
minimum voltage deviation and minimum feeder load balancing index are marked
by the red circle yellow circle and green circle respectively as shown in Fig 9-15
The objective values of these solutions and relevant tie-switches locations are
presented in Table 9-18 In minimum loss solution the network reconfiguration and
DG allocation result in a reduction of 6721 2517 and 1554 in feeder loss
compared to Case I Case II and Case III respectively If improving voltage profiles
is the principle objective the solution with maximum node voltage deviation of
00428 is optimum which represents a 5388 1816 and 1801 improvement
compared to Case I Case II and Case III respectively If balancing feeder load is the
Chapter 9 Multi-objective Distribution Network Reconfiguration amp DG Allocation
Considering Loss Voltage Deviation and Load Balancing
Page | 187
main objective the solution with load balancing index of 00125 pu is optimum
where the index decreases by 5174 2236 and 1497 in comparison with Case
I Case II and Case III respectively
Table 9-18 Minimum solutions along each objective for 69-bus system in Case IV
Feeder loss (kW) Maximum node
voltage deviation
(pu)
Feeder Load
balancing index
Tie-switches
location
DGs location
Minimum Loss
7397 00429 00158 14 55 61 71 72 B60 B60 B60
Minimum Voltage Deviation
8032 00428 00183 11 55 61 71 72 B60 B60 B60
Minimum Feeder Load Balancing Index
10962 00577 00125 14 63 69 71 72 B62 B62 B62
95 Summary
In this study the DNR and DG allocation problem is formulated either within a
fuzzy satisfaction objective function or within a multi-objective Pareto optimal
framework This formulation incorporates the minimisation of three conflicting
objectives feeder loss maximum node voltage deviation and feeder load balancing
index In the fuzzy multi-objective formulation all three objectives are transformed
into a single fuzzy satisfaction objective function and the ACO algorithm is used to
provide decision support The AIS-ACO algorithm has been presented in this study
for the assessment of the multi-objective DNR problem from a Pareto optimality
point of view The proposed methods have been successfully applied on a 33-bus and
a 69-bus radial distribution system The results illustrate that the proposed algorithm
is able to generate a set of non-dominated solutions with high quality and great
diversity This allows the network operators to choose any one from the non-
dominated solutions for implementation based on utilitiesrsquo priorities And the corner
non-dominated solutions which represent the minimum value of each objective
function are presented in the Pareto front chart
Chapter 9 Multi-objective Distribution Network Reconfiguration amp DG Allocation
Considering Loss Voltage Deviation and Load Balancing
Page | 188
Future work could include the assessment of the DNR and DG allocation problem
with more than three objectives These objectives may include balancing loads on
transformers minimising the number of switching operations etc The proposed
methodologies can be evaluated further by applying them to actual systems
Page | 189
CHAPTER 10
CONCLUSION amp FUTURE WORK
101 Conclusion
The aim of this thesis is to improve service efficiency and quality in distribution
networks Optimal distribution automation (DA) is one of the best solutions to
achieve this goal The multiple objectives are transformed into different forms based
on utilitiesrsquo priorities For this purpose the Monte Carlo method is used to solve
power system issues involving uncertain load values And a set of ant colony
optimisation (ACO)-based algorithms has been developed for objectives
optimisation This section summarises the conclusions drawn from the research
results
A comprehensive review of the network configurations switchgears DA
assessment of loss and reliability indices and different forms of multi-objective
functions was provided in Chapter 2 This has demonstrated the need for DA to
provide a reliable and high efficiency power supply to all customers with a minimum
cost
In Chapter 3 the thesis reviewed the techniques for the assessment of mono-
objectivemulti-objective optimisation problems which were categorised into two
groups simulation methods and analytical methods The Monte Carlo method is a
typical simulation technique and is generally used to deal with power system
calculations involving uncertain parameters It can find the best solution with a high
Chapter 10 Conclusion amp Future Work
Page | 190
degree of accuracy but requires a considerable amount of CPU time and memory
The ant colony optimisation (ACO) algorithm is one of the metaheuristic techniques
designed for assessing the DA problems It can find the global optimum solution in a
reasonable computation time The artificial immune systems (AIS)-ACO hybrid
algorithm was used for assessing the DA problems in order to obtain a set of non-
dominated solutions by using the concept of Pareto dominance
The thesis illustrates why transformer economic operation (TEO) is an economical
solution to reduce transformer loss The TEO mode with minimum loss and
satisfactory voltages is achieved by operating with one or two transformers This
can be summarised as when the transformer load factor is less than the TCLF
transformers should operate separately However when the transformer load factor is
higher than the TCLF it is recommended that transformers operate in parallel In
Chapter 4 a Monte Carlo simulation platform was established to tackle load
uncertainties A methodology based on TEO to reduce transformer loss was then
described This results in a reduction over the conventional transformer loss ie
when two transformers are in parallel operation However simulation studies also
indicate voltage profiles are improved when transformers operate in parallel
Therefore a slight reduction in TCLF results in an increased loss but an
improvement in voltage performance
In Chapter 4 the thesis also demonstrates why distribution network reconfiguration
(DNR) is an effective strategy for transformer loss reduction The presented results
illustrate the optimal locations of tie-switch statuses have successfully reduced the
transformer losses and improved the voltages profiles during a 24 hour operating
period The further away the nodes are from the tie-switch the better the voltage
profiles obtained In addition when the tie-switch moves closer to the middle of the
linked feeder the voltage performance is improved In this case the daily energy
loss in Scenario 5 is 11162 kWh After the introduction of Scenario 9 the annual
saving energy could be 59641 kWh
One conclusion of this thesis is that the network can be reconfigured and DGs can be
relocated simultaneously for feeder loss reduction In Chapter 5 an ACO algorithm
was used for assessing the DNR and DG allocation problems in terms of feeder loss
reduction The numerical results showed that for best performance the existing tie-
Chapter 10 Conclusion amp Future Work
Page | 191
switches were relocated and DGs were optimally placed at the same time The feeder
losses are reduced by 4662 and 6721 for the 33-bus and 69-bus system
respectively The inappropriate network configuration and DG location might result
in loss increment when the size of DG is increased The proposed methodology has
also successfully reduced the total feeder loss and improved the voltage profiles for
different capacities of DG by determining the most suitable network topology and
the DG locations In addition the simulation results have been compared with other
classical methods in literature and it is demonstrated that the proposed ACO is more
efficient and is more likely to obtain the global optimum solution
Another conclusion of this thesis is that the distribution network loss including
transformer loss and feeder loss can be minimised by using a new optimal planning
strategy This strategy is a combination of TEO and network reconfiguration as
presented in Chapter 6 In this chapter the distribution loads experience daily and
seasonal variations and the day is divided into two periods The proposed ACO
algorithm has successfully found the optimum network configuration and economic
operation mode of transformers in all substations during each time interval The
annual energy loss is reduced by 506 compared to the original network Both
transformer loss and feeder loss are reduced through this optimal planning using
DNR and TEO Furthermore simulation results obtained with numerical studies
have demonstrated the capability of applying the ACO algorithm to distribution
network planning including networks with DGs and EVs The proposed
methodology has successfully reduced the total network loss for different capacities
of DG and different penetration levels of EVs by determining the most suitable
network topology compared to the original configuration Comparative results also
show that coordinated charging plan results in less energy loss compared to
uncoordinated charging strategy with the same EV penetration level This is due to
the postponement of charging time which avoids a clash with the peak power
demand times
The thesis develops an effective strategy of sectionalising switch placement (SSP)
for system reliability improvement This is achieved by installing new switches and
relocating existing switches In Chapter 7 an ACO algorithm was proposed for the
assessment of the SSP problem based on reliability improvement and switch costs
minimisation using either a single objective function with weighted aggregation of a
Chapter 10 Conclusion amp Future Work
Page | 192
multi-objective function with fuzzy variables The selection of pheromone
evaporation rate and number of ants is a trade-off between the global search ability
and convergence rate of the ACO algorithm In comparison with the original system
existing sectionalising switches were relocated and new automatic switches were
installed For this practical system the total system costs are reduced by 4289
compared to the original network The impact of installing sectionalising switches on
reducing the total system costs decreases as the number of sectionalising switches is
increased Furthermore a benefit-to-cost analysis which offered a comparison
between ECOST and switch costs was implemented The analysis reveals that the
installing and relocating sectionalising switches is a profitable investment In
addition a set of compromise solutions was obtained by assessing the SSP problem
in terms of ECOST and SAIDI reduction during fault contingencies The placement
of sectionalising switches results in a reduction of 60 in ECOST and 7148 in
SAIDI
The thesis also proposes a strategy for assessing the DNR problems if the
distribution network operator (DNO) desires to know all possible optimal solutions
for all the multiple conflicting objectives simultaneously This formulates the DNR
problem within a multi-objective formulation in the Pareto optimal framework In
Chapter 8 The MOACO and AIS-ACO algorithms were used for assessing this
problem in terms of loss reduction and reliability improvement Both algorithms
have obtained the same Pareto optimal solutions but the AIS-ACO algorithm
performs better in comparison with the MOACO algorithm in terms of computation
time Feeder loss maximum node voltage deviation and feeder load balancing were
simultaneous optimised in Chapter 9 A set of non-dominated solutions with high
quality and great diversity was obtained This set of solutions represent different
trade-offs among the objective functions And the corner non-dominated solutions
which represent the minimum value of each objective function are presented in the
Pareto front chart For IEEE 69-bus system compared to the base case the network
reconfiguration and DG allocation result in a reduction of 6721 in minimum loss
solution If improving the voltage profiles is the principle objective the best solution
represents a 5388 improvement of this index If balancing feeder load is the main
objective this index decreases by 5174 By varying the weighting factors for the
Chapter 10 Conclusion amp Future Work
Page | 193
parameters the decision makers can select the best compromise among the three
objectives for implementation depending on the utilitiesrsquo priorities
102 Future Work
Based on the findings of this project the suggestions for future work are
In this thesis the transformers have the same characteristics In the future as the
cost of replacing an existing transformer with a new one is cheaper than
replacing both transformers the situation that two transformers with different
characteristics in a substation is not uncommon Therefore an optimisation
method for two transformers with different characteristics will be investigated
and four operation modes can occur
1) First transformer operates alone
2) Second transformer operates alone
3) Two transformers operate in parallel
4) Optimisation mode optimum selection of the transformers needed to
supply each feeder
At present in the UK customers pay for losses in the network In this thesis the
losses are analysed as a whole without allocating them to the users in the network
In the future a loss allocation scheme to customers in the distribution network
will be developed However after reconfiguration the total network loss is
reduced but the loss allocation to some customers may increase The customers
with more loss allocated will be dissatisfied with the network reconfiguration It
is therefore important to change the tariff structure for these customers so that
they are not obliged to pay more for the increase in loss allocation as a result of
network reconfiguration
In this thesis the maximum number of objectives to be optimised simultaneously
is three However the work could be extended to solve the DA problem with
more than three objectives These objectives may include balancing load on
transformers minimising the number of switch operations and maximising the
load on feeders
Chapter 10 Conclusion amp Future Work
Page | 194
The optimal DNR DG allocation TEO and SSP will be combined together to
solve the multi-objective optimisation problem The proposed methodologies
could be tested in large-scale practical systems
In this thesis the evaluation of reliability indices only considers the faults in the
line sections And all the feeders are supposed to have the same parameters and
hence the same failure rates However historical data shows the failure rates of a
feeder vary with geographical location and the weather Therefore different
types of feeders and seasonal varying data of feeder section failure rates will be
considered in future work Moreover the impacts of contingencies on the system
such as faults in the transformers and protective devices could also be considered
The integration of large number of electric vehicles (EVs) into the distribution
network places an extra burden on the electricity grid such as increases in energy
loss overloading in feeders decrease in reliability and power quality Therefore
network reconfiguration techniques and smart charging strategies will be
proposed to moderate the charging effects of EVs In addition the vehicle-to-grid
(V2G) technique which returns electricity to the gird will also be studied The
bi-directional of EVs in the network can provide power to improve load
balancing by ldquovalley fillingrdquo (charging) and ldquopeak shavingrdquo (discharging) [118]
The simulation results show ACO-based algorithms could find a set of good
solutions within a reasonable computation time The ACO control parameters are
set experimentally using information from several trial runs More work is
needed to improve the performance of the proposed algorithms by determining
the optimum set of parameter values It is expected that new ACO-based
algorithms will outperform any existing ones or at worst match their results
In the future a multi-objective stochastic optimal flow problem with the
consideration of load DG EV uncertainties will be addressed The load DG
and EV models are obtained by using a Monte Carlo probabilistic power flow
The objectives are then optimised by using a suitable metaheuristic technique
Page | 195
References
[1] L M Faulkenberry Electrical power distribution and transmission Pearson
Education India 1996
[2] Parliamentary Office of Science and Technology ldquoUK Electricity Networksrdquo
2001
[3] R Das et al ldquoDistribution automation strategies evolution of technologies
and the business caserdquo IEEE Trans Smart Grid vol 6 no 4 pp 2166ndash2175
2015
[4] P Balakrishna K Rajagopal and K S Swarup ldquoApplication benefits of
Distribution Automation and AMI systems convergence methodology for
distribution power restoration analysisrdquo Sustain Energy Grids Networks vol
2 pp 15ndash22 2015
[5] ofgem ldquoEnergy Efficiency Directive An assessment of the energy efficiency
potential of Great Britainrsquos gas and electricity infrastructurerdquo 2015
[6] R C Dugan M F McGranaghan and H W Beaty ldquoElectrical power
systems qualityrdquo 1996
[7] British Standards Institution DECC UK Office for National Statistic and
Met Office UK ldquoVoltage characteristics of electricity supplied by public
distribution systemsrdquo Whether and Climate change no December pp 1ndash18
2010
[8] Y F Niu Z Y Gao and W H K Lam ldquoEvaluating the reliability of a
stochastic distribution network in terms of minimal cutsrdquo Transp Res Part E
Logist Transp Rev vol 100 pp 75ndash97 2017
[9] R Billinton and J E Billinton ldquoDistribution system reliability indicesrdquo
IEEE Trans Power Deliv vol 4 no 1 pp 561ndash568 1989
[10] Ofgem ldquoElectricity Distribution Annual Report for 2010-11rdquo 2012
[11] J Hamachi K Eto ldquoUnderstanding the Cost of Power Interruption to US
Electric Consumers LBNL-55718rdquo 2004
[12] R M Vitorino H M Jorge and L P Neves ldquoLoss and reliability
optimization for power distribution system operationrdquo Elsevier BV 2013
[13] E M Carreno R Romero and A Padilha-Feltrin ldquoAn efficient codification
to solve distribution network reconfiguration for loss reduction problemrdquo
IEEE Trans Power Syst vol 23 no 4 pp 1542ndash1551 2008
[14] A Y Abdelaziz R A Osama and S M El-Khodary ldquoReconfiguration of
distribution systems for loss reduction using the hyper-cube ant colony
optimisation algorithmrdquo IET Gener Transm Distrib vol 6 no 2 p 176
References
Page | 196
2012
[15] European commission ldquoRoadmap for moving to a low-carbon economy in
2050rdquo DG Clim Action portal pp 1ndash2 2011
[16] A Mohamed Imran M Kowsalya and D P Kothari ldquoA novel integration
technique for optimal network reconfiguration and distributed generation
placement in power distribution networksrdquo Int J Electr Power Energy Syst
vol 63 pp 461ndash472 2014
[17] W Guan Y Tan H Zhang and J Song ldquoDistribution system feeder
reconfiguration considering different model of DG sourcesrdquo Int J Electr
Power Energy Syst vol 68 pp 210ndash221 2015
[18] S A Yin and C N Lu ldquoDistribution feeder scheduling considering variable
load profile and outage costsrdquo IEEE Trans Power Syst vol 24 no 2 pp
652ndash660 2009
[19] I Richardson M Thomson D Infield and C Clifford ldquoDomestic electricity
use A high-resolution energy demand modelrdquo Energy Build vol 42 no 10
pp 1878ndash1887 2010
[20] K Deb A Pratap S Agarwal and T Meyarivan ldquoA fast and elitist
multiobjective genetic algorithm NSGA-IIrdquo IEEE Trans Evol Comput vol
6 no 2 pp 182ndash197 2002
[21] M E Elkhatib R El Shatshat and M M A Salama ldquoDecentralized reactive
power control for advanced distribution automation systemsrdquo IEEE Trans
Smart Grid vol 3 no 3 pp 1482ndash1490 2012
[22] C-L Su and J-H Teng ldquoOutage costs quantification for benefitndashcost
analysis of distribution automation systemsrdquo Int J Electr Power Energy
Syst vol 29 no 10 pp 767ndash774 2007
[23] I Goroohi Sardou M Banejad R Hooshmand and a Dastfan ldquoModified
shuffled frog leaping algorithm for optimal switch placement in distribution
automation system using a multi-objective fuzzy approachrdquo IET Gener
Transm Distrib vol 6 no 6 p 493 2012
[24] C L Smallwood and J Wennermark ldquoBenefits of distribution automationrdquo
IEEE Ind Appl Mag vol 16 no 1 pp 65ndash73 2010
[25] T Goumlnen Electric power distribution system engineering McGraw-Hill New
York 1986
[26] V Madani et al ldquoDistribution automation strategies challenges and
opportunities in a changing landscaperdquo IEEE Trans Smart Grid vol 6 no 4
pp 2157ndash2165 2015
[27] J J Burke ldquoPower distribution engineering fundamentals and applicationsrdquo
1994
[28] A Elmitwally E Gouda and S Eladawy ldquoRestoring recloser-fuse
coordination by optimal fault current limiters planning in DG-integrated
References
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distribution systemsrdquo Int J Electr Power Energy Syst vol 77 pp 9ndash18
2016
[29] L He J R Mayor R G Harley H Liles G Zhang and Y Deng ldquoMulti-
physics modeling of the dynamic response of a circuit breaker recloser
Systemrdquo in IEEE International Electric Machines amp Dirves Conference 2013
vol 1 pp 1001ndash1008
[30] J M Gers and E J Holmes Protection of electricity distribution networks
vol 47 The Institution of Electrical Engineers 2004
[31] E-J-A Zehra M Moghavvemi M M I Hashim and M Kashem ldquoNetwork
reconfiguration using PSAT for loss reduction in distribution systemsrdquo in 1st
International Conference on Energy Power and Control (EPC-IQ) 2010 pp
62ndash66
[32] J J S Grainger W D J J Grainger and W D Stevenson Power system
analysis McGraw-Hill New York 1994
[33] R D Laramore An introduction to electrical machines and transformers
Wiley 1990
[34] D Borge-Diez A Colmenar-Santos M Castro-Gil and J Carpio-Ibaacutentildeez
ldquoParallel distribution transformer loss reductions A proposed method and
experimental validationrdquo Int J Electr Power Energy Syst vol 49 no 1 pp
170ndash180 2013
[35] Y Wang and hui chao Liu ldquoThe information system for economic operation
of transformer based on ASPrdquo in Intertational Power Engineering
Conference 2007 pp 1914ndash1917
[36] X Chen and Z Guo ldquoEconomic operation of power transformer based on real
time parameter checkingrdquo in Power Engineering Society General Meeting
2006 pp 4ndash6
[37] W Yuan and Y Zhang ldquoEconomic operation of transformers in the area
power network based on real-time analysis and controlrdquo in China
International Conference on Electricity Distribution 2008 pp 1ndash5
[38] R Song and X Zhang ldquoThe application research of load smoothing algorithm
in the transformer economic operationrdquo in International Conference on
Energy and Environment Technology 2009 vol 2 pp 328ndash331
[39] C Mamane ldquoTransformer loss evaluation user-manufacturer
communicationsrdquo IEEE Trans Ind Appl vol IA-20 no 1 pp 11ndash15 1984
[40] E I Amoiralis M A Tsili and A G Kladas ldquoEconomic evaluation of
transformer selection in electrical power systemsrdquo in 19th International
Conference on Electrical Machines 2010 pp 1ndash5
[41] B Suechoey J Ekburanawat N Kraisnachinda S Banjongjit C Chompoo
and M Kando ldquoAn analysis and selection of distribution transformer for
losses reductionrdquo in IEEE Power Engineering Society Winter Meeting 2000
pp 2290ndash2293
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[42] B Suechoey S Bunjongjit and M Kando ldquoThe result analysis of economic
distribution transformer design in Thailandrdquo in Transmission and Distribution
Conference and Exhibition 2002 pp 1820ndash1823
[43] A Merlin and H Back ldquoSearch for a minimal-loss operating spanning tree
configuration in an urban power distribution systemrdquo in Proc 5th Power
System Computation Conf 1975 pp 1ndash18
[44] S Civanlar J J Grainger H Yin and S S H Lee ldquoDistribution feeder
reconfiguration for loss reductionrdquo IEEE Trans Power Deliv vol 3 no 3
pp 1217ndash1223 1988
[45] M-R Andervazh J Olamaei and M-R Haghifam ldquoAdaptive multi-
objective distribution network reconfiguration using multi-objective discrete
particles swarm optimisation algorithm and graph theoryrdquo IET Gener Transm
Distrib vol 7 no 12 pp 1367ndash1382 2013
[46] K Nara A Shiose M Kitagawa and T Ishihara ldquoImplementation of genetic
algorithm for distribution systems loss minimum re-configurationrdquo IEEE
Trans Power Syst vol 7 no 3 pp 1044ndash1051 1992
[47] J Z Zhu ldquoOptimal reconfiguration of electrical distribution network using
the refined genetic algorithmrdquo Electr Power Syst Res vol 62 no 1 pp 37ndash
42 2002
[48] B Enacheanu B Raison R Caire O Devaux W Bienia and N HadjSaid
ldquoRadial network reconfiguration using genetic algorithm based on the matroid
theoryrdquo IEEE Trans Power Syst vol 23 no 1 pp 186ndash195 2008
[49] J C Cebrian and N Kagan ldquoReconfiguration of distribution networks to
minimize loss and disruption costs using genetic algorithmsrdquo Electr Power
Syst Res vol 80 no 1 pp 53ndash62 2010
[50] H D Chiang and R Jean-Jumeau ldquoOptimal network reconfigurations in
distribution systems part 1 A new formulation and a solution methodologyrdquo
IEEE Trans Power Deliv vol 5 no 4 pp 1902ndash1909 1990
[51] Y J Jeon J C Kim and J O Kim ldquoAn efficient simulted annealing
algorithm for network reconfiguration in large-scale distribution systemsrdquo
IEEE Trans Power Deliv vol 17 no 4 pp 1070ndash1078 2002
[52] H Mori and Y Ogita ldquoA parallel tabu search based method for
reconfigurations of distribution systemsrdquo in Power Engineering Society
Summer Meeting 2000 pp 73ndash78
[53] D Zhang Z Fu and L Zhang ldquoAn improved TS algorithm for loss-
minimum reconfiguration in large-scale distribution systemsrdquo Electr Power
Syst Res vol 77 no 5ndash6 pp 685ndash694 2007
[54] A Y Abdelaziz F M Mohamed S F Mekhamer and M A L Badr
ldquoDistribution system reconfiguration using a modified Tabu Search algorithmrdquo
Electr Power Syst Res vol 80 no 8 pp 943ndash953 2010
[55] A Y Abdelaziz F M Mohammed S F Mekhamer and M A L Badr
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ldquoDistribution systems reconfiguration using a modified particle swarm
optimization algorithmrdquo Electr Power Syst Res vol 79 no 11 pp 1521ndash
1530 2009
[56] A Skoonpong and S Sirisumrannukul ldquoNetwork reconfiguration for
reliability worth enhancement in distribution systems by simulated annealingrdquo
5th Int Conf Electr Eng Comput Telecommun Inf Technol ECTI-CON pp
937ndash940 2008
[57] S Elsaiah M Benidris and J Mitra ldquoReliability improvement of power
distribution system through feeder reconfigurationrdquo in 13th International
Conference on Probabilistic Methods Applied to Power Systems 2014
[58] A Kavousi-Fard and T Niknam ldquoOptimal distribution feeder reconfiguration
for reliability improvement considering uncertaintyrdquo IEEE Trans Power
Deliv vol 29 no 3 pp 1344ndash1353 2014
[59] S Ghasemi ldquoBalanced and unbalanced distribution networks reconfiguration
considering reliability indicesrdquo Ain Shams Eng J 2015
[60] A Saffar R Hooshmand and A Khodabakhshian ldquoA new fuzzy optimal
reconfiguration of distribution systems for loss reduction and load balancing
using ant colony search-based algorithmrdquo Appl Soft Comput J vol 11 no 5
pp 4021ndash4028 2011
[61] D Das ldquoA fuzzy multiobjective approach for network reconfiguration of
distribution systemsrdquo IEEE Trans Power Deliv vol 21 no 1 pp 202ndash209
2006
[62] J E Mendoza E A Loacutepez M E Loacutepez and C A Coello Coello
ldquoMicrogenetic multiobjective reconfiguration algorithm considering power
losses and reliability indices for medium voltage distribution networkrdquo IET
Gener Transm Distrib vol 3 no 9 pp 825ndash840 2009
[63] K M Muttaqi J Aghaei V Ganapathy and A E Nezhad ldquoTechnical
challenges for electric power industries with implementation of distribution
system automation in smart gridsrdquo Renew Sustain Energy Rev vol 46 pp
129ndash142 2015
[64] A Abiri-Jahromi M Fotuhi-Firuzabad M Parvania and M Mosleh
ldquoOptimized sectionalizing switch placement strategy in distribution systemsrdquo
IEEE Trans Power Deliv vol 27 no 1 pp 362ndash370 2012
[65] J Northcote-Green and R G Wilson Control and automation of electrical
power distribution systems vol 28 CRC Press 2006
[66] H Falaghi M R Haghifam and C Singh ldquoAnt colony optimization-based
method for placement of sectionalizing switches in distribution networks
using a fuzzy multiobjective approachrdquo IEEE Trans Power Deliv vol 24
no 1 pp 268ndash276 2009
[67] M Nematollahi and M Tadayon ldquoOptimal sectionalizing switches and DG
placement considering critical system conditionrdquo in 21st Iranian Conference
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on Electrical Engineering 2013 pp 1ndash6
[68] J H Teng and C N Lu ldquoFeeder-switch relocation for customer interruption
cost minimizationrdquo IEEE Trans Power Deliv vol 17 no 1 pp 254ndash259
2002
[69] J H Teng and Y H Liu ldquoA novel ACS-based optimum switch relocation
methodrdquo IEEE Trans Power Syst vol 18 no 1 pp 113ndash120 2003
[70] V Miranda ldquoUsing fuzzy reliability in a decision aid environment for
establishing interconnection and switching location policiesrdquo in CIRED 1991
pp 1ndash6
[71] A Heidari V G Agelidis and M Kia ldquoConsiderations of sectionalizing
switches in distribution networks with distributed generationrdquo IEEE Trans
Power Deliv vol 30 no 3 pp 1401ndash1409 2015
[72] I v Zhezhelenko Y Papaika and others ldquoEstimating economic equivalent of
reactive power in the systems of enterprise electric power supplyrdquo Sci Bull
Natl Min Univ no 5 2016
[73] L Li and R Li ldquoStudy on the analysis software of economic operation of
transformerrdquo Adv Mater Res vol 1008ndash1009 pp 497ndash500 2014
[74] J Shang Z Tan C Zhang and L Ju ldquoThe transformer equipment selectionrsquos
update decision technical and economic analysis modelrdquo in Energy and
Power Engineering 2013 vol 5 no 4 pp 143ndash147
[75] B Amanulla S Chakrabarti and S N Singh ldquoReconfiguration of power
distribution systems considering reliability and power lossrdquo IEEE Trans
Power Deliv vol 27 no 2 pp 918ndash926 2012
[76] R E Brown Electric power distribution reliability CRC press 2008
[77] P Zhou R Y Jin and L W Fan ldquoReliability and economic evaluation of
power system with renewables A reviewrdquo Renew Sustain Energy Rev vol
58 pp 537ndash547 2016
[78] R Billington and R N Allan Reliability evaluation of power systems
Plenum Publishing Corp New York NY 1996
[79] N G Paterakis et al ldquoMulti-objective reconfiguration of radial distribution
systems using reliability indicesrdquo IEEE Trans Power Syst vol 31 no 2 pp
1048ndash1062 2016
[80] B Sultana M W Mustafa U Sultana and A R Bhatti ldquoReview on
reliability improvement and power loss reduction in distribution system via
network reconfigurationrdquo Renew Sustain Energy Rev vol 66 pp 297ndash310
2016
[81] K Xie J Zhou and R Billinton ldquoReliability evaluation algorithm for
complex medium voltage electrical distribution networks based on the shortest
pathrdquo IEE Proceedings-Generation Transm Distrib vol 150 no 6 pp
686ndash690 2003
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[82] Z Ghofrani-Jahromi M Kazemi and M Ehsan ldquoDistribution switches
upgrade for loss reduction and reliability improvementrdquo IEEE Trans Power
Deliv vol 30 no 2 pp 684ndash692 2015
[83] P Ngatchou A Zarei and A El-Sharkawi ldquoPareto multi objective
optimizationrdquo in Proceedings of the 13th International Conference on
Intelligent Systems Application to Power Systems 2005 pp 84ndash91
[84] J S Savier and D Das ldquoImpact of network reconfiguration on loss allocation
of radial distribution systemsrdquo IEEE Trans Power Deliv vol 22 no 4 pp
2473ndash2480 2007
[85] T T Nguyen T T Nguyen A V Truong Q T Nguyen and T A Phung
ldquoMulti-objective electric distribution network reconfiguration solution using
runner-root algorithmrdquo Appl Soft Comput J vol 52 pp 93ndash108 2017
[86] N Gupta A Swarnkar R C Bansal and K R Niazi ldquoMulti-objective
reconfiguration of distribution systems using adaptive genetic algorithm in
fuzzy frameworkrdquo IET Gener Transm Distrib vol 4 no 12 pp 1288ndash1298
2010
[87] M R Narimani A Azizi Vahed R Azizipanah-Abarghooee and M
Javidsharifi ldquoEnhanced gravitational search algorithm for multi-objective
distribution feeder reconfiguration considering reliability loss and operational
costrdquo IET Gener Transm Distrib vol 8 no 1 pp 55ndash69 2014
[88] A Ahuja S Das and A Pahwa ldquoAn AIS-ACO hybrid approach for multi-
objective distribution system reconfigurationrdquo IEEE Trans Power Syst vol
22 no 3 pp 1101ndash1111 2007
[89] M Rostami A Kavousi-Fard and T Niknam ldquoExpected cost minimization
of smart grids with plug-in hybrid electric vehicles using optimal distribution
feeder reconfigurationrdquo Ind Informatics IEEE Trans vol 11 no 2 pp
388ndash397 2015
[90] S Oh J Kim S Kwon and S Chung ldquoMonte Carlo simulation of
phytosanitary irradiation treatment for mangosteen using MRI-based
geometryrdquo vol 39 no 3 pp 205ndash214 2014
[91] N HadjSaid and J C Sabonnadiere Electrical Distribution Networks
London ISTE Ltd 2011
[92] Y Li ldquoVoltage balancing on three-phase low voltage feederrdquo The Univerisity
of Manchester 2015
[93] K Bell and P R Allan ldquoComputation of the Value of Securityrdquo 1999
[94] M Dorigo V Maniezzo and A Colorni ldquoThe ant systems optimization by a
colony of cooperative agentsrdquo IEEE Trans Syst Man Cybern B vol 26 no
1 pp 1ndash13 1996
[95] M Dorigo and L M Gambardella ldquoAnt colony system a cooperative
learning approach to the traveling salesman problemrdquo IEEE Trans Evol
Comput vol 1 no 1 pp 53ndash66 1997
References
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[96] M Lopez-Ibanez and T Stuetzle ldquoThe automatic design of multiobjective ant
colony optimization algorithmsrdquo IEEE Trans Evol Comput vol 16 no 6
pp 861ndash875 2012
[97] L Charles Daniel and S Ravichandran ldquoDistribution network reconfiguration
for loss reduction using ant colony system algorithmrdquo in IEEE Indicon 2005
Conference 2005 pp 1ndash4
[98] J F Goacutemez et al ldquoAnt colony system algorithm for the planning of primary
distribution circuitsrdquo IEEE Trans Power Syst vol 19 no 2 pp 996ndash1004
2004
[99] J Lu N Wang J Chen and F Su ldquoCooperative path planning for multiple
UCAVs using an AIS-ACO hybrid approachrdquo Proc 2011 Int Conf Electron
Mech Eng Inf Technol EMEIT 2011 vol 8 no 2 pp 4301ndash4305 2011
[100] J E Hunt and D E Cooke ldquoAn adaptive distributed learning system based
on the immune systemrdquo 1995 IEEE Int Conf Syst Man Cybern Intell Syst
21st Century vol 3 pp 2494ndash2499 1995
[101] C A C Coello and N C Cortes ldquoSolving multiobjective optimization
problems using an artificial immune systemrdquo Genet Program Evolvable
Mach vol 6 no 2 pp 163ndash190 2005
[102] L N De Castro and F J Von Zuben ldquoLearning and optimization using the
clonal selection principlerdquo IEEE Trans Evol Comput vol 6 no 3 pp 239ndash
251 2002
[103] Office for National Statistics Population and household estimates for the
United Kingdom UK 2011
[104] S Ingram S Probert and K Jackson ldquoThe impact of small scale embedded
generation on the operating parameters of distribution networksrdquo Department
of Trade and Industry (DTI) 2003 [Online] Available
httpwebarchivenationalarchivesgovuk20100919182407httpwwwensg
govukassets22_01_2004_phase1b_report_v10b_web_site_finalpdf
[105] 63 EDS 02-0027 Engineering design standard EDS 02-007 11 kV Triplex
Cable 2012
[106] TTH ldquo75 MVA-33-11 KV-GTP TTHrdquo 2014 [Online] Available
httpwwwtranstechtransformerscompdf75mva3311kvgtptth24012008pdf
[107] A M Tahboub V R Pandi and H H Zeineldin ldquoDistribution system
reconfiguration for annual energy loss reduction considering variable
distributed generation profilesrdquo IEEE Trans Power Deliv vol 30 no 4 pp
1677ndash1685 2015
[108] M E Baran and F F Wu ldquoNetwork reconfiguration in distribution systems
for loss reduction and load balancingrdquo Power Deliv IEEE Trans vol 4 no
2 pp 1401ndash1407 1989
[109] D Shirmohammadi and H W Hong ldquoReconfiguration of electric distribution
networks for resistive line losses reductionrdquo IEEE Trans Power Deliv vol 4
References
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no 2 pp 1492ndash1498 1989
[110] R S Rao K Ravindra K Satish and S V L Narasimham ldquoPower loss
minimization in distribution system using network reconfiguration in the
presence of distributed generationrdquo IEEE Trans Power Syst vol 28 no 1
pp 1ndash9 2012
[111] D Sudha Rani N Subrahmanyam and M Sydulu ldquoMulti-objective invasive
weed optimization - an application to optimal network reconfiguration in
radial distribution systemsrdquo Int J Electr Power Energy Syst vol 73 pp
932ndash942 2015
[112] R L Haupt and S E Haupt Practical genetic algorithms John Wiley amp
Sons 2004
[113] X S Yang and S Deb ldquoCuckoo search via Levy flightsrdquo 2009 World Congr
Nat Biol Inspired Comput NABIC 2009 - Proc pp 210ndash214 2009
[114] R N Allan R Billinton I Sjarief L Goel and K S So ldquoA reliability test
system for educational purposes-basic distribution system data and resultsrdquo
IEEE Trans Power Syst vol 6 no 2 pp 813ndash820 1991
[115] G Li and X-P Zhang ldquoModeling of plug-in hybrid electric vehicle charging
demand in probabilistic power flow calculationsrdquo Smart Grid IEEE Trans
vol 3 no 1 pp 492ndash499 2012
[116] UK Department for Transport ldquoNational Travel Survey England 2013 -
Statistical Releaserdquo no July p 26 2014
[117] A Mazza G Chicco and A Russo ldquoOptimal multi-objective distribution
system reconfiguration with multi criteria decision making-based solution
ranking and enhanced genetic operatorsrdquo Int J Electr Power Energy Syst
vol 54 pp 255ndash267 2014
[118] E Sortomme and M A El-Sharkawi ldquoOptimal charging strategies for
unidirectional vehicle-to-gridrdquo IEEE Trans Smart Grid vol 2 no 1 pp
119ndash126 2011
Page | 204
APPENDIX A Network Model Data
A1 UK generic distribution network
The line parameters given here is related to the single line diagram of the network
shown in Fig 45 which are used in the simulation study in Section 451 and 452
Table A-1 Typical configurations and parameters of 11 kV triplex cables in the UK
11 kV line type Cross
Sectional
Area
(CSA)
Positive sequence
Z
Zero-phase
sequence
Z
Approximate
Capacitance
C
Id Configuration Rph Xph R0 X0 C
(mm2) (Ωkm) (μFkm)
A Nexans
635011000
Volt Triplex
Cable
185 0415 0112 0988 0236 036
B 95 0220 0012 0530 0102 028
Appendix A Network Data
Page | 205
A2 33-bus system
Table A-2 Line and load data of 33-bus system
Branch
number
Sending end
node
Receiving end
node
R
(Ω)
X
(Ω)
P at receiving
end (kW)
Q at receiving
end (kVAr)
1 0 1 00922 0047 100 60
2 1 2 04930 02511 90 40
3 2 3 03660 01864 120 80
4 3 4 03811 01941 60 30
5 4 5 08190 07070 60 20
6 5 6 01872 06188 200 100
7 6 7 07114 02351 200 100
8 7 8 10300 07400 60 20
9 8 9 10440 07400 60 20
10 9 10 01966 00650 45 30
11 10 11 03744 01238 60 35
12 11 12 14680 11550 60 35
13 12 13 05416 07129 120 80
14 13 14 05910 05260 60 10
15 14 15 07463 05450 60 20
16 15 16 12890 17210 60 20
17 16 17 03720 05740 90 40
18 17 18 01640 01565 90 40
19 18 19 15042 13554 90 40
20 19 20 04095 04784 90 40
21 20 21 07089 09373 90 40
22 21 22 04512 03083 90 50
23 22 23 08980 07091 420 200
24 23 24 08960 07011 420 200
25 24 25 02030 01034 60 25
26 25 26 02842 01447 60 25
27 26 27 10590 09337 60 20
28 27 28 08042 07006 120 70
29 28 29 05075 02585 200 600
30 29 30 09744 09630 150 70
31 30 31 03105 03619 210 100
32 31 32 03410 05362 60 40
33 7 20 2 2 -- --
34 11 21 2 2 -- --
35 8 14 2 2 -- --
36 17 32 05 05 -- --
37 24 28 05 05 -- --
Appendix A Network Data
Page | 206
A3 69-bus system
Table A-3 Line and load data of 69-bus system
Branch
number
Sending end
node
Receiving end
node
R
(Ω)
X
(Ω)
P at receiving
end (kW)
Q at receiving
end (kVAr)
1 0 1 00005 00012 0 0
2 1 2 00005 00012 0 0
3 2 3 00015 00036 0 0
4 3 4 00251 00294 0 0
5 4 5 0366 01864 26 22
6 5 6 0381 01941 404 30
7 6 7 00922 0047 75 54
8 7 8 00493 00251 30 22
9 8 9 0819 02707 28 19
10 9 10 01872 00619 145 104
11 10 11 07114 02351 145 104
12 11 12 103 034 8 5
13 12 13 1044 0345 8 55
14 13 14 1058 03496 0 0
15 14 15 01966 0065 455 30
16 15 16 03744 01238 60 35
17 16 17 00047 00016 60 35
18 17 18 03276 01083 0 0
19 18 19 02106 0069 1 06
20 19 20 03416 01129 114 81
21 20 21 0014 00046 5 35
22 21 22 01591 00526 0 0
23 22 23 03463 01145 28 20
24 23 24 07488 02475 0 0
25 24 25 03089 01021 14 10
26 25 26 01732 00572 14 10
27 26 27 00044 00108 26 186
28 27 28 0064 01565 26 186
29 28 29 03978 01315 0 0
30 29 30 00702 00232 0 0
31 30 31 0351 0116 0 0
32 31 32 0839 02816 14 10
33 32 33 1708 05646 195 14
34 33 34 1474 04873 6 4
35 34 35 00044 00108 26 1855
36 35 36 0064 01565 26 1855
37 36 37 01053 0123 0 0
38 37 38 00304 00355 24 17
39 38 39 00018 00021 24 17
40 39 40 07283 08509 12 1
41 40 41 031 03623 0 0
Appendix A Network Data
Page | 207
42 41 42 0041 00478 6 43
43 42 43 00092 00116 0 0
44 43 44 01089 01373 3922 263
45 44 45 00009 00012 3922 263
46 45 46 00034 00084 0 0
47 46 47 00851 02083 79 564
48 47 48 02898 07091 3847 2745
49 48 49 00822 02011 3847 2745
50 49 50 00928 00473 405 283
51 50 51 03319 01114 36 27
52 51 52 0174 00886 435 35
53 52 53 0203 01034 264 19
54 53 54 02842 01447 24 172
55 54 55 02813 01433 0 0
56 55 56 159 05337 0 0
57 56 57 07837 0263 0 0
58 57 58 03042 01006 100 72
59 58 59 03861 01172 0 0
60 59 60 05075 02585 1244 888
61 60 61 00974 00496 32 23
62 61 62 0145 00738 0 0
63 62 63 07105 03619 227 162
64 63 64 1041 05302 59 42
65 64 65 02012 00611 18 13
66 65 66 00047 00014 18 13
67 66 67 07394 02444 28 20
68 67 68 00047 00016 28 20
69 49 58 2 1 -- --
70 26 64 1 05 -- --
71 12 20 05 05 -- --
72 10 42 05 05 -- --
73 14 45 1 05 -- --
A4 RBTS Bus 4 system
Table A-4 Feeder data of RBTS Bus 4
Feeder
Type
Length
(km)
Feeder section number
1 060 2 6 10 14 17 21 25 28 30 34 38 41 43 46 49 51 55 58 61 64 67
68 69 70 71
2 075 1 4 7 9 12 16 19 22 24 27 29 32 3537 40 42 45 48 50 53 56 60
63 65
3 080 3 5 8 11 13 15 18 20 23 26 31 33 36 3944 47 52 54 57 59 62 66
Appendix A Network Data
Page | 208
Table A-5 Reliability Data for RBTS Bus 4
Equipment λA λP λM λt R RM
Lines 004 0 0 0 5 0
Buses 0001 0 1 001 2 8
Switches 0004 0002 1 006 4 72
Distribution Transformers 0015 0 1 0 200 120
λA Active failure rate in (fryrkm) for lines and (fryr) for other components
λP Passive failure rate in (fryrkm) for lines and (fryr) for other components
λM Maintenance outage rate in (fryrkm) for lines and (fryr) for other components
λP Transient failure rate in (fryrkm) for lines and (fryr) for other components
R Repair time of failures in (hr)
RM Maintenance outage time in (hr)
Page | 209
APPENDIX B Simulation Results
B1 Simulation results of Chapter 4
B11Tie-switch location
As discussed in Section 452 the location of tie-switch in Scenario 9 is changeable
and the relevant results are presented in Table B-1 It can be clearly seen that the
NOP is located in lsquoTW1rsquo between 0730 and 1000 1600 and 1630 while in lsquoTW5rsquo
for the rest of the day
Table B-1 The locations of tie-switch in Scenario 9
Time Loc Time Loc Time Loc Time Loc Time Loc Time Loc
0000 TW5 0400 TW5 0800 TW1 1200 TW5 1600 TW1 2000 TW5
0010 TW5 0410 TW5 0810 TW1 1210 TW5 1610 TW1 2010 TW5
0020 TW5 0420 TW5 0820 TW1 1220 TW5 1620 TW1 2020 TW5
0030 TW5 0430 TW5 0830 TW1 1230 TW5 1630 TW1 2030 TW5
0040 TW5 0440 TW5 0840 TW1 1240 TW5 1640 TW5 2040 TW5
0050 TW5 0450 TW5 0850 TW1 1250 TW5 1650 TW5 2050 TW5
0100 TW5 0500 TW5 0900 TW1 1300 TW5 1700 TW5 2100 TW5
0110 TW5 0510 TW5 0910 TW1 1310 TW5 1710 TW5 2110 TW5
0120 TW5 0520 TW5 0920 TW1 1320 TW5 1720 TW5 2120 TW5
0130 TW5 0530 TW5 0930 TW1 1330 TW5 1730 TW5 2130 TW5
0140 TW5 0540 TW5 0940 TW1 1340 TW5 1740 TW5 2140 TW5
0150 TW5 0550 TW5 0950 TW1 1350 TW5 1750 TW5 2150 TW5
0200 TW5 0600 TW5 1000 TW1 1400 TW5 1800 TW5 2200 TW5
0210 TW5 0610 TW5 1010 TW5 1410 TW5 1810 TW5 2210 TW5
0220 TW5 0620 TW5 1020 TW5 1420 TW5 1820 TW5 2220 TW5
0230 TW5 0630 TW5 1030 TW5 1430 TW5 1830 TW5 2230 TW5
0240 TW5 0640 TW5 1040 TW5 1440 TW5 1840 TW5 2240 TW5
0250 TW5 0650 TW5 1050 TW5 1450 TW5 1850 TW5 2250 TW5
0300 TW5 0700 TW5 1100 TW5 1500 TW5 1900 TW5 2300 TW5
0310 TW5 0710 TW5 1110 TW5 1510 TW5 1910 TW5 2310 TW5
0320 TW5 0720 TW5 1120 TW5 1520 TW5 1920 TW5 2320 TW5
0330 TW5 0730 TW1 1130 TW5 1530 TW5 1930 TW5 2330 TW5
0340 TW5 0740 TW1 1140 TW5 1540 TW5 1940 TW5 2340 TW5
0350 TW5 0750 TW1 1150 TW5 1550 TW5 1950 TW5 2350 TW5
Appendix B Simulation Results
Page | 210
B12 Voltage variations
For Test Case 2 in Section 452 the detailed voltage values of the mean and the
corresponding 95th
profiles at each node in the linked feeder are recorded in Table
B-2 and Table B-3
Table B-2 Mean voltage profiles at each node in the linked feeder
Node
No
Scenarios
S1 S2 S3 S4 S5 S6 S7 S8 S9
A4_1 09675 09787 09787 09766 09859 09859 09748 09825 09815
A4_2 09676 09784 09784 09766 09856 09856 09748 09822 09813
A4_3 09677 09782 09782 09767 09854 09854 09749 09819 09811
A4_4 09678 09780 09780 09768 09851 09851 09750 09817 09810
A4_5 09681 09777 09777 09771 09849 09849 09753 09814 09808
A4_6 09685 09775 09775 09775 09846 09846 09757 09812 09807
A4_7 09689 09773 09773 09779 09845 09845 09762 09811 09807
A4_8 09694 09772 09772 09784 09844 09844 09767 09810 09807
B4_8 09700 09772 09772 09790 09844 09844 09773 09810 09808
B4_7 09707 09773 09773 09797 09845 09845 09779 09811 09810
B4_6 09714 09775 09775 09804 09846 09846 09787 09812 09813
B4_5 09722 09777 09777 09813 09849 09849 09795 09814 09816
B4_4 09731 09780 09780 09821 09851 09851 09804 09817 09820
B4_3 09737 09782 09782 09827 09854 09854 09809 09819 09823
B4_2 09743 09784 09784 09833 09856 09856 09815 09822 09826
B4_1 09749 09787 09787 09839 09859 09859 09821 09825 09830
Table B-3 95th
voltage profiles at each node in the linked feeder
Node
No
Scenarios
S1 S2 S3 S4 S5 S6 S7 S8 S9
A4_1 09352 09573 09573 09537 09721 09721 09537 09721 09715
A4_2 09353 09567 09567 09537 09715 09715 09537 09715 09709
A4_3 09355 09562 09562 09539 09711 09711 09539 09711 09704
A4_4 09357 09558 09558 09541 09707 09707 09541 09707 09702
A4_5 09363 09553 09553 09547 09701 09701 09547 09701 09679
A4_6 09370 09548 09548 09555 09697 09697 09555 09697 09694
A4_7 09379 09545 09545 09563 09694 09694 09563 09794 09691
A4_8 09389 09544 09544 09573 09692 09692 09573 09792 09692
B4_8 09400 09544 09544 09585 09692 09692 09585 09792 09692
B4_7 09413 09545 09545 09598 09694 09694 09598 09794 09694
B4_6 09427 09548 09548 09613 09697 09697 09613 09697 09697
B4_5 09443 09553 09553 09628 09701 09701 09628 09701 09701
B4_4 09460 09558 09558 09646 09707 09707 09646 09707 09707
Appendix B Simulation Results
Page | 211
B4_3 09471 09562 09562 09656 09711 09711 09656 09711 09711
B4_2 09482 09567 09567 09668 09715 09715 09668 09715 09715
B4_1 09494 09573 09573 09680 09721 09721 09680 09721 09721
B2 Simulation results of Chapter 5
The network losses in each branch for all test cases of 33-bus system and 69-bus
system are listed in Table B-4 and Table B-5 respectively
Table B-4 Network losses in each branch of 33-bus system
Branch number Feeder loss (kW)
Case I Case II Case III Case IV
1 1227 1189 1010 1003
2 5192 2686 2051 2060
3 1995 756 112 490
4 1874 667 074 415
5 3833 1321 122 807
6 192 006 006 006
7 484 0 0 0
8 418 124 211 124
9 357 0 0 0
10 055 001 001 001
11 088 003 003 003
12 267 045 045 045
13 073 008 008 008
14 036 0 0 0
15 028 045 092 045
16 025 048 115 048
17 003 007 022 007
18 016 226 232 226
19 083 1809 1859 1808
20 01 424 436 423
21 004 118 071 118
22 319 316 914 315
23 516 512 1618 510
24 129 128 869 128
25 26 224 005 124
26 334 285 003 155
27 1133 962 003 510
28 786 664 0 345
29 391 326 199 159
30 160 110 018 003
Appendix B Simulation Results
Page | 212
31 021 012 0 000
32 001 0 013 0
33 0 563 809 563
34 0 215 215 215
35 0 174 320 174
36 0 002 033 002
37 0 0 263 0
Total 20314 13981 11753 10844
Table B-5 Network losses in each branch of 69-bus system
Branch number Feeder loss (kW)
Case I Case II Case III Case IV
1 008 007 006 006
2 008 007 006 006
3 020 012 012 010
4 194 011 011 011
5 2829 159 155 159
6 2939 164 160 164
7 691 035 034 035
8 338 012 012 012
9 477 143 137 142
10 101 029 027 028
11 219 032 030 032
12 128 000 000 000
13 124 000 0 000
14 120 0 000 0
15 022 083 043 083
16 032 138 067 138
17 000 001 001 001
18 010 080 032 080
19 007 052 021 052
20 011 083 033 083
21 000 003 001 002
22 001 022 006 022
23 001 049 013 049
24 001 091 021 091
25 000 037 009 037
26 000 019 004 019
27 000 000 000 000
28 000 000 000 000
29 001 001 001 001
30 000 000 000 000
31 001 001 001 001
Appendix B Simulation Results
Page | 213
32 001 001 001 001
33 001 001 001 001
34 000 000 000 000
35 000 003 001 003
36 001 041 019 041
37 002 064 028 064
38 000 018 008 018
39 000 001 000 001
40 005 391 161 391
41 002 166 068 166
42 000 022 009 022
43 000 005 002 005
44 001 057 023 057
45 000 000 000 000
46 002 017 017 013
47 058 416 416 316
48 164 1321 1321 991
49 012 253 253 178
50 000 000 000 000
51 000 000 000 000
52 580 001 001 001
53 673 001 001 000
54 916 000 000 000
55 882 0 0 0
56 4986 000 000 000
57 2458 000 000 000
58 954 000 000 000
59 1071 627 626 379
60 1408 824 823 498
61 011 0 0 0
62 014 000 000 000
63 066 001 001 001
64 004 071 069 071
65 000 000 000 000
66 000 000 000 000
67 002 002 002 002
68 000 000 000 000
69 0 3783 3782 2384
70 0 102 052 102
71 0 0 0 0
72 0 0 0 0
73 0 423 252 423
Total 22562 9885 8758 7397
Appendix B Simulation Results
Page | 214
B3 Simulation results of Chapter 8
Table B-6 Pareto optimal solutions of multi-objective DNR (loss ECOST and SAIDI)
Tie-switches location Feeder loss (kW) ECOST ($yr) SAIDI
(hrscustomeryr)
70 68 71 69 321415 4640359 130895231648616
70 10 41 54 364131 431068083000 102819629963899
17 10 41 70 354092 411445783000000 105858799638989
17 26 10 70 383269 530285525000000 0968805806257521
7 26 54 69 435225 578907612000000 0825265794223827
7 54 41 69 406035 460067870000000 0915047984356197
7 26 54 70 442913 571756512000000 0836828971119134
17 10 71 70 345231 439663189000000 106361687725632
70 10 71 69 331470 443747189000000 110465057160048
70 10 41 69 340330 415529783000000 109962169073406
70 68 41 69 330274 435818516000000 130392343561974
7 54 71 69 397170 488285276000000 0920076865222623
41 10 54 69 356448 438219183000000 101663312274368
70 10 54 26 393311 549907825000000 0938414109506619
70 7 71 69 381047 465595876000000 100306543321300
70 7 41 17 403678 433294470000000 0957002858002407
70 10 54 71 355269 459285489000000 103322518050542
7 54 71 70 404856 481134176000000 0931640042117930
7 26 17 70 432867 552134212000000 0867220667870036
7 70 41 69 389911 437378470000000 0998036552346570
7 26 69 70 419096 556218212000000 0908254362214200
17 7 71 70 394813 461511876000000 0962031738868833
71 10 54 69 347586 466436589000000 102166200361011
10 26 54 69 385625 557058925000000 0926850932611312
70 26 10 69 369504 534369525000000 100983950060168
7 54 41 70 413721 452916770000000 0926611161251504
Appendix B Simulation Results
Page | 215
B4 Simulation results of Chapter 9
Table B-7 Pareto optimal solutions of multi-objective DNR (loss maximum node voltage deviation
feeder load balancing index) for 33-bus system in Case II
Tie-switches location Feeder loss
(kW)
Maximum node
Voltage deviation
Feeder load
balancing index
7 34 35 31 37 176962 0108696024464801 00228687361961248
7 11 35 32 28 143474 00613272038422790 00305387759787611
7 9 14 31 37 142477 00768537372742428 00252628392269486
6 8 12 36 37 151849 00696765908940439 00259144961258893
7 8 14 31 37 155399 00924077518455773 00239781364880477
6 8 12 31 37 169382 0104485611067200 00236077543160956
6 8 12 32 37 152876 00776641110366926 00250547432924683
33 8 14 30 37 171441 0108063061643879 00230652089068052
7 9 14 32 28 140261 00604355611623940 00310349101268755
7 11 35 32 37 143028 00639069227083702 00273727965037185
6 8 14 31 37 159752 00968913958755809 00236540473688646
6 33 35 32 37 170278 00826562726566354 00249194843739843
6 11 35 32 37 144683 00656445815841987 00261947314082027
6 8 14 32 37 146983 00705648561488426 00256096967694280
7 9 14 32 37 139815 00639015456844128 00280407351785895
6 9 14 32 37 143097 00625183468485540 00270001779728268
7 11 35 31 37 148829 00852978398065017 00245113845932977
7 34 35 30 37 202483 0130888991378581 00223050578905545
6 8 14 36 37 146991 00643933147100736 00266176555168500
6 11 35 31 37 154281 00897759906819439 00242838273201709
6 8 13 32 37 150430 00753226918458818 00253604605496161
Table B-8 Pareto optimal solutions of multi-objective DNR (loss maximum node voltage deviation
feeder load balancing index) for 33-bus system in Case III
Tie-switches location Feeder loss
(kW)
Maximum node
Voltage deviation
Feeder load
balancing index
7 14 8 32 28 121696 00575193535569366 00264544805354717
7 11 35 31 37 123007 00712785797883380 00213250141648472
6 12 8 32 37 128324 00630309398395457 00223824361844486
6 14 8 30 37 145672 0101299721228755 00194921779245086
7 33 35 32 28 130184 00583420082867310 00261406698684195
7 14 8 30 37 140274 00967924815464314 00195001911353607
7 21 35 30 37 164190 0113945920950777 00189031534924873
6 13 8 32 37 126434 00607661484850486 00227035446761735
7 14 9 32 28 117726 00575130414815478 00271215548731366
Appendix B Simulation Results
Page | 216
6 14 8 32 28 125920 00566904604559002 00265195832133384
6 12 8 31 37 137974 00889877482038002 00200083704114662
7 11 35 30 37 133030 00891516445489180 00199682922816912
6 11 35 32 37 123013 00593840879899440 00235298833627789
7 14 9 32 37 121070 00631040005210335 00255168322432724
6 14 9 32 28 123916 00566872316455769 00273594084038335
7 14 9 30 37 126587 00812324184971598 00206873922472966
7 14 9 31 28 117529 00642736861104275 00240537048868074
6 14 9 32 37 122047 00593825021727904 00240927348267257
6 11 35 32 28 124883 00566888115014094 00269082055980326
6 11 35 31 37 126802 00756552348586014 00207586957663036
6 14 8 32 37 124050 00593857418451058 00230337877365745
7 13 8 32 28 124039 00575225874614865 00262247242500743
7 11 35 32 28 119522 00575159230231156 00267430211390231
7 14 9 31 37 118759 00642740886891275 00220228862077971
6 14 8 31 37 130316 00816654599427028 00201908840890301
33 14 8 30 37 140110 00923831702765571 00197570883486903
7 12 8 32 28 125895 00587758838819431 00259864524009700
6 13 8 31 37 134936 00865715938530326 00201790772057552
Table B-9 Pareto optimal solutions of multi-objective DNR (loss maximum node voltage deviation
feeder load balancing index) for 33-bus system in Case IV
Tie-switches location DG location Feeder
loss
(kW)
Maximum node
Voltage deviation
Feeder load
balancing index
7 9 14 30 37 15 17 16 112506 00655990339384582 00207847799664288
6 8 14 31 37 14 11 15 120818 00728143829651942 00199639595336255
7 11 35 30 37 16 16 12 118637 00756705031931788 00198888055963062
6 8 14 31 37 11 29 14 125736 00822955381260978 00194988443664523
6 11 35 32 37 29 11 29 116999 00602917954784902 00213598898907595
7 9 14 31 37 15 14 16 110931 00518306996442978 00223689972435171
7 34 35 30 37 16 13 13 140652 00983575865184194 00182688360250883
7 8 14 30 37 14 11 15 128617 00876913785424229 00190954012999288
7 8 14 30 37 11 16 14 127141 00860397262006276 00191601352391895
7 9 14 36 37 30 30 29 109157 00520335391274761 00229564125698243
7 8 14 30 37 10 14 16 126706 00857230143750372 00192117850059117
7 11 35 30 37 13 16 12 121130 00786215737441328 00196617519208137
7 34 35 30 37 13 10 9 151352 0106960621828031 00178195736666725
7 34 35 30 37 10 12 9 152310 0107688512235453 00178046268710843
6 8 14 30 37 11 15 16 130550 00897068798318073 00189590122249633
6 8 14 30 37 16 14 10 130869 00901533044670202 00189271311922809
7 34 35 30 37 10 13 12 148089 0104837492639545 00178736074180585
Appendix B Simulation Results
Page | 217
7 34 35 30 37 13 11 16 143317 0100615335666250 00181553323058751
6 8 14 30 37 10 14 14 133299 00925968739633617 00188139999335965
7 34 35 30 37 13 9 12 148392 0105013682219175 00178453713901855
6 8 14 30 37 14 11 10 137593 00963962506644021 00186232592604301
6 8 14 30 37 11 8 14 136046 00951731865531927 00187106569470356
6 8 14 30 37 11 11 16 135639 00942616575802945 00187170876179048
7 8 14 30 37 15 16 14 122935 00815907052491111 00195198923102276
7 34 35 30 37 12 14 16 140640 00983915740315128 00182784576692257
6 33 35 31 37 11 11 13 146017 00888852225316270 00188548348595259
7 34 35 30 37 12 16 12 142144 00997534014352579 00181578155086060
6 8 14 30 37 14 11 15 132819 00921338781311946 00188143081376993
6 8 14 30 37 10 15 11 136651 00956093119043262 00186781475357014
7 9 14 31 37 14 14 16 111382 00525319705640723 00222591386298574
7 34 35 30 37 13 14 16 139957 00977014014811679 00183484070331887
7 34 35 30 37 12 15 16 139849 00976123852270839 00183745698300515
7 34 35 30 37 12 16 16 138589 00959671533698319 00184842191427931
7 34 35 30 37 16 13 16 137912 00952795751906571 00185525366651277
6 33 35 31 37 11 11 11 148785 00910856464605774 00187751047204272
7 34 35 30 37 12 16 13 141338 00990484927061306 00181980491991251
7 34 35 30 37 12 13 12 145536 0102926179499332 00179590185768212
6 8 14 30 37 14 10 15 132373 00918145642214576 00188660639598312
6 8 14 30 37 16 11 14 131312 00904718190224125 00188759872087077
7 34 35 30 37 13 15 16 139168 00969230570394858 00184436609617936
7 34 35 30 37 13 9 11 150730 0106620666560267 00178315514588942
6 8 14 30 37 14 11 14 133746 00929165522686308 00187615074100094
7 34 35 30 37 9 9 12 152656 0107867658396772 00178031242058681
6 8 14 30 37 10 11 16 135118 00939381882085281 00187414815201857
7 34 35 30 37 12 12 9 149341 0105739135263959 00178316539838164
7 9 14 36 28 32 32 32 110385 00489797931328652 00256323647901629
7 9 14 36 37 32 31 31 108599 00498935433820196 00235262740306846
7 9 14 32 37 31 30 31 108436 00537552050723257 00227898958267559
7 9 14 36 28 32 31 31 110203 00489682960875768 00259015702487973
7 34 35 30 37 8 12 9 154427 0108962750550623 00178021823053241
Appendix B Simulation Results
Page | 218
Table B-10 Pareto optimal solutions of multi-objective DNR (loss maximum node voltage deviation
feeder load balancing index) for 69-bus system in Case II
Tie-switches location Feeder loss
(kW)
Maximum node
Voltage deviation
Feeder load
balancing index
55 61 71 72 12 99036 00524391619987274 00196366946903149
69 61 71 9 14 145213 00664127006601768 00185315761508749
55 61 71 72 14 98845 00524393494628415 00194882148961848
69 70 71 10 14 145135 00666490251240782 00182871906896542
69 61 71 72 12 150267 00699556148777123 00161708619074924
55 61 71 10 14 104521 00524349487665904 00238104755589364
69 61 71 72 13 150383 00700225094171628 00161512783956020
55 61 71 72 13 98937 00524392488739880 00195710324132613
69 61 71 72 11 150792 00682108082577803 00171029450547815
55 61 71 9 14 105348 00524349082167884 00242117051986541
69 61 71 72 14 150513 00700911373758199 00161129748303495
55 61 71 72 11 105195 00524380932334678 00218572363716938
Table B-11 Pareto optimal solutions of multi-objective DNR (loss maximum node voltage deviation
feeder load balancing index) for 69-bus system in Case III
Tie-switches location Feeder loss
(kW)
Maximum node
Voltage deviation
Feeder load
balancing index
55 61 12 14 9 97461 00523081449765275 00226112450860475
69 61 71 14 9 130761 00662843002557533 00155527078006889
55 61 71 14 7 97263 00523080911134007 00226177446060770
55 61 12 71 72 87588 00523152959484715 00174558059214037
55 61 71 14 8 93176 00523082195004728 00211109499855264
55 61 71 13 72 87581 00523154440245970 00174392153380541
55 61 12 14 72 87755 00523153511186373 00174538759436512
55 61 12 71 7 97289 00523080869366065 00226232791264600
69 61 71 11 9 134009 00662855052002667 00154463391981039
69 61 12 14 9 130989 00662843776081034 00155381836375260
55 61 71 13 7 97273 00523080879708534 00227249951330579
55 61 71 14 9 90907 00523086904216601 00201865894567423
55 61 71 14 10 90291 00523088955157064 00199034032147027
69 61 71 14 10 130894 00665207578684145 00154263271797149
55 61 71 14 72 87582 00523156072908145 00174100597226583
69 61 71 11 10 134197 00665220013747228 00153401360203180
69 61 71 11 72 136858 00680828895070073 00147368269784675
69 61 12 14 10 131126 00665208386694061 00154135530565384
55 61 71 11 72 91274 00523126048676607 00184393848480773
Appendix B Simulation Results
Page | 219
Table B-12 Pareto optimal solutions of multi-objective DNR (loss maximum node voltage deviation
feeder load balancing index) for 69-bus system in Case IV
Tie-switches location DG location Feeder
loss
(kW)
Maximum node
Voltage deviation
Feeder load
balancing index
69 63 71 10 14 60 60 60 105879 00543213716422435 00153740505896722
69 63 12 72 71 60 62 62 109324 00575466375767690 00126779733811642
55 61 71 72 11 60 60 60 80324 00429183191505871 00183159151221229
69 63 12 72 71 61 61 62 109323 00575465740537586 00126842028893447
55 61 71 72 12 60 60 60 74165 00429193759769601 00159264876998350
69 63 14 10 71 62 62 62 106070 00543012249613587 00150279825984642
69 63 11 72 71 60 62 60 110547 00558290844078126 00139841427388105
69 63 14 9 71 62 62 62 106271 00540689205567605 00153025056850459
69 61 71 72 11 60 60 60 108838 00542584369620998 00141625735067141
55 61 71 72 14 60 56 60 75837 00436673338725839 00157367114339890
69 63 14 10 71 62 62 60 105960 00542966739560918 00151430448212008
69 61 71 10 14 60 60 60 104307 00527268149576859 00155323687715422
69 63 11 72 71 61 62 62 110652 00558333983851442 00137892112215884
69 63 13 72 71 62 62 62 109522 00576169823075075 00125440050970194
55 61 71 72 14 60 55 60 75975 00436701836501366 00156758120818947
69 63 71 10 14 60 60 62 105896 00542940500362948 00152768514567046
69 63 14 9 71 62 61 61 106159 00540643102892876 00154245882374843
55 61 71 72 13 60 60 60 74066 00429194617185072 00158554987038681
69 62 71 10 14 61 60 60 105886 00542959390978505 00153513700764165
69 63 14 72 71 62 62 62 109622 00576844280930477 00125002240983144
55 63 71 72 14 62 61 62 74382 00440379610790336 00155858821619573
69 63 71 72 11 60 60 60 110530 00558564471048234 00140822204796308
55 63 71 72 14 60 60 62 74285 00440350644694274 00157371695186626
55 63 14 72 71 62 62 62 74448 00440399072962552 00155438948075735
55 63 71 72 14 60 62 62 74344 00440368353288504 00156312863856681
69 63 71 9 14 60 61 60 105882 00542934725670071 00153515485666183
55 63 71 72 14 60 61 62 74305 00440356668532606 00156816031788752
55 61 20 72 13 60 60 60 80533 00429326269571468 00157463174391893
55 63 71 72 14 61 61 62 74343 00440367927398261 00156346520711234
69 61 71 72 14 60 60 60 107187 00561022028435777 00126909641069497
69 63 71 72 11 60 61 60 110533 00558285040786375 00140595150870697
69 63 12 72 71 62 62 62 109436 00575512407997617 00125707103016452
69 63 14 10 71 61 62 62 106000 00542983427485794 00150838099664421
69 63 11 72 71 60 61 62 110569 00558299818740340 00139149694834405
69 63 14 9 71 61 62 60 106118 00540626433897020 00154840963668230
69 61 71 72 12 60 60 60 107041 00559693311798567 00127785892138089
55 61 71 72 14 60 60 60 73974 00429195606297569 00157682511572302
69 63 14 10 71 61 61 62 105958 00542966109653011 00151492343922130
69 63 12 72 71 62 62 61 109365 00575483243249972 00126225992147273
Appendix B Simulation Results
Page | 220
69 63 11 72 71 62 62 60 110611 00558317226735644 00138490567525274
69 63 14 9 71 62 62 61 106201 00540660395254129 00153587525958041
69 63 14 10 71 61 60 62 105917 00542949434469265 00152083287358888
69 63 14 9 71 62 62 60 106160 00540643732226493 00154184014811756
69 63 11 72 71 61 61 62 110610 00558316590719640 00138552654427231
69 63 71 72 11 62 62 62 110723 00558362979744786 00137328015545176
69 61 71 72 13 60 60 60 107108 00560349171634668 00127435051911921
Page | 221
APPENDIX C Control Parameters of
Algorithms
C1 Control parameters of ACO algorithm in Chapter 5
Table C-1 ACO parameters for distribution network reconfiguration and DG allocation in Test Case
2amp3
Parameter Value
Number of ants 50
Maximum number of iteration 200
Pheromone evaporation rate 120530 03
Higher bound of pheromone level 120533119846119834119857 1
Lower bound of pheromone level 120533119846119842119847 001
Constant accumulation number 120533119836 0002
Table C-2 ACO parameters for distribution network reconfiguration and DG allocation in Test Case 4
Parameter Value
Number of ants 100
Maximum number of iteration 500
Pheromone evaporation rate 120530 03
Higher bound of pheromone level 120533119846119834119857 1
Lower bound of pheromone level 120533119846119842119847 001
Constant accumulation number 120533119836 0002
C2 Control parameters of ACO algorithm in Chapter 6
Table C-3 ACO parameters for distribution network reconfiguration and transformer economic
operation
Parameter Value
Number of ants 150
Maximum number of iteration 500
Pheromone evaporation rate 120530 03
Higher bound of pheromone level 120533119846119834119857 1
Lower bound of pheromone level 120533119846119842119847 001
Constant accumulation number 120533119836 0002
Appendix C Control Parameters of Algorithms
Page | 222
C3 Control parameters of ACO algorithm in Chapter 7
Table C-4 ACO parameters for sectionalising switch placement in Test Case 1
Parameter Value
Number of ants 400
Maximum number of iteration 400
Pheromone evaporation rate 120530 04
Higher bound of pheromone level 120533119846119834119857 1
Lower bound of pheromone level 120533119846119842119847 001
Constant accumulation number 120533119836 0002
Table C-5 ACO parameters for sectionalising switch placement in Test Case 2amp3
Parameter Value
Number of ants 500
Maximum number of iteration 200
Pheromone evaporation rate 120530 01
Higher bound of pheromone level 120533119846119834119857 1
Lower bound of pheromone level 120533119846119842119847 001
Constant accumulation number 120533119836 0002
C4 Control parameters of MOACO and AIS-ACO algorithm in
Chapter 8
Table C-6 MOACO parameters for multi-objective distribution network reconfiguration (loss
ECOST and SAIDI)
Parameter Value
Number of ants 100
Maximum number of iteration 100
Pheromone evaporation rate 120530 01
Higher bound of pheromone level 120533119846119834119857 1
Lower bound of pheromone level 120533119846119842119847 001
Constant accumulation number 120533119836 0002
Appendix C Control Parameters of Algorithms
Page | 223
Table C-7 AIS-ACO parameters for multi-objective distribution network reconfiguration (loss
ECOST and SAIDI)
Parameter Value
Maximum number of iteration 50
Pheromone evaporation rate 120530 01
Higher bound of pheromone level 120533119846119834119857 1
Lower bound of pheromone level 120533119846119842119847 001
Constant accumulation number 120533119836 0002
C5 Control parameters of ACO and AIS-ACO algorithm in
Chapter 9
Table C-8 ACO parameters for multi-objective DNR (loss maximum node voltage deviation feeder
load balancing index)
Parameter Value
Number of ants 200
Maximum number of iteration 800
Pheromone evaporation rate 120530 03
Higher bound of pheromone level 120533119846119834119857 1
Lower bound of pheromone level 120533119846119842119847 001
Constant accumulation number 120533119836 0002
Table C-9 AIS-ACO parameters for multi-objective DNR (loss maximum node voltage deviation
feeder load balancing index)
Parameter Value
Maximum number of iteration 3000
Pheromone evaporation rate 120530 01
Higher bound of pheromone level 120533119846119834119857 1
Lower bound of pheromone level 120533119846119842119847 001
Constant accumulation number 120533119836 0002
Page | 224
APPENDIX D List of Publications
1 B Zhang and P A Crossley ldquoMinimum transformer losses based on transformer
economic operation and optimized tie-switches placementrdquo in Proceedings of the 6th
International Conference on Advanced Power System Automation and Protection
(APAP) pp 1-7 20-25 September 2015
2 B Zhang and P A Crossley ldquoReliability improvement using ant colony
optimization applied to placement of sectionalizing switchesrdquo in Proceedings of the
9th
International Conference on Applied Energy (ICAE) pp 1-7 21-24 August 2017
3 B Zhang and P A Crossley ldquoMinimization of distribution network loss using
ant colony optimization applied to transformer economic operation and relocation of
tie-switchesrdquo to be submitted to IEEE Transactions on Smart Grid
4 B Zhang and PA Crossley ldquoOptimized sectionalising switch placement for
reliability improvement in distribution systemsrdquo to be submitted to IEEE
Transactions on Power Delivery
5 B Zhang and P A Crossley ldquoAn ant colony optimization ndashbased method for
multi-objective distribution system reconfigurationrdquo in Proceedings of the 14th
International Conference on Developments in Power System Protection (DPSP) pp
1-6 12-15 March 2018
Page | 5
724 Evaluation of ECOST 132
725 Evaluation of SAIDI 133
726 Evaluation of Switch Costs 133
73 Applying ACO to Sectionalising Switch Placement Problem 134
74 Benefit-to-cost Analysis 135
75 Application Studies 136
751 Test Case 1 138
752 Test Case 2 147
753 Test Case 3 147
76 Summary 148
CHAPTER 8 150
DISTRIBUTION NETWORK RECONFIGURATION FOR LOSS REDUCTION amp
RELIABILITY IMPROVEMENT 150
81 Introduction 150
82 Problem Formulation 152
821 Multi-objective Reconfiguration Problem 152
822 Best Compromise Solution 153
83 Solution Methodology 154
831 Applying MOACO to Multi-objective DNR Problem 154
832 Applying AIS-ACO to Multi-objective DNR Problem 158
84 Application Studies 161
85 Best Compromise Solution 163
86 Summary 164
CHAPTER 9 166
MULTI-OBJECTIVE DISTRIBUTION NETWORK RECONFIGURATION amp DG
ALLOCATION CONSIDERING LOSS VOLTAGE DEVIATION AND LOAD
BALANCING 166
91 Introduction 166
92 Problem Formulation 168
921 Single Fuzzy Satisfaction Objective Function 168
922 Multi-objective Reconfiguration Problem Using Pareto Optimality 170
93 Solution methodology 171
931 Applying ACO to DNR and DG Allocation in the Fuzzy Domain 171
932 Applying AIS-ACO to Multi-objective DNR and DG Allocation Using
Pareto Optimality 171
Page | 6
94 Application Studies 171
941 33-bus System 172
942 69-bus System 180
95 Summary 187
CHAPTER 10 189
CONCLUSION amp FUTURE WORK 189
101 Conclusion 189
102 Future Work 193
References 195
APPENDIX A Network Model Data 204
APPENDIX B Simulation Results 209
APPENDIX C Control Parameters of Algorithms 221
APPENDIX D List of Publications 224
Word count 51012
Page | 7
List of Figures
Fig 2-1 Typical Distribution network [27] 29
Fig 2-2 Recloser operation 30
Fig 2-3 Transformer loss versus transformer load 32
Fig 2-4 Daily load curve of a typical substation before and after load smoothing [38]
34
Fig 2-5 Radial test system 35
Fig 2-6 Fully automated distribution feeder 40
Fig 2-7 Partially automated distribution feeder 41
Fig 2-8 Elements of a single phase transformer [33] 43
Fig 2-9 Construction of a three-phase transformer [33] 43
Fig 2-10 The open-circuit test [33] 44
Fig 2-11 The short-circuit test [33] 45
Fig 2-12 Simple two-bus network 47
Fig 2-13 Reliability model for static components 51
Fig 2-14 Procedure for reliability evaluation 52
Fig 2-15 Sample network 53
Fig 2-16 Linear membership function 54
Fig 3-1 Example of ant colony system [69] 63
Fig 3-2 Flowchart of the ant colony algorithm 65
Fig 3-3 Flowchart of the AIS-ACO algorithm 67
Fig 4-1 Procedure of domestic electricity demand profile generation 72
Fig 4-2 Monte Carlo simulation platform for three transformer operation modes
comparison 74
Fig 4-3 Flowchart of transformer loss assessment 75
Fig 4-4 Monte Carlo simulation platform for distribution network reconfiguration 76
Fig 4-5 Generic distribution network topology 78
Fig 4-6 Transformer load factor variation 79
Fig 4-7 Transformer loss variations in different scenarios 80
Fig 4-8 11 kV 4th
feeder voltage profiles in different scenarios 81
Fig 4-9 Voltage profiles of Load 4_1 in different scenarios 82
Fig 4-10 Voltage profiles of Load 4_8 in different scenarios 83
Page | 8
Fig 4-11 11 kV 4th
feeder mean voltage profile of various TCLFs 84
Fig 4-12 Test system 86
Fig 4-13 Daily load variations for different load groups 87
Fig 4-14 Mean voltage profiles in S1 S2 and S3 89
Fig 4-15 Mean voltage profiles in S1 S4 and S7 89
Fig 5-1 Search space of DNR and DGs Placement 95
Fig 5-2 Flowchart of the ACO applied to DNR and DGs placement 98
Fig 5-3 33-bus system 100
Fig 5-4 33-bus system for feeder loss minimisation Case II 101
Fig 5-5 33-bus system for feeder loss minimisation Case III 102
Fig 5-6 33-bus system for feeder loss minimisation Case IV 103
Fig 5-7 Comparison of feeder loss for different DG capacities before and after
simultaneous reconfiguration and DG allocation 104
Fig 5-8 Comparison of voltage profiles in different cases of 33-node system 104
Fig 5-9 69-bus system 105
Fig 5-10 69-bus system for feeder loss minimisation Case II 106
Fig 5-11 69-bus system for feeder loss minimisation Case III 107
Fig 5-12 69-bus system for feeder loss minimisation Case IV 107
Fig 5-13 Comparison of feeder loss for different DG capacities before and after
simultaneous reconfiguration and DG allocation 108
Fig 5-14 Comparison of voltage profiles in different cases of 69-node system 109
Fig 6-1 The reconfiguration hours for a typical day 113
Fig 6-2 Search space of DNR and TEO 115
Fig 6-3 Sample network with three substations 116
Fig 6-4 Flowchart of the ACO applied to DNR and TEO for a specific type of day
117
Fig 6-5 Distribution feeder connected to RBTS Bus 4 118
Fig 6-6 Daily load profile of residential consumers 119
Fig 6-7 Daily load profile of commercial consumers 120
Fig 6-8 Daily load profile of industrial consumers 120
Fig 6-9 Daily load profile (MW) of the main feeder 120
Fig 6-10 Annual energy loss with different DG capacities 123
Fig 6-11 Annual energy loss in uncoordinated charging strategy 125
Fig 6-12 Annual energy loss in coordinated charging strategy 126
Page | 9
Fig 7-1 Membership function for SAIDI and switch cost reduction 131
Fig 7-2 Membership function for ECOST reduction 132
Fig 7-3 Search space of sectionalising switch placement 134
Fig 7-4 Distribution feeder connected to RBTS Bus 4 with 6 sectionalising switches
136
Fig 7-5 Optimal relocation of sectionalising switches in Test Case 11 139
Fig 7-6 Optimal installation of sectionalising switches in Test Case 12 141
Fig 7-7 Optimal installation and relocation of sectionalising switches in Test Case
13 142
Fig 7-8 BCR versus years 143
Fig 7-9 Variation of cost versus change in CDF 144
Fig 7-10 Number of installed sectionalising switches versus change in CDF 145
Fig 8-1 Flowchart of the MOACO algorithm applied to multi-objective DNR
problem 157
Fig 8-2 Flowchart of the AIS-ACO algorithm applied to multi-objective DNR
problem 158
Fig 8-3 Distribution feeder connected to RBTS Bus 4 161
Fig 8-4 Pareto solutions obtained (minimisation of feeder loss ECOST and SAIDI)
162
Fig 9-1 Membership function for feeder loss reduction 168
Fig 9-2 Membership function for maximum node voltage deviation reduction 169
Fig 9-3 Membership function for load balancing index reduction 170
Fig 9-4 33 bus-system for fuzzy multi-objective optimisation Case II 173
Fig 9-5 Pareto front obtained for 33-bus system in Case II 174
Fig 9-6 33 bus-system for fuzzy multi-objective optimisation Case III 175
Fig 9-7 Pareto front obtained for 33-bus system in Case III 176
Fig 9-8 33 bus-system for fuzzy multi-objective optimisation Case IV 178
Fig 9-9 Pareto front obtained for 33-bus system in Case IV 178
Fig 9-10 69 bus system for fuzzy multi-objective optimisation Case II 180
Fig 9-11 Pareto front obtained for 69-bus system in Case II 181
Fig 9-12 69-bus system for fuzzy multi-objective optimisation Case III 183
Fig 9-13 Pareto front obtained for 69-bus system in Case III 183
Fig 9-14 69-bus system for fuzzy multi-objective optimisation Case IV 185
Fig 9-15 Pareto front obtained for 69-bus system in Case IV 186
Page | 10
List of Tables
Table 2-1 Transformer economic operation area 33
Table 2-2 Transformer technical specifications and costs 35
Table 3-1 Relationship of 119911 lowast and 119862 62
Table 4-1 Household size by number of people in household as a proportion [103] 72
Table 4-2 Parameters of a typical 3311 kV two-winding transformer [106] 78
Table 4-3 Daily transformer loss in different scenarios 80
Table 4-4 Transformer loss with different TCLF 85
Table 4-5 Average number of switching operations with different TCLF 85
Table 4-6 Transformer loss in Test Case 2 88
Table 5-1 Results of different cases for the 33-bus system 100
Table 5-2 Comparison of simulation results for 33-bus system in Case II 101
Table 5-3 Comparison of ACO with CGA and CSA for the 33-bus system in Case II
102
Table 5-4 Results of different cases for the 69-bus system 105
Table 5-5 Comparison of simulation results for 69-bus system in Case II 106
Table 6-1 Revised customer data (peak load) 119
Table 6-2 The distribution of load types for a whole year 121
Table 6-3 Results of DNR and TEO with different load types in Test Case 1 122
Table 6-4 Characteristics of EV 124
Table 7-1 Customer data (Average load) 137
Table 7-2 Sector interruption cost estimation ($kW) 138
Table 7-3 Results of sectionalising switches relocation in Test Case 11 140
Table 7-4 Results of sectionalising switches installation in Test Case 12 141
Table 7-5 Results of sectionalising switches relocation and installation in Test Case
13 143
Table 7-6 Impacts of 120588 variation on objective function 119869 146
Table 7-7 Impacts of variation in number of ants on objective function 119869 146
Table 7-8 Results of sectionalising switches relocation and installation in Test Case
2 147
Table 7-9 Results of sectionalising switches installation and relocation in Test Case
3 148
Page | 11
Table 8-1 Revised customer data (Average load) 162
Table 8-2 Mean and standard deviation of Pareto Front (loss ECOST and SAIDI)
163
Table 8-3 Minimum solutions along each objective (loss ECOST and SAIDI) 163
Table 8-4 Best compromise solutions (loss ECOST and SAIDI) 164
Table 9-1 Results of DNR in fuzzy multi-objective formulation for 33-bus system in
Case II 173
Table 9-2 Mean and standard deviations of Pareto Front for 33-bus system in Case II
174
Table 9-3 Minimum solutions along each objective for 33-bus system in Case II 175
Table 9-4 Results of DNR in fuzzy multi-objective formulation for 33-bus system in
Case III 176
Table 9-5 Mean and standard deviations of Pareto Front for 33-bus system in Case
III 176
Table 9-6 Minimum solutions along each objective for 33-bus system in Case III 177
Table 9-7 Results of DNR and DG allocation in fuzzy multi-objective formulation
for 33-bus system in Case IV 178
Table 9-8 Mean and standard deviations of Pareto Front for 33-bus system in Case
IV 179
Table 9-9 Minimum solutions along each objective for 33-bus system in Case IV 179
Table 9-10 Results of DNR in fuzzy multi-objective formulation for 69-bus system
in Case II 181
Table 9-11 Mean and standard deviations of Pareto Front for 69-bus system in Case
II 181
Table 9-12 Minimum solutions along each objective for 69-bus system in Case II 182
Table 9-13 Results of DNR in fuzzy multi-objective formulation for 69-bus system
in Case III 183
Table 9-14 Mean and standard deviations of Pareto Front for 69-bus system in Case
III 184
Table 9-15 Minimum solutions along each objective for 69-bus system in Case III
184
Table 9-16 Results of DNR and DGs allocation in fuzzy multi-objective formulation
for 69-bus system in Case IV 185
Page | 12
Table 9-17 Mean and standard deviations of Pareto Front for 69-bus system in Case
IV 186
Table 9-18 Minimum solutions along each objective for 69-bus system in Case IV
187
Table A-1 Typical configurations and parameters of 11 kV triplex cables in the UK
204
Table A-2 Line and load data of 33-bus system 205
Table A-3 Line and load data of 69-bus system 206
Table A-4 Feeder data of RBTS Bus 4 207
Table A-5 Reliability Data for RBTS Bus 4 208
Table B-1 The locations of tie-switch in Scenario 9 209
Table B-2 Mean voltage profiles at each node in the linked feeder 210
Table B-3 95th
voltage profiles at each node in the linked feeder 210
Table B-4 Network losses in each branch of 33-bus system 211
Table B-5 Network losses in each branch of 69-bus system 212
Table B-6 Pareto optimal solutions of multi-objective DNR (loss ECOST and
SAIDI) 214
Table B-7 Pareto optimal solutions of multi-objective DNR (loss maximum node
voltage deviation feeder load balancing index) for 33-bus system in Case II 215
Table B-8 Pareto optimal solutions of multi-objective DNR (loss maximum node
voltage deviation feeder load balancing index) for 33-bus system in Case III 215
Table B-9 Pareto optimal solutions of multi-objective DNR (loss maximum node
voltage deviation feeder load balancing index) for 33-bus system in Case IV 216
Table B-10 Pareto optimal solutions of multi-objective DNR (loss maximum node
voltage deviation feeder load balancing index) for 69-bus system in Case II 218
Table B-11 Pareto optimal solutions of multi-objective DNR (loss maximum node
voltage deviation feeder load balancing index) for 69-bus system in Case III 218
Table B-12 Pareto optimal solutions of multi-objective DNR (loss maximum node
voltage deviation feeder load balancing index) for 69-bus system in Case IV 219
Table C-1 ACO parameters for distribution network reconfiguration and DG
allocation in Test Case 2amp3 221
Table C-2 ACO parameters for distribution network reconfiguration and DG
allocation in Test Case 4 221
Page | 13
Table C-3 ACO parameters for distribution network reconfiguration and transformer
economic operation 221
Table C-4 ACO parameters for sectionalising switch placement in Test Case 1 222
Table C-5 ACO parameters for sectionalising switch placement in Test Case 2amp3222
Table C-6 MOACO parameters for multi-objective distribution network
reconfiguration (loss ECOST and SAIDI) 222
Table C-7 AIS-ACO parameters for multi-objective distribution network
reconfiguration (loss ECOST and SAIDI) 223
Table C-8 ACO parameters for multi-objective DNR (loss maximum node voltage
deviation feeder load balancing index) 223
Table C-9 AIS-ACO parameters for multi-objective DNR (loss maximum node
voltage deviation feeder load balancing index) 223
Page | 14
List of Abbreviations
Abbreviations Definition
ACO Ant Colony Optimisation
ACS Ant Colony System
AENS Average Energy Not Supplied
AIS Artificial Immune Systems
AIS-ACO Artificial Immune Systems-Ant Colony Optimisation
ANN Artificial Neutral Network
ASP Active Server Pages
BCR Benefit-to-cost Ratio
BEM Branch Exchange Method
BPSO Binary Particle Swarm Optimisation
CDF Customer Damage Function
CGA Continuous Genetic Algorithm
CSA Cuckoo Search Algorithm
DA Distribution Automation
DNO Distribution Network Operator
DNR Distribution Network Reconfiguration
DG Distributed Generation
DPSO Discrete Particle Swarm Optimisation
ECOST Expected Customer Damaged Cost
EDNS Expected Demand Not Supplied
ENS Energy not supplied
EV Electric Vehicle
FMEA Failure-mode-and-effect Analysis
FWA Firework Algorithm
FRTU Feeder Remote Terminal Unit
GA Genetic Algorithm
HC Hyper Cube
HSA Harmony Search Algorithm
HV High Voltage
Page | 15
IWO Invasive Weed Optimisation
LV Low Voltage
MDC Maximum Driving Capability
MILP Mixed Integer Linear Programming
MOACO Multi-objective Ant Colony Optimisation
MV Medium Voltage
PSO Particle Swarm Optimisation
RBTS Roy Billinton Test System
RGA Refined Genetic Algorithm
SA Simulated Annealing
SAIDI System Average Interruption Duration Index
SAIFI System Average Interruption Frequency Index
SCADA Supervisory Control and Data Acquisition
SSP Sectionalising Switch Placement
TS Tabu Search
TCLF Transformer Critical Load Factor
TEO Transformer Economic Operation
TOM Transformer Operation Mode
VML Vector Markup Language
Page | 16
Abstract
The University of Manchester
Submitted by Boyi Zhang
for the degree of Doctor of Philosophy
Distribution Network Automation for Multi-objective Optimisation
December 2017
Asset management and automation are acknowledged by distribution utilities as a
useful strategy to improve service quality and reliability However the major
challenge faced by decision makers in distribution utilities is how to achieve long-
term return on the projects while minimising investment and operation costs
Distribution automation (DA) in terms of transformer economic operation (TEO)
distribution network reconfiguration (DNR) and sectionalising switch placement
(SSP) is recognised as the most effective way for distribution network operators
(DNOs) to increase operation efficiency and reliability Automated tie-switches and
sectionalising switches play a fundamental role in distribution networks
A method based on the Monte Carlo simulation is discussed for transformer loss
reduction which comprises of profile generators of residential demand and a
distribution network model The ant colony optimisation (ACO) algorithm is then
developed for optimal DNR and TEO to minimise network loss An ACO algorithm
based on a fuzzy multi-objective approach is proposed to solve SSP problem which
considers reliability indices and switch costs Finally a multi-objective ant colony
optimisation (MOACO) and an artificial immune systems-ant colony optimisation
(AIS-ACO) algorithm are developed to solve the reconfiguration problem which is
formulated within a multi-objective framework using the concept of Pareto
optimality The performance of the optimisation techniques has been assessed and
illustrated by various case studies on three distribution networks The obtained
optimum network configurations indicate the effectiveness of the proposed methods
for optimal DA
Page | 17
Declaration
No portion of the work referred to in the thesis has been submitted in support of an
application for another degree or qualification of this or any other university or other
institute of learning
Page | 18
Copyright Statement
i The author of this thesis (including any appendices andor schedules to this
thesis) owns certain copyright or related rights in in (the ldquoCopyrightrdquo) she
has given The University of Manchester certain rights to use such Copyright
including for administrative purposes
ii Copies of this thesis either in full or in extracts and whether in hard or
electronic copy may be made only in accordance with the Copyright
Designs and Patents Act 1988 (as amended) and regulations issued under it
or where appropriate in accordance with licensing agreements which the
University has from time to time This page must form part of any such
copies made
iii The ownership of certain Copyright patents designs trademarks and other
intellectual property (the ldquoIntellectual Propertyrdquo) and any reproductions of
copyright works in the thesis for example graphs and tables
(ldquoReproductionsrdquo) which may be described in this thesis may not be owned
by the author and may be owned by third parties Such Intellectual Property
and Reproductions cannot and must not be made available for use without the
prior written permission of the owner(s) of the relevant Intellectual Property
andor Reproductions
iv Further information on the conditions under which disclosure publication
and commercialisation of this thesis the Copyright and any Intellectual
Property andor Reproductions described in it may take place is available in
the University IP Policy (see
httpdocumentsmanchesteracukDocuInfoaspxDocID=24420) in any
relevant Thesis restriction declarations deposited in the University Library
The University Libraryrsquos regulations (see
httpwwwlibrarymanchesteracukaboutregulations) and in The
Universityrsquos policy on Presentation of Theses
Page | 19
Acknowledgements
First and foremost I would like to express my deepest gratitude to my supervisor
Prof Peter Crossley for his invaluable guidance and continuous encouragement
throughout the project
I would like to thank my friends and colleagues in the Ferranti Building at The
University of Manchester Prof Zhongdong Wang and Dr Qiang Liu for the fruitful
research discussions and their encouragement throughout the period of my PhD
I wish to thank North China Electric Power University PR China for the 2+2
course and also to Prof Chunming Duan and Prof Sangao Hu for their help and
encouragement
I also wish to thank Prof Bo Zhang Prof Jianguo Zhao and Prof Li Zhang from
Shandong University PR China who continued to support my research with their
valuable feedback and advice
Finally I would like to express my gratitude to my parents for their encouragement
and support
Page | 20
CHAPTER 1
INTRODUCTION
11 Motivation
The electricity ldquoutilityrdquo distribution network is part of a power system that carries
electricity from a high voltage transmission grid to industrial commercial and
residential customers [1] In England and Wales the voltage level of distribution
networks ranges from 132 kV to 230 V [2] Generally most distribution networks
operating at voltages below 25 kV are designed in closed loop but are operated
radially due to the simplicity of operation the ease of protection coordination and
the minimisation of overall economics [3] [4]
The electric power generation transmission and distribution companies are not only
energy producers but also significant power consumers Power loss occurs when
electricity is supplied to customers In 2013 the total distribution losses of GBrsquos
networks were estimated to be 196 TWh which indicates that about 6 of the total
power generation is wasted in the form of losses at distribution level [5] Utility
statistics also indicate that distribution transformers account for approximately 22
of these losses and the line and cable losses make up the remaining 78 Reduction
in active power loss can help distribution network operators (DNOs) save costs and
increase profits
The expression ldquoPower quality = Voltage qualityrdquo has been widely accepted as the
wave shape and magnitude of voltage that strongly influences the power quality
Chapter 1 Introduction
Page | 21
received by customers [6] According to the EN50160 standard [7] under normal
conditions at least 95 of the mean 10 minutes average rms voltage magnitudes in
an 11 kV electricity distribution network should be within the range 09 pu to 11 pu
during one week
Distribution network reliability has proved to be another fundamental attribute for
the safe operation of any modern power system [8] Data show that about 80 of
customer outages are due to distribution system failures [9] Based on the resource
from [10] in 2011 the average number of minutes of lost supply per customer in GB
is 70 minutes According to [11] electricity breakdowns cost the United States
around $80 billion per year With improved reliability the DNOs can save expenses
that are spent on networkrsquos maintenances after a failure [12]
The major challenge faced by DNOs is how to distribute the power in a low-cost
reliable and efficient way Distribution automation (DA) is recognised as the most
effective method for DNOs to increase operation efficiency and reliability The three
main parts of DA are transformer economic operation (TEO) distribution network
reconfiguration (DNR) and sectionalising switch placement (SSP) TEO refers to the
optimum selection of the transformers needed to supply each feeder This is related
to the economic evaluation of network performance and the resilience of the
network DNR is a process that involves changing the network topology by altering
the openclose status of sectionalising (normally closed) and tie (normally open)
switches [13] [14] Installation of new sectionalising switches and relocation of
existing sectionalising switches are defined as SSP
Mathematically DA is a discrete non-linear constrained combinational optimisation
problem that is subject to operating constraints As it is not a practical solution to
investigate all possible network configurations ant colony optimisation (ACO)-
based heuristic search algorithms have been developed
To build a cleaner climate-friendly community the European Union has set a target
on carbon emissions for a 40 60 and 80 below 1990 levels by 2030 2040
and 2050 respectively [15] Therefore a large number of renewable distributed
generations (DGs) are deployed DG is a small electric generation unit that is
connected directly to the distribution network or appears on side of the meter
accessed by the customer [16] Since the number of DGs has increased in recent
Chapter 1 Introduction
Page | 22
years this has resulted in bidirectional power flows and locally looped networks [17]
The integration of high numbers of DGs strongly affects network operation and
planning Therefore optimal placement and sizing of DGs strongly improve
distribution network performance
12 Objectives
The aim of this research is to improve service quality and efficiency based on the
results of DA To achieve this aim the objectives of this thesis are as follows
To review distribution networks DA loss and reliability assessment and
optimisation functions
To propose three optimisation techniques namely the Monte Carlo Method the
ACO algorithm and the artificial immune systems-ant colony optimisation (AIS-
ACO) algorithm
To develop an optimal strategy consisting of TEO and DNR for transformer loss
reduction Statistic models of customer electrical demands should be established
to evaluate their impact from the perspective of probability
To assess the DNR and DG placement problems simultaneously in terms of
distribution feeder loss minimisation
To assess the TEO and DNR problem simultaneously in terms of distribution
network loss minimisation including transformer loss and feeder loss under
different load scenarios
To assess the SSP problem simultaneously based on three objectives namely
reduction of unserved energy cost decrease in the average time that a customer is
interrupted and minimisation of switch costs and using the fuzzy set theory
To propose a benefit-to-cost analysis to justify whether the benefits of installing
and relocating sectionalising switches can justify the cost or not
To formulate the optimal network reconfiguration problem within a multi-
objective framework using the Pareto optimality concept where network loss
and reliability indices are simultaneously optimised
Chapter 1 Introduction
Page | 23
To assess the DNR and DG allocation problem in terms of three conflicting
objectives optimisation network loss maximum node voltage deviation and
load balancing index in order to obtain a set of non-dominated solutions
13 Contribution of the work
This thesis has presented three methodologies of DA All of them are designed to
achieve service quality and efficiency improvement
The contributions of this thesis are summarised below
Load profiles In most literatures the load variations are ignored in their studies
which could underestimate the total energy loss for the utility [18] The
stochastic nature associated with load variety is considered in Chapter 4 In this
chapter the value of the load associated with domestic demand profiles are
obtained from the research described in [19] this can produce a random 1-min
resolution model for UK households A pool of load profiles is randomly
generated by this model in MATLAB Following this each node in the feeders
from the system is assigned with residential demand profiles from the pool based
on the Monte Carlo methodology
In Chapter 6 the distribution loads experience daily and seasonal variations The
study considers the daily load curves of different types of consumers (residential
commercial and industrial) In addition the days are divided into eight types
spring weekdays spring weekends summer weekdays summer weekends
autumn weekdays autumn weekends winter weekdays and winter weekends
Optimisation problems Previously it was observed that sufficient work has
been completed in terms of examining the TEO and the DNR problems
separately In Chapter 4 and 6 both the TEO and network reconfiguration
problems are integrated to benefit the whole distribution network effectively
Different combinations of locations of tie-switches in the network and operation
modes of all transformers in the substations represent different network
configurations Network reconfiguration and transformer operation modes
variation are dealt simultaneously using the ACO algorithm with an objective of
network loss minimisation as presented in Chapter 6
Chapter 1 Introduction
Page | 24
Most research projects have focused only on the optimisation of either the DNR
or the DG allocation problem An ACO algorithm is proposed in Chapter 5 to
deal with the DNR and DG allocation problems simultaneously in terms of
feeder loss minimisation In Chapter 9 the study aims to determine the optimum
network configurations and DG locations that minimise the active power loss
maximum node voltage deviation and feeder load balancing simultaneously
Multi-objective optimisation framework When there are multiple and
conflicting objectives that need to be satisfied all objective can be converted into
a single objective function which reflects a compromise among all objectives
The single objective function has two forms weighted aggregation and fuzzy
satisfaction objective function The selection of the form depends on the number
of objectives as well as their units and dimensions In Chapter 7 the system
expected outage cost to customers (ECOST) and switch costs can be converted
into a single objective function by aggregating these objectives in a weighted
function However as system interruption duration index (SAIDI) and switch
costs have different dimensions and units the two conflicting objectives are
modelled with fuzzy sets and then combined into a single objective function
Also a fuzzy membership function based on max-min principle is presented for
optimising ECOST SAIDI and switch costs simultaneously In Chapter 9 a new
operator called lsquomax-geometric meanrsquo has been introduced to determine the
degree of overall fuzzy satisfaction
However the above simple optimisation processes only obtain a compromise
solution It is no longer suitable if the DNO wishes to obtain all possible optimal
solutions for all the conflicting objectives at the same time [20] Therefore a set
of Pareto optimal solutions is introduced in this study And the corresponding
objective values constitute the Pareto front It allows decision makers to select
the most suitable topology from the Pareto optimal solutions for implementation
depending on the utilitiesrsquo priorities In Chapter 8 the study formulates the
optimal network reconfiguration problem within a multi-objective framework
using the concept of Pareto optimality where network loss and reliability indices
are simultaneously optimised In Chapter 9 active power loss maximum node
voltage deviation and feeder load balancing are optimised simultaneously
After obtaining the Pareto optimal solutions the best compromise solution
among the multiple objectives can be selected by comparing the fitness value of
Chapter 1 Introduction
Page | 25
each member in the Pareto front The best compromise solution is varied by
changing the values of weighting factors based on the tendencies of the network
decision makers A set of best compromise solutions can be obtained by varying
the weighing factors of each objective function and this is presented in Chapter 8
Proposal of ACO-based algorithms for assessment of optimisation problems
The ACO algorithm is a population-based approach based on the behaviour of
real ants [14] The proposed algorithm is not only used for assessment of the
TEO problem but also with DNR DG allocation and SSP problems The ACO
control parameters are different for each test case The selection of parameters is
a balance between the convergence rate and the global search ability of the
algorithm They are set experimentally using information from several trial runs
The results obtained by the ACO algorithm have been compared to those from
other algorithms in Chapter 5 and the ACO parameter sensitivity analysis is
provided in Chapter 7
In Chapter 8 the multi-objective ant colony optimisation (MOACO) and AIS-
ACO algorithms have been proposed and compared for assessment of multi-
objective DNR problems Both algorithms focus on problems in terms of Pareto
optimality where the objective functions are multidimensional and not scalar
A full list of publications resulting from this thesis is included in Appendix D
14 Structure of the thesis
The thesis is organised as follows
Chapter 2 introduces the distribution network configurations and associated
equipment It also gives a comprehensive literature survey which reviews the
existing knowledge and research activities in the distribution automation (DA)
including transformer economic operation (TEO) distribution network
reconfiguration (DNR) and sectionalising switch placement (SSP) The assessment
of transformer loss feeder loss and reliability indices as well as the multi-objective
optimisation functions are also described in this chapter
Chapter 3 summarises the optimisation techniques for assessment of the multi-
objective problem The Monte Carlo Method ACO algorithm and AIS-ACO hybrid
algorithm are described in detail
Chapter 1 Introduction
Page | 26
Chapter 4 proposes two methodologies for transformer loss reduction whilst
maintaining satisfactory voltages which are TEO and DNR The demand profiles are
randomly generated by the profile generators in MATLAB Following this each
node in the feeders from the system is assigned with demand profiles based on the
Monte Carlo Method The effectiveness of the two investigated methods
implemented either alone or together are presented and discussed
Chapter 5 describes an ACO algorithm to assess the network reconfiguration and
DG placement problems simultaneously in terms of distribution feeder loss
minimisation The results of four scenarios carried out on two standard IEEE 33-
node and 69-node systems are presented to show the effectiveness of the proposed
approach The effect of DG capacities on DNR for feeder loss reduction is also
discussed Moreover the results obtained by ACO algorithm have been compared to
those from other algorithms in the literature
Chapter 6 presents the ACO algorithm for minimisation of the losses associated
with a network loss including transformer loss and feeder loss under different load
scenarios This is achieved by the optimum selection of which transformers need to
supply each feeder and by determining the optimal locations of the tie-switches The
performance of this approach to minimise power loss is assessed and illustrated by
various case studies on a typical UK distribution network The impact of DGs and
electrical vehicles (EVs) in reducing the loss is also discussed
Chapter 7 explores an ACO-based methodology for the placement of sectionalising
switches in distribution networks The objectives of the proposed sectionalising
switch placement problem are reduction of unserved energy costs decrease in the
average time that a customer is interrupted and minimisation of switch costs These
objectives are formulated in either a single objective function or a fuzzy satisfaction
objective function The performance of the proposed methodology is assessed and
illustrated by various test cases on a well-known reliability test system
Chapter 8 formulates the optimal network reconfiguration problem within a multi-
objective framework using the Pareto optimality concept where network loss and
reliability indices are simultaneously optimised The MOACO algorithm and AIS-
ACO algorithm are proposed and compared for assessment of DNR problems The
Chapter 1 Introduction
Page | 27
proposed approaches are tested on Bus 4 of the RBTS and a set of high quality non-
dominated solutions are obtained
Chapter 9 addresses two algorithms to assess the DNR and DG allocation problems
in terms of the three conflicting objectives minimisation network loss maximum
node voltage deviation and load balancing index The ACO algorithm is used to
solve the problem in the fuzzy domain and the AIS-ACO algorithm is adopted to
obtain a set of non-dominated solutions using the concept of Pareto optimality The
effectiveness and the efficiency of the proposed methods are implemented on two
standard test systems as case studies
Chapter 10 concludes the thesis by summarising the main findings of the work
Finally possible future research ideas associated with this thesis are proposed
All the network models are built in OpenDSS and all the algorithms are coded in
MATLAB They are carried on a 340-GHz processor with 16 GBs of RAM memory
for all studies
Page | 28
CHAPTER 2
DISTRIBUTION AUTOMATION
21 Introduction
Distribution automation (DA) is an important part of a Smart Grid [21] It enables a
distribution network operator (DNO) to monitor coordinate and operate distribution
components in real-time from a remote control centre [22] [23] This improves the
reliability performance and operational efficiency of the electrical distribution
system and helps increase the market penetration of distributed generations (DGs)
and electrical vehicles (EVs) [24]ndash[26]
The remainder of this chapter is structured as follows Sections 22-23 introduce the
network configurations and associated equipment Sections 24-26 present the three
main parts of DA namely transformer economic operation (TEO) distribution
network reconfiguration (DNR) and sectionalising switch placement (SSP)
Transformer loss feeder loss and reliability indices assessments are described in
Sections 27-29 Three methods for assessment of multi-objective optimisation
problems are reviewed in Section 210 A summary of the main conclusions in this
chapter is given in Section 211
Chapter 2 Distribution Automation
Page | 29
Tie-switch
Sectionalising switch
22 Distribution Network Configurations
In England and Wales the voltage level of distribution networks ranges from 132 kV
to 230 V [2] Generally most distribution networks are designed in closed loop but
are operated radially due to the simplicity of operation the ease of protection
coordination and the minimisation of overall economics [3] [4]
There are three typical system configurations shown in Fig 2-1 [27] The radial
system in Fig 2-1 (a) is common in rural areas but does not include any backup
supplies Consequently the lack of feeder interconnections means a short-circuit
fault will interrupt power to all the downstream customers and power will not be
restored until the faulted equipment is repaired The tie-switches (normally open) in
Fig 2-1 (b) connect two feeders and make the system radial in a primary loop There
are multiple tie-switches between multiple feeders in distribution systems Fig 2-1 (c)
describes a link arrangement and during normal conditions the systems are operated
radially However when a fault occurs the part affected by the fault is isolated by
tripping the breakers The unaffected areas can then be restored from a different
busbar by closing the tie-switches and feeding the supply
(a) Radial system (b) Primary loop (c) Link Arrangement
Fig 2-1 Typical Distribution network [27]
Chapter 2 Distribution Automation
Page | 30
23 Switchgear for Distribution Network
There is a large variety of switchgears used in distribution networks this includes
reclosers sectionalising switches tie-switches fuses and circuit breakers This
section mainly focuses on reclosers sectionalising switches and tie-switches
231 Reclosers
Reclosers are automatic self-contained protection devices installed on main feeders
and operate as a part of the protection schemes [28] [29] They are a type of circuit
breakers with control measurement and automatic re-closing functions Most faults
on distribution feeders are temporary ie they last from a few cycles to a few
seconds and are cleared by protection tripping a circuit breaker [1] Reclosers
normally count the number of overcurrent pulses followed by the line de-
energisation sequences [1] They always coordinate with other types of protection
equipment These include such as fuses and sectionalising switches for the purpose
of fault isolation and system restoration The process of recloser operation is shown
in Fig 2-2 The time between reclosures and the time of the reclose can be
programmed If the fault is transient the recloser will operate 1-3 times and then
restore service quickly If the fault is permanent after a pre-set number of trip-
reclose operations the recloser is locked and the recloser interrupter triggers a final
trip
Fig 2-2 Recloser operation
Time between reclosures
Time of the reclose Fault current
Recloser locks
out on 2nd
reclose
as programmed
Recloser opens
Recloser recloses
fault still present
Recloser recloses
fault still present
Recloser re-opens
fault still present
Load current
Chapter 2 Distribution Automation
Page | 31
232 Sectionalising Switches
Sectionalising switches are the protective devices that operate in conjunction with
backup circuit breakers or reclosers [25] They are isolating devices that
automatically isolate the faulted sections from a distribution network after a
permanent fault has occurred and after the line is de-energised by the feeder breaker
[1] This is because sectionalising switches are not designed to interrupt the fault
current and must be used with the feeder breaker that can break and reclose a circuit
under all conditions ie normal or faulty operating conditions [25] [30] A detailed
operation of sectionalising switches is presented in Section 26
233 Tie-switches
Tie-switches refer to the normally open switches of the network By closing the
opened tie-switch the load is transferred from one feeder to another but this requires
an appropriate sectionalising switch to be opened to restore the radial topology [31]
The tie-switch placement should follow certain principles ie all the loads are
energised and the network is operated in radial configurations The tie-switches are
designed to operate in normal condition but are not suitable for the interruption of
fault currents They are designed to operate after a switching device (circuit breaker
of fuse) has interrupted the fault current
24 Transformer Economic Operation
241 Basic Concepts
Power transformers are the interface between the generators and the transmission
lines and between lines operating at different voltage levels [32] They are a critical
part of an electric power system and transform the ac voltage based on the principle
of electromagnetic induction A step-up transformer ensures the efficient
transmission of power ie high voltage-low current and a step-down transformer
permits the transmitted power to be used at a lower and safer voltage [33]
Distribution transformers are used to reduce the primary system voltages to the
Chapter 2 Distribution Automation
Page | 32
Tran
sfo
rme
r Lo
ss
Transformer Load Factor
1 Transformer
2 Transformers
utilisation voltages [25] normally 132 kV for high voltage (HV) 11 kV-33 kV for
medium voltage (MV) and 400 V for low voltage (LV) in UK distribution networks
For transformers currently in operation developing a new strategy for transformer
loss reduction is required rather than replacing them with high efficiency
transformers [34] Transformer economic operation refers to the optimum selection
of transformers needed to supply each feeder This is related to the economic
evaluation of network performance and the resilience of the network
In order to meet reliability requirements the load factor of each transformer should
not go beyond 50 when two transformers are operated in parallel In other words
the transformer load factor must be within 100 in separate operation modes
The integrated power loss curves of onetwo transformers in operations are shown in
Fig 2-3 The intersection of the two curves is 119878119871 which is called the transformer
critical load factor (TCLF) Therefore it can be concluded that
When the total load 119878 lt 119878119871 a single transformer produces less integrated
power loss than parallel transformers
When 119878 gt 119878119871 parallel operation of transformer is more economical
When 119878 = 119878119871 the losses in single or parallel operation modes are identical
Fig 2-3 Transformer loss versus transformer load
119878119871
Core loss for 2 transformers
Core loss for 1 transformer
Chapter 2 Distribution Automation
Page | 33
As a result Table 2-1 presents the transformer commercial operation area
Table 2-1 Transformer economic operation area
Operation modes Single Transformer Two Parallel Transformers
Economic operation area 0 ~ 119878119871 119878119871 ~ 119878
242 Literatures on Transformer Economic Operation
Several papers that discuss research on transformer economic operation not only
focuse on transformer loss reduction but also discuss cost reduction and reliability
improvement
The papers concerned with transformer economic operation based on loss reduction
were presented in [35]ndash[37] Wang and Liu [35] used the ASP (Active Server Pages)
language as a foundation to analyse transformer economic operation on-line The
operation curves and interval graph of commercial operation were achieved from the
VML (Vector Markup Language) and the simulation results In the interest of the
economical and profitable operation of transformer real-time data was obtained
using the SCADA (Supervisory Control and Data Acquisition) and this included the
measurement of active power load and voltage [36] [37] Then the transformers
were monitored in real-time and the methods used to ensure their economical and
profitable operation were suggested online
However if the active power loss of transformers was measured based on the real-
time load data transformers would frequently be switched to a new state associated
with instantaneous economical and profitable operation As the number of switching
operations increases the lifetime of the transformers decreases As a result Song and
Zhang [38] developed a load smoothing algorithm to reduce the number of switching
operations of the transformer effectively The curves of transformer loads before and
after smoothing are presented in Fig 2-4 Table 2-2 and 2-3 illustrate the transformer
operation mode variation before and after smoothing respectively The results show
that the active loss achieved when using the load smoothing algorithm was a little
higher than when smoothing was not used However the total number of switching
operations of transformers with load smoothing was reduced from 6 to 2 which
would expand the transformer life cycle
Chapter 2 Distribution Automation
Page | 34
(a) Before load smoothing (b) After load smoothing
Fig 2-4 Daily load curve of a typical substation before and after load smoothing [38]
Table 2-2 Transformer operation mode variation before load smoothing
Time Transformer operation mode The sum of active power loss
(Kw)
000-300 1 transformer in operation 12363
300-1600 2 transformer in operation
1600-2100 Parallel operation
2100-2400 2 transformer in operation
Table 2-3 Transformer operation mode variation before load smoothing
Time Transformer operation mode The sum of active power loss
(Kw)
000-600 2 transformer in operation 12768
600-2100 Parallel operation
2100-2400 2 transformer in operation
Generally the cost of the energy loss of a transformer over its service life is much
higher than its initial capital price As a result the transformer selection decision is
based not only on the purchase price but also includes the cost of installation
maintenance and loss over the lifetime of the equipment [39]
Amoiralis etc [40] have investigated the cost of two transformers that have the same
capacity but different specifications The transformers were loaded at 50 of full
load and with an increase of 37 for each year The technical characteristics and the
costs associated with the two transformers are presented in Table 2-4 The total cost
is the summation of loss and capital cost of a transformer over 30 years Purchasing a
Chapter 2 Distribution Automation
Page | 35
transformer with low efficiency (Transformer A) reduced the initial cost but resulted
in higher energy costs during the transformer lifetime in comparison with
Transformer B The economic approach in [41] and [42] were used to determine the
suitable size of transformers in Thailand The choice of a high capacity transformer
could improve voltage profiles and provide extra room for emergency conditions and
load increments in the future
Table 2-4 Transformer technical specifications and costs [40]
Transformer Size
(kVA)
No load loss
(kW)
Load loss
(kW)
Capital
price (euro)
Cost of loss
(euro)
Total cost
(euro)
A 1000 11 9 9074 34211 43285
B 1000 094 76 11362 28986 40348
25 Distribution Network Reconfiguration
251 Basic Concepts
DNR refers to a process that involves changing the network topology at normal and
abnormal operating conditions by altering the openclose status of sectionalising
(normally closed) and tie (normally open) switches [13] [14] In fact DNR can be
used as a tool for distribution network planning and real-time operation [14]
As presented in Fig 2-5 the openclosed status of the tie switches and sectionalising
switches determines the structure of the system To achieve a new system
configuration the tie-switch 3 is closed which will create a new loop In order to
restore the network back to a radial structure a switch from 1 2 4 and 5 is selected
and opened
Fig 2-5 Radial test system
Chapter 2 Distribution Automation
Page | 36
Since there are various combinations of switching DNR is treated as a discrete and
constrained optimisation problem Recently optimal DNR strategies discussed in
many literatures have been implemented to achieve active power loss reduction and
system reliability improvement
252 Literatures on Distribution Network Reconfiguration
Network reconfiguration was first introduced by Merlin and Back [43] using a
discrete branch and bound optimisation method to reduce network loss Firstly all
the switches were closed to build a meshed network and then in each step one
branch was removed until the radial configuration was found
Another early study on loss reduction through network reconfiguration was
presented in [44] which discussed how to achieve minimum power loss in
distribution feeders through feeder reconfiguration It is possible to determine loss
variation by analysing the load flow results This involved simulating the system
configuration before and after the feeder was reconfigured [44] It was based on a
single pair switch operation per iteration The relevant results showed that the loss
was reduced only if the voltage across the tie-switch was significant and if the loads
connected at the lower voltage side were transferred to the other side [44] This
criterion was developed to eliminate undesirable switching options The best
switching option was then obtained from the results of load flow studies simulating
all feasible feeder configurations
Zehra etc [31] have proposed a branch exchange algorithm based on two stages of
the solution methodology It started with a feasible network operating in a radial
configuration The first step determined the loop that achieved maximum loss
reduction by comparing the circle sizes for each loop The largest circle indicated the
maximum loss reduction The second phase determined the switching options to be
operated in that loop to provide maximum loss reduction The smallest circle was
identified for the best solution In comparison with [44] the introduction of the
branch exchange method allowed the number of load flow solutions related to the
computation time to be greatly reduced However the results were strongly related to
the initial configuration of the electrical network [45] The above methodologies [31]
[43] [44] were able to obtain the global optimal solution but were only applied to
simplified network models
Chapter 2 Distribution Automation
Page | 37
Later on the artificial intelligent and modern heuristic optimisation algorithms such
as genetic algorithm (GA) [46]ndash[49] simulated annealing (SA) [50] [51] tabu
search (TS) [52]ndash[54] and particle swarm optimisation (PSO) [55] etc were
developed with minor computational effort These intelligent techniques which are
affected by the selection of parameters are able to obtain the optimum solution of
good quality The GA based network reconfiguration method was presented and
tested in a real 136-bus distribution network in [13] Various radial topologies were
generated after the implementation of the genetic operators and the search space was
enlarged by a local improvement method The results show that after network
reconfiguration the power loss is reduced from 3203 kW to 2801 kW which
amounts to a 1255 reduction
Other important objectives including reliability improvement and service restoration
by DNR were mentioned in [56]ndash[58] An intelligent binary particle swarm
optimisation (BPSO) based search method was presented in [57] for assessment of
the DNR problem in terms of reliability improvement The failure of all distribution
equipment such as transformers feeders breakers etc was considered In this paper
the reliability index was in the form of expected demand not supplied (EDNS) The
EDNS of the original configuration is 1008 kW and after reconfiguration the best
result is reached with 849 kW
Network reconfiguration can be formulated not only as a single objective problem
but also as a multi-objective problem that considers various parameters
simultaneously [45] [59]ndash[62] In [59] the objective function was to minimise the
combination of loss cost and consumer interruption cost thus the multiple objectives
were aggregated into an single objective function In order to achieve optimal DNR
a new method was proposed in [60] using a fuzzy multi-objective function to
balance feeder loads and reduce power loss of the distribution systems Depending
on the operatorrsquos preferences the weighting factors of each of the variables could be
varied Das [61] introduced another fuzzy membership formulation to handle the
multiple objectives In this work the degree of overall satisfaction was the minimum
of all the above membership values and the final optimal solution was the maximum
of all such overall degrees of satisfaction [61] Mendoza etc [62] introduced a
micro-genetic algorithm to deal with the trade-offs between the power loss and
reliability indices in order to obtain a set of optimal network configurations using
Chapter 2 Distribution Automation
Page | 38
the concept of Pareto optimality Andervazh etc [45] have presented another Pareto-
based multi-objective DNR method using discrete PSO The objectives were the
minimisation of power loss bus voltage deviations and number of switching
operations
In addition an optimal planning strategy based on network reconfiguration and DGs
placement was presented in [16] The primary objective was power loss reduction
and voltage stability improvement The performance of the methodology was tested
on a 33-bus network and three DGs were installed The power loss was reduced by
3093 by DNR 5624 by DG installation and 6689 by employing
reconfiguration and DG installation simultaneously
26 Placement of Sectionalising Switches
261 Basic Concepts
The implementation of DA requires the installation of various new devices [63]
Among other things DA involves the placement of sectionalising switches ie the
installation of new switches and relocation of existing switches DA in terms of
automatic and remote controlled sectionalising switch placement brings major
benefits to distribution network operators (DNOs) [64] [65] The duration and
number of outages per year determines the annual interruption time of customers
[66] It is possible to shorten outage duration by decreasing the restoration time and
to reduce the number of outages by improving failure rates [67] SSP is useful for the
reduction of the time required to detect and locate a fault and the improvement of
the speed of isolating the faulty sections in the primary distribution network [64]
The effectiveness of these objectives depends on the number and location of
sectionalising switches
In a distribution feeder the section is defined as a group of line segments between
adjacent sectionalising switches [68] And the equivalent load of the section is the
sum of the individual load points in this section [69] When a permanent fault occurs
the switch actions need to respond as follows
Chapter 2 Distribution Automation
Page | 39
1 Detect and locate the fault and initiate tripping to clear the fault A transient
fault is normally cleared by two or three trips and reclose cycles
2 However if the fault persists beyond the predefined cycles reclosure will be
inhibited and the protection will initiate a final trip The load breaker will open and
all the downstream loads will be de-energised
3 The faulty section is then isolated by opening the upstream and downstream
sectionalising switches located next to the fault
4 Restore the loads in the healthy area by closing the upstream and downstream
circuit breakers automatically
5 Repair the faulty section of the feeder and manually restore the loads (ie
reconnect loads to the supply)
A fully and a partially automated distribution feeder are shown in Fig 2-6 and Fig
2-7 respectively The fault occurs on line section 4 It can be clearly seen in Fig 2-6
that all loads are restored after the faulty area is isolated and the total outage time is
the same as the switching time of circuit breakers and sectionalising switches [64]
However as shown in Fig 2-7 only Loads LP1 LP5 LP6 are restored after the
isolation of the faulty section the outage duration of other loads is equal to the repair
time ie significantly longer than the switching time As a result the installation of
sectionalising switches could increase the network reliability as well as the
investment and operation cost of automation [64]
Chapter 2 Distribution Automation
Page | 40
LP1 LP2 LP3 LP4 LP5 LP6
1 2 3 4 5 6 7
LP1 LP2 LP3 LP4 LP5 LP6
1 2 3 4 5 6 7
LP1 LP2 LP3 LP4 LP5 LP6
1 2 3 4 5 6 7
LP1 LP2 LP3 LP4 LP5 LP6
1 2 3 4 5 6 7
Fault occurred on line section 4
CB1 opened
Sectionalising switches adjacent to the faulted area are opened
Energy restored to un-faulted area by closing CB1 and CB2
CB1 CB2
CB1CB2
CB1 CB2
CB1 CB2
Normally closed circuit breaker
Normally open circuit breaker
Closed sectionalising switch
Open sectionalising switch
Interrupted
load
Fig 2-6 Fully automated distribution feeder
Chapter 2 Distribution Automation
Page | 41
LP1 LP2 LP3 LP4 LP5 LP6
1 2 3 4 5 6 7
LP1 LP2 LP3 LP4 LP5 LP6
1 2 3 4 5 6 7
LP1 LP2 LP3 LP4 LP5 LP6
1 2 3 4 5 6 7
LP1 LP2 LP3 LP4 LP5 LP6
1 2 3 4 5 6 7
Fault occurred on line section 4
CB1 opened
Sectionalising switches adjacent to the faulted area are opened
Energy restored to un-faulted area by closing CB1 and CB2
CB1 CB2
CB1CB2
CB1 CB2
CB1 CB2
Normally closed circuit breaker
Normally open circuit breaker
Closed sectionalising switch
Open sectionalising switch
Interrupted
load
Fig 2-7 Partially automated distribution feeder
262 Literatures on Sectionalising Switch Placement
The earliest work that discussed SSP in distribution networks was presented by
Miranda [70] A fuzzy-logic-based optimisation technique has been used to
determine the location of sectionalising switches
In [69] the optimum sectionalising switch relocation problem has been solved by
using the ant colony system (ACS) based method to reduce feeder interruption costs
Chapter 2 Distribution Automation
Page | 42
after a fault In this work it is assumed that there were no additional capital
investments brought by switch relocation However the investment and operation
cost of a sectionalising switch is an important issue which cannot be ignored when
considering the problem of unsupplied energy costs minimisation since they conflict
with each other Therefore the information provided by the multi-objective model is
more valuable than the traditional mono-objective model Abiri-Jahromi etc [64]
have developed a mixed-integer linear programming (MILP) to deal with the new
sectionalising switch installation problem which considers customer outage costs as
well as switch capital operation and maintenance costs After the placement of
sectionalising switches the total system cost over the life period of the switches was
greatly reduced [64] In addition the impacts of customer damage function and load
density variations on SSP were also investigated through sensitivity analysis
The impacts of DG on the optimal number and location of sectionalising switches
were discussed in [71] The introduction of DGs connects a mono-source distribution
network to a multi-source one [66] This potentially improves network reliability
since it reduces the duration and restoration time of interruptions Many loads can be
restored through DGs when operating in islanding mode A mathematical
optimisation methodology has been proposed to minimise the reliability cost when
operating with a minimum number of sectionalising switches The results indicate
the reliability indices of distribution networks are affected by the number and
location of sectionalising switches
27 Transformer Loss Assessment
271 Operating Principles
A transformer has three essential elements a primary winding a secondary winding
and a core [33] As shown in Fig 2-8 the winding connected to the electrical source
is called the primary winding and the secondary winding is linked with the loads All
the windings are connected by the common magnetic flux in the core
Chapter 2 Distribution Automation
Page | 43
Fig 2-8 Elements of a single phase transformer [33]
Usually the power is generated and distributed in a three-phase system Therefore it
is necessary to use a three-phase transformer to increasedecrease the voltage The
structure of the three-phase transformer is presented in Fig 2-9
Fig 2-9 Construction of a three-phase transformer [33]
272 Transformer Quantities Measurement
The transformer quantities present the self-loss during power transmission which
consists of active power loss together with increase in the reactive power of the
network unit [72]
Open-circuit test
The equivalent circuit for the open-circuit test is shown in Fig 2-10 The test is made
on the low-voltage side by applying rated voltage at rated frequency with the high-
voltage winding open [33] The input power and current are measured which are
named no-load loss 119875119874119862 and no-load current 119868119874119862
Chapter 2 Distribution Automation
Page | 44
(a) Test circuit
(b) Equivalent circuit
Fig 2-10 The open-circuit test [33]
As the secondary is open the primary current is equal to the no-load current The no-
load current is used to produce the primary magnetic flux when the transformer is in
no-load operation which is also called the exciting current The voltage drops in the
primary winding can be ignored so the no-load loss is the summation of hysteresis
and eddy current losses [33] The input power is practically equal to the no-load loss
at rated voltage and frequency
119875119874119862 = 119875ℎ+119890 =119880119874119862
2
119877119888119871119881= 119880119874119862119868ℎ+119890 (2-1)
where 119877119888119871119881 is the resistance referred to the low-voltage side 119868ℎ+119890 is the core loss
current
Short-circuit test
The short-circuit test is used to measure the equivalent resistance and reactance of
the winding [6] As shown in Fig 2-11 the low-voltage terminal is shorted together
and the high-voltage side of the transformer is connected to a low-voltage high-
119880119900119888
119868ℎ+119890 119868120601
119868119900119888 119885119890119902 119871119881
119877119888 119871119881 119883119898 119871119881
Chapter 2 Distribution Automation
Page | 45
current source at rated frequency [33] The source voltage is increased until the short
circuit current reaches the rated value At this time value of the source voltage is
known as the short-circuit source voltage 119880119878119862
(a) Test circuit
(b) Equivalent circuit
Fig 2-11 The short-circuit test [33]
As the secondary side is shorted the voltage applied to the full load current is low
compared to the rated voltage and the exciting current 119868119890119909 is negligible during this
test [33] Since the rated current is used the input power is equal to the full-load loss
and expressed as
119875119878119862 = 1198681198781198622 119877119890119902119867119881 (2-2)
where 119877119890119902119867119881 is the winding resistance referred to the high voltage side
As the full-load loss depends on the value of the full load current the loss in the
winding resistance is varied under different loading conditions
119880119904119888
119868119890119909
119868119904119888 119877119890119902 119867119881 119883119890119902 119867119881
(119899119890119892119897119890119888119905)
Chapter 2 Distribution Automation
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Active power loss
The active power loss ∆119875 of a two-winding transformer is decided by the no-load
loss 119875119874119862 full-load loss 119875119878119862 and the transformer load factor [73]
∆119875 = 119875119874119862 + 1205732119875119878119862 (2-3)
where 120573 =119878119871
119878119873 represents the transformer load factor 119878119871 is the transformer actual
loading (kVA) 119878119873 is the transformer rated capacity (kVA) Assuming the voltages
are held constant at 10 pu
Reactive power loss
The no-load current 119868119900119888 and short-circuit source voltage 119880119878119862 represent the change of
reactive power ∆119876 in other words the reactive power loss which can be simplified
as
∆119876 = 119876119874119862 + 1205732119876119878119862 (2-4)
119876119874119862 = 119878119874119862 =119868119874119862
119868119873∙ 119878119873 (2-5)
119876119878119862 = 119878119878119862 = 119880119878119862
119880119873∙ 119878119873 (2-6)
273 Integrated Transformer Loss
In general the power loss of a transformer is related to the active power [74]
However if a transformer draws reactive power (it takes current) this causes real
power loss in the network The integrated power loss refers to the sum of active
power loss of the transformer and the increased active power loss contributed by the
reactive power of the transformer [72]
The integrated power loss of a two-winding transformer is calculated by
1198791198711 = 11988002119875119885119874119862 +
1205732
11988002 119875119885119878119862 (2-7)
119875119885119874119862 = 119875119874119862 + 119870119876119876119874119862 (2-8)
Chapter 2 Distribution Automation
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119875119885119878119862 = 119875119878119862 + 119870119876119876119878119862 (2-9)
where 119875119885119874119862 and 119875119885119878119862 are the integrated no-load loss (kW) and the full-load loss (kW)
120573 =119878119871
119878119873 represents the transformer load factor 119878119871 is the transformer actual loading
(kVA) 119878119873 is the rated capacity of the transformer (kVA) 119875119874119862 and 119876119874119862 are the no-
load active power loss (kW) and no-load reactive power loss (kVAr) 119875119878119862 and 119876119878119862
are the full load active power loss (kW) and full load reactive power loss (kVAr) 119870119876
represents the reactive equivalent which is the ratio of increased active power loss to
the change of the node reactive power (kWkVAr) [72] 1198800 is the operational voltage
of the transformer low voltage side in per unit
The no-load and full-load power losses are obtained from the open-circuit and short-
circuit test separately
For two transformers operating in parallel with the same capacity the current
flowing through each transformer is reduced by half Thus the full-load loss of each
transformer becomes a quarter of the previous case The total integrated power loss
is twice the no-load loss and half (2 times1
4) of the full-load loss of one transformer
1198791198712 = 211988002119875119885119874119862 +
1
2
1205732
11988002 119875119885119878119862 (2-10)
28 Feeder Loss Assessment
The distribution network power loss is mainly due to resistive loss in distribution
feeders which is obtained through a power flow study [75] The calculation of
power loss is explained using a two-bus network as shown in Fig 2-12
Fig 2-12 Simple two-bus network
Chapter 2 Distribution Automation
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Assume there is no capacitance on either the sending or receiving bus and 119868119887119904 =
119868119887119903 = 119868119887 As a result the current flowing through branch b and the real power loss
are derived using the following equations
119875119887119877 + 119895119876119887119877 = 119887119877 times 119868lowast (2-11)
119875119887 = 1198681198872 times 119877119887 (2-12)
From (2-11) and (2-12) it is calculated as
119875119887 =119875119887119877
2 +1198761198871198772
1198811198871198772 times 119877119887 (2-13)
where 119875119887 is the real power loss of branch b (W) 119875119887119877 and 119876119887119877 are the real power (W)
and reactive power (VAr) at the receiving end of branch b 119881119887119877 represents the rms
voltage at the receiving end of branch b (V) 119868119887 is the rms current through branch b
(A) and 119877119887 is the resistance of branch b (Ω)
The real power losses in the other branches are evaluated similarly and the network
real loss is the sum of the power losses in all branches as presented in (2-14)
119864119871 = sum 119875119887119899119873119887119899 (2-14)
where 119873119887 is the set of all the distribution network branches
29 Reliability Evaluation
291 Reliability Indices
Reliability is a fundamental attribute for the safe operation of any modern power
system [8] A distribution network which is directly connected to customers has a
large impact on power reliability Distribution reliability primarily relates to
equipment outages and customer interruptions [76] The reliability indices of
distribution network can be classified into two groups ie load point reliability
indices and system reliability indices [77]
Chapter 2 Distribution Automation
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The three primary load point reliability indices average failure rate (120582) average
annual outage time (119880) and average outage time (119903) are calculated by [73]
120582 = sum 120582119895119895 (2-15)
119880 = sum 120582119895119895 119903119895 (2-16)
119903 =119880
120582 (2-17)
where 120582119895 and 119903119895 are the failure rate and outage time of contingency j for this load
point
The system reliability indices mainly include system average interruption frequency
index (SAIFI) system average interruption duration index (SAIDI) average energy
not supplied (AENS) and expected customer damaged cost (ECOST) [78] The
Formulae for these reliability indicators are presented in (2-18) to (2-21) [78]
119878119860119868119865119868 =sum 120582119894119873119894119894
sum 119873119894119894 (2-18)
119878119860119868119863119868 =sum 119880119894119873119894119894
sum 119873119894119894 (2-19)
119860119864119873119878 =sum 119880119894119871119894119894
sum 119873119894119894 (2-20)
119864119862119874119878119879 = sum 119888119898(119889119898)119891119898119871119898119872119898=1 (2-21)
where 119873119894 is the total number of customers of load point 119894 120582119894 119880119894 and 119871119894is the failure
rate outage time and average load connected to load point i 119872 is quantity of load
outage events 119871119898 is load curtailed (kW) due to outage event m 119891119898 and 119889119898 are the
frequency and duration of outage event m 119888119898(119889119898) is the outage cost (poundkW) of
outage duration 119889119898 using the customer damage function (CDF)
SAIFI is a measure of the number of outages an average customer will experience
SAIDI states the average interruption hours for a customer in the system AENS
presents the effect of interruptions on the energy that is not supplied to the customers
during failures [79] ECOST is the index that connects reliability with economics
Chapter 2 Distribution Automation
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292 Reliability Evaluation Methods
The methods used to calculate reliability indicators for distribution network are
classified into two groups namely the simulation method and analytical method
Simulation method
The simulation method has better scalability and flexibility when incorporating
complex considerations in comparison with the analytical technique And it is more
capable of dealing with large-scale power systems and the variation of load points
[77] The Monte Carlo method is a typical example of a simulation method and
takes into account the time varying and stochastic nature of load models in
evaluating the power system reliability [80] Vitorino etc [12] proposed a non-
sequential Monte Carlo method based on branch reliability to estimate energy not
supplied (ENS) index Contingencies were simulated by randomly selecting a faulty
branch from a candidate network pool based on failure probabilities [12] However
although the Monte Carlo method can simulate the behaviour of a complex system
with a high degree of accuracy it requires a considerable amount of CPU time and
memory
Analytical method
The first step of an analytical technique is to build a reliability probabilistic model
for the system according to network topology as well as the relationships between
the system and components [77] The model is then solved by calculating the
reliability indices in iterations [77] The most common analytical methods are
minimal path method minimal cutset method and failure-mode-and-effect analysis
(FMEA)
In [81] the minimal path method which identifies the shortest paths from a node to
a source and between any two nodes was described The minimal path of the source
node to the load points was obtained by searching for the upstream node from the
load points [82] As the distribution network was radial each node had only one
upstream node The sections out of service after a fault occurred were identified and
separate subsystems were formed The nodes were classified in terms of the effect of
a failure on them Using the node class and amount of load shedding data the
reliability indexes could then be evaluated [81]
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FMEA is a classical analytical algorithm for distribution network reliability
evaluation based on the analysis of all the failure modes of each static component
[82] As shown in Fig 2-13 there are four failure modes which are 1) active failure
2) transient failure 3) passive failure and 4) maintenance The active and transient
failures can cause the operation of breakers and hence the healthy components can
be removed from service [75] The passive failures are similar to maintenance outage
and have no effect on the protection system and remaining heathy zone [82]
Fig 2-13 Reliability model for static components
The proposed reliability evaluation method is based on the N-1 criterion and its
computation procedure is demonstrated in Fig 2-14
Normal operation
Active
failure
Transient
failure
Passive
failure
Maintenance
120582119860 120582119879 120582119875 120582119872
120583119860 120583119879 120583119875
120583119872
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Start
Read system topology load
data and reliability parameters
Initialise failure number i=1
All failures are considered
Search for the upstream feeder breaker
Search for the upstream and downstream
sectionalising switches and tie-switch
The load points are classified into three categories
Evaluate the reliability of load points
and whole system when fault at line i
Next failure i=i+1
Calculate the reliability of the whole system
End
No
Yes
Fig 2-14 Procedure for reliability evaluation
The system failure events are enumerated first For a failure event the scope of the
failure is determined by searching for the adjacent circuit breaker or tie switch The
isolation zone is then confirmed by the location of the upstream and downstream
sectionalising switches and the appropriate tie-switch Subsequently all the load
points are classified based on their interruption times Finally the consequence of
each contingency and a value for total system reliability are evaluated
When a fault occurs all the load points can be categorised as follows
Healthy points are load points not affected by the fault and refer to upstream
nodes of the upstream circuit breaker or downstream nodes of the
Chapter 2 Distribution Automation
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downstream circuit breaker or tie-switch For example when a fault occurs at
L2 in Fig 2-15 LP1 and LP5 are healthy points
Temporary damaged points when the protection systems are in operation
they cause the load points to be interrupted but the load points can be
restored by isolating the faulty area and by using a supply through another
path When a fault occurs at L2 in Fig 2-15 LP2 and LP4 are isolated by
opening the sectionalising switches S1 and S2 LP2 is restored by closing B1
and LP4 is supplied by closing the tie-switch As a result LP2 and LP4 are
temporary damaged points The interruption time is 119879119878 which is the average
switching time after failure
Permanent damaged points are load points that are interrupted by the
operation of protection devices and cannot be restored until the fault is
cleared [82] When a fault occurs at L2 in Fig 2-15 LP3 is the permanent
damaged point The interruption time is 119879119877 which is the average repair time
after failure
Fig 2-15 Sample network
Overall the analytical method which is based on a reliability model of each
component evaluates system reliability by enumeration of all failure states However
the increasing number of devices in a complex system results in an increase in the
quantity of failure states and the complexity of calculation As such the scale of the
network might be limited
210 Multi-objective Optimisation
The aim of this section is to provide fundamental information in order to assess
multi-objective optimisation problems The objectives are conflicting and can be
Chapter 2 Distribution Automation
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0
1
converted into three forms which are 1) single objective function 2) single fuzzy
satisfaction objective function and 3) Pareto front
2101 Single Objective Function
The single objective function is generally done by simply aggregating the objectives
with the same dimension and transforming others into constraints [83] It can be
solved by traditionally scalar-valued optimisation techniques However this function
has several limits 1) it results in only one solution 2) the analysis of the objectives
that are converted into constraints is limited
In [64] a sectionalising switch placement strategy was proposed to minimise the
sum of ECOST and sectionalising switch costs The above mentioned objectives
were simply aggregated and calculated in US dollars Other objectives such as the
number of available switches were converted into constraints
2102 Single Fuzzy Satisfaction Objective Function
In the fuzzy domain each variable is associated with a membership function varying
from zero to unity which indicates the satisfaction level of the objective [84] The
higher the membership value is the better the solution is Generally the linear
membership function is formulated as given in (2-22) and is presented in Fig 2-16
120572 =
1 119883 le 119883119898119894119899119883119898119886119909minus119883
119883119898119886119909minus119883119898119894119899119883119898119894119899 lt 119883 lt 119883119898119886119909
0 119883 ge 119883119898119886119909
(2-22)
Fig 2-16 Linear membership function
If 119883 is equal or less than 119883119898119894119899 the membership value is one As 119883 becomes greater
than 119883119898119894119899 the degree of satisfaction decreases This decrease is continued until 119883
reaches 119883119898119886119909 and the membership function becomes zero
120572
119883119898119894119899 119883119898119886119909 119883
Chapter 2 Distribution Automation
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The fuzzy-based optimisation procedure is used for handling multiple conflicting
objectives with different dimensions and units [66] The degrees of satisfaction level
can be formulated into a single objective function in three methods which are 1)
weighted aggregation 2) max-min method 3) max-geometric-mean method The
objective is to maximise such degree of satisfaction
Weighted aggregation
In this method the degree of satisfaction level is the weighted aggregation of the
membership values of all objectives [85] Thus the final compromise solution for
multi-objective functions is described as follows
119872119886119909 119869 = 12059611205721 + 12059621205722 + ⋯ + 120596119899120572119899 (2-23)
where 120596119894 is the constant weighting factor for each of the membership values and
they should meet the condition sum 120596119894119894 = 1
The weighting factors are decided by the decision makers and a higher weighting
factor indicates that this parameter is more important However the disadvantage of
this technique is that DNOs may have difficulty in obtaining enough information
about the relative importance of each objective to determine the trade-offs among the
selected objectives
Saffar etc [60] have developed a network reconfiguration technique to reduce power
loss and equal load balancing of feeders As these objectives had different
dimensions and units they were transformed into a single objective function with
fuzzy variables A set of compromised solutions was obtained by varying the
weighting factors of each element
Max-min method
In this technique the degree of overall satisfaction is the minimal value among the
membership values of all objectives [85] Thus the final compromise solution for
multi-objective functions is described as follows
119872119886119909 119869 = min 1205721 1205722 hellip 120572119899 (2-24)
The solution is optimised by maximising the overall satisfaction of all objectives
However the max-min method might not predict the best compromise solution
Chapter 2 Distribution Automation
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because even if one membership value is weak it does not necessarily mean that
other membership values are also weak [86]
The max-min principle was adopted in [84] for the multi-objective optimisation with
fuzzy sets The aim was to minimise real power loss and the absolute value of branch
current as well as to minimise nodes voltage deviation Finally an optimal solution
was obtained which indicated a concession among all the objectives The results also
revealed that although network reconfiguration resulted in a significant reduction in
total system loss the loss allocated to a certain number of customers increased [84]
It is important to change the tariff structure for these consumers so that they are not
obliged to pay more for the increase in loss allocation as a result of network
reconfiguration
Max-geometric-mean method
Like the above max-min method the geometric-mean function is also used to
evaluate the degree of overall fuzzy satisfaction but in different forms The objective
is computed as follows
119872119886119909 119869 = (1205721 ∙ 1205722 ∙ hellip ∙ 120572119873)1 119899frasl (2-25)
In [86] firstly all the variables (real power loss branch current loading maximum
voltage deviation and switching numbers) were assigned by truncated sinusoidal
fuzzy membership functions The overall degree of satisfaction was the geometric
mean of all fuzzy membership values [86] The best compromise solution was then
obtained by maximising this satisfaction level
2103 Multi-objective Formulation in the Pareto Optimality
Framework
All the studies mentioned above are solved by a single-objective optimisation
technique In contrast a Pareto optimal solution is provided for the treatment of
multi-objective problems This produces a range of solutions rather than just one
which represents a compromise that goes some way to optimise objective functions
[87] [88] The Pareto optimal solution is based on a dominance concept The
solution 119883 dominates 119884 means that 119865(119883) is no worse than 119865(119884) for all objectives
Chapter 2 Distribution Automation
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and there is at least one objective for which 119865(119883) is better than 119865(119884) as expressed in
(2-26) and (2-27) The following conditions should be satisfied concurrently
forall 119894 = 12 hellip 119873119900119887119895 119865119894(119883) le 119865119894(119884) (2-26)
exist 119894 = 12 hellip 119873119900119887119895 119865119894(119883) lt 119865119894(119884) (2-27)
where 119873119900119887119895 is the number of objective functions
If a solution 119883 and solution 119884 do not dominate each other these two solutions are
incomparable For example the objective is to minimise 1198911 and 1198912 and there are
three solutions whose objective function values are 119865(119883) = (24) 119865(119884) = (44)
119865(119885) = (52) It can be seen that 119883 dominates 119884 as 1198911(119883) lt 1198911(119884) and 1198912(119883) le
1198912(119884) And the solution 119883 and 119885 are incomparable because 1198911(119883) lt 1198911(119885) and
1198912(119883) gt 1198912(119885) Similarly solutions 119884 and 119885 are also incomparable
A solution belongs to Pareto optimal solutions if there is no other solution that can
improve at least one objective without degradation of any other objectives [83] In
other words there is no another solution that dominates it The Pareto set is the set of
all non-dominated solutions and its corresponding objective values constitute the
Pareto front [88] The goal of the multi-objective optimisation is to select the most
suitable one from the Pareto set for implementation according to decision makersrsquo
preferences
In [45] the study proposed a Pareto-based multi-objective DNR method using a
discrete PSO algorithm It aims to reduce power loss voltage deviations and the
number of switching operations Firstly each objective function was optimised
separately and the best results were found All objectives were then optimised
simultaneously and the Pareto optimal set was obtained The best results for each
objective were included in the Pareto front and the corresponding solutions were
stored in the Pareto optimal set Finally the best compromise solutions among the
multiple objectives were derived Different scenarios were modelled by assigning
different weighting factors based on the preferences of the decision makers
Chapter 2 Distribution Automation
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211 Summary
Generally most distribution networks are designed in closed loop but are operated
radially There are three typical distribution network topologies which are the radial
system primary loop and link arrangement The descriptions of three switchgears ie
recloser sectionalising switch and tie-switch are also included in this chapter
TEO DNR and SSP are the three main parts of DA In this chapter there are several
reviews of these techniques TEO which refers to optimum selection of which
transformers need to supply each feeder can not only reduce loss but also reduce
total costs and improve network reliability DNR is defined as a process that
involves changing the network topology under normal and abnormal operating
conditions by relocation of tie-switches [13] [14] The methodologies from a branch
and bound optimisation method to modern heuristic optimisation algorithms
designed for loss reduction are reviewed In addition DNR is also able to improve
service quality and efficiency at the same time The placement of sectionalising
switches refers to the installation of new switches and relocation of existing switches
It is used for distribution network reliability improvement and service restoration
However so far few studies have been carried out that consider the combination of
the above three techniques
The major challenge facing DNOs is how to distribute the power in a low-cost
reliable and efficient way Thus the assessments of transformer loss feeder loss and
reliability indices are proposed in Section 27-29 The integrated transformer loss
consists of not only real power loss but also reactive power loss The transformer
quantities such as no-load loss and full-load loss are obtained from open-circuit test
and short-circuit test The distribution network power loss is achieved through power
flow study The reliability indices can be calculated through reliability evaluation
methods namely simulation methods and analytical methods The most common one
is FMEA which is also used for reliability evaluation in this thesis Although there
are many research projects that consider feeder loss and reliability simultaneously
few consider transformer loss and feeder loss at the same time
Three objective functions for optimising multiple conflicting objectives are 1) single
objective function 2) single fuzzy satisfaction objective function and 3) Pareto front
Chapter 2 Distribution Automation
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The single objective function is generally done by simply aggregating some
objectives and transforming others into constraints In the fuzzy objective function
each variable is associated with a membership function and then aggregated into a
single objective function [84] The first two functions only obtain a single solution
However Pareto optimal solutions can obtain a set of non-dominated solutions
rather than one which represents a compromise that goes some way to optimising
objective functions In this thesis all three objectives functions will be studied and
results will be presented in the following chapters
This thesis will deal with single objective and multiple objectives through different
methods of DA based on various algorithms The next chapter will introduce the
Monte Carlo method and modern heuristic optimisation algorithms such as ant
colony optimisation (ACO) and artificial immune systems (AIS)
Page | 60
CHAPTER 3
OPTIMISATION TECHNIQUES
31 Introduction
Mathematically distribution automation (DA) is categorised as a discrete non-linear
constrained and combinational optimisation problem since the problem is to
determine the status of all transformers and switches In general the optimisation
techniques for assessment of this problem can be divided into two large groups 1)
simulation methods and 2) analytical methods
The Monte Carlo method is a typical example of a simulation method which will be
discussed in Section 32 in detail It can handle uncertainties and solve the
probabilistic optimal power flow [89] In a complex system with hundreds of
switches although the Monte Carlo method can find the best solution with a high
degree of accuracy it is generally not practical to carry out an extensive search of all
possible configurations as it consumes a great deal of CPU time and memory [88]
Therefore most DA problems are solved by analytical methods
The analytical methods can obtain a solution of good quality or even the global
optimal solution of the problem [13] It can be classified into four types 1) branch
and bound 2) optimal flow pattern 3) branch exchange and 4) metaheuristic
techniques Recently the last type has become the most popular
Chapter 3 Optimisation Techniques
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The metaheuristic method is a process that attempts to find a solution to the problem
beginning from a starting point or a set of starting points and exploring all the search
space [13] It also includes a strategy to explore the search space and provide an
escape from the local optimal This process does not guarantee a globally optimal
solution but can offer near optimal solutions with a reasonable computational effort
This includes genetic algorithm (GA) ant colony optimisation (ACO) particle
swarm optimisation (PSO) and artificial immune systems (AIS) Different
metaheuristic techniques use different strategies that pass through and explore the
search space [13]
As for the remainder of the chapter the Monte Carlo method is discussed in Section
32 Section 33 presents the proposed ACO algorithm Section 34 discusses a new
hybrid AIS-ACO framework and the summary of this chapter is provided in Section
35
32 Monte Carlo Method
The Monte Carlo method is a simulation algorithm that can be carried out many
times to produce numerical samples that accurately reflect the probability
distribution of the real results [90] [91] This method is always used to solve power
system issues involving uncertain parameters [92] The uncertainties are allocated
randomly and each simulation is operated numerous times In theory the more
simulations are running the less deviation error between actual mean value and
sample mean value Therefore it is important to determine the overall running times
of the Monte Carlo simulation The convergence or stopping criteria is used to
determine the simulation times required to obtain acceptable accurate results
The confidence interval acts as a good estimate of the unknown parameters The
probability that the true parameter remains in the confidence interval is calculated as
follows [93]
119862 = 119875(119883 minus 119871 le 120583 le 119883 + 119871) = int 119866(119883)119889119909119883+119871
119883minus119871 (3-1)
119871 = 119911lowast 120590
radic119899 (3-2)
Chapter 3 Optimisation Techniques
Page | 62
where 119862 is the degree of confidence is the estimated mean value 119871 is the
confidence interval which provides an estimate range of values which probably
contains an unknown population parameter 120583 is the true population mean value
119866(119883) is the Gaussian distribution 120590 is the sample standard deviation and 119899 is the
number of samples the estimation of 119911lowast is based on the degree of confidence 119862 as
presented in Table 3-1 The most common 119911lowast is 196 and the corresponding 119862 is
095
Table 3-1 Relationship of 119911lowast and 119862
119862 09 095 099 0999
119911lowast 1645 1960 2576 3291
The required number of samples could be expressed as
119899 = (119911lowast120590
119871)2 (3-3)
There are several methods used to determine the sample size and to obtain results
with acceptable accuracy One is by predefining the maximum sample size 119873 when
119899 reaches 119873 the simulation is stopped Another one is by using the degree of
confidence 119862 The confidence interval 119871 is calculated and compared with the
predefined 119871 for each sample and the simulation reaches the stopping criteria when
the confidence interval is less than the critical value
33 Ant Colony Optimisation
The ant colony optimisation method is one of the metaheuristic techniques that has
been employed for the solution of combinational optimisation problems in recent
years [60] The ant colony system (ACS) simulates the behaviour of real ants [94]
[95] The moving paths of artificial ants construct the candidate solutions to a
problem [96] The ants communicate with other ants by a chemical substance called
pheromones [97] Originally all the ants start from their nest and search for their
food in a random manner When the food source is found the ants leave a chemical
Chapter 3 Optimisation Techniques
Page | 63
substance trail on the way home The pheromone deposited by the ants is used as the
primary guide function for the other ants The pheromones will then evaporate after a
period of time As all of the ants travel approximately at the same speed the shortest
path has the largest probability to contain more pheromones because more ants
choose this one The ants tend to follow the path that has more pheromones than
others After a brief period the shortest path with the most intensity of pheromones
could attract more and more ants providing feedback to the system that promotes the
use of best paths [98] Fig 3-1 represents the behaviours of real ants [69]
Fig 3-1 Example of ant colony system [69]
As shown in Fig 3-1 (a) all the ants are travelling in the same path which connects
point A and point B by a straight line The environment is changed due to the
occurrence of an obstacle in Fig 3-1 (b) and (c) At first all the ants choose the left
or right path randomly because they have no guide It is assumed that they move
through path C or D with the same probability Later on the ants that choose path C
will move faster than that choose path D As a result the pheromones deposited on
path C accumulate faster than those on the path D and this attracts more ants to
choose path C Finally all the ants tend to choose the shortest path (path C) as this
contains the most pheromones
The flowchart of ACO algorithm is shown in Fig 3-2 and the main stages of the
algorithm are presented as follows [69] [94] [95] [97] [98]
Initialisation In this stage the trail intensity on each edge in the search
space is initialised to a constant positive value and all the ants are located in
Chapter 3 Optimisation Techniques
Page | 64
the nest
Ant Dispatch In this step each ant begins its tour at the starting point and
chooses the next node to move to according to a probabilistic selection rule
which involves the intensity of pheromones deposited on each node by other
ants [88] [99] The ants prefer to choose the path with a higher pheromones
This process is repeated until all the ants have reached the food source
Quality Function Evaluation After all the ants have completed a tour the
relevant quality function of the optimisation problem is calculated to evaluate
the performance of each ant If any constraint is violated the configuration is
discarded Otherwise the objective function is evaluated
Trail Intensity Update There are two pheromone updating rules applied in
this step One is called the global pheromone update It accumulates the
pheromone values on the high-quality solution path to improve convergence
However the pheromone intensity of each edge evaporates over time due to
another rule called the local pheromone update This update is used to
enlarge the search space and to avoid premature convergence for local
minima Ants travelling between two nodes update the relevant pheromone
intensity in the corresponding edge
Convergence Determination This process is operated until the maximum
iteration number is reached or all the ants choose the same path between their
home colony and food source
Chapter 3 Optimisation Techniques
Page | 65
Start
Set Iteration n=1
Maximum iteration
reached
End
No
Yes
Initialise the parameters for ACO algorithm
searching space and build graph of the tours
Dispatch ants based on the
amount of pheromones on edges
Quality function evaluation
Trail intensity update
Record the high quality solutions of this
iteration and empty all location lists
n=n+1
Fig 3-2 Flowchart of the ant colony algorithm
The above procedure should be modified to a computational procedure to solve
different optimisation problems and this is discussed in the following chapters
Several factors need to be taken into account when designing an ACO algorithm
such as search space transition probability etc
34 AIS-ACO Hybrid Algorithm
341 Artificial Immune Systems
The immune system acts as a defensive barrier to recognise and eliminate foreign
antigens ie bacteria virus etc B lymphocytes are the main immune cells in the
biological immune system and originate in the bone marrow Being exposed to an
Chapter 3 Optimisation Techniques
Page | 66
antigen a specific antibody is produced on the surfaces of B cells and an immune
response is elicited to make antibodies recognise and bind the antigen [88] [100]
Those B cells whose antibodies best match the antigen are activated and cloned
several times [88] This process is called cloning To identify the most suitable
antibodies for the antigen it is necessary to cause the antibody and the antigen to
interact more closely with each other This is achieved through a process call
hypermutation in which random changes are introduced into the genes of the cloned
B cells [88] One such change might lead to an increase or decrease in the closeness
between antibody and antigen [88] The new B cells can only survive if they are
closely related to the antigen and therefore the B cells that are closely related are
then chosen to enter the pool of memory cells [100] These cloning hypermutation
and selection processes are called the clonal selection principle [101] By repeating
this principle a number of times the immune system learns to respond more
efficiently for the same antigen
Several computational models of the AIS have been developed recently as the
immune system is an adaptive learning system that has the following specifications
learning memory recognition of foreigners and pattern recognition [102]
342 Proposed AIS-ACO Hybrid Algorithm
The proposed AIS-ACO hybrid algorithm combines the advantages of AIS and ACO
The hypermutation developed from the AIS is used as a random operator by
adopting random changes to perturb a solution and hence to enlarge the search space
However the pheromones provided by the ACO can store information about the
quality of solution components for improving the objective functions [88] In
addition the information obtained from pheromone updating guides the algorithm in
its search and improves the convergence rate [88]
The limitation of ACO is that the algorithm can easily fall into a local optimum
which might be due to an insufficient range of candidate solutions This can be made
up by the random changes of solutions in AIS through hypermutation Also the
weakness of the global searching ability in AIS is improved by the pheromone tables
in ACO Thus the new hybrid AIS-ACO framework based on the pheromone-based
hypermutation method has better diversity and convergence in comparison with
either the AIS or ACO algorithms
Chapter 3 Optimisation Techniques
Page | 67
Start
Cloning
Maximum iteration
reached
End
No
Yes
Initialise and set iteration number n=1
Hypermutation
Fitness evaluation
Non-dominated solutions extraction
Pheromone updating
n=n+1
Record the Pareto front and
Pareto optimal solutions
In this thesis the AIS-ACO hybrid approach is used to generate a set of non-
dominated solutions The antigen is the multi-objective function and the antibody is
the solution to the problem The affinity between the antibody and the antigen is the
Pareto dominance among solutions which indicates the quality of the solution [88]
All the non-dominated solutions experience cloning hypermutation and selection
until the maximum number of iterations is reached The flowchart of the AIS-ACO
algorithm for Pareto optimality is presented in Fig 3-3
Fig 3-3 Flowchart of the AIS-ACO algorithm
Chapter 3 Optimisation Techniques
Page | 68
The key parts of the algorithm are explained as follows
Initialisation At the beginning of this algorithm a set of initial solutions is
generated These solutions should meet the condition of constraints The
information related to each objective is represented by an individual
pheromone table Each pheromone value represents the probability of
selection of the corresponding edge in the network model [88] All
pheromone values are initially set as the same value
Cloning The number of clones for each non-dominated solution should be
the same as the number of objectives and also as the number of pheromone
tables [88]
Hypermutation The selection of an edge in each cloned solution for
hypermutation is dependent on its pheromone values [88] A higher
pheromone value of a cell in the table indicates that the corresponding edge
in the network is more likely to be selected
Non-dominated solutions extraction This is the process of selecting non-
dominated solutions according to their affinity value [99] All the solutions
are compared as presented in Section 2103 and all the non-dominated
solutions are then extracted for the next iteration
Pheromone updating The aim of this stage is to accumulate the pheromone
values on the edges that belong to a part of the non-dominated solutions and
this is called the global pheromone update However the pheromone
intensity of all edges will evaporate over time by the local pheromone update
This update is used to explore the entire search space
Termination This process is operated until the maximum iteration number
is reached The set of final non-dominated solutions is called the Pareto set
which is used to solve the problem [88]
35 Summary
This chapter introduces the techniques for assessment of mono-objectivemulti-
objective optimisation problems The optimisation techniques are categorised into
two groups simulation methods and analytical methods
Chapter 3 Optimisation Techniques
Page | 69
The Monte Carlo method is a typical simulation technique and is generally used to
handle uncertain parameters It can find the best solution with a high degree of
accuracy but requires a considerable amount of CPU time and memory The
application of this methodology is discussed in Chapter 4 In that chapter an
efficient methodology based on the Monte Carlo Method is proposed for finding
transformer economic operation modes and optimal tie-switch placement strategies
to minimise transformer loss
The ACO algorithm is one of the metaheuristic techniques designed for assessment
of distribution automation (DA) problems It simulates the behaviour of artificial
ants with positive feedback and distributed computation The positive feedback
enhances the search speed in order to find the global solution and the distributed
computation explores the search space The ACO algorithm is able to find the global
solution in a reasonable computation time It is used for either loss reduction or
reliability improvement as discussed in Chapter 5-7 In addition a new multi-
objective ACO (MOACO) algorithm for assessment of multi-objective DNR
problems in terms of Pareto optimality is provided in Chapter 8
The AIS-ACO hybrid algorithm is a combination of AIS and ACO Hypermutation
is used in AIS as a random operator by using random changes to perturb a solution to
maintain the diversity of the solutions avoiding premature convergence for local
minima The pheromone tables used in the ACO are used to direct the algorithm
towards high quality solutions [88] The AIS-ACO hybrid algorithm is always used
for assessing the DA problem in terms of multiple objectives optimisation in order
to obtain a set of non-dominated solutions In addition the advantages of the AIS-
ACO algorithm over the MOACO algorithm for the assessment of multi-objective
optimisation problems are also discussed in Chapter 8
Page | 70
CHAPTER 4
TRANSFORMER ECONOMIC
OPERATION amp DISTRIBUTION
NETWORK RECONFIGURATION FOR
TRANSFORMER LOSS REDUCTION
41 Introduction
The electrical power generation transmission and distribution companies are not
only energy producers but also significant power consumers Energy loss occurs in
the process of power transfer and takes place in all electrical equipment including
generators power lines and transformers The large number and power capacity of
transformers used in a transformer and distribution network means transformer loss
is a significant component in energy loss The lifetime cost of energy loss in a
transformer is significant especially when one considers rising electricity demand
and the cost of the energy supplied For this reason it is important to tackle the
causes of transformer loss and the problems which then ensue so that energy
consumption can be reduced To support this statement several research projects
that have focused on transformer loss reduction are discussed in Section 242
Chapter 4 Transformer Economic Operation amp Distribution Network
Reconfiguration for Transformer Loss Reduction
Page | 71
An efficient methodology based on the Monte Carlo Method for the 3311 kV
transformer loss reduction with consideration of the voltage issues observed on a
distribution network is proposed in this chapter For a substation with two
transformers there are three operation modes that can occur 1) single transformer in
separate operation 2) two transformers in parallel operation 3) transformer
economic operation (TEO) as mentioned in Section 24 With regard to the load
models which are also discussed in this chapter a database containing numerous
domestic electricity demand profiles is imported into MATLAB to work as the
profile generators A Monte Carlo simulation platform is established by combining
the residential demand profiles with a 3311 kV distribution network model built in
OpenDSS Based on this platform the impacts of three operation modes of
transformers on transformer loss minimisation are investigated and compared
In addition an enumeration approach used for the optimum relocation of tie-switches
in a linked 11 kV distribution network is also suggested The process that involves
changing the distribution network topology by relocation of tie-switches is called
distribution network reconfiguration (DNR) [13] [14] The control centre can
change the location of tie-switches and the transformer operation modes (TOMs) in
each substation based on load data and simulated power loss from the test system at
each time interval The proposed approach is applied to the test system and the
effectiveness of an optimal planning strategy using TEO and DNR to achieve
minimum transformer loss is demonstrated through the results obtained
The remainder of this chapter is structured as follows Section 42 explains the load
models Section 43 describes the mathematical formulation of transformer loss
Section 44 analyses the methodology used to minimise transformer loss whilst
maintaining satisfactory voltages and the case studies and the results are presented
and discussed in Section 45 Finally the main conclusions are summarised in
Section 46
Chapter 4 Transformer Economic Operation amp Distribution Network
Reconfiguration for Transformer Loss Reduction
Page | 72
42 Load Model
In order to access the performance of the distribution feeders with different operation
modes of transformers in the substation the time-series behaviour of loads has to be
modelled
The value of the load associated with domestic electricity demand customers has
been obtained from the research described in [19] this can produce a random 1-min
resolution model for UK households There are six steps for creating a domestic
electricity demand model as shown in Fig 4-1 Table 4-1 presents the proportion of
household sizes based on UK statistics [103]
Fig 4-1 Procedure of domestic electricity demand profile generation
Table 4-1 Household size by number of people in household as a proportion [103]
Number of people
in household
1 2 3 4 ge5
Percentage () 3058 341 1557 1288 686
A pool of 10000 different load profiles covering 24 hours in a typical February
weekday are generated by this model For computation reasons the 1440 1-min
time-step load profiles are integrated as 144 10-min resolution profiles in this study
Specify the number of residents in the house from 1 to 5
Specify either a weekday or
weekend
Select the month of the year from 1 to
12
Random allocate appliances to the
dwelling
Run the active occupancy model
Run the electricity demand simulation
Chapter 4 Transformer Economic Operation amp Distribution Network
Reconfiguration for Transformer Loss Reduction
Page | 73
(active power is recorded for each minute and then averaged at intervals of 10
minutes) The power factors of all the loads are set to 095
43 Problem Formulation
The objective of this study is to minimise transformer loss through TEO and optimal
DNR The energy loss of the transformer is related to active power However as a
transformer draws reactive power (it takes current) it causes real power loss in the
network The integrated power loss refers to the sum of active power loss of the
transformer itself and the increased active power loss contributed by reactive power
loss of the transformer [73] The mathematical formulation can be expressed as
follows
Minimise 119891 = 1198800
2119875119885119874119862 +1205732
11988002 119875119885119878119862 119905119903119886119899119904119891119900119903119898119890119903 119894119899 119904119894119899119892119897119890 119900119901119890119903119886119905119894119900119899
211988002119875119885119874119862 +
1
2
1205732
11988002 119875119885119878119862 119905119903119886119899119904119891119900119903119898119890119903119904 119894119899 119901119886119903119886119897119897119890119897 119900119901119890119903119886119905119894119900119899
(4-1)
where 119875119885119874119862 and 119875119885119878119862 are the integrated no-load loss (kW) and the full-load loss (kW)
120573 =119878119871
119878119873 represents the transformer load factor S is the transformer actual loading
(kVA) 119878119873 is the transformer rated capacity (kVA) 1198800 is the operational voltage of
the transformer secondary side in per unit
44 Methodology
In this study there are two methodologies used for transformer loss reduction which
are called TEO and DNR
441 Transformer Economic Operation
In this section a Monte Carlo simulation platform for three TOMs comparison is
established as shown in Fig 4-2 and the flowchart of the transformer loss assessment
is presented in Fig 4-3
Chapter 4 Transformer Economic Operation amp Distribution Network
Reconfiguration for Transformer Loss Reduction
Page | 74
Fig 4-2 Monte Carlo simulation platform for three transformer operation modes comparison
Firstly a pool of 10000 10-min daily domestic electricity demand profiles is
randomly generated by the profile generators in MATLAB Following this each
node in the feeders from the system is assigned with residential demand profiles
from the pool using the Monte Carlo Method Theses profiles and one of the TOMs
are then imported into the distribution network model built in OpenDSS After this a
sequential load flow calculation is performed and the simulation results are returned
including voltage profiles and transformer losses to MATLAB The obtained
results are then analysed and compared with the system constraints for each time
step In this study for each TOM the calculation is set to be repeated 10000 times
in order to satisfy the convergence criteria When the losses of all TOMs are
calculated the minimum transformer loss and its associated operation mode are
obtained
Profile
generator of
domestic
electricity
demand profiles
Transformer
operation
modes
MATLAB
Distribution
network
model built
in OpenDSS
Analyse and
compare
simulation
results in
MATLAB
Load flow calculation
Chapter 4 Transformer Economic Operation amp Distribution Network
Reconfiguration for Transformer Loss Reduction
Page | 75
Start
Monte Carlo trail number N=1
All transformer operation
modes considered
End
No
Yes
Select demand profiles to each
customer randomly
Select transformer operation
mode
Sequentially run power flow
calculation for 144 10-minute time step
Record results
Change
transformer
operation
mode
N=N+1
Maximum iteration reached
Minimum transformer loss and its associated
transformer operation mode are obtained
No
Yes
Load and aggregate the domestic
electricity demand profiles pool
(144 10-minute time steps)
Fig 4-3 Flowchart of transformer loss assessment
Chapter 4 Transformer Economic Operation amp Distribution Network
Reconfiguration for Transformer Loss Reduction
Page | 76
442 Distribution Network Reconfiguration
Reconfiguration of radial distribution system is achieved by local control of tie-
switches located in linked feeders The Monte Carlo simulation platform through
DNR is presented in Fig 4-4
Fig 4-4 Monte Carlo simulation platform for distribution network reconfiguration
In the proposed strategy the tie-switch status is modified by the control centre and
the detailed control algorithm is discussed below
Step 1 Random load profiles are first selected
Step 2 When the load profiles have been imported into the network model a
sequential load flow calculation is performed to calculate and compare the
transformer loss under different network configurations (different tie-switches
location) at each time interval
Step 3 Minimum transformer loss and its associated network configuration are
obtained
Step 4 Location of tie-switches based on minimum transformer loss over a whole
day is recorded
Step 5 Optimal DNR strategy is obtained
Profile
generator of
domestic
electricity
demand profiles
Tie-switch
status
MATLAB
Distribution
network
model built
in OpenDSS
Analyse and
compare
simulation
results in
MATLAB
Load flow calculation
Chapter 4 Transformer Economic Operation amp Distribution Network
Reconfiguration for Transformer Loss Reduction
Page | 77
45 Application Studies
To demonstrate the impact of TOMs and DNR on transformer loss the proposed
methodologies are applied to two test networks Several scenarios are tested and the
results are analysed and reported
451 Test Case 1
The single line diagram of the network shown in Fig 4-5 is developed from the UK
generic distribution network [104] The network model is built to incorporate a 3311
kV substation supplying the downstream loads in the OpenDSS software
environment The two transformers have the same specifications and their
characteristics are presented in Table 4-2 The corresponding TCLF is calculated as
5244 The 11 kV network is represented by four outgoing feeders from a single
busbar For computation reasons three of the feeders are simplified lumped loads
whilst the 4th
feeder is modelled in detail The 4th
11 kV feeder consists of eight
nodes which represents a small system with a total of 252 domestic single phase
house loads connected on each node A Monte Carlo simulation approach is
implemented to select these load profiles randomly from a pool of domestic
electricity demand profiles Each house in the 4th
feeder is then assigned with a
residential demand profile The loads in the other three feeders are then lumped with
the same daily profile of the 4th
feeder All the values of the network components are
based on a broad collection from [104] [105] and are recorded in Appendix A1
In this test a comparison of the three TOM methods for transformer loss
minimisation is provided A time-series load flow algorithm is implemented to
quantify the changes in feeder voltage and transformer loss in the previous described
3311 kV UK distribution network for different TOMs In this test three scenarios
are studied and summarised as follows
Scenario 1 Single transformer in separate operation
Scenario 2 Two transformers in parallel operation
Scenario 3 Transformer economic operation in this mode if the transformer load
factor is less than TCLF only one transformer remains in service if the transformer
load factor is higher than TCLF two transformers are operated in parallel
Chapter 4 Transformer Economic Operation amp Distribution Network
Reconfiguration for Transformer Loss Reduction
Page | 78
A
A
A
A
B
B
B
B
Load1Load2Load3Load4_1
Load4_2
Load4_3
Load4_4
Load4_5
Load4_6
Load4_7
Load4_8
75 MVA
33 kV
11 kV
33 kV
Voltage
Source
75 MVA
Fig 4-5 Generic distribution network topology
Table 4-2 Parameters of a typical 3311 kV two-winding transformer [106]
Sub-
sector
Transf
Rating
(kVA)
Conn Tapping
Range
Load
Losses
at
75
(kW)
No-
Load
Losses
(kW)
Impedance voltage
at rated current for
the principle
tapping
()
Reference
standard
Urban 7500 YY0 plusmn75
6 steps of 25
Each
50
75
835 BS 171 amp
IEC 60076
1) Test 1-1 Base Case
The simulation results of transformer load factor variation are shown in Fig 4-6 and
the transformer loss variation curves are presented in Fig 4-7 It is observed that the
transformer loss in Scenario 3 is the same as in Scenario 1 between 000 to 630 and
Chapter 4 Transformer Economic Operation amp Distribution Network
Reconfiguration for Transformer Loss Reduction
Page | 79
0
10
20
30
40
50
60
70
80
90
100
0 2 4 6 8 10 12 14 16 18 20 22
Tran
sfo
rme
r Lo
ad F
acto
r
Time (h)
0
10
20
30
40
50
60
70
0 2 4 6 8 10 12 14 16 18 20 22
Tran
sfo
rme
r Lo
sse
s (k
W)
Time (h)
0
10
20
30
40
50
60
70
0 2 4 6 8 10 12 14 16 18 20 22
Tran
sfo
rme
r Lo
sse
s (k
W)
Time (h)
the same in Scenario 2 from 1800 to 2200 With the introduction of Scenario 3 the
minimum loss is around 9 kW at 000 which is below the 18 kW of Scenario 2 The
maximum loss of Scenario 3 is nearly 40 kW at 1900 which is far below the 60 kW
of Scenario 1
Fig 4-6 Transformer load factor variation
(a) Scenario 1
(b) Scenario 2
Chapter 4 Transformer Economic Operation amp Distribution Network
Reconfiguration for Transformer Loss Reduction
Page | 80
0
10
20
30
40
50
60
70
0 2 4 6 8 10 12 14 16 18 20 22
Tran
sfo
rme
r Lo
sse
s (k
W)
Time (h)
(c) Scenario 3
Fig 4-7 Transformer loss variations in different scenarios
The mean values of 3311 kV transformer energy loss during one day under different
scenarios are presented in Table 4-3 As shown in Fig 4-6 the average transformer
load factor during a whole day is slightly below the TCLF (5244 in this test) This
situation is more suitable for a single transformer than two transformers The loss in
Scenario 3 reaches the lowest value and results in a reduction of 1133 and 1441
in comparison with Scenario 1 and Scenario 2
Table 4-3 Daily transformer loss in different scenarios
Scenario 1 Scenario 2 Scenario 3
Transformer losses (kWh) 53982 55922 47865
According to the EN50160 standard [7] under normal conditions at least 95 of the
10-min average mean rms voltage magnitude in the 11 kV electricity distribution
network should be within the range 09 pu to 11 pu over one week In other words
the 95th
percentile voltage profile is compared with the allowed voltage range to
check the networkrsquos reliability
The mean and 95th
percentile voltage profiles at each node in the fourth feeder are
presented in Fig 4-8 It can be seen that the voltage level at each node can change
considerably after the scenario changes It also appears that the nodes in Scenario 1
experience the most severe voltage drop in comparison with the other two scenarios
The worst 95 voltage value of the node lsquoLoad4_8rsquo at the end of the studied feeder
in Scenario 1 is around 098 pu which is not as satisfactory as the results of 0987 pu
and 0984 pu observed in Scenario 2 and Scenario 3
Chapter 4 Transformer Economic Operation amp Distribution Network
Reconfiguration for Transformer Loss Reduction
Page | 81
0976
0978
098
0982
0984
0986
0988
099
0992
Load4_1 Load4_2 Load4_3 Load4_4 Load4_5 Load4_6 Load4_7 Load4_8
Vo
ltag
e (
pu
)
Scenario1
Scenario2
Scenario3
0974
0976
0978
098
0982
0984
0986
0988
099
Load4_1 Load4_2 Load4_3 Load4_4 Load4_5 Load4_6 Load4_7 Load4_8
Vo
ltag
e (
pu
)
Scenario1
Scenario2
Scenario3
(a) Mean value
(b) 95th
value
Fig 4-8 11 kV 4th
feeder voltage profiles in different scenarios
To show in detail the voltage profiles affected by different TOMs the load at the
start of the 4th
feeder lsquoLoad4_1rsquo and the end one lsquoLoad4_8rsquo have been selected
Since the Monte Carlo method produces many loss and voltage values it is
preferable to present the averages of all these values and their deviations
As shown in the charts from Fig 4-9 and Fig 4-10 the voltage drops severely from
1800 to 2000 which is also the maximum daily demand period It also appears that
the voltage profile in Scenario 3 is the same as in Scenario 1 between 000 to 630
and the same as in Scenario 2 from 1800 to 2200 With the introduction of Scenario
Chapter 4 Transformer Economic Operation amp Distribution Network
Reconfiguration for Transformer Loss Reduction
Page | 82
088
09
092
094
096
098
1
0 2 4 6 8 10 12 14 16 18 20 22
Bu
s V
olt
age
(p
u)
Time (h)
088
09
092
094
096
098
1
0 2 4 6 8 10 12 14 16 18 20 22
Bu
s V
olt
age
(p
u)
Time (h)
088
09
092
094
096
098
1
0 2 4 6 8 10 12 14 16 18 20 22
Bu
s V
olt
age
(p
u)
Time (h)
3 the lowest voltage of lsquoLoad4_8rsquo is around 097 pu which is significantly above
the lower limit 090 pu
(a) Scenario 1
(b) Scenario 2
(c) Scenario 3
Fig 4-9 Voltage profiles of Load 4_1 in different scenarios
Lower Limit
Lower Limit
Lower Limit
Chapter 4 Transformer Economic Operation amp Distribution Network
Reconfiguration for Transformer Loss Reduction
Page | 83
088
09
092
094
096
098
1
0 2 4 6 8 10 12 14 16 18 20 22
Bu
s V
olt
age
(p
u)
Time (h)
088
09
092
094
096
098
1
0 2 4 6 8 10 12 14 16 18 20 22
Bu
s V
olt
age
(p
u)
Time (h)
088
09
092
094
096
098
1
0 2 4 6 8 10 12 14 16 18 20 22
Bu
s V
olt
age
(p
u)
Time (h)
(a) Scenario 1
(b) Scenario 2
(c) Scenario 3
Fig 4-10 Voltage profiles of Load 4_8 in different scenarios
Lower Limit
Lower Limit
Lower Limit
Chapter 4 Transformer Economic Operation amp Distribution Network
Reconfiguration for Transformer Loss Reduction
Page | 84
0976
0978
098
0982
0984
0986
0988
099
0992
Load4_1 Load4_2 Load4_3 Load4_4 Load4_5 Load4_6 Load4_7 Load4_8
0 25
5244 75
100
As most people are sleeping late at night and the transformer load factor is less than
the TCLF transformers are in individual operation mode When most people are at
home again from 1800 the transformer load factor increases beyond the TCLF As a
result the voltage profiles are improved when transformers are operated in parallel
In conclusion when the transformer load factor is less than the TCLF transformers
in a separate service result in less loss but more voltage dips however transformers
operating in parallel cause lower voltage drops but more loss When the transformer
load factor is higher than the TCLF transformers in parallel operation cause less loss
and lower voltage drops As a result based on the economic operation theory the
transformer in Scenario 3 significantly reduces transformer loss and maintains the
voltages at a satisfactory level
2) Test 1-2 TCLF Sensitivity Analysis
In this test the value of TCLF used to distinguish whether the transformer should be
in separate or parallel operation is discussed The complete process presented
previously is carried out again but takes into account the effect of different critical
values 0 25 5244 75 and 100
Fig 4-11 shows the effect on the mean voltage magnitudes of various TCLFs The
results indicate that the voltage profile is closely related to the TCLF and the TCLF
should be decreased to increase the region in which transformers operate in parallel
This will improve the voltage profiles
Fig 4-11 11 kV 4th
feeder mean voltage profile of various TCLFs
Chapter 4 Transformer Economic Operation amp Distribution Network
Reconfiguration for Transformer Loss Reduction
Page | 85
Table 4-4 describes the effect on the transformer loss when TCLF is changed It
reaches the lowest value when TCLF is 5244 If the TCLF is decreased or
increased above this value the loss increases Overall the TCLF should be set to
5244 in order to minimise transformer loss
Table 4-4 Transformer loss with different TCLF
TCLF () 0 25 5244 75 100
Transformer loss
(kWh)
55922 50783 47865 49414 53982
As presented in Table 4-5 the average number of switching operations is increased
as the TCLF is approached to its optimum value
Table 4-5 Average number of switching operations with different TCLF
TCLF () 0 25 5244 75 100
Average number of
switching operations
0 2 4 2 0
452 Test Case 2
The impacts of TOMs and DNR on transformer loss are evaluated in this section As
presented in Fig 4-12 the model of the test system is developed from the
duplication of the generic distribution network shown in Fig 4-5 All the values of
the network parameters are obtained from [104]ndash[106] The system is supplied by
two 3311 kV substations and each bus has four feeders There is one linked feeder
with nine tie-switches Tie-switches refer to the switches of the network that are
normally open The function of the tie-switches is to alter the network topology to
provide various routes for supplying loads In order to feed all loads and keep the
systemrsquos radial topology only one tie-switch is open and all the others are closed
Chapter 4 Transformer Economic Operation amp Distribution Network
Reconfiguration for Transformer Loss Reduction
Page | 86
0
02
04
06
08
1
12
14
16
0 2 4 6 8 10 12 14 16 18 20 22
Act
ive
Po
we
r (k
W)
Time (h)
TW1 TW2 TW3 TW4 TW5
A1
A2
A3
A4_1 A4_2 A4_3 A4_4 A4_5 A4_6 A4_7 A4_8 B4_8 B4_7 B4_6 B4_5 B4_4 B4_3 B4_2 B4_1
B1
B2
B3
EndA EndB
TW9TW8TW7TW6
Tie-Switch (close) Tie-Switch (open)
Fig 4-12 Test system
For simplicity the daily load variations in each feeder are the same and the load
profiles of each node in the linked feeder are also the same Therefore the loads
could be categorised into two groups
Group 1 A1 A2 A3 B1 B2 B3
Group 2 A4_1 A4_2 A4_3 A4_4 A4_5 A4_6 A4_7 A4_8 B4_1 B4_2
B4_3 B4_4 B4_5 B4_6 B4_7 B4_8
On the basis of transformer load factor variation shown in Fig 4-6 the relevant 10-
min resolution load models of the two groups are presented in Fig 4-13 The power
factors of all the loads are set to 095
(a) Group 1
Chapter 4 Transformer Economic Operation amp Distribution Network
Reconfiguration for Transformer Loss Reduction
Page | 87
0
002
004
006
008
01
012
014
016
018
02
0 2 4 6 8 10 12 14 16 18 20 22
Act
ive
Po
we
r (k
W)
Time (h)
(b) Group 2
Fig 4-13 Daily load variations for different load groups
As this test system is developed from the duplication of the generic distribution
network and all the loads have the same profiles the position of the tie-switch is
selected from lsquoTW1rsquo to lsquoTW5rsquo For example the tie-switch located in lsquoTW1rsquo has the
same effect as lsquoTW9rsquo The control strategy is used to quantify the changes in feeder
voltage and transformer loss in the previously described test system under different
scenarios which could be categorised as
Scenario 1 each end has one transformer in operation and the tie-switch is located
at TW1 ie entire feeder supplied from end B
Scenario 2 each end has one transformer in operation and the tie-switch is located
in TW5 ie feeder split at mid-point
Scenario 3 each end has one transformer in operation and the location of the tie-
switch is based on minimum transformer loss operation
Scenario 4 each end has two transformers in operation and the tie-switch is located
at TW1
Scenario 5 each end has two transformers in operation and the tie-switch is located
at TW5
Scenario 6 each end has two transformers in operation and the location of the tie-
switch is based on minimum transformer loss operation
Chapter 4 Transformer Economic Operation amp Distribution Network
Reconfiguration for Transformer Loss Reduction
Page | 88
Scenario 7 each end has onetwo transformers in operation based on the transformer
load factor and the tie-switch is located at TW1
Scenario 8 each end has onetwo transformers in operation based on the transformer
load factor and the tie-switch is located at TW5
Scenario 9 each end has onetwo transformers in operation based on the transformer
load factor and the location of the tie-switch is based on minimum transformer loss
operation
Table 4-6 indicates the mean value of 3311 kV transformer loss during one day
under different scenarios As can be seen from the table when the tie-switches have
the same location TW1 transformer loss in Scenario 7 results in a reduction of
1396 and 1456 in comparison with Scenario 1 and Scenario 4 In conclusion
the mode introducing a flexible number of transformers in operation based on TCLF
reduces the loss In addition the transformer loss in Scenario 9 is 9528 kWh per day
which is 217 and 014 lower than Scenario 7 and Scenario 8 As a result the
variation of tie-switch locations could reduce transformer loss The detailed location
of the tie-switch in Scenario 9 is included in Appendix B1
Table 4-6 Transformer loss in Test Case 2
Scenarios S1 S2 S3 S4 S5 S6 S7 S8 S9
Loss
(kWhday)
11319 10848 10848 11399 11162 11162 9739 9572 9528
The graph presented in Fig 4-14 illustrates the voltage variation caused by the tie-
switch relocation The node voltages in Scenario 1 experience the worst profile
which increases to a peak of 09749 pu from 09675 pu along the linked feeder In
order to reduce the loss the tie-switch is always located in the middle of the feeder
TW5 in Scenario 3 As a result the voltage profiles of Scenario 2 and Scenario 3 are
the same It should be noted that Scenario 2 experiences a slight drop from 09787 pu
to 0972 pu and then climbs back to 09827 pu It can also be clearly seen that the
voltage reaches the lowest value where the tie-switch is located The further away
the nodes are from the tie-switch the better the voltage profiles that can be obtained
In addition when the tie-switch moves closer to the middle of the linked feeder the
Chapter 4 Transformer Economic Operation amp Distribution Network
Reconfiguration for Transformer Loss Reduction
Page | 89
096
0962
0964
0966
0968
097
0972
0974
0976
0978
098
A4_1A4_2A4_3A4_4A4_5A4_6A4_7A4_8B4_8B4_7B4_6B4_5B4_4B4_3B4_2B4_1
Vo
ltag
e (
pu
)
Scenario1
Scenario2
Scenario3
0955
096
0965
097
0975
098
0985
099
A4_1A4_2A4_3A4_4A4_5A4_6A4_7A4_8B4_8B4_7B4_6B4_5B4_4B4_3B4_2B4_1
Vo
ltag
e (
pu
)
Scenario1
Scenario4
Scenario7
voltage performance is improved And the detailed voltage values at each node in the
linked feeder for different scenarios are presented in Appendix B1
Fig 4-14 Mean voltage profiles in S1 S2 and S3
As shown in Fig 4-15 the voltage variation is due to a change in TOMs
Fig 4-15 Mean voltage profiles in S1 S4 and S7
As in the case of the tie-switch located in lsquoTW1rsquo all the node voltages experience a
rise along the linked feeder from lsquoEndArsquo to lsquoEndBrsquo It should be noted that the node
voltages in Scenario 4 achieve the best profile which increase to a peak of 0984 pu
from 0976 pu As discussed in Test Case 1 the transformers in parallel operation
could improve the voltage profiles In addition the flexible number of transformers
Chapter 4 Transformer Economic Operation amp Distribution Network
Reconfiguration for Transformer Loss Reduction
Page | 90
in operation based on TCLF (Scenario 7) shows a slight difference in voltage from
that in Scenario 4
As discussed above the location of the tie-switch and the change of TOMs have an
impact on the feeder voltage variation The tie-switch located in the middle of the
feeder and transformers with parallel operation defines the best voltage profiles
46 Summary
This chapter illustrates why transformer economic operation (TEO) is an economical
solution to reduce transformer loss The substation composed of two transformers
with the same characteristics has been used as an example to introduce the general
approach of determining the TCLF and TEO area A Monte Carlo simulation
platform was established to tackle load uncertainties A methodology to prove that
the TOM variation affects the performance of the 11kV distribution network is
discussed and analysed The TEO mode with minimum loss and satisfactory voltages
is achieved depending on the the transformer load factors by operating with either
one or two transformers and can be summarised as when the transformer load factor
is less than the TCLF transformers should be in separate operation when the
transformer load factor is higher than the TCLF transformers are recommended to
operate in parallel This results in a reduction of 1441 over the conventional
transformer loss ie when two transformers are in parallel operation However
simulation studies also indicate voltage profiles are improved when transformers
operate in parallel Therefore a slight reduction in TCLF results in an increased loss
but an improvement in voltage performance
The effectiveness of a DNR strategy has also been proposed through the results
obtained The presented results illustrate the impact of different TOMs in each
substation and tie-switch statuses on transformer loss and the voltages measured
along the feeder during a 24 hour operating period The optimal economic operation
strategy with TEO and DNR have successfully reduced the transformer loss and
improved the voltage profiles The further away the nodes are from the tie-switch
the better the voltage profiles obtained In addition when the tie-switch moves closer
to the middle of the linked feeder the voltage performance is improved
Chapter 4 Transformer Economic Operation amp Distribution Network
Reconfiguration for Transformer Loss Reduction
Page | 91
In normal operating conditions transformers operate in parallel and the tie-switch is
located in the middle of the linked feeder As indicated by Table 46 the daily
energy loss in Scenario 5 is 11162 kWh After the introduction of Scenario 9 the
annual saving energy could be 59641 kWh
Page | 92
CHAPTER 5
DISTRIBUTION NETWORK
RECONFIGURATION amp DG ALLOCATION
FOR FEEDER LOSS REDUCTION
51 Introduction
Distribution networks generally operate in radial configuration to ease protection
coordination and to reduce short circuit current [107] Distribution feeders can be
reconfigured to alter the network topology at normal and abnormal operating
conditions by changing the openclose status of switches to satisfy the operatorrsquos
objectives [13] [14]
DG is a small electric generation unit that is connected directly to the distribution
network or appears on side of the meter accessed by the customer [16] With the
increasing number of DGs bidirectional power flows have appeared and locally
looped networks have become inevitable [17] Therefore the type size and location
of DGs in the distribution networks strongly affect power system operation and
planning
The studies in [5] indicate that about 5 of the total power generation is wasted in
the form of feeder loss at the distribution level Reduction in active power loss can
help distribution network operators (DNOs) save costs and increase profits The
Chapter 5 Distribution Network Reconfiguration amp DG Allocation for Feeder Loss
Reduction
Page | 93
optimal distribution network reconfiguration (DNR) placement and sizing of DGs
strategies should be used to reduce feeder loss while satisfying the operating
constraints
The ant colony optimisation (ACO) developed by M Dorigo is a metaheuristic
algorithm for the assessment of optimisation problems [94] It is based on the
pheromones deposited by ants as a guide for finding the shortest path between a food
source and their home colony The detailed description of ACO algorithm has been
presented in Section 33 In this chapter an ACO algorithm is proposed to solve the
network reconfiguration and DG placement problems simultaneously based on
distribution feeder loss minimisation The proposed technique is tested on two
standard IEEE 33-node and 69-node systems and the simulation results show the
performance and effectiveness of the proposed method Four scenarios are
considered during network reconfiguration and DG allocation The impacts of DG
capacity on assessing the DNR and DG allocation problems in terms of feeder loss
reduction are also studied Moreover the results obtained by ACO algorithm have
been compared to those from other algorithms in the literature
As for the remainder of this chapter the mathematical formulation of the objective
function and its constraints are explained in Section 52 Section 53 discusses the
application of ACO algorithms in order to solve the problem Section 54 provides a
detailed analysis of the numerical results and Section 55 provides the final
conclusions
52 Problem Formulation
The proposed objective function (F) of the problem is formulated to minimise the
feeder loss of a distribution network which is described as follows
119872119894119899119894119898119894119904119890 119891 = sum 119896119894119877119894(119875119894
2+1198761198942
1198801198942 )
119873119887119894=1 (5-1)
where 119877119894 is the resistance of the ith branch 119875119894 and 119876119894 are the real power (W) and
reactive power (VAr) at the receiving end of branch i 119880119894 represents the rms voltage
at the receiving end of branch i (V) 119896119894 is a binary variable 119896119894 = 0 indicates that
Chapter 5 Distribution Network Reconfiguration amp DG Allocation for Feeder Loss
Reduction
Page | 94
branch 119894 is open and 119896119894 = 1 indicates that branch 119894 is closed The detailed feeder loss
assessment has been given in Section 28
Subject to
∆119881119899 le ∆119881119898119886119909 for all load points (5-2)
119868119887 le 119868119898119886119909 for all branches (5-3)
119875119894 le 119875119894119898119886119909 (5-4)
det(119860) = 1 119900119903 minus 1 (5-5)
Constraints (5-2) ndash (5-3) represent the computed voltages and currents and should be
in their permissible range Constraint (5-4) indicates that the power flow at all
branches should be within the limits defined for each branch Constraint (5-5)
ensures the radial topology of the network [32] The branch to node incidence matrix
Arsquo has one row for each branch and one column for each node 119886119894119895 represents the
coefficient in row i and column j 119886119894119895 = 0 if branch i is not connected with node j
119886119894119895 = 1 if branch i is directed away from node j and 119886119894119895 = minus1 if branch i is directed
towards node j When the column corresponding to the reference node and the rows
of open branches are deleted from matrix Arsquo a new square branch-to-node matrix A
is obtained Then the determinant of A is calculated If det(A) is 1 or -1 the system is
radial Otherwise the system is not radial
53 Solution Method
531 Distribution Network Reconfiguration
With regard to the DNR problem each solution is represented by a string of integers
which indicates the location of tie-switches As the number of tie-switches that keep
the network radial is always constant the number of the solutionrsquos elements is equal
to the number of tie-switches in the network
Chapter 5 Distribution Network Reconfiguration amp DG Allocation for Feeder Loss
Reduction
Page | 95
Home
1 2 NP1NP1-1
1 2 NP1-1 NP1
1 2 NP1NP1-1
1 2 NP2-1 NP2
1 2 NP2NP2-1
1 2 NP2-1 NP2
1 2 NP2NP2-1
1 2 NP2-1 NP2
Food
Stage
1
2
NT-1
NT
NT+1
NT+2
NT+NDG-1
NT+NDG
Part 1 Number of
existing tie-switches
Part 2 Number
of DGs
532 Applying ACO to DNR and DGs Placement
In this chapter an ACO algorithm is adopted to find the optimum locations of tie-
switches and sites of DGs placement in the network in terms of feeder loss
minimisation When the locations of tie-switches and DGs are changed a new
network configuration will be formed For each network configuration the feeder
loss is evaluated by using the approach presented in Section 52
Fig 5-1 Search space of DNR and DGs Placement
Chapter 5 Distribution Network Reconfiguration amp DG Allocation for Feeder Loss
Reduction
Page | 96
The search space of the DNR and DG allocation problems is modelled as a directed
graph as shown in Fig 5-1 In Part I the states signify the location of tie switches
and the sites for DGs installation are represented by states in Part II The number of
stages in this graph is the sum of the amount of existing tie-switches 119873119905 and the
number of installed DGs 119873119863119866 1198731199011is the number of possible locations for the tie-
switches relocation and 1198731199012 is the number of candidate buses for DGs installation
Artificial ants start their tours at home moving along the paths in the graph and end
at the food source Each location list consists of a string of integers and represents a
solution to the problem Different orders of the solutionrsquos elements indicate different
routes However several routes might indicate a certain solution as the order of the
solutionrsquos elements makes no difference to the network configuration For example
the solution vector (1 2 3) represents the same network configuration as the solution
vector (3 2 1) And the objective functions of these two routes are the same In this
study the first route that the ants found will be chosen as the feasible solution The
flowchart of the proposed ACO algorithm is presented in Fig 5-2 and is expressed in
five steps
Step 1 Initialisation First of all all the ants are initially located at home The
pheromone values of the edges in the search space are all set to a small positive
constant value
Step 2 Ant Dispatch All the ants are sent in parallel from the home colony and one
of the states is chosen in the next stage according to a probabilistic selection rule
which involves the intensity of pheromones deposited on the states [66] The
locations of the tie-switches are determined first and the sites for the DGs
installation are then selected The probability of an ant choosing state j of the next
stage y is
119875119895119910(119873) =
120591119895119910
(119873)
sum 120591119895119910
(119873)ℎisin∆119910
(5-6)
where 120591119895119910
(119873) is the pheromone value of state j of stage y at iteration N ∆119910 is the set
of available states which an ant can choose at stage y
Chapter 5 Distribution Network Reconfiguration amp DG Allocation for Feeder Loss
Reduction
Page | 97
Step 3 Objective Function Evaluation After all the ants have completed their tour
the location list and corresponding objective function in (5-1) for each ant are
evaluated If any constraint in (5-2) - (5-5) is violated the corresponding solution is
assigned with a huge value and is discarded If not all the objective functions are
assessed and the best configuration of the Nth iteration with minimum objective
function 119891119887119890119904119905(119873) is recorded This should be compared to the best configuration
obtained so far 119891119887119890119904119905 if 119891119887119890119904119905(119873) lt 119891119887119890119904119905 the best solution should be updated such
that 119891119887119890119904119905 = 119891119887119890119904119905(119873) [14] If not the best configuration found in the previous
iteration is retained After this the location list is emptied and all the ants are free to
choose a new trail
Step 4 Pheromone Updating The aim of this step is to favour transitions towards
states involving high quality solutions with greater pheromones There are two rules
of pheromone updating the local rule and global rule
Local rule The amount of pheromone deposited in the search space should be
evaporated to make paths less attractive The local pheromone update rule is
calculated as following
120591119895119910
(119873) = (1 minus 120588)120591119895119910
(119873 minus 1) + 120591119888 (5-7)
where 120588 is the pheromone evaporation rate which is set between 0 and 1 120591119888 is a
small positive constant value Even if the amount of pheromone deposited on an
edge is at the lowest value of 120591119888 there is a slight chance that an ant will still choose
this edge
Global rule The global pheromone updating rule involves ants depositing large
amounts of pheromone to the edges that belong to the highest quality solution per
iteration This rule is to guide the search to find the global optimal solution The
pheromones of those edges can be modified by
120591119895119910(119873) = 120591119895
119910(119873) + 120588119891119887119890119904119905
119891119887119890119904119905(119873) (5-8)
After applying the local and global pheromone updating rules the method Max-Min
ACO algorithm is integrated into the proposed approach
120591119895119910(119873) = 120591119898119886119909 119894119891 120591119895
119910(119873) ge 120591119898119886119909 (5-9)
120591119895119910(119873) = 120591119898119894119899 119894119891 120591119895
119910(119873) le 120591119898119894119899 (5-10)
Chapter 5 Distribution Network Reconfiguration amp DG Allocation for Feeder Loss
Reduction
Page | 98
Start
Set Iteration n=1
Maximum iteration
reached
Output best
configuration and end
No
Yes
Initialise the parameters for ACO algorithm
searching space and build graph of the tours
Dispatch ants based on the
amount of pheromones on edges
Relocate tie-switches and DGs by location lists
Calculate the objective function for each ant
The pheromones are updated according
to local and global rules
n=n+1
Record the best solution so far and empty
all location lists
Read system topology
and load data
where 120591119898119886119909and 120591119898119894119899 are the higher and lower bound of the pheromone level on each
edge respectively The trail limit of the pheromone ensures the probabilities of all
the edges are greater than zero which maintains the diversity of the solutions and
avoids premature convergence for local minima
Step 5 Termination The computation continues until the predefined maximum
number iterations is reached The best tour selected among all iterations implies the
optimal solution
Fig 5-2 Flowchart of the ACO applied to DNR and DGs placement
Chapter 5 Distribution Network Reconfiguration amp DG Allocation for Feeder Loss
Reduction
Page | 99
54 Application Studies
To demonstrate the performance and effectiveness of the proposed technique in
assessing the network reconfiguration and placement of DG problems
simultaneously the proposed ACO is implemented on two 1266 kV test systems
consisting of 33 and 69 buses The network models are built in OpenDSS and the
solution algorithm is developed in MATLAB For both test systems the substation
voltage is assumed to be 10 pu and all the branches and buses are considered as
candidate locations for tie-switches and DG placement respectively In this study
for simplicity the number of installed DGs is three All the DGs are synchronous
generators and are represented as PQ models with a 100 kVA capability and a
power factor equal to 10 For the purpose of better illustration and comparison four
cases are considered to analyse the superiority and performance of the proposed
method
Case I System is without reconfiguration and has no DGs (base case)
Case II System is optimally reconfigured and has no DGs
Case III System is optimally reconfigured after DGs are placed at certain buses
Case IV System is optimally reconfigured and DGs are optimally placed
simultaneously
It is to be noted that the ACO control parameters are different for each test case
They are set experimentally using information from several trial runs The final
combinations that provide the best results for all of the above tests are given in
Appendix C1
541 33-bus System
In this section the proposed procedure is implemented on a 33-bus 1266 kV radial
distribution system with 37 branches and 5 tie-switches whose single-line diagram
is shown in Fig 5-3 The tie-switches are located at L33 to L37 represented by red
dotted lines The data of line and load are taken from [108] and summarised in
Appendix A2 The total real and reactive power loads of the system are 3715 kW
and 2300 kVAr respectively The performance of the presented method for the four
Chapter 5 Distribution Network Reconfiguration amp DG Allocation for Feeder Loss
Reduction
Page | 100
10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
18 19 20 21
22 23 24
25 26 27 28 29 30 31 32
L1 L2 L3 L4 L5 L6 L7 L8 L9 L10 L11 L12 L13 L14 L15 L16 L17
L18
L19 L20 L21
L22
L23 L24
L25
L26 L27 L28 L29 L30 L31 L32
L33
L34
L35
L36
L37
cases is given in Table 5-1 The network losses in each branch for all test cases are
listed in Appendix B2
Fig 5-3 33-bus system
Table 5-1 Results of different cases for the 33-bus system
Case Active feeder
loss (kW)
Minimum voltage
(pu)
(Bus No)
Location of tie-switches
on Fig 53
DG location
Case I 20314 09116 (B17) L33 L34 L35 L36 L37 NA
Case II 13981 09361 (B31) L7 L9 L14 L32 L37 NA
Case III 11753 09357 (B31) L7 L9 L14 L28 L31 B17 B21 B24
Case IV 10844 09462 (B32) L7 L9 L14 L32 L37 B30 B31 B31
Case I base case
For the base case without reconfiguration and DGs the initial active feeder loss of
this system is 20314 kW The lowest bus voltage is 09116 pu and this occurs at
Bus 17
Case II with reconfiguration only (no DGs)
In this case only reconfiguration is considered and no DGs are installed The
network configuration after DNR is shown in Fig 5-4 The number of the solutionrsquos
elements for this case is 5 which is the number of tie-switches After DNR the total
feeder loss is 13981 kW which corresponds to a 3118 reduction in loss In
addition the minimum voltage also increases from 09116 pu to 09361 pu
Chapter 5 Distribution Network Reconfiguration amp DG Allocation for Feeder Loss
Reduction
Page | 101
10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
18 19 20 21
22 23 24
25 26 27 28 29 30 31 32
L1 L2 L3 L4 L5 L6 L7 L8 L9 L10 L11 L12 L13 L14 L15 L16 L17
L18
L19 L20 L21
L22
L23 L24
L25
L26 L27 L28 L29 L30 L31 L32
L33
L34
L35
L36
L37
Fig 5-4 33-bus system for feeder loss minimisation Case II
To illustrate the performance of the proposed ACO the results are compared with
the results obtained using the branch exchange method (BEM) [109] harmony
search algorithm (HSA) [110] fireworks algorithm (FWA) [16] particle swarm
optimisation (PSO) [55] and invasive weed optimisation (IWO) [111] these are all
described in the literature and are presented in Table 5-2 It is observed that the
results obtained from the ACO are identical to those from the HAS PSO and IWO
but better than the results from the BEM and FWA This is because that BEM and
FWA have plunged into a local optimal solution and they lack the ability to escape
from it
Table 5-2 Comparison of simulation results for 33-bus system in Case II
Method Feeder loss
(kW)
Loss reduction
()
Tie-switches location Minimum
voltage (pu)
The proposed ACO 13981 3118 L7 L9 L14 L32 L37 09361
BEM [109] 14054 3082 L7 L10 L14 L32 L37 09361
HSA [110] 13981 3118 L7 L9 L14 L32 L37 09361
FWA [16] 14026 3095 L7 L9 L14 L28 L32 09396
PSO [55] 13981 3118 L7 L9 L14 L32 L37 09361
IWO [111] 13981 3118 L7 L9 L14 L32 L37 09361
Moreover both the continuous genetic algorithm (CGA) [112] and cuckoo search
algorithm (CSA) [113] are implemented to further investigate the performance of the
proposed ACO It is important to note that the performance of the ACO CGA and
CSA depends on the selection of their control parameters All three algorithms are
solved 100 times The average maximum minimum and standard deviation of the
100 runs are compared and shown in Table 5-3 The convergence number is defined
Chapter 5 Distribution Network Reconfiguration amp DG Allocation for Feeder Loss
Reduction
Page | 102
10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
18 19 20 21
22 23 24
25 26 27 28 29 30 31 32
L1 L2 L3 L4 L5 L6 L7 L8 L9 L10 L11 L12 L13 L14 L15 L16 L17
L18
L19 L20 L21
L22
L23 L24
L25
L26 L27 L28 L29 L30 L31 L32
L33
L34
L35
L36
L37
DG2
DG1
DG3
as the number of the iterations when the objective function is convergence It can be
seen that all three algorithms have obtained the same minimum loss However the
proposed ACO method has a higher probability in finding the global optimum
solution as the mean and standard deviation of the fitness values of the ACO
algorithm are less than those obtained by the other algorithms Furthermore as the
average value of convergence number of the ACO is less than that of the other two
algorithms this means the proposed algorithm has a higher convergence rate In
terms of the computation times the proposed ACO runs faster when compared with
CGA and CSA
Table 5-3 Comparison of ACO with CGA and CSA for the 33-bus system in Case II
Method Feeder loss (kW) Convergence number Average
computation
times
(second)
AVG MAX MIN STD AVG STD
ACO 13981 13981 13981 0 228 821 1448
CGA [112] 14002 14619 13981 12121 5463 2986 3926
CSA [113] 13986 14028 13981 01328 8363 3425 7258
AVG MAX MIN and STD mean the average maximum minimum and standard deviation of the 100 runs
Case III with reconfiguration only (with DGs)
In this case the three DGs are located at the end of the feeders ie Bus 17 21 24
The network configuration after DNR is illustrated in Fig 5-5 As shown in Table 5-
1 the network reconfiguration results in a reduction of 4214 in feeder loss in
comparison with the original network without DGs and a reduction of 1594 in
comparison with the reconfigured system without DGs
Fig 5-5 33-bus system for feeder loss minimisation Case III
Chapter 5 Distribution Network Reconfiguration amp DG Allocation for Feeder Loss
Reduction
Page | 103
10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
18 19 20 21
22 23 24
25 26 27 28 29 30 31 32
L1 L2 L3 L4 L5 L6 L7 L8 L9 L10 L11 L12 L13 L14 L15 L16 L17
L18
L19 L20 L21
L22
L23 L24
L25
L26 L27 L28 L29 L30 L31 L32
L33
L34
L35
L36
L37
DG2DG1
DG3
Case IV with reconfiguration and DG allocation
Fig 5-6 illustrates the optimal network configuration and DG locations The network
is reconfigured and DGs are allocated simultaneously in this case Therefore the
number of the solutionrsquos elements for this case becomes 8 which is the sum of the
number of tie-switches and DGs The results show the final configuration with a
feeder loss of 10844 kW with 4662 2244 and 773 reduction in comparison
with that in Case I Case II and Case III respectively
Fig 5-6 33-bus system for feeder loss minimisation Case IV
In this case the impacts of DG capacity on assessing the DNR and DG allocation
problems in terms of feeder loss reduction are also studied The capacity of each DG
is set as 100 400 700 and 1000 kVA respectively The feeder losses for different
DG capacities are shown in Fig 5-7 Before simultaneous reconfiguration and DG
allocation the feeder loss decreases from 1783 kW to 1023 kW when the capacity
of DG is increased from 100 kVA to 700 kVA However the feeder loss increases to
1042 kW if the capacity of DG continuously grows to 1000 kVA The inappropriate
network configuration and DG location might result in loss increment when the size
of the DG is increased However with the introduction of network reconfiguration
and DG allocation feeder loss is reduced no matter what the capacity of DG is This
proves that the proposed methodology can reduce the total feeder loss by
determining the most suitable network topology and DG locations in comparison
with the original configuration
Chapter 5 Distribution Network Reconfiguration amp DG Allocation for Feeder Loss
Reduction
Page | 104
086
088
09
092
094
096
098
1
102
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32
Vo
ltag
e (
pu
)
Bus No
Case I
Case II
Case III
Case IV
0
20
40
60
80
100
120
140
160
180
200
100 400 700 1000
Fee
de
r lo
ss (
kW)
DG Capacity (kVA)
Before simultaneousreconfiguration and DG allocation
After simultaneous reconfigurationand DG allocation
Fig 5-7 Comparison of feeder loss for different DG capacities before and after simultaneous
reconfiguration and DG allocation
The voltage profiles of four cases are compared and shown in Fig 5-8 It can be seen
that the voltage profiles at most buses in Case IV have been improved in comparison
with the other three cases In terms of Case III and Case IV the buses which inject
DGs show the improvement in voltage profiles ie the voltage of Bus 31 is
improved from 09357 pu in Case III to 09537 pu in Case IV In Case IV as Bus 32
is the furthest bus being supplied its voltage is the lowest value among all buses In
conclusion the systemrsquos voltage profiles are improved by optimal DNR and DG
allocation
Fig 5-8 Comparison of voltage profiles in different cases of 33-node system
Chapter 5 Distribution Network Reconfiguration amp DG Allocation for Feeder Loss
Reduction
Page | 105
10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
27
28
29
30
31 32 33 34
35
36
37
38 39 40 41 42 43 44 45
46 47 48 49
50
51
52
53 54 55 56 57 58 59 60 61 62 63 64
65 66
67 68
L1 L2 L3 L4 L5 L6 L7 L8 L9 L10 L11 L12 L13 L14 L15 L16 L17 L18 L19 L20 L21 L22 L23 L24 L25 L26
L27
L28
L29
L30
L31 L32 L33 L34
L35
L36
L37
L38 L39 L40 L41 L42 L43 L44 L45
L46
L47 L48 L49
L50
L51
L52
L53 L54 L55 L56 L57 L58 L59 L60 L61 L62 L63 L64
L65
L66
L67
L68
L69
L70
L71
L72L73
542 69-bus System
This is a large-scale radial distribution system consisting of 73 branches and 5 tie-
switches whose single-line diagram is shown in Fig 5-9 The tie-switches are
located at L69 to L73 represented by red dotted lines The line and load data of the
system are taken from [84] and summarised in Appendix A3 The total power loads
are 379589 kW and 26891 kVAr respectively Similar to 33-bus system this
system is also simulated for four cases and the results are given in Table 5-4 The
network losses in each branch for all test cases are listed in Appendix B2
Fig 5-9 69-bus system
Table 5-4 Results of different cases for the 69-bus system
Case Active feeder
loss (kW)
Minimum voltage
(pu)
(Bus No)
Tie-switches location DG location
Case I 22562 09072 (B64) L69 L70 L71 L72 L73 NA
Case II 9885 09476 (B60) L14 L55 L61 L71 L72 NA
Case III 8758 09477 (B60) L13 L55 L61 L71 L72 B26 B45 B64
Case IV 7397 09571 (B60) L14 L55 L61 L71 L72 B60 B60 B60
Case I base case
Base case active feeder loss in the system is 22562 kW The lowest bus voltage is
09072 pu and occurs at bus 64
Chapter 5 Distribution Network Reconfiguration amp DG Allocation for Feeder Loss
Reduction
Page | 106
10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
27
28
29
30
31 32 33 34
35
36
37
38 39 40 41 42 43 44 45
46 47 48 49
50
51
52
53 54 55 56 57 58 59 60 61 62 63 64
65 66
67 68
L1 L2 L3 L4 L5 L6 L7 L8 L9 L10 L11 L12 L13 L14 L15 L16 L17 L18 L19 L20 L21 L22 L23 L24 L25 L26
L27
L28
L29
L30
L31 L32 L33 L34
L35
L36
L37
L38 L39 L40 L41 L42 L43 L44 L45
L46
L47 L48 L49
L50
L51
L52
L53 L54 L55 L56 L57 L58 L59 L60 L61 L62 L63 L64
L65
L66
L67
L68
L69
L70
L71
L72L73
Case II with reconfiguration only (no DGs)
After DNR switches at L14 L55 L61 L71 and L72 are opened as shown in Fig 5-
10 The total feeder loss is reduced by 5619 and the minimum voltage is
increased to 09476 pu in comparison with the base case
Fig 5-10 69-bus system for feeder loss minimisation Case II
The comparisons of results among the proposed ACO with FWA [16] HSA [110]
and genetic algorithm (GA) [110] are presented in Table 5-5 It is observed that the
results obtained from the ACO are better than those from the FWA HSA and GA
as these algorithms are trapped into the local optimal solution
Table 5-5 Comparison of simulation results for 69-bus system in Case II
Method Feeder loss
(kW)
Loss reduction
()
Tie-switches location Minimum
voltage (pu)
The proposed ACO 9885 5619 L14 L55 L61 L71 L72 09476
FWA [16] 9886 5618 L14 L56 L61 L71 L72 09476
HSA [110] 10546 5326 L13 L18 L56 L61 L72 09475
GA [110] 10242 5461 L14 L53 L61 L71 L72 09462
Case III with reconfiguration only (with DGs)
In this case the three DGs are located at the end of the feeders ie Bus 26 45 64
The network configuration after DNR is illustrated in Fig 5-11 As shown in Table
Chapter 5 Distribution Network Reconfiguration amp DG Allocation for Feeder Loss
Reduction
Page | 107
10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
27
28
29
30
31 32 33 34
35
36
37
38 39 40 41 42 43 44 45
46 47 48 49
50
51
52
53 54 55 56 57 58 59 60 61 62 63 64
65 66
67 68
L1 L2 L3 L4 L5 L6 L7 L8 L9 L10 L11 L12 L13 L14 L15 L16 L17 L18 L19 L20 L21 L22 L23 L24 L25 L26
L27
L28
L29
L30
L31 L32 L33 L34
L35
L36
L37
L38 L39 L40 L41 L42 L43 L44 L45
L46
L47 L48 L49
L50
L51
L52
L53 L54 L55 L56 L57 L58 L59 L60 L61 L62 L63 L64
L65
L66
L67
L68
L69
L70
L71
L72L73
DG3
DG1
DG2
10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
27
28
29
30
31 32 33 34
35
36
37
38 39 40 41 42 43 44 45
46 47 48 49
50
51
52
53 54 55 56 57 58 59 60 61 62 63 64
65 66
67 68
L1 L2 L3 L4 L5 L6 L7 L8 L9 L10 L11 L12 L13 L14 L15 L16 L17 L18 L19 L20 L21 L22 L23 L24 L25 L26
L27
L28
L29
L30
L31 L32 L33 L34
L35
L36
L37
L38 L39 L40 L41 L42 L43 L44 L45
L46
L47 L48 L49
L50
L51
L52
L53 L54 L55 L56 L57 L58 L59 L60 L61 L62 L63 L64
L65
L66
L67
L68
L69
L70
L71
L72L73
DG3DG1
DG2
5-5 the network reconfiguration results in a reduction of 6118 in feeder losses as
compared with the original network without DGs and a reduction of 1140 in
comparison with the reconfigured system without DGs
Fig 5-11 69-bus system for feeder loss minimisation Case III
Case IV with reconfiguration and DG allocation
Fig 5-12 illustrates the optimal network configuration and DG locations In this case
the results show the final configuration with a feeder loss of 7397 kW with 6721
2517 and 1554 reduction in comparison with that in Case I Case II and Case
III respectively
Fig 5-12 69-bus system for feeder loss minimisation Case IV
Chapter 5 Distribution Network Reconfiguration amp DG Allocation for Feeder Loss
Reduction
Page | 108
0
50
100
150
200
250
100 400 700 1000
Fee
de
r lo
ss (
kW)
DG Capacity (kVA)
Before simultaneousreconfiguration and DG allocation
After simultaneous reconfigurationand DG allocation
In this case the impacts of DG capacity on assessing the DNR and DG allocation
problems in terms of feeder loss reduction are also studied The capacity of each DG
is set as 100 500 900 and 1300 kVA respectively The feeder loss curves for
different DG capacities are shown in Fig 5-13 After simultaneous reconfiguration
and DG allocation the feeder loss decreases from 7397 kW to 873 kW when the
DG capacity is increased from 100 kVA to 900 kVA However the loss bounces
back to 114 kW if the DG capacity continues to increase to 1300 kVA This means
that the capability of network reconfiguration and DG allocation on feeder loss
reduction is limited when the size of DGs is large But the proposed methodology
can still reduce the total feeder loss for all DG capacities by determining the most
suitable network topology and DG locations in comparison with the original
configuration
Fig 5-13 Comparison of feeder loss for different DG capacities before and after simultaneous
reconfiguration and DG allocation
Fig 5-14 shows the voltage profile of the 69-bus system It can be seen that the
voltage profiles at most buses in Case IV have been improved in comparison with
the other three cases Compared with Case III and Case IV the buses which inject
DGs show improvement in voltage profiles ie the voltage of Bus 60 is improved
from 09477 pu in Case III to 09571 pu in Case IV In Case IV although there are
three DGs connected as Bus 60 as the value of load connected at this bus is the
largest (1244 kW) this bus voltage is the lowest among all buses In conclusion the
systemrsquos voltage profiles are improved by optimal DNR and DG allocation
Chapter 5 Distribution Network Reconfiguration amp DG Allocation for Feeder Loss
Reduction
Page | 109
086
088
09
092
094
096
098
1
102
0 5 10 15 20 25 30 35 40 45 50 55 60 65
Vo
ltag
e (
pu
)
Bus No
Case I
Case II
Case III
Case IV
Fig 5-14 Comparison of voltage profiles in different cases of 69-node system
55 Summary
In this chapter the application of optimal planning using DNR and DG allocation for
the problem of distribution feeder loss minimisation has been implemented The
method based on ACO has been successfully applied to the 1266 kV 33-bus and 69-
bus systems to find the optimum system configuration and DG locations
There are four cases used to analyse the superiority and performance of the proposed
method The proposed ACO is capable of finding the optimal solutions in all cases
In Case IV the feeder losses are reduced by 4662 and 6721 for the 33-bus and
69-bus system respectively in comparison with the base case Therefore Case IV is
found to be more effective in minimising the total loss and improving voltage
profiles compared to the other cases The numerical results show that for best
performance the existing tie-switches are relocated and the DGs are optimally
placed in comparison with the original network In addition the impacts of DG
capacity on assessing the DNR and DG allocation problems in terms of feeder loss
reduction are also studied The inappropriate network configuration and DG location
might result in loss increment when the size of DG is increased The proposed
methodology has successfully reduced the total feeder loss for different capacities of
DG by determining the most suitable network topology and the DG locations
Chapter 5 Distribution Network Reconfiguration amp DG Allocation for Feeder Loss
Reduction
Page | 110
compared to the original configuration The minimum loss obtained by DNR and DG
allocation decreases as the capacities of DGs are increased However this decrease
stops when DGs can supply all the loads without the main supply After that the
minimum loss increases as the capacities of DGs are increased
Moreover the simulation results have been compared with other classical methods in
literature and the proposed ACO is more efficient and is more likely to obtain the
global optimum solution
Page | 111
CHAPTER 6
DISTRIBUTION NETWORK
RECONFIGURATION amp TRANSFORMER
ECONOMIC OPERATION FOR NETWORK
LOSS REDUCTION
61 Introduction
Rapid increases in electricity demand have forced electric power utilities throughout
the world into major reconstructing processes As a significant proportion of electric
energy is dissipated in the operation of a distribution network the reduction of loss
should be considered an important problem for the economic operation of the overall
system [82]
Load variations have been disregarded in most studies on distribution automation
(DA) problems ie average loads were used in their reconfiguration schemes In this
chapter distribution loads experience daily and seasonal variations The study
considers the daily load curves of different types of consumers (residential
commercial and industrial) and in addition the days are divided into eight types
spring weekdays spring weekends summer weekdays summer weekends autumn
Chapter 6 Distribution Network Reconfiguration amp Transformer Economic
Operation for Network Loss Reduction
Page | 112
weekdays autumn weekends winter weekdays and winter weekends The best
reconfiguration hours during each of these typical days are then selected
The objective function for finding the best configuration of the network when
considering feeder loss and transformer loss will be studied in this chapter Different
combinations of locations of tie-switches in the network and operation modes of all
transformers in the substations represent different network configurations An Ant
colony optimisation (ACO) algorithm is adopted on an 11 kV distribution network
developed from Bus 4 of the Roy Billinton Test System (RBTS) to determine the
optimal network configuration during each type of day Furthermore the effects of
DGs and EVs in solving distribution network reconfiguration (DNR) and
transformer economic operation (TEO) based on network loss reduction are also
investigated
This chapter is organised as follows the next section discusses the variation of loads
and the reconfiguration hours Section 63 presents the objective function and
constraints for DNR Section 64 describes the application of ACO algorithms to the
problem Numerical studies are presented and discussed in Section 65 and finally
Section 66 summarises the main conclusions
62 Time-varying Load Model
As distribution loads experience daily and seasonal variations the optimum network
configuration constantly changes [82] However it is not reasonable to reconfigure a
network frequently ie based on hourly schedule since each switch has a maximum
number of allowable switching operations during its lifetime and frequent switching
actions will increase its maintenance costs [82]
However infrequent actions cause the system to work well below its optimum state
In order to determine the best reconfiguration time during a day the daily load
profiles should be smoothed In other words the daily load curves are divided into a
number of periods As the maintenance cost of a switch increases with the increasing
number of switching actions the number of intervals is a trade-off between the
optimum reconfiguration and switch cost As there is a peak and a valley of network
Chapter 6 Distribution Network Reconfiguration amp Transformer Economic
Operation for Network Loss Reduction
Page | 113
Actual daily load curve
Smoothed daily load curve
load variations during a day it is appropriate to divide the 24 hours daily load curves
into two periods Increasing the number of intervals will not change the nature of the
problem but will increase its complexity
Fig 6-1 The reconfiguration hours for a typical day
As the difference between 1198751 and 1198752 is increased the effect of DNR on loss
reduction increases where 1198751 and 1198752 are the average active power of the loads
during the first and second time periods respectively As shown in Fig 6-1 hours
1199051and 1199052 are calculated to maximise |1198751 minus 1198752| It should also be noted that the above
load smoothing methodology is only used to determine the reconfiguration intervals
and the active power loss during each interval is calculated based on the actual daily
load curve [82]
63 Problem Formulation
In this study the 24 hours of a typical day is divided into two periods The first time
period is 0000 to 1199051 and 1199052 to 2400 and the second time period is between 1199051 and 1199052
The following objective function is calculated for all possible network configurations
during each time interval and the one that minimises the total power loss and
satisfies all constraints is selected The energy losses of the distribution network over
the first and second time interval are presented in (6-1) and (6-2) the objective
function (6-3) is to minimise f the sum of f1 and f2
P1
P2
1199051 1199052 Time (h)
Chapter 6 Distribution Network Reconfiguration amp Transformer Economic
Operation for Network Loss Reduction
Page | 114
1198911 = sum (119864119871119905 + 119879119871119905)1199051minus1119905=1 + sum (119864119871119905 + 119879119871119905) 1199051
24119905=1199052 isin 1 2 hellip 24 (6-1)
1198912 = sum (119864119871119905 + 119879119871119905)1199052minus1119905=1199051 1199052 isin 1 2 hellip 24 (6-2)
Min 119891 = 1198911 + 1198912 (6-3)
where 119864119871119905 is the feeder loss of the distribution network during hour t (kWh) 119879119871119905
represents the transformer loss during hour t (kWh) The detailed calculation of
transformer loss and feeder loss are presented in Section 27 and 28 respectively
The computed voltages currents and the power flow at all branches should be kept
in their permissible range and the network should be operated in radial The
configurations that violate any constraint are assigned with huge objective functions
and are disregarded
64 Applying ACO to DNR and TEO
In this chapter the objective of simultaneous reconfiguring network and changing
transformer operation modes is to deal with energy loss minimisation including
transformer loss and feeder loss To implement the optimisation problem the
developed ACO algorithm is adopted to find the optimum location of tie-switches
and transformer operation modes in the network When the location of tie-switches
and operation modes of transformers are changed a new network configuration will
be formed For each network configuration the objective function is evaluated by
using the approach presented in Section 63
The search space of the DNR and TEO problems is modelled as a directed graph as
shown in Fig 6-2 Each solution is represented by a string of integers which
indicates the transformer operation modes and the location of tie-switches The
number of the solutionrsquos elements is equal to the number of stages in this graph
which is the sum of the amount of main feeders (the number of transformer pairs 119873119904)
and the number of existing tie-switches 119873119905
Chapter 6 Distribution Network Reconfiguration amp Transformer Economic
Operation for Network Loss Reduction
Page | 115
Home
0 1
0 1
0 1
0 1
1 2 NPNP-1
1 2 NP-1 NP
1 2 NPNP-1
1 2 NP-1 NP
Food
Stage
1
2
Ns-1
Ns
Ns+1
Ns+2
Ns+Nt-1
Ns+Nt
Part 1
Number of
substations
Ns
Part 2 Number
of existing tie-
switches Nt
Number of candidate locations for the tie-switches NP
Fig 6-2 Search space of DNR and TEO
As shown in Fig 6-3 the number of transformer pairs is 3 and the number of
existing tie-switches is 4 Therefore the number of the solutionrsquos elements for this
system is 7 In addition the possible branches for tie-switch placement are 4
Chapter 6 Distribution Network Reconfiguration amp Transformer Economic
Operation for Network Loss Reduction
Page | 116
Tie-switch
Transformer
Fig 6-3 Sample network with three substations
For transformer operation mode selection in Part I the ACO algorithm is applied to
assign each bit of the front part of the solution vector to the status of substations and
hence the number of transformers in operation in each substation can be represented
as a binary vector
State 0 this substation has one transformer in operation
State 1 this substation has two transformers in operation
However for the relocation of existing tie-switches in Part II the states indicate the
location of switches Artificial ants will start their tours at home move along the
paths in the graph and end at the food source
The 24 hour load curve is divided into two time intervals for all load types in terms
of the principle presented in Section 62 Fig 6-4 demonstrates the computation
procedure for the transformer operation mode selection and tie-switches relocation
problem at each of the time interval The application of the ACO algorithm to the
TEO and DNR problem is similar to that in Section 532 For each time interval the
operation modes of the transformers are selected first and the locations of tie-
switches are then determined
Chapter 6 Distribution Network Reconfiguration amp Transformer Economic
Operation for Network Loss Reduction
Page | 117
Start
Set time interval T=1
Maximum iteration
reached
Output best
configuration and end
No
Yes
Divide the 24-h daily load curve into two
intervals using the technique in Section 62
Iteration N=1
Initialise the parameters for ACO
algorithm searching space
Dispatch ants based on the amount
of pheromone on edges
Relocate tie-switches and select the
number of transformers to be operated in
all substations by location lists
N=N+1
Calculate the objective function
for each ant at this time interval
Read system topology
and load data
The pheromones are updates
according to local and global rules
Record the best solution so far
and empty all location lists
T=T+1
Tgt2
Yes
t=t+1
No
Fig 6-4 Flowchart of the ACO applied to DNR and TEO for a specific type of day
Chapter 6 Distribution Network Reconfiguration amp Transformer Economic
Operation for Network Loss Reduction
Page | 118
LP11 LP12 LP13 LP14 LP15 LP16 LP17
LP8 LP9 LP10
LP1 LP2 LP3 LP4 LP5 LP6 LP7
LP32 LP33 LP34 LP35 LP36 LP37 LP38
LP29 LP30 LP31
LP26 LP27 LP28
LP18 LP19 LP20 LP21 LP22 LP23 LP24 LP25
19
20
21
22
23
24
26
25 27
28
29 30
71
13 15
14 16
17
18
69
1 3
2
5
4
7
6 8
10
9
68
11 12
56
57
58 60
59 61 62
65
64 66 67
50 52
51
54
53 55
44
45
46
47
48
49
70
31
32
33
34
36
35
39
37 38 40
41
42 43
63
F3
F2
F1
F7
F6
F5
F4
Normally Open Circuit BreakerNormally Closed Circuit Breaker
Subbus1
Subbus2
Subbus3
T1
T3
T5
Main
feeder
Main
feeder
Main
feeder
T2
T4
T6
65 Application Studies
In this study the proposed methodology is applied to an 11 kV distribution network
developed from Bus 4 of the RBTS a single-line diagram of the network is shown in
Fig 6-5 The network consists of 38 load points and 4 tie-switches the associated
data can be found in [114] The types and lengths of 11 kV feeders are listed in
Appendix A4 The network built in OpenDSS incorporates three 3311 kV double
transformer substations supplying the downstream loads
Fig 6-5 Distribution feeder connected to RBTS Bus 4
This typical urban distribution network supplies residential commercial and
industrial consumers The maximum value of active and reactive power and the
Chapter 6 Distribution Network Reconfiguration amp Transformer Economic
Operation for Network Loss Reduction
Page | 119
customer type of each node are modified from the original values and the new values
are listed in Table 6-1
Table 6-1 Revised customer data (peak load)
Number
of load
points
Load points Customer type P
(kW)
Q
(kVAr)
Number of
customers
4 1-2 9-10 residential 8869 8426 220
6 3-5 13-15 residential 8137 7731 200
12 6-7 16-17 23-25 28
30-31 37-38
commercial 6714 6378 10
6 8 11 18 26 32-33 industrial 2445 23228 1
10 12 19-22 27 29 34-
36
industrial 1630 15485 1
The days of the year are divided into eight categories spring weekdays spring
weekends summer weekdays summer weekends autumn weekdays autumn
weekends winter weekdays and winter weekends Typical loads profiles for
different consumer types are shown in Fig 6-6-6-8 which are multiplied by the
values of Table 6-1 to obtain the real demand of each node [82] In order to find the
reconfiguration hours for each day type the aggregated load profiles of the main
feeder shown in Fig 6-9 are used
Fig 6-6 Daily load profile of residential consumers
Chapter 6 Distribution Network Reconfiguration amp Transformer Economic
Operation for Network Loss Reduction
Page | 120
Fig 6-7 Daily load profile of commercial consumers
Fig 6-8 Daily load profile of industrial consumers
Fig 6-9 Daily load profile (MW) of the main feeder
Chapter 6 Distribution Network Reconfiguration amp Transformer Economic
Operation for Network Loss Reduction
Page | 121
In this case eight types of day and two time intervals for each of them are
considered As a result the optimisation problem has to be solved 16 times to obtain
a yearly reconfiguration scheme The distribution of load types for a whole year is
shown in Table 6-2
Table 6-2 The distribution of load types for a whole year
Load Types Number of days Total days
Spring
(Mar Apr May)
Weekdays 66 92
Weekends 26
Summer
(Jun Jul Aug)
Weekdays 66 92
Weekends 26
Autumn
(Sep Oct Nov)
Weekdays 65 91
Weekends 26
Winter
(Dec Jan Feb)
Weekdays 64 90
Weekends 26
Year 365 Days
For the purpose of better illustration and comparison three test cases are considered
to analyse the superiority and performance of the proposed method
Test Case 1 The system is optimally reconfigured and has no DGs and EVs
Test Case 2 The system is optimally reconfigured after DGs are placed at certain
buses
Test Case 3 The system is optimally reconfigured after integration of EVs
The proposed ACO algorithm is coded in the MATLAB to obtain the location of tie-
switches and operation modes of transformers for the optimum configuration The
settings of the ACO parameters that provided the optimum solution for these three
cases are presented in Appendix C2 The selection of parameters is a balance
between the convergence rate and the global search ability of the algorithm
Chapter 6 Distribution Network Reconfiguration amp Transformer Economic
Operation for Network Loss Reduction
Page | 122
651 Test Case 1
In this test the tie-switches are relocated and the operation modes of transformers in
all substations are changed to obtain the best network configuration with minimum
network loss
Table 6-3 Results of DNR and TEO with different load types in Test Case 1
As shown in Fig 6-5 the tie-switches are located in L68-71 and each substation has
two transformers operating in parallel for the base network configuration The test
results with different load conditions are presented in Table 6-3 Reconfiguration of
the network and changes in the operation modes of transformers in all substations
using the proposed algorithm result in a reduction of loss for all load conditions As
a result the annual energy loss is reduced from 4337150 kWh to 4117681 kWh
which amounts to a 506 reduction Both transformer loss and feeder loss are
reduced through this optimal planning using DNR and TEO It can be noted that on
winter weekdays the loading of the main feeders is very high from 800 to 2100
Spring
weekday
Spring
weekend
Summer
weekday
Summer
weekend
Autumn
weekday
Autumn
weekend
Winter
weekday
Winter
weekend
Before
Reconfiguration
Whole Day Open branches L68L69
L70L71
L68L69
L70L71
L68L69
L70L71
L68L69
L70L71
L68L69
L70L71
L68L69
L70L71
L68L69
L70L71
L68L69
L70L71
Number of operated
transformers
1st substation 2 2 2 2 2 2 2 2
2nd substation 2 2 2 2 2 2 2 2
3rd substation 2 2 2 2 2 2 2 2
Loss
(kWh)
Cable 9233 3498 8050 3151 9660 3665 11009 4080
Transformer 4301 3410 4109 3350 4372 3437 4597 3507
Total 13534 6908 12159 6501 14032 7102 15606 7587
After
Reconfiguration
1st interval Time (h) 0-7
23-24
0-6 0-7
23
0-7 0-7
22-23
0-6
0-7
22-23
0-6
Open branches L48L68
L69L71
L68L69
L70L71
L17L68
L70L71
L17L68
L70L71
L17L68
L70L71
L68L69
L70L71
L17L68
L70L71
L68L69
L70L71
Number of operated
transformers
1st substation 1 1 1 1 1 1 1 1
2nd substation 1 1 1 1 1 1 1 1
3rd substation 1 1 1 1 1 1 1 1
2nd interval Time (h) 8-22 7-23 8-22 8-23 8-21 7-23 8-21 7-23
Open branches L17L41
L65L70
L68L69
L70L71
L41L48
L65L69
L68L69
L70L71
L17L41
L65L70
L68L69
L70L71
L17L41
L65L70
L68L69
L70L71
Number of operated
transformers
1st substation 2 2 2 2 2 2 2 2
2nd substation 2 1 2 1 2 1 2 1
3rd substation 2 1 2 1 2 1 2 1
Loss
(kWh)
Cable 9043 3516 7851 3169 9519 3685 10845 4103
Transformer 3955 2616 3759 2517 4036 2656 4264 2755
Total 12998 6132 11610 5686 13479 6341 15109 6858
Chapter 6 Distribution Network Reconfiguration amp Transformer Economic
Operation for Network Loss Reduction
Page | 123
0
05
1
15
2
25
3
35
4
45
05 1 15 2 25 3
Before reconfiguration
After reconfiguration
Thus transformers in all substations are operated in parallel However during spring
weekends from 000 to 700 as the loadings supplied by all feeders are lower than
the critical transformer load factor (TCLF) and hence transformers in all substations
are operated in single In addition the loadings supplied by Feeder 4 are much larger
than that of Feeder 3 in summer weekdays between 800 to 2200 Thus the tie-
switch is moved from L71 to L41 and LP24amp25 are moved from Feeder 4 to Feeder
3 This ensures balancing of the loads between the two feeders
652 Test Case 2
In this test the presence of three DG units is taken into consideration The effect of
DGs on assessing the DNR and TEO problems in terms of loss minimisation is
studied The introduction of DGs converts a mono-source distribution network to a
multi-source one [66] The three DGs are located at the end of the feeders ie Bus
17 41 and 65 All the DGs are synchronous generators and considered as PQ models
The capacity of DG is assumed to be 05 1 15 2 25 and 3 MVA respectively
The results are shown in Fig 6-10 and show that the proposed methodology has
successfully reduced the total energy loss for different capacities of DG by
determining the most suitable network topology
Fig 6-10 Annual energy loss with different DG capacities
To
tal
loss
(G
Wh
)
DG Capacity (MW)
Chapter 6 Distribution Network Reconfiguration amp Transformer Economic
Operation for Network Loss Reduction
Page | 124
653 Test Case 3
The objective of this section is to illustrate the behaviour of the proposed
optimisation process when EVs are integrated into the existing distribution network
The impacts of EV penetration levels and charging strategies are studied This
section utilises the optimal planning using DNR and TEO as a technique to decrease
network loss whilst respecting the operation constraints It is assumed that the
battery starts charging once the EV is connected to the charger at home
The charging duration can be calculated according to the following formula [89]
119905119888 =119862119864119881times(1minus119878119874119862)times119863119874119863
120578times119875119862 (6-4)
where 119862119864119881 is the battery capacity In this section EVs are divided into four types
with different market shares and batteries as in Table 6-4 [115] 119863119874119863 and 120578 are
depth of discharge and charger efficiency (assumed to be 80 and 90 separately)
Two types of chargers with different charging rates (119875119862) are commonly used for
consumer EVs at home charging points this study assumes that 80 of EVs are
charged at 3kW (13A) and 20 at 7kW (30A) [92] SOC is state-of-charge and is
defined as the ratio of available energy to maximum battery capacity [89] It is
determined by the distance covered by the EV in terms of number of miles during
the day
Table 6-4 Characteristics of EV
Types 119862119864119881 (kWh) Maximum driving
capability (mile)
Market share ()
Micro car 12 50 20
Economy car 14 53 30
Mid-size car 18 56 30
Light truck SUV 23 60 20
According to [116] the average number of miles covered by a vehicle was reported
to be 2164 milesday in 2014 Then the SOC for an EV is calculated based on
number of miles (m) and the maximum driving capability (MDC) as follows
Chapter 6 Distribution Network Reconfiguration amp Transformer Economic
Operation for Network Loss Reduction
Page | 125
4
42
44
46
48
5
30 60 90
Before reconfiguration
After reconfiguration
119878119874119862 = 0 119898 gt 119872119863119862
119872119863119862minus119898
119872119863119862 119898 le 119872119863119862 (6-5)
As mentioned before the EVs are distributed over all the residential load points The
number of customers of residential loads is given in Table 6-1 It is reported that
each customer has 15 vehicles [92] The problem is solved for three different
penetration levels of EVs in the test network 30 60 and 90 respectively In
addition two charging strategies are introduced (1) uncoordinated charging and (2)
coordinated charging The thermal problems of cables which caused by high
penetration levels of EVs are ignored in this study
1) Uncoordinated Charging Strategy
In this part all EVs are plugged in and immediately start charging when they arrive
home In most cases the EV plug-in time is modelled by normal distribution which
increases uncertainty However in order to simplify the discussion the charging start
time is assumed to be 1800 when most people are back home from work The total
losses in the network for the different penetration levels of EVs are compared in Fig
6-11 It can be seen that as the penetration of EVs is increased the total loss also
increases But the total loss for all penetration levels decreases by implementing the
optimal planning strategy in comparison with the original network
Fig 6-11 Annual energy loss in uncoordinated charging strategy
To
tal
loss
(G
Wh
)
Penetration level ()
Chapter 6 Distribution Network Reconfiguration amp Transformer Economic
Operation for Network Loss Reduction
Page | 126
4
42
44
46
48
5
30 60 90
Before reconfiguration
After reconfiguration
2) Coordinated Charging Strategy
In this case the DNOs tend to charge the EVs during off-peak hours to avoid a clash
with the evening peak hours As a result the charging start time is delayed to 0100
when most people are sleeping The total network loss for different EV penetrations
is compared in Fig 6-12 The results show that the postponement of charging time
and optimal planning strategy has been successful in reducing the total energy loss in
comparison with the uncoordinated charging method
Fig 6-12 Annual energy loss in coordinated charging strategy
66 Summary
This study has presented a new optimal planning strategy using DNR and TEO for
distribution network loss minimisation including transformer loss and feeder loss In
this study the distribution loads experience daily and seasonal variations The day is
divided into two periods The proposed ACO algorithm has been successfully
applied to the modified Bus 4 of the RBTS to find the optimum network
configuration and economic operation mode of transformers in all substations during
each time interval Using the results obtained for reconfiguration the existing tie-
switches are relocated and the transformer operation modes are changed
Furthermore the simulation results obtained with numerical studies further
demonstrate the capability of applying the ACO algorithm to distribution network
planning including networks with DGs and EVs The proposed methodology has
successfully reduced the total network loss for different capacities of DG and
To
tal
loss
(G
Wh
)
Penetration level ()
Chapter 6 Distribution Network Reconfiguration amp Transformer Economic
Operation for Network Loss Reduction
Page | 127
different penetration levels of EVs by determining the most suitable network
topology compared to the original configuration The benefits associated with the
increasing capacity of DGs and increasing penetration levels of EVs are also
presented Comparative results show that coordinated charging of EVs results in less
energy loss compared to uncoordinated charging plan with the same EV penetration
level This is due to the postponement of charging time which avoids a clash with
the peak power demand times
The proposed ACO algorithm is suitable for planning a future network based on the
load estimation results Hence there is no limitation on the calculation time An
additional interesting point about DNR and TEO is that although the opening and
closing of switches and transformers result in the life reduction of plants the
additional costs for utilities is insignificant in comparison with the benefits they
bring All the results have proved that a distribution network can be reconfigured and
the operation modes of transformers can be changed to reduce network power loss
which can increase the profits of the distribution utilities
Page | 128
CHAPTER 7
OPTIMAL PLACEMENT OF
SECTIONALISING SWITCHES FOR
RELIABILITY IMPROVEMENT
71 Introduction
Failures in the distribution network cause the majority of service interruptions [78]
And reliability improvement becomes a motivation for distribution utilities to launch
research and demonstration projects [64] An effective method to reduce customer
minutes lost is the greater and more effective use of automated and remote controlled
sectionalising switches and feeder breaker automation This approach will reduce
customer restoration time and minimise the region of a network affected by a short-
circuit fault The effectiveness depends on the number location and type of
sectionalising switches and feeder breakers
Reliability improvement by reduction of expected customer damaged cost (ECOST)
and system interruption duration index (SAIDI) as well as the minimisation of
switch costs are considered in formulating the objective function used in this study
When there are multiple objectives to be considered a compromise solution has to
be made to obtain the best solution ECOST and switch costs can be converted into a
single objective function by aggregating these objectives in a weighted function
Chapter 7 Optimal Placement of Sectionalising Switches for Reliability
Improvement
Page | 129
However as SAIDI and switch costs have different dimensions and units a single
fuzzy satisfaction objective function is used to transform the two conflicting
objectives into fuzzy memberships and then finally to combine them into a single
objective function Also a fuzzy membership function based on the max-min
principle is presented for optimising ECOST SAIDI and switch costs
simultaneously These are achieved by the optimal installation of new switches and
the relocation of existing switches Therefore identifying the number and location of
switches becomes an optimisation problem The ant colony optimisation (ACO) is
adopted which has the ability to find near optimal solutions close to the global
minimum in a finite number of steps This algorithm is proposed for the assessing
the sectionalising switch placement (SSP) problem based on reliability improvement
and switch costs minimisation using a multi-objective function with fuzzy variables
The impact of benefit-to-cost analysis is then investigated to justify investment
expenses Furthermore the importance of the customer damage function (CDF)
variation in determining the SSP is investigated through sensitivity analysis And the
ACO parameter sensitivity analysis is also provided in this study
The mathematical formulation of the objective function is presented in Section 72
and in Section 73 the applied ACO algorithm used to address the problems of SSP
is discussed Section 74 describes the benefit-cost analysis and the numerical case
studies are presented and discussed in Section 75 The main conclusions of the study
are summarised in Section 76
72 Problem Formulation
The primary objective of this study is to resolve the three conflicting objectives
reduction of unserved energy cost decrease in the average time a customer is
interrupted and minimisation of switch costs Three formulations of objective
functions are presented and the solution is a trade-off between each objective
721 Weighted Aggregation
As ECOST and switch costs have the same units and dimensions they are
transformed into a single objective function by aggregating all the objectives in a
weighted function
Chapter 7 Optimal Placement of Sectionalising Switches for Reliability
Improvement
Page | 130
119872119894119899 119869 = micro1 ∙ 119864119862119874119878119879 + micro2 ∙ 119878119862 (7-1)
where ECOST is the system expected outage cost to customers ($) and SC is the cost
of sectionalising switches ($) micro1and micro2 are the weighting factors given to the
reliability index and the cost of switches
722 Single Fuzzy Satisfaction Objective Function with Two
Parameters
SAIDI and switch costs are associated with a membership function in a fuzzy
domain due to different dimensions The satisfaction level of each objective is
represented by the membership function [66] The higher the membership value is
the better the solution is The two objectives are combined into a fuzzy environment
and a final objective function is formulated as follows
119872119886119909 119870 = 1205961 ∙ 120572119878119860 + 1205962 ∙ 120572119878119862 (7-2)
where 120572119878119860 is the membership function value to distribution reliability improvement
by SAIDI reduction 120572119878119862 is the value of membership function for a decrease in the
switch costs 1205961and 1205962 are the constant weighting factors for each of the parameters
The optimisation process can be changed for different purposes by varying the
values of weighting factors which should satisfy the condition 1205961 + 1205962 = 1 A
higher weighting factor indicates that this parameter is more important [66] In the
fuzzy domain each objective has a membership value varying from zero to unity
[66] The proposed membership function for each objective is described below
Membership function for SAIDI reduction
The basic purpose of this membership function is to improve reliability or obtain the
minimum SAIDI Therefore the placement of sectionalising switches with a lower
SAIDI value obtains a higher membership value The membership function for
reliability improvement is formulated in (7-3) and presented in Fig 7-1 (a) As
SAIDI becomes greater than 119878119860119868119863119868119898119894119899 the degree of satisfaction is decreased This
reduction is continued until SAIDI reaches 119878119860119868119863119868119900119903119894
Chapter 7 Optimal Placement of Sectionalising Switches for Reliability
Improvement
Page | 131
0
1
0
1
120572119878119860 =
1 119878119860119868119863119868 le 119878119860119868119863119868119898119894119899119878119860119868119863119868119900119903119894minus119878119860119868119863119868
119878119860119868119863119868119900119903119894minus119878119860119868119863119868119898119894119899119878119860119868119863119868119898119894119899 lt 119878119860119868119863119868 lt 119878119860119868119863119868119900119903119894
0 119878119860119868119863119868 ge 119878119860119868119863119868119900119903119894
(7-3)
where 119878119860119868119863119868119900119903119894 is the SAIDI of the original network 119878119860119868119863119868119898119894119899 is the minimum
value of SAIDI which is obtained by placing sectionalising switches in all candidate
locations As it is not appropriate for decision makers to obtain a combination of
sectionalising switches which reduces reliability after switch placement the
minimum value of 120572119878119860 is selected as 0 if SAIDI is greater than or equal to 119878119860119868119863119868119900119903119894
(a) SAIDI reduction (b) SC reduction
Fig 7-1 Membership function for SAIDI and switch cost reduction
Membership function for switch cost reduction
The membership function for switch costs reduction is shown in Fig 7-1(b) The
mathematical equation is presented below
120572119878119862 =
1 119878119862 le 119878119862119900119903119894119878119862119898119886119909minus119878119862
119878119862119898119886119909minus119878119862119900119903119894119878119862119900119903119894 lt 119878119862 lt 119878119862119898119886119909
0 119878119862 ge 119878119862119898119886119909
(7-4)
where 119878119862119900119903119894 and 119878119862119898119886119909 are the original and maximum value of switch costs
respectively The maximum switch costs are obtained by installing sectionalising
switches in all candidate sites
723 Single Fuzzy Satisfaction Objective Function with Three
Parameters
When there are more than two objectives with different dimensions and units to be
satisfied simultaneously a single fuzzy satisfaction objective function based on the
120572119878119860
119878119860119868119863119868119898119894119899 119878119860119868119863119868119900119903119894 119878119860119868119863119868
120572119878119862
119878119862119900119903119894 119878119862119898119886119909 119878119862
Chapter 7 Optimal Placement of Sectionalising Switches for Reliability
Improvement
Page | 132
0
1
max-min principle is considered The three conflicting objectives to be optimised are
ECOST SAIDI and switch costs The membership functions for SAIDI and switch
costs are presented in the previous section The function for ECOST is shown in Fig
7-2 and expressed as
120572119864119862 =
1 119864119862119874119878119879 le 119864119862119874119878119879119898119894119899119864119862119874119878119879119900119903119894minus119864119862119874119878119879
119864119862119874119878119879119900119903119894minus119864119862119874119878119879119898119894119899119864119862119874119878119879119898119894119899 lt 119864119862119874119878119879 lt 119864119862119874119878119879119900119903119894
0 119864119862119874119878119879 ge 119864119862119874119878119879119900119903119894
(7-5)
where 119864119862119874119878119879119900119903119894 and 119864119862119874119878119879119898119894119899 are the original and minimum value of ECOST
respectively The minimum ECOST is obtained by installing sectionalising switches
in all candidate locations
Fig 7-2 Membership function for ECOST reduction
The degree of overall satisfaction for these objective functions is the minimum value
of all the membership functions [85] The fuzzy decision for a final compromised
solution is the maximum degree of overall satisfaction and is formulated in (7-6)
Max 119871 = min (120572119878119860 120572119878119862 120572119864119862) (7-6)
724 Evaluation of ECOST
ECOST is an index that combines reliability with economics The best way to
present customer interruption costs is in the form of CDF A CDF provides the
interruption cost versus interruption duration for a various class of customers and
can be aggregated to produce a composite CDF at any particular load point [67] [69]
Generally ECOST is used to represent the customer outage costs since it not only
considers the effects of the system configuration interruption durations load
variations and equipment failure probability but also accounts for the various
customer types and their damage functions [52]
120572119864119862
119864119862119874119878119879119898119894119899 119864119862119874119878119879119900119903119894 119864119862119874119878119879
Chapter 7 Optimal Placement of Sectionalising Switches for Reliability
Improvement
Page | 133
The calculation of ECOST of the total system over T years is based on failure-mode-
and-effect analysis (FMEA) and can be quantified as follows
1 ( 1)
1 1 1 1 1 1
( ) ( ) ( ) ( ) (1 ) (1 )b b b b bN CT NR CT NST
t t
b b k R k s
t b k j k j
ECOST L P k j C d P k j C d IR DR
(7-7)
where T is time period (year) 119873119887 is the total number of branches 120582119887and 119871119887 are the
average failure rate (failurekm-year) and length (km) of branch b 119862119879119887 119873119877119887 and
119873119878119887 are the total number of customer types permanent damaged and temporary
damaged load points when the fault is at branch b P(k j) is the average load of the
kth-type customers at the jth load point (kW) 119862119896(119889) is the CDF for kth-type
customer lasting d hours ($kW) 119889119877 and 119889119878 are the average repair time and the
switch time after failure IR and DR are the annual load increase rate and discount
rate
725 Evaluation of SAIDI
The SAIDI which represents the average outage duration time of each customer
over T years can be expressed as
119878119860119868119863119868 = sum sum 120582119887∙119871119887[sum 119889119877
119873119862119877(119887)119899=1 +sum 119889119878
119873119862119878(119887)119899=1 ]
119873119887119887=1
119873119862119905119900119905119886119897119879
119905=1 (7-8)
where 119873119862119877(119887) and 119873119862119878(119887) are the number of permanent damaged and temporary
damaged customers when the fault is at branch b 119873119862119905119900119905119886119897 is the total number of
served customers SAIDI is measured in hours
726 Evaluation of Switch Costs
In this study reliability is improved by the installation of new sectionalising
switches and relocation of existing switches Thus the total cost of switches can be
determined as following
119878119862 = 119862119868119878 ∙ 119873119899119890119908 + 119862119877119878 ∙ 119873119903119890119897 + sum 119872119862119879119905=1 ∙ (119873119899119890119908 + 119873119890119909119894119904) ∙ (1 + 119863119877)minus(119905minus1) (7-9)
where CIS is the investment and installation cost of a new sectionalising switch ($)
119873119899119890119908 119873119903119890119897 and 119873119890119909119894119904 are the number of newly installed relocated and existing
sectionalising switches respectively CRS is the relocation cost of an existing
Chapter 7 Optimal Placement of Sectionalising Switches for Reliability
Improvement
Page | 134
Home
0
1
0
1
0
1
0
1
Food
Number of candidate locations for sectionalising switches
sectionalising switch ($) and MC is the maintenance and operation cost of a
sectionalising switch ($)
73 Applying ACO to Sectionalising Switch Placement
Problem
This study uses ACO algorithm for distribution automation in terms of the
installation of new sectionalising switches and relocation of existing switches When
the locations of sectionalising switches are changed a new network configuration
will be formed The search method is used for finding the optimal value of objective
functions as presented in Section 721-723
The search space of the automation problem in terms of SSP is modelled as a
directed graph as shown in Fig 7-3 The number of stages is the candidate locations
for all the sectionalising switches 119873119878 For this problem the switch status can be
represented as a binary vector in each stage State 0 ldquono sectionalising switch in this
locationrdquo State 1 is ldquoa sectionalising switch in this locationrdquo The artificial ant
searches for the values of the bits and produces a solution to the problem after it
completes a tour between the home and food source which is similar to the process
described in Section 532
Fig 7-3 Search space of sectionalising switch placement
Chapter 7 Optimal Placement of Sectionalising Switches for Reliability
Improvement
Page | 135
74 Benefit-to-cost Analysis
The benefit-to-cost analysis is a financial term that describes the expected balance of
benefits made from the investment and costs incurred during the production process
It helps predict if an investmentdecision is feasible and whether its benefits
outweigh the costs during a predefined time interval [82]
In this study the benefit-to-cost ratio (BCR) offers a comparison between ECOST
and SC The benefit to the distribution network operator (DNO) is the reduction of
ECOST which is equal to
119887119890119899119890119891119894119905 = sum119864119862119874119878119879119887119886119904119890
119905 minus119864119862119874119878119879119900119901119905119905
(1+119863119877)119905119879119905=1 (7-10)
where 119864119862119874119878119879119887119886119904119890119905 and 119864119862119874119878119879119900119901119905
119905 are the value of ECOST of year t before and after
the placement of switches ($)DR is the annual discount rate
The cost for the DNO is the total switching cost including investment maintenance
and operation cost as presented in (7-9) and BCR is defined as
119861119862119877 =119887119890119899119890119891119894119905
119878119862 (7-11)
A higher value for BCR indicates that the benefits relative to the costs are greater
The investment return time refers to the time when BCR starts to exceed 10 If the
investment return time is less than the lifetime of a switch adding a switch will bring
benefits to the investors
Chapter 7 Optimal Placement of Sectionalising Switches for Reliability
Improvement
Page | 136
LP11 LP12 LP13 LP14 LP15 LP16 LP17
LP8 LP9 LP10
LP1 LP2 LP3 LP4 LP5 LP6 LP7
LP32 LP33 LP34 LP35 LP36 LP37 LP38
LP29 LP30 LP31
LP26 LP27 LP28
LP18 LP19 LP20 LP21 LP22 LP23 LP24 LP25
9 10 11 12 13 33
6 7 8 31
1 2 3 4 5 30
25 26 27 29
22 23 24
19 20 21
32
14 15 16 17 18
28
F3
F2
F1
F7
F6
F5
F4
Normally Open Circuit BreakerNormally Closed Circuit Breaker
Subbus1
Subbus2
Subbus3
T1
T3
T5
Main
feeder
Main
feeder
Main
feeder
T2
T4
T6
75 Application Studies
In this study the proposed methodology is applied to an 11 kV distribution network
developed from Bus 4 of the Roy Billinton Test System (RBTS) The single-line
diagram of the network with 6 existing sectionalising switches is shown in Fig 7-4
Fig 7-4 Distribution feeder connected to RBTS Bus 4 with 6 sectionalising switches
In this study there are 51 locations considered as candidates for switch placement
[114] All the values of the required data ie feeder type and length as well as
component failure rate are available in [114] and summarised in Appendix A4 The
failure rate of the feeders is proportional to their physical length and all other
Chapter 7 Optimal Placement of Sectionalising Switches for Reliability
Improvement
Page | 137
components ie transformers buses and breakers are assumed to be completely
reliable This typical urban distribution network supplies residential commercial and
industrial consumers The average value of active power and the customer type of
each node were also found in [114] and listed in Table 7-1 The power factors of all
the loads are set to 10
Table 7-1 Customer data (Average load)
Number
of load
points
Load points Customer type P
(kW)
Number of
customers
15 1-4 11-13 18-21 32-35 residential 545 220
7 5 14 15 22 23 36 37 residential 500 200
7 8 10 26-30 industrial 1000 1
2 9 31 industrial 1500 1
7 6 7 16 17 24 25 38 commercial 415 10
The relocation cost of a sectionalising switch is US $ 500 The investment and
installation cost of a sectionalising switch is US $ 4700 [64] The annual
maintenance and operation cost is considered to be 2 of the investment cost [64]
All the sectionalising switches and circuit breakers are remotely controlled The
costs of the feeder terminal unit which is used for data acquisition of the switch
status and communication equipment have also been added to the automated
sectionalising switches The overall switching time of sectionalising switch and
circuit breakers for temporary damage load points in other words the time between
the occurrence of a fault and the restoration of energy to unaffected areas is set to 10
minutes [64] And the average repair time of the permanent faulty section is assumed
to be 5 hours The lifetime of a switch depends on various factors such as the
maximum number of allowable switching operations the number of annual
switching operations of the switch etc Based on these factors the life period of the
switches is calculated to be 15 years The load growth rate and the annual interest
rate are set to 3 and 8 respectively The CDF data are extracted from [64] and
summarised in Table 7-2
Chapter 7 Optimal Placement of Sectionalising Switches for Reliability
Improvement
Page | 138
Table 7-2 Sector interruption cost estimation ($kW)
User Sector Interruption Duration
10 min 1 hour 2 hour 4 hour 5 hour 10 hour
Residential 006 11 16 26 316 5
Industrial 288 806 95 124 1387 276
Commercial 205 96 125 185 2151 6306
The proposed ACO algorithm was coded in the MATLAB to obtain the location of
the sectionalising switches In this study three cases with different objective
functions are considered to analyse the superiority and performance of the proposed
method
Test Case 1 Minimisation of ECOST and switch costs
Test Case 2 Minimisation of SAIDI and switch costs
Test Case 3 Minimisation of ECOST SAIDI and switch costs
The final combinations of the ACO control parameters that provide the best results
for all the above tests are given in Appendix C3
751 Test Case 1
In this test the minimisation of ECOST and switch costs are considered in the
formulation of a single objective function this involves aggregating the objective
functions as presented in Section 721 For simplicity both weighting factors micro1
and micro2 are set to 1 ie these two objectives are assumed to be equally important
Three cases are studied as follows
Case 11 Optimal relocation of existing sectionalising switches
Case 12 Optimal installation of new sectionalising switches
Case 13 Optimal installation of new sectionalising switches and relocation of
existing sectionalising switches
Chapter 7 Optimal Placement of Sectionalising Switches for Reliability
Improvement
Page | 139
LP11 LP12 LP13 LP14 LP15 LP16 LP17
LP8 LP9 LP10
LP1 LP2 LP3 LP4 LP5 LP6 LP7
LP32 LP33 LP34 LP35 LP36 LP37 LP38
LP29 LP30 LP31
LP26 LP27 LP28
LP18 LP19 LP20 LP21 LP22 LP23 LP24 LP25
9 10 11 12 13 33
6 7 8 31
1 2 3 4 5 30
25 26 27 29
22 23 24
19 20 21
32
14 15 16 17 18
28
F3
F2
F1
F7
F6
F5
F4
Normally Open Circuit BreakerNormally Closed Circuit Breaker
Subbus1
Subbus2
Subbus3
T1
T3
T5
Main
feeder
Main
feeder
Main
feeder
T2
T4
T6
Case 11 Optimal relocation of existing sectionalising switches
The objective of this case is to investigate the optimum sectionalising switch
relocation problem The optimal locations of sectionalising devices are shown in Fig
7-5 Before relocation the total cost including ECOST operation and maintenance
cost of existing switches over 15 years is US $ 477090 After relocation the total
cost including the addition of relocation cost obtained by the ACO approach is US
$ 343620 which amounts to a reduction of 2798
Fig 7-5 Optimal relocation of sectionalising switches in Test Case 11
Chapter 7 Optimal Placement of Sectionalising Switches for Reliability
Improvement
Page | 140
In comparison with the original configuration 4 switches change their locations The
optimal locations of sectionalising switches and the number and types of loads
adjacent to each switch are presented in Table 7-3 The results indicate that each
feeder attempts to have at least one switch As there are 6 switches and 7 feeders
and the total load level of Feeder 5 is 3000 kW which is the lowest value for all the
feeders no switch is placed on Feeder 5 It should also be noted that the load
density and customer types play an important role in determining the locations of
sectionalising switches For instance the adjacent load of Switch 1 is LP6 and LP7
which has the highest CDF value (commercial load) and relatively high load levels
In addition Switch 2 is placed on 7D whose adjacent load is LP9 and this has the
largest load density
Table 7-3 Results of sectionalising switches relocation in Test Case 11
Switch
No
Feeder Location Total Feeder
Load (kW)
Adjacent Load Adjacent Load Levels (kW) and
Type
1 1 5D 3510 LP6 LP7 415 (commercial) 415 (commercial)
2 2 7D 3500 LP9 1500 (industrial)
3 3 13D 3465 LP16 LP17 415 (commercial) 415 (commercial)
4 4 18D 4010 LP24 LP25 415 (commercial) 415 (commercial)
5 6 23D 3500 LP30 1000 (industrial)
6 7 28D 3595 LP36 500 (commercial)
( Each section has two candidate locations for sectionalising switch placement U means upstream side of the section and D
means downstream side of the section)
Case 12 Optimal installation of new sectionalising switches
In this case the effect of installing new sectionalising switches without relocating
the existing switches is studied As shown in Fig 7-6 there are 11 new
sectionalising switches installed
The detailed results of ECOST capital and installation as well as the operation and
maintenance cost of sectionalising switches over 15 years are shown in Table 7-4
After the installation of sectionalising switches the total system cost is decreased
from US $ 477090 to US $ 286980 ie a reduction of 3984
Chapter 7 Optimal Placement of Sectionalising Switches for Reliability
Improvement
Page | 141
LP11 LP12 LP13 LP14 LP15 LP16 LP17
LP8 LP9 LP10
LP1 LP2 LP3 LP4 LP5 LP6 LP7
LP32 LP33 LP34 LP35 LP36 LP37 LP38
LP29 LP30 LP31
LP26 LP27 LP28
LP18 LP19 LP20 LP21 LP22 LP23 LP24 LP25
9 10 11 12 13 33
6 7 8 31
1 2 3 4 5 30
25 26 27 29
22 23 24
19 20 21
32
14 15 16 17 18
28
F3
F2
F1
F7
F6
F5
F4
Normally Open Circuit BreakerNormally Closed Circuit Breaker
Subbus1
Subbus2
Subbus3
T1
T3
T5
Main
feeder
Main
feeder
Main
feeder
T2
T4
T6
Fig 7-6 Optimal installation of sectionalising switches in Test Case 12
Table 7-4 Results of sectionalising switches installation in Test Case 12
ECOST
($)
Number of
installed
switches
Capital and
installation cost
($)
Maintenance
and operation
cost ($)
Total system
cost ($)
Before switches
installation
472260 0 0 4830 477090
After switches
installation
221610 11 51700 13670 286980
Chapter 7 Optimal Placement of Sectionalising Switches for Reliability
Improvement
Page | 142
LP11 LP12 LP13 LP14 LP15 LP16 LP17
LP8 LP9 LP10
LP1 LP2 LP3 LP4 LP5 LP6 LP7
LP32 LP33 LP34 LP35 LP36 LP37 LP38
LP29 LP30 LP31
LP26 LP27 LP28
LP18 LP19 LP20 LP21 LP22 LP23 LP24 LP25
9 10 11 12 13 33
6 7 8 31
1 2 3 4 5 30
25 26 27 29
22 23 24
19 20 21
32
14 15 16 17 18
28
F3
F2
F1
F7
F6
F5
F4
Normally Open Circuit BreakerNormally Closed Circuit Breaker
Subbus1
Subbus2
Subbus3
T1
T3
T5
Main
feeder
Main
feeder
Main
feeder
T2
T4
T6
Case 13 Optimal relocation and installation of sectionalising switches
A Base case
The main objective of this test is to reduce the total system cost including ECOST
and switch costs by the relocation of existing sectionalising switches and the
installation of new ones The switch locations are presented in Fig 7-7
Fig 7-7 Optimal installation and relocation of sectionalising switches in Test Case 13
In comparison with the original configuration there are 8 new sectionalising
switches installed and 5 existing switches relocated As expected the sectionalising
switches are placed adjacent to the load centres with either the highest load density
Chapter 7 Optimal Placement of Sectionalising Switches for Reliability
Improvement
Page | 143
0
1
2
3
4
5
6
7
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
BC
R
Years
or the highest CDF For example the adjacent load of switch 13D is LP6 and LP7
which has the highest CDF value (commercial loads) In addition switch 7D is
placed adjacent to LP9 which has the largest load density The detailed results for
ECOST and switch costs are shown in Table 7-5 After the installation and relocation
of the switches the total system cost is decreased from US $ 477090 to US
$ 272480 ie a reduction of 4289
Table 7-5 Results of sectionalising switches relocation and installation in Test Case 13
ECOST
($)
Number of
relocated
switches
Relocation
cost ($)
Number of
installed
switches
Capital and
installation
cost ($)
Maintenance
and operation
cost ($)
Total
system
cost ($)
Before switch
placement
472260 0 0 0 0 4830 477090
After switch
placement
221120 5 2500 8 37600 11260 272480
B Benefit-to-Cost analysis
BCR analysis is used to verify the benefits and costs of sectionalising switch
placement for distribution operators The results are presented in Fig 7-8 The
benefits and costs are accumulated during the predefined life period There is no
return on investment for the first year as the BCR for Year 1 is 055 However the
BCR for Year 2 is 108 which means the investors start to get benefits in Year 2 In
addition switch placement proved to be a feasible investment since the BCR is
increased to 620 when the switch achieves its service life 15 years in this study
Fig 7-8 BCR versus years
Chapter 7 Optimal Placement of Sectionalising Switches for Reliability
Improvement
Page | 144
0
20
40
60
80
100
120
140
160
05 1 15 2 25 3 35 4 45 5 55 6 65 7 75 8
Co
st (
th
ou
san
d $
)
CDF multiplier
ECOST
Switch costs
Total costs
C Sensitivity analysis
To demonstrate the impact of changing the values of different parameters on the
corresponding results several sensitivity analysis studies are discussed
CDF variation sensitivity analysis
The main objective of this test is to assess the behaviour of the proposed approach
when the CDF (customer damage function) is varied The CDF is increased from 50
to 800 of its initial value in 50 increments The original value of the CDF
multiplier is 100 The effect of variation in the CDF on the ECOST switching
costs and the total system cost is plotted in Fig 7-9 Switch costs include
sectionalising switch installation relocation operation and maintenance cost The
ECOST and switching costs increase as the CDF is increased However the
difference between ECOST and switching costs is also increased
Fig 7-9 Variation of cost versus change in CDF
Variations of the optimal number of installed sectionalising switches versus the CDF
are presented in Fig 7-10 The optimal number of newly installed switches increases
from 7 to 34 as the CDG multiplier is increased from 05 to 8 This indicates the
network needs to be more automated especially if the consequence of customer
damage becomes more serious However the growth in the optimal number of
sectionalising switches is slowing down As shown in Fig 7-10 when the CDF
multiplier increases above 3 the number of sectionalising switches remains at 32 as
Chapter 7 Optimal Placement of Sectionalising Switches for Reliability
Improvement
Page | 145
0
5
10
15
20
25
30
35
40
05 1 15 2 25 3 35 4 45 5 55 6 65 7 75 8
Nu
mb
er
of
swit
che
s
CDF multiplier
the reduction of ECOST brought by installing a sectionalising switch is small
compared to the increase in switch costs Only when the CDF multiplier reaches 55
does the reduction of ECOST outweigh the installation cost of a switch and hence
acquiring a sectionalising switch is a cost-effective investment This is due to the fact
that the installation of the first sectionalising switch has the largest effect on
reducing the total system cost and the impact of sectionalising switch installation on
ECOST decreases as the network becomes more automated
Fig 7-10 Number of installed sectionalising switches versus change in CDF
ACO parameters sensitivity analysis
The ACO parameter analysis is provided in this section In each test only one
parameter is changed whilst the others remain constant The convergence number is
defined as the number of the iterations when the objective function is convergence
The assessment of the impact of the pheromone evaporation rate ρ on the proposed
algorithm is presented in Table 7-6 The number of ants is 200 and the iteration time
is 400 Parameter ρ is varied from 01 to 06 with an increment of 01 For each ρ the
test is run 100 times Table 7-6 shows the impacts of the ρ variation on the objective
function J It can be seen the evaporation rate ρ has a considerable impact on the
convergence performance of the ACO algorithm When ρ is small the residual
pheromone on the path is dominant and the positive feedback of pheromone is weak
This results in an increment in the stochastic performance and global search ability
Chapter 7 Optimal Placement of Sectionalising Switches for Reliability
Improvement
Page | 146
of the ACO algorithm but a reduction in the convergence rate When ρ is large the
positive feedback of the pheromone is dominant which results in an improvement in
the convergence rate but a reduction in the search ability of the algorithm In other
words the algorithm is more easily trapped into a local optimal solution In summary
the selection of ρ is based on two factors of the algorithm 1) convergence rate 2)
global search ability As shown in the table the best value of ρ for this case is 04
which results in the minimum average value and has a suitable convergence rate
Table 7-6 Impacts of 120588 variation on objective function 119869
120588 Objective function value Average convergence
number Average Maximum Minimum
01 273120 274810 272480 223
02 273400 275960 272480 175
03 273480 274810 272480 132
04 273100 274810 272480 110
05 273550 274810 272480 94
06 273440 274810 272480 81
Table 7-7 presents the impacts of the variation in the number of ants on objective
function J The evaporation rate is 04 and the iteration number is 400 The number
of ants is changed from 100 to 500 with an increment of 100 The greater the
number of ants the more likely the global optimum value is achieved This is due to
the growth in global search capability However the convergence rate decreases To
balance the global search ability and convergence rate the number of ants is set to
400
Table 7-7 Impacts of variation in number of ants on objective function 119869
Number of ants Objective function value Average convergence
number Average Maximum Minimum
100 273865 276120 272480 91
200 273100 274810 272480 110
300 273030 274370 272480 135
400 272820 274230 272480 168
500 273170 274230 272480 245
Chapter 7 Optimal Placement of Sectionalising Switches for Reliability
Improvement
Page | 147
However in this study the proposed approach is used for planning a future network
Thus the computation time is not an issue The number of ants and iteration should
be large enough for the ACO algorithm to find the global optimum solution
752 Test Case 2
The objective of this test is to minimise SAIDI and switch costs by maximising the
fuzzy bi-objective function as presented in Section 722 The results of the
membership values of objectives SAIDI as well as switch costs are listed in Table
7-8 The weighting factors of the system objectives can be changed by the network
operator which make it possible to give preference to one over the other Three
cases are studied in which the weighting factors 1205961and 1205962vary from 01 to 09
As shown in the table as the weighing factor of SAIDI 1205961 is increased more
sectionalising switches are installed and reliability is improved The results show the
algorithm can adapt itself to the variation of the weighting factors For decision
making appropriate weighting factors for each objective are selected and a
compromised switch placement plan is obtained using the proposed approach
Table 7-8 Results of sectionalising switches relocation and installation in Test Case 2
Test Cases 1205961 1205962 120572119878119860 120572119878119862 Objective
Function
SAIDI
(hrscustomer)
Switch costs ($)
Case 21 01 09 04909 09970 09464 1157 68275
Case 22 05 05 08456 09061 08758 556 67378
Case 23 09 01 09384 07761 09221 39936 153950
( Each section has two candidate locations for sectionalising switch placement U means upstream side of the section and D
means downstream side of the section)
753 Test Case 3
In this test the three objective functions of the problem to be optimised are ECOST
SAIDI and switch costs The detailed test results before and after switch placement
are listed in Table 7-9 The placement of sectionalising switches results in a
reduction of 60 in ECOST and 7148 in SAIDI It is observed that the
installation and relocation of sectionalising switches has obtained a compromise
solution of three objectives optimisation
Chapter 7 Optimal Placement of Sectionalising Switches for Reliability
Improvement
Page | 148
Table 7-9 Results of sectionalising switches installation and relocation in Test Case 3
Objective
Function
120572119864119862 120572119878119860 120572119878119862 ECOST
($)
SAIDI
(hrscustomer)
Switch costs
($)
Before
switch
placement
0 0 0 1 472260 1989 4830
After switch
placement
08327 08327 08392 08384 188950 56723 112410
76 Summary
This study has presented an ACO algorithm for assessing the SSP problem in terms
of three conflicting objectives optimisation reduction of unserved energy cost
decrease in the average time that a customer is interrupted and minimisation of
switch costs The proposed model has been successfully applied on Bus 4 of the
RBTS In comparison with the original system the existing sectionalising switches
are relocated and new automatic switches are installed The effectiveness of the
proposed approach has been demonstrated through the results obtained which
indicates switch placement using the ACO algorithm reduces the customer outage
costs and interruption duration times during fault contingencies Furthermore the
importance of the CDF variation in determining the SSP is investigated through
sensitivity analysis The impact of installing sectionalising switches on reducing the
total system costs decreases as the number of sectionalising switches is increased As
the parameters of ACO algorithm affect the performance of the proposed method an
ACO parameter sensitivity analysis is also provided in this study The selection of
pheromone evaporation rate and number of ants is a trade-off between the global
search ability and convergence rate of the algorithm In addition a benefit-to-cost
analysis is implemented and used to prove switch investment is profitable The
procedure is used for system planning and is applied off-line so there is no
limitation in calculation times
The main contribution of this study is the conversion of all the multiple objectives
into a single objective function in two forms weighted aggregation and fuzzy
satisfaction objective function considering ECOST SAIDI and cost of
sectionalising switches simultaneously The selection of each form depends on the
Chapter 7 Optimal Placement of Sectionalising Switches for Reliability
Improvement
Page | 149
number of objectives as well as their units and dimensions Another contribution is
the incorporation of FMEA to evaluate the impact on distribution system reliability
of increased automation
Page | 150
CHAPTER 8
DISTRIBUTION NETWORK
RECONFIGURATION FOR LOSS
REDUCTION amp RELIABILITY
IMPROVEMENT
81 Introduction
Optimal distribution network reconfiguration (DNR) can not only solve a single
objective function such as feeder loss minimisation but can also deal with multiple
objectives The presence of multiple objectives raises the issue of how to consider
them simultaneously [117] In the previous section the multiple objectives are
transformed into a single equation using fuzzy logic based approaches The
optimisation is then formulated either as the weighted sum of the fuzzy membership
functions or with the application of the max-min principle
However the above simple optimisation processes only find a compromise solution
It is no longer acceptable for a system with multiple conflicting objectives if the
distribution network operator (DNO) desires to know all possible optimal solutions
for all the objectives simultaneously [20] Therefore a set of trade-off solutions
using the Pareto optimality concept is now proposed These solutions can be
Chapter 8 Distribution Network Reconfiguration for Loss Reduction amp Reliability
Improvement
Page | 151
compared by using the concept of dominance [88] In this concept a solution is non-
dominated when no other solution exists with better values for all the individual
objectives The Pareto set is the set of all non-dominated solutions and the
corresponding objective values constitute the Pareto front [88] This allows the
DNOs to select the most suitable one for implementation depending on the utilitiesrsquo
priorities Pareto analysis is suitable for addressing problems whose conflicting
solutions cannot be addressed using a single solution [117]
This study formulates the optimal network reconfiguration problem within a Pareto
optimal framework where feeder loss and system reliability indices are
simultaneously optimised Two types of reliability indices are considered system
expected outage costs to customers (ECOST) and system interruption duration index
(SAIDI) The multi-objective ant colony optimisation (MOACO) and artificial
immune systems-ant colony optimisation (AIS-ACO) algorithms are proposed and
compared for the assessment of DNR problems Both algorithms focus on problems
in terms of Pareto optimality where the objective functions are multidimensional In
MOACO each objective function is assigned with a pheromone matrix and all
values from multiple pheromone matrices are aggregated into a single pheromone
value by a weighted sum [96] In AIS-ACO the quality of elements that make up the
solution to the problem is represented by the pheromones developed from the ACO
And the hypermutation from the AIS is used as a random operator to enlarge the
search space [88] To verify the suitability of the proposed algorithms they have
been tested on Bus 4 of the Roy Billinton Test System (RBTS) system and the Pareto
set is obtained
The remaining parts of this chapter are organised as follows Section 82 deals with
the framework of multi-objective optimisation and DNR problem formulation The
implementation details of the MOACO and AIS-ACO algorithms to the problem are
discussed in Section 83 The simulation results and the best compromise solutions
are presented and discussed in Section 84 and 85 Section 86 summarises the main
conclusions
Chapter 8 Distribution Network Reconfiguration for Loss Reduction amp Reliability
Improvement
Page | 152
82 Problem Formulation
This section formulates the DNR problems in the Pareto optimal framework
821 Multi-objective Reconfiguration Problem
In this study three objectives are considered and they are feeder loss unserved
energy cost and the average time that a customer is interrupted Therefore the multi-
objective DNR problem can be defined as the minimisation of the vector
119865(119866) = [1198911(119866)1198912(119866)1198913(119866)]119879 (8-3)
where 1198911(119866) 1198912(119866) and 1198913(119866) are described below for a given network
configuration G
8211 Minimisation of feeder loss
The total feeder loss of the network is formulated as
1198911(119866) = sum 119896119894119877119894(119875119894
2+1198761198942
1198801198942 )
119873119887119894=1 (8-4)
where 119877119894 is the resistance of the ith branch 119875119894 and 119876119894 are the real power (W) and
reactive power (VAr) at the receiving end of branch i 119880119894 represents the rms voltage
at the receiving end of branch i (V) 119896119894 is a binary variable 119896119894 = 0 indicates that
branch 119894 is open and 119896119894 = 1 indicates that branch 119894 is closed The detailed feeder loss
assessment is presented in Section 28
8212 Minimisation of ECOST
The ECOST represents the unserved energy cost and is described as
1 ( 1)
1 1 1 1 1 1
( ) ( ) ( ) ( ) (1 ) (1 )b b b b bN CT NR CT NST
t t
b b k R k s
t b k j k j
ECOST L P k j C d P k j C d IR DR
(8-5)
where T is time period (year) 119873119887 is the total number of branches 120582119887and 119871119887 are the
average failure rate (failurekm-year) and length (km) of branch b 119862119879119887 119873119877119887 and
119873119878119887 are the total number of customer types permanent damaged and temporary
Chapter 8 Distribution Network Reconfiguration for Loss Reduction amp Reliability
Improvement
Page | 153
damaged load points when the fault is at branch b P(k j) is the average load of the
kth-type customers at the jth load point (kW) 119862119896(119889) is the customer damage
function for kth-type customer lasting d hours ($kW) 119889119877 and 119889119878 are the average
repair time and the switch time after failure IR and DR are the annual load increase
rate and discount rate
8213 Minimisation of SAIDI
The average time that a customer is interrupted is represented by a reliability index
SAIDI and is defined as
119878119860119868119863119868 = sum sum 120582119887∙119871119887[sum 119889119877
119873119862119877(119887)119899=1 +sum 119889119878
119873119862119878(119887)119899=1 ]
119873119887119887=1
119873119862119905119900119905119886119897119879
119905=1 (8-6)
where 119873119862119877(119887) and 119873119862119878(119887) are the number of permanent damaged and temporary
damaged customers when the fault is at branch b 119873119862119905119900119905119886119897 is the total number of
served customers SAIDI is measured in hours
8214 Constraints
The computed voltages currents and the power flow at all branches should be kept
in their permissible range and the network should be operated in radial The
configurations that violate any constraint should be disregarded
822 Best Compromise Solution
After obtaining the Pareto set the best compromise solution among the multiple
objectives can be selected by comparing the fitness value of each member in the
Pareto front as follows [45]
119891119901119904(119894) = sum 120596119895max(119900119891119895)minus119900119891119895(119875119878119894)
max(119900119891119895)minusmin (119900119891119895)
119873119900119887119895
119895=1 (8-7)
where 119873119900119887119895 is the number of objectives which is three in this study max(119900119891119895) and
min(119900119891119895) are the maximum and minimum value of the jth objective function
obtained by all the members in the Pareto front respectively 1205961 1205962 and 1205963 are the
weighting factor for feeder loss ECOST and SAIDI respectively
The best compromise solution is varied by changing the values of the weighting
factors based on the tendencies of the decision makers
Chapter 8 Distribution Network Reconfiguration for Loss Reduction amp Reliability
Improvement
Page | 154
83 Solution Methodology
In this study there are two methodologies proposed for generating the Pareto set to
the multi-objective DNR problem which are MOACO and AIS-ACO algorithm
Each solution is represented by a string of integers which indicates the locations of
tie-switches
831 Applying MOACO to Multi-objective DNR Problem
Generally ACO algorithm is developed for the assessment of a single objective
optimisation problem However a MOACO algorithm is proposed for assessing
multiple objective functions in the Pareto optimality framework which can generate
diverse solutions rather than just one The flowchart of the MOACO algorithm is
presented in Fig 8-1 and is divided into six steps
Step 1 Initialisation First of all all the ants are initially located at home The
number of pheromone matrices is equal to the number of objectives Each
pheromone matrix has 33 rowsstates (candidate locations for tie-switches) and 4
columnsstages (number of tie-switches) The pheromone values of the edges in the
search space are all initialised at an equal value which is a small positive constant
number
Step 2 Pheromone matrix generation and ant dispatch As there are multiple
pheromone matrices 1205911 1205912 and 1205913 are associated with feeder loss ECOST and
SAIDI respectively All matrices are aggregated into a single pheromone matrix by
weighted sum as
120591119894119909 = 1199011 ∙ 1205911198941199091 + |1199011 minus 1199012| ∙ 120591119894119909
2 + (1 minus 1199012) ∙ 1205911198941199093 (8-8)
where 1205911198941199091 120591119894119909
2 and 1205911198941199093 are the levels of pheromone deposited on state i of stage x for
feeder loss ECOST and SAIDI respectively where 1199011 and 1199012 are uniform random
numbers between 0 and 1 and 1199011 is less than 1199012 This ensures the selection of the
three pheromone matrices all have the same probability and can be used to build the
new matrix
All the ants begin their tours from the home colony and choose the next node to
move to based on the intensity of pheromones from a new pheromone matrix They
Chapter 8 Distribution Network Reconfiguration for Loss Reduction amp Reliability
Improvement
Page | 155
experience different pheromone matrices according to the random variation of
weights The probability of an ant choosing state i of stage x is
119875119894119909(119873) =120591119894119909(119873)
sum 120591119894119909(119873)ℎisin∆119909
(8-9)
where 120591119894119909(119873) is the level of pheromone deposited on state i of stage x at iteration
N ∆119909 is the set of available states which an ant can choose at stage x
Step 3 Objective Function Evaluation After all the ants have completed their tour
the location list and corresponding objective functions in (8-3) for each ant are
evaluated If any constraint is violated the corresponding solutions are discarded
Step 4 Non-dominated Solutions Extraction and Diversity Measure The non-
dominated solutions extraction extracts solutions from a pool based on the concept
of dominance as presented in Section 821 The crowding distance is used to
measure the extent to which non-dominated solutions are spread over the objective
space [20] As there are three objectives to be optimised the crowding distance of a
solution is equal to the side length of the cuboid which is built by two adjacent
solutions [88] Regarding the boundary solutions (the corner solutions) they are
assigned with an infinite distance The solutions are assigned with a small distance
value if they are located in a crowded area The decision makers tend to choose the
solutions from less crowded regions of the search space (with higher crowding
distance) if the maximum number of non-dominated solutions is restricted to a
certain number [88]
Step 5 Pheromone Updating The aim of this step is to favour transitions towards
states by non-dominated solutions with greater pheromone values There are two
rules of pheromone updating the local rule and global rule
Local rule The pheromones deposited in the search space should be evaporated to
make the paths less attractive The local pheromone update rule is calculated as
follow
120591119894119909119899 (119873) = (1 minus 120588)120591119894119909
119899 (119873 minus 1) + 120591119888 (8-10)
where 120588 is the pheromone evaporation rate which is set between 0 and 1 120591119894119909119899 (119873 minus
1) is pheromone value deposited on state i of stage x of matrix n at iteration N-1 120591119888
Chapter 8 Distribution Network Reconfiguration for Loss Reduction amp Reliability
Improvement
Page | 156
is a small positive constant value Even if the amount of pheromone deposited on an
edge is at the lowest value of 120591119888 there is a slight chance that an ant will still choose
this edge
Global rule The global pheromone updating rule involves ants depositing large
amounts of pheromone to the edges that belong to the corner non-dominated
solutions which are the solutions that have minimum values along each objective
The pheromones of those edges can be updated by
120591119894119909119899 (119873) = 120591119894119909
119899 (119873) + 120588119891119887119890119904119905
119899 (119873)
119891119887119890119904119905119899 (119873minus1)
(8-11)
where 119891119887119890119904119905119899 (119873 minus 1) and 119891119887119890119904119905
119899 (119873) are the minimum values of objective function n
obtained by the non-dominated solutions at iteration N-1 and N respectively
After applying the local and global pheromone updating rules the method Max-Min
ACO algorithm is integrated into the proposed approach
120591119894119909119899 (119873) = 120591119898119886119909 119894119891 120591119894119909
119899 (119873) ge 120591119898119886119909 (8-12)
120591119894119909119899 (119873) = 120591119898119894119899 119894119891 120591119894119909
119899 (119873) le 120591119898119894119899 (8-13)
where 120591119898119886119909and 120591119898119894119899 are the higher and lower bound of pheromone level on each
edge respectively Even if the amount of pheromone deposited to a path is at the
lowest value 120591119898119894119899 there is a slight chance that an ant will still choose this path This
enlarges the search space and prevents convergence from occurring too rapidly
After this the non-dominated solutions with their location lists and corresponding
fitness values in the current iteration are retained and all the ants are free to choose a
new path for the next iteration
Step 6 Termination The computation continues until the predefined maximum
number of iterations is reached The final non-dominated solutions are considered as
the Pareto set to the multi-objective DNR problem
Chapter 8 Distribution Network Reconfiguration for Loss Reduction amp Reliability
Improvement
Page | 157
Start
Iteration N=1
Maximum ant number
reaches
Output Pareto
optimal set and end
No
Yes
Initialise the parameters for MOACO
algorithm search space
Ant number m=1
Random select weights and
aggregate multiple pheromone
matrices into one
Dispatch the ant based on the
amount of pheromone on edges
Calculate the multiple objective functions
for this ant
N=N+1
Read system topology
and load data
Diversity measure and extract non-
dominated solutions
Maximum iteration
reaches
Yes
m=m+1
No
The pheromones are updated according
to local and global rules
Fig 8-1 Flowchart of the MOACO algorithm applied to multi-objective DNR problem
Chapter 8 Distribution Network Reconfiguration for Loss Reduction amp Reliability
Improvement
Page | 158
Start
Cloning
Maximum iteration
reached
Output Pareto
optimal set and end
No
Yes
Initialise and set iteration n=1
Pheromone based hypermutation
Diversity measure and extract non-
dominated solutions
The pheromones are updated according to
local and global rules
n=n+1
832 Applying AIS-ACO to Multi-objective DNR Problem
The general description of AIS-ACO algorithm is presented in Section 34 In this
study the AIS-ACO hybrid approach is used to handle multi-objective formulation
using the Pareto optimality concept The antigen is the multi-objective function and
the antibody is the solution to the problem The affinity between the antibody and the
antigen is the Pareto dominance among solutions which indicates the quality of the
solution [88] The information related to each objective is represented by an
individual pheromone table All the non-dominated solutions experience cloning
hypermutation selection and updating until the maximum number of iterations is
reached The flowchart of the AIS-ACO algorithm for Pareto optimality is presented
in Fig 8-2
Fig 8-2 Flowchart of the AIS-ACO algorithm applied to multi-objective DNR problem
Chapter 8 Distribution Network Reconfiguration for Loss Reduction amp Reliability
Improvement
Page | 159
The key parts of the algorithm are explained as follows
Step 1 Initialisation At the beginning of this algorithm a set of initial solutions is
generated These solutions should satisfy the constraints An individual pheromone
table is also built for each objective Each pheromone table has 33 cells (candidate
locations for tie-switches) The pheromone value of each cell represents the
probability of selecting the corresponding switch to be opened in the network model
The pheromone values of all cells are initially set at the same value
Step 2 Cloning All the non-dominated solutions are subjected to cloning In this
study as there are three objectives to be optimised the number of clones for each
non-dominated solution is three
Step 3 Hypermutation The selection of a cell in each clone for hypermutation is
obtained by applying a roulette wheel on its pheromone table [88] The probability of
selecting a cell is dependent on its pheromone intensity A higher pheromone value
of a cell in the table indicates that the corresponding edge in the network is more
likely to be selected The probability of selection cell i in table n is given by
119901119894119899 =
120591119894119899
sum 120591119895119899
119895 (8-14)
where 120591119894119899 is the pheromone value of cell i in table n sum 120591119895
119899119895 represents the sum of
pheromone values of all cells in table n
Step 4 Non-dominated Solutions Extraction and Diversity Measure This step is
same to the step which has been discussed in Section 831
Step 5 Pheromone Updating The aim of this step is to favour transitions toward
non-dominated solutions with great pheromone values There are two rules of
pheromone updating the local rule and global rule
Local rule Pheromones deposited in the search space should be evaporated to make
the paths less attractive The local pheromone update rule is calculated as follows
120591119894119899(119873) = 119898119886119909 (1 minus 120588)120591119894
119899(119873 minus 1) 120591119898119894119899 (8-15)
where 120588 is the pheromone evaporation rate which is set between 0 and 1 120591119894119899(119873 minus 1)
is pheromone value deposited on cell i of table n at iteration N-1 120591119898119894119899 is the lower
Chapter 8 Distribution Network Reconfiguration for Loss Reduction amp Reliability
Improvement
Page | 160
bound of pheromone level on each edge Even if the amount of pheromone deposited
to a path is at the lowest value 120591119898119894119899 there is a slight chance that an ant will still
choose this path This enlarges the entire search space
Global rule The global pheromone updating rule involves depositing large amounts
of pheromone to the edges that are a part of all the non-dominated solutions in the
current iteration [88] At iteration N the edges of the non-dominated solutions can be
updated as
120591119894119899(119873) = 119898119894119899120591119894
119899(119873) + 120588min (119891119899(119866))
119891119899(119866) 120591119898119886119909 (8-16)
where each 119894 isin edge set of G 119899 isin objective set and 119866 isin non-dominated solutions set
119891119899(119866) is the value of objective function n obtained by the non-dominated solution G
120591119898119886119909 is the higher bound of pheromone level on each edge
After this the non-dominated solutions with their location lists and fitness values in
the current iteration are retained and all the ants are free to choose a new path for the
next iteration
Step 6 Termination The computation continues until the predefined maximum
number iteration is reached The final non-dominated solutions are considered as the
Pareto set to the multi-objective DNR problem
Chapter 8 Distribution Network Reconfiguration for Loss Reduction amp Reliability
Improvement
Page | 161
LP11 LP12 LP13 LP14 LP15 LP16 LP17
LP8 LP9 LP10
LP1 LP2 LP3 LP4 LP5 LP6 LP7
LP32 LP33 LP34 LP35 LP36 LP37 LP38
LP29 LP30 LP31
LP26 LP27 LP28
LP18 LP19 LP20 LP21 LP22 LP23 LP24 LP25
19
20
21
22
23
24
26
25 27
28
29 30
71
13 15
14 16
17
18
69
1 3
2
5
4
7
6 8
10
9
68
11 12
56
57
58 60
59 61 62
65
64 66 67
50 52
51
54
53 55
44
45
46
47
48
49
70
31
32
33
34
36
35
39
37 38 40
41
42 43
63
F3
F2
F1
F7
F6
F5
F4
Normally Open Circuit BreakerNormally Closed Circuit Breaker
Subbus1
Subbus2
Subbus3
T1
T3
T5
Main
feeder
Main
feeder
Main
feeder
T2
T4
T6
84 Application Studies
The proposed MOACO and AIS-ACO algorithms have been tested on an 11 kV
distribution network developed from Bus 4 of the Roy Billinton Test System (RBTS)
a single-line diagram of the network is shown in Fig 8-3 The network consists of 38
load points and 4 tie-switches the associated data can be found in [114] The types
and lengths of 11 kV feeders are listed in Appendix A4 The network built in
OpenDSS incorporates three 3311 kV double transformer substations supplying the
downstream loads
Fig 8-3 Distribution feeder connected to RBTS Bus 4
This typical urban distribution network supplies residential commercial and
industrial consumers The average value of active and reactive power and the
customer type of each node are modified from the original values and the new values
are listed in Table 8-1
Chapter 8 Distribution Network Reconfiguration for Loss Reduction amp Reliability
Improvement
Page | 162
300
350
400
450
4
45
5
55
6
x 104
08
09
1
11
12
13
14
15
Feeder loss (kW)ECOST ($yr)
SA
IDI
(hrs
custo
mer
yr)
Table 8-1 Revised customer data (Average load)
Number
of load
points
Load points Customer type P
(kW)
Q
(kVAr)
Number of
customers
4 1-2 9-10 residential 545 51775 220
6 3-5 13-15 residential 500 475 200
12 6-7 16-17 23-25 28 30-
31 37-38
commercial 415 39425 10
6 8 11 18 26 32-33 industrial 1500 1425 1
10 12 19-22 27 29 34-36 industrial 1000 950 1
The proposed MOACO and AIS-ACO algorithms are coded in the MATLAB to
obtain the location of tie-switches for the optimum configuration The settings of the
algorithm parameters that provided the optimum solution for these two cases are
presented in Appendix C4
The number of Pareto optimal solutions obtained by the two algorithms is 26 and its
Pareto front is presented in Fig 8-4 in three dimensions The Pareto set is listed in
Appendix B3 in detail These solutions provide the network operator with various
configurations for the system to choose from Both algorithms have obtained the
same results However for 100 runs the average computation time of AIS-ACO
algorithm is 402s which is significantly lower than the MOCAO algorithm 1053s
Fig 8-4 Pareto solutions obtained (minimisation of feeder loss ECOST and SAIDI)
Chapter 8 Distribution Network Reconfiguration for Loss Reduction amp Reliability
Improvement
Page | 163
Table 8-2 presents the mean and standard deviation of the Pareto front
Table 8-2 Mean and standard deviation of Pareto Front (loss ECOST and SAIDI)
Feeder loss (kW) ECOST ($yr) SAIDI (hrscustomeryr)
Mean
38074 48139 09975
Standard deviation
3431 5291 01165
The corner non-dominated solutions representing minimum feeder loss minimum
ECOST and minimum SAIDI are marked by the red circle yellow circle and green
circle respectively as shown in Fig 8-4 The objective values of these solutions and
relevant tie-switches locations are presented in Table 8-3 It is obvious that the three
objectives are conflicting with each other and the algorithm is able to find the global
optimal solution for each objective function The minimum loss configuration is the
base configuration of RBTS-Bus4 In minimum ECOST solution the unserved
energy cost is reduced by 1133 in comparison with that in the original network
The minimum SAIDI solution shows a reduction of 3695 in the average time that
a customer is interrupted
Table 8-3 Minimum solutions along each objective (loss ECOST and SAIDI)
Feeder loss (kW) ECOST ($yr) SAIDI
(hrscustomeryr)
Tie-switches location
Minimum Loss
32142 46404 13090 68 69 70 71
Minimum ECOST
35409 41145 10586 10 17 41 70
Minimum SAIDI
43523 57891 08253 7 26 54 69
85 Best Compromise Solution
After obtaining the Pareto set the best compromise solution is the member which
has the largest fitness value as calculated in Eq (8-7) The results are presented in
Table 8-4 The importance of each objective function is represented by its weighting
Chapter 8 Distribution Network Reconfiguration for Loss Reduction amp Reliability
Improvement
Page | 164
factor which ranges from 1 to 10 A higher weighing factor indicates this objective
function is more important It can be seen that the solutions are different if the
weighing factors of each objective function are varied based on the tendencies of
DNO For example as shown in the table Case 2 (1205961 = 10 1205962 = 1 1205963 = 1)
indicates that the importance of feeder loss reduction is higher than the other two
objectives and hence the best compromise solution for this case obtains the
minimum loss among all the solutions which is the same as the results obtained
from Table 8-3 In comparison of Case 5 with Case 2 as the importance of ECOST
reduction is increased the network is reconfigured and its feeder loss increases by
588 to compensate for a 1045 decrease in the ECOST If there is no preferred
objective the best solution is obtained by setting 1205961 = 1205962 = 1205963 (Case 1)
Table 8-4 Best compromise solutions (loss ECOST and SAIDI)
Case No Weighting factors Best
compromise
solution
Feeder
loss
(kW)
ECOST
($yr)
SAIDI
(hrscustomeryr) 1205961 1205962 1205963
1 10 10 10 10 41 69 70 34033 41553 10996
2 10 1 1 68 69 70 71 32142 46404 13090
3 1 10 1 10 17 41 70 35409 41145 10586
4 1 1 10 7 26 54 69 43523 57891 08253
5 10 10 1 10 41 69 70 34033 41553 10996
6 10 1 10 10 54 69 71 34759 46644 10217
7 1 10 10 7 17 41 70 40368 43329 09570
86 Summary
The MOACO and AIS-ACO algorithms have been presented in this study for the
assessment of the multi-objective DNR problem using the Pareto optimality concept
The proposed DNR problem is formulated taking into account three objectives to be
minimised feeder loss ECOST and SAIDI The algorithms have been successfully
tested in an RBTS-Bus 4 network The results illustrate that the proposed algorithm
is able to generate a set of non-dominated solutions with high quality and great
diversity This set of solutions represent different trade-offs among the objective
functions And the corner non-dominated solutions which represent the minimum
Chapter 8 Distribution Network Reconfiguration for Loss Reduction amp Reliability
Improvement
Page | 165
value of each objective function are presented in the Pareto front chart By varying
the weighting factors for the parameters the decision makers can select the best
compromise strategy among the three objectives for implementation depending on
the utilitiesrsquo priorities
According to the obtained results both algorithms have obtained the same Pareto
optimal solutions but the AIS-ACO algorithm performs better in comparison with
the MOACO algorithm in terms of computation time The pheromone tables in AIS-
ACO algorithm are used to guide the search process and improve the solution quality
In addition the hypermutation is used as a random operator to enlarge the search
space and to prevent the algorithm from easily falling into the local optimum Future
work could include the assessment of the DNR problem with other objectives such
as balancing loads on feeders and minimising the maximum node voltage deviation
The AIS-ACO algorithm can also be applied to larger systems
Page | 166
CHAPTER 9
MULTI-OBJECTIVE DISTRIBUTION
NETWORK RECONFIGURATION amp DG
ALLOCATION CONSIDERING LOSS
VOLTAGE DEVIATION AND LOAD
BALANCING
91 Introduction
As discussed in the previous chapters distribution network reconfiguration (DNR)
can not only be used for single objective optimisation but also multi-objective
optimisation The study aims to determine a system topology that simultaneously
minimises feeder loss maximum node voltage deviation and feeder load balancing
This is achieved by optimal DNR and DG allocation
There are two methods presented in this chapter that tackle these objectives a single
fuzzy satisfaction objective function is used to transform the three conflicting
objectives into fuzzy memberships and then finally to combine them into a single
function The ultimate goal is to find a solution that maximises this single objective
while maintaining the constraints of the network [20] In Chapter 7 the degree of
Chapter 9 Multi-objective Distribution Network Reconfiguration amp DG Allocation
Considering Loss Voltage Deviation and Load Balancing
Page | 167
overall fuzzy satisfaction is determined by the max-min principle However there is
no guarantee that if one membership value is weaker than the other membership
values then for the same option the optimised single function will also be weak [86]
Therefore the max-min principle may not predict the best compromise solution In
this study a new operator called lsquomax-geometric meanrsquo has been introduced to
determine the degree of overall fuzzy satisfaction
Another methodology used for assessing the multi-objective DNR and DG allocation
problem is based on the Pareto optimality concept The proposed method provides a
set of non-dominated solutions with high quality and great diversity This constructs
a full Pareto front which represents different trade-offs among the objective
functions It allows the decision makers to select the most suitable one from all the
non-dominated solutions and use this for implementation which depends on the
utilitiesrsquo priorities
The optimisation algorithms for DNR and DG allocation can be classified into two
groups
Ant colony optimisation (ACO) algorithm which is used to solve the
problem in the fuzzy domain
Artificial immune systems-ant colony optimisation (AIS-ACO) algorithm
which is adopted to formulate the optimal network reconfiguration problem
within a multi-objective framework based on the Pareto optimality concept
The effectiveness and the efficiency of the proposed methods are implemented on
two standard IEEE 33-node and 69-node systems as case studies
The remainder of this chapter is organised as follows in Section 92 the
mathematical models of the problem are developed Then the solution procedures
are presented in Section 93 Numerical studies are presented and discussed in
Section 94 and finally Section 95 summarises the main conclusions
Chapter 9 Multi-objective Distribution Network Reconfiguration amp DG Allocation
Considering Loss Voltage Deviation and Load Balancing
Page | 168
0
1
92 Problem Formulation
The primary objective of this study is to minimise the three conflicting objectives
feeder loss maximum node voltage deviation and the feeder load balancing index
Two formulations of objective functions are presented as follow
921 Single Fuzzy Satisfaction Objective Function
In this study the three conflicting objectives are transformed into a single objective
function in the fuzzy domain The best compromise solution is obtained using a
lsquomax-geometric meanrsquo principle and is formulated as follows
Max 119871 = (120572119871 times 120572119881 times 120572119861)1 3frasl (9-1)
where 120572119871 120572119881 120572119861 represents the value of the membership functions for the feeder loss
the maximum node voltage deviation and the feeder load balancing index
respectively
The membership functions used to describe the three objectives of the DNR and DG
allocation problem are presented in the following sections
Membership function for feeder loss reduction
The calculation of feeder loss has been discussed in Section 28 The basic purpose
of this membership function is to reduce feeder loss Therefore the network
topology with a lower loss value obtains a higher membership value The
membership function for loss reduction is formulated in (9-2) and presented in Fig
9-1
Fig 9-1 Membership function for feeder loss reduction
As feeder loss becomes greater than 119871119874119878119878119898119894119899 the degree of satisfaction decreases
This reduction is continued until feeder loss reaches 119871119874119878119878119900119903119894
120572119871
119871119874119878119878119898119894119899 119871119874119878119878119900119903119894 119871119874119878119878
Chapter 9 Multi-objective Distribution Network Reconfiguration amp DG Allocation
Considering Loss Voltage Deviation and Load Balancing
Page | 169
0
1
120572119871 =
1 119871119874119878119878 le 119871119874119878119878119898119894119899119871119874119878119878119900119903119894minus119871119874119878119878
119871119874119878119878119900119903119894minus119871119874119878119878119898119894119899119871119874119878119878119898119894119899 lt 119871119874119878119878 lt 119871119874119878119878119900119903119894
0 119871119874119878119878 ge 119871119874119878119878119900119903119894
(9-2)
where 119871119874119878119878119900119903119894 is the loss of the original network 119871119874119878119878119898119894119899 is the minimum loss that
a network can achieve As it is not appropriate for decision makers to obtain a
network topology which increases loss after DNR and DG allocation the minimum
value of 120572119871 is selected as 0 if the loss is greater than or equal to 119871119874119878119878119900119903119894
Membership function for maximum node voltage deviation reduction
The maximum deviation of bus voltages from their rated values is formulated as
119881119863 = max|119881119903119890119891 minus 119898119894119899(119881119894)| |119881119903119890119891 minus 119898119886119909(119881119894)| 119894 120598 1 2 hellip 119873119887 (9-2)
where 119881119903119890119891 is the reference value for the node voltage which is the substation voltage
it is assumed to be 10 per unit in this study 119881119894 is the voltage at the ith node and 119873119887
is the number of nodes
The membership function for maximum node voltage deviation is shown in Fig 9-2
Fig 9-2 Membership function for maximum node voltage deviation reduction
The mathematical equation is presented below
120572119881 =
1 119881119863 le 119881119863119898119894119899119881119863119900119903119894minus119881119863
119881119863119900119903119894minus119881119863119898119894119899119881119863119898119894119899 lt 119881119863 lt 119881119863119900119903119894
0 119881119863 ge 119881119863119900119903119894
(9-3)
where 119881119863119900119903119894 and 119881119863119898119894119899 are the original and minimum values of the maximum node
voltage deviation respectively
120572119881
119881119863119898119894119899 119881119863119900119903119894 119881119863
Chapter 9 Multi-objective Distribution Network Reconfiguration amp DG Allocation
Considering Loss Voltage Deviation and Load Balancing
Page | 170
0
1
Membership function for feeder load balancing index reduction
The feeder load balancing index is calculated as
119871119861119868 = 119881119886119903[1198681
1198681119898119886119909
1198682
1198682119898119886119909 hellip
119868119894
119868119894119898119886119909 hellip
119868119899
119868119899119898119886119909] (9-4)
where 119868119894 is the current flowing through branch 119894 119868119894119898119886119909 represents the maximum
current limit of branch 119894
The function for feeder load balancing index is shown in Fig 9-3 and expressed as
120572119861 =
1 119871119861119868 le 119871119861119868119898119894119899119871119861119868119900119903119894minus119871119861119868
119871119861119868119900119903119894minus119871119861119868119898119894119899119871119861119868119898119894119899 lt 119871119861119868 lt 119871119861119868119900119903119894
0 119871119861119868 ge 119871119861119868119900119903119894
(9-5)
where 119871119861119868119900119903119894 and 119871119861119868119898119894119899 are the original and minimum values of the feeder load
balancing index respectively
Fig 9-3 Membership function for load balancing index reduction
922 Multi-objective Reconfiguration Problem Using Pareto
Optimality
In this study the multi-objective DNR problem can be defined as the minimisation
of the vector
119865(119866) = [1198911(119866)1198912(119866)1198913(119866)]119879 (9-6)
where 1198911(119866) 1198912(119866) and 1198913(119866) are feeder loss maximum node voltage deviation and
feeder load balancing index respectively The calculation of these three parameters
is discussed in Section 921
120572119861
119871119861119868119898119894119899 119871119861119868119900119903119894 119871119861119868
Chapter 9 Multi-objective Distribution Network Reconfiguration amp DG Allocation
Considering Loss Voltage Deviation and Load Balancing
Page | 171
93 Solution methodology
931 Applying ACO to DNR and DG Allocation in the Fuzzy
Domain
In this study the objective of reconfiguring the network and allocating DGs
simultaneously is to deal with the single fuzzy satisfaction objective function In
order to tackle this optimisation problem an ACO algorithm is adopted to find the
optimum configuration of tie-switches and the location of DGs in the network When
the locations of tie-switches and DGs are changed a new network configuration will
be formed For each network configuration the overall satisfaction of the plan is
calculated using Eq (9-1) The search space of the DNR and DG allocation problems
is modelled as a directed graph as shown in Fig 5-1 The flowchart of the proposed
ACO algorithm is presented in Fig 5-2
932 Applying AIS-ACO to Multi-objective DNR and DG
Allocation Using Pareto Optimality
The application of the AIS-ACO algorithm to the multi-objective DNR and DG
allocation problem using the concept of Pareto optimality is similar to that in Section
832 with an additional process for DG allocation
94 Application Studies
To demonstrate the performance and effectiveness of the proposed techniques in
solving the network reconfiguration and placement of DG problems simultaneously
the proposed ACO and AIS-ACO are implemented on two 1266 kV test systems
consisting of 33 and 69 buses The network models are built in OpenDSS and the
solution algorithms are developed in MATLAB For both test systems the substation
voltage is assumed to be 10 pu and all the sections and buses are considered as
candidate locations for tie-switches and DG placement respectively In this study
for simplicity the number of installed DGs is three All the DGs are synchronous
generators and are represented as PQ models with a 100 kVA and a power factor
Chapter 9 Multi-objective Distribution Network Reconfiguration amp DG Allocation
Considering Loss Voltage Deviation and Load Balancing
Page | 172
equal to 10 However the proposed methodology can be implemented for any
number of DGs For the purpose of better illustration and comparison four cases are
considered to analyse the superiority and performance of the proposed methods
Case I System is without reconfiguration and has no DGs (base case)
Case II System is optimally reconfigured and has no DGs
Case III System is optimally reconfigured after DGs are placed at certain buses
Case IV System is optimally reconfigured and DGs are optimally placed
simultaneously
It is to be noted that the ACO and AIS-ACO control parameters are different for
each test case They are set experimentally using information from several trial runs
The final combinations that provide the best results for all of the above tests are
given in Appendix C5 And the Pareto sets for all test cases are listed in Appendix
B4 in detail
941 33-bus System
In this section the proposed procedure is implemented on a 33-bus 1266 kV radial
distribution system with 37 branches and 5 tie-switches whose single line diagram is
shown in Fig 5-3 The tie-switches are located at L33 to L37 represented by red
dotted lines The data of lines and loads are taken from [108] and summarised in
Appendix A2 The current carrying capacity of all branches is 255A The total real
and reactive power loads of the system are 3715 kW and 2300 kVAr respectively
Case I base case
For the base case without reconfiguration and DGs the initial active feeder loss
maximum node voltage deviation and feeder load balancing index of this system are
20314 kW 00884 pu and 00419 respectively
Chapter 9 Multi-objective Distribution Network Reconfiguration amp DG Allocation
Considering Loss Voltage Deviation and Load Balancing
Page | 173
10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
18 19 20 21
22 23 24
25 26 27 28 29 30 31 32
L1 L2 L3 L4 L5 L6 L7 L8 L9 L10 L11 L12 L13 L14 L15 L16 L17
L18
L19 L20 L21
L22
L23 L24
L25
L26 L27 L28 L29 L30 L31 L32
L33
L34
L35
L36
L37
Case II with reconfiguration only (no DGs)
In this case only reconfiguration is considered and no DGs are installed
After DNR the best compromise solution obtained using ACO algorithm in a single
fuzzy satisfaction objective function is presented in Table 9-1 It can be seen that the
DNR has resulted in a reduction of 2956 in feeder loss 2930 in maximum node
voltage deviation and 3556 in feeder load balancing index compared to the base
case This solution is one of the Pareto optimal solutions which are obtained by
using AIS-ACO algorithm And the network configuration after DNR is shown in
Fig 9-4
Table 9-1 Results of DNR in fuzzy multi-objective formulation for 33-bus system in Case II
Objective function Feeder loss
(kW)
Maximum node
voltage deviation
(pu)
Feeder Load
balancing index
Tie-switches
location
08734 14310 00625 00270 6 9 14 32 37
Fig 9-4 33 bus-system for fuzzy multi-objective optimisation Case II
The number of Pareto optimal solutions obtained using AIS-ACO algorithm is 21
and its Pareto front is presented in Fig 9-5 in three dimensions Table 9-2 presents
the mean and standard deviations of the objective values of the Pareto solutions
Chapter 9 Multi-objective Distribution Network Reconfiguration amp DG Allocation
Considering Loss Voltage Deviation and Load Balancing
Page | 174
120140
160180
200220
006
008
01
012
014
016
0022
0024
0026
0028
003
0032
0034
0036
Feeder loss (kW)Maximum node voltage deviation (pu)
Feeder
load b
ala
ncin
g index
Fig 9-5 Pareto front obtained for 33-bus system in Case II
Table 9-2 Mean and standard deviations of Pareto Front for 33-bus system in Case II
Feeder loss (kW) Maximum node voltage
deviation (pu)
Feeder Load balancing index
Mean
15499 00815 00256
Standard deviation
1549 00194 00023
The corner non-dominated solutions which represent minimum feeder loss
minimum voltage deviation and minimum feeder load balancing index are marked
by the red circle yellow circle and green circle respectively as shown in Fig 9-5
The objective values of these solutions and relevant tie-switches locations are
presented in Table 9-3 In minimum loss solution the feeder loss is reduced by 3118
compared to the initial state If improving voltage profiles is the principle objective
the solution with maximum node voltage deviation of 00604 pu is optimum which
represents a 3167 improvement compared to the base case If balancing feeder
Chapter 9 Multi-objective Distribution Network Reconfiguration amp DG Allocation
Considering Loss Voltage Deviation and Load Balancing
Page | 175
10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
18 19 20 21
22 23 24
25 26 27 28 29 30 31 32
L1 L2 L3 L4 L5 L6 L7 L8 L9 L10 L11 L12 L13 L14 L15 L16 L17
L18
L19 L20 L21
L22
L23 L24
L25
L26 L27 L28 L29 L30 L31 L32
L33
L34
L35
L36
L37
DG2
DG1
DG3
load is the main objective the solution with load balancing index of 00223 is
optimum where the index decreases by 4678 in comparison with the initial case
Table 9-3 Minimum solutions along each objective for 33-bus system in Case II
Feeder loss (kW) Maximum node
voltage deviation (pu)
Feeder Load balancing
index
Tie-switches location
Minimum Loss
13981 00639 00280 7 9 14 32 37
Minimum Voltage Deviation
14026 00604 00310 7 9 14 28 32
Minimum Feeder Load Balancing Index
20248 01309 00223 7 30 34 35 37
Case III with reconfiguration only (with DGs)
In this case the three DGs are located at the end of the feeders ie Bus 17 21 24
The feeder loss maximum node voltage deviation and feeder load balancing of the
original network with DGs are 17831 kW 00823 pu and 00389 pu respectively
After DNR the best compromise solution obtained using ACO algorithm in a single
fuzzy satisfaction objective function is presented in Table 9-4 Compared to the Case
I feeder loss maximum node voltage deviation and feeder load balancing decrease
by 3893 3281 and 4511 respectively This solution belongs to the Pareto
set which are obtained by using AIS-ACO algorithm Fig 9-6 illustrates the optimal
network configuration
Fig 9-6 33 bus-system for fuzzy multi-objective optimisation Case III
Chapter 9 Multi-objective Distribution Network Reconfiguration amp DG Allocation
Considering Loss Voltage Deviation and Load Balancing
Page | 176
110120
130140
150160
170
004
006
008
01
0120018
002
0022
0024
0026
0028
003
Feeder loss (kW)Maximum node voltage deviation (pu)
Feeder
load b
ala
ncin
g index
Table 9-4 Results of DNR in fuzzy multi-objective formulation for 33-bus system in Case III
Objective function Feeder loss
(kW)
Maximum node
voltage deviation
(pu)
Feeder Load
balancing index
Tie-switches
location
08590 12405 00594 00230 6 8 14 32 37
Fig 9-7 shows the Pareto front obtained by the AIS-ACO method and the number
of Pareto optimal solutions for this case is 28 The mean and standard deviations of
the objective values of the Pareto solutions are listed in Table 9-5
Fig 9-7 Pareto front obtained for 33-bus system in Case III
Table 9-5 Mean and standard deviations of Pareto Front for 33-bus system in Case III
Feeder loss (kW) Maximum node voltage
deviation (pu)
Feeder load balancing index
Mean
12850 00711 00231
Standard deviation
1003 00166 00029
Chapter 9 Multi-objective Distribution Network Reconfiguration amp DG Allocation
Considering Loss Voltage Deviation and Load Balancing
Page | 177
The corner non-dominated solutions which represent minimum feeder loss
minimum voltage deviation and minimum feeder load balancing index are marked
by the red circle yellow circle and green circle respectively as shown in Fig 9-7
Table 9-6 presents the objective values of these solutions and relevant tie-switches
locations In minimum loss solution the network reconfiguration results in a
reduction of 4214 in feeder loss compared to the original network and a
reduction of 1594 compared to the reconfigured network without DGs If
improving voltage profiles is the principle objective the solution with maximum
node voltage deviation of 00567 pu is optimum which represents a 3586 and
613 improvement compared to Case I and Case II If balancing feeder load is the
main objective the solution with load balancing index of 00189 is optimum where
the index decreases by 5489 and 1525 in comparison with Case I and Case II
Table 9-6 Minimum solutions along each objective for 33-bus system in Case III
Feeder loss (kW) Maximum node
voltage deviation (pu)
Feeder Load balancing
index
Tie-switches location
Minimum Loss
11753 00643 00241 7 9 14 28 31
Minimum Voltage Deviation
12592 00567 00265 6 8 14 28 32
Minimum Feeder Load Balancing Index
16419 01139 00189 7 21 30 35 37
Case IV with reconfiguration and DG allocation
The network is reconfigured and DGs are allocated simultaneously in this case The
best compromise solution obtained using the proposed algorithm in a single fuzzy
satisfaction objective function after DNR and DG allocation is presented in Table 9-
7 Feeder loss maximum node voltage deviation and feeder load balancing decrease
by 4645 4355 and 4463 respectively in comparison with the base case
This solution is one of the Pareto optimal solutions which are obtained by using
AIS-ACO algorithm Fig 9-8 illustrates the optimal network configuration and DG
locations
Chapter 9 Multi-objective Distribution Network Reconfiguration amp DG Allocation
Considering Loss Voltage Deviation and Load Balancing
Page | 178
10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
18 19 20 21
22 23 24
25 26 27 28 29 30 31 32
L1 L2 L3 L4 L5 L6 L7 L8 L9 L10 L11 L12 L13 L14 L15 L16 L17
L18
L19 L20 L21
L22
L23 L24
L25
L26 L27 L28 L29 L30 L31 L32
L33
L34
L35
L36
L37
DG1
DG3
DG2
100110
120130
140150
160
004
006
008
01
012
0016
0018
002
0022
0024
0026
0028
Feeder loss (kW)Maximum node voltage deviation (pu)
Feeder
load b
ala
ncin
g index
Table 9-7 Results of DNR and DG allocation in fuzzy multi-objective formulation for 33-bus system
in Case IV
Objective
function
Feeder loss
(kW)
Maximum node
voltage
deviation (pu)
Feeder Load
balancing
index
Tie-switches
location
DGs location
08961 10878 00499 00232 7 9 14 36 37 B32 B32 B32
Fig 9-8 33 bus-system for fuzzy multi-objective optimisation Case IV
The number of non-dominated solutions obtained by the AIS-ACO algorithm is 295
However the maximum number for Pareto optimal solutions is restricted to 50
Therefore the solutions with a high value of crowding distance are selected Fig 9-9
shows the Pareto front obtained by the proposed method
Fig 9-9 Pareto front obtained for 33-bus system in Case IV
Chapter 9 Multi-objective Distribution Network Reconfiguration amp DG Allocation
Considering Loss Voltage Deviation and Load Balancing
Page | 179
The mean and standard deviations of the Pareto front are listed in Table 9-8
Table 9-8 Mean and standard deviations of Pareto Front for 33-bus system in Case IV
Feeder loss (kW) Maximum node voltage
deviation (pu)
Feeder Load balancing index
Mean
13295 00873 00194
Standard deviation
1354 00179 00019
The corner non-dominated solutions which represent minimum feeder loss
minimum voltage deviation and minimum feeder load balancing index are marked
by the red circle yellow circle and green circle respectively as shown in Fig 9-9
The objective values of these solutions and relevant tie-switches locations are
presented in Table 9-9 In minimum loss solution the network reconfiguration and
DG allocation result in a reduction of 4662 2244 and 773 in feeder loss
compared to Case I Case II and Case III respectively If improving voltage profiles
is the principle objective the solution with maximum node voltage deviation of
00490 pu is optimum which represents a 4457 1887 and 1358
improvement compared to Case I Case II and Case III respectively If balancing
feeder load is the main objective the solution with load balancing index of 00178 is
optimum where the index decreases by 5752 2018 and 582 in comparison
with Case I Case II and Case III respectively
Table 9-9 Minimum solutions along each objective for 33-bus system in Case IV
Feeder loss (kW) Maximum node
voltage deviation
(pu)
Feeder Load
balancing index
Tie-switches
location
DGs location
Minimum Loss
10844 00538 00228 7 9 14 32 37 B30 B31 B31
Minimum Voltage Deviation
11020 00490 00259 7 9 14 28 36 B31 B31 B32
Minimum Feeder Load Balancing Index
15443 01090 00178 7 30 34 35 37 B8 B9 B12
Chapter 9 Multi-objective Distribution Network Reconfiguration amp DG Allocation
Considering Loss Voltage Deviation and Load Balancing
Page | 180
10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
27
28
29
30
31 32 33 34
35
36
37
38 39 40 41 42 43 44 45
46 47 48 49
50
51
52
53 54 55 56 57 58 59 60 61 62 63 64
65 66
67 68
L1 L2 L3 L4 L5 L6 L7 L8 L9 L10 L11 L12 L13 L14 L15 L16 L17 L18 L19 L20 L21 L22 L23 L24 L25 L26
L27
L28
L29
L30
L31 L32 L33 L34
L35
L36
L37
L38 L39 L40 L41 L42 L43 L44 L45
L46
L47 L48 L49
L50
L51
L52
L53 L54 L55 L56 L57 L58 L59 L60 L61 L62 L63 L64
L65
L66
L67
L68
L69
L70
L71
L72L73
942 69-bus System
This is a large-scale radial distribution system consisting of 73 branches and 5 tie-
switches whose single-line diagram is shown in Fig 5-9 The tie-switches are
located at L69 to L73 represented by red dotted lines The line and load data of the
system are taken from [84] and summarised in Appendix A3 The current carrying
capacity of the branches 1-9 is 400 A 46-49 and 52-64 is 300 A and for all other
branches it is 200 A The total power loads are 379589 kW and 26891 kVAr
respectively
Case I base case
For the base case without reconfiguration and DGs the initial active feeder loss
maximum node voltage deviation and feeder load balancing index of this system are
22562 kW 00928 pu and 00259 respectively
Case II with reconfiguration only (no DGs)
In this case only reconfiguration is considered and no DGs are installed After DNR
the best compromise solution obtained using ACO algorithm in a single fuzzy
satisfaction objective function is presented in Table 9-10 and the network
configuration is shown in Fig 9-10 Reconfiguring the network brings a reduction of
5619 4353 and 2355 in feeder loss maximum node voltage deviation and
feeder load balancing index respectively compared to the base case This solution
belongs to the Pareto set which are obtained by using AIS-ACO algorithm
Fig 9-10 69 bus system for fuzzy multi-objective optimisation Case II
Chapter 9 Multi-objective Distribution Network Reconfiguration amp DG Allocation
Considering Loss Voltage Deviation and Load Balancing
Page | 181
80
100
120
140
160
005
006
007
0080016
0018
002
0022
0024
0026
0028
Feeder loss (kW)Maximum node voltage deviation (pu)
Feeder
load b
ala
ncin
g index
Table 9-10 Results of DNR in fuzzy multi-objective formulation for 69-bus system in Case II
Objective function Feeder loss
(kW)
Maximum node
voltage deviation
(pu)
Feeder Load
balancing index
Tie-switches
location
09676 9885 00524 00195 14 55 61 71 72
The number of Pareto optimal solutions obtained by the AIS-ACO algorithm is 12
and its Pareto front are presented in Fig 9-11 in three dimensions
Fig 9-11 Pareto front obtained for 69-bus system in Case II
The mean and standard deviations of the objective values of the Pareto solutions are
listed in Table 9-11
Table 9-11 Mean and standard deviations of Pareto Front for 69-bus system in Case II
Feeder loss (kW) Maximum node voltage
deviation (pu)
Feeder Load balancing index
Mean
12535 00605 00192
Standard deviation
2458 00085 00028
Chapter 9 Multi-objective Distribution Network Reconfiguration amp DG Allocation
Considering Loss Voltage Deviation and Load Balancing
Page | 182
The corner non-dominated solutions which represent minimum feeder loss
minimum voltage deviation and minimum feeder load balancing index are marked
by the red circle yellow circle and green circle respectively as shown in Fig 9-11
The objective values of these solutions and relevant tie-switches locations are
presented in Table 9-12 In minimum loss solution the feeder loss is reduced by
5619 compared to the initial state If improving voltage profiles is the principle
objective the solution with maximum node voltage deviation of 00523 pu is
optimum which represents a 4364 improvement compared to the base case If
balancing feeder load is the main objective the solution with load balancing index of
00161 is optimum where the index decreases by 3784 in comparison with the
initial case
Table 9-12 Minimum solutions along each objective for 69-bus system in Case II
Feeder loss (kW) Maximum node
voltage deviation (pu)
Feeder load balancing
index
Tie-switches location
Minimum Loss
9885 00524 00195 14 55 61 71 72
Minimum Voltage Deviation
10535 00523 00242 9 14 55 61 71
Minimum Feeder Load Balancing Index
15051 00701 00161 14 61 69 71 72
Case III with reconfiguration only (with DGs)
In this case the three DGs are located at the end of the feeders ie Bus 26 45 64
The feeder loss maximum node voltage deviation and feeder load balancing of the
original network with DGs are 19472 kW 00855 pu and 00234 pu respectively
After DNR Table 9-13 presents the best compromise solution obtained using ACO
algorithm in a single fuzzy satisfaction objective function and the optimal network
configuration is shown in Fig 9-12 Compared to the base case feeder loss
maximum node voltage deviation and feeder load balancing decrease by 6118
4364 and 3282 respectively This solution is one of the Pareto optimal
solutions which are obtained by using AIS-ACO algorithm
Chapter 9 Multi-objective Distribution Network Reconfiguration amp DG Allocation
Considering Loss Voltage Deviation and Load Balancing
Page | 183
10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
27
28
29
30
31 32 33 34
35
36
37
38 39 40 41 42 43 44 45
46 47 48 49
50
51
52
53 54 55 56 57 58 59 60 61 62 63 64
65 66
67 68
L1 L2 L3 L4 L5 L6 L7 L8 L9 L10 L11 L12 L13 L14 L15 L16 L17 L18 L19 L20 L21 L22 L23 L24 L25 L26
L27
L28
L29
L30
L31 L32 L33 L34
L35
L36
L37
L38 L39 L40 L41 L42 L43 L44 L45
L46
L47 L48 L49
L50
L51
L52
L53 L54 L55 L56 L57 L58 L59 L60 L61 L62 L63 L64
L65
L66
L67
L68
L69
L70
L71
L72L73
DG3
DG1
DG2
8090
100110
120130
140
005
006
007
008
0014
0016
0018
002
0022
0024
Feeder loss (kW)Maximum node voltage deviation (pu)
Feeder
load b
ala
ncin
g index
Table 9-13 Results of DNR in fuzzy multi-objective formulation for 69-bus system in Case III
Objective function Feeder loss
(kW)
Maximum node
voltage deviation
(pu)
Feeder Load
balancing index
Tie-switches
location
08829 8758 00523 00174 14 55 61 71 72
Fig 9-12 69-bus system for fuzzy multi-objective optimisation Case III
Fig 9-13 shows the Pareto front obtained by the AIS-ACO method and the number
of Pareto optimal solutions for this case is 19
Fig 9-13 Pareto front obtained for 69-bus system in Case III
Chapter 9 Multi-objective Distribution Network Reconfiguration amp DG Allocation
Considering Loss Voltage Deviation and Load Balancing
Page | 184
The mean and standard deviations of the objective values of the Pareto solutions are
listed in Table 9-14
Table 9-14 Mean and standard deviations of Pareto Front for 69-bus system in Case III
Feeder loss (kW) Maximum node voltage
deviation (pu)
Feeder Load balancing index
Mean
10707 00576 00183
Standard deviation
2042 00071 00029
The corner non-dominated solutions which represent minimum feeder loss
minimum voltage deviation and minimum feeder load balancing index are marked
by the red circle yellow circle and green circle respectively as shown in Fig 9-13
Table 9-15 presents the objective values of these solutions and relevant tie-switches
locations are presented In minimum loss solution the network reconfiguration
results in a reduction of 6118 in feeder loss compared to the original network and
a reduction of 1140 compared to the reconfigured network without DGs If
improving voltage profiles is the principle objective the solution with maximum
node voltage deviation of 00522 pu is optimum which represents a 4375 and
019 improvement compared to Case I and Case II If balancing feeder load is the
main objective the solution with load balancing index of 00147 is optimum where
the index decreases by 4324 and 745 in comparison with Case I and Case II
Table 9-15 Minimum solutions along each objective for 69-bus system in Case III
Feeder loss (kW) Maximum node
voltage deviation (pu)
Feeder Load balancing
index
Tie-switches location
Minimum Loss
8758 00523 00174 13 55 61 71 72
Minimum Voltage Deviation
9729 00522 00226 7 12 55 61 71
Minimum Feeder Load Balancing Index
13686 00681 00147 11 61 69 71 72
Chapter 9 Multi-objective Distribution Network Reconfiguration amp DG Allocation
Considering Loss Voltage Deviation and Load Balancing
Page | 185
10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
27
28
29
30
31 32 33 34
35
36
37
38 39 40 41 42 43 44 45
46 47 48 49
50
51
52
53 54 55 56 57 58 59 60 61 62 63 64
65 66
67 68
L1 L2 L3 L4 L5 L6 L7 L8 L9 L10 L11 L12 L13 L14 L15 L16 L17 L18 L19 L20 L21 L22 L23 L24 L25 L26
L27
L28
L29
L30
L31 L32 L33 L34
L35
L36
L37
L38 L39 L40 L41 L42 L43 L44 L45
L46
L47 L48 L49
L50
L51
L52
L53 L54 L55 L56 L57 L58 L59 L60 L61 L62 L63 L64
L65
L66
L67
L68
L69
L70
L71
L72L73
DG3DG1
DG2
Case IV with reconfiguration and DGs allocation
In this case the network is reconfigured and DGs are allocated simultaneously
Table 9-16 presents the best compromise solution obtained using the ACO algorithm
in a single fuzzy satisfaction objective function after DNR and DGs allocation and
the optimal network configuration and DG locations are shown in Fig 9-14 Feeder
loss maximum node voltage deviation and feeder load balancing decrease by
6721 5377 and 3840 respectively in comparison with the base case This
solution is one of the Pareto optimal solutions which are obtained by using AIS-
ACO algorithm
Table 9-16 Results of DNR and DGs allocation in fuzzy multi-objective formulation for 69-bus
system in Case IV
Objective
function
Feeder loss
(kW)
Maximum
node voltage
deviation (pu)
Feeder Load
balancing
index
Tie-switches
location
DGs location
08882 7397 00429 00158 14 55 61 71 72 B60 B60 B60
Fig 9-14 69-bus system for fuzzy multi-objective optimisation Case IV
The number of non-dominated solutions obtained by the AIS-ACO algorithm is 46
Fig 9-15 shows the Pareto front obtained by the proposed method The mean and
standard deviations of the objective values of the Pareto solutions are listed in Table
9-17
Chapter 9 Multi-objective Distribution Network Reconfiguration amp DG Allocation
Considering Loss Voltage Deviation and Load Balancing
Page | 186
70
80
90
100
110
120
004
0045
005
0055
006
0012
0013
0014
0015
0016
0017
0018
0019
Feeder loss (kW)Maximum node voltage deviation (pu)
Feeder
load b
ala
ncin
g index
Fig 9-15 Pareto front obtained for 69-bus system in Case IV
Table 9-17 Mean and standard deviations of Pareto Front for 69-bus system in Case IV
Feeder loss (kW) Maximum node voltage
deviation (pu)
Feeder Load balancing index
Mean
9872 00520 00147
Standard deviation
1491 00055 00013
The corner non-dominated solutions which represent minimum feeder loss
minimum voltage deviation and minimum feeder load balancing index are marked
by the red circle yellow circle and green circle respectively as shown in Fig 9-15
The objective values of these solutions and relevant tie-switches locations are
presented in Table 9-18 In minimum loss solution the network reconfiguration and
DG allocation result in a reduction of 6721 2517 and 1554 in feeder loss
compared to Case I Case II and Case III respectively If improving voltage profiles
is the principle objective the solution with maximum node voltage deviation of
00428 is optimum which represents a 5388 1816 and 1801 improvement
compared to Case I Case II and Case III respectively If balancing feeder load is the
Chapter 9 Multi-objective Distribution Network Reconfiguration amp DG Allocation
Considering Loss Voltage Deviation and Load Balancing
Page | 187
main objective the solution with load balancing index of 00125 pu is optimum
where the index decreases by 5174 2236 and 1497 in comparison with Case
I Case II and Case III respectively
Table 9-18 Minimum solutions along each objective for 69-bus system in Case IV
Feeder loss (kW) Maximum node
voltage deviation
(pu)
Feeder Load
balancing index
Tie-switches
location
DGs location
Minimum Loss
7397 00429 00158 14 55 61 71 72 B60 B60 B60
Minimum Voltage Deviation
8032 00428 00183 11 55 61 71 72 B60 B60 B60
Minimum Feeder Load Balancing Index
10962 00577 00125 14 63 69 71 72 B62 B62 B62
95 Summary
In this study the DNR and DG allocation problem is formulated either within a
fuzzy satisfaction objective function or within a multi-objective Pareto optimal
framework This formulation incorporates the minimisation of three conflicting
objectives feeder loss maximum node voltage deviation and feeder load balancing
index In the fuzzy multi-objective formulation all three objectives are transformed
into a single fuzzy satisfaction objective function and the ACO algorithm is used to
provide decision support The AIS-ACO algorithm has been presented in this study
for the assessment of the multi-objective DNR problem from a Pareto optimality
point of view The proposed methods have been successfully applied on a 33-bus and
a 69-bus radial distribution system The results illustrate that the proposed algorithm
is able to generate a set of non-dominated solutions with high quality and great
diversity This allows the network operators to choose any one from the non-
dominated solutions for implementation based on utilitiesrsquo priorities And the corner
non-dominated solutions which represent the minimum value of each objective
function are presented in the Pareto front chart
Chapter 9 Multi-objective Distribution Network Reconfiguration amp DG Allocation
Considering Loss Voltage Deviation and Load Balancing
Page | 188
Future work could include the assessment of the DNR and DG allocation problem
with more than three objectives These objectives may include balancing loads on
transformers minimising the number of switching operations etc The proposed
methodologies can be evaluated further by applying them to actual systems
Page | 189
CHAPTER 10
CONCLUSION amp FUTURE WORK
101 Conclusion
The aim of this thesis is to improve service efficiency and quality in distribution
networks Optimal distribution automation (DA) is one of the best solutions to
achieve this goal The multiple objectives are transformed into different forms based
on utilitiesrsquo priorities For this purpose the Monte Carlo method is used to solve
power system issues involving uncertain load values And a set of ant colony
optimisation (ACO)-based algorithms has been developed for objectives
optimisation This section summarises the conclusions drawn from the research
results
A comprehensive review of the network configurations switchgears DA
assessment of loss and reliability indices and different forms of multi-objective
functions was provided in Chapter 2 This has demonstrated the need for DA to
provide a reliable and high efficiency power supply to all customers with a minimum
cost
In Chapter 3 the thesis reviewed the techniques for the assessment of mono-
objectivemulti-objective optimisation problems which were categorised into two
groups simulation methods and analytical methods The Monte Carlo method is a
typical simulation technique and is generally used to deal with power system
calculations involving uncertain parameters It can find the best solution with a high
Chapter 10 Conclusion amp Future Work
Page | 190
degree of accuracy but requires a considerable amount of CPU time and memory
The ant colony optimisation (ACO) algorithm is one of the metaheuristic techniques
designed for assessing the DA problems It can find the global optimum solution in a
reasonable computation time The artificial immune systems (AIS)-ACO hybrid
algorithm was used for assessing the DA problems in order to obtain a set of non-
dominated solutions by using the concept of Pareto dominance
The thesis illustrates why transformer economic operation (TEO) is an economical
solution to reduce transformer loss The TEO mode with minimum loss and
satisfactory voltages is achieved by operating with one or two transformers This
can be summarised as when the transformer load factor is less than the TCLF
transformers should operate separately However when the transformer load factor is
higher than the TCLF it is recommended that transformers operate in parallel In
Chapter 4 a Monte Carlo simulation platform was established to tackle load
uncertainties A methodology based on TEO to reduce transformer loss was then
described This results in a reduction over the conventional transformer loss ie
when two transformers are in parallel operation However simulation studies also
indicate voltage profiles are improved when transformers operate in parallel
Therefore a slight reduction in TCLF results in an increased loss but an
improvement in voltage performance
In Chapter 4 the thesis also demonstrates why distribution network reconfiguration
(DNR) is an effective strategy for transformer loss reduction The presented results
illustrate the optimal locations of tie-switch statuses have successfully reduced the
transformer losses and improved the voltages profiles during a 24 hour operating
period The further away the nodes are from the tie-switch the better the voltage
profiles obtained In addition when the tie-switch moves closer to the middle of the
linked feeder the voltage performance is improved In this case the daily energy
loss in Scenario 5 is 11162 kWh After the introduction of Scenario 9 the annual
saving energy could be 59641 kWh
One conclusion of this thesis is that the network can be reconfigured and DGs can be
relocated simultaneously for feeder loss reduction In Chapter 5 an ACO algorithm
was used for assessing the DNR and DG allocation problems in terms of feeder loss
reduction The numerical results showed that for best performance the existing tie-
Chapter 10 Conclusion amp Future Work
Page | 191
switches were relocated and DGs were optimally placed at the same time The feeder
losses are reduced by 4662 and 6721 for the 33-bus and 69-bus system
respectively The inappropriate network configuration and DG location might result
in loss increment when the size of DG is increased The proposed methodology has
also successfully reduced the total feeder loss and improved the voltage profiles for
different capacities of DG by determining the most suitable network topology and
the DG locations In addition the simulation results have been compared with other
classical methods in literature and it is demonstrated that the proposed ACO is more
efficient and is more likely to obtain the global optimum solution
Another conclusion of this thesis is that the distribution network loss including
transformer loss and feeder loss can be minimised by using a new optimal planning
strategy This strategy is a combination of TEO and network reconfiguration as
presented in Chapter 6 In this chapter the distribution loads experience daily and
seasonal variations and the day is divided into two periods The proposed ACO
algorithm has successfully found the optimum network configuration and economic
operation mode of transformers in all substations during each time interval The
annual energy loss is reduced by 506 compared to the original network Both
transformer loss and feeder loss are reduced through this optimal planning using
DNR and TEO Furthermore simulation results obtained with numerical studies
have demonstrated the capability of applying the ACO algorithm to distribution
network planning including networks with DGs and EVs The proposed
methodology has successfully reduced the total network loss for different capacities
of DG and different penetration levels of EVs by determining the most suitable
network topology compared to the original configuration Comparative results also
show that coordinated charging plan results in less energy loss compared to
uncoordinated charging strategy with the same EV penetration level This is due to
the postponement of charging time which avoids a clash with the peak power
demand times
The thesis develops an effective strategy of sectionalising switch placement (SSP)
for system reliability improvement This is achieved by installing new switches and
relocating existing switches In Chapter 7 an ACO algorithm was proposed for the
assessment of the SSP problem based on reliability improvement and switch costs
minimisation using either a single objective function with weighted aggregation of a
Chapter 10 Conclusion amp Future Work
Page | 192
multi-objective function with fuzzy variables The selection of pheromone
evaporation rate and number of ants is a trade-off between the global search ability
and convergence rate of the ACO algorithm In comparison with the original system
existing sectionalising switches were relocated and new automatic switches were
installed For this practical system the total system costs are reduced by 4289
compared to the original network The impact of installing sectionalising switches on
reducing the total system costs decreases as the number of sectionalising switches is
increased Furthermore a benefit-to-cost analysis which offered a comparison
between ECOST and switch costs was implemented The analysis reveals that the
installing and relocating sectionalising switches is a profitable investment In
addition a set of compromise solutions was obtained by assessing the SSP problem
in terms of ECOST and SAIDI reduction during fault contingencies The placement
of sectionalising switches results in a reduction of 60 in ECOST and 7148 in
SAIDI
The thesis also proposes a strategy for assessing the DNR problems if the
distribution network operator (DNO) desires to know all possible optimal solutions
for all the multiple conflicting objectives simultaneously This formulates the DNR
problem within a multi-objective formulation in the Pareto optimal framework In
Chapter 8 The MOACO and AIS-ACO algorithms were used for assessing this
problem in terms of loss reduction and reliability improvement Both algorithms
have obtained the same Pareto optimal solutions but the AIS-ACO algorithm
performs better in comparison with the MOACO algorithm in terms of computation
time Feeder loss maximum node voltage deviation and feeder load balancing were
simultaneous optimised in Chapter 9 A set of non-dominated solutions with high
quality and great diversity was obtained This set of solutions represent different
trade-offs among the objective functions And the corner non-dominated solutions
which represent the minimum value of each objective function are presented in the
Pareto front chart For IEEE 69-bus system compared to the base case the network
reconfiguration and DG allocation result in a reduction of 6721 in minimum loss
solution If improving the voltage profiles is the principle objective the best solution
represents a 5388 improvement of this index If balancing feeder load is the main
objective this index decreases by 5174 By varying the weighting factors for the
Chapter 10 Conclusion amp Future Work
Page | 193
parameters the decision makers can select the best compromise among the three
objectives for implementation depending on the utilitiesrsquo priorities
102 Future Work
Based on the findings of this project the suggestions for future work are
In this thesis the transformers have the same characteristics In the future as the
cost of replacing an existing transformer with a new one is cheaper than
replacing both transformers the situation that two transformers with different
characteristics in a substation is not uncommon Therefore an optimisation
method for two transformers with different characteristics will be investigated
and four operation modes can occur
1) First transformer operates alone
2) Second transformer operates alone
3) Two transformers operate in parallel
4) Optimisation mode optimum selection of the transformers needed to
supply each feeder
At present in the UK customers pay for losses in the network In this thesis the
losses are analysed as a whole without allocating them to the users in the network
In the future a loss allocation scheme to customers in the distribution network
will be developed However after reconfiguration the total network loss is
reduced but the loss allocation to some customers may increase The customers
with more loss allocated will be dissatisfied with the network reconfiguration It
is therefore important to change the tariff structure for these customers so that
they are not obliged to pay more for the increase in loss allocation as a result of
network reconfiguration
In this thesis the maximum number of objectives to be optimised simultaneously
is three However the work could be extended to solve the DA problem with
more than three objectives These objectives may include balancing load on
transformers minimising the number of switch operations and maximising the
load on feeders
Chapter 10 Conclusion amp Future Work
Page | 194
The optimal DNR DG allocation TEO and SSP will be combined together to
solve the multi-objective optimisation problem The proposed methodologies
could be tested in large-scale practical systems
In this thesis the evaluation of reliability indices only considers the faults in the
line sections And all the feeders are supposed to have the same parameters and
hence the same failure rates However historical data shows the failure rates of a
feeder vary with geographical location and the weather Therefore different
types of feeders and seasonal varying data of feeder section failure rates will be
considered in future work Moreover the impacts of contingencies on the system
such as faults in the transformers and protective devices could also be considered
The integration of large number of electric vehicles (EVs) into the distribution
network places an extra burden on the electricity grid such as increases in energy
loss overloading in feeders decrease in reliability and power quality Therefore
network reconfiguration techniques and smart charging strategies will be
proposed to moderate the charging effects of EVs In addition the vehicle-to-grid
(V2G) technique which returns electricity to the gird will also be studied The
bi-directional of EVs in the network can provide power to improve load
balancing by ldquovalley fillingrdquo (charging) and ldquopeak shavingrdquo (discharging) [118]
The simulation results show ACO-based algorithms could find a set of good
solutions within a reasonable computation time The ACO control parameters are
set experimentally using information from several trial runs More work is
needed to improve the performance of the proposed algorithms by determining
the optimum set of parameter values It is expected that new ACO-based
algorithms will outperform any existing ones or at worst match their results
In the future a multi-objective stochastic optimal flow problem with the
consideration of load DG EV uncertainties will be addressed The load DG
and EV models are obtained by using a Monte Carlo probabilistic power flow
The objectives are then optimised by using a suitable metaheuristic technique
Page | 195
References
[1] L M Faulkenberry Electrical power distribution and transmission Pearson
Education India 1996
[2] Parliamentary Office of Science and Technology ldquoUK Electricity Networksrdquo
2001
[3] R Das et al ldquoDistribution automation strategies evolution of technologies
and the business caserdquo IEEE Trans Smart Grid vol 6 no 4 pp 2166ndash2175
2015
[4] P Balakrishna K Rajagopal and K S Swarup ldquoApplication benefits of
Distribution Automation and AMI systems convergence methodology for
distribution power restoration analysisrdquo Sustain Energy Grids Networks vol
2 pp 15ndash22 2015
[5] ofgem ldquoEnergy Efficiency Directive An assessment of the energy efficiency
potential of Great Britainrsquos gas and electricity infrastructurerdquo 2015
[6] R C Dugan M F McGranaghan and H W Beaty ldquoElectrical power
systems qualityrdquo 1996
[7] British Standards Institution DECC UK Office for National Statistic and
Met Office UK ldquoVoltage characteristics of electricity supplied by public
distribution systemsrdquo Whether and Climate change no December pp 1ndash18
2010
[8] Y F Niu Z Y Gao and W H K Lam ldquoEvaluating the reliability of a
stochastic distribution network in terms of minimal cutsrdquo Transp Res Part E
Logist Transp Rev vol 100 pp 75ndash97 2017
[9] R Billinton and J E Billinton ldquoDistribution system reliability indicesrdquo
IEEE Trans Power Deliv vol 4 no 1 pp 561ndash568 1989
[10] Ofgem ldquoElectricity Distribution Annual Report for 2010-11rdquo 2012
[11] J Hamachi K Eto ldquoUnderstanding the Cost of Power Interruption to US
Electric Consumers LBNL-55718rdquo 2004
[12] R M Vitorino H M Jorge and L P Neves ldquoLoss and reliability
optimization for power distribution system operationrdquo Elsevier BV 2013
[13] E M Carreno R Romero and A Padilha-Feltrin ldquoAn efficient codification
to solve distribution network reconfiguration for loss reduction problemrdquo
IEEE Trans Power Syst vol 23 no 4 pp 1542ndash1551 2008
[14] A Y Abdelaziz R A Osama and S M El-Khodary ldquoReconfiguration of
distribution systems for loss reduction using the hyper-cube ant colony
optimisation algorithmrdquo IET Gener Transm Distrib vol 6 no 2 p 176
References
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2012
[15] European commission ldquoRoadmap for moving to a low-carbon economy in
2050rdquo DG Clim Action portal pp 1ndash2 2011
[16] A Mohamed Imran M Kowsalya and D P Kothari ldquoA novel integration
technique for optimal network reconfiguration and distributed generation
placement in power distribution networksrdquo Int J Electr Power Energy Syst
vol 63 pp 461ndash472 2014
[17] W Guan Y Tan H Zhang and J Song ldquoDistribution system feeder
reconfiguration considering different model of DG sourcesrdquo Int J Electr
Power Energy Syst vol 68 pp 210ndash221 2015
[18] S A Yin and C N Lu ldquoDistribution feeder scheduling considering variable
load profile and outage costsrdquo IEEE Trans Power Syst vol 24 no 2 pp
652ndash660 2009
[19] I Richardson M Thomson D Infield and C Clifford ldquoDomestic electricity
use A high-resolution energy demand modelrdquo Energy Build vol 42 no 10
pp 1878ndash1887 2010
[20] K Deb A Pratap S Agarwal and T Meyarivan ldquoA fast and elitist
multiobjective genetic algorithm NSGA-IIrdquo IEEE Trans Evol Comput vol
6 no 2 pp 182ndash197 2002
[21] M E Elkhatib R El Shatshat and M M A Salama ldquoDecentralized reactive
power control for advanced distribution automation systemsrdquo IEEE Trans
Smart Grid vol 3 no 3 pp 1482ndash1490 2012
[22] C-L Su and J-H Teng ldquoOutage costs quantification for benefitndashcost
analysis of distribution automation systemsrdquo Int J Electr Power Energy
Syst vol 29 no 10 pp 767ndash774 2007
[23] I Goroohi Sardou M Banejad R Hooshmand and a Dastfan ldquoModified
shuffled frog leaping algorithm for optimal switch placement in distribution
automation system using a multi-objective fuzzy approachrdquo IET Gener
Transm Distrib vol 6 no 6 p 493 2012
[24] C L Smallwood and J Wennermark ldquoBenefits of distribution automationrdquo
IEEE Ind Appl Mag vol 16 no 1 pp 65ndash73 2010
[25] T Goumlnen Electric power distribution system engineering McGraw-Hill New
York 1986
[26] V Madani et al ldquoDistribution automation strategies challenges and
opportunities in a changing landscaperdquo IEEE Trans Smart Grid vol 6 no 4
pp 2157ndash2165 2015
[27] J J Burke ldquoPower distribution engineering fundamentals and applicationsrdquo
1994
[28] A Elmitwally E Gouda and S Eladawy ldquoRestoring recloser-fuse
coordination by optimal fault current limiters planning in DG-integrated
References
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distribution systemsrdquo Int J Electr Power Energy Syst vol 77 pp 9ndash18
2016
[29] L He J R Mayor R G Harley H Liles G Zhang and Y Deng ldquoMulti-
physics modeling of the dynamic response of a circuit breaker recloser
Systemrdquo in IEEE International Electric Machines amp Dirves Conference 2013
vol 1 pp 1001ndash1008
[30] J M Gers and E J Holmes Protection of electricity distribution networks
vol 47 The Institution of Electrical Engineers 2004
[31] E-J-A Zehra M Moghavvemi M M I Hashim and M Kashem ldquoNetwork
reconfiguration using PSAT for loss reduction in distribution systemsrdquo in 1st
International Conference on Energy Power and Control (EPC-IQ) 2010 pp
62ndash66
[32] J J S Grainger W D J J Grainger and W D Stevenson Power system
analysis McGraw-Hill New York 1994
[33] R D Laramore An introduction to electrical machines and transformers
Wiley 1990
[34] D Borge-Diez A Colmenar-Santos M Castro-Gil and J Carpio-Ibaacutentildeez
ldquoParallel distribution transformer loss reductions A proposed method and
experimental validationrdquo Int J Electr Power Energy Syst vol 49 no 1 pp
170ndash180 2013
[35] Y Wang and hui chao Liu ldquoThe information system for economic operation
of transformer based on ASPrdquo in Intertational Power Engineering
Conference 2007 pp 1914ndash1917
[36] X Chen and Z Guo ldquoEconomic operation of power transformer based on real
time parameter checkingrdquo in Power Engineering Society General Meeting
2006 pp 4ndash6
[37] W Yuan and Y Zhang ldquoEconomic operation of transformers in the area
power network based on real-time analysis and controlrdquo in China
International Conference on Electricity Distribution 2008 pp 1ndash5
[38] R Song and X Zhang ldquoThe application research of load smoothing algorithm
in the transformer economic operationrdquo in International Conference on
Energy and Environment Technology 2009 vol 2 pp 328ndash331
[39] C Mamane ldquoTransformer loss evaluation user-manufacturer
communicationsrdquo IEEE Trans Ind Appl vol IA-20 no 1 pp 11ndash15 1984
[40] E I Amoiralis M A Tsili and A G Kladas ldquoEconomic evaluation of
transformer selection in electrical power systemsrdquo in 19th International
Conference on Electrical Machines 2010 pp 1ndash5
[41] B Suechoey J Ekburanawat N Kraisnachinda S Banjongjit C Chompoo
and M Kando ldquoAn analysis and selection of distribution transformer for
losses reductionrdquo in IEEE Power Engineering Society Winter Meeting 2000
pp 2290ndash2293
References
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[42] B Suechoey S Bunjongjit and M Kando ldquoThe result analysis of economic
distribution transformer design in Thailandrdquo in Transmission and Distribution
Conference and Exhibition 2002 pp 1820ndash1823
[43] A Merlin and H Back ldquoSearch for a minimal-loss operating spanning tree
configuration in an urban power distribution systemrdquo in Proc 5th Power
System Computation Conf 1975 pp 1ndash18
[44] S Civanlar J J Grainger H Yin and S S H Lee ldquoDistribution feeder
reconfiguration for loss reductionrdquo IEEE Trans Power Deliv vol 3 no 3
pp 1217ndash1223 1988
[45] M-R Andervazh J Olamaei and M-R Haghifam ldquoAdaptive multi-
objective distribution network reconfiguration using multi-objective discrete
particles swarm optimisation algorithm and graph theoryrdquo IET Gener Transm
Distrib vol 7 no 12 pp 1367ndash1382 2013
[46] K Nara A Shiose M Kitagawa and T Ishihara ldquoImplementation of genetic
algorithm for distribution systems loss minimum re-configurationrdquo IEEE
Trans Power Syst vol 7 no 3 pp 1044ndash1051 1992
[47] J Z Zhu ldquoOptimal reconfiguration of electrical distribution network using
the refined genetic algorithmrdquo Electr Power Syst Res vol 62 no 1 pp 37ndash
42 2002
[48] B Enacheanu B Raison R Caire O Devaux W Bienia and N HadjSaid
ldquoRadial network reconfiguration using genetic algorithm based on the matroid
theoryrdquo IEEE Trans Power Syst vol 23 no 1 pp 186ndash195 2008
[49] J C Cebrian and N Kagan ldquoReconfiguration of distribution networks to
minimize loss and disruption costs using genetic algorithmsrdquo Electr Power
Syst Res vol 80 no 1 pp 53ndash62 2010
[50] H D Chiang and R Jean-Jumeau ldquoOptimal network reconfigurations in
distribution systems part 1 A new formulation and a solution methodologyrdquo
IEEE Trans Power Deliv vol 5 no 4 pp 1902ndash1909 1990
[51] Y J Jeon J C Kim and J O Kim ldquoAn efficient simulted annealing
algorithm for network reconfiguration in large-scale distribution systemsrdquo
IEEE Trans Power Deliv vol 17 no 4 pp 1070ndash1078 2002
[52] H Mori and Y Ogita ldquoA parallel tabu search based method for
reconfigurations of distribution systemsrdquo in Power Engineering Society
Summer Meeting 2000 pp 73ndash78
[53] D Zhang Z Fu and L Zhang ldquoAn improved TS algorithm for loss-
minimum reconfiguration in large-scale distribution systemsrdquo Electr Power
Syst Res vol 77 no 5ndash6 pp 685ndash694 2007
[54] A Y Abdelaziz F M Mohamed S F Mekhamer and M A L Badr
ldquoDistribution system reconfiguration using a modified Tabu Search algorithmrdquo
Electr Power Syst Res vol 80 no 8 pp 943ndash953 2010
[55] A Y Abdelaziz F M Mohammed S F Mekhamer and M A L Badr
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ldquoDistribution systems reconfiguration using a modified particle swarm
optimization algorithmrdquo Electr Power Syst Res vol 79 no 11 pp 1521ndash
1530 2009
[56] A Skoonpong and S Sirisumrannukul ldquoNetwork reconfiguration for
reliability worth enhancement in distribution systems by simulated annealingrdquo
5th Int Conf Electr Eng Comput Telecommun Inf Technol ECTI-CON pp
937ndash940 2008
[57] S Elsaiah M Benidris and J Mitra ldquoReliability improvement of power
distribution system through feeder reconfigurationrdquo in 13th International
Conference on Probabilistic Methods Applied to Power Systems 2014
[58] A Kavousi-Fard and T Niknam ldquoOptimal distribution feeder reconfiguration
for reliability improvement considering uncertaintyrdquo IEEE Trans Power
Deliv vol 29 no 3 pp 1344ndash1353 2014
[59] S Ghasemi ldquoBalanced and unbalanced distribution networks reconfiguration
considering reliability indicesrdquo Ain Shams Eng J 2015
[60] A Saffar R Hooshmand and A Khodabakhshian ldquoA new fuzzy optimal
reconfiguration of distribution systems for loss reduction and load balancing
using ant colony search-based algorithmrdquo Appl Soft Comput J vol 11 no 5
pp 4021ndash4028 2011
[61] D Das ldquoA fuzzy multiobjective approach for network reconfiguration of
distribution systemsrdquo IEEE Trans Power Deliv vol 21 no 1 pp 202ndash209
2006
[62] J E Mendoza E A Loacutepez M E Loacutepez and C A Coello Coello
ldquoMicrogenetic multiobjective reconfiguration algorithm considering power
losses and reliability indices for medium voltage distribution networkrdquo IET
Gener Transm Distrib vol 3 no 9 pp 825ndash840 2009
[63] K M Muttaqi J Aghaei V Ganapathy and A E Nezhad ldquoTechnical
challenges for electric power industries with implementation of distribution
system automation in smart gridsrdquo Renew Sustain Energy Rev vol 46 pp
129ndash142 2015
[64] A Abiri-Jahromi M Fotuhi-Firuzabad M Parvania and M Mosleh
ldquoOptimized sectionalizing switch placement strategy in distribution systemsrdquo
IEEE Trans Power Deliv vol 27 no 1 pp 362ndash370 2012
[65] J Northcote-Green and R G Wilson Control and automation of electrical
power distribution systems vol 28 CRC Press 2006
[66] H Falaghi M R Haghifam and C Singh ldquoAnt colony optimization-based
method for placement of sectionalizing switches in distribution networks
using a fuzzy multiobjective approachrdquo IEEE Trans Power Deliv vol 24
no 1 pp 268ndash276 2009
[67] M Nematollahi and M Tadayon ldquoOptimal sectionalizing switches and DG
placement considering critical system conditionrdquo in 21st Iranian Conference
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on Electrical Engineering 2013 pp 1ndash6
[68] J H Teng and C N Lu ldquoFeeder-switch relocation for customer interruption
cost minimizationrdquo IEEE Trans Power Deliv vol 17 no 1 pp 254ndash259
2002
[69] J H Teng and Y H Liu ldquoA novel ACS-based optimum switch relocation
methodrdquo IEEE Trans Power Syst vol 18 no 1 pp 113ndash120 2003
[70] V Miranda ldquoUsing fuzzy reliability in a decision aid environment for
establishing interconnection and switching location policiesrdquo in CIRED 1991
pp 1ndash6
[71] A Heidari V G Agelidis and M Kia ldquoConsiderations of sectionalizing
switches in distribution networks with distributed generationrdquo IEEE Trans
Power Deliv vol 30 no 3 pp 1401ndash1409 2015
[72] I v Zhezhelenko Y Papaika and others ldquoEstimating economic equivalent of
reactive power in the systems of enterprise electric power supplyrdquo Sci Bull
Natl Min Univ no 5 2016
[73] L Li and R Li ldquoStudy on the analysis software of economic operation of
transformerrdquo Adv Mater Res vol 1008ndash1009 pp 497ndash500 2014
[74] J Shang Z Tan C Zhang and L Ju ldquoThe transformer equipment selectionrsquos
update decision technical and economic analysis modelrdquo in Energy and
Power Engineering 2013 vol 5 no 4 pp 143ndash147
[75] B Amanulla S Chakrabarti and S N Singh ldquoReconfiguration of power
distribution systems considering reliability and power lossrdquo IEEE Trans
Power Deliv vol 27 no 2 pp 918ndash926 2012
[76] R E Brown Electric power distribution reliability CRC press 2008
[77] P Zhou R Y Jin and L W Fan ldquoReliability and economic evaluation of
power system with renewables A reviewrdquo Renew Sustain Energy Rev vol
58 pp 537ndash547 2016
[78] R Billington and R N Allan Reliability evaluation of power systems
Plenum Publishing Corp New York NY 1996
[79] N G Paterakis et al ldquoMulti-objective reconfiguration of radial distribution
systems using reliability indicesrdquo IEEE Trans Power Syst vol 31 no 2 pp
1048ndash1062 2016
[80] B Sultana M W Mustafa U Sultana and A R Bhatti ldquoReview on
reliability improvement and power loss reduction in distribution system via
network reconfigurationrdquo Renew Sustain Energy Rev vol 66 pp 297ndash310
2016
[81] K Xie J Zhou and R Billinton ldquoReliability evaluation algorithm for
complex medium voltage electrical distribution networks based on the shortest
pathrdquo IEE Proceedings-Generation Transm Distrib vol 150 no 6 pp
686ndash690 2003
References
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[82] Z Ghofrani-Jahromi M Kazemi and M Ehsan ldquoDistribution switches
upgrade for loss reduction and reliability improvementrdquo IEEE Trans Power
Deliv vol 30 no 2 pp 684ndash692 2015
[83] P Ngatchou A Zarei and A El-Sharkawi ldquoPareto multi objective
optimizationrdquo in Proceedings of the 13th International Conference on
Intelligent Systems Application to Power Systems 2005 pp 84ndash91
[84] J S Savier and D Das ldquoImpact of network reconfiguration on loss allocation
of radial distribution systemsrdquo IEEE Trans Power Deliv vol 22 no 4 pp
2473ndash2480 2007
[85] T T Nguyen T T Nguyen A V Truong Q T Nguyen and T A Phung
ldquoMulti-objective electric distribution network reconfiguration solution using
runner-root algorithmrdquo Appl Soft Comput J vol 52 pp 93ndash108 2017
[86] N Gupta A Swarnkar R C Bansal and K R Niazi ldquoMulti-objective
reconfiguration of distribution systems using adaptive genetic algorithm in
fuzzy frameworkrdquo IET Gener Transm Distrib vol 4 no 12 pp 1288ndash1298
2010
[87] M R Narimani A Azizi Vahed R Azizipanah-Abarghooee and M
Javidsharifi ldquoEnhanced gravitational search algorithm for multi-objective
distribution feeder reconfiguration considering reliability loss and operational
costrdquo IET Gener Transm Distrib vol 8 no 1 pp 55ndash69 2014
[88] A Ahuja S Das and A Pahwa ldquoAn AIS-ACO hybrid approach for multi-
objective distribution system reconfigurationrdquo IEEE Trans Power Syst vol
22 no 3 pp 1101ndash1111 2007
[89] M Rostami A Kavousi-Fard and T Niknam ldquoExpected cost minimization
of smart grids with plug-in hybrid electric vehicles using optimal distribution
feeder reconfigurationrdquo Ind Informatics IEEE Trans vol 11 no 2 pp
388ndash397 2015
[90] S Oh J Kim S Kwon and S Chung ldquoMonte Carlo simulation of
phytosanitary irradiation treatment for mangosteen using MRI-based
geometryrdquo vol 39 no 3 pp 205ndash214 2014
[91] N HadjSaid and J C Sabonnadiere Electrical Distribution Networks
London ISTE Ltd 2011
[92] Y Li ldquoVoltage balancing on three-phase low voltage feederrdquo The Univerisity
of Manchester 2015
[93] K Bell and P R Allan ldquoComputation of the Value of Securityrdquo 1999
[94] M Dorigo V Maniezzo and A Colorni ldquoThe ant systems optimization by a
colony of cooperative agentsrdquo IEEE Trans Syst Man Cybern B vol 26 no
1 pp 1ndash13 1996
[95] M Dorigo and L M Gambardella ldquoAnt colony system a cooperative
learning approach to the traveling salesman problemrdquo IEEE Trans Evol
Comput vol 1 no 1 pp 53ndash66 1997
References
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[96] M Lopez-Ibanez and T Stuetzle ldquoThe automatic design of multiobjective ant
colony optimization algorithmsrdquo IEEE Trans Evol Comput vol 16 no 6
pp 861ndash875 2012
[97] L Charles Daniel and S Ravichandran ldquoDistribution network reconfiguration
for loss reduction using ant colony system algorithmrdquo in IEEE Indicon 2005
Conference 2005 pp 1ndash4
[98] J F Goacutemez et al ldquoAnt colony system algorithm for the planning of primary
distribution circuitsrdquo IEEE Trans Power Syst vol 19 no 2 pp 996ndash1004
2004
[99] J Lu N Wang J Chen and F Su ldquoCooperative path planning for multiple
UCAVs using an AIS-ACO hybrid approachrdquo Proc 2011 Int Conf Electron
Mech Eng Inf Technol EMEIT 2011 vol 8 no 2 pp 4301ndash4305 2011
[100] J E Hunt and D E Cooke ldquoAn adaptive distributed learning system based
on the immune systemrdquo 1995 IEEE Int Conf Syst Man Cybern Intell Syst
21st Century vol 3 pp 2494ndash2499 1995
[101] C A C Coello and N C Cortes ldquoSolving multiobjective optimization
problems using an artificial immune systemrdquo Genet Program Evolvable
Mach vol 6 no 2 pp 163ndash190 2005
[102] L N De Castro and F J Von Zuben ldquoLearning and optimization using the
clonal selection principlerdquo IEEE Trans Evol Comput vol 6 no 3 pp 239ndash
251 2002
[103] Office for National Statistics Population and household estimates for the
United Kingdom UK 2011
[104] S Ingram S Probert and K Jackson ldquoThe impact of small scale embedded
generation on the operating parameters of distribution networksrdquo Department
of Trade and Industry (DTI) 2003 [Online] Available
httpwebarchivenationalarchivesgovuk20100919182407httpwwwensg
govukassets22_01_2004_phase1b_report_v10b_web_site_finalpdf
[105] 63 EDS 02-0027 Engineering design standard EDS 02-007 11 kV Triplex
Cable 2012
[106] TTH ldquo75 MVA-33-11 KV-GTP TTHrdquo 2014 [Online] Available
httpwwwtranstechtransformerscompdf75mva3311kvgtptth24012008pdf
[107] A M Tahboub V R Pandi and H H Zeineldin ldquoDistribution system
reconfiguration for annual energy loss reduction considering variable
distributed generation profilesrdquo IEEE Trans Power Deliv vol 30 no 4 pp
1677ndash1685 2015
[108] M E Baran and F F Wu ldquoNetwork reconfiguration in distribution systems
for loss reduction and load balancingrdquo Power Deliv IEEE Trans vol 4 no
2 pp 1401ndash1407 1989
[109] D Shirmohammadi and H W Hong ldquoReconfiguration of electric distribution
networks for resistive line losses reductionrdquo IEEE Trans Power Deliv vol 4
References
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no 2 pp 1492ndash1498 1989
[110] R S Rao K Ravindra K Satish and S V L Narasimham ldquoPower loss
minimization in distribution system using network reconfiguration in the
presence of distributed generationrdquo IEEE Trans Power Syst vol 28 no 1
pp 1ndash9 2012
[111] D Sudha Rani N Subrahmanyam and M Sydulu ldquoMulti-objective invasive
weed optimization - an application to optimal network reconfiguration in
radial distribution systemsrdquo Int J Electr Power Energy Syst vol 73 pp
932ndash942 2015
[112] R L Haupt and S E Haupt Practical genetic algorithms John Wiley amp
Sons 2004
[113] X S Yang and S Deb ldquoCuckoo search via Levy flightsrdquo 2009 World Congr
Nat Biol Inspired Comput NABIC 2009 - Proc pp 210ndash214 2009
[114] R N Allan R Billinton I Sjarief L Goel and K S So ldquoA reliability test
system for educational purposes-basic distribution system data and resultsrdquo
IEEE Trans Power Syst vol 6 no 2 pp 813ndash820 1991
[115] G Li and X-P Zhang ldquoModeling of plug-in hybrid electric vehicle charging
demand in probabilistic power flow calculationsrdquo Smart Grid IEEE Trans
vol 3 no 1 pp 492ndash499 2012
[116] UK Department for Transport ldquoNational Travel Survey England 2013 -
Statistical Releaserdquo no July p 26 2014
[117] A Mazza G Chicco and A Russo ldquoOptimal multi-objective distribution
system reconfiguration with multi criteria decision making-based solution
ranking and enhanced genetic operatorsrdquo Int J Electr Power Energy Syst
vol 54 pp 255ndash267 2014
[118] E Sortomme and M A El-Sharkawi ldquoOptimal charging strategies for
unidirectional vehicle-to-gridrdquo IEEE Trans Smart Grid vol 2 no 1 pp
119ndash126 2011
Page | 204
APPENDIX A Network Model Data
A1 UK generic distribution network
The line parameters given here is related to the single line diagram of the network
shown in Fig 45 which are used in the simulation study in Section 451 and 452
Table A-1 Typical configurations and parameters of 11 kV triplex cables in the UK
11 kV line type Cross
Sectional
Area
(CSA)
Positive sequence
Z
Zero-phase
sequence
Z
Approximate
Capacitance
C
Id Configuration Rph Xph R0 X0 C
(mm2) (Ωkm) (μFkm)
A Nexans
635011000
Volt Triplex
Cable
185 0415 0112 0988 0236 036
B 95 0220 0012 0530 0102 028
Appendix A Network Data
Page | 205
A2 33-bus system
Table A-2 Line and load data of 33-bus system
Branch
number
Sending end
node
Receiving end
node
R
(Ω)
X
(Ω)
P at receiving
end (kW)
Q at receiving
end (kVAr)
1 0 1 00922 0047 100 60
2 1 2 04930 02511 90 40
3 2 3 03660 01864 120 80
4 3 4 03811 01941 60 30
5 4 5 08190 07070 60 20
6 5 6 01872 06188 200 100
7 6 7 07114 02351 200 100
8 7 8 10300 07400 60 20
9 8 9 10440 07400 60 20
10 9 10 01966 00650 45 30
11 10 11 03744 01238 60 35
12 11 12 14680 11550 60 35
13 12 13 05416 07129 120 80
14 13 14 05910 05260 60 10
15 14 15 07463 05450 60 20
16 15 16 12890 17210 60 20
17 16 17 03720 05740 90 40
18 17 18 01640 01565 90 40
19 18 19 15042 13554 90 40
20 19 20 04095 04784 90 40
21 20 21 07089 09373 90 40
22 21 22 04512 03083 90 50
23 22 23 08980 07091 420 200
24 23 24 08960 07011 420 200
25 24 25 02030 01034 60 25
26 25 26 02842 01447 60 25
27 26 27 10590 09337 60 20
28 27 28 08042 07006 120 70
29 28 29 05075 02585 200 600
30 29 30 09744 09630 150 70
31 30 31 03105 03619 210 100
32 31 32 03410 05362 60 40
33 7 20 2 2 -- --
34 11 21 2 2 -- --
35 8 14 2 2 -- --
36 17 32 05 05 -- --
37 24 28 05 05 -- --
Appendix A Network Data
Page | 206
A3 69-bus system
Table A-3 Line and load data of 69-bus system
Branch
number
Sending end
node
Receiving end
node
R
(Ω)
X
(Ω)
P at receiving
end (kW)
Q at receiving
end (kVAr)
1 0 1 00005 00012 0 0
2 1 2 00005 00012 0 0
3 2 3 00015 00036 0 0
4 3 4 00251 00294 0 0
5 4 5 0366 01864 26 22
6 5 6 0381 01941 404 30
7 6 7 00922 0047 75 54
8 7 8 00493 00251 30 22
9 8 9 0819 02707 28 19
10 9 10 01872 00619 145 104
11 10 11 07114 02351 145 104
12 11 12 103 034 8 5
13 12 13 1044 0345 8 55
14 13 14 1058 03496 0 0
15 14 15 01966 0065 455 30
16 15 16 03744 01238 60 35
17 16 17 00047 00016 60 35
18 17 18 03276 01083 0 0
19 18 19 02106 0069 1 06
20 19 20 03416 01129 114 81
21 20 21 0014 00046 5 35
22 21 22 01591 00526 0 0
23 22 23 03463 01145 28 20
24 23 24 07488 02475 0 0
25 24 25 03089 01021 14 10
26 25 26 01732 00572 14 10
27 26 27 00044 00108 26 186
28 27 28 0064 01565 26 186
29 28 29 03978 01315 0 0
30 29 30 00702 00232 0 0
31 30 31 0351 0116 0 0
32 31 32 0839 02816 14 10
33 32 33 1708 05646 195 14
34 33 34 1474 04873 6 4
35 34 35 00044 00108 26 1855
36 35 36 0064 01565 26 1855
37 36 37 01053 0123 0 0
38 37 38 00304 00355 24 17
39 38 39 00018 00021 24 17
40 39 40 07283 08509 12 1
41 40 41 031 03623 0 0
Appendix A Network Data
Page | 207
42 41 42 0041 00478 6 43
43 42 43 00092 00116 0 0
44 43 44 01089 01373 3922 263
45 44 45 00009 00012 3922 263
46 45 46 00034 00084 0 0
47 46 47 00851 02083 79 564
48 47 48 02898 07091 3847 2745
49 48 49 00822 02011 3847 2745
50 49 50 00928 00473 405 283
51 50 51 03319 01114 36 27
52 51 52 0174 00886 435 35
53 52 53 0203 01034 264 19
54 53 54 02842 01447 24 172
55 54 55 02813 01433 0 0
56 55 56 159 05337 0 0
57 56 57 07837 0263 0 0
58 57 58 03042 01006 100 72
59 58 59 03861 01172 0 0
60 59 60 05075 02585 1244 888
61 60 61 00974 00496 32 23
62 61 62 0145 00738 0 0
63 62 63 07105 03619 227 162
64 63 64 1041 05302 59 42
65 64 65 02012 00611 18 13
66 65 66 00047 00014 18 13
67 66 67 07394 02444 28 20
68 67 68 00047 00016 28 20
69 49 58 2 1 -- --
70 26 64 1 05 -- --
71 12 20 05 05 -- --
72 10 42 05 05 -- --
73 14 45 1 05 -- --
A4 RBTS Bus 4 system
Table A-4 Feeder data of RBTS Bus 4
Feeder
Type
Length
(km)
Feeder section number
1 060 2 6 10 14 17 21 25 28 30 34 38 41 43 46 49 51 55 58 61 64 67
68 69 70 71
2 075 1 4 7 9 12 16 19 22 24 27 29 32 3537 40 42 45 48 50 53 56 60
63 65
3 080 3 5 8 11 13 15 18 20 23 26 31 33 36 3944 47 52 54 57 59 62 66
Appendix A Network Data
Page | 208
Table A-5 Reliability Data for RBTS Bus 4
Equipment λA λP λM λt R RM
Lines 004 0 0 0 5 0
Buses 0001 0 1 001 2 8
Switches 0004 0002 1 006 4 72
Distribution Transformers 0015 0 1 0 200 120
λA Active failure rate in (fryrkm) for lines and (fryr) for other components
λP Passive failure rate in (fryrkm) for lines and (fryr) for other components
λM Maintenance outage rate in (fryrkm) for lines and (fryr) for other components
λP Transient failure rate in (fryrkm) for lines and (fryr) for other components
R Repair time of failures in (hr)
RM Maintenance outage time in (hr)
Page | 209
APPENDIX B Simulation Results
B1 Simulation results of Chapter 4
B11Tie-switch location
As discussed in Section 452 the location of tie-switch in Scenario 9 is changeable
and the relevant results are presented in Table B-1 It can be clearly seen that the
NOP is located in lsquoTW1rsquo between 0730 and 1000 1600 and 1630 while in lsquoTW5rsquo
for the rest of the day
Table B-1 The locations of tie-switch in Scenario 9
Time Loc Time Loc Time Loc Time Loc Time Loc Time Loc
0000 TW5 0400 TW5 0800 TW1 1200 TW5 1600 TW1 2000 TW5
0010 TW5 0410 TW5 0810 TW1 1210 TW5 1610 TW1 2010 TW5
0020 TW5 0420 TW5 0820 TW1 1220 TW5 1620 TW1 2020 TW5
0030 TW5 0430 TW5 0830 TW1 1230 TW5 1630 TW1 2030 TW5
0040 TW5 0440 TW5 0840 TW1 1240 TW5 1640 TW5 2040 TW5
0050 TW5 0450 TW5 0850 TW1 1250 TW5 1650 TW5 2050 TW5
0100 TW5 0500 TW5 0900 TW1 1300 TW5 1700 TW5 2100 TW5
0110 TW5 0510 TW5 0910 TW1 1310 TW5 1710 TW5 2110 TW5
0120 TW5 0520 TW5 0920 TW1 1320 TW5 1720 TW5 2120 TW5
0130 TW5 0530 TW5 0930 TW1 1330 TW5 1730 TW5 2130 TW5
0140 TW5 0540 TW5 0940 TW1 1340 TW5 1740 TW5 2140 TW5
0150 TW5 0550 TW5 0950 TW1 1350 TW5 1750 TW5 2150 TW5
0200 TW5 0600 TW5 1000 TW1 1400 TW5 1800 TW5 2200 TW5
0210 TW5 0610 TW5 1010 TW5 1410 TW5 1810 TW5 2210 TW5
0220 TW5 0620 TW5 1020 TW5 1420 TW5 1820 TW5 2220 TW5
0230 TW5 0630 TW5 1030 TW5 1430 TW5 1830 TW5 2230 TW5
0240 TW5 0640 TW5 1040 TW5 1440 TW5 1840 TW5 2240 TW5
0250 TW5 0650 TW5 1050 TW5 1450 TW5 1850 TW5 2250 TW5
0300 TW5 0700 TW5 1100 TW5 1500 TW5 1900 TW5 2300 TW5
0310 TW5 0710 TW5 1110 TW5 1510 TW5 1910 TW5 2310 TW5
0320 TW5 0720 TW5 1120 TW5 1520 TW5 1920 TW5 2320 TW5
0330 TW5 0730 TW1 1130 TW5 1530 TW5 1930 TW5 2330 TW5
0340 TW5 0740 TW1 1140 TW5 1540 TW5 1940 TW5 2340 TW5
0350 TW5 0750 TW1 1150 TW5 1550 TW5 1950 TW5 2350 TW5
Appendix B Simulation Results
Page | 210
B12 Voltage variations
For Test Case 2 in Section 452 the detailed voltage values of the mean and the
corresponding 95th
profiles at each node in the linked feeder are recorded in Table
B-2 and Table B-3
Table B-2 Mean voltage profiles at each node in the linked feeder
Node
No
Scenarios
S1 S2 S3 S4 S5 S6 S7 S8 S9
A4_1 09675 09787 09787 09766 09859 09859 09748 09825 09815
A4_2 09676 09784 09784 09766 09856 09856 09748 09822 09813
A4_3 09677 09782 09782 09767 09854 09854 09749 09819 09811
A4_4 09678 09780 09780 09768 09851 09851 09750 09817 09810
A4_5 09681 09777 09777 09771 09849 09849 09753 09814 09808
A4_6 09685 09775 09775 09775 09846 09846 09757 09812 09807
A4_7 09689 09773 09773 09779 09845 09845 09762 09811 09807
A4_8 09694 09772 09772 09784 09844 09844 09767 09810 09807
B4_8 09700 09772 09772 09790 09844 09844 09773 09810 09808
B4_7 09707 09773 09773 09797 09845 09845 09779 09811 09810
B4_6 09714 09775 09775 09804 09846 09846 09787 09812 09813
B4_5 09722 09777 09777 09813 09849 09849 09795 09814 09816
B4_4 09731 09780 09780 09821 09851 09851 09804 09817 09820
B4_3 09737 09782 09782 09827 09854 09854 09809 09819 09823
B4_2 09743 09784 09784 09833 09856 09856 09815 09822 09826
B4_1 09749 09787 09787 09839 09859 09859 09821 09825 09830
Table B-3 95th
voltage profiles at each node in the linked feeder
Node
No
Scenarios
S1 S2 S3 S4 S5 S6 S7 S8 S9
A4_1 09352 09573 09573 09537 09721 09721 09537 09721 09715
A4_2 09353 09567 09567 09537 09715 09715 09537 09715 09709
A4_3 09355 09562 09562 09539 09711 09711 09539 09711 09704
A4_4 09357 09558 09558 09541 09707 09707 09541 09707 09702
A4_5 09363 09553 09553 09547 09701 09701 09547 09701 09679
A4_6 09370 09548 09548 09555 09697 09697 09555 09697 09694
A4_7 09379 09545 09545 09563 09694 09694 09563 09794 09691
A4_8 09389 09544 09544 09573 09692 09692 09573 09792 09692
B4_8 09400 09544 09544 09585 09692 09692 09585 09792 09692
B4_7 09413 09545 09545 09598 09694 09694 09598 09794 09694
B4_6 09427 09548 09548 09613 09697 09697 09613 09697 09697
B4_5 09443 09553 09553 09628 09701 09701 09628 09701 09701
B4_4 09460 09558 09558 09646 09707 09707 09646 09707 09707
Appendix B Simulation Results
Page | 211
B4_3 09471 09562 09562 09656 09711 09711 09656 09711 09711
B4_2 09482 09567 09567 09668 09715 09715 09668 09715 09715
B4_1 09494 09573 09573 09680 09721 09721 09680 09721 09721
B2 Simulation results of Chapter 5
The network losses in each branch for all test cases of 33-bus system and 69-bus
system are listed in Table B-4 and Table B-5 respectively
Table B-4 Network losses in each branch of 33-bus system
Branch number Feeder loss (kW)
Case I Case II Case III Case IV
1 1227 1189 1010 1003
2 5192 2686 2051 2060
3 1995 756 112 490
4 1874 667 074 415
5 3833 1321 122 807
6 192 006 006 006
7 484 0 0 0
8 418 124 211 124
9 357 0 0 0
10 055 001 001 001
11 088 003 003 003
12 267 045 045 045
13 073 008 008 008
14 036 0 0 0
15 028 045 092 045
16 025 048 115 048
17 003 007 022 007
18 016 226 232 226
19 083 1809 1859 1808
20 01 424 436 423
21 004 118 071 118
22 319 316 914 315
23 516 512 1618 510
24 129 128 869 128
25 26 224 005 124
26 334 285 003 155
27 1133 962 003 510
28 786 664 0 345
29 391 326 199 159
30 160 110 018 003
Appendix B Simulation Results
Page | 212
31 021 012 0 000
32 001 0 013 0
33 0 563 809 563
34 0 215 215 215
35 0 174 320 174
36 0 002 033 002
37 0 0 263 0
Total 20314 13981 11753 10844
Table B-5 Network losses in each branch of 69-bus system
Branch number Feeder loss (kW)
Case I Case II Case III Case IV
1 008 007 006 006
2 008 007 006 006
3 020 012 012 010
4 194 011 011 011
5 2829 159 155 159
6 2939 164 160 164
7 691 035 034 035
8 338 012 012 012
9 477 143 137 142
10 101 029 027 028
11 219 032 030 032
12 128 000 000 000
13 124 000 0 000
14 120 0 000 0
15 022 083 043 083
16 032 138 067 138
17 000 001 001 001
18 010 080 032 080
19 007 052 021 052
20 011 083 033 083
21 000 003 001 002
22 001 022 006 022
23 001 049 013 049
24 001 091 021 091
25 000 037 009 037
26 000 019 004 019
27 000 000 000 000
28 000 000 000 000
29 001 001 001 001
30 000 000 000 000
31 001 001 001 001
Appendix B Simulation Results
Page | 213
32 001 001 001 001
33 001 001 001 001
34 000 000 000 000
35 000 003 001 003
36 001 041 019 041
37 002 064 028 064
38 000 018 008 018
39 000 001 000 001
40 005 391 161 391
41 002 166 068 166
42 000 022 009 022
43 000 005 002 005
44 001 057 023 057
45 000 000 000 000
46 002 017 017 013
47 058 416 416 316
48 164 1321 1321 991
49 012 253 253 178
50 000 000 000 000
51 000 000 000 000
52 580 001 001 001
53 673 001 001 000
54 916 000 000 000
55 882 0 0 0
56 4986 000 000 000
57 2458 000 000 000
58 954 000 000 000
59 1071 627 626 379
60 1408 824 823 498
61 011 0 0 0
62 014 000 000 000
63 066 001 001 001
64 004 071 069 071
65 000 000 000 000
66 000 000 000 000
67 002 002 002 002
68 000 000 000 000
69 0 3783 3782 2384
70 0 102 052 102
71 0 0 0 0
72 0 0 0 0
73 0 423 252 423
Total 22562 9885 8758 7397
Appendix B Simulation Results
Page | 214
B3 Simulation results of Chapter 8
Table B-6 Pareto optimal solutions of multi-objective DNR (loss ECOST and SAIDI)
Tie-switches location Feeder loss (kW) ECOST ($yr) SAIDI
(hrscustomeryr)
70 68 71 69 321415 4640359 130895231648616
70 10 41 54 364131 431068083000 102819629963899
17 10 41 70 354092 411445783000000 105858799638989
17 26 10 70 383269 530285525000000 0968805806257521
7 26 54 69 435225 578907612000000 0825265794223827
7 54 41 69 406035 460067870000000 0915047984356197
7 26 54 70 442913 571756512000000 0836828971119134
17 10 71 70 345231 439663189000000 106361687725632
70 10 71 69 331470 443747189000000 110465057160048
70 10 41 69 340330 415529783000000 109962169073406
70 68 41 69 330274 435818516000000 130392343561974
7 54 71 69 397170 488285276000000 0920076865222623
41 10 54 69 356448 438219183000000 101663312274368
70 10 54 26 393311 549907825000000 0938414109506619
70 7 71 69 381047 465595876000000 100306543321300
70 7 41 17 403678 433294470000000 0957002858002407
70 10 54 71 355269 459285489000000 103322518050542
7 54 71 70 404856 481134176000000 0931640042117930
7 26 17 70 432867 552134212000000 0867220667870036
7 70 41 69 389911 437378470000000 0998036552346570
7 26 69 70 419096 556218212000000 0908254362214200
17 7 71 70 394813 461511876000000 0962031738868833
71 10 54 69 347586 466436589000000 102166200361011
10 26 54 69 385625 557058925000000 0926850932611312
70 26 10 69 369504 534369525000000 100983950060168
7 54 41 70 413721 452916770000000 0926611161251504
Appendix B Simulation Results
Page | 215
B4 Simulation results of Chapter 9
Table B-7 Pareto optimal solutions of multi-objective DNR (loss maximum node voltage deviation
feeder load balancing index) for 33-bus system in Case II
Tie-switches location Feeder loss
(kW)
Maximum node
Voltage deviation
Feeder load
balancing index
7 34 35 31 37 176962 0108696024464801 00228687361961248
7 11 35 32 28 143474 00613272038422790 00305387759787611
7 9 14 31 37 142477 00768537372742428 00252628392269486
6 8 12 36 37 151849 00696765908940439 00259144961258893
7 8 14 31 37 155399 00924077518455773 00239781364880477
6 8 12 31 37 169382 0104485611067200 00236077543160956
6 8 12 32 37 152876 00776641110366926 00250547432924683
33 8 14 30 37 171441 0108063061643879 00230652089068052
7 9 14 32 28 140261 00604355611623940 00310349101268755
7 11 35 32 37 143028 00639069227083702 00273727965037185
6 8 14 31 37 159752 00968913958755809 00236540473688646
6 33 35 32 37 170278 00826562726566354 00249194843739843
6 11 35 32 37 144683 00656445815841987 00261947314082027
6 8 14 32 37 146983 00705648561488426 00256096967694280
7 9 14 32 37 139815 00639015456844128 00280407351785895
6 9 14 32 37 143097 00625183468485540 00270001779728268
7 11 35 31 37 148829 00852978398065017 00245113845932977
7 34 35 30 37 202483 0130888991378581 00223050578905545
6 8 14 36 37 146991 00643933147100736 00266176555168500
6 11 35 31 37 154281 00897759906819439 00242838273201709
6 8 13 32 37 150430 00753226918458818 00253604605496161
Table B-8 Pareto optimal solutions of multi-objective DNR (loss maximum node voltage deviation
feeder load balancing index) for 33-bus system in Case III
Tie-switches location Feeder loss
(kW)
Maximum node
Voltage deviation
Feeder load
balancing index
7 14 8 32 28 121696 00575193535569366 00264544805354717
7 11 35 31 37 123007 00712785797883380 00213250141648472
6 12 8 32 37 128324 00630309398395457 00223824361844486
6 14 8 30 37 145672 0101299721228755 00194921779245086
7 33 35 32 28 130184 00583420082867310 00261406698684195
7 14 8 30 37 140274 00967924815464314 00195001911353607
7 21 35 30 37 164190 0113945920950777 00189031534924873
6 13 8 32 37 126434 00607661484850486 00227035446761735
7 14 9 32 28 117726 00575130414815478 00271215548731366
Appendix B Simulation Results
Page | 216
6 14 8 32 28 125920 00566904604559002 00265195832133384
6 12 8 31 37 137974 00889877482038002 00200083704114662
7 11 35 30 37 133030 00891516445489180 00199682922816912
6 11 35 32 37 123013 00593840879899440 00235298833627789
7 14 9 32 37 121070 00631040005210335 00255168322432724
6 14 9 32 28 123916 00566872316455769 00273594084038335
7 14 9 30 37 126587 00812324184971598 00206873922472966
7 14 9 31 28 117529 00642736861104275 00240537048868074
6 14 9 32 37 122047 00593825021727904 00240927348267257
6 11 35 32 28 124883 00566888115014094 00269082055980326
6 11 35 31 37 126802 00756552348586014 00207586957663036
6 14 8 32 37 124050 00593857418451058 00230337877365745
7 13 8 32 28 124039 00575225874614865 00262247242500743
7 11 35 32 28 119522 00575159230231156 00267430211390231
7 14 9 31 37 118759 00642740886891275 00220228862077971
6 14 8 31 37 130316 00816654599427028 00201908840890301
33 14 8 30 37 140110 00923831702765571 00197570883486903
7 12 8 32 28 125895 00587758838819431 00259864524009700
6 13 8 31 37 134936 00865715938530326 00201790772057552
Table B-9 Pareto optimal solutions of multi-objective DNR (loss maximum node voltage deviation
feeder load balancing index) for 33-bus system in Case IV
Tie-switches location DG location Feeder
loss
(kW)
Maximum node
Voltage deviation
Feeder load
balancing index
7 9 14 30 37 15 17 16 112506 00655990339384582 00207847799664288
6 8 14 31 37 14 11 15 120818 00728143829651942 00199639595336255
7 11 35 30 37 16 16 12 118637 00756705031931788 00198888055963062
6 8 14 31 37 11 29 14 125736 00822955381260978 00194988443664523
6 11 35 32 37 29 11 29 116999 00602917954784902 00213598898907595
7 9 14 31 37 15 14 16 110931 00518306996442978 00223689972435171
7 34 35 30 37 16 13 13 140652 00983575865184194 00182688360250883
7 8 14 30 37 14 11 15 128617 00876913785424229 00190954012999288
7 8 14 30 37 11 16 14 127141 00860397262006276 00191601352391895
7 9 14 36 37 30 30 29 109157 00520335391274761 00229564125698243
7 8 14 30 37 10 14 16 126706 00857230143750372 00192117850059117
7 11 35 30 37 13 16 12 121130 00786215737441328 00196617519208137
7 34 35 30 37 13 10 9 151352 0106960621828031 00178195736666725
7 34 35 30 37 10 12 9 152310 0107688512235453 00178046268710843
6 8 14 30 37 11 15 16 130550 00897068798318073 00189590122249633
6 8 14 30 37 16 14 10 130869 00901533044670202 00189271311922809
7 34 35 30 37 10 13 12 148089 0104837492639545 00178736074180585
Appendix B Simulation Results
Page | 217
7 34 35 30 37 13 11 16 143317 0100615335666250 00181553323058751
6 8 14 30 37 10 14 14 133299 00925968739633617 00188139999335965
7 34 35 30 37 13 9 12 148392 0105013682219175 00178453713901855
6 8 14 30 37 14 11 10 137593 00963962506644021 00186232592604301
6 8 14 30 37 11 8 14 136046 00951731865531927 00187106569470356
6 8 14 30 37 11 11 16 135639 00942616575802945 00187170876179048
7 8 14 30 37 15 16 14 122935 00815907052491111 00195198923102276
7 34 35 30 37 12 14 16 140640 00983915740315128 00182784576692257
6 33 35 31 37 11 11 13 146017 00888852225316270 00188548348595259
7 34 35 30 37 12 16 12 142144 00997534014352579 00181578155086060
6 8 14 30 37 14 11 15 132819 00921338781311946 00188143081376993
6 8 14 30 37 10 15 11 136651 00956093119043262 00186781475357014
7 9 14 31 37 14 14 16 111382 00525319705640723 00222591386298574
7 34 35 30 37 13 14 16 139957 00977014014811679 00183484070331887
7 34 35 30 37 12 15 16 139849 00976123852270839 00183745698300515
7 34 35 30 37 12 16 16 138589 00959671533698319 00184842191427931
7 34 35 30 37 16 13 16 137912 00952795751906571 00185525366651277
6 33 35 31 37 11 11 11 148785 00910856464605774 00187751047204272
7 34 35 30 37 12 16 13 141338 00990484927061306 00181980491991251
7 34 35 30 37 12 13 12 145536 0102926179499332 00179590185768212
6 8 14 30 37 14 10 15 132373 00918145642214576 00188660639598312
6 8 14 30 37 16 11 14 131312 00904718190224125 00188759872087077
7 34 35 30 37 13 15 16 139168 00969230570394858 00184436609617936
7 34 35 30 37 13 9 11 150730 0106620666560267 00178315514588942
6 8 14 30 37 14 11 14 133746 00929165522686308 00187615074100094
7 34 35 30 37 9 9 12 152656 0107867658396772 00178031242058681
6 8 14 30 37 10 11 16 135118 00939381882085281 00187414815201857
7 34 35 30 37 12 12 9 149341 0105739135263959 00178316539838164
7 9 14 36 28 32 32 32 110385 00489797931328652 00256323647901629
7 9 14 36 37 32 31 31 108599 00498935433820196 00235262740306846
7 9 14 32 37 31 30 31 108436 00537552050723257 00227898958267559
7 9 14 36 28 32 31 31 110203 00489682960875768 00259015702487973
7 34 35 30 37 8 12 9 154427 0108962750550623 00178021823053241
Appendix B Simulation Results
Page | 218
Table B-10 Pareto optimal solutions of multi-objective DNR (loss maximum node voltage deviation
feeder load balancing index) for 69-bus system in Case II
Tie-switches location Feeder loss
(kW)
Maximum node
Voltage deviation
Feeder load
balancing index
55 61 71 72 12 99036 00524391619987274 00196366946903149
69 61 71 9 14 145213 00664127006601768 00185315761508749
55 61 71 72 14 98845 00524393494628415 00194882148961848
69 70 71 10 14 145135 00666490251240782 00182871906896542
69 61 71 72 12 150267 00699556148777123 00161708619074924
55 61 71 10 14 104521 00524349487665904 00238104755589364
69 61 71 72 13 150383 00700225094171628 00161512783956020
55 61 71 72 13 98937 00524392488739880 00195710324132613
69 61 71 72 11 150792 00682108082577803 00171029450547815
55 61 71 9 14 105348 00524349082167884 00242117051986541
69 61 71 72 14 150513 00700911373758199 00161129748303495
55 61 71 72 11 105195 00524380932334678 00218572363716938
Table B-11 Pareto optimal solutions of multi-objective DNR (loss maximum node voltage deviation
feeder load balancing index) for 69-bus system in Case III
Tie-switches location Feeder loss
(kW)
Maximum node
Voltage deviation
Feeder load
balancing index
55 61 12 14 9 97461 00523081449765275 00226112450860475
69 61 71 14 9 130761 00662843002557533 00155527078006889
55 61 71 14 7 97263 00523080911134007 00226177446060770
55 61 12 71 72 87588 00523152959484715 00174558059214037
55 61 71 14 8 93176 00523082195004728 00211109499855264
55 61 71 13 72 87581 00523154440245970 00174392153380541
55 61 12 14 72 87755 00523153511186373 00174538759436512
55 61 12 71 7 97289 00523080869366065 00226232791264600
69 61 71 11 9 134009 00662855052002667 00154463391981039
69 61 12 14 9 130989 00662843776081034 00155381836375260
55 61 71 13 7 97273 00523080879708534 00227249951330579
55 61 71 14 9 90907 00523086904216601 00201865894567423
55 61 71 14 10 90291 00523088955157064 00199034032147027
69 61 71 14 10 130894 00665207578684145 00154263271797149
55 61 71 14 72 87582 00523156072908145 00174100597226583
69 61 71 11 10 134197 00665220013747228 00153401360203180
69 61 71 11 72 136858 00680828895070073 00147368269784675
69 61 12 14 10 131126 00665208386694061 00154135530565384
55 61 71 11 72 91274 00523126048676607 00184393848480773
Appendix B Simulation Results
Page | 219
Table B-12 Pareto optimal solutions of multi-objective DNR (loss maximum node voltage deviation
feeder load balancing index) for 69-bus system in Case IV
Tie-switches location DG location Feeder
loss
(kW)
Maximum node
Voltage deviation
Feeder load
balancing index
69 63 71 10 14 60 60 60 105879 00543213716422435 00153740505896722
69 63 12 72 71 60 62 62 109324 00575466375767690 00126779733811642
55 61 71 72 11 60 60 60 80324 00429183191505871 00183159151221229
69 63 12 72 71 61 61 62 109323 00575465740537586 00126842028893447
55 61 71 72 12 60 60 60 74165 00429193759769601 00159264876998350
69 63 14 10 71 62 62 62 106070 00543012249613587 00150279825984642
69 63 11 72 71 60 62 60 110547 00558290844078126 00139841427388105
69 63 14 9 71 62 62 62 106271 00540689205567605 00153025056850459
69 61 71 72 11 60 60 60 108838 00542584369620998 00141625735067141
55 61 71 72 14 60 56 60 75837 00436673338725839 00157367114339890
69 63 14 10 71 62 62 60 105960 00542966739560918 00151430448212008
69 61 71 10 14 60 60 60 104307 00527268149576859 00155323687715422
69 63 11 72 71 61 62 62 110652 00558333983851442 00137892112215884
69 63 13 72 71 62 62 62 109522 00576169823075075 00125440050970194
55 61 71 72 14 60 55 60 75975 00436701836501366 00156758120818947
69 63 71 10 14 60 60 62 105896 00542940500362948 00152768514567046
69 63 14 9 71 62 61 61 106159 00540643102892876 00154245882374843
55 61 71 72 13 60 60 60 74066 00429194617185072 00158554987038681
69 62 71 10 14 61 60 60 105886 00542959390978505 00153513700764165
69 63 14 72 71 62 62 62 109622 00576844280930477 00125002240983144
55 63 71 72 14 62 61 62 74382 00440379610790336 00155858821619573
69 63 71 72 11 60 60 60 110530 00558564471048234 00140822204796308
55 63 71 72 14 60 60 62 74285 00440350644694274 00157371695186626
55 63 14 72 71 62 62 62 74448 00440399072962552 00155438948075735
55 63 71 72 14 60 62 62 74344 00440368353288504 00156312863856681
69 63 71 9 14 60 61 60 105882 00542934725670071 00153515485666183
55 63 71 72 14 60 61 62 74305 00440356668532606 00156816031788752
55 61 20 72 13 60 60 60 80533 00429326269571468 00157463174391893
55 63 71 72 14 61 61 62 74343 00440367927398261 00156346520711234
69 61 71 72 14 60 60 60 107187 00561022028435777 00126909641069497
69 63 71 72 11 60 61 60 110533 00558285040786375 00140595150870697
69 63 12 72 71 62 62 62 109436 00575512407997617 00125707103016452
69 63 14 10 71 61 62 62 106000 00542983427485794 00150838099664421
69 63 11 72 71 60 61 62 110569 00558299818740340 00139149694834405
69 63 14 9 71 61 62 60 106118 00540626433897020 00154840963668230
69 61 71 72 12 60 60 60 107041 00559693311798567 00127785892138089
55 61 71 72 14 60 60 60 73974 00429195606297569 00157682511572302
69 63 14 10 71 61 61 62 105958 00542966109653011 00151492343922130
69 63 12 72 71 62 62 61 109365 00575483243249972 00126225992147273
Appendix B Simulation Results
Page | 220
69 63 11 72 71 62 62 60 110611 00558317226735644 00138490567525274
69 63 14 9 71 62 62 61 106201 00540660395254129 00153587525958041
69 63 14 10 71 61 60 62 105917 00542949434469265 00152083287358888
69 63 14 9 71 62 62 60 106160 00540643732226493 00154184014811756
69 63 11 72 71 61 61 62 110610 00558316590719640 00138552654427231
69 63 71 72 11 62 62 62 110723 00558362979744786 00137328015545176
69 61 71 72 13 60 60 60 107108 00560349171634668 00127435051911921
Page | 221
APPENDIX C Control Parameters of
Algorithms
C1 Control parameters of ACO algorithm in Chapter 5
Table C-1 ACO parameters for distribution network reconfiguration and DG allocation in Test Case
2amp3
Parameter Value
Number of ants 50
Maximum number of iteration 200
Pheromone evaporation rate 120530 03
Higher bound of pheromone level 120533119846119834119857 1
Lower bound of pheromone level 120533119846119842119847 001
Constant accumulation number 120533119836 0002
Table C-2 ACO parameters for distribution network reconfiguration and DG allocation in Test Case 4
Parameter Value
Number of ants 100
Maximum number of iteration 500
Pheromone evaporation rate 120530 03
Higher bound of pheromone level 120533119846119834119857 1
Lower bound of pheromone level 120533119846119842119847 001
Constant accumulation number 120533119836 0002
C2 Control parameters of ACO algorithm in Chapter 6
Table C-3 ACO parameters for distribution network reconfiguration and transformer economic
operation
Parameter Value
Number of ants 150
Maximum number of iteration 500
Pheromone evaporation rate 120530 03
Higher bound of pheromone level 120533119846119834119857 1
Lower bound of pheromone level 120533119846119842119847 001
Constant accumulation number 120533119836 0002
Appendix C Control Parameters of Algorithms
Page | 222
C3 Control parameters of ACO algorithm in Chapter 7
Table C-4 ACO parameters for sectionalising switch placement in Test Case 1
Parameter Value
Number of ants 400
Maximum number of iteration 400
Pheromone evaporation rate 120530 04
Higher bound of pheromone level 120533119846119834119857 1
Lower bound of pheromone level 120533119846119842119847 001
Constant accumulation number 120533119836 0002
Table C-5 ACO parameters for sectionalising switch placement in Test Case 2amp3
Parameter Value
Number of ants 500
Maximum number of iteration 200
Pheromone evaporation rate 120530 01
Higher bound of pheromone level 120533119846119834119857 1
Lower bound of pheromone level 120533119846119842119847 001
Constant accumulation number 120533119836 0002
C4 Control parameters of MOACO and AIS-ACO algorithm in
Chapter 8
Table C-6 MOACO parameters for multi-objective distribution network reconfiguration (loss
ECOST and SAIDI)
Parameter Value
Number of ants 100
Maximum number of iteration 100
Pheromone evaporation rate 120530 01
Higher bound of pheromone level 120533119846119834119857 1
Lower bound of pheromone level 120533119846119842119847 001
Constant accumulation number 120533119836 0002
Appendix C Control Parameters of Algorithms
Page | 223
Table C-7 AIS-ACO parameters for multi-objective distribution network reconfiguration (loss
ECOST and SAIDI)
Parameter Value
Maximum number of iteration 50
Pheromone evaporation rate 120530 01
Higher bound of pheromone level 120533119846119834119857 1
Lower bound of pheromone level 120533119846119842119847 001
Constant accumulation number 120533119836 0002
C5 Control parameters of ACO and AIS-ACO algorithm in
Chapter 9
Table C-8 ACO parameters for multi-objective DNR (loss maximum node voltage deviation feeder
load balancing index)
Parameter Value
Number of ants 200
Maximum number of iteration 800
Pheromone evaporation rate 120530 03
Higher bound of pheromone level 120533119846119834119857 1
Lower bound of pheromone level 120533119846119842119847 001
Constant accumulation number 120533119836 0002
Table C-9 AIS-ACO parameters for multi-objective DNR (loss maximum node voltage deviation
feeder load balancing index)
Parameter Value
Maximum number of iteration 3000
Pheromone evaporation rate 120530 01
Higher bound of pheromone level 120533119846119834119857 1
Lower bound of pheromone level 120533119846119842119847 001
Constant accumulation number 120533119836 0002
Page | 224
APPENDIX D List of Publications
1 B Zhang and P A Crossley ldquoMinimum transformer losses based on transformer
economic operation and optimized tie-switches placementrdquo in Proceedings of the 6th
International Conference on Advanced Power System Automation and Protection
(APAP) pp 1-7 20-25 September 2015
2 B Zhang and P A Crossley ldquoReliability improvement using ant colony
optimization applied to placement of sectionalizing switchesrdquo in Proceedings of the
9th
International Conference on Applied Energy (ICAE) pp 1-7 21-24 August 2017
3 B Zhang and P A Crossley ldquoMinimization of distribution network loss using
ant colony optimization applied to transformer economic operation and relocation of
tie-switchesrdquo to be submitted to IEEE Transactions on Smart Grid
4 B Zhang and PA Crossley ldquoOptimized sectionalising switch placement for
reliability improvement in distribution systemsrdquo to be submitted to IEEE
Transactions on Power Delivery
5 B Zhang and P A Crossley ldquoAn ant colony optimization ndashbased method for
multi-objective distribution system reconfigurationrdquo in Proceedings of the 14th
International Conference on Developments in Power System Protection (DPSP) pp
1-6 12-15 March 2018