Monitor Placement for Estimation of Voltage Sags in Power ...

Monitor Placement for Estimation

of Voltage Sags in Power Systems

A thesis submitted to The University of Manchester for the degree of

Doctor of Philosophy

in the Faculty of Engineering and Physical Sciences

2012

José Manuel Avendaño Mora, M. Sc.

School of Electrical and Electronic Engineering

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Contents

Abstract ................................................................................................................... 10

Declaration ................................................................................................................... 11

Copyright Statement .......................................................................................................... 12

Acknowledgments ............................................................................................................. 13

Chapter 1 Introduction .............................................................................................. 15

1.1 Power Quality ............................................................................................ 15

1.2 Voltage sags ............................................................................................... 16

1.2.1 Causes and Characteristics ......................................................................... 17

1.2.2 Consequences ............................................................................................. 20

1.2.3 Indices ........................................................................................................ 21

1.2.4 Monitoring ................................................................................................. 23

1.3 Literature review ........................................................................................ 24

1.3.1 Monitor Placement for Sag Performance Assessment ............................... 24

1.3.2 Sag Performance Estimation ...................................................................... 30

1.3.3 Voltage Sag State Estimation .................................................................... 33

1.3.4 Summary .................................................................................................... 36

1.4 Aims of Research ....................................................................................... 36

1.5 Major Contributions of the Research ......................................................... 37

1.6 Overview of the Thesis .............................................................................. 38

Chapter 2 Modeling and Simulation Tools .............................................................. 40

2.1 Simulation Tools for Voltage Sag Studies ................................................. 40

2.2 Modeling of System Components .............................................................. 42

2.2.1 Cables and Lines ........................................................................................ 42

2.2.2 Generators .................................................................................................. 43

2.2.3 Loads .......................................................................................................... 44

2.2.4 Transformers .............................................................................................. 44

2.3 Bus Impedance Matrix ............................................................................... 47

2.4 Fault Calculation Based on System Impedance Matrix ............................. 50

2.4.1 Three-Phase Faults ..................................................................................... 54

2.4.2 Single Line-to-Ground Faults .................................................................... 55

2.4.3 Line-to-Line Faults .................................................................................... 57

2.4.4 Line-to-Line-to-Ground Faults .................................................................. 58

2.5 Voltage Sag Assessment Software ............................................................ 60

2.6 Test Systems .............................................................................................. 60

2.6.1 10-bus Power System ................................................................................. 60

2.6.2 IEEE Reliability Test System .................................................................... 61

2.6.3 IEEE 118-bus Power Flow Test Case ........................................................ 62

2.6.4 Generic Distribution System ...................................................................... 62

2.7 Summary .................................................................................................... 63

Chapter 3 Optimal Monitor Placement for Voltage Sag Characterization .......... 65

3.1 Monitor Reach Area Method ..................................................................... 65

3.1.1 Formulation of the Optimization Problem ................................................. 68

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3.1.2 Voltage Sag Estimation at Non-Monitored Buses ..................................... 68

3.1.3 Factors Influencing Accuracy of Voltage Sag Detection .......................... 69

3.1.4 Variability in Number of Optimally Placed Monitors ............................... 72

3.2 Enhanced Fault Location Algorithm .......................................................... 75

3.2.1 Fault Location of Three-phase Symmetrical Faults ................................... 75

3.2.2 Fault Location of Line to Line Faults ........................................................ 78

3.2.3 Fault Location of Line to Ground Faults ................................................... 80

3.2.4 Fault Location of Line to Line to Ground Faults ....................................... 80

3.3 Enhanced Monitor Reach Area Algorithm ................................................ 83

3.4 Enhancement of Sag Estimation Accuracy with EMRAA ........................ 85

3.5 Summary .................................................................................................... 88

Chapter 4 Generalized Formulation of the Optimal Monitor Placement Problem

for Fault Location .................................................................................... 89

4.1 Optimal Monitor Placement for Fault Location ........................................ 90

4.2 Generalized Formulation of the Optimal Monitor Placement Problem ..... 93

4.2.1 Definition of new variables ........................................................................ 93

4.2.2 Reduction of Number of Constraints ......................................................... 95

4.2.3 Problem Formulation ................................................................................. 96

4.2.4 Application in the 4-bus Sample System ................................................... 97

4.3 Application in Large Power Networks ...................................................... 97

4.3.1 10-bus 500 kV Power Network ................................................................. 98

4.3.2 IEEE 24-bus Reliability Test System (RTS) ........................................... 100

4.3.3 IEEE 118-bus Test System ...................................................................... 101

4.4 Summary .................................................................................................. 104

Chapter 5 Heuristic Approach for Determining Optimal Monitor Placement for

Voltage Sag Estimation ......................................................................... 105

5.1 Review of Proposed Formulation of Optimal Monitor Placement for Fault

Location ................................................................................................... 106

5.2 The Greedy Search Algorithm ................................................................. 107

5.2.1 Set-Covering Problem .............................................................................. 107

5.2.2 The Greedy Algorithm ............................................................................. 108

5.2.3 Application of the Greedy Algorithm to the Optimal Monitor Placement

Problem .................................................................................................... 109

5.3 Greedy Monitor Placement with Custom Objective Functions ............... 111

5.3.1 Observability Weight Factors .................................................................. 112

5.3.2 Sag Magnitude Estimation Error ............................................................. 116

5.3.3 Sag Event Estimation Error ..................................................................... 122

5.4 Summary .................................................................................................. 130

Chapter 6 Techno-Economic Assessment of Voltage Sags Using Optimal

Monitoring Programs ............................................................................ 131

6.1 Hybrid Methodology for Monitoring and Estimation of Voltage Sags ... 132

6.1.1 Selection of Most Probable Fault Location ............................................. 132

6.1.2 Hybrid Monitor Placement Method ......................................................... 137

6.1.3 Simplified Voltage Sag Estimation .......................................................... 138

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6.2 Case Study 1: Assessment of Voltage Sag Events .................................. 138

6.2.1 Size of Monitoring Programs ................................................................... 139

6.2.2 Sag Event Estimation ............................................................................... 139

6.3 Risk-Based Assessment of Financial Losses due to Voltage Sags .......... 142

6.4 Case Study 2: Assessment of Financial Losses Caused by Voltage Sags 143

6.4.1 Conventional and Optimal Monitoring Schemes ..................................... 143

6.4.2 Assessment of Financial Losses .............................................................. 144

6.5 Summary .................................................................................................. 150

Chapter 7 Conclusions and Future Work.............................................................. 151

7.1 Conclusions .............................................................................................. 151

7.2 Future Work ............................................................................................. 154

Chapter 8 References ............................................................................................... 156

Appendix A Network Data of Test Systems .............................................................. 167

Appendix B Minimization of SMEE by greedy monitor placement ....................... 183

Appendix C Minimization of SEEE by greedy monitor placement ........................ 188

Appendix D Distribution of SNPV from 1000 trials for all customers’ plants at

different locations .................................................................................. 193

Appendix E Distribution of SNPV from 1000 trials at all locations for different

types of customer plants ........................................................................ 201

Appendix F List of Publications ................................................................................. 210

Final word count: 40,101

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List of Figures

Figure 1-1 Basic procedure to evaluate voltage sags, modified from [2] ..................... 17

Figure 1-2 Origin of voltage sags. ................................................................................ 18

Figure 1-3 Measured voltage sag due to a short circuit fault, voltage in three phases in

time domain (reproduced from [1])................................................................................. 19

Figure 1-4 Rms voltages for the sag shown in Figure 1-3 (reproduced from [1]). ....... 19

Figure 1-5 Sag duration as a function of the voltage threshold for the three phases of

the sag shown in Figure 1-3 (reproduced from [1]). ....................................................... 19

Figure 1-6 Types of voltage sags in phasor-diagram form. .......................................... 20

Figure 2-1 Lumped parameters model of cables and lines. .......................................... 43

Figure 2-2 Model of generators..................................................................................... 44

Figure 2-3 Constant impedance load model. ................................................................ 44

Figure 2-4 Transformer representation, (a) equivalent circuit with an ideal transformer

and (b) equivalent circuit with magnetizing current neglected (adopted from [83]). ..... 45

Figure 2-5 Zero-sequence equivalent circuits of five three-phase transformer banks and

their respective symbols and connection diagrams (adopted form [83]). ....................... 46

Figure 2-6 Equivalent circuit for tap changing transformer (adopted from [85]). ........ 47

Figure 2-7 Single line diagram of a three-phase system (a), the three sequence

networks of the system (b-d), and the Thévenin equivalent circuit of each network for a

fault at point P , identified as bus k (e-g) (adopted from [83]). ..................................... 51

Figure 2-8 Three-phase fault through fault impedance fZ , (a) symbolic representation

and (b) connection of the Thévenin equivalent circuit (adopted from [83]). .................. 55

Figure 2-9 Single line-to-ground fault through fault impedance fZ , (a) symbolic

representation and (b) connection of the Thévenin equivalent circuits (adopted from

[83]). ................................................................................................................................ 56

Figure 2-10 Line-to-line fault with fault impedance fZ , (a) symbolic representation

and (b) connection of the Thévenin equivalent circuits (adopted from [83]). ................ 58

Figure 2-11 Double line-to-ground fault with fault impedance fZ , (a) symbolic

representation and (b) connection of the Thévenin equivalent circuits (adopted from

[83]). ................................................................................................................................ 60

Figure 2-12 A sample 10-bus network. ........................................................................ 61

Figure 2-13 IEEE Reliability Test System (RTS). ........................................................ 61

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Figure 2-14 IEEE 118-bus power flow test case. .......................................................... 62

Figure 2-15 Single line diagram of the generic distribution system (GDS). ................ 64

Figure 3-1 Symbolic representation of three monitor reach areas for bus 9 of the IEEE-

RTS. ................................................................................................................................ 66

Figure 3-2 Illustrative power system. ........................................................................... 67

Figure 3-3 Voltage sag magnitude at monitored buses (3, 6, 8, and 17) and bus 5 (one

of the ends of faulted line) as a function of fault impedance. ......................................... 70

Figure 3-4 Voltage sag magnitude at monitored buses (3, 6, 8, and 17) and bus 5 (one

of the ends of faulted line) as a function of fault distance. ............................................. 71

Figure 3-5 Voltage sag magnitude at monitored buses as a function of pre-fault

voltage. ............................................................................................................................ 71

Figure 3-6 Number of voltage sags with a residual voltage of 90% or less (SARFI90).

......................................................................................................................................... 87


......................................................................................................................................... 87


......................................................................................................................................... 88

Figure 4-1 Flowchart for generating constrains for fault point F1 (adopted from [53]).

......................................................................................................................................... 91

Figure 4-2 Sample 4-bus system. .................................................................................. 91

Figure 4-3 Line segments (length is labeled) of the system used in [53] where faults

cannot be uniquely located with 2 monitors. .................................................................. 98

Figure 4-4 Observable lines by monitors installed at buses 7 and 8 in the IEEE-RTS.

....................................................................................................................................... 101

Figure 4-5 Optimal monitoring locations that lead to full fault observability of the

IEEE 118-bus system. ................................................................................................... 103

Figure 5-1 Illustration of set-covering problem. ......................................................... 108

Figure 5-2 Flowchart of the greedy approximation algorithm. ................................... 109

Figure 5-3 Flowchart for implementing the weighted greedy algorithm. ................... 113

Figure 5-4 Buses (red numbered) designated by greedy monitor placement algorithms

as optimal locations for voltage measurement devices. ................................................ 115

Figure 5-5 Flowchart detailing the process of building an optimal sag monitoring

program (OSMP) aimed at minimizing the sag magnitude estimation error (SMEE). . 118

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Figure 5-6 Proportions of the GDS network where line to ground faults can be located

by the ordered addition of voltage measurement devices. ............................................ 120

Figure 5-7 Sag Magnitude Estimation Error (SMEE) obtained during each iteration of

the greedy monitor placement procedure. ..................................................................... 121

Figure 5-8 Increase in network’s coverage of different types of faults obtained during

each iteration of the greedy monitor placement procedure. .......................................... 122

Figure 5-9 No Damage Region of the ITIC Curve. .................................................... 125

Figure 5-10 GDS network’s voltage sag profile. ........................................................ 126

Figure 5-11 SEMI F47 Curve – required semiconductor equipment voltage sag

immunity (adopted from [117]). ................................................................................... 127

Figure 6-1 Difference between calculated and real phase residual voltages of line to

line to ground faults on the IEEE-RTS. ........................................................................ 135

Figure 6-2 Difference between calculated and real magnitude of sags caused by line to

line and three-phase faults not correctly localized using the residual voltages from bus

12. .................................................................................................................................. 136

Figure 6-3 Monitoring schemes and customer’s plant locations in the generic

distribution system. Engineering monitoring sites are indicated through color squares

with Roman numerals and uppercase letters; optimal monitoring locations (25) are

numbered with color circles; the eight plant locations analyzed are symbolized and

represented with minuscule letters. ............................................................................... 146

Figure 6-4 Distribution of SNPV from 1000 trials for all customers’ plants at location

h estimated using all monitoring schemes. ................................................................... 147

Figure 6-5 Distribution of SNPV from 1000 trials for a semiconductor factory at all

locations (a-h) estimated using all monitoring schemes. .............................................. 149

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List of Tables

Table 1-1 Transformation of sag type to lower voltage levels (adopted from [1]) ....... 19

Table 1-2 Impact of sag characteristics on equipment immunity (adopted from [19] .. 20

Table 1-3 Economic consequences of voltage sags (adopted from [12]) ..................... 21

Table 1-4 Voltage sag table recommended by IEC 61000-2-8 and range of SARFI80

index ................................................................................................................................ 23

Table 1-5 Number of monitors at different voltage levels in current European

monitoring systems (adopted from [35]) ........................................................................ 27

Table 2-1 Voltage sag calculation methodology (adopted from [11]) .......................... 41

Table 2-2 Overview of voltage sag studies (adopted from [11]) .................................. 42

Table 2-3 Number and characteristics of generic distribution system components ...... 63

Table 3-1 Number of Voltage Measurement Devices Required to Record Voltage Sags

in the GDS ....................................................................................................................... 72

Table 3-2 Number of Voltage Measurement Devices Required for Full Sag-

Observability of the GDS Network Using the MRA Method ......................................... 74

Table 3-3 Number of Fault Location Estimates Determined Using Original MRA

Method and Enhanced MRA Algorithm (EMRAA) ....................................................... 84

Table 3-4 Inputs Randomly Generated During Monte Carlo Simulation (1000 trials)

and their Corresponding Probability Distributions ......................................................... 86

Table 4-1 Single monitors and pairs of monitors required to locate fault α .................. 92

Table 4-2 Compliance of monitoring solutions of the sample system of 4-bus system

(Figure 4-2) with generic linear constraints .................................................................... 97

Table 4-3 Optimal monitoring programs obtained with original and proposed

formulations for the sample system of Figure 4-3 .......................................................... 99

Table 4-4 Fault location estimates [from-bus, to-bus, mile] using voltage at buses 1, 3,

and 6 of the sample system of Figure 4-3 ....................................................................... 99

Table 4-5 Optimal pairs of monitor locations required for full observability of LL,

LLG and LLL faults in the IEEE 118-bus test system .................................................. 102

Table 4-6 Optimal monitor program to locate LG faults in the IEEE 118-bus test

system ............................................................................................................................ 103

Table 4-7 Optimal monitoring programs for locating all types of fault in the IEEE 118-

bus test system. (Complement to monitors fixed at buses 39, 41, 67, 84, 88, 93, 95, 97,

and 117) ......................................................................................................................... 104

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Table 5-1 Number of Voltage Measurement Devices Required for Sag Detection in the

GDS Network ................................................................................................................ 110

Table 5-2 Number of Voltage Measurement Devices Required for Full Fault Location

Observability of the IEEE 118-bus Network ................................................................ 111

Table 5-3 Number of Voltage Measurement Devices Obtained by Three Different

Methods ......................................................................................................................... 114

Table 5-4 Monitor Placement for Fault Location in the 118-bus Network Utilizing

Greedy Algorithms ........................................................................................................ 115

Table 5-5 Minimum Number of Monitors Required for Fault Location in the 295-bus

GDS Network ................................................................................................................ 116

Table 5-6 Sag Magnitude Estimation Error of Each Phase for Line to Ground Faults

Occurring in the GDS Network..................................................................................... 119

Table 5-7 EN 50160 classification of voltage sags according to residual voltage and

duration (adopted from [112]) ....................................................................................... 123

Table 5-8 Fault clearing times in the GDS network ................................................... 124

Table 5-9 SARFI indices for three voltage levels in the GDS network ...................... 127

Table 5-10 Minimization of the Overall Sag Event Estimation Error in the GDS

Network with Greedy Monitor Placement .................................................................... 129

Table 6-1 Percentiles of the Absolute Values of the Imaginary Parts of Fault Location

Estimates ....................................................................................................................... 133

Table 6-2 Fault Location Estimates for a Line to Line to Ground Fault at 0.3636 on

Line 14 of the IEEE-RTS and the Corresponding Residual Voltages at Bus 12 .......... 134

Table 6-3 Ratio between Negative-Sequence and Zero-Sequence Residual Voltages at

Bus 12 for the Fault Location Estimates of Table 6-2 .................................................. 135

Table 6-4 Number of Voltage Measurement Devices Required for Distinct Functions

in the 295-bus GDS ....................................................................................................... 139

Table 6-5 System Fault Statistics (adopted from [90]) ............................................... 140

Table 6-6 Probability of Occurrence of Loading Profiles (adopted from [80]) .......... 140

Table 6-7 Difference between Estimated and Actual Number of Sag Events ............ 141

Table 6-8 Customer Plant Characteristics, adopted from [120] .................................. 144

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Abstract

Title: Monitor Placement for Estimation of Voltage Sags in Power Systems

Mr. José Manuel Avendaño Mora, The University of Manchester, July 5th

2012.

Power quality related problems cause large financial losses in the order of billions

worldwide. The evaluation process aimed at determining effective remedial actions

starts with the correct identification and characterization of power quality disturbances.

Measurements performed in the electrical power network and the corresponding

collection and process of data are the primary method of characterization of the

phenomena. The ideal deployment of monitoring devices would entail a monitor

installed at each node of the network so that the power quality throughout the system

could be directly assessed. In reality, however, technical and mostly economical

constraints limit the number of monitors a network operator can install in the system.

Power quality at non-monitored sites, therefore, has to be estimated by extrapolating the

data from monitored sites. Consequently, it is crucial to identify the sites that provide

the most accurate picture of the system’s overall power quality. Unfortunately, no

recommended practices or guidelines for determining the minimum number and the best

locations for optimal power quality monitoring have been prescribed in standards or

reports. This thesis investigates voltage sag monitoring as part of a larger power quality

monitoring scheme. The aim is to develop a methodology for optimal monitor

placement for fault location and sag estimation. The thesis, divided in four main parts,

focuses on network sag performance estimation and optimal monitor placement for fault

localization and sag estimation. The introductory part of the thesis gives an overview of

power quality surveys conducted around the world in recent years with special emphasis

on the monitor placement criteria used. It also summarizes the main methods for

network sag performance estimation proposed to date. The main part of the thesis firstly

reviews the most referred optimal monitor placement method for sag estimation

proposed in academia, highlighting its limitations. Then a robust fault location

algorithm is proposed to enhance this method and overcome the identified limitations.

The enhanced method is thereafter used as the basis for the generalization of one of the

leading methods for optimal monitor placement for fault location in the second part of

the thesis. The formulation of its optimization problem is extended for application in

large power networks by adapting the modeling approach for the sag monitor placement

problem. To reduce the high computational and memory burden associated with finding

the optimal fault location monitor program, the thesis introduces a less memory

intensive heuristic search algorithm in the third part of the thesis. A series of custom

objective functions are proposed to be used with this algorithm to find optimal fault

location and sag monitoring programs aimed at estimating the most critical events for

customers. In the final part of the thesis, the main concepts and techniques introduced in

the first three sections are combined to develop a synergistic approach to optimal

monitor placement for sag characterization based on fault location. The suitability of the

new method for techno-economic assessment of voltage sags using strategically or

conventionally deployed monitors is established.

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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.

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Copyright Statement

i. The author of this thesis (including any appendices and/or schedules to this

thesis) owns certain copyright or related rights in it (the “Copyright”) and s/he

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, trade marks and other

intellectual property (the “Intellectual Property”) and any reproductions of

copyright works in the thesis, for example graphs and tables (“Reproductions”),

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 and/or Reproductions.

iv. Further information on the conditions under which disclosure, publication and

commercialisation of this thesis, the Copyright and any Intellectual Property

and/or Reproductions described in it may take place is available in the

University IP Policy (see http://documents.manchester.ac.uk/DocuInfo.aspx?

DocID=487), in any relevant Thesis restriction declarations deposited in the

University Library, The University Library‟s regulations (see

http://www.manchester.ac.uk/library/aboutus/regulations) and in The

University‟s policy on Presentation of Theses.

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Acknowledgments

Firstly, I would like to acknowledge the financial support provided by the National

Council on Science and Technology (CONACYT), México, without which my research

and this thesis would not have been possible.

My deepest gratitude and recognition goes to my supervisor Prof. Jovica V. Milanović

for his expert technical guidance and encouragement throughout this process. He has

been a very special mentor and an inspiration to pursue professional excellence.

I would like to extend my appreciation to all my friends and colleagues of the Electrical

Energy and Power Systems research group for providing an excellent academic and

social environment for enjoying research. In particular, I wish to thank Mr. Alejandro

Martínez for his continuous help and advice on the issues faced in the research. Special

thanks to Mr. Nick Woolley, our collaboration was very productive and helpful for my

research. Many thanks to Mr. Muhammad Ali for his endless willingness to discuss and

help with my research problems. Special thanks must also go to Mr. Robin Preece who

has selflessly given up countless hours to discuss the research and correct my English.

The help provided by Dr. Jhan Yhee Chan throughout the research and particularly for

the last chapter of the thesis is very much appreciated.

I am very grateful to Dr. Miguel A. Ortega Vázquez and Dr. Ricardo Rubio Barros who

became my true friends and teachers during my time in Manchester.

I would also like to express my gratitude to Dr. Luis (Nando) Ochoa and Dr. Joseph

Mutale for their invaluable comments and discussions, which have contributed to the

enhancement of the work embodied in this thesis.

Lastly, but certainly not least, I am especially appreciative for the crucial mental and

moral support throughout the period of this research of my dear girlfriend, Maria

Kiousi. Σ’ ευχαριστώ πολύ αγάπη μου!

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A mis padres,

Sandra Leticia Mora Robles y José Manuel Avendaño Reyes,

por su infinito amor e incondicional apoyo durante mi

intenso proceso educativo.

A mis abuelos,

Aurora Reyes de Avendaño, Ana Rosa Robles de Mora (†),

José Trinidad Mora Guzmán (†) y Manuel Edgar Avendaño

Sumano (†), cuyas vidas me han inspirado a la búsqueda

constante y permanente por ser un mejor ser humano.

(To my parents,

Sandra Leticia Mora Robles and José Manuel Avendaño

Reyes, for their endless love and unconditional support

during my intense educational process.

To my grandparents,

Aurora Reyes de Avendaño, Ana Rosa Robles de Mora (†),

José Trinidad Mora Guzmán (†) and Manuel Edgar

Avendaño Sumano (†), whose lives have inspired me in my

constant and permanent quest to be a better human being.)

Chapter 1 • Introduction

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Chapter 1

Introduction

1.1 Power Quality

Power quality is the characteristic property that stems from the combination of voltage

quality and current quality. Voltage quality describes the significant deviation of the

actual voltage from a sine wave of statutory frequency and magnitude, whereas current

quality depicts the same for the current. Power quality related issues are of the most

concern for customers, and therefore a power quality problem is any unbalance or

deviation in frequency, current, or voltage that causes customer equipment to fail or

misoperate. The economic impact of power quality problems is the primary reason for

interest in power quality [1, 2].

The interest in power quality has increased from the early 1970’s mainly because the

economic losses from power quality phenomena have also risen steadily. Recent studies

estimate the annual power quality related losses at billions of funds for the European

Union and United States alone [3-5]. The key reason behind the rise in costs has been

the proliferation of electronic and power electronic equipment. Modern converter-driven

equipment (from consumer electronics and computers, up to adjustable-speed drives)

has become much more sensitive to voltage disturbances than their older

electromechanical counterparts and, paradoxically, it is a source of voltage disturbances

itself.

Other factors have contributed to the increase in engagement in power quality as well.

Notable among them are the growing need to agree on adequate standards that clearly

define performance criteria (especially in a deregulated electric industry), the higher

expectations of customers that see electricity as a rightful commodity that must be of

premium quality, and the advancement of monitoring technologies that enable obtaining

a very accurate picture of the power quality performance.


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The terms power quality phenomenon and power quality disturbance are synonyms of

deviations of the ideal voltage or current from their quasi-ideal waveforms. Power

quality phenomena can be broadly classified into two big groups: variations and events.

Current and voltage variations are moderate deviations of voltage or current from their

nominal or ideal values. Typical examples include variations in current magnitude,

voltage frequency, and voltage magnitude, harmonic current distortion, and harmonic

voltage distortion. Power quality events in contrast, are significant deviations of voltage

or current from their nominal or ideal wave shapes. Interruptions, undervoltages,

overvoltages, and fast voltage events (transients) are the most common events. The

characterization of both power quality events and variations requires monitoring of

current and or voltage signals.

Short-duration undervoltages known as voltage dips or voltage sags are generally

believed to be the most pressing power quality problem. It is the extensive disruption of

industrial processes caused by these disturbances and the corresponding economic

losses which have led to this view [4, 6-8]. This thesis focuses on the monitoring of

voltage sags.

1.2 Voltage sags

A voltage sag or dip is a decrease in root mean square (rms) voltage at the power

frequency for a duration of between half a cycle to one minute [9]. This reduction of the

rms value of the ac voltage is below a specified dip threshold and followed by its

recovery after a brief interval [10]. Several comprehensive power quality surveys

conducted as early as the 1970’s have reported the incidence of voltage sags to be close

to 65% of all recorded power quality phenomena [11]. Electrical equipment in

commercial and industrial facilities, like adjustable speed-drives, computers, contactors,

process-control equipment and relays, is often disrupted by voltage sags. The cost of

each of these disruptions has been estimated as high as €6 million/hour for the financial

sector and €3.8 million per disturbance for a semiconductor factory [12]. It can be seen

therefore that voltage sags are one of the most common and also most costly power

quality problems.

A general procedure to evaluate many power quality problems including voltage sags is

shown in Figure 1-1 [2]. Measurements are essential to characterize the problem at hand

or the overall power quality performance of the system. A range of potential solutions


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has to be identified at all levels of the system from utility supply to end-use sensitive

equipment. Possible solutions are then evaluated in terms of technical feasibility and

those considered viable are compared on an economic basis to determine the optimal

solution. Figure 1-1 highlights the stage of the power quality evaluation framework in

which this dissertation is concentrated, i.e., measurement/data collection, along with the

major considerations that must be addressed in this step; namely causes, characteristics,

consequences, and indices. All of these are described in the next section with the

emphasis on voltage sags.

Figure 1-1 Basic procedure to evaluate voltage sags, modified from [2]

1.2.1 Causes and Characteristics

Voltage sags are caused by increases in current magnitude mostly happening elsewhere

in the system, as illustrated in Figure 1-2, where a voltage drop occurs at the point of

common coupling (PCC) between the customer and the source of the increase in

current. The main causes for a temporary increase of current are short circuit faults,

starting of induction motors, and energizing of transformers. However, the majority of

power quality literature has focused on voltage sags induced by faults since these sags

lead to most of the equipment malfunctions. In this dissertation too, only sags caused by

faults have been considered.

Voltage magnitude

variation

Voltage sags Interruptions TransientsHarmonic

distortion

Measurements/data collection

Causes and characteristics

Consequences

Utility

transmission

system

Utility

distribution

system

End-use

customer

interface

End-use

customer

system

Equipment

design/

specifications

Modeling/analysis procedures Evaluate technical alternatives

Evaluate economics of possible solutions

Identify problem category

Problem characterization

Identify range of solutions

Evaluate solutions

Optimum solution

Power Quality Problem Evaluation

Indices


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Figure 1-2 Origin of voltage sags.

The only two sag characteristics defined by IEC 61000-4-30 [13] are residual voltage

and duration. The residual voltage is the lowest rms voltage measured once per cycle in

any of the voltage channels during the event. A voltage channel can be one, two, or

three phase-to-phase, phase-to-neutral or phase-to-ground voltages. The duration is the

time during which the one-cycle rms voltage at any voltage channel is below a voltage

dip (sag) threshold. Although it is not prescribed in the standard the most common

voltage sag threshold is 90% of the nominal voltage.

An example of a voltage sag caused by a fault at 132 kV and measured at 11 kV is

illustrated in Figure 1-3 to Figure 1-5. Figure 1-3 shows the voltage waveforms for the

three phases with voltages in per unit. The rms voltage versus time for the sag is plotted

in Figure 1-4 showing the residual voltage of the event and its duration for a threshold

of 90%. Figure 1-5 plots the duration as a function of the threshold, for the three phases.

Since the residual voltage in one of the phases is 88% any voltage threshold setting

below 88% results in duration of zero cycles for that phase. The sag duration for the

other two phases is approximately 4 cycles using a voltage threshold of 90%.

Residual voltage and duration are the most widely used characteristics to describe

voltage sags but not the only ones. Other characteristics like phase-angle jump, point on

wave, sag energy and three-phase characteristics have been introduced in the literature

to complement the description of load behavior during voltage sags [14]. The phase-

angle jump is the difference in voltage phase angle between the pre-sag voltage and the

voltage during the sag. The point-on-wave of sag initiation and point-on-wave of

voltage recovery are used to identify more accurately the phase angle at which the

voltage sag starts and the phase angle at which the voltage recovers, respectively. The

voltage sag-energy is a measure of the non-delivered energy to an impedance load that

merges both residual voltage and duration.

Transmission system

Customer experiencing

voltage sag

Short circuit faults

Starting of induction motors

Energizing of transformersIncrease

in current

PCC


19 |

Figure 1-3 Measured voltage sag due to a short circuit fault, voltage in three phases in time domain

(reproduced from [1]).

Figure 1-4 Rms voltages for the sag shown in Figure 1-3 (reproduced from [1]).

Figure 1-5 Sag duration as a function of the voltage threshold for the three phases of the sag shown in

Figure 1-3 (reproduced from [1]).

The three-phase characteristics of voltage sags are described through a classification

method proposed in [15]. This classification is summarized in Figure 1-6. The types A,

C and D are the base of the classification, corresponding to an equal drop in amplitude

in three phases, a drop in two phases, and a drop in one phase only, respectively. The

propagation of all types of sags (7 types) to lower voltage levels through transformers

with different winding connections is summarized in Table 1-1. Detailed description of

all sag characteristics can be found in [1, 16-18].

Table 1-1 Transformation of sag type to lower voltage levels (adopted from [1])

Transformer connection Sag on primary side

Type A Type B Type C Type D Type E Type F Type G

YNyn A B C D E F G

Yy, Dd, Dz A D C D G F G

Yd, Dy, Yz A C D C F G F

0 2 4 6 8 10 12 14 16

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Time in cycles

Voltag

e in p

.u.

4 5 6 7 8 9 10 11 12

0.55

0.6

0.65

0.7

0.75

0.8

0.85

0.9

0.95

1

1.05

Time in cycles

RM

S v

oltag

e in p

u

Sag magnitude or residual voltage

Sag duration

0.8 0.82 0.84 0.86 0.88 0.9 0.92 0.94 0.96 0.98 10

2

4

6

8

10

12

Threshold in p.u.

Estim

ate

d s

ag d

ura

tion (

cycle

s)


20 |

Figure 1-6 Types of voltage sags in phasor-diagram form.

1.2.2 Consequences

The majority of voltage sags caused by faults have adverse consequences on the utility

system and ultimately on the end–user side. The reduction in voltage experienced

during a voltage sag abates the energy-transfer capability of the system, limits the fault-

clearing time in transmission systems or results in tripping of embedded generation

from the grid [11]. On the customer side, the main consequence of voltage sags is the

misoperation of sensitive equipment. Many modern devices like computers, process

controllers, and adjustable-speed drives experience operational problems when the

voltage drops below 85% for more than 40 ms [11]. Equipment sensitivity to voltage

sags varies according to load type, control settings, and applications. Equipment

immunity to voltage sags is represented by the sag characteristics that influence the

behavior of the equipment (the most commonly used are residual voltage and duration).

The sag characteristics that affect different equipment are shown in Table 1-2.

Table 1-2 Impact of sag characteristics on equipment immunity (adopted from [19]

Equipment Sag

Magnitude

Sag

Duration

Point on

wave

Phase-angle

jump Types A-G

AC Contactors

DC Contactors

Induction Motor

AC Adjustable Speed Drives

DC Adjustable Speed Drives

Personal Computers

Programmable Logic

Controller

Type A

Type B Type C Type D

Type E Type F Type G

Sags caused by three-phase faults

Sags caused by single line-to-ground and line-to-line faults

Sags caused by double line-to-ground faults


21 |

The trip of equipment at industrial installations can lead to process disruption depending

on process immunity time (PIT). PIT is the maximum time a process could continue

operating after its equipment has tripped due to a sag [20]. When process disruptions do

occur they can entail substantial economic losses as shown in Table 1-3.

Table 1-3 Economic consequences of voltage sags (adopted from [12])

Industry Typical financial loss per event €

Computer centre 750 000

Financial trading 6 000 000 per hour

Glass industry 250 000

Semiconductor production 3 800 000

Steel works 350 000

Telecommunications 30 000 per minute

1.2.3 Indices

The aim of voltage-sag indices is to describe the performance of the power system

through a limited number of parameters [21]. This description is usually given by means

of averages and distributions over time and space. The IEEE 1564 Task Force, currently

working towards the creation of the IEEE Guide for Voltage Sag Indices, proposes the

following five-step procedure to quantify the sag performance of a power system [21]:

1. Obtain sampled voltages with a certain sampling rate and resolution.

2. Calculate characteristics as a function of time from the sampled voltages.

3. Calculate single-event characteristics from the characteristics as a function of

time.

4. Calculate site indices from the single-event characteristics of all events

measured during a certain period of time.

5. Calculate system indices from the site indices for all sites within a certain power

system.

The first step when calculating voltage-sag indices is to obtain sampled voltage

waveforms, typically for the three phases. In most cases the equipment used for

monitoring the harmonic spectrum will also be used for monitoring voltage sags. These

monitoring devices have typical sampling rates of 128 or 256 samples per cycle, which

exceed the sampling requirements for calculating sag indices.

The second step consists of calculating one or more characteristics from the voltages

sampled in step one as a function of time for each event recorded. The event can be

characterized by the rms voltage, the peak voltage or the amplitude of the fundamental


22 |

voltage component. Most equipment uses the rms voltage as a function of time as the

only event characteristic.

In the third step the retained voltage and the duration of the event are calculated. The

duration is the time the rms voltage stays below the threshold and the retained voltage is

the lowest rms voltage during the event. Recommended threshold values are in the

range 85-90% of the voltage reference for troubleshooting or statistical applications, and

70% for contractual applications [13].

The fourth step is quantifying the sag performance of each monitored site through one

or more site indices. Site indices typically give the frequency for events with given

values of residual voltage and duration. A commonly used method of presenting the

performance is by means of a voltage sag table whose cells are given by the division of

the residual voltage and duration ranges into a small number of intervals. The choice of

the magnitude and duration ranges is a point of discussion and different publications use

different values. Table 1-4 is the voltage sag table proposed in IEC technical report

61000-2-8 [10]. Tables with different resolutions in the duration and residual voltages

ranges are proposed in [22] and used in [23].

An alternative and widely used approach to counting voltage sags is the system average

rms frequency index (SARFI). The SARFI index was originally proposed in [24] and is

recommended by standard-setting organizations (CIGRE, CIRED, IEEE) in [25] and

[26]. The SARFIX index gives the number of events per year with duration of up to 1

minute and a residual voltage less than X%. For instance, SARFI80 gives the number of

events with residual voltage less than 80% as highlighted in Table 1-4. The SARFICURVE

index (where “CURVE” is the name of a predefined immunity curve) gives the annual

number of events below the predefined curve. For example SARFISEMI gives the

number of events more severe than the SEMI curve [27]. Although the index refers to

system average it can be used to quantify the occurrence of sags at a single site.

The fifth and final step of the procedure to quantify the system sag performance is to

calculate the system indices from the site indices from all the monitored sites. The

system indices are usually the same as the site indices but with typically lower level of

detail. System indices can be calculated either from the average of the site indices or

from the value not exceeded by a high-percentile of monitored sites, e.g. 95%.

A full description of the calculation of sag indices and others reporting methods can be

found among others, in [1], [14], [21], [25] and [26].


23 |

Table 1-4 Voltage sag table recommended by IEC 61000-2-8 and range of SARFI80 index

1 cycle-0.1 s 0.1-0.25 s 0.25-0.5 s 0.5-1 s 1-3 s 3-20 s 20-60 s 1-3 min

80-90%

70-80% SARFI80

60-70%

50-60%

40-50%

30-40%

20-30%

10-20%

<10%

1.2.4 Monitoring

The overview of the main aspects of voltage sags presented above shows that

monitoring plays an absolutely crucial role in the assessment of voltage sags. It is

through monitoring that the causes of sags can be discerned and their characteristics

defined, so that the possible consequences are estimated. Monitoring of voltage sags is

also the main source of data for calculating sag indices. As previously stated, sag

monitoring is the central topic within the scope of this investigation. A general summary

of the monitoring aspects most relevant to this thesis is given next.

First, two types of power quality monitoring should be distinguished [1, 2]:

On-site monitoring, aimed at assessing the power quality at particular sites.

Reasons for this type of monitoring include characterization of specific problems

and verification of compliance of power quality contracts. Only one monitoring

device installed at the site of interest is required.

System-level monitoring, intended to estimate the overall power quality of the

entire system. This approach requires monitoring usually at a large number of

sites and estimating the voltages at sites without monitors, i.e. power quality

state estimation (PQSE).

Monitoring of voltage sags at system level is the factual framework for this research and

therefore only this approach will be discussed further. The main aspects that need to be

considered when executing a system-wide sag monitoring campaign are:

Monitor placement. Ideally, monitors would be placed at all locations

throughout the system to completely understand the overall power quality. Such

deployment of monitors however may be unaffordable and the challenges related

to data management, analysis, and interpretation can be significant.

Nevertheless, full coverage is usually not required since measurements from

several strategic locations can be used to characterize the sag performance of the


24 |

whole system. Hence careful selection of monitoring locations based on

monitoring objectives is of paramount importance. By recognizing the most

important influencing factors and considering site categorization it should be

possible to install monitors in a targeted way such that full coverage of the

network is achieved. The sag data from monitored sites can then be mapped on

to non-monitored sites and verified based on known faults statistics [2], [25],

[26].

Estimation of sags at non-monitored sites. It was stated before that the main

cause of voltage sags is short-circuit faults. With this in mind, the procedure to

estimate sags at sites without monitors involves finding a fault location that

produces voltages and currents that most closely match the measurements from

the few available monitors [2].

Monitor connection. Voltage sag statistics in three-phase systems can be

collected through monitors connected phase-to-phase or phase-to-ground. Power

quality monitoring standards do not prescribe a monitor connection. However, a

joint report from CIGRE and CIRED recommends the use of phase-to-phase

voltages for system indices derived from monitoring HV and EHV sites because

they give a better indication of the voltage experienced by the end-user

equipment than phase-to-ground voltages [25]. If monitors are connected phase-

to-ground, methods like the one proposed in [28] can be used to estimate the

phase-to-phase rms voltages from phase-to-neutral voltages.

The main facets of the sag monitoring in power systems discussed above are addressed

by this thesis. An overview of these aspects is presented in following sections.

1.3 Literature review

1.3.1 Monitor Placement for Sag Performance Assessment

Monitoring the electrical environment of power systems is the best way to assess

voltage sag performance [1, 2, 29]. Two streams of monitor placement for sag

characterization can be distinguished: the selection of monitoring locations adopted in

practice to undertake power quality surveys, and the optimal monitor placement

proposed in academia. Both approaches are discussed further in this section.


25 |

1.3.1.1 Power Quality Surveys

In recent years, several monitoring programs have been performed with the main

objective of assessing the overall power quality of power systems at different voltage

levels. The power quality disturbances considered in these surveys include voltage sags.

The results of a four year power quality monitoring program conducted by the National

Power Laboratory (NPL) are analyzed in [30]. The monitored area covered 112

locations in USA and Canada. Single phase, line-to-neutral voltages were recorded at

standard wall receptacles. The wide statistical variation of the data collected hindered

the definition of a typical site representing the overall power quality of the power

system.

The difficulty in utilizing data from monitoring programs to estimate the expected

electrical environment is also reported in [31], where a comparison was carried out

between the monitoring results of the NPL survey and the data from two additional

monitoring programs, one conducted by the Canadian Electrical Association (CEA) and

one by the Electric Power Research Institute (EPRI). The CEA survey was conducted

with the participation of twenty-two utilities throughout Canada. In this survey, 550

sites were monitored for 25 days each. Residential, commercial, and industrial customer

sites were monitored at the PCC. Only line-to-neutral voltages were monitored (120 V

or 347 V). The EPRI survey lasted for more than 2 years, and around 50 GB of power

quality data was obtained. The survey was performed in distribution systems with

voltages ratings from 4.16 kV to 34.5 kV supplying residential, commercial, and

industrial customers. Monitors were placed at substations and along three-phase

sections of feeders.

The data from the power quality surveys conducted in North America by the NPL, the

CEA, and the EPRI showed that voltage sags occur more frequently at the point of use

than at the substation or on the utility distribution feeders. It also demonstrated that

most of the sags had a voltage magnitude between 80% and 90% while the most severe

sags were the fewest recorded. Although the surveys’ data were combined to obtain the

range of sag events that might be expected at the majority of locations, it was pointed

out that there is a difficulty in doing so due to the differences in the recording and

classification of sags by each brand of monitor, the voltage threshold settings used in

each survey, the monitored locations, and the sources and propagation characteristics of

sags.


26 |

The voltage sag data of the EPRI survey was briefly compared against two European

power quality surveys in [32]. One of the European surveys was performed in nine

countries by the Distribution Study Committee of Eurelectric (formerly UNIPEDE),

which collected statistical data based on over 80 years from 85 monitoring locations on

medium voltage networks. The second survey was performed by the Norwegian Electric

Power Research Institute (EFI) by monitoring 400 sites in Norway. The examination of

the similarities of the data shows that the vast majority of the registered events were less

than 1 second in duration and had magnitude between 70% and 90%.

The need for long monitoring periods is evidenced in [33] and [34], where data from

short-term monitoring programs and for single monitoring points is considered. In [33],

monitoring data from a period of eight months in three locations is presented, while in

[34] the results of voltage sag measurements in two industrial facilities for a period of

17 months are studied. It can be deduced from both, that short monitoring periods are

generally insufficient to obtain accurate sag performance data.

The surveys discussed above are by no means the only ones conducted in recent years

but they were the ones for which detailed results were available and comparable.

Although it is difficult to establish the typical duration of the monitoring surveys

examined since it ranges from few months to several decades, an average duration of

2.4 years is calculated neglecting the 80 year survey performed by Eurelectric.

Significant efforts in surveying power quality are also evidenced in the latest (2011)

Benchmarking Report on the Quality of Electricity Supply of the Council of European

Energy Regulators (CEER) [35]. Table 1-5 shows the number of measurement devices

currently installed at different voltage levels in 14 European countries. It can be seen

from this table that the largest number of monitors is deployed in France whereas Latvia

and The Netherlands report less than 30 monitors installed. In no instance, however, is

an optimal deployment strategy reported in [35].

In summary, it can be said that monitoring programs require significant investment in

measurement equipment and in data collection and processing. The latter must be

automated in order to maintain reliable statistics on voltage sags [36]. Moreover, the

requirement for high accuracy of monitoring data may necessitate long monitoring

periods, typically several years [1].


27 |

Table 1-5 Number of monitors at different voltage levels in current European monitoring systems

(adopted from [35])

Country Period of

monitoring since

Number of measuring units installed

EHV / HV MV LV Total

Austria April 2011 299 299

Bulgaria June 2010 495 1 372 1 867

Cyprus Distribution: 2000

Transmission: 2010

Czech Republic 2006 160 694 14 525 15 379

France EHV and HV: 1998

MV: not available

LV: March 2010

208 30 000 250 000 280 208

Greece March 2008 500 500

Hungary 2004 157 585 742

Italy 2006 165 600 (Through smart meters) 765

Latvia 1999 20 20

The Netherlands EHV and HV: 2004

For all DSOs: 1996 28 60

† 60

† 28

Norway 2006

Portugal 53 101 166 320

Romania 2008 22 130 152

Slovenia 2004 183 183 366 † Number of measurement periods with duration of one week being performed with several measuring

instruments per year.

Alternatively, the assessment of voltage sag performance can be done stochastically by

computer simulations. This option is more appropriate to estimate the expected voltage

sag performance of systems in planning stage considering different operating scenarios,

generator scheduling and loading profiles [29], [37]. In addition, the accuracy of the

stochastic approaches is not subject to long monitoring periods.

1.3.1.2 Optimal Monitor Placement for Sag Estimation

As stated previously, monitoring of the power supply can provide a direct assessment of

the voltage sag performance of the monitored site. However, since it might be

economically unfeasible to monitor the whole power system, only a limited number of

monitors can be located in a network. Therefore, it is necessary to determine the

minimum number of monitors and their best possible locations that lead to an accurate

description of the system sag performance. Few methods have been published for the

optimal allocation of power quality monitors aimed at maximizing the observability of

voltage sags. These are discussed next.

The monitor reach area (MRA) is defined in [38] as the area of the network for which a

monitor is able to capture voltage sags of a given magnitude. This area includes all the

points where the occurrence of faults will cause sags more severe than a given

threshold. Building the monitor reach area for all buses in the system allow us to find

the minimum number of monitors subject to complete observability of voltage sags. In


28 |

[39] the optimal set of monitors is used to identify accurately the average sag

performance of the network and multiple solutions for the optimization problem are

explored through a genetic algorithm. However, in reported studies only symmetrical

faults at buses were considered.

The MRA-based method is extended in [40] to consider unsymmetrical faults and faults

along lines. The analytical formulae derived in [41] are used to calculate the residual

voltage caused by any type of fault at both buses and lines. The optimal placement of

monitors is carried out utilizing both analytical expressions and the fault positions

method [41]. The study indicates that only the method based on analytical expressions

assures the complete observability of voltage sags in the network.

Although the algorithm introduced in [42] was not strictly developed for optimal

monitoring of sags it is very similar to the MRA-based method. It incorporates the cost

associated with the monitoring system and ranks the monitoring programs based on data

redundancy.

1.3.1.3 Optimal Monitor Placement for Fault Location

Since the voltage sags caused by short-circuit faults are of the most concern any monitor

placement methods whose objective is the localization of faults could lead to an

improvement in sag estimation accuracy. The most relevant approaches proposed to

date for monitor placement for fault location are discussed separately in the section

reviewing monitor placement for sag estimation.

A technique for optimal allocation of fault indicators on distribution feeders to reduce

the number of potential fault location estimates is proposed in [43]. Two additional

objective functions namely, minimization of the distance between fault location

estimates and prioritization of buses based on critical customers, are incorporated in

[44] to develop a method for optimal placement of fault indicators in distribution

networks. In both approaches the optimization problems are solved using a genetic

algorithm.

In terms of measurement devices, the relatively recent developments and investments in

the synchrophasor technology have influenced investigations on optimal monitor

placement for fault location. A deterministic allocation method is proposed in [45] to

determine optimal sets of phasor measurement units (PMU) that maximize the accuracy

of localization of single line to ground faults. Single line to ground, line to line, and


29 |

three-phase faults are taken into account in the development of a stochastic model for

optimal PMU placement for fault location in [46]. These two methods obtain optimal

sets of PMUs using metaheuristic search algorithms but require the user to define the

number of PMUs available. The performance of both approaches for faults occurring at

points other than buses is not presented.

A three step PMU placement procedure is described in [47] to achieve fault location

observability in transmission networks. The first step consists of placing PMUs on

buses with the highest number of incident branches. Secondly, PMUs are positioned so

that every two devices are spaced by one bus. During the final step, redundant PMUs

are eliminated until the one-bus-spaced criterion is violated. The deployment strategy is

therefore, pretty involved (“manual” to a certain extent) and might be cumbersome for

application in large systems.

The one-bus-spaced deployment strategy is also implemented in [48] and [49] to

minimize the number of PMUs while preserving fault location observability. In these

two methods the optimization problem is formulated as an integer programming

problem following the modeling approach of [50] and solved using a branch and bound

algorithm [48] and a genetic algorithm [49]. However, it is argued in [51] that the

method proposed in [48] and [49] is not complete and might provide incorrect results.

The optimal PMU placement for fault location is also modeled in [51] as an integer

linear programming problem. The work was extended to include zero injection buses in

the formulation, as it was shown this can reduce the total number of PMUs required.

The requisite of placing PMUs on terminal buses to maintain fault observability under

faulted conditions is demonstrated in [52], where the PMU placement is optimized in

conjunction with the placement of conventional power flow measurements.

The methods proposed in [47]-[49], [51], and [52] determine the optimal placement of

PMUs so that a two-terminal fault location algorithm like the one described in [47] can

be applied to all lines of the network. This algorithm requires synchronized

measurements of the voltage phasor at both ends of the faulted line and the current at

any end of the line to determine the fault location.

An alternative and more comprehensive method is the one proposed in [53]. This

method determines the minimum number of monitors and identifies the best locations

for installing not only PMUs but any other device with voltage measurement

capabilities, such as power quality monitors or digital fault recorders, in order to


30 |

uniquely locate every fault occurring throughout the network. Since the one-terminal

fault location algorithm employed in [53] relies on only one voltage measurement (that

can be distant from the fault location) and no current measurements, a reduction in the

total number of measurement devices can be expected. This method is similar to, and

uses the same data as, the MRA-based method. In theory, the two methods should

provide the same sag estimation results. The method presented in [53] however has only

been tested in a simple 10-bus system and a generalized formulation applicable to an

arbitrary system is still missing.

1.3.2 Sag Performance Estimation

Stochastic estimation methods calculate the number and characteristics of voltage sags

of a single site or an entire power system based on the network model and the fault

statistics data of the system. The accuracy of these methods relies on the correctness of

the models employed and the knowledge of the number and characteristics of faults in

the system. Several methods have been proposed in the past for the stochastic estimation

of voltage sags. These methods will be reviewed next.

1.3.2.1 The method of critical distances

This method determines the exposed area, or area of vulnerability, for a given voltage

sag magnitude. The exposed area of a sensitive load is the part of the system where a

fault can produce a sag of critical magnitude for the load of interest. The expected

number of voltage sags is obtained by adding the expected number of faults within the

exposed area [54],[55], [56]. Since the expressions used by this method are based on a

simple voltage divider model of a radial feeder, the applicability of the method is

limited to radial systems. Although expressions for non-radial systems have been

derived their implementation is rather complex [54], [57].

1.3.2.2 The method of fault positions

This method determines the voltage sag magnitude at all, or selected, buses in the

network for faults occurring in previously selected fault positions. For each fault

position the sag magnitude at the point of interest is calculated for balanced and

unbalanced faults. Since faults can occur throughout the power system, fault positions

are randomly distributed and a fault rate is assigned to each position. The accuracy of


31 |

this method is directly proportional to the number of fault positions, i.e., the higher the

number of fault positions, the more accurate the estimation[58], [59], [60],[61].

Monte Carlo based approaches can be seen as a variation of the method of fault

positions [62]. In the Monte Carlo method, random variables such as fault location, fault

resistance, fault duration and fault type are iteratively calculated according to their

statistical distributions every time a simulation is performed [63].

1.3.2.3 Analytical approaches to the method of fault positions

These approaches are based on the algebraic description of the residual voltage at a

given bus when a fault location moves along a line. In other words, the residual voltage

at an observation bus is expressed as a function of the position of a moving fault node

providing a deterministic relation between two stochastic variables: 1) fault position and

2) residual voltage. Firstly, in [64] the probability density function (PDF) of voltage

sags as a function of fault distributions on transmission lines is calculated. Probability

density functions can be used to predict the number of voltage sags, and to analyze the

influence of generation scheduling and fault distributions of lines. The study shows

variations in the sag incidence due to different generation patterns and multiple fault

distributions. The main limit of this method is that it was developed for symmetrical

faults only.

Similarly, in [65] the cumulative frequency function (CFF) of sags of a given voltage

magnitude is determined. The main reason to use cumulative frequency functions of

sags is that for a sensitive load it is necessary to estimate the number of sags with

voltage magnitude below a given threshold. Again only symmetrical faults were

addressed.

In [41] the previous analytical methods are extended for the estimation of voltage sags

due to symmetrical and unsymmetrical faults. The study reveals the better

computational efficiency of the analytical approach over the fault position method for

similar accuracy levels.

A different way to find critical points on lines is proposed in [66], where quadratic

interpolation and the secant method are used to find the exact points on lines where the

occurrence of a fault will lead to sags with a specific voltage magnitude at an

observation bus. The same method is used in [67] to determine the influence of

generation scheduling and time-varying fault rates in the stochastic estimation of


32 |

voltage sags. The study shows that both factors strongly influence the estimation of

voltage sags.

1.3.2.4 Analytical approaches to the method of critical distances

Slight modifications or additions to the base method reported in [54] and

implementations in radial systems fall into this category. For example, in [68] the basic

principles of the method of critical distances are used to determine the areas of

vulnerability to voltage sags. Then, the reliability of the protection scheme in the

calculation of number of voltage sags is taken into account and finally the estimated

voltage sag performance is compared with tolerance curves of sensitive loads in order to

calculate the expected load trips.

Analytical expressions for the calculation of voltage sag magnitude considering the

effect of power transformers are derived in [69]. A comparison between the method of

critical distances, the method of fault positions, and Monte Carlo simulation shows that

a high number of fault positions and iterations are required to obtain results with

acceptable accuracy.

1.3.2.5 The voltage sag matrix method

The method proposed in [70] is based on a re-formulation of the bus impedance matrix.

Assuming limited phase angle differences among pre-fault voltages, pre-fault voltages

equal to 1 p. u., and neglecting the resistances of the network components, the voltage

sag at bus i, caused by the fault at bus j is given by the quotient of the transfer

impedance between the buses i and j and the driving-point impedance of the faulted

point j. The elements of the “voltage sag matrix” are these quotients for all the buses of

the network. In this way, the voltage sag matrix directly provides voltage drops in

percentage at each bus due to symmetrical faults in each bus of the network. The main

limitation of this method is that it is exclusively suitable under the aforementioned

assumptions.

A common feature of all the stochastic methods analyzed before is the use of fault

statistic data. Fault rates can be obtained from historical records for existing systems or

simply take theoretical values for research purposes. However, since the probability of

fault occurrence is strongly influenced by several factors such as weather conditions,

maintenance, tree trimming, etc., the fault rate for a given system can be considerably

different from one year to another [1], [71]. In this respect, stochastic methods are


33 |

suitable only for long term estimations because the estimation of voltage sags for a

specific year can differ significantly from the sags measured by power quality monitors

[72]. The estimation of stochastic methods can be improved by tuning them using

monitoring data [73], [74]. The next section discusses voltage sag estimation

approaches that combine power quality monitoring data and statistical prediction

techniques.

1.3.3 Voltage Sag State Estimation

Monitoring of the power supply can provide a direct assessment of the sag performance

of the monitored site. However, since it is economically unfeasible to monitor the whole

power system, only a limited number of monitors can be located in a network. This

leads to the problem of voltage sag estimation at non-monitored buses.

Voltage sag state estimation (VSSE) techniques have been proposed to circumvent this

obstacle. These approaches are based on estimating the voltage sag frequency at non-

monitored buses by using the data collected at a limited number of metering points [72].

In recent years, interest in voltage sag state estimation has emerged, especially on

distribution systems with radial topology.

The power quality state estimation (PQSE) process can be described as follows [75]: the

first step is the selection of a model that will be used to estimate the state of an entire

network based on a limited set of monitoring data. Differently from traditional power

system state estimation, in PQES there is a lack of redundant metering data. Once the

model is selected, the next steps are filtering the measured data, pre-processing the

measurements, and verification of system observability. The final step of PQES is the

model validation which implies testing the fitness of the predicted data to the observed

data. The absence of full state measurement is recognized as the most challenging issue

for PQES.

Two main groups of VSSE methods can be distinguished: methods for radial systems

and statistical methods. Both are discussed next.

1.3.3.1 Methods for Radial Systems

As its name suggest, these methods were specially developed for radial networks. They

take advantage of the monotonic form of the variation of the remaining voltage at an

observation bus with the distance of the fault. In other words, the voltage magnitude


34 |

curve increases or decreases monotonically with fault distance. In short, these methods

try to fit the monotonic curve.

A voltage sag estimation algorithm for radial distribution feeders is proposed in [76].

This algorithm uses a limited number of voltage measurements to estimate the voltage

profile of a faulted feeder. It utilizes a least-square method to fit the trend followed by

the voltage along the fault path. Linear and 2nd

order equations for the voltage sag

magnitude are derived. These equations relate the sag magnitude at certain point to the

normalized feeder length. The study shows a sag state estimation error of less than

0.35%. However, improvement of the algorithm for robustness and efficiency and

verification with field data is suggested.

The method of disturbance circuit is introduced in [77] as another algorithm to estimate

the voltage sags of radial distribution systems with limited monitoring points. This

algorithm involves substituting the loads at buses along a radial feeder with equivalent

voltage disturbance sources in order to calculate the voltage sags in all the buses of the

feeder. The efficiency of the method was compared against the efficiency of the method

proposed in [76]. The mean square error between simulated and estimated values was

1.76%. Although the error is greater than the error in [76], it is still negligible and the

results were obtained with 70% fewer monitors.

Similar work to that presented in [76] and [77] is performed in [78]. The authors’

approach to voltage sag estimation is based on the distribution system model and the

Kalman filter algorithm. The latter is used as estimation technique to obtain the voltage

profiles of a radial feeder based on limited metering points. The estimation error

between the estimated values and the simulated values is less than 0.0011%, which is

considerably less than those incurred in [79] and [76], although the number of monitors

considered in the study is not specified.

1.3.3.2 Methods Based on Statistical Analysis of Monitoring Data

These methods develop models for the estimation of voltage sags based on statistical

analysis of monitoring data and system parameters. The models derived relate the

number of sags with certain characteristics (duration and magnitude) with system

characteristics such as length of feeders, transformers’ impedance; weather conditions;

and historical records of sags.


35 |

A methodology to validate the voltage sag data derived from short monitoring periods is

proposed in [80]. The accuracy of the monitoring data is evaluated through a

comparison with simulated data. This involves calculating the confidence intervals for

the sag frequency found in simulation results. The measured sag frequency is

considered valid if it lies within the simulation confidence interval. Then, a sequence of

hypothesis tests is performed for monitoring and simulation data obtaining probability

values for each monitoring point. In order to validate the sag magnitude data of a

measured point, its probability value has to be greater than the adopted significance

level (α%) of the confidence intervals.

A multiple regression analysis is performed in [81] in order to find a relationship

between the expected number of sags at certain low voltage (LV) points and influencing

parameters from medium voltage (MV) and high voltage (HV) in Belgian systems.

Meteorological information and sag statistics collected from 18 HV substations (over 5

years) and from 15 MV substations (over 3 years) were used in the statistical analysis.

Regression models describing the relationship between the expected number of sags and

the aforementioned parameters were obtained. The results showed that for the case of 3

phase sags originating in the HV network, the most influential parameter is the altitude

of the substations. The incidence of 2 phase sags originating in the HV network is

affected by the altitude, the interconnection, and the lightning density. On the other

hand, the number of 3 phase sags in the MV network is mainly influenced by the short

circuit impedance of the substations.

An extensive statistical analysis of data from power quality studies is completed in [82]

to obtain models for the estimation of power quality disturbances. The analyzed data

was collected from 24 utility systems at 276 locations on 100 distribution feeders over a

27 month period. Further analysis of the data shows that the three strongest indicators of

voltage sags are circuit exposure, lightning, and a term involving transformer size and

number of feeders. Similarly to the work presented in [81], the authors employed

regression techniques to find a model to estimate the annual number of sags which will

fall under the lower ITIC curve. The fitness of the model may be considered fair, since

34% of the observed values are within 25% of the prediction intervals, and 60% of the

observed values are within 50% of the prediction intervals.


36 |

1.3.4 Summary

Review of past research in the field identified several areas that need to be addressed.

These areas are summarized as follows:

The influence of fault impedance, fault location, pre-fault voltage (loading

conditions) on optimal monitor placement methods for sag estimation and fault

location has not been investigated. These factors could affect the number and

locations of monitoring devices deployed in the network.

The possibility of developing a unified approach to monitor placement for sag

estimation and fault location has not been explored. These two objectives have

been mainly treated separately and the synergy of both has not been fully

addressed.

Following the previous point, a monitor placement method for fault location that

could be combined with sag monitor placement lacks a generic formulation

applicable to any power system.

Existing methods proposed for optimal monitor placement for sag estimation

and fault location do not evaluate sub-optimal solutions or provide a ranking of

importance of monitoring locations.

Current monitor placement methods for sag estimation do not take into account

sag indices, immunity curves, or standards when determining optimal

monitoring locations.

The problem of optimal monitor placement for fault location is a non-

deterministic polynomial time-hard (NP-hard) problem, meaning that is not

possible to find an optimal solution in polynomial time. Alternative algorithms

for its solution have not been proposed.

1.4 Aims of Research

This research aims to address some of the issues that have not been satisfactorily

resolved in the past and to provide answers to the problems identified. The ultimate aim

is to establish comprehensive understanding of all relevant aspects involved in efficient

monitor placement for accurate voltage sag estimation at non-monitored sites, and to

propose a methodology for development of optimal sag monitoring programs. The main

aims of the research are therefore:


37 |

1. To summarize existing methodologies for estimation of sag performance at non-

monitored sites using limited monitoring data.

2. To provide a critical overview of existing methodologies for optimal monitor

placement for voltage sag estimation and investigate potential ways of

improvement.

3. To develop a general approach to monitor placement for fault location in power

systems.

4. To develop a unified approach to monitor placement for estimation of sag

magnitude at all buses in the network and fault location.

5. To develop a methodology for choosing optimal sag monitoring programs in the

network.

6. To develop a flexible methodology for reliable estimation of voltage sags and

strategic monitor placement suitable for assessment of economic losses due to

sags.

1.5 Major Contributions of the Research

The research has contributed to the field of optimal monitor placement for voltage sag

estimation. These contributions are summarized next. (Paper numbers given in the

parentheses indicate that the related results are published or submitted for publication in

international journals or in proceedings of international conferences. A full list of thesis-

based publications is given in Appendix F).

The leading optimal monitor placement for voltage sag characterization, the

monitor reach area (MRA) method, was enhanced by incorporating a recently

proposed fault location algorithm. The limitations of the MRA were overcome

and the accuracy of sag estimation was increased without increasing the number

of monitors (F7, F9).

A generalized formulation for optimal monitor placement for fault location was

developed (F1, F2). The proposed formulation reduces significantly the number

of constraints of the problem.

The monitor location area (MLA) was designed to map the area of a power

network where combinations of monitors can determine the exact location of

faults (F1, F2).


38 |

A series of heuristic (greedy) algorithms was developed to solve the problem of

optimal monitor placement for fault location and sag estimation with much

lesser computational burden (F7, F9, F11).

Custom objective functions for the monitor placement optimization process were

developed. These functions minimize the sag estimation error and maximize the

fault location observability (F7, F9, F11).

A new methodology for reliable estimation of voltage sags based on hybrid

monitor placement suitable for assessment of economic losses due to sags was

developed (F1).

The feasibility of assessment of financial losses due to voltage sags based on a

limited number of existing monitors in the network and optimally deployed

monitors was established (F6, F13).

1.6 Overview of the Thesis

The thesis is organized into seven chapters. This chapter, Chapter 1 , is the introductory

chapter. An outline of each of the remaining six chapters of the thesis follows.

Chapter 2 Modeling and Simulation Tools

In this chapter a summary of the existing methodology for voltage sag studies is

presented. The simulation and calculation methods along with the power system

component models used throughout this thesis are explained. The bus impedance matrix

building algorithm and the use of this matrix for fault analysis in power systems is

discussed thoroughly. The custom-made software employed to perform sag studies is

briefly commented on. The last part of this chapter introduces all the test systems on

which the thesis’ studies were performed.

Chapter 3 Optimal Monitor Placement for Voltage Sag Characterization

This chapter provides an overview of the first and still the most referred optimal

monitor placement method for voltage sag characterization, the MRA method. The

limitations of this method are highlighted through extensive simulations on IEEE and

generic systems. A recently proposed fault location algorithm that can be used to

overcome these limitations and enhance the robustness of the method is also reviewed

and discussed in this chapter. The improvement of the MRA method by incorporating

the aforesaid fault location algorithm is presented in the last section of this chapter.


39 |

Chapter 4 Generalized Formulation of the Optimal Monitor Placement for Fault

Location

This chapter reviews an optimal monitor placement for fault location and extends and

generalizes its modeling approach. New sets of generic linear constraints for the

problem of optimal monitor placement are introduced so it can be solved by integer

linear programming. The novel concept of monitor location area is proposed also in this

chapter to facilitate the formulation of generic constraints. Simulation studies performed

in several test systems that validate the proposed formulation are shown in the last

section of the paper.

Chapter 5 Heuristic Approach for Determining Optimal Monitor Placement for

Voltage Sag Estimation

This chapter develops a heuristic methodology that finds optimal monitor placement

solutions with techniques considerably less computationally taxing than integer

programming. The methodology includes three custom objective functions formulated

for greedy monitor placement. Lastly, the proposed approach is used to determine a

range of monitoring programs for estimating sag performance in a generic distribution

network using different sag characteristics and sag benchmarking methodologies.

Chapter 6 Techno-Economic Assessment of Voltage Sags Using Optimal Monitoring

Programs

This chapter develops a new methodology for monitoring and estimation of voltage sags

in power systems. The proposed methodology encompasses a hybrid monitor placement

method and a simplified technique for fault location that allows network sag

characterization. The sag monitoring schemes obtained with the proposed methodology

are then tested in two case studies utilizing Monte Carlo simulation. In the first case

study the characteristics of voltage sags are estimated to quantify the number of ITIC

and SARFI-90 events occurring in the network. In the second case study the financial

losses incurred by different sensitive customers due to voltage sags are assessed using a

risk-based methodology.

Chapter 7 Conclusions and Future Work

In this chapter the main conclusions of the research are discussed and suggestions are given

for future works and potential improvements on the methodologies developed.

Chapter 2 • Modeling and Simulation Tools

40 |

Chapter 2

Modeling and Simulation

Tools

This chapter describes the existing methodology for voltage sag studies including the

different types of simulations tools, calculation methods, sag studies, and solution

techniques. The simulation and calculation framework used throughout the thesis is

chosen from these groups, and the corresponding modeling requirements are discussed.

The models of the main power system components used in the thesis are also presented.

The building of the bus impedance matrix and its use for fault analysis in power systems

is explained in detail. The different test systems employed for all the studies carried out

in the thesis are also presented.

2.1 Simulation Tools for Voltage Sag Studies

Voltage sags can be calculated and analyzed utilizing two main types of simulation

tools: custom-made tools usually developed on commercial software platforms and

general purpose simulation packages, e.g. EMTP-like tools. The selection between these

two instruments depends on many factors including the study objectives, accuracy

required, and the user’s experience [11].

There are three main approaches to calculate the characteristics of voltage sags: fault-

current calculations, time-varying phasors, and time-domain calculations. Table 2-1

summarizes the voltage sag characteristics, modeling guidelines, and software tool

capabilities of each approach. Fault-current calculation is the simplest method but its

only output is residual voltage in steady-state. The method of time-varying phasors can

calculate the duration of sags by incorporating models of protective devices and

dynamic behavior of generators and control systems. Time-domain calculations can


41 |

capture all voltage sag characteristics (magnitude, duration, phase angle jump, point of

wave) at the expense of more detailed models and the requirement for higher simulation

capabilities [11].

Table 2-1 Voltage sag calculation methodology (adopted from [11])

Calculation method Voltage sag

characteristics Modeling guidelines Software tool capabilities

Fault-current

calculations Retained voltage Steady-state models

Three-phase phasor calculations.

Models adequate for steady-state

calculations.

Time-varying

phasors

Retained voltage

and duration Steady-state models

Three-phase phasor calculations.

Models to reproduce the dynamic

behavior and the control systems of

generators.

Protective device models.

Time-domain

calculations All

Time-domain low-

frequency transient

models

Three-phase calculations.

Models to reproduce the transient

behavior of power components,

protective devices, and generators.

Options to capture voltage-sag

characteristics.

Load modeling options.

Frequency-domain and time-domain are the two basic solution techniques applied to

voltage sag calculations. In the frequency-domain, solutions are obtained using either

the bus admittance matrix or the bus impedance matrix. The bus impedance matrix is

preferred due to its suitability for calculating fault currents and residual voltages,

efficiency at determining sag magnitudes, and suitability for voltage sag propagation

studies [11].

Voltage sag studies can be classified according to their goals as: single-event

calculations, statistical simulations, sensitivity studies, or calculations of voltage sag

indices. Single-event calculations aim to characterize sags at particular buses. Statistical

simulations obtain the probability density function (PDF) of the sag characteristics and

the respective rate of occurrence. The goal of sensitivity studies is to determine the

effect of a system or fault parameter on voltage sag performance. Voltage sag indices

are used to quantify the sag performance of a single event, a site or a system. A

summary of the simulation tool capabilities required to obtain the aforesaid goals is

shown in Table 2-2. A fourth column has been included in this table to indicate the type

of voltage sag study performed in each chapter of this thesis. The results presented in

Chapter 3 to Chapter 6 of the thesis involve all types of voltage sag studies.


42 |

Table 2-2 Overview of voltage sag studies (adopted from [11])

Study Goals Required capabilities

Chapters

of this

thesis

Single-event

calculations

Obtain some or all

characteristics of voltage sags

at buses of a power system

See Table 2-1 3,4

Stochastic

predictions

Obtain the PDF of some or all

characteristics of voltage sags

at buses of a power system.

Obtain the rate of occurrence

of different voltage sag

characteristics.

Capabilities shown in Table 2-1 plus

multiple run option (this should include

all options required to perform a Monte

Carlo solution) and post-processing

capabilities (i.e. those capabilities needed

to determine probability density functions

and rates of occurrence).

3,6

Sensitivity

analyses

Deduce the effect that some

system and fault parameter can

have on the voltage sag

performance; e.g. the number

of trips at a given load bus.

Capabilities shown in Table 2-1 plus

multiple run option and post-processing

capabilities. If the analysis is used to

obtain the sensitivity of a stochastic

assessment, then the options to perform

Monte Carlo method are also required.

3

Voltage dip

index

calculations

Obtain index values for either

sites or the entire system

Similar to those required for stochastic

predictions. 3, 5, 6

2.2 Modeling of System Components

The voltage sag characteristic most relevant to this research is the retained voltage at the

bus, i.e., the voltage sag magnitude. It was previously shown that fault-current

calculations in the frequency-domain using the bus impedance matrix are the most

suitable and efficient method when the goal is to obtain the retained voltage. Models

adequate for steady-state calculations are required by fault-current calculations. Steady-

state models can be obtained by converting system components into equivalent

resistance ( )R and reactance ( )X on common bases. The steady-state modeling of the

main system components, i.e. cables and lines, generators, loads, and transformers, is

described in this section.

2.2.1 Cables and Lines

The modeling of lines and cables of short and medium length using lumped parameters

is sufficiently accurate [83]. Shunt capacitance ( )C can be neglected in short lines and

cables and those of medium length can be modeled by the series resistance R and the

series reactance X for the total length of the line or cable, with half of the susceptance

for the total length lumped at each end of the equivalent circuit, as shown in Figure 2-1.

In terms of handling of capacitance, open-wire 60-Hz lines less than 80 km (50 mi) long


43 |

are considered short lines. Lines having length between 80 km (50 mi) and 240 km (150

mi) are of medium length. Lines longer than 240 km (150 mi) require models based on

distributed parameters ( , , )R X C if a high degree of accuracy is required.

Figure 2-1 Lumped parameters model of cables and lines.

The positive- and negative-sequence series-impedance and shunt-capacitances of fully

transposed lines are equal. The zero-sequence impedance of overhead lines depends of

the existence of a return path provided by ground wires, tower footing resistance, and

grounding. The zero-sequence impedance value of lines is usually between two and six

times the value of the positive-sequence impedance [84].

2.2.2 Generators

After a fault occurs in a generator, the subtransient, transient, and steady state periods

are characterized by values in positive-sequence of the subtransient reactance dX , the

transient reactance dX , and the steady-state reactance dX , respectively. These

reactances have increasing values, i.e. d d dX X X and the corresponding fault

currents have decreasing values that is, f f fI I I . Subtransient reactances are

generally used to determine the initial current drawn by a short-circuit fault and

resistance is taken into account if greater accuracy is desired [83]. Values for the

negative- and zero-sequence impedances for synchronous machines are specified by

manufacturers based on test results. The negative-sequence is usually approximated to

half of the sum of the direct and the quadrature axis subtransient reactances [84]. A

practical approximation for short-circuit studies is to use a value for the zero-sequence

reactance of synchronous machines between 15% and 60% of the subtransient reactance

[85]. Generators have been modeled here as a constant driving voltage in series with

corresponding sequence resistances and subtransient reactances [86] as shown in Figure

2-2.

R jX

jB/2 jB/2


44 |

Figure 2-2 Model of generators.

2.2.3 Loads

Several load models have been developed for voltage sag studies including constant

impedance, voltage dependant load, induction motor load, and hybrid load model. Load

modeling can be very important for some calculations, for example the calculation of

energy based voltage sag indices or when the interaction between a load and the system

during the fault that causes the voltage sag is of interest. However, load modeling is not

a critical issue in many other voltage sag studies, like fault-current calculations to

determine the retained voltage. For this application loads can be represented sufficiently

well as constant impedances and hence statics loads can be converted into equivalent

impedances with equal values of positive- and negative-sequence as shown in Figure

2-3.

Figure 2-3 Constant impedance load model.

The resistance R and the reactance X of the load are given by

2

*

VR jX

P jQ

(2.1)

where P , Q , and V are the active power (kW), reactive power (kVAr), and rated

voltage (kV) of the load, respectively, and the symbol *denotes the complex conjugate.

2.2.4 Transformers

Only voltage sags caused by faults are simulated throughout this thesis. Since in most

cases transformers do not saturate during the occurrence of fault-induced voltage sags a

R jXd//

E

Bus n

R jXd Bus n


45 |

linear model can be used [87]. The sequence equivalent circuits of three-phase

transformers are determined by the connections of the primary and secondary windings.

Different connections of delta and wye windings defined the configurations of the zero-

sequence circuits and the phase shift in the positive- and negative-sequence circuits.

The equivalent circuit of an ideal transformer can be reduced to obtain the positive- and

negative-sequence equivalent circuits of the transformer by defining, with reference to

Figure 2-4, the following:

2

1 2R r a r (2.2) 2

1 2X x a x

(2.3)

where

a turns ratio;

1r ,1x winding resistance and leakage reactance of primary side;

2r ,2x winding resistance and leakage reactance of secondary side;

,R X resistance and reactance of equivalent circuit.

The parameters R and X are determined by the short-circuit test, in which impedance is

measured across the terminals of one winding when applying a short-circuit to the other

winding (usually the low-voltage side). Winding resistance is often omitted in the

transformer equivalent circuit since R is typically less than 1% [83]. The values of the

conductance cG and magnetizing susceptancemB can be calculated for the equivalent

circuit by an open-circuit test, which consists of applying rated voltage to the low-

voltage terminals of the transformer to measure the power input and currents. Both

parameters are very small (μS) and thus the exciting current is often neglected [83].

Positive- and negative-sequence impedances of a transformer are equal because it is a

static apparatus and the sequence impedances do not change with the phase sequence

when balanced voltages are applied to the terminals.

Figure 2-4 Transformer representation, (a) equivalent circuit with an ideal transformer and (b)

equivalent circuit with magnetizing current neglected (adopted from [83]).

r1 x1 a2x2 a2r2

Gc Bm

I1I2/a

a:1

V1

+

_

V2

+

_

I2

(a)

R jX

V1

+

_

V2

+

_

I1

(b)


46 |

The zero-sequence impedance of a transformer can vary from a low value to an infinite

value depending on the transformer winding connection, method of neutral grounding

and the core construction [83]. The most common connections of two-winding

transformers and the respective zero-sequence equivalent circuits are summarized in

Figure 2-5. The arrows on the connection diagrams indicate the possible paths for the

flow of zero-sequence current. The absence of an arrow denotes that the transformer

connection lacks a flowing path for the zero-sequence current. The zero-sequence

equivalent circuits are approximations because winding resistance and the magnetizing-

susceptance have been neglected.

Figure 2-5 Zero-sequence equivalent circuits of five three-phase transformer banks and their respective

symbols and connection diagrams (adopted from [83]).

Figure 2-5 shows that delta and ungrounded wye windings impede the flow of zero-

sequence current by means of an open-circuit. In the presence of a path for the zero-

sequence current through at least one grounded wye winding, the total zero-sequence

impedance 0 3 3N nZ R jX Z Z when both the high-voltage and the low-voltage

windings are grounded and 0 3 NZ R jX Z if only the high-voltage side is

grounded.

P Q

P Q

P Q

P Q

P Q

N

ZN

P n

Zn

Q

N

ZN

P n Q

P Q

N

ZN

P Q

NP Q

QP Z0

Reference

QP Z0

Reference

QP Z0

Reference

QP Z0

Reference

QP Z0

Reference

Symbols Connection diagrams Zero-sequence equivalent circuits


47 |

Almost all transformers in power systems feature taps on windings to vary the ratio of

transformation by changing tap position when the transformer in not energized [83].

However, load-tap-changing (LTC) transformers can automatically change taps while

the transformer is energized. The tap changing is operated by motors which respond to

relays responsible for maintaining the voltage within a prescribed band. Transformers

with off-nominal ratios can be represented by a π equivalent circuit according to the tap

ratio [85]. The π equivalent of a transformer connected between buses j and k with tap

ratio n :1 where n is variable, and impedance Z is shown in Figure 2-6.

Figure 2-6 Equivalent circuit for tap changing transformer (adopted from [85]).

Phase shift occurs in delta-wye transformers. Although practical systems are designed

with such phase shifts summing to zero around all loops, the calculation of

unsymmetrical faults might require taking into account the effects of phase shift. This

can be accomplished by advancing all positive-sequence voltages and current by 30°

when stepping up from the low-voltage side to the high-voltage side of a delta-wye or

wye-delta transformer [83].

2.3 Bus Impedance Matrix

The modeling of the main components of the typical power transmission network is

developed in previous sections. In this section a composite representation of the

interconnection and interaction of those components is formulated as a network model.

In the analysis of large power networks, the network model takes on the form of a

network matrix whose elements are determined by the relationship between the current

flow through a network component and the voltage drop across it. There are two types

of network matrices depending on the parameter used to relate the current flows to the

voltage drops: the bus admittance matrix and the bus impedance matrix. Both describe

the steady-state behavior of all the components acting together as a system and can be

obtained by nodal analysis of the network equations. The bus admittance matrix is

widely used for power-flow analysis whereas the bus impedance matrix is preferred for

power system fault analysis [83].

nZ

1

nZ

n

2

1

n Z

nVj

+

_

j

+

_

Vk

k


48 |

By definition the bus impedance matrix is the inverse of the bus admittance matrix, that

is

1

bus bus

Z Y (2.4)

The standard form of the bus impedance matrix is illustrated below for a network with

three independent buses:

11 12 13

21 22 23

31 33 33

bus

Z Z Z

Z Z Z

Z Z Z

Z (2.5)

The bus impedance matrix is symmetrical around the principal diagonal. The elements

of busZ on the principal diagonal are called driving-point impedances of the buses and

the off-diagonal elements are called the transfer impedances of the buses. The bus

impedance matrix and can be obtained directly without inverting the bus admittance

matrix. For instance, starting with the bus equations expressed as

busV Z I (2.6)

where V and I are column vectors of the bus voltages and the currents entering the

buses from current sources. Expanding (2.6) for the network expressed by (2.5) results

in

1 11 1 12 2 13 3V Z I Z I Z I (2.7)

2 21 1 22 2 23 3V Z I Z I Z I

(2.8)

3 31 1 32 2 33 3V Z I Z I Z I

(2.9)

It can be seen from (2.7) that the driving point impedance of bus 1 is determined by

open-circuiting the current sources at buses 2 and 3 and by injecting the source current

1I at bus 1. Thus,

2 3

111

1 0I I

VZ

I

(2.10)

Transfer impedances can be obtained in a similar way. For example, (2.8) indicates that

if current sources 2I and 3I are open-circuited it is possible to determine the transfer

impedance of bus 1 and 2 as in (2.11).


49 |

2 3

221

1 0I I

VZ

I

(2.11)

Equation (2.9) states that injecting a current into bus 3 with current sources at buses 1

and 2 open leaves impedance33Z as the only one through which

3I flows. Under the same

conditions, (2.7) and (2.8) show that 3I causes voltages at buses 1 and 2 expressed by

1 13 3V Z I

(2.12)

2 23 3V Z I

(2.13)

Once the bus impedance matrix has been built the Thévenin impedances at buses can be

readily obtained. The Thévenin impedance at bus k is given by

,th k kkZ Z (2.14)

where kkZ is the diagonal entry in row k and column k of

busZ . The Thévenin impedance

between bus j and bus k can be calculated as:

, 2th jk jj kk jkZ Z Z Z (2.15)

The analysis embodied in equations (2.6)-(2.15) shows that the change in voltage at a

bus can be approximated by the product of the current and the appropriate driving-point

or transfer impedance. A further approximation can be made by adding these estimates

to the original values to obtain the new voltages [83]. These approximations form the

basis for power system fault analysis, which is addressed in the next section.

It was previously stated that the bus impedance matrix can be constructed without

having to invert the bus admittance matrix. This is accomplished by the busZ building

algorithm. It starts by selecting a branch tied to the reference from a bus and adding to

this bus a second branch connected from a new bus. The outcome of the first step is a 2

by 2 bus impedance matrix. In the next step, a third branch connected to one or both of

the already chosen buses is added to expand both the evolving network and its bus

impedance matrix. This procedure is repeated until all branches of the physical network

have been incorporated into busZ [83].


50 |

2.4 Fault Calculation Based on System Impedance

Matrix

Conceptually, a voltage sag is the change in voltage due to a change in current or

resistance as stated by Ohm’s law. Since power systems have non-zero impedances any

increase in current causes a reduction in voltage. In the vast majority of these reductions

however the voltage remains within statuary limits. The voltage reduction is

proportional to the current increment, and therefore short-circuit currents generally

cause a greater voltage drop than the starting current of induction motors, the inrush

current of transformer energizing, and overload currents. In practice, voltage sags

induced by short-circuit faults cause the most equipment trips and accordingly interest

has been focused on this type of sags [1]. The bus voltage changes, i.e., voltage sags or

voltage swells that occur in the system due to a fault are obtained from fault

calculations, which are discussed in this subsection.

The bus impedance matrix is most often used for fault analysis as equivalent circuits

based on its elements can simplify the calculation of currents and voltages throughout

the system upon the occurrence of a fault [83]. Both symmetrical and unsymmetrical

faults can be analyzed with this approach but the method of symmetrical components

must be used to handle the unbalanced currents caused by unsymmetrical faults. The

solution method is based on Thévenin’s theorem, which allows finding the fault current

by replacing the entire system with an equivalent circuit consisting of a single generator

and series impedance.

A simple power system has been used in [83] to derive general equations applicable to

any balanced system regardless of its complexity. The system contains three

synchronous machines, two are grounded through a reactance and the other one is not

grounded. These generators are connected through three-phase transformers to a

transmission line. The single-line diagram of the system, its sequence networks, and the

Thévenin equivalent circuits of the sequence networks are shown in Figure 2-7.

Generators are modeled by their subtransient internal voltages in series with their

subtransient reactances (since subtransient reactances of generators and motors are

generally used to calculate the initial current drawn by a short-circuit fault [83]). It is

assumed that a fault occurs at point P , which is identified as bus k in the single-line

diagram and in the sequence networks.


51 |

Figure 2-7 Single line diagram of a three-phase system (a), the three sequence networks of the system

(b-d), and the Thévenin equivalent circuit of each network for a fault at point P , identified as bus k (e-g)

(adopted from [83]).

The negative-, positive-, and zero-sequence networks can be represented symbolically

by the bus impedance matrix as follows:

( ) ( ) ( ) ( )

11 12 1 1

( ) ( ) ( ) ( )

21 22 2 2

( )

( ) ( ) ( ) ( )

1 2

( ) ( ) ( ) ( )

1 2

s s s s

k N

s s s s

k N

s

bus s s s s

k k kk kN

s s s s

N N Nk NN

Z Z Z Z

Z Z Z Z

Z Z Z Z

Z Z Z Z

Z (2.16)

where s = 0, 1, or 2 indicates zero, positive, or negative sequence impedance values,

respectively.

Alternatively, each of the sequence networks can be also represented by its Thévenin

equivalent between any bus and the Reference node. For example, Figure 2-7 shows the

Thévenin equivalent circuit between the fault point P and the Reference node for each

sequence network. The voltage source in the positive-sequence network and its

k

P

+

_

+

_

+

_

k

P

Vf

+

_ Reference

Ifa(1)

k

P

Reference

Ifa(2)

+

_Vf

Zkk(1)

P

+

_

Ifa(1)

Vka(1)

k

Zkk(2)

P

+

_

Ifa(2)

Vka(2)

k

Zkk(0)

P

+

_

Ifa(0)

Vka(0)

k

(a) Single-line diagram of balanced three-phase system.

(b) Positive-sequence network.

(c) Negative-sequence network.

(d) Zero-sequence network.

(e) Thévenin equivalent of the

positive sequence network.

(f) Thévenin equivalent of the

negative sequence network.

(g) Thévenin equivalent of the

zero sequence network.

k

Reference

Ifa(0)


52 |

Thévenin equivalent circuit is fV , the voltage to neutral at the fault point P (bus k )

before the occurrence of the fault. The absence of voltage sources in the negative- and

zero-sequence networks and their Thévenin equivalent circuits is explained by the

assumption that no negative- or zero-sequence currents flow before the fault occurs. The

Thévenin impedance existing between bus k (fault point P ) and the Reference node of

the negative-, positive-, and zero-sequence networks are (2)

kkZ , (1)

kkZ , and (0)

kkZ (diagonal

elements of (2)

busZ , (1)

busZ , and (0)

busZ ), respectively and their values depend on the values of

the reactances used in the network.

Let faI be the current of phase a flowing out from the original balanced system into the

fault. As can be seen in Figure 2-7 the symmetrical components of faI , that is

(0)

faI , (1)

faI ,

and (2)

faI , are being drawn out of the respective sequence networks and their Thévenin

equivalent circuits at fault point P . The currents flowing out of faulted bus k can be

represented as current injections into bus k as (0)

faI , (1)

faI , and (2)

faI . These current

injections cause voltage changes (sags and swells) at the buses of the zero-, positive,

and negative-sequence networks, respectively. The voltage changes ( ) in the sequence

networks ( s = 0, 1, or 2) of the N-bus network due to the current injections are given in

general terms by

( ) ( ) ( ) ( ) ( )

1 11 12 1 1

( ) ( ) ( ) ( ) ( )

2 21 22 2 2

( )( ) ( ) ( ) ( ) ( )

1 2

( ) ( ) ( ) ( ) ( )

1 2

0

0

0

s s s s s

a k N

s s s s s

a k N

ss s s s s

faka k k kk kN

s s s s s

Na N N Nk NN

V Z Z Z Z

V Z Z Z Z

IV Z Z Z Z

V Z Z Z Z

( ) ( )

1

( ) ( )

2

( ) ( )

( ) ( )

s s

k fa

s s

k fa

s s

kk fa

s s

Nk fa

Z I

Z I

Z I

Z I

(2.17)

It can be seen that only column k , which represents the bus where the faults occurs,

needs to be considered. The total positive-sequence voltage of phase a at each bus

during the fault can be then calculated using the corresponding prefault voltages as:


53 |

(1) (1) (1) (1)(1) (1)1 1 11 1

(1) (1) (1) (1)(1) (1)2 2 22 2

(1) (1)(1) (1)

(1)(1) (1)

af af k faa a

af af k faa a

f f kk faka ka

NafNa Na

V V Z IV V

V V Z IV V

V V Z IV V

VV V

(1) (1) (1)

Naf Nk faV Z I

(2.18)

In industry practice, load currents are usually omitted in fault calculations [83]. This

means that all prefault currents are regarded as being zero and the prefault voltage at all

buses as fV . Both prefault voltages equal to

fV and actual prefault voltages determined

taking into account load currents have been used in this thesis.

Under the assumption that prefault voltages in the negative- and zero-sequence

networks are zero, the voltage changes are equivalent to the total negative- and zero-

sequence voltages during the fault as expressed by

( ) ( )( )11

( ) ( )( )22

( ) ( )( )

( ) ( )( )

s ssk faa

s ssk faa

s sskk faka

s ssNk faNa

Z IV

Z IV

Z IV

Z IV

(2.19)

where s is either 0 or 2, the former representing zero-sequence quantities and the latter

negative-sequence quantities.

A generalization can be made from (2.18) and (2.19) such that once the symmetrical

components of the fault current at any bus are known, the sequence voltages at any

other bus of the system can be determined. That is, during the fault at bus k the

sequence voltages of phase a at any bus j are

(0) (0) (0)

ja jk faV Z I

(1) (1) (1) (1)

ja jaf jk faV V Z I (2.20)

(2) (2) (2)

ja jk faV Z I

From the set of sequence voltages of phase a the set of line-to-neutral voltages of

phases a ( )janV , b ( )jbnV , and c ( )jcnV at bus j can be determined using symmetrical

components as follows:


54 |

(0) (1) (2)

(0) 2 (1) (2)

(0) (1) 2 (2)

jan ja ja ja

jbn ja ja ja

jcn ja ja ja

V V V V

V V V V

V V V V

(2.21)

where = 1 120°is an operator that causes a rotation of 120° in the anticlockwise

direction. The line-to-line voltages at bus j are then given by

jab jan jbn

jbc jbn jcn

jca jcn jan

V V V

V V V

V V V

(2.22)

A voltage measurement device (e.g. a power quality monitor) connected phase-to-

neutral at bus j will measure a voltage sag or swell as defined by (2.21) upon the

occurrence of fault, whereas the same monitor connected phase-to-phase will measure

the event as expressed by (2.22). The magnitude of the sag measured by each monitor

will depend on the type of fault and on the relative location of the fault, i.e., if there is a

delta-wye transformer between the fault location and the monitored bus.

Equation (2.20) states that calculation of the voltages changes caused by a fault requires

knowledge of the values of the symmetrical components (0)

faI ,(1)

faI , and(2)

faI of the

fault current. These values are determined by the type of fault and the fault impedance

fZ . The calculation of the symmetrical components of the fault current for the most

common types of faults is discussed next.

2.4.1 Three-Phase Faults

Faults involving the three phases represent only about 5% of the total but are the most

severe [83]. A symmetrical three-phase fault with the same fault impedance fZ in all

phases and a common point is represented in Figure 2-8. The common point may or

may not be connected to ground. Both of these cases are essentially equal unless the

fault occurs simultaneously with a second unbalanced fault involving ground [88]. The

equation to calculate the fault current can be obtained directly from the Thévenin

equivalent circuit of the system at the fault bus k (see Figure 2-8 (b)) by incorporating

the fault impedance:


55 |

(1)

(1)

f

fa

kk f

VI

Z Z

(2.23)

As can be seen from (2.23) only positive-sequence fault currents are drawn by three-

phase faults. Assuming bolted faults (fZ = 0) equates to a direct short circuit that entails

the highest value of fault current, which can be taken as the most conservative value to

assess the effects of faults. Faults however often involve fault impedances greater than

zero.

Figure 2-8 Three-phase fault through fault impedance fZ , (a) symbolic representation and (b)

connection of the Thévenin equivalent circuit (adopted from [83]).

2.4.2 Single Line-to-Ground Faults

Most of the faults on transmission lines (70% - 80%) are unsymmetrical single line-to-

ground faults caused by insulator flashovers resulting from a lightning strike or by

conductors making contact with grounded structures [83]. Figure 2-9 (a) shows the

representation of a single line-to-ground occurring in phase a (without any loss of

generality) through a fault impedancefZ . The conditions at the faulted bus k are given

by

0fb fcI I (2.24)

ka fa fV I Z (2.25)

Therefore, the symmetrical components of fault currents are

(0)

(1) 2

(0) 2

1 1 11

1 03

1 0

fa fa

fa

fa

I I

I

I

(2.26)

Ifa

Ifb

Ifc

Zf

Zf

Zf

a

b

c

k

k

k

+

_Vf

+

_

Ifa(1)

Vka(1)

k

Zkk(1)

Zf

(a) (b)


56 |

which yields

(0) (1) (2)

3

fa

fa fa fa

II I I (2.27)

Replacing (1)

faI and (2)

faI with (0)

faI shows that (0)3fa faI I , and from (2.20) the following

applies

(0) (0) (0)

(1) (1) (0)

(2) (2) (0)

ka kk fa

ka f kk fa

ka kk fa

V Z I

V V Z I

V Z I

(2.28)

The voltage to neutral in phase a at the fault bus k can be then calculated as

(0) (1) (2) (0) (1) (2) (0) (0)3ka ka ka ka f kk kk kk fa f faV V V V V Z Z Z I Z I (2.29)

Solving for (0)

faI and combining the result with (2.27) gives

(0) (1) (2)

(0) (1) (2) 3

f

fa fa fa

kk kk kk f

VI I I

Z Z Z Z

(2.30)

The symmetrical components of the fault current for a single line-to-ground fault

through fault impedance fZ are determined by (2.29). The series connection of

Thévenin equivalents of the three sequence networks as depicted in Figure 2-9 (b)

simulate a single line-to-ground fault on phase a at bus k of the system. Since the

currents and voltages in this circuit satisfy (2.29) all the required equations for the fault

point can be derived from this sequence-network connection.

Figure 2-9 Single line-to-ground fault through fault impedance fZ , (a) symbolic representation and (b)

connection of the Thévenin equivalent circuits (adopted from [83]).

Ifa

Ifb

Ifc

a

b

c

Zf

k

k

k

+

_Vf

+

_

Ifa(1)

Vka(1)

k

Zkk(1)

Ifa(2) k

Zkk(2) +

_

Vka(2)

Ifa(0) k

Zkk(0) +

_

Vka(0)

3Zf

Ifa(0)

Ifa(1)

= = Ifa(2)

(b)(a)


57 |

2.4.3 Line-to-Line Faults

Faults involving two lines but not ground are also unsymmetrical faults and the rate of

occurrence is similar to three-phase faults [89]. A line-to-line fault on phases b and c

through fault impedance fZ is represented in Figure 2-10 (a) and a schematic model of

the fault is shown in Figure 2-10 (b). The following relations hold at the fault point k :

0faI (2.31)

fb fcI I (2.32)

kb kc fb f fc fV V I Z I Z (2.33)

Therefore, the symmetrical components of the unsymmetrical fault current are

(0)

(1) 2

(0) 2

1 1 1 01

13

1

fa

fa fb

fa fb

I

I I

I I

(2.34)

which results in

(0) 0faI

(2.35)

(1) (2)

fa faI I

(2.36)

Since zero-sequence sources are absent and zero-sequence currents do not flow line-to-

line fault calculations do not require zero-sequence components. From the connection of

negative- and positive-sequence networks shown in Figure 2-10 the following can be

derived:

(1) (2) (1) (2) (1) (1) (2) (1)

2 (1) 2 (2) 2 (1) (2)

kb kc kb kb kc kc kb kc kb kc

ka ka ka ka

V V V V V V V V V V

V V V V

(2.37)

(1) (2) 2 (1) (2)

fb f fb fb f fa fa fI Z I I Z I I Z (2.38)

Since (2.37) and (2.38) are equal and substituting (2.36) the following is obtained:

2 (1) (2) 2 (1)

ka ka fa fV V I Z (2.39)

which is equivalent to the voltage-drop equation for impedance fZ in Figure 2-10 (b):

(1) (2) (1)

ka ka fa fV I I Z (2.40)


58 |

Figure 2-10 Line-to-line fault with fault impedance fZ , (a) symbolic representation and (b) connection

of the Thévenin equivalent circuits (adopted from [83]).

The equations for the negative- and positive-sequence components of the fault current

can be obtained from the connection of the Thévenin equivalent circuits shown in

Figure 2-10 as follows:

(1) (2)

(1) (2)

f

fa fa

kk kk f

VI I

Z Z Z

(2.41)

There are no zero-sequence components in the current of line-to-line faults. The phase

shift of the negative- and positive-sequence caused by delta-wye transformers must be

taken into account in the calculations.

2.4.4 Line-to-Line-to-Ground Faults

Faults involving two phases and ground are another type of unsymmetrical fault that

usually occur more often than line-to-line and three-phase faults [89]. The graphical

representation of a double line-to-ground fault at bus k between phases b and c is

shown in Figure 2-11 (a) and the connection of the Thévenin equivalents of the

sequence networks for the fault is shown in Figure 2-11 (b). The following applies for

the fault at bus k :

0faI

(2.42)

(0)

3

fb fc

fa

I II

(2.43)

(0)3kb kc fb fb f fa fV V I I Z I Z (2.44)

Replacing kcV with

kbV to perform the symmetrical-component transformation yields:

Ifa

Ifb

Ifc

Zf

a

b

c

k

k

k

+

_Vf

+

_

Ifa(1)

Vka(1)

k

Zkk(1)

Ifa(2)Zf

Zkk(2)

k

+

_

Vka(2)

(a) (b)


59 |

(0)

(1) 2

(0) 2

1 1 11

13

1

ka ka

ka kb

ka kb

V V

V V

V V

(2.45)

which results in

(1) (2)

ka kaV V (2.46)

(0) (0) (1) (2) (0)3 2 2 3ka ka kb ka ka ka fa fV V V V V V I Z (2.47)

The characterizing equations of the double line-to-ground fault can then be obtained by

solving for (1)

kaV :

(1) (2) (0) (0)3ka ka ka fa fV V V I Z (2.48)

(0) (1) (2) 0fa fa faI I I (2.49)

The symmetrical components of the fault current can be obtained from the diagram of

sequence network connections as follows:

(1)

(2) (0)

(1)

(0) (2)

3

3

f

fa

kk kk f

kk

kk kk f

VI

Z Z ZZ

Z Z Z

(2.50)

(0)

(2) (1)

(0) (2)

3

3

kk f

fa fa

kk kk f

Z ZI I

Z Z Z

(2.51)

(2)(0) (1)

(0) (2) 3

kkfa fa

kk kk f

ZI I

Z Z Z

(2.52)

As a final observation from the calculation of symmetrical and symmetrical faults,

recall that the symmetrical components (0)

faI , (1)

faI , and (2)

faI of the fault current can be

treated as negative current injections into the sequence networks at the fault bus k to

calculate the voltage changes, i.e., the voltage sags or swells, at all buses of the system

using the bus impedance matrices.


60 |

Figure 2-11 Double line-to-ground fault with fault impedance fZ , (a) symbolic representation and (b)

connection of the Thévenin equivalent circuits (adopted from [83]).

2.5 Voltage Sag Assessment Software

Throughout this thesis a custom-made program developed on MATLAB® named vSAS

(“Voltage Sag Assessment Software”) has been used to calculate the voltage sag

characteristics in several networks. vSAS was developed in [90] to provide an analytical

tool for the techno-economic assessment of voltage sag performance and mitigating

solutions. The numerical results and graphical descriptions generated by vSAS have

been published, among others, in [91-93]. The software calculates all the voltage sag

characteristics required in this thesis by means of fault-current calculations based on the

bus impedance matrix.

2.6 Test Systems

2.6.1 10-bus Power System

The sample 500-kV power network depicted in Figure 2-12 is introduced in [53] to

perform monitor placement studies and is used in Chapter 4 of this thesis. The network

consists of 10 buses, 10 lines, and 5 generators. The network data is given in [53] and is

also provided in Appendix A.

Ifa

Ifb

Ifc

Zf

a

b

c

k

k

k

Ifb + Ifc

+

_Vf

+

_

Ifa(1)

Vka(1)

k

Zkk(1)

3Zf

+

_

Ifa(2)

Vka(2)

k

Zkk(2) +

_

Ifa(0)

Vka(0)

k

Zkk(0)

(a) (b)


61 |

Figure 2-12 A sample 10-bus network.

2.6.2 IEEE Reliability Test System

The IEEE Reliability Test System (RTS) was developed by the IEEE Reliability

subcommittee and publicized in 1978. The purpose of this system is to provide a

benchmark system for testing reliability methods [94]. The system is used in Chapter 3

and Chapter 4 and is depicted in Figure 2-13. The RTS consists of 24 buses, 33 lines, 10

generators, and 5 transformers and it was recently modeled as a 24-substation, breaker-

oriented, three-phase model in [95] for use in research for three-phase power flow

analysis, reliability analysis, fault analysis, and transient stability, among other

applications. The updated system parameters were taken from [96] and are provided in

Appendix A.

Figure 2-13 IEEE Reliability Test System (RTS).

9

1

8

10

6

5

432

7

1 2 7

45

3 9

24 11 12

10

8

6

15

14

16

17

19

13

18

2320

21 22

138 kV 230 kV


62 |

2.6.3 IEEE 118-bus Power Flow Test Case

The IEEE 118-bus test system diagrammed in Figure 2-14 represents a portion of the

electric power system in the Midwestern USA dating back to 1962 [97]. This system is

used in Chapter 4 and it consists of 35 generators, 118 buses, 177 transmission lines,

and 9 transformers. The network data is provided in [97] and reproduced in Appendix

A.

Figure 2-14 IEEE 118-bus power flow test case.

2.6.4 Generic Distribution System

The generic distribution system (GDS) depicted in Figure 2-15 was developed using

typical parameters and configurations present in UK distribution networks [98-100]. It

has been utilized to perform technical and economical studies on voltage sags in [29, 91,

93, 101] among others, and it is used in all the chapters of the thesis. The system

consists of 295 buses and 278 overhead lines and underground cables with lengths

between 0.05 and 11 kilometers. It also comprises a 400-kV/275-kV transmission

system in-feed, a 33-kV predominantly meshed sub-transmission network, and an 11-

kV predominantly radial distribution network. The system supplies 373 MW and 77

1 2

3

4

11733

1211

56 7

13

14

15

19

18

17

30113

16

8

9

10

29

27

32

114

26

25

23

2221

2031

35

34

36

73

7224

74

75

83

84

85

86

88 89

82

90 9187

95 94

93

92

102 101112

111

110103

109

108107

105

106

104100

99

8179

96

80

78

76

77

118

70

71

116

68

69

38

4137

4345

48

46

47

39

40 42 54

5253

56

59

55

58

51 6064

6149

67

6662

65

63

50

115

44

57

9897

28


63 |

MVAR through 39 transformers to 148 load buses at which static loads (constant

impedance) are connected. The system data is provided in Appendix A and summarized

in Table 2-3.

Table 2-3 Number and characteristics of generic distribution system components

400 V 11 kV 33 kV 132 kV 275 kV 400 kV Total

Buses 5 233 25 23 4 5 295

Loads 0 139 6 3 0 0 148

P (MW) 0 47.79 144.88 180.13 0 0 372.8

Q (MVAR) 0 9.44 31.44 35.77 0 0 76.65

Overhead lines 0 136 5 4 0 0 145

Underground cables 0 93 18 22 0 0 133

Average X/R ratio of

lines and cables

N/A 0.6212 2.5816 4.1345 N/A N/A 1.1119

Transformers 0 2 8 13 4 12 39

2.7 Summary

The sag characteristic most relevant to this thesis is the residual voltage. Therefore,

from the range of simulation tools available for voltage sag studies described in section

2.1, the fault-current calculation method was deemed as the most convenient for this

research due to its high suitability for calculating residual voltages, ease of

implementation, and the relatively simple required capabilities of the simulation tool. In

accordance with this selection, steady-state models of the main system components and

the fault calculation method based on bus impedance matrix are utilized throughout the

thesis. Results are obtained from a previously developed program on MATLAB®

named vSAS.


64 |

Figure 2-15 Single line diagram of the generic distribution system (GDS).

28

4

24

46

17

28

16

14

12

26

21

19

23

22

22

2

18

15

54

52

53

22

9

50

75

22

7

74

22

8

20

22

0

51

76

13

26

7

87

48

47

49

22

1

43

42

41

40

39

38

37

26

8

23

42

35

23

0

78

79

80

81

85

88

28

5

82

83

84

28

6

90

91

92

94

93

95

96

97

10

09

8 99

10

1

10

21

03

10

4

10

51

06

10

7

10

8

10

9

11

0

11

1

11

2

11

31

14

11

5

12

0

12

1

12

21

23

12

4

12

5

12

6

12

7

11

6

11

7

11

81

19

86

11

10

8

97654

55

1

65

64

63

57

22

52

26

58

14

8

14

6

15

3

15

4

14

91

52

15

5

14

71

45

14

4

14

0

14

2

14

1

14

3

13

9

13

8

12

8

12

91

32

13

0

13

4

13

61

35

13

7

13

3

15

6

16

0

15

7

18

5

18

3

13

1

15

9

16

4

16

1

16

2

16

3

16

5

16

6

16

71

68

16

9

17

9

18

0

18

11

82

18

4

18

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Chapter 3 • Optimal Monitor Placement for Voltage Sag Characterization

65 |

Chapter 3

Optimal Monitor

Placement for Voltage Sag

Characterization

This chapter provides an overview of the first and still the most referred optimal

monitor placement method for voltage sag characterization. The monitor reach area

(MRA) method determines minimum monitoring programs that estimate the sag

performance of all non-monitored buses of the system. This method, however, has

important limitations which are highlighted through simulations on the IEEE 24-bus

reliability test system (IEEE-RTS) and on the 295-bus generic distribution system

(GDS). A recently proposed fault location method that can be used to overcome these

limitations and enhance the robustness of the MRA method is also reviewed and

discussed in the chapter. Finally, the chapter presents the improvement of the MRA

method by incorporating the previous fault location method in the MRA algorithm. This

improvement of MRA method presents the first original contribution of the thesis.

3.1 Monitor Reach Area Method

The monitor reach area (MRA) is defined as the region of the network where a monitor

is able to register voltage sags caused by faults [39]. This region encompasses the buses

and lines where the occurrence of faults causes a voltage drop at the bus where the

monitor is installed. The size of the MRA is proportional to the voltage drop, i.e. the

bigger the voltage drop the smaller the size of the MRA, as depicted in Figure 3-1. The

voltage drop, measured as the magnitude of the voltage sag, is determined from short


66 |

circuit analysis based on the bus impedance matrix. The classical symmetrical

component method is used to calculate the magnitude of voltage sags, e.g., [1], [91-93].

Figure 3-1 Symbolic representation of three monitor reach areas for bus 9 of the IEEE-RTS.

Consider the illustrative power system shown in Figure 3-2 and assume that a fault takes

place at fault point t on line connecting buses j and k . The fault distance per unit

from bus j is denoted by d and s

z is the total impedance of the line, with s = 0, 1, or

2 indicating zero, positive, or negative sequence impedance values. The sequence

voltages at bus i [83] can be calculated by:

1 1 1 (1)pf

i i it fV V Z I (3.1)

2 2 2

i it fV Z I (3.2)

0 0 0

i it fV Z I (3.3)

where

1 2 0, ,i i iV V V positive, negative, and zero sequence voltage at bus i during the fault;

(1) pf

iV pre-fault positive sequence voltage at bus i ;

1 2 0, ,it it itZ Z Z positive, negative, and zero sequence transfer bus impedance between

bus i and fault point t ;

1 2 0, ,f f fI I I positive, negative, and zero sequence current at fault point t .

1 2 7

45

3 9

24 11 12

10

8

6

15

14

16

17

19

13

18

2320

21 22

S.C.

0.90 p.u. 0.70 p.u. 0.40 p.u.

V

138 kV 230 kV

V Voltage measurement device


67 |

And the three-phase voltages at bus i can be calculated as the product of a component

of aV (voltage of phase a ) and some function of operator 1 120 as follows:

0

12

2 2

1 1 1

1

1

aa

b a

c a

VV

V V

V V

(3.4)

Power system network

j k

i

tdz(s) (1-d)z(s)

Figure 3-2 Illustrative power system.

The monitor reach areas of a network’s buses can be modeled as a binary matrix of

order N F , where N is the number of buses, and F is the number of fault positions.

Fault positions can represent potential faults at buses, discrete points on lines, or line

segments. The MRA matrix is built for each type of fault and for a given voltage

threshold thV , using the magnitude of the phase voltages calculated with (3.4) as

follows:

,

,

,

1,if min , ,

0,if min , ,

a b c thx y

x y

a b c thx y

V V V V

V V V V

MRA (3.5)

The value of ,x yMRA equals one only if faults occurring at fault point y produce a

voltage sag with magnitude below or equal to thV at bus x in any of the three phases.

As stated previously, the size of the monitor reach area is proportional to the sag

magnitude and thus the lower the voltage threshold thV used to build MRA the more

monitors are required to cover the entire network.

A single MRA matrix represents the area of the network where a monitor can detect

and capture the voltage sags originated by faults with specific characteristics, such as

type, location, and fault resistance, and taking place under particular system conditions


68 |

such as network topology and generation schedule. Therefore, a considerable number of

MRA matrices should be built in order to study a reasonable number of fault scenarios.

3.1.1 Formulation of the Optimization Problem

In order to formulate the optimal monitor placement problem the binary vector M of

length N (number of buses) is defined as a decision variable whose element xM takes

the value 1 if a monitor is placed at bus x and equals 0 in absence of a monitor. The

monitor placement problem has been formulated as an integer linear programming

problem as [39]:

Minimize1

N

x

x

M (3.6)

subject to ,

1

1,N

x x y

x

y

M MRA (3.7)

The solution of the problem described by (3.6) and (3.7) provides an optimal sag

monitoring program (OSMP), i.e. the minimum set of monitors required to capture all

the voltage sags with magnitude equal to or less than thV caused by faults in the

network. There can be more than one OSMP for a network, all of them having the same

number of monitors but indicating different buses for their location.

3.1.2 Voltage Sag Estimation at Non-Monitored Buses

The number and characteristics of voltage sags at non-monitored buses can be estimated

by finding a set of fault positions likely to cause the residual voltages registered by the

OSMP [65, 102]. For every possible fault position identified, the residual voltage at all

non-monitored buses can be determined by simulating the fault at such a position.

Since the method is not designed to pinpoint the exact fault position, the residual

voltage is calculated as a weighted average of all potential residual voltages as in (3.8),

using the per-unit fault rate of potential fault positions as weighing factors.

1

1

1 fp

iu k ikfpk

k

k

V V

(3.8)


69 |

where iuV is the estimated residual voltage at bus i caused by a fault at an unknown

position u , fp is the number of possible fault positions, k is the fault rate of fault

position k , and ikV is the residual voltage at bus i caused by a fault at position k .

The effectiveness of sag performance estimation at non-monitored buses obtained from

OSMPs is strictly dependant on the triggering of monitors after the voltage of any phase

has dropped below thV . The voltage measured by a monitor during a fault depends,

among the other factors, on the fault characteristics (type, fault impedance, etc.), the

distance between the monitored bus and the fault location, and the pre-fault conditions

of the networks (loading profile, pre-fault voltages at buses, etc). So far the effects of

these factors on sag detection by OSMPs and consequently on the accuracy of sag

performance estimation at non-monitored buses have not been investigated. The effects

of two of these factors, namely, fault impedance and pre-fault voltages are looked into

in the next section.

3.1.3 Factors Influencing Accuracy of Voltage Sag Detection

The estimation of voltage sags using the OSMPs discussed above is strongly dependent

on detection of sags below a fixed voltage threshold. Therefore, if none of the monitors

captures a sag event no estimation can be done. The OSMPs are designed so that every

sag occurring throughout the network can be recorded by at least one monitor; however

there are situations in which the OSMP can overlook voltage sags. Examples of such

situations are discussed below.

In [72] an OSMP for the IEEE-RTS network is obtained by applying the MRA method

for a voltage threshold of 0.7 p.u. The resulting OSMP comprises four monitors

installed at buses 3, 6, 8, and 17. In theory any three-phase (LLL) fault causing a

voltage sag with magnitude below 0.7 p.u. should be detected and recorded by, at least,

one of the monitors placed at these buses.

Line-to-ground (LG) faults have been simulated in the middle of line between buses 5

and 10 using different values of pre-fault voltages and fault resistance. A total of 21 pre-

fault voltage profiles have been calculated using Matpower [103] varying all loads of

the system from 90% to 110% of base values as stated in [95] in steps of 1%. The fault

resistance values used range from 0 to 20Ω [104].


70 |

The voltage sag magnitudes at buses 3, 6, 8, 17 (selected for optimal sag monitoring)

and bus 5 (one end of the faulted line) caused by LG faults and base load (load factor =

100%) are presented in Figure 3-3. It can be seen, for example, that the voltage sag

magnitude at bus 3 is lower than 0.9 p.u. for fault resistance between 0 and 7 Ω and

rises above 0.9 p.u. for greater values of fault resistance. Voltage sag magnitudes at bus

5 lie between 0.32 and 0.74 p.u. The voltage at bus 6 can decrease to 0.71 p.u. but with

a fault resistance of 17 Ω or higher it remains over 0.9 p.u., etc.

Since the most common voltage threshold for which a monitor is set to register voltage

sags is 0.9 p.u. [14], the OSMP determined for the IEEE-RTS network will not capture

LG faults occurring in the middle of line between buses 5 and 10 when the fault

resistance is 17 Ω or higher because the sag magnitude at buses 3, 6, 8, and 17 is greater

than 0.9 p.u. A LG fault with a fault resistance between 17 Ω and 20 Ω however, causes

voltage sags at bus 5 with magnitudes between 0.67 and 0.74 p.u.

Figure 3-3 Voltage sag magnitude at monitored buses (3, 6, 8, and 17) and bus 5 (one of the ends of

faulted line) as a function of fault impedance.

The residual voltage at buses 3, 5, 6, 8, and 17 upon occurrence of a LG fault with fault

impedance of 17 Ω along the line connecting buses 5 and 10 is shown in Figure 3-4. It

is apparent from this figure that none of the monitors at optimal locations would trigger

and therefore record the voltage sag caused by the fault taking place up to 0.57 of the

line because the residual voltage stays above 90% of the nominal voltage (138 kV).

Nevertheless, faults beyond this point generate residual voltages at buses 6 and 8 below

0.9 p.u., as can be observed in the magnified portions of the plot (inset) with an

exception at the very end of the line (length of segment is less than 0.02 p.u.) for bus 6.

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Vo

ltag

e S

ag

Mag

nit

ud

e (

p.u

.)

Fault Impedance (Ohm)

BUS 3 BUS 5 BUS 6 BUS 8 BUS 17


71 |

Figure 3-4 Voltage sag magnitude at monitored buses (3, 6, 8, and 17) and bus 5 (one of the ends of

faulted line) as a function of fault distance.

The variation in magnitude of voltage sags at the OSMP buses due to fluctuation in pre-

fault voltages (21 different values) is depicted in Figure 3-5. The same LG fault

(midway between buses 5 and 10) is simulated with fault resistance of 17 Ω. It can be

seen from Figure 3-5 that the sag magnitude at buses 3, 8, and 17 remains above 0.9 p.u.

in all cases. In three cases the voltage sag magnitude at bus 6 drops below 0.9 p.u. The

voltage sag magnitude at bus 5 drops constantly to 0.7 p.u. over the whole range of pre-

fault voltages. Under these conditions the OSMP however, fails to detect the fault

causing a sag at bus 5 for 18 out of 21 loading scenarios.

Figure 3-5 Voltage sag magnitude at monitored buses as a function of pre-fault voltage.

The simple analysis presented above demonstrates that system’s loading conditions (i.e.

pre-fault voltages at buses) and fault resistance can prevent OSMPs from detecting and

recording voltage sags when the typical triggering threshold value of 90% of the

nominal voltage is used. This lack of sag detection could lead to an increase in the

0.6

0.65

0.7

0.75

0.8

0.85

0.9

0.95

1

1.05

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Vo

ltag

e S

ag

Mag

nit

ud

e (

p.u

.)

Fault Distance from Bus 5 (p.u.)

BUS 3 BUS 5 BUS 6 BUS 8 BUS 17

0.88

0.89

0.9

0.57 0.64 0.71 0.78 0.85 0.92 0.99

0.915

0.925

0.935

0.978 0.986 0.993

a) Bus 3

0.890

0.910

0.930

1.075 1.086 1.094

b) Bus 6

0.900

0.907

0.914

0.993 1.000 1.005

c) Bus 8

1.014

1.015

1.016

1.0398 1.0401 1.0403

d) Bus 17

Vo

ltag

e S

ag

Mag

nit

ud

e (p

.u.)

Pre-fault Voltage (p.u.) Pre-fault Voltage (p.u.)

Vo

ltag

e S

ag

Mag

nit

ud

e (p

.u.)


72 |

number of monitors required to cover the network. The same problem could arise for

other voltage sag thresholds. The actual effects of these factors, namely, pre-fault

voltages, fault resistance, and voltage thresholds on the size of OSMPs are investigated

further in the next section.

3.1.4 Variability in Number of Optimally Placed Monitors

The variation in number of monitors that must be deployed to detect and register every

voltage sag occurring in the GDS network is shown in Table 3-1. Data shown in this

table has been obtained using a pre-fault voltage profile associated with base loading

profile and is presented according to fault impedance, type of faults, and voltage

thresholds thV . From this it can be seen that for low values of fault impedance (0 Ω

and 5 Ω) and all types of faults, the lower the voltage threshold the greater the number

of monitors required to cover the network, i.e., sags with magnitude lower than 0.9 p.u.

entail the fewest monitors whereas sags with magnitude lower than 0.7 p.u. entail the

most. This finding (lower threshold = more monitors) was also established in [40],

however, when the fault impedance is 10 Ω or higher the relationship only holds for

LLG faults, meaning that the monitor reach areas for this type of fault remain

practically the same despite the increase in fault impedance.

For LG faults with fault impedance of 10 Ω or higher and modeled as showed in Section

2.4.2 (see Figure 2-9), less monitors are needed for sags with magnitude lower than 0.7

p.u. than the monitors needed for shallower sags. This is an indication that the total area

of the network where these faults cause voltage drops below 0.7 p.u. is smaller than the

area where the same faults cause sags with magnitude above 0.7 p.u., and thus fewer

monitors are required. The only exception arises when LG faults have a fault impedance

of 25 Ω since the number of monitors for covering sags with magnitude of 0.8 p.u. and

0.7 p.u. is the same.

Table 3-1 Number of Voltage Measurement Devices Required to Record Voltage Sags in the GDS

Rf

(Ω)

LG LL LLG LLL

thV (p.u.) thV (p.u.) thV (p.u.) thV (p.u.)

0.90 0.80 0.70 0.90 0.80 0.70 0.90 0.80 0.70 0.90 0.80 0.70

0 7 10 16 4 6 8 4 5 8 4 7 8

5 14 24 25 5 15 24 4 5 7 10 13 10

10 16 24 15 8 21 8 4 5 7 14 7 8

25 17 8 8 16 6 15 4 6 8 7 8 0

50 10 6 1 5 9 0 4 6 8 3 0 0


73 |

No general relation can be drawn from LL and LLL faults having fault impedance

values of 10 Ω or higher since there is not homogeneous variation in number of

monitors for these cases. In some cases higher voltage threshold entails more monitors

than lower threshold and in other instances the opposite applies. For example, 8

monitors are sufficient to detect both sags with magnitude lower than 0.9 p.u. and sags

with magnitude lower than 0.7 p.u. when these are caused by LL faults having a fault

impedance of 10 Ω, but this number increases to 21 monitors for sags with magnitude

lower than 0.8 p.u. An inverse effect is seen for a fault impedance of 25 Ω. Sags with a

magnitude of 0.9 p.u. and 0.7 p.u. entail 16 and 15 monitors, respectively whereas sags

with magnitude of 0.8 p.u. require only 6 monitors. With regard to LLL faults, the

number of monitors required to register every voltage sag with magnitude of 0.9 p.u.,

0.8 p.u., and 0.7 p.u. is 14, 7, and 8, respectively for fault impedance of 10 Ω. These

numbers change to 7, 8 and 0 in the same order as above when the fault impedance is 25

Ω. LLL faults with fault impedance of 25 Ω and 50 Ω do not cause voltage drops below

0.7 p.u. at any bus and thus no monitors are required for this type of sags. The same

occurs for voltage sags with magnitude of 0.7 p.u. caused by LL faults with fault

impedance of 50 Ω.

Because of these inconsistencies, a new study was performed to determine OSMPs

incorporating all types of faults simultaneously. The three voltage sag thresholds used

previously (0.9, 0.8, and 0.7 p.u.) and the five values of fault impedance (0, 5, 10, 25,

and 50 Ω) were considered in the study. Four different pre-fault voltage profiles were

used to determine the OSMPs. Three pre-fault voltage profiles were determined using

Matpower according to low, base, and high loading profiles, which correspond to

system loading factors of 90%, 100%, and 110%, respectively. Voltages equal to 1 p.u.

at all buses constitute the fourth pre-fault voltage profile.

The minimum number of monitors required to detect all fault-induced voltage sags

occurring throughout the GDS network is shown in Table 3-2. Data from this table can

be compared with the data in Table 3-1 which shows similar results. The principle that

lower sag thresholds entail more monitors does not always hold for faults with fault

impedance greater that 0 Ω. Consider, for example, faults having an impedance of 10 Ω

and occurring during base loading conditions. The number of monitors required to

detect all the voltage sags caused by these faults are shaded in green in Table 3-2. It can

be seen that sags with magnitude lower than or equal to 0.7 p.u. require fewer monitors


74 |

than sags with magnitude greater that 0.7 p.u. This is because the total area of the

network where the aforesaid faults cause sags with magnitude lower than 0.7 p.u. is

smaller than the area where the same faults cause sags with magnitude above 0.7 p.u.,

and thus fewer monitors are required.

Table 3-2 Number of Voltage Measurement Devices Required for Full Sag-Observability of the GDS

Network Using the MRA Method

Rf

(Ω)

1 p.u. Low loading profile Base loading profile High loading profile

thV (p.u.) thV (p.u.)


0.90 0.80 0.70 0.90 0.80 0.70 0.90 0.80 0.70 0.90 0.80 0.70

0 7 11 18 7 11 17 7 11 16 7 11 16

5 22 36 43 18 30 41 16 30 40 14 30 40

10 32 45 29 27 32 23 24 32 22 21 32 22

25 35 20 25 22 19 22 19 19 21 17 17 23

50 19 18 9 14 17 9 13 14 9 12 14 9

As can be seen from Table 3-1 and Table 3-2, the number of monitors required to

achieve full observability of voltage sags in the GDS network varies between 7 and 45

due to combination of the following four factors: 1) fault impedance, 2) pre-fault

voltage, 3) voltage sag threshold, and 4) fault type. The impact of these factors on the

size of the monitor reach areas causes the variability in number of monitors needed for

OSMPs. The results shown in Table 3-1 and Table 3-2 demonstrate that the variation in

number of sag monitors is not uniform due to a non-uniform expansion and waning of

the MRAs of the network’s buses. This variation in MRAs size is not only given by the

voltage sag threshold but also by a rather complex combination between impedance of

faults and pre-fault voltages.

Two important limitations of the MRA method resulting from the use of voltage sag

triggering thresholds have been demonstrated. The first one, shown in Section 3.1.3, is

the potential loss of sag detection capability of OSMPs when sag magnitude at

monitored buses remains above 90% of nominal voltage but falls below this level at

other (non-monitored) buses. The second one, presented in Section 3.1.4, is the high

variability in the number of monitors that might be required to cover the same network

for faults with different characteristics. The underlying reason behind these limitations

is the susceptibility of the fault detection and fault location algorithms employed by the

MRA method to fault resistance, pre-fault voltage profile, and voltage sag thresholds.

An adequate fault location method that can pinpoint the fault position regardless of

these three parameters is therefore needed. One such method is discussed below.


75 |

3.2 Enhanced Fault Location Algorithm

The method proposed in [104] pinpoints the location of faults using the same network

data as the MRA method and solving equations (3.1)-(3.3) for the point t where the

fault occurs (see Figure 3-2). The approach was originally developed to locate faults on

single-circuit transmission lines using voltage measurements that do not have to be from

the ends of the faulted line (no current measurements are involved). The method has

been extended in [105] to locate faults on double-circuit transmission lines using only

limited voltage measurements. The basic assumptions of the method include: the

transmission system is transposed, pre-fault voltages are 1.0 p.u., fault impedance is

purely resistive, and the network data required to build the system’s bus-impedance

matrix of each sequence is available.

The method comprises different fault location algorithms formulated neglecting and

including shunt-capacitance and using measurements from one and two buses (both

synchronized and unsynchronized). Clearly, a one-bus algorithm requires fewer

monitors than a two-bus algorithm at the expense of a decrease in accuracy. Ignoring

shunt capacitance simplifies the algorithm and reduces the use of iterative solution

methods. Iterative solution methods are usually required for distributed-parameter line

models however, they lead to the detriment of accuracy. The maximum difference

between the fault location errors from one-bus and two-bus algorithms, and from

lumped line parameter and distributed line parameter approaches reported in [104] is

8.05%. In line with the objective of optimal monitor placement and given the acceptable

loss of accuracy, the one-bus algorithm that omits shunt capacitance is reviewed in the

next section and subsequently employed to enhance the fault location capability of the

MRA method.

3.2.1 Fault Location of Three-phase Symmetrical Faults

Assume that a three-phase symmetrical fault takes place at fault point t of the sample

power system shown in Figure 3-2 and that the voltage measurement from bus i is

available. For this type of fault only positive-sequence fault current flows and it can be

calculated (ignoring prefault currents) as:


76 |

(1)(1)

1

pf

tf

tt f

VI

Z R

(3.9)

Replacing (1)

fI in (3.1) with (3.9) results in

(1)(1) (1) (1)

(1)

pfpf t

i i it

tt f

VV V Z

Z R

(3.10)

where (1) pf

tV is the pre-fault positive-sequence voltage at fault location t , (1)

ttZ is the

positive-sequence driving-point impedance at fault location t , and fR is the fault

resistance.

1

itZ , and 1

ttZ are calculated as:

(1) (1) (1) (1)

it ij ik ijZ Z Z Z d (3.11)

1 1(1) (1) (1) (1) 2 (1) (1) (1)2 2tt jj kk jk jj jk jjZ Z Z Z z d z Z Z d Z

(3.12)

where d is the fault location (fault distance p.u. from bus j ), (1)

ijZ , (1)

ikZ , (1)

jjZ , (1)

jkZ , and

(1)

kkZ are the positive-sequence transfer impedances corresponding to buses i , j and k ,

and 1

z is the total positive-sequence impedance of line j k .

Substituting (3.11) and (3.12) into (3.10) results in

(1) (1) (1) (1)

(1) (1)

1 1(1) (1) (1) 2 (1) (1) (1)2 2

pf

t ij ik ijpf

i i

jj kk jk jj jk jj f

V Z Z Z dV V

Z Z Z z d z Z Z d Z R

(3.13)

The unknowns in (3.13) are fault location, fault resistance, and pre-fault positive-

sequence voltage at the fault location, thus (3.13) is unsolvable. However, the pre-fault

voltage at the fault location can be approximated to 1.0 p.u. and (3.13) can be separated

into real and imaginary parts to formulate two new equations, then the fault location and

fault resistance can be determined. Alternatively, the following exact equation for the

pre-fault voltage at the fault location can be used:

(1) (1) (1) (1)pf pf pf pf

t j k jV V V V d

(3.14)

where (1) pf

jV and (1) pf

kV are the pre-fault positive sequence voltages at buses j and k ,

which can be calculated by a load-flow simulation tool or state estimation. As (3.14)

shows, assuming pre-fault voltages equal to 1.0 p.u. results in pre-fault voltage at the


77 |

fault location equal to 1.0 p.u., as in the original approach. Given that with (3.14) it is

possible to handle calculated pre-fault voltages and pre-fault voltages approximated to

1.0 p.u., this new equation will be incorporated in the enhanced method to derive more

accurate fault location equations.

To facilitate the separation of (3.13) into real and imaginary parts, let:

(1) (1)

ik ijA Z Z

(3.15)

(1) (1)pf pf

k jB V V

(3.16)

1(1) (1) (1)2jj kk jkC Z Z Z z (3.17)

1 (1) (1)2 jj jkD z Z Z (3.18)

Substituting (3.11), (3.12), (3.14), and (3.15)-(3.18) to (3.10) leads to:

(1) (1)

(1) (1)

2 (1)

pf

ij jpf

i i

jj f

Z Ad V BdV V

Cd Dd Z R

(3.19)

Defining (1) (1) pf

i iE V V and solving for fault location d we get:

(1) (1) (1) (1)

2 (1) 0

pf pfj ij j ij

f jj

AV BZ V ZABd C d D R Z

E E E

(3.20)

The unknown variables in (3.20) are d and fR and hence this equation is unsolvable.

However, it is possible to decompose (3.20) into real and imaginary parts to formulate

two equations so the fault location can be determined. In order to separate the real and

imaginary parts define the following:

1 2

ABC c jc

E (3.21)

(1) (1)

3 4

pf

j ijAV BZD c jc

E

(3.22)

(1) (1)

(1)

5 6

pf

j ij

jj

V ZZ c jc

E (3.23)

Then (3.20) is separated into:

2

1 3 5 0fc d c d c R (3.24)

2

2 4 6 0c d c d c (3.25)


78 |

The solution of (3.25) provides two possible values for d . The value lying between 0

and 1 is the fault location as it is the feasible solution. The other value is an unfeasible

solution (negative value or greater than 1 in the vast majority of cases). As can be seen

from (3.25), fault resistance is not needed to determine the fault location and can be

readily computed once the fault location has been determined. Overall, the quadratic

equation defining the fault location of three-phase symmetrical faults is a function of the

following positive-sequence parameters: 1) the transfer impedance between monitored

bus i and buses j and k , 2) the driving-point impedance of buses j and k , 3) the

impedance of the faulted line, 4) the pre-fault voltages at buses i , j and k and, 5) the

voltage during the fault at monitored bus i .

3.2.2 Fault Location of Line to Line Faults

For a fault between phases b and c, (1) (2) (0), 0f f fI I I holds, and the following applies:

(1)(1)

1 2

pf

tf

f tt tt

VI

R Z Z

(3.26)

(1)(1) (1) (1)

1 2

pfpf t

i i it

f tt tt

VV V Z

R Z Z

(3.27)

where


(3.28)

being (2)

ijZ , (2)

jkZ , (2)

jjZ , (2)

jkZ , and (2)

kkZ the negative-sequence transfer impedance

corresponding to buses i , j and k ; and 2

z the total negative sequence impedance of

line j k .

Let

2(2) (2) (2)2jj kk jkH Z Z Z z (3.29)

2 (2) (2)2 jj jkI z Z Z

(3.30)

Substituting (3.11), (3.12), (3.14), and (3.15)-(3.18), (3.29), and (3.30) into (3.27),

yields:

(1) (1)

(1) (1)

2 (1) (2)

pf

ij jpf

i i

jj jj f

Z Ad V BdV V

C H d D I d Z Z R

(3.31)


79 |

Recalling (1) (1) pf

i iE V V and solving for fault location d gives:

(1) (1) (1) (1)

2 (1) (2) 0

pf pfj ij j ij

f jj jj

AV BZ V ZABd C H d D I R Z Z

E E E

(3.32)

Similar to (3.20) for three-phase faults, the unknown variables in (3.32) are the fault

location and the fault resistance and hence the equation is unsolvable. However, it is

also possible to decompose (3.32) into real and imaginary parts to formulate two

equations so the fault location can be determined. In order to separate the real and

imaginary parts define:

7 8

ABC H c jc

E (3.33)

(1) (1)

9 10

pf

j ijAV BZD I c jc

E

(3.34)

(1) (1)

(1) (2)

11 12

pf

j ij

jj jj

V ZZ Z c jc

E (3.35)

Then (3.32) is separated into:

2

7 9 11 0fc d c d c R (3.36)

2

8 10 12 0c d c d c (3.37)

The quadratic equation (3.37) has two solutions for d , and the one lying between 0 and

1 corresponds to the fault location. The other one can also be a feasible solution but this

occurs rarely. Since fR is not included in this equation, the fault location can be

estimated without knowing the fault resistance, which can be readily computed solving

(3.36) once the fault location has been determined. The expression that determines the

fault location of line to line faults is a function of: 1) the positive-sequence transfer

impedance between monitored bus i and buses j and k , 2) the negative- and positive-

sequence driving-point impedance of buses j and k , 3) the negative- and positive-

sequence impedance of the faulted line, 4) the positive-sequence pre-fault voltages at

buses i , j and k and, 5) the positive-sequence voltage during the fault at monitored bus

i .


80 |

3.2.3 Fault Location of Line to Ground Faults

For a fault between phase a and ground, (0) (1) (2)

f f fI I I holds. Dividing (3.2) by (3.3)

yields:

(2) (2)

(0) (0)

i it

i it

V Z

V Z (3.38)

where

(0) (0) (0) (0)

it ij ik ijZ Z Z Z d (3.39)

(2) (2) (2) (2)

it ij ik ijZ Z Z Z d

(3.40)

Defining (2) (0)

i iG V V and utilizing (3.39) and (3.40), gives:

(2) (2) (2)

(0) (0) (0)

ij ik ij

ij ik ij

Z Z Z dG

Z Z Z d

(3.41)

The fault location is obtained solving (3.41):

(2) (0)

(0) (0) (2) (2)

ij ij

ik ij ik ij

Z GZd

G Z Z Z Z

(3.42)

As can be seen from (3.42), the linear equation describing the fault location of line to

ground faults is a function of: 1) the negative- and zero-sequence transfer impedance of

buses i , j and k , and 2) the ratio of negative- and zero- sequence voltage at bus i

during the fault.

3.2.4 Fault Location of Line to Line to Ground Faults

For a fault involving phase b and c to ground fault. The following holds:

2

(0) (1)

0 23

ttf f

tt tt f

ZI I

Z Z R

(3.43)

(1)(1)

2 0

1

0 2

pf

tf

tt tt f

tt

tt f tt

VI

Z Z RZ

Z R Z

(3.44)

0

(2) (1)

0 2

3

3

tt f

f f

tt tt f

Z RI I

Z Z R

(3.45)


81 |

Dividing (3.45) by (3.43) results in:

0(2)

(0) 2

3f tt f

f tt

I Z R

I Z

(3.46)

Using (3.2), (3.3), and (3.46) leads to:

0(2)(2)

(0) 2(0)

3it tt fi

i it tt

Z Z RV

V Z Z

(3.47)

where


(3.48)

being (0)

ijZ , (0)

jkZ , (0)

jjZ , (0)

jkZ , and (0)

kkZ the zero-sequence transfer impedance

corresponding to buses i , j and k ; and 0

z the total zero sequence impedance of line

j k .

Let

0(0) (0) (0)2jj kk jkJ Z Z Z z (3.49)

0 (0) (0)2 jj jkK z Z Z (3.50)

By employing (3.28)-(3.30), (3.39)-(3.41), and (3.48)-(3.50), (3.47) becomes:

(2) (2) (2) 2 (0)

(0) (0) (0) 2 (2)

3ij ik ij jj f

ij ik ij jj

Z Z Z d Jd Kd Z RG

Z Z Z d Hd Id Z

(3.51)

Define the following two terms:

(0) (0)

ik ijR Z Z (3.52)

(2) (2)

ik ijS Z Z (3.53)

Rearranging (3.51) using (3.52) and (3.53) yields:

2 2 0

0 0 23 2

2 0

0 2

3...

3... 0

ij ij jj f

ij ij jj

ij jj f

ij jj

JZ KS KZ SZ SRJSd HR d HZ IR d IZ RZ

G G G

Z Z RZ Z

G

(3.54)

Then define:


82 |

13 14

JSHR c jc

G

(3.55)

2

0

15 16

ij

ij

JZ KSHZ IR c jc

G

(3.56)

2 0

0 2

17 18

ij jj

ij jj

KZ SZIZ RZ c jc

G

(3.57)

19 20

3Sc jc

G (3.58)

0 2

0 2

21 22

jj ij

ij jj

Z ZZ Z c jc

G (3.59)

2

23 24

3 ijZc jc

G

(3.60)

Applying (3.55)-(3.60) and separating (3.54) into real and imaginary part produces:

3 2

13 15 17 21 19 23 0fc d c d c d c c d c R (3.61)

3 2

14 16 18 22 20 24 0fc d c d c d c c d c R (3.62)

Fault resistance can be calculated from (3.61) as:

3 2

13 15 17 21

19 23

f

c d c d c d cR

c d c

(3.63)

Substituting (3.63) into (3.62) results in:

4 3 2

25 26 27 28 29 0c d c d c d c d c (3.64)

where

25 14 19 13 20c c c c c (3.65)

26 14 23 16 19 13 24 15 20c c c c c c c c c (3.66)

27 16 23 18 19 15 24 17 20c c c c c c c c c (3.67)

28 18 23 19 22 17 24 20 21c c c c c c c c c (3.68)

29 22 23 21 24c c c c c (3.69)

From the solutions of (3.64), the one falling between 0 and 1 is chosen as the fault

location estimate. The others are unfeasible solutions (negative values or greater than 1).

In very rare occasions though, a second feasible solution exists. In these cases the

correct fault location can be identified through voltage matching of multiple monitors.

Equation (3.64) shows that the fault location for line to line to ground faults is a bi-


83 |

quadratic function relating: 1) the zero- and negative-sequence transfer impedances

between monitored bus i and buses j and k , 2) the zero- and negative-sequence

transfer impedances of buses j and k , 3) the zero- and negative-sequence impedances

of the faulted line and, 4) the quotient of zero- and negative-sequence residual voltages

at bus i during the fault.

3.3 Enhanced Monitor Reach Area Algorithm

Fault location tests have been performed on the IEEE-RTS network using both the

original MRA method recapitulated in Section 3.1, and the enhanced version of the

original obtained by implementing the fault location algorithms reviewed in Section

Chapter 3 . Symmetrical and asymmetrical faults with different values of fault

resistance have been simulated at all buses and at different locations along the lines (i.e.,

0.25, 0.5, and 0.75 p.u. of each line length). The fault resistance values used for line to

line faults and three-phase faults were 0 Ω and 5 Ω, whereas for line to ground and line

to line to ground fault resistance values were 0 Ω, 5 Ω, 25 Ω, and 50 Ω.

The pseudo-measurements of the OSMP determined in [72] for the IEEE-RTS network,

i.e. the residual voltages registered by monitors at buses 3, 6, 8, and 17, were used to

formulate the equations of the fault location algorithm. Fault location equations were

developed for every line and a solution having a value between 0 and 1 was considered

as a possible fault location on the line. The potential fault locations determined by all, or

most of the monitors, constitute the list of fault location estimates of the enhanced

monitor reach area algorithm (EMRAA).

For the original MRA method, nine voltage thresholds were used to build the monitor

reach areas for each monitored bus. The voltage thresholds utilized range from 0.1 p.u.

to 0.9 p.u. in steps of 0.1 p.u. Fault positions on each bus and on ten uniformly

distributed points along every line were considered. Accordingly, the matrix

representing the monitor reach areas of the monitoring program has 4 rows (monitored

buses) and 354 columns (fault positions).

Fault location through the original MRA method was done by intersection of monitor

reach areas, which were selected according to the magnitude of the residual voltages

registered at the monitored buses. The fault positions encompassed by most of the


84 |

monitor reach areas were assumed as the most probable fault locations. This set of fault

positions common to all monitors constitutes the list of fault location estimates of the

original MRA method.

The mean, standard deviation, and the largest value of the number of fault location

estimates determined by both methods are compared in Table 3-3. Each row of the

Table pertains to a specific value of fault resistance, which is indicated in the first

column. In addition, the percentage of faults detected by each method is indicated in the

last two columns.

As can be seen from Table 3-3, the EMRAA outperforms the original MRA approach in

all cases. The average number of fault location estimates determined by the EMRAA

remains close to 19 in all instances, whereas the same measure for the original MRA

method ranges from 52 to 81. Moreover, much less variability in the number of

estimates can be expected from the EMRAA than from the original MRA method; the

standard deviation of the EMRAA stays around 4 while it varies between 68 and 88 in

case of the original MRA method.

The data in Table 3-3 also reveals that about 30% and 45% of faults with a value of

fault impedance of 25 Ω and 50 Ω, respectively, are not detected by the monitoring

program when using the original MRA approach. In contrast, the same monitoring

program estimates the location of all faults regardless of fault impedance values if the

EMRAA is employed.

The results of the application of EMRAA and the original MRA method on the IEEE-

RTS network corroborate that the former method is not affected by fault impedance.

Since higher values of fault impedance can cause shallower voltage sags, the use of

fixed voltage thresholds by the original MRA method prevents the detection of some

high-impedance faults.

Table 3-3 Number of Fault Location Estimates Determined Using Original MRA Method and Enhanced

MRA Algorithm (EMRAA)

Rf

(Ω)

Average Std. Dev. Max % Detection

EMRAA MRA EMRAA MRA EMRAA MRA EMRAA MRA

0 19.26 62.16 4.02 68.69 30 336 100 100

5 19.47 81.82 4.08 75.51 29 352 100 100

25 19.45 73.00 3.97 88.30 28 325 100 71.54

50 19.50 52.58 4.13 81.91 28 325 100 55.69


85 |

Another important fact is that since the locations along the lines where the faults were

simulated do not match the points used to build the monitor reach areas, none of the

fault location estimates provided by the MRA method can be the actual fault location.

By contrast, the EMRAA can determine the actual fault location without the use of

monitor reach areas.

The results of the fault location tests show that the EMRAA can be used to increase the

overall robustness of optimal sag monitoring programs. Enhanced fault detection and

location capabilities can be achieved implementing the EMRAA while keeping the

same number of monitors. This enhancement can lead to an increase in sag estimation

accuracy of OSMPs.

3.4 Enhancement of Sag Estimation Accuracy with

EMRAA

Additionally, more thorough simulation tests have been carried out on the IEEE-RTS

network to illustrate the accuracy enhancement of sag estimation that can be attained

through the implementation of the EMRAA. A total of 1000 faults obtained from Monte

Carlo simulation has been applied to the IEEE-RTS and the number of sags caused by

these faults has been estimated for all buses using the OSMP (monitors placed at buses

3, 6, 8, and 17). The list of inputs generated randomly from probability distributions

during the Monte Carlo experiment is presented in Table 3-4. It can be seen from this

data that most of the faults simulated were line to ground faults occurring on lines and

having an average fault resistance value of 25 Ω, plus or minus 5 Ω, or an approximate

range of 20 Ω to 30 Ω. As also shown in Table 3-4, the numeric values representing the

faulted lines, i.e. 1 to 33, and the faulted buses, i.e. 1 to 24, were drawn from uniform

distribution on the intervals [1,33] and [1,24], respectively.

The number of voltage sags at the 24 buses of the network was estimated using the

pseudo-measurements at buses 3, 6, 8, and 17 (OSMP) and applying the original MRA

method and the EMRAA. Sag magnitude estimation was performed with both methods

by calculating the average of the residual voltages corresponding to all the possible fault

locations determined following the procedures described in Section 3.3.

For the MRA method, the monitor reach areas of buses 3, 6, 8, and 17 for voltage

thresholds of 0.9 p.u. to 0.1 p.u. (in steps of 0.1 p.u.) were used. Two groups of monitor


86 |

reach areas, for 0 Ω and 5 Ω, were utilized for line to line and three-phase faults, and

five groups of monitor reach areas, for 0 Ω, 5 Ω, 10 Ω, 25 Ω, and 50 Ω, were applied

for line to ground and line to line to ground faults. In the MRA approach, the sets of

possible fault locations were defined by the intersection of these groups of monitor

reach areas of the triggered monitors.

With the EMRAA, the fault location algorithms described in Section Chapter 3 were

applied to each line using the voltage measurements at the four monitored buses after

the triggering of at least one monitor. Both fault location and fault resistance were

calculated with the fault location algorithm. The sets of possible fault locations for this

approach were built with the fault location estimates obtained by most of the monitors.

Table 3-4 Inputs Randomly Generated During Monte Carlo Simulation (1000 trials) and their

Corresponding Probability Distributions

Input Probability distribution

Type of fault 0.85 LG faults, 0.08 LL faults, 0.05 LLG faults, and 0.02

LLL faults

Faulted element: line or bus 0.98 line faults and 0.02 bus faults

Faulted line Uniform distribution on the interval [1,33]

Fault point on lines Uniform distribution on the interval [0,1]

Faulted bus Uniform distribution on the interval [1,24]

Fault resistance of LG and LLG faults Normal distribution: = 25 Ω, = 5 Ω

Fault resistance of LL and LLL faults Normal distribution: = 2.5 Ω, = 1 Ω

The System Average Rms-variation Frequency Index (SARFI) has been used to count

the number of voltage sags at every bus of the IEEE-RTS network. The SARFI90 index,

i.e. the number of voltage sags with a residual voltage of 90% or less, is presented in

Figure 3-6. The real number of events and the number of events estimated using the

EMRAA and the original MRA method are indicated with blue diamond, red square,

and green triangle markers, respectively.

As shown in Figure 3-6, the MRA method overestimates the SARFI90 index at all sites

except, of course, the monitored buses (3, 6, 8, and 17). The biggest overestimate is 278

events at bus 13 and the lowest is 6 at bus 22. A different trend is observed for the

EMRAA since sags are underestimated at most sites apart from buses 1, 2, 10 and the

monitored buses. The biggest discrepancy between real and estimated sags with the

EMRAA is 112 for bus 20 and the smallest is 6 for bus 13. This underestimation is

explained by the fact that a triggering threshold of 0.9 p.u. was also used to apply the

EMRAA.


87 |


The better performance of the EMRAA can also be evidenced in Figure 3-7, where the

three SARFI80 indices are shown. It can be seen that the biggest overestimation by the

MRA method occurs at bus 14 where 349 sags are counted in excess of their true value.

The lowest underestimation by the EMRAA consists of 38 sags at bus 20.


The actual and estimated SARFI70 indices are shown in Figure 3-8. The number of sags

estimated with the MRA method exceeds the actual number at eleven buses (9, 11, 12,

15, 16, 18-21, 23, and 24) and is inferior at nine buses (1, 2, 4, 5, 7, 10, 14, and 22). The

overestimation varies between 7 and 101 events and the underestimation range lies

between 1 and 35 events. The EMRAA overestimates the SARFI70 index at nine sites

(buses 14, 15, 18-24) by as much as 7 events and underestimates the index at nine buses

(1, 4, 5, 7, 9-11, 13, and 16) by 18 or less sags.

0

100

200

300

400

500

600

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

SA

RF

I90

ind

ex

Buses

REAL-SARFI 90 EMRAA-SARFI 90 MRA-SARFI 90

0

100

200

300

400

500

600

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

SA

RF

I80

ind

ex

Buses



88 |


3.5 Summary

In this chapter the leading optimal monitor placement method for voltage sag

characterization, the MRA method, was reviewed. Two important limitations of this

method were demonstrated. The first one is the potential loss of sag detection capability

of OSMPs when sag magnitude at monitored buses remains above 90% of nominal

voltage (the most used triggering threshold). The second one is the high variability in

the number of monitors that might be required to cover the same network for faults with

different characteristics. The underlying reason behind these limitations is the

susceptibility of the fault detection and fault location algorithms employed by the MRA

method to fault resistance, pre-fault voltage profile, and voltage sag thresholds. A fault

location method that can of overcome these limitations and enhance the robustness and

sag estimation accuracy of the MRA method was also reviewed. This robust fault

location method is then implemented in the original MRA method resulting in the

enhanced monitor reach area algorithm (EMRAA). The EMRAA will be used to

determine the optimal monitor placement for fault location in the next chapter.

0

20

40

60

80

100

120

140

160

180

200

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

SA

RF

I70

ind

ex

Buses


Chapter 4 • Generalized Formulation of the Optimal Monitor Placement for Fault Location

89 |

Chapter 4

Generalized Formulation

of the Optimal Monitor

Placement Problem for

Fault Location

A fault location method that enhances the robustness of the MRA method was analyzed

in the previous chapter. The approach was used in [53] to develop a method for optimal

monitor placement for fault location. This method determines the minimum number of

monitors and identifies the best locations for installing power quality monitors, or any

other device with voltage measurement capabilities, in order to uniquely locate every

fault occurring throughout the network. This enables virtually exact voltage sag

estimation at all buses in the network. The method however has only been tested in a

simple 10-bus system and a generalized formulation applicable to an arbitrary system is

still missing.

This chapter reviews the optimal monitor placement for fault location proposed in [53]

and extends and generalizes its modeling approach. The generalized formulation

determines a set of generic linear constraints for the problem of optimal monitor

placement so it can be solved by integer linear programming. The generalization of the

optimal monitor placement for complete fault location observability in the system

represents the second original contribution of this research.


90 |

4.1 Optimal Monitor Placement for Fault Location

The problem of optimal monitor placement for fault location is defined as finding the

minimum number and optimal locations for monitors in a system so that the system is

completely observable [53]. It is necessary here to clarify exactly what is meant by

observable. In a fault location sense, a system is fully observable if all faults occurring

anywhere in the system are uniquely localized. A fault that is uniquely localized is one

for which only one fault location estimate is determined. Sets of fault location estimates

are obtained from single monitors or constructed from the intersection of sets of

multiple monitors.

Similar to the monitor placement for voltage sag characterization, the optimal monitor

placement problem for fault location has been formulated as an integer linear

programming problem with the following objective function:

1

MinimizeN

x x

x

r

M (4.1)

where xr is the cost of placing a monitor at bus x , M is a binary-decision-variable

vector of length N indicating the need for a monitor at bus x , and N is the number of

buses in the network. The entries of M are xm as shown below:

1 if a monitor is required at bus ,

0 otherwise x

xm x

(4.2)

The set of linear constraints that guarantee full fault location observability are derived

from a list of pre-defined fault points and the combinations of monitors that can

uniquely determine their location. A six-step procedure to generate the constraints for a

fault point, shown in Figure 4-1, and an example of a set of linear constraints have been

given in [53]. That example is reviewed here for illustration purposes and for a later

comparison.


91 |

Figure 4-1 Flowchart for generating constrains for fault point F1 (adopted from [53]).

The fictitious 4-bus network depicted in Figure 4-2 has been built to illustrate the

procedure to formulate the linear constraints. Assume that a fault is simulated at point α

and residual voltages at all buses are calculated. Next, the fault location equations

presented in [104] and reviewed in the previous chapter are solved for every line using

the voltage at each bus, i.e. a total of 16 equations are solved (four equations for each

bus). The solutions of these equations are then used to find the combinations of

monitors that identify point α as the only or most likely fault location. Lastly, the linear

constraints are derived from the combinations of monitors that can uniquely determine

the actual fault point α .

Figure 4-2 Sample 4-bus system.

As Figure 4-2 shows, bus 1 estimates only one fault location whereas the rest of buses

yield two estimates. The fault location estimate from bus 1 corresponds to the actual

fault location. Buses 2, 3, and 4 also locate the fault correctly but not uniquely. Bus 2

estimates an additional fault location at point β while buses 3 and 4 estimate a second

Obtain the residual voltage at each bus

Obtain set S1, the set of fault locations, using voltage at bus i

i = 1,…,N

Identify all the sets with a single element and record the

corresponding bus number

Obtain all the combinations of monitors that can uniquely determine

the fault location and record corresponding bus numbers

Simulate a fault at point F1

Derive the linear constraints based on the sets of recorded bus

numbers

1

2

3

4

α

β

γ

Fault location estimates of :

bus 1 bus 2 bus 3 bus 4


92 |

fault location at point γ . Accordingly, the sets of possible fault locations obtained from

buses 1, 2, 3, and 4, respectively are:

1 αS

(4.3)

2 α,βS

(4.4)

3 α,γS

(4.5)

4 α,γS

(4.6)

It is evident from these solution sets that:

1 1 2 1 3 1 4 2 3 2 4 αS S S S S S S S S S S (4.7)

The only element of 1S , the intersection of

1S and any other set, and the intersections of

2S and either 3S or

4S , are equal to α , the actual fault location. Thus, there are six

combinations of monitors that can uniquely determine fault point α and these are listed

in Table 4-1. It can be seen from this table that placing one monitor at bus 1, or two

monitors, the first one at bus 2 and the second one at bus 3 or 4, are sufficient to

uniquely locate fault point α . Mathematically, this constraint can be represented as:

1 2 3 2 4 1M M M M M (4.8)

Logical constraint (4.8) is modeled in [53] with binary variables 2_ 3M and

2_ 4M as:

1 2_3 2_ 4 1M M M (4.9)

2_3 2M M (4.10)

2_3 3M M (4.11)

2_3 2 3 1M M M (4.12)

2_ 4 2M M (4.13)

2_ 4 4M M (4.14)

2_ 4 2 4 1M M M (4.15)

Table 4-1 Single monitors and pairs of monitors required to locate fault α

Combination number First monitored bus Second monitored bus

1 1 1

2 1 2

3 1 3

4 1 4

5 2 3

6 2 4


93 |

If linear constraints (4.9)-(4.15) are satisfied fault point α becomes observable. Since

the overall aim of the optimization problem is the minimization of monitoring costs, one

monitor at bus 1 would be chosen as the most economical monitor combination (from

the six analyzed) that ensures observability of fault point α .

A procedure like the one described above should be followed to determine the full set of

linear constraints for all pre-defined fault points and all types of fault. For example, in a

1000-bus system, it is required to determine the fault location observability of almost

half a million of pairs of monitors or more than 166 million sets of three monitors.

Assume that the system has 1500 lines, 10 fault points are posed on each line, and that

all faults (15000) can be uniquely localized by 5 pairs of monitors. For this case 225000

linear constraints like (4.9)-(4.15) are generated for each type of fault. As can be seen,

formulating the linear constraints is the most arduous task of the optimal monitor

placement problem, especially for large systems, since it entails finding pairs of

monitors that can uniquely locate faults. In order to facilitate efficient formulation of

linear constraints the modeling approach proposed in [53] is extended and generalized

in the next section.

4.2 Generalized Formulation of the Optimal Monitor

Placement Problem

The substantial number of linear constraints that can be derived from the optimal

monitor placement problem for fault location can be reduced and integrated into a single

compact array that simplifies the original model. An approach similar to the one used in

[39] (and reviewed in the previous chapter) to formulate the optimal monitor placement

problem for voltage sag monitoring is utilized here. In this section, a new set of

variables is first introduced and then utilized to reformulate the optimal monitor

placement problem. The new formulation is applied first to the aforementioned 4-bus

sample network at the end of this section, and then to a much larger power network to

validate its suitability for application in realistic power systems.

4.2.1 Definition of new variables

Recalling Chapter 3 , the monitor reach area (MRA) of a monitor is defined as the area

of the network where the monitor can detect voltage sags caused by short circuit faults


94 |

[39]. In a similar fashion, the monitor location area (MLA) is defined here as the

observable area of a monitor or a combination of monitors, i.e. the area of the network

where a monitor or a combination of monitors can uniquely locate faults. The monitor

location areas of the network’s buses can be modeled as a binary matrix based on the

following conditions:

1, if a fault at is uniquely located by monitor combination 1;

0, otherwise 1ij

j i i Q

j F

MLA (4.16)

where i can represent one monitor or a combination of monitors, and j is a fault

position at a bus or on a line. The order of matrix MLA is Q F , where Q is the

number of combinations of monitors and F is the number of pre-defined fault

positions. The number of combinations having m monitors that can be obtained from a

network with N buses is given by (4.19).

!

! !

NC

m N m

(4.17)

The second variable introduced here is the indexing matrix L of size Q m whose

purpose is to list the buses of each combination of monitors. The monitor location area

and the monitoring indexing matrix corresponding to the 4-bus sample network (see

Figure 4-2) have the following structure (fictitious values have been used for fault β

and γ ):

st nd

1

2

3

4

5

6

7

8

9

10

1 monitor 2 monitor α β γ

1 1 1 0 0

1 2 1 1 1

1 3 1 1 0

1 4 1 0 0

2 2 0 0 1

2 3 1 1 1

2 4 1 0 1

3 3 0 1 0

3 4 0 0 0

4 4 0 1 0

Q

Q

Q

Q

Q

Q

Q

Q

Q

Q

L MLA

The indexing matrix has been built for single buses and pairs of buses, i.e. for 2m .

The two values of each row iQ denote the buses where monitors are placed. A

progressive numeration is used to fill the entries of matrix L , so that all pairs of


95 |

monitors involving bus 1 are listed first, followed by pairs having bus 2, then bus 3, and

finishing with bus 4. Therefore, the first combination of L , 1Q , represents only one

monitor placed at bus 1. The next pair, 2Q , refers to two monitors, the first one at bus 1

and the second one at bus 2. The last pair of monitors having one monitor at bus 1 is 4Q

in which the second monitor is at bus 4. Since the pair of monitors representing

measurements at buses 1 and 2 is already covered by 2Q , the pseudo-pair

5Q ,

representing one single monitor at bus 2, is the first one starting with bus 2. 6Q is the

pair that places monitors at buses 2 and 3. This numeration continues so that the

penultimate pair 9Q , represents monitors at buses 3 and 4, and the last set,

10Q ,

corresponds to just one monitor at bus 4.

The six combinations of monitors that locate fault point α can be identified readily by

means of the matrix representation of the monitor location area. In addition, the total

number of pairs of monitors that locate fault point α can be determined by adding up

the elements of the first column of the matrix. In general, the sum of a column of the

monitor location area matrix gives the total number of monitor combinations that locate

a given fault, whereas the sum of one of its rows provides the total number of faults that

a specific combination of monitors locates.

The third variable defined here is a binary vector, similar to M , to handle the decision

of placing monitors at the buses of monitor combinations. The entries of this vector take

the following values:

1, if meters are placed at buses of combination

0, if meters are not placed at buses of combination i

i

i

P ; 1i Q (4.18)

A causal relationship between variables M and P must be enforced so that every value

of P causes a change in M . For example, in the 4-bus network 1 1P should entail one

monitor placed at bus 1, that is 1 1M . If 4 1P , 1 1M and 4 1M must be satisfied,

which requires placing monitors at buses 1 and 4.

4.2.2 Reduction of Number of Constraints

It was shown in [104] and [53] and that a single monitor provides a set with more than

one fault location estimate in some cases and thus combinations of two, three or more

monitors must be used to derive a unique fault location estimate. Clearly, a unique fault


96 |

location estimate can be obtained when the intersection of no more than two sets of

possible fault locations contains only one fault location estimate, and therefore two

monitors at most are required to derive a unique fault location estimate for every fault in

any network. For this reason the number of monitor combinations to be analyzed is

limited to the number of pairs of monitors in the system. Under this new principle, the

total number of monitor combinations that need to be considered in the formulation of

the optimization problem for a network with N buses is:

!

2! 2 !

NQ N

N

(4.19)

That is, the total number of monitor combinations is given by the sum of the number of

buses of the system and the number of pairs of monitors that can be obtained from the

system. This premise reduces considerably the number of monitor combinations to be

studied and consequently the number of constraints of the optimization problem.

4.2.3 Problem Formulation

The new variables defined in the previous sections i.e. L , MLA , P , and Q provide the

framework for generalizing the formulation of the optimal monitor placement problem.

Objective function (4.1) therefore, has to be optimized subject to the following general

linear constraints:

1

1,C

ij i

i

j

MLA P (4.20)

10,

ii i LP M (4.21)

20,

ii i L

P M (4.22)

1 2

1,i i i i L LM M P

(4.23)

where i represents the i-th combination of monitors and j the j-th pre-defined fault.

Constraint (4.20) ensures that all faults simulated in the system are uniquely located by

at least one monitor or a pair of monitors. Indexing matrix L is used in inequalities

(4.21)-(4.23) to enforce the causal relationship between variables M and P .


97 |

4.2.4 Application in the 4-bus Sample System

The generalized formulation of the optimal monitor placement problem has been

applied to the 4-bus sample system. The combinations of monitors that can uniquely

determine fault point α are 1, 1,2, 1,3, 1,4, 2,3, and 2,4. The compliance

of these combinations with constraints (4.20)-(4.23) has been verified. Table 4-2 shows

the values of these constraints solved for the six combinations. The first and second

columns of Table 4-2 show monitored buses and monitor combinations, respectively;

the rest of the columns show the values of the restrictions. It is apparent from this table

that all monitoring solutions satisfy the constraints of the general formulation of the

optimal monitor placement problem. Minimization of monitoring costs guarantees that

the optimal solution is 1. In the next section, the generalized model is further

validated through its implementation on much larger systems.

Table 4-2 Compliance of monitoring solutions of the sample system of 4-bus system (Figure 4-2) with

generic linear constraints

iM iP

Value of constraint

(4.20)

Value of constraint

(4.21)

Value of constraint

(4.22)

Value of constraint

(4.23)

1 1 1 0 0 1

1, 2 2 1 0 0 1

1, 3 3 1 0 0 1

1, 4 4 1 0 0 1

2, 3 6 1 0 0 1

2, 4 7 1 0 0 1

As it has been shown, the proposed generalized formulation for the optimal monitor

placement for fault location yields the same results as the original modeling approach

presented in [53] for the 4-bus sample system. In the next section, the generalized model

is further validated through its implementation on much larger systems.

4.3 Application in Large Power Networks

The generalized model developed in the previous section has been used to determine the

minimum monitoring programs required for full fault observability in three systems, the

10-bus network used in [53], the IEEE reliability test system (RTS) [106], and the IEEE

118-bus power flow test case [97]. The optimal monitoring programs have been

determined employing FICO’s Xpress optimization suite [107].


98 |

4.3.1 10-bus 500 kV Power Network

As stated before, the groundwork for the proposed generalization of the optimal monitor

placement problem was established in [53]. There the method was tested in the

transmission network depicted in Figure 4-3. The network consists of 10 buses, 10 lines,

and 5 generators. The network data is also given in [53] and is provided in Appendix A.

Prefault voltages were assumed to be 1 p.u. as in the original study.

Figure 4-3 Line segments (length is labeled) of the system used in [53] where faults cannot be uniquely

located with 2 monitors.

In [53] fault points were defined at every 2 miles on each line and since the length of

lines is not equal, each line had a different number of fault positions. The line

connecting buses 5 and 6 is the longest of the network (86.81 miles) and thus it is the

one having the greatest number of fault positions (44). In order to build a uniform

monitor location area, 44 fault positions were defined on all lines in an equidistant

manner. Since there are 10 single monitor locations and 45 pairs of monitors, the total

number of monitor combinations is 55. Under these considerations the monitor location

area of the network is represented by a 55 × 44 binary matrix.

Table 4-3 shows the optimal monitoring programs determined with both the original and

the enhanced formulation proposed in this thesis. The main difference between the

results obtained with both approaches is the minimum number of required monitors.

The original modeling approach determines that 3 monitors are required to locate all


99 |

types of faults while the generalized formulation finds that 2 monitors are sufficient for

the same purpose. The discrepancy between results has been further investigated.

Table 4-3 Optimal monitoring programs obtained with original and proposed formulations for the

sample system of Figure 4-3

Fault

Type

Optimal monitor locations (3)

obtained with original formulation

Optimal monitor locations (2)

obtained with generalized formulation

LG 1,3,6,3,6,7,3,7,8,

3,7,10,1,3,10,1,3,8

1,6,1,8,1,10,6,7,7,8,7,10

LL 1,3,6,3,6,7,3,7,8,

3,7,10,1,3,10,1,3,8

1,6,1,8,1,10,6,7,7,8,7,10

LLG Any single bus 1,3,1,4,1,5,1,6,1,8,1,9,1,10,

3,7,4,7,5,7,6,7,7,8,7,9,7,10

LLL 1,3,6,3,6,7,3,7,8,

3,7,10,1,3,10,1,3,8

1,6,1,8,1,10,6,7,7,8,7,10

All

types

1,3,6,3,6,7,3,7,8,

3,7,10,1,3,10,1,3,8

1,6,1,8,1,10,6,7,7,8,7,10

Examples of LG and LLL faults declared in [53] as observable only through 3 monitors

are shown in Table 4-4. The locations of these faults are in the unobservable segments

depicted in Figure 4-3. The second column of Table 4-4 present the estimated locations

of LG faults previously found in [53], i.e. using voltage at buses 1 and 3. The third

column shows the fault location estimates determined with the generalized formulation

and using voltage from bus 6. Similarly, the last two columns of Table 4-4 list the

estimated locations of LLL faults found in [53], i.e. using voltage at buses 3 and 6, as

well as the fault location estimates determined using voltage at bus 1. The results, as

shown in Table 4-4, confirm that a LG fault at 5 miles from bus 5 on line connecting

bus 5 and bus 8 cannot be uniquely localized using voltage at buses 1 and 3, but that a

unique fault location can be derived based on voltage measurements from bus 1 and bus

6 or from bus 3 and bus 6. The same conclusion can be drawn for a LG fault at 2.68

miles from bus 5 on line connecting buses 5 and 6.

Table 4-4 Fault location estimates [from-bus, to-bus, mile] using voltage at buses 1, 3, and 6 of the

sample system of Figure 4-3

Monitored

bus

Actual location of LG faults Actual location of LLL faults

[5,8,5.0] [5,6,2.68] [1,2,43.95] [2,7,41.0]

1 [5,8,5.0],

[5,6,2.68]

[5,6,2.68],

[5,8,5.01]

[1,2,43.95] [2,7,41.0],

[4,5,11.85]

3 [5,8,5.0],

[5,6,2.68]

[5,6,2.68],

[5,8,5.01]

[1,2,43.95],

[2,7,40.95]

[1,2,8.58],

[2,7,41.0]

6 [4,5,27.20],

[5,8,5.0]

[5,6,2.68] [1,2,43.95],

[2,7,40.95]

[1,2,8.58],

[2,7,41.0]

1, 3 [5,8,5.0],

[5,6,2.68]

[5,6,2.68],

[5,8,5.01]

[1,2,43.95] [2,7,41.0]

1, 6 [5,8,5.0] [5,6,2.68] [1,2,43.95] [2,7,41.0]

3, 6 [5,8,5.0] [5,6,2.68] [1,2,43.95],

[2,7,40.95]

[1,2,8.58],

[2,7,41.0]


100 |

The data from Table 4-4 also confirms that voltage measurements from bus 3 and bus 6

are not sufficient to determine uniquely the location of a LLL fault simulated at 43.95

miles from bus 2 on line connecting bus 1 and bus 2. However, monitors placed at buses

1 and 3 or at buses 1 and 6 are able to pinpoint the location of this fault and the location

of a LLL fault at 41 miles from bus 2 on line connecting bus 2 with bus 7. It is stated in

[53] that the four faults analyzed in Table 4-4 (2 LG and 2 LLL) required at least 3

monitors to be uniquely localized. Nevertheless, as Table 4-4 shows, voltage

measurements from bus 1 and bus 6 yield intersects of a unique element for these faults.

Furthermore, it was found that monitors at buses 1 and 6 constitute an optimal solution

for full observability of all types of faults in the 10-bus system, as Table 4-3 shows. The

difference in results from the proposed formulation and [53] can be attributed to

difference in the criteria used to select valid fault location estimates. The solutions of

the fault location equations for LG faults can be complex numbers hence a maximum

tolerance for the imaginary part must be set to validate a fault location estimate. The

maximum tolerance used in this study was 1×10-6

but no information regarding the

criteria to validate fault location estimates is given in [53].

4.3.2 IEEE 24-bus Reliability Test System (RTS)

The optimal monitoring locations for fault location have been determined with the

generalized modeling approach for the IEEE reliability test system. The network

consists of 24 buses, 33 lines, 10 generators, 5 transformers, and 1 synchronous

condenser. The system parameters were taken from [106] and are provided in Appendix

A. Prefault voltages were assumed to be 1 p.u at all buses and 10 fault points were

distributed uniformly on every line and thus the total number of fault positions is 330.

In addition to the 24 single monitoring locations, 276 pairs of monitors can be drawn

from the IEEE-RTS and therefore the total number of monitor combinations is 300. The

resulting monitor location area for each type of fault is a 300 × 330 binary matrix.

The number of monitors was minimized subject to constraints (4.20)-(4.23). It was

found that the minimum number of monitors required to uniquely pinpoint the location

of all simulated faults is 2. Apart from pair 7, 8 any pair of monitors can be used to

determine the location of all types of fault occurring throughout the network. That is,

placing a monitor in any 2 buses other than 7 and 8 makes the IEEE reliability test

system fully observable with respect to fault location. Figure 4-4 depicts the lines where


101 |

faults can be uniquely located using the voltage measurements from buses 7 and 8. All

types of faults occurring on the line connecting these two buses can be localized. In

addition, the location of phase-to-phase and three-phase faults can be uniquely

identified if these occur on line connecting buses 17 and 22. Phase-to-phase-to-ground

faults can be pinpointed when they take place on line between buses 21 and 22. For the

rest of the network multiple fault location estimates are derived using the voltage

measurements from buses 7 and 8.

Figure 4-4 Observable lines by monitors installed at buses 7 and 8 in the IEEE-RTS.

4.3.3 IEEE 118-bus Test System

The IEEE 118-bus test system represents a portion of the electric power system in the

Midwestern USA dating back to 1962 [97]. The network consists of 35 generators, 118

buses, 177 transmission lines, and 9 transformers. The system data is provided in [97]

and reproduced in Appendix A. A prefault voltage profile equal to 1 p.u was taken

1 2 7

4 5

3 9

24 11 12

10

8

6

15

14

16

17

19

13

18

23

20

21 22

S.C.

LLG faultsAll types of faultsLL and LLL faults

138 kV 230 kV

V

V

V Voltage measurement


102 |

across the network. Three fault points were allocated at 0.25, 0.50, and 0.75 on every

line. The total number of fault positions is 531. Taking into account individual monitor

locations and pairs of monitors, the total number of monitor combinations is 7021. The

binary matrix representing the monitor location area for this case has 7021 rows and 531

columns.

Table 4-5 provides the minimum number of monitors and their optimal position in the

network required to locate all LL, LLG, and LLL faults. It was found that 2 monitors

suffice to determine the exact location of these types of faults. There are 204 pairs of

monitors that can pinpoint both LL and LLL faults. The first monitored bus can be any

of the 102 buses listed in the top row of the second column of Table 4-5, whilst the

second monitored bus can be either bus 111 or bus 112. This means that in order to

achieve full fault location observability of LL and LLL faults, the voltages at bus 111 or

bus 112 should be measured along with the voltages at one of the 102 buses enumerated

accordingly in Table 4-5.

In the case of LLG faults, 989 pairs exist that can locate the 531 LLG faults simulated in

the IEEE 118-bus system. Almost all buses of the system can be an optimal location for

a monitor if they are paired with a second optimal location as indicated in the second to

fifth rows of Table 4-5. The only non-optimal monitoring buses of the system are 70 to

73, 77, 100, and 117 (7 in total). A comparison between the optimal combinations of

monitors presented in Table 4-5 reveals that 192 pairs are common to all sets of

monitors. These pairs of monitors are presented in the last row of Table 4-5.

Table 4-5 Optimal pairs of monitor locations required for full observability of LL, LLG and LLL faults

in the IEEE 118-bus test system

Type of fault Alternative locations for first

monitor

Alternative locations for second

monitor

LL and LLL 1-93, 95, 96, 98,102, 113-116, 118 111, 112

LLG 1-69, 74-76, 78-92, 94-96, 98-99, 102 103-112

LLG 93 104, 105, 107

LLG 97, 101 103, 110, 112

LLG 103-112 113-116, 118

LL, LLG, and

LLL 1-69, 74-76,78-92,95,96,102,113-116, 118 111, 112

The optimal monitoring program to locate LG faults is described in Table 4-6. It was

determined that 13 monitors is the minimum number of voltage measurements required

to ensure complete fault location observability of LG faults. It was also found that it is

mandatory to install monitors at buses 39, 41, 67, 84, 88, 93, 95, 97, and 117, otherwise

the system becomes unobservable. Apart from these nine the remaining four optimal


103 |

monitor locations must be selected singly from four different sets of monitors. The tenth

monitored bus should be either 78 or 79; the eleventh measurement has to be at bus 101

or bus 102; the possible locations for the twelfth monitor are buses 111 or 112; and the

buses to place the thirteenth monitor are 114 or 115.

Table 4-6 Optimal monitor program to locate LG faults in the IEEE 118-bus test system

The overall optimal monitoring schemes for fault location are shown in

Table 4-7. Full observability of all types of faults requires 13 monitors. The 16 sets of

13 monitors that locate LG faults also cover LL, LLG, and LLL faults. The deployment

of the optimal monitoring scheme is depicted in Figure 4-5, which can be seen as the

graphical representation of Table 4-6.

Figure 4-5 Optimal monitoring locations that lead to full fault observability of the IEEE 118-bus system.

Required locations for

1st to 9

th monitors

Alternative locations for

10th

monitor 11th

monitor 12th

monitor 13th

monitor

39, 41, 67, 84, 88,

93, 95, 97, 117 78, 79 101, 102 111, 112 114, 115


104 |

Table 4-7 Optimal monitoring programs for locating all types of fault in the IEEE 118-bus test system.

(Complement to monitors fixed at buses 39, 41, 67, 84, 88, 93, 95, 97, and 117)

No. Additional optimal monitor locations No. Additional optimal monitor locations

1 78,101,111,114 9 79,101,111,114

2 78,101,111,115 10 79,101,111,115

3 78,101,112,114 11 79,101,112,114

4 78,101,112,115 12 79,101,112,115

5 78,102,111,114 13 79,102,111,114

6 78,102,111,115 14 79,102,111,115

7 78,102,112,114 15 79,102,112,114

8 78,101,112,115 16 79,101,112,115

4.4 Summary

A generalized formulation for optimal monitor placement for fault location is proposed

in this chapter. This formulation determines a set of generic linear constraints for the

problem of optimal monitor placement so it can be solved by integer linear

programming. This set of linear constraints can be derived for any power system

network from its monitor location area, which is introduced in this chapter to

characterize the overall fault location observability of the system. The principle that a

maximum of two monitors are sufficient in order to correctly locate any fault leads to a

significant reduction of linear constraints in the problem. The generalized formulation

determines the minimum number of voltage measurements and their optimal location

required to pinpoint any type of fault occurring throughout the network. Simulation

studies performed in several test systems validate the proposed formulation. However,

an optimal monitoring program for full fault observability of the 295-bus GDS network

could not be obtained due to high computer memory usage. Therefore a much less

memory intensive metaheuristic method capable of finding a solution in any case has

been developed in the next chapter.

Chapter 5 • Heuristic Approach for Determining Optimal Monitor Placement for Voltage Sag Estimation

105 |

Chapter 5

Heuristic Approach for

Determining Optimal

Monitor Placement for

Voltage Sag Estimation

In Chapter 4 a generalized formulation for the optimal monitor placement problem for

fault location was developed. The optimization problem was formulated as an integer

linear programming problem. Although optimal monitoring programs were found for

the IEEE 24-bus reliability test system (RTS) and the IEEE 118-bus power flow test

system using the generalized model, a global optimal solution could not be found in the

295-bus generic distribution system (GDS) due to high computational memory usage.

For this reason a less memory intensive method to determine fault location monitoring

schemes is developed in this chapter. The base of this method is a greedy algorithm that

searches for set of monitors which cover the entire network. Three custom objective

functions have been formulated and incorporated into the greedy algorithm to enhance

its robustness and assess the sag estimation accuracy of limited monitoring programs.

The proposed approach is tested in the IEEE 118-bus test system and in a 295-bus

generic distribution system (GDS). The test results show the practical efficiency of the

developed method. This heuristic approach for monitor placement represents the third

original contribution of this thesis.


106 |

5.1 Review of Proposed Formulation of Optimal Monitor

Placement for Fault Location

The fundamentals of the method developed in the previous chapter are reviewed briefly

in this chapter for completeness of discussion and as it forms a basis for the

development of the new algorithm. The optimal monitor placement problem for fault

location has been formulated as an integer linear programming problem as follows:

1

1, ; 1, ,C

ij i

i

j j F

MLA P (5.1)

subject to:

10, ; 1, ,

ii i i Q LP M (5.2)

20, ; 1, ,

ii i i Q LP M (5.3)

1 2

1, ; 1, ,i i i i i Q L LM M P

(5.4)

where

F number of pre-defined fault positions;

1iL first monitored bus of pair i ;

2iL second monitored bus of pair i ;

xM binary-decision-variable vector of length N indicating the need for a monitor at

bus x ;

MLA monitor location area of all buses in the network;

N number of buses in the network;

iP binary-decision-variable vector of length Q indicating the need for monitors at

the buses indicated by pair i ;

Q number of pairs of monitors that can be drawn from the system;

xr cost of placing a monitor at bus x .

Although the generalized optimal monitor placement method is proven to yield

satisfactory results, its implementation in large systems can be hampered due to the

existence of a prohibitively great number of monitor combinations to be analyzed. For

example, if during the optimization process a set of 21 monitors is found as the best

current solution in a 300-bus system, an exhaustive search might be necessary to verify

if a set of 20 monitors is a feasible (and better) solution. The upper bound of this search

space would be greater than 7.5×1030

combinations.


107 |

The memory usage required to solve the optimal monitor placement problem in realistic

size power systems can be so intensive that convergence might not be achieved. This

means that the sets of monitors found are not guaranteed to be an optimal solution. Most

importantly, in some cases no solution can be found at all. For this reason a heuristic

search algorithm, which is faster and less memory intensive, is proposed here to ensure

that a solution is always obtained regardless of the system’s size and, as will be

demonstrated, is also capable of obtaining optimal set of monitors for fault location.

5.2 The Greedy Search Algorithm

Solving the linear integer programming problem of optimal monitor placement utilizing

an enumerative method such as Branch and Bound can lead to computational explosion,

which hinders finding an optimal solution. Therefore a simple, yet effective greedy

search algorithm that requires a much lesser usage of computational resources can be

used. For this purpose, a reconsideration of the optimal monitor placement problem as a

minimum set cover problem is introduced next.

5.2.1 Set-Covering Problem

An instance ,U F of the set-covering problem consists of a finite set U and a family

F of subsets of U , such that every element of U belongs to at least one subset in F :

S

U S

F

(5.5)

Assume that a subset S F covers its elements. The problem is to find a minimum-size

subset F whose members cover all of U :

S

U S

(5.6)

Any subset satisfying equation (5.6) covers U . The size of is the number of sets it

contains, rather than the number of individual elements in these sets, since every subset

that covers U must contain all U individual elements. An example ,U F of the

set-covering problem is illustrated in Figure 5-1, where U consists of 12 black points

and 1 2 3 4 5 6, , , , ,S S S S S SF . The minimum set cover is 3 4 5, ,S S SF , with size 3.


108 |

Figure 5-1 Illustration of set-covering problem.

The set-covering problem is an optimization problem that models many problems that

require resources to be allocated [108], e.g. monitors in a network [109]. In the decision

version of the set-covering problem, it is determined if a set cover of size n exists,

where n is an integer given in the problem. The decision version of set covering is NP-

complete, and the optimization version of set cover is NP-hard [108], meaning that is

not possible to find an optimal solution in polynomial time. For this reason, polynomial-

time approximation algorithms are required to find near-optimal solutions. The greedy

algorithm is possibly the most used strategy in the set cover problem [110].

5.2.2 The Greedy Algorithm

The greedy algorithm applies naturally to the set cover problem: iteratively pick the set

S that covers the greatest number of remaining elements that are uncovered [108].

Figure 5-2 shows the flowchart of the greedy algorithm. The algorithm work as follows.

The set X contains, at each stage, the set of remaining uncovered elements. The set

contains the cover being constructed. In every iteration a subset S that covers as many

uncovered elements as possible is chosen. After S is selected, the covered elements are

removed from X , and S is placed into . The algorithm terminates (in polynomial

time) when all elements of X have been covered. The outcome is the set that

contains a subfamily of F that covers X .

In the example of Figure 5-1, the greedy algorithm produces a cover of size 4 by

selecting, in order, the sets 1S , 4S , and 5S , followed by either 3S or 6S . As it can be

seen, the greedy algorithm might fail to find the optimal solution, nevertheless this type

of algorithm is essentially the best available for the minimum set cover problem [110].

S3 S5S4

S6

S2

S1


109 |

Figure 5-2 Flowchart of the greedy approximation algorithm.

5.2.3 Application of the Greedy Algorithm to the Optimal

Monitor Placement Problem

Recalling the characteristics of both optimal monitor placement problems for fault

location and for sag detection, it can be observed that such problems are equivalent to

the optimization version of the minimum set cover problem. The finite set U can be

seen as the set of fault positions to be located or the faults causing voltage sags below a

given threshold; F can be a collection of subsets of faults positions located/detected by a

monitor or groups of monitors; and would be a minimal set of monitors able to locate

or detect all the fault positions of U . Hence, finding a minimal subset is equivalent

to finding a set of monitors which uses the fewest monitors to either locate all faults or

detect all sags with a given magnitude.

The application of the greedy algorithm to both monitor placement problems is

straightforward: at each stage (see flowchart of Figure 5-2), select the combination of

monitors which contains the largest number of non-located/detected fault positions.

Since the space search is limited to the MRA matrix in the sag detection problem and to

the MLA matrix in the fault location problem, the computational burden is considerably

lower than the one entailed by enumerative methods.

X = U

Γ = Æ

Select an S F that maximizes |S X|

X = X – S; Γ = Γ È S

X ≠ Æ

End

Yes

No


110 |

The greedy algorithm has been implemented in the 295-bus GDS network to obtain sets

of monitors that cover all the faults causing voltage sags. The heuristic search has also

been applied to the 118-bus test system to determine groups of monitors required for

full fault location observability. The results of both tests have been compared to the

optimal sag monitoring programs (OSMP) and the optimal fault location monitoring

programs (OFLMP) found in Chapter 3 and Chapter 4 , respectively. Table 5-1 and

Table 5-2 compare the results obtained from a linear programming-based branch-and-

bound algorithm and the greedy algorithm; the former for full sag observability of the

GDS network and the latter for full fault location observability of the IEEE 118-bus

network.

It can be seen from the data in Table 5-1 that the greedy algorithm obtains the optimal

number of voltage measurement devices in 13 out of 15 cases analyzed. The only two

cases where the greedy algorithm does not provide the minimum number of monitors

are for voltage sags having magnitude of 0.8 p.u. and 0.7 p.u. or less and caused by

faults with fault resistance of 5 Ω. In both instances, shaded in green in Table 5-1, the

greedy algorithm determines one monitor in excess of the minimum required, that is 31

monitors for voltage sag threshold of 0.8 p.u. and 41 monitors for threshold of 0.7 p.u.

The results presented in Table 5-1 correspond to base loading profile but similar results

were obtained for the rest of the loading profiles (low, high, and pre-fault voltages equal

to 1 p.u.) since the maximum surplus determined by the greedy algorithm remained at

one monitor.

Table 5-1 Number of Voltage Measurement Devices Required for Sag Detection in the GDS Network

Rf

(Ω)

Linear programming Greedy algorithm


0.90 0.80 0.70 0.90 0.80 0.70

0 7 11 16 7 11 16

5 16 30 40 16 31 41

10 24 32 22 24 32 22

25 19 19 21 19 19 21

50 13 14 9 13 14 9

As Table 5-2 shows, a simple greedy algorithm is also capable of yielding the same

results as a linear programming-based algorithm when optimal fault location monitoring

programs are determined. In all instances the heuristic method found the same minimum

number of measurement devices as its analytical counterpart.


111 |

Table 5-2 Number of Voltage Measurement Devices Required for Full Fault Location Observability of

the IEEE 118-bus Network

Type of fault Linear programming Greedy algorithm

Line to ground 13 13

Line to line 2 2

Line to line to ground 2 2

Three phase 2 2

All types 13 13

The results obtained with the greedy algorithm establish that this less memory intensive

heuristic approach can be used to obtain optimal and near-optimal monitoring programs.

Two inherent characteristics of the greedy algorithm, namely, the simplicity of its

objective function and its iterative procedure have been further exploited to gain insight

into the accuracy of sag estimation trough limited monitoring programs. This

development is shown in the next section.

5.3 Greedy Monitor Placement with Custom Objective

Functions

As has been demonstrated previously, the use of the greedy algorithm to obtain

monitoring programs consists of selecting iteratively the monitor that covers the largest

number of uncovered fault positions until all fault positions have been included. This

procedure, in its simplest form, provides in each iteration only two data: the best bus to

place a voltage measurement device and the percentage of the network covered by the

addition of this device in terms of fault location or voltage sag detection. The network’s

coverage gained by the addition of monitors enables to prioritize the installation of new

monitors in networks where some monitoring already exists; moreover, it can be further

exploited to obtain more information, particularly regarding the estimation of sags

caused by uncovered faults, by means of custom objective functions incorporated into

the greedy search algorithm.

Three new objective functions have been developed to assign different types of values

to the solutions found in each iteration of the greedy algorithm. The aim is to determine

fault location monitoring programs based on the degree of observability of faults and

sag monitoring programs according to sag estimation accuracy.


112 |

5.3.1 Observability Weight Factors

The first custom objective function has been designed to identify the less observable

sections of the network, i.e. the areas where faults are localized or voltage sags are

detected by only few monitors, based on weighting factors assigned to every fault

position. The observability weight factor of a fault position is defined as in equation

(5.7) for the fault location problem and as in equation (5.8) for the sag detection

problem.

1

1j C

ij

i

w

MLA

(5.7)

1

1j N

ij

i

w

MRA

(5.8)

In the fault location problem, the weight factor of a fault position is given by the inverse

of the sum of the number of monitor combinations that locate such fault position,

whereas in the sag detection problem the weight factor is given by the inverse of the

sum of the number of monitors that detect the voltage sag caused by the fault at this

position. A fault position located by many monitors has lower weight than one located

by few monitors. In the same way, a position where faults cause voltage sags detected

by many monitors has lower weight than a position where faults lead to sags triggering

fewer monitors. The weighting of fault positions represents a measure of the

observability of each fault position and can be readily integrated into the greedy

algorithm.

The flowchart for implementing the proposed weighted search algorithm is

fundamentally the same as the flowchart of the original greedy algorithm with the

addition of the custom objective function, as shown in Figure 5-3. The algorithm work

as follows. The vector X is initialized with all the pre-defined fault positions to be

covered; vector W includes the observability weight factors of all the fault positions in

X . The monitoring program to be built can either be an optimal sag monitoring

program (OSMP) or an optimal fault location monitoring program (OFLMP). In every

iteration the bus that maximizes the sum of the observability weight factors of the

uncovered fault positions S is selected as the best place for a voltage measurement


113 |

device. The search terminates when all fault positions are uniquely located or all voltage

sags are detected. The outcome is a monitoring program obtained from MLA or MRA

that covers X .

In summary, with the weighted search algorithm monitors are selected based on both the

number of faults localized or sags detected and the respective degree of observability.

Since the space search is limited to the binary matrices MLA or MRA , the

computational burden is considerably lower than the one entailed by enumerative

methods.

The size of several sag monitoring programs determined for the GDS network by the

proposed weighted greedy algorithm is shown in Table 5-3. The number of

measurements optimized using linear programming and the simple greedy algorithm is

also presented for comparison. In nine of the eleven cases where the simple greedy

algorithm overestimates the size of the monitoring programs, the weighted version of

the algorithm determines correctly the minimum number of monitors required. In the

other two instances, shaded in green in Table 5-3, the weighted algorithm obtained the

same number as the simple greedy algorithm (one more than the minima).

Figure 5-3 Flowchart for implementing the weighted greedy algorithm.

X = 1, 2,…, F;

OSMP = Æ; OFLMP = Æ; W

X = X – S; OSMP = OSMP È i

or OFLMP = OFLMP È i

X ≠ Æ

End

Yes

No

Select bus i whose S MLA or MRA

maximizes W S X


114 |

Table 5-3 Number of Voltage Measurement Devices Obtained by Three Different Methods

Loading

profile

Rf

(Ω)

thV

(p.u.)

Linear

programming

Simple greedy

algorithm

Weighted greedy

algorithm

Low 0 0.8 11 12 12

Low 5 0.8 30 31 30

Low 5 0.7 41 42 41

Medium 5 0.8 30 31 30

Medium 5 0.7 40 41 40

High 5 0.8 30 31 30

High 5 0.7 40 41 40

1 p.u. 0 0.7 18 19 18

1 p.u. 5 0.9 22 23 22

1 p.u. 25 0.9 35 36 36

1 p.u. 25 0.7 25 26 25

Table 5-4 compares the measurement placement for the IEEE 118-bus network

performed by simple and weighted greedy algorithms. The bus selection sequence, the

value of the weighted objective function, and the coverage of the network of the two

algorithms are contrasted in this table. Both techniques produce the same optimal fault

location monitoring programs (number and positions of monitors) but they differ in the

monitor placement sequence on account of the objective functions used in each

approach. The simple greedy algorithm finds the buses for monitoring that maximize

the coverage of the whole network while the weighted algorithm determines the buses

that maximize the coverage of the less observable areas of the network. Although

different objective functions were used to select the optimal buses for monitoring, all

the values presented in Table 5-4 correspond to the objective function of the weighted

greedy algorithm, i.e. the sum of the observability weight factors of uncovered faults.

The simple greedy algorithm, as can be seen in Table 5-4, starts by selecting the pair of

buses 78 and 111, where the presence of measurement devices leads to location of faults

in the largest area of the network (95.34%) but a relatively low value of the objective

function at 0.51, meaning that faults occurring in this area can be located by high

number of monitors. The weighted greedy algorithm instead, chooses only bus 117 as

the best initial site for voltage monitoring since its measurements are the only ones that

can be used to locate the faults occurring on the line connecting bus 117 with the rest of

the network (see Figure 5-4). For this reason, each of the three faults simulated on this

line have a weight factor equal to 1 and summed together they add 3 units of the

objective function in the first iteration.


115 |

Table 5-4 Monitor Placement for Fault Location in the 118-bus Network Utilizing Greedy Algorithms

Order

Simple greedy algorithm Weighted greedy algorithm

Bus Objective

function

Percentage of

network covered Bus

Objective

function

Percentage of

network covered

1 78 and 111 0.51 95.34 117 3.01 4.66

2 101 0.56 95.90 111 3.47 94.55

3 114 0.62 96.46 39 3.55 95.39

4 39 0.69 96.88 41 3.62 95.81

5 41 0.77 97.30 67 3.70 96.23

6 67 0.85 97.72 84 3.79 96.65

7 84 0.92 98.14 88 3.85 97.07

8 88 1.00 98.56 93 3.93 97.49

9 93 1.08 98.98 95 4.01 97.91

10 95 1.15 99.40 97 4.10 98.32

11 97 1.23 99.81 78 4.14 98.88

12 117 4.24 100.00 101 4.19 99.44

13 — — — 114 4.24 100.00

After the first iteration, both heuristic algorithms continue selecting only single buses

until the coverage of the whole network is reached, which is equivalent to the objective

function having a total value of 4.24 units. The simple greedy algorithm terminates the

search one iteration before the weighted algorithm due to the selection of two buses in

the first iteration. The buses selected by the greedy algorithms are shown in Figure 5-4

and these conform to the optimal monitor placement determined in Chapter 4 .

Figure 5-4 Buses (red numbered) designated by greedy monitor placement algorithms as optimal

locations for voltage measurement devices.

117

114

84

88

95

93

101

111

78

4139

67

97

Faults on this line can only be

(uniquely) located by bus 117


116 |

Although it is apparent from Table 5-3 that in most cases the proposed weighted greedy

algorithm can obtain better results than the simple greedy algorithm, the main advantage

of the proposed approach resides in its much reduced computer memory usage since it

allows finding sets of monitors when linear programming fails to do so, for example in

the 295-bus GDS network.

The number of monitors required to locate each and all types of faults in the GDS

network is presented in Table 5-5. It can be seen that both approaches found that 8

monitors can locate all line to ground faults in the network. The weighted greedy

algorithm found that 16 monitors are sufficient to determine the location of line to line

and three phase faults. The memory requirements entailed by FICO’s Xpress

optimization suite are so vast that a PC with an Intel® CoreTM

2 Duo processor with a

2.00 GHz clock and with 4.00 GB of RAM ran out of memory while attempting to find

a solution for these two types of fault. With respect to line to line to ground faults, the

branch and bound search tree drawn by the commercial software kept growing after 1

hour of execution (more than 60000 active nodes were defined) and for this reason the

optimization was intentionally stopped after this period having found that 23 monitors

can estimate a unique location for this type of faults. The proposed search algorithm

also found 23 monitors in just few seconds. An optimal fault location monitoring

program for all types of faults was not found using Xpress due to its associated

computational and memory burden. The greedy algorithm determined that 25 monitors

suffice to localize all types of faults.

Table 5-5 Minimum Number of Monitors Required for Fault Location in the 295-bus GDS Network

Type of fault Linear programming Weighted greedy algorithm

Line to ground 8 8

Line to line No solution found 16

Line to line to ground 23 23

Three phase No solution found 16

All types No solution found 25

5.3.2 Sag Magnitude Estimation Error

The second custom objective function is aimed at assessing the sag estimation accuracy

of monitoring programs. It was shown in Chapter 3 that the enhanced MRA algorithm

(EMRAA) can pinpoint a fault or determine multiple estimates of its location, and


117 |

therefore the estimated voltage sag magnitude at bus i due to fault at point j can take

one of the following values:

1

1

,

,

,

ij

fpest k

ij ijfpk

pf

i

V

V V

V

if fault at point j is uniquely located

(5.9) if fault at point j has fp estimated locations

if fault at point j is not located

If a fault location can be pinpointed using the voltage measurements from one or more

buses, it is assumed that the estimated sag magnitude is the true value of the voltage sag

caused by the fault. If multiple estimates for the fault location are determined using the

set of voltage measurements available, the estimated sag magnitude is given by the

average of the voltage sags caused by the faults occurring at all the possible locations. If

the fault cannot be located, e.g. in the presence of a delta-wye transformer between the

monitored bus and the location of a single line to ground fault, no fault occurrence is

assumed and the estimated sag magnitude equals the pre-fault voltage.

The sag magnitude estimation error ( )SMEE is introduced here as a measure of the

overall sag estimation accuracy of a monitoring program and it is calculated as the

average percentage difference between the real and estimated magnitude of sags at all

buses:

1

1100,

real estN

ij ij

reali

ij

V VSMEE j

N V

(5.10)

where real

ijV and est

ijV are the real and estimated magnitudes of the sag at bus i caused by

a fault at point j , respectively. This error can be calculated for every phase and for each

type of fault.

The iterative process that builds optimal sag monitoring programs based on

minimization of the SMEE is similar to the greedy monitor placement procedures as

can be seen in Figure 5-5. The aim in each iteration is to determine the bus whose

voltage measurements can be used to reduce the SMEE to minimum. The voltage sag

magnitude at all buses is estimated according to (5.9) based on the location estimates for

all faults derived from a given bus. The SMEE is then calculated using (5.10) for the

three phases and for the four types of faults discussed previously. These operations are

executed using the measurements from each bus of the system. The bus for which the

SMEE results in the minimum is selected as the best voltage monitoring site. The


118 |

process is repeated incorporating the selected buses until the number of buses selected

equals the size of an optimal fault location monitoring program; by then all simulated

faults are uniquely located, i.e., the estimated magnitude of all sags are the true values

of the voltage sags and hence the SMEE is zero.

Figure 5-5 Flowchart detailing the process of building an optimal sag monitoring program (OSMP)

aimed at minimizing the sag magnitude estimation error (SMEE).

The results of applying the procedure explained above to the 295-bus GDS network are

presented in Table 5-6. As previously found (see Table 5-5), with eight monitors all

single line to ground faults can be located throughout the network and thus the SMEE is

zero. Over 33% of the network is covered by the first bus chosen for voltage monitoring

and five voltage measurement devices can locate line to ground faults in practically

99% of the network. The low standard deviation and the maximum error of 100%

obtained in every step indicate that the magnitude estimation of sags caused by faults

occurring outside the areas covered by the monitors is due to undetected faults. For

example, while the addition of the first monitor provides a virtually perfect estimation

( 0)SMEE of the sag magnitude in 33.45% of the network, the voltage measurements

of this monitor cannot be used to estimate the location of line to ground faults in the

remaining 66.55% of the network, i.e. faults are undetected leading to a SMEE of

OSMP = Æ;

nm = size of OFLMP

End

Yes

No

Calculate according to (3.9) for all

faults and for all buses.

est

ijV

Calculate SMEE according to (3.10) for

every phase and for all types of faults.

Select bus i that minimizes SMEE

OSMP = OSMP È i

Size of OSMP = nm


119 |

almost 100%. The selection of every bus for voltage monitoring is limited by its fault

location capability which is determined by the presence of delta-wye transformers in the

network in the case of line to ground faults.

Table 5-6 Sag Magnitude Estimation Error of Each Phase for Line to Ground Faults Occurring in the

GDS Network

Number

of buses

SMEE (%) Std. dev. (%) Maximum (%) Network

coverage (%) A B C A B C A B C

1 99.47 99.46 99.46 0.04 0.00 0.00 100 99.46 99.46 33.45

2 99.15 99.15 99.15 0.07 0.00 0.00 100 99.15 99.15 57.91

3 98.46 98.44 98.44 0.13 0.00 0.00 100 98.44 98.45 76.98

4 95.88 95.83 95.84 0.35 0.00 0.00 100 95.85 95.86 91.37

5 67.04 66.68 66.69 2.76 0.02 0.04 100 66.82 66.88 98.92

6 50.56 50.01 50.03 4.14 0.03 0.06 100 50.23 50.31 99.28

7 1.13 0.03 0.06 8.29 0.06 0.11 100 0.47 0.63 99.64

8 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 100.00

The influence of delta-wye transformers in the monitor placement is illustrated in Figure

5-6. The sections of the network covered by each selected bus are confined to the color

meshed areas. The size of the sections, relative to the whole network, and the sequence

in which buses are selected is also shown. A closer examination of the topology of the

network reveals that each section is isolated, in terms of location of single line to ground

faults, by a delta-wye transformer. For this reason, only monitors installed within these

sections can detect and locate single line to ground faults occurring at the buses and on

the lines encompassed by these areas.

The last three buses selected for monitoring are required to locate the faults occurring

on the lines connected to those buses. In the cases of the sixth and seventh monitor both

lines are connecting two buses where delta-wye transformers are attached, forcing the

deployment of a monitor at any end of the line. The last (eighth) monitor is

indispensable at the end of a feeder to obtain only one estimate for the location of line to

ground faults taking place on the line connecting the last two buses of such feeder.


120 |

Figure 5-6 Proportions of the GDS network where line to ground faults can be located by the ordered

addition of voltage measurement devices.

2n

d:

25

%

4th

: 1

4%

5th

: 8

%

3rd

: 1

9%

8th

: 0

.33

%

1s

t : 3

3%

6th

: 0

.33

%

7th

: 0

.33

%

24

46

17

28

16

14

12

26

21

19

23

22

22

2

18

15

54

52

53

22

9

50

75

22

7

74

22

8

20

22

0

51

76

13

26

7

87

48

47

49

22

1

43

42

41

40

39

38

37

26

8

23

42

35

23

0

78

79

80

81

85

88

28

5

82

83

84

28

6

90

91

92

94

93

95

96

97

10

09

8 99

10

1

10

21

03

10

4

10

51

06

10

7

10

8

10

9

11

0

11

1

11

2

11

31

14

11

5

12

0

12

1

12

21

23

12

4

12

5

12

6

12

7

11

6

11

7

11

81

19

86

11

10

8

97654

55

1

65

64

63

57

22

52

26

58

14

8

14

6

15

3

15

4

14

91

52

15

5

14

71

45

14

4

14

0

14

2

14

1

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3

13

9

13

8

12

8

12

91

32

13

0

13

4

13

61

35

13

7

13

3

15

6

16

0

15

7

18

5

18

3

13

1

15

9

16

4

16

1

16

2

16

3

16

5

16

6

16

71

68

16

9

17

9

18

0

18

11

82

18

4

18

6

18

7

18

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18

91

90

19

1

19

2

19

3

19

6

19

7

19

91

98

20

0

20

1

20

22

03

20

4

20

5

20

6

20

72

08

15

0

15

1

22

3

23

1

77

15

8

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4

21

4

21

5

21

0

21

12

09

21

2

21

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21

71

70

21

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9

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1

17

2

17

3

17

4

17

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17

6

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7

62

60

59

61

2

3

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70

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8

25

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29

30

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33

34

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71

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67

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89

45

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24

82

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24

1

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26

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6

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27

7

24

7

27

923

3

27

8

23

22

54

25

6

28

82

87

28

92

90

29

22

91

29

42

93

29

5

26

42

37

28

3

23

8

28

22

80

28

1

56

13

2k

V

33

kV

11

kV

3.3

kV

27

5k

V

40

0k

V

66

18

2

18

3

18

41

85

18

61

87

18

81

89

19

0

19

1

19

2

19

31

94

19

51

96

19

71

98

19

92

00

20

1

20

2

20

3

20

42

05

20

6

20

7

20

8

20

9

21

0

21

1

21

2

21

3

21

4

21

5

21

6

21

72

18

21

92

20

22

1

22

2

22

32

24

22

5

22

6

22

7

22

82

29

23

02

31

23

2

23

3

23

4

23

52

36

23

72

38

23

92

40

24

1

24

2

24

3

24

42

45

24

6

24

72

48

24

92

50

25

1

25

2

25

3

25

4

25

5

25

6

25

7

25

82

59

26

0

19

426

1

19

526

22

63

26

42

65

26

62

67

26

8

26

9

27

0

27

12

72

27

4

27

52

78

27

3

27

62

77

1

2 8

33

34

5

5

6

7

9

10

11

12

13

13

13

14

15

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87

88

89

90

91

92

9394

95

96

96

97

98

99

10

0

10

1

10

2

10

3

10

41

05

10

6

10

7

10

8

10

9

11

0

11

1

11

21

13

11

4

11

51

15

11

6

11

71

18 1

19

12

0

12

1

12

2

12

3

12

3

12

41

25

12

61

27

12

8

12

9

13

0

13

1

13

2

13

31

34

13

5

13

6

13

7

13

81

39

14

0

14

11

42

14

3

14

41

45

14

6

14

7

14

8

14

9

15

0

15

1

15

21

53

15

4

15

5

15

6

15

71

58

15

9

16

0

16

11

62

16

3

16

4

16

5

16

6

16

7

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8

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9

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0

17

1

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2

17

3

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4

17

51

76

17

71

78

17

9

18

01

80

18

0

18

1

V

V

V

V

V

V

V

V


121 |

The overall SMEE calculated for all types of faults during the greedy monitor

placement is shown in Figure 5-7 along with the values of the standard deviation and

the largest errors. An almost constant reduction of the SMEE is achieved with the

addition of every measurement device. The comprehensive detection and estimation of

location of line to line and three-phase faults account for this steady reduction. Although

both the estimation error and the standard deviation remain under 5% from the seventh

monitor chosen, the maximum errors vary between 13% and 42% until the whole

network has been covered with 25 monitors.

Figure 5-7 Sag Magnitude Estimation Error (SMEE) obtained during each iteration of the greedy

monitor placement procedure.

The normalized size of the areas where faults can be located is depicted in Figure 5-8

according to the type of fault. Full fault location observability of line to ground faults,

representing 25% of the total coverage, is attained after the addition of ten monitors,

which can be used to locate 92% (23% of total) of line to line faults, 62% (15% of total)

of line to line to ground faults, and 91% (23% of total) of three-phase faults. All types

of faults can be localized anywhere in the network (each type of fault representing 25%

of the total coverage) once 25 buses have been selected.

The detailed data of Figure 5-7 and Figure 5-8 is presented in tabular form in Appendix

B. Tables containing the results of minimization of SMEE by greedy monitor

placement for each type of fault are also given in Appendix B.

0

10

20

30

40

50

60

70

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

Perc

en

tag

e e

rro

r

Number of voltage measurement devices

SMEE Std dev. Maximum


122 |

Figure 5-8 Increase in network’s coverage of different types of faults obtained during each iteration of

the greedy monitor placement procedure.

5.3.3 Sag Event Estimation Error

The third custom objective function has been designed to jointly minimize the number

of monitors deployed and the number of sag events estimated at non-monitored buses.

The sag estimation at non-monitored buses is done by counting the number of sag

events based on the average of the residual voltages corresponding to all the possible

fault locations calculated following the procedures described in Section 3.3. The

accuracy of the sag estimation is given by the difference between the real and the

estimated number of sags. Voltage-tolerance curves such as CBEMA, voltage sag

immunity standards like SEMI F47, performance indices like SARFI-X, voltage quality

standards like EN 50160, or voltage-sag tables such as generalized sag table can be used

to specify the type of sags (sag characteristics) that the monitoring program will use for

assessment of the accuracy of the estimation. For example, the sag event estimation

error ( )SEEE for voltage sags specified by SARFI-X indices is calculated as:

1

- -N

rea est

i i

i

SARFI X SARFI X

SEEEN

(5.11)

where - rea

iSARFI X is the real number of voltage sags with magnitude equal to or less

than X at bus i , - est

iSARFI X is the estimated number of sags with the same

characteristics at bus i , and N is the total number of buses.

0

10

20

30

40

50

60

70

80

90

100

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

Perc

en

tag

e o

f n

etw

ork

co

vere

d

Number of voltage measurement devices

LG faults LL faults LLG faults LLLfaults


123 |

An iterative search strategy similar to the ones previously described in sections 5.3.1

and 5.3.2 is used to determine sag monitoring programs that minimize (5.11). At every

iteration, the sag event estimation error at each bus is calculated and the bus with the

minimum error is chosen as the monitor location corresponding to that iteration. The

gradual search is run repeatedly increasing the number of monitors and reducing the

estimation error at each stage. The search is terminated when the SEEE has been

reduced to a pre-defined value or a pre-defined number of monitors have been placed.

Voltage sags with characteristics specified by the aforesaid voltage-tolerance and sag

immunity curves, sag performance indices, European standards, and voltage-sag tables

have been analyzed. The next five subsections describe the occurrence of these types of

sags in the GDS network. These descriptions are followed by the results of the greedy

monitor placement aimed at minimizing the SEEE of each of type of event.

5.3.3.1 Occurrence of voltage sags as classified by standard EN 50160

The European standard EN 50160 defines, describes, and specifies the characteristics of

the supply voltage in public electricity networks [111]. The standard classifies voltage

dips (sags) according to Table 5-7 for statistics collection. Typical values of sag

incidence for each cell of the table are not given due to the high spatial and temporal

variability of voltage sags. Nevertheless, the vast majority of voltage sags last less than

1 second and have a residual voltage above 40% [111] and thus most of the events will

typically lie in cells A1, A2, A3, B1, B2, B3, C1, C2, and C3. Moreover, the standard

suggests the use of Table 5-7 to identify the expected performance of the network and to

assess the probable behavior of the equipment connected. It is expected that equipment

tested according to product standards EN 61000-4-11 and EN 610000-4-34 will ride

through sags indicated in the cells A1, A2, B1, and B2 for class 2 equipment and A1,

A2, A3, A4, B1, B2, and C1 for class 3 equipment.

Table 5-7 EN 50160 classification of voltage sags according to residual voltage and duration (adopted

from [111])

Residual

voltage u (%)

Duration t (ms)

10 ≤ t ≤ 200 200 ≤ t ≤ 500 500 ≤ t ≤ 1 000 1 000 ≤ t ≤ 5 000 5 000 ≤ t ≤ 60 000

90 > u ≥ 80 Cell A1 Cell A2 Cell A3 Cell A4 Cell A5

80 > u ≥ 70 Cell B1 Cell B2 Cell B3 Cell B4 Cell B5

70 > u ≥ 40 Cell C1 Cell C2 Cell C3 Cell C4 Cell C5

40 > u ≥ 5 Cell D1 Cell D2 Cell D3 Cell D4 Cell D5

5 > u Cell X1 Cell X2 Cell X3 Cell X4 Cell X5


124 |

Faults occurring throughout the network can generally cause residual voltages as low as

0% in at least one bus. The duration of voltage sags, however, is mainly limited by the

fault clearing time of the protection scheme, which depends among other factors, on

voltage level. In the case when there is a significant presence of dynamic loads in the

network, induction motors in particular, sags can last longer than the time determined

by protection settings [112]. The maximum duration of the sag considered in this thesis

is assumed to be equivalent to the fault clearing time, and it can be used to determine if

a certain type of sag, as indicated in the cells of Table 5-7, can occur in the network.

The fault clearing times assumed for the GDS network are listed in Table 5-8. It can be

seen that the maximum duration of a fault is 300 milliseconds (ms) or 15 cycles barring

a protection system failure. Under this assumption most of the sags occurring in the

GDS network would appear in cells A1, A2, B1, B2, C1, and C2 and consequently the

monitoring program should be focused on these types of sags.

Table 5-8 Fault clearing times in the GDS network

Faulted element Voltage level (kV) Fault clearing time (ms) Fault clearing time (cycles)

Line 11 300 15

Line 33 150 7.5

Line 132 80 4

Bus 11, 33, and 132 60 3

5.3.3.2 Occurrence of voltage sags as classified by the ITIC Curve

The Information Technology Industry Council (ITIC), formerly known as the Computer

& Business Equipment Manufacturer’s Association (CBEMA) published the ITIC

Curve, which describes the AC input voltage envelope that can be withstood by most

information technology equipment (ITE) without interruption in their function [113]. In

terms of voltage sags the ITIC Curve describes a region of the composite envelope

where the normal functional state of the ITE can be disrupted but no damage to the ITE

should result. The No Damage Region encompasses events with duration between 20

ms and 500 ms and residual voltage of less than 70% of the nominal voltage. Since the

fastest fault clearing time specified in the GDS network is 60 ms and the longest is 300

ms (see Table 5-8 ) all voltage sags having residual voltage lower than or equal to 70%

lie in the No Damage Region as shown in Figure 5-9. Monitoring programs can also be

determined to minimize the estimation error of these types of sags.


125 |

Figure 5-9 No Damage Region of the ITIC Curve.

5.3.3.3 Occurrence of voltage sags as classified by the generalized sag

table

The generalized sag table includes information about the three phase residual voltages

individually to provide a more comprehensive assessment of the sag performance

severity. The columns and rows of the table are divided in ten magnitude ranges in steps

of 10% from 0% to 100% of the nominal voltage. Intersections of columns and rows

then determine cells and the figures to be put in the cells refer to the number of

equivalent events with particular combinations of three-phase voltage magnitudes [114].

A sag profile of the GDS network has been constructed by simulating symmetrical and

asymmetrical faults (four types of faults) at 0.25, 0.50, and 0.75 of the length of each of

the 278 lines of the system (3 336 faults in total) and calculating the residual voltages of

the three phases at each of the 295 buses. Every fault simulated then causes sags with

different combinations of three-phase voltage magnitudes at every bus, i.e., every fault

event accounts for 295 sag events (984 120 sags in total). The generalized sag table built

from these results is shown in Figure 5-10. The majority of sags (62.48%) are non-

disruptive since the voltage in the three phases remain between 90% and 100% as can

be seen in the top rightmost cell (614 901 events). The three types of potentially

disruptive sags with the greatest number of occurrences are indicated with red ellipses

and these are:

1) Voltage sags with residual voltage in two phases between 40% and 50% and

residual voltage in third phase between 90% and 100%,


residual voltage in third phase between 90% and 100% and,

0

10

20

30

40

50

60

70

80

90

100

14-Apr-12 15-Apr-12 16-Apr-12 17-Apr-12 18-Apr-12

Perc

en

t o

f N

om

inal V

olt

ag

e

Duration in miliseconds

20 500 10000300

GDS sag ocurrence

region

No Interruption in Function Region

No Damage Region(but possible interruption)


126 |


residual voltage in third phase between 70% and 80%.

These types of sags constitute nearly 9% of the total number of events and can be

treated as an initial focus of a sag monitoring program.

Figure 5-10 GDS network’s voltage sag profile.

5.3.3.4 Occurrence of voltage sags as classified by SARFI indices

The System Average Rms-variations Frequency Index (SARFI), originally proposed in

[24], is a simple yet widely used approach to counting voltage sags with magnitudes and

durations outside of some specifications. For example, SARFI80 would provide a count

of all voltage sags with a residual voltage less than 80% of nominal (regardless of

duration). SARFIITIC would provide a count of all voltage sags exceeding the ride

through specifications of the ITIC Curve. Although the acronym expresses System

Average, SARFI indices are also used to quantify sag performance at individual sites.

Some selected SARFI indices have been calculated for three voltage levels in the GDS

network based on the fault simulations performed in the previous section. The results,

summarized in Table 5-9 as total and average number of events, show higher incidence

of sags at 11 kV sites than at 33 kV and 132 kV sites for all SARFI indices. Since every

SARFI index includes all the events counted by a lower SARFI index, e.g. SARFI40

includes all the events being counted by SARFI10, SARFI90 will always count the

highest number of events. This index (or any other) can be used to guide the sequential

monitor placement.

0 10 20 30 40 50 60 70 80 90 1000

10

20

30

40

50

60

70

80

90

100

Voltage in two phases (% of nominal)

Voltage in t

he t

hird p

hase (

% o

f nom

inal)

19239

120

126

6

114

0

285

804

282

10695

12

14550

18

24

6

9

51

513

219

5856

0

0

13281

0

363

1929

456

681

339

4080

6

0

0

8166

0

804

7059

4470

864

4653

198

69

0

0

7377

3

48

3180

558

38520

72

585

30

0

3

5193

0

36

900

27453

339

357

423

87

0

6

4338

0

3

7989

243

336

852

948

576

15

27

12846

309

5439

1671

1398

2787

2967

2043

579

384

4815

11538

18288

11367

5916

6357

10824

11265

8676

9954

21636

17316

614901


127 |

Table 5-9 SARFI indices for three voltage levels in the GDS network

SARFI index 11 kV (233 sites) 33 kV (25 sites) 132 kV (23 sites)

Total Average Total Average Total Average

SARFI90 334 542 1435.80 19 349 773.96 18 075 785.87

SARFI85 310 084 1330.83 15 999 639.96 15 921 692.22

SARFI70 255 788 1097.80 12 783 511.32 10 660 463.48

SARFI40 134 505 577.27 7 420 296.80 6 413 278.83

SARFI10 46 792 200.82 1 240 49.60 1 076 46.78

5.3.3.5 Occurrence of voltage sags as classified by the SEMI F47 Curve

Semiconductor Equipment and Materials International (SEMI®) is a global industry

association of manufacturers of equipment and materials used in the micro- and nano-

electronics industries, including semiconductors, photovoltaics, and LED, among

others. SEMI developed the SEMI F47 standard to define the voltage sag immunity

required for semiconductor processing, metrology, and automated test equipment [115].

The standard is shown in Figure 5-11. The equipment shut-down region of the SEMI

F47 was determined for the GDS network according to the maximum fault clearing

times presented in Table 5-8. This region is represented in Figure 5-11 as the area below

the SEMI F47 Curve limited by a dashed line, which represents the maximum fault

clearing time of the network (300 ms). The GDS sag occurrence region encompasses all

sags of 50% of nominal voltage occurring throughout the network and sags of 70% of

nominal voltage but caused by faults occurring only on 11 kV buses and lines.

Monitoring programs can be specially design to estimate the incidence of these types of

sags.

Figure 5-11 SEMI F47 Curve – required semiconductor equipment voltage sag immunity (adopted from

[116]).

0

10

20

30

40

50

60

70

80

90

50 200 350 500 650 800 950

Perc

en

t o

f E

qu

ipm

en

t N

om

inal V

olt

ag

e

Duration in milliseconds

GDS sag ocurrence

region


128 |

5.3.3.6 Results of monitor placement

Monitor placement aimed at minimizing the SEEE of the sags described above has been

performed in the GDS network. The following types of sags have been considered

individually:

1) Sags with residual voltage between 40% and 90% in any phase (EN 50160).

2) Sags with residual voltage of 70% or less in any phase (ITIC Curve).

3) Sags with residual voltage in two phases between 40% and 60% and residual

voltage in third phase between 90% and 100% and sags with residual voltage in

two phases between 90% and 100% and voltage in third phase between 70% and

80% (Generalized Sag Table).

4) Sags with a residual voltage of 90% or less in any phase (SARFI90 index).

5) Sags with a residual voltage of 50% or less in any phase and sags with a residual

voltage of 70% or less in any phase but caused by faults occurring only on 11

kV buses and lines (SEMI F47).

A total of 25 buses have been selected to reduce the event estimation errors to zero

(when full fault location observability is achieved) but only the results of the first 11 are

summarized in Table 5-10. Less than a third of the full monitoring program, i.e. eight

monitors cut down the SEEE to less that 4 events for all types of sags, being the

SARFI90 index error reduced the furthest (0.63). Adding three more monitors results in

a reduction of the SEEE to less than 0.5 for all types of sags with standard deviation

ranging from 0.25 to 1.16. This means that on average the difference between real and

estimated sags at all buses lies within 0 and less than 1 event for sags described by

standard EN 50160, ITIC Curve, Generalized Sag Table (GST), and SARFI90 index and

within 0 and less than 2 events for sags below the SEMI F47 Curve. Complete results of

the deployment of the full monitoring program and the minimization of SEEE for each

type of sag separately are provided in Appendix C.


129 |

Tab

le 5

-10

M

inim

izat

ion o

f th

e O

ver

all

Sag

Ev

ent

Est

imat

ion

Err

or

in t

he

GD

S N

etw

ork

wit

h G

reed

y M

on

itor

Pla

cem

ent


130 |

5.4 Summary

An optimal fault location monitoring program can lead to virtually exact sag estimation

at non-monitored buses. However, determining these monitoring programs for large

power systems by integer linear programming can fail due to the computational and

memory usage entailed, and in some instances no set of monitors can be found at all.

A heuristic methodology has been developed that ensures finding fault location and sag

detection monitoring programs where integer programming fails to do so due to

considerably less memory usage. The proposed methodology found optimal monitoring

programs (determined with integer linear programming) in most cases. In the few

instances where the heuristic approach failed to find the minimum number of monitors,

the size of the monitoring programs exceeded only by one the minima.

The methodology developed and presented in this chapter includes three custom

objective functions formulated for greedy monitor placement. The first objective

function is aimed at determining fault location monitoring programs based on the degree

of observability of faults. The second objective function is designed to assess the sag

magnitude estimation accuracy of limited monitoring programs; whereas the third

objective function advances the sag magnitude estimation into sag event estimation and

incorporates a range of sag performance indices that can be used in the design and

specification of monitoring programs.

The heuristic approach proposed for efficient monitor placement can be used to

determine a range of monitoring programs for estimating sag performance in the

network using different sag characteristics and sag benchmarking methodologies. This

feature offers the opportunity to utilities to choose a monitoring program specifically

designed to estimate, not only general sag performance in the network but also number

of sags with characteristics relevant to their customers, while balancing the accuracy

and the cost of the monitoring program.

Chapter 6 • Techno-Economic Assessment of Voltage Sags Using Optimal Monitoring Programs

131 |

Chapter 6

Techno-Economic

Assessment of Voltage Sags

Using Optimal Monitoring

Programs

In Chapter 5 a heuristic monitor placement method with custom objective functions

aimed at reducing the sag estimation error at non-monitored buses was presented. It was

shown that the proposed method can determine both optimal and sub-optimal

monitoring programs even when linear programming does not achieve finite-time

convergence to a global optimum due to high memory requirements.

In this chapter a hybrid method to facilitate the identification of strategic sites for

voltage sag monitoring and estimation will be developed. The simplified hybrid method

combines the monitor placement methods for sag estimation and for fault location

reviewed in Chapter 3 and Chapter 4 , respectively. The work includes network

simulations to characterize voltage sags at non-monitored sites using the hybrid

monitoring programs and the assessment of the financial losses caused by voltage sags

utilizing a risk-based methodology. This hybrid method for assessing voltage sag

performance in the network using optimal monitoring represents the fourth original

contribution of this research.


132 |

6.1 Hybrid Methodology for Monitoring and Estimation

of Voltage Sags

In Chapter 3 it was demonstrated that when triggering thresholds are used for monitors

to detect the occurrence of fault-induced voltage sags, high-impedance faults and

changes in the loading condition of the network can cause sag-events that the monitors

might fail to register. However, the enhanced MRA algorithm (EMRAA) also

developed in Chapter 3 can be implemented effectively by the same monitoring

program to overcome this limitation without the need of additional data. This section

describes how both monitor placement methods, for sag estimation and for fault

location, can be combined to determine a more flexible and cost-effective sag

monitoring program.

6.1.1 Selection of Most Probable Fault Location

A drawback common to all impedance-based fault location methods is the existence of

multiple estimates for the fault location due to the presence of laterals and branched

nature of the network. Since in most cases the residual voltages caused by faults

occurring at these multiple locations are very similar and close to the real ones, a safe

approach is to take the average of all the voltages as the expected residual voltage at

non-monitored buses [39]. The proposed approach, instead, select the most likely fault

location (only one) according to the type of fault. The criteria to select the most

probable fault location for each type of fault are described next.

6.1.1.1 Most Probable Fault Location of Line to Ground Faults

The most probable fault location of line to ground faults is selected by verifying the

numeric validity of all the estimates, i.e., they should be a real number between 0 and 1.

For example, equation (6.1), firstly presented in Section 3.2.3, defines the location of

line to ground faults and results in a complex number with a (relatively) significant

imaginary component when solved for lines other than the actual faulted line. A simple

yet sound principle to discard possible fault locations is checking their imaginary

component.


133 |

(2) (0)

(0) (0) (2) (2)

ij ij

ik ij ik ij

Z GZd

G Z Z Z Z

(6.1)

The value of the imaginary part of the fault location estimates of 1650 line to ground

faults simulated in the IEEE 24-bus reliability test system was assessed. Ten faults

uniformly distributed on each line of the system were applied with fault impedance

values of 0 Ω, 5 Ω, 10 Ω, 25 Ω, and 50 Ω. The distribution of the values of the

imaginary parts corresponding to the actual fault location and the rest of the fault

location estimates is presented in Table 6-1. It can be seen that 99% of the values of the

actual fault locations are lower or equal than 0.5486×10-14

, which can be considered as

machine dependent round-off errors. Fault locations estimated on lines other than the

actual faulted line have considerable much higher imaginary components since 99% of

their values are within 3.58. A comparison of the two results confirms that only the

solutions corresponding to the actual fault locations have a negligible imaginary part.

Table 6-1 Percentiles of the Absolute Values of the Imaginary Parts of Fault Location Estimates

Percentile Actual fault location Rest of fault location estimates

25th 0.0035×10

-14 0.0127

50th 0.0082×10

-14 0.0437

75th 0.0179×10

-14 0.1077

99th 0.5489×10

-14 3.5804

6.1.1.2 Most Probable Fault Location of Line to Line to Ground Faults

The principle of zero imaginary part of fault location estimates cannot be applied to

identify the most probable fault location of line to line to ground faults because their

quartic (fourth-degree) fault location equation can have real roots between 0 and 1 for

lines other than the faulted lines. Probable locations for this type of fault can be ruled

out by comparing the measured voltage at the monitored bus to the calculated residual

voltage caused by simulating each possible fault. For example, the voltages at bus 12

during a line to line to ground fault with fault resistance of 50 Ω at 0.3636 on line

connecting buses 11 and 14 of the IEEE 24-bus reliability test system (RTS), are 1.0134

p.u. for phase a, 0.6237 p.u. for phase b, and 0.7439 p.u. for phase c. Applying the

enhanced fault location method results in 14 possible fault locations.

Table 6-2 lists the possible fault locations along lines and the magnitude of the residual

voltage of each phase at bus 12. The last column indicates the difference between the

calculated and the measured residual voltages at bus 12. It is apparent from this table

that the actual location and fault resistance can be correctly identified (shaded in gray in


134 |

Table 6-2) from a group of estimates since the minimum difference between simulated

and measured voltages at bus 12 correspond to the actual fault location.

The significant discrepancy between three-phase residual voltages is explained by the

use of the ratio between negative- and zero-sequence residual voltages in the location of

line to line to ground faults, as can be seen in equation (6.2), which is solved for d to

derive the quartic equation that determines the fault location. Equal values for this ratio

can be obtained with different complex values of negative-and zero-sequence residual

voltages at the monitored bus.

22000

02222

0

2 3

jjijikij

fjjijikij

i

i

ZIdHddZZZ

RZKdJddZZZ

V

V

(6.2)

It can be seen from the data in Table 6-3 that, although different negative- and zero-

sequence voltages are registered at bus 12 for each simulated fault, the ratio between

them is equal in all cases. The results presented in Table 6-2 and Table 6-3 show that

different combinations of fault locations and fault resistance can be determined as

potential fault locations for the same line to line to ground fault but that the actual fault

location can be distinguished from all the fault location estimates based on the

calculated residual voltages at monitored buses.

Table 6-2 Fault Location Estimates for a Line to Line to Ground Fault at 0.3636 on Line 14 of the IEEE-

RTS and the Corresponding Residual Voltages at Bus 12

Estimate Line Point fR

(Ω)

estimated

aV

(p.u.)

estimated

bV

(p.u.)

estimated

cV

(p.u.)

c

ax

estimated

x

real

x VV

(p.u.)

1 2 0.0032 3.92 0.905 0.680 0.827 0.248

2 3 0.0099 4.41 0.914 0.677 0.828 0.237

3 4 0.0056 4.30 0.911 0.676 0.828 0.238

4 5 0.6729 121.83 1.011 0.827 0.891 0.352

5 6 0.5151 94.94 1.012 0.776 0.856 0.266

6 7 0.4371 115.17 1.013 0.787 0.869 0.290

7 8 0.5726 97.68 1.014 0.721 0.834 0.188

8 11 0.6102 116.19 1.013 0.782 0.867 0.282

9 12 0.7213 111.73 1.014 0.741 0.848 0.221

10 13 0.9405 5.91 0.840 0.321 0.546 0.674

11 14 0.3636 50.00 1.013 0.624 0.744 0

12 17 0.9961 1.49 0.693 0.456 0.548 0.684

13 31 0.9856 1.49 0.693 0.456 0.549 0.683

14 32 0.9856 1.49 0.693 0.456 0.549 0.683

Results like the ones presented in Table 6-2 were obtained for 1650 line-to-line-to-

ground faults simulated in the IEEE 24-bus RTS. Ten faults uniformly distributed on

each line of the system were applied with fault impedance values of 0 Ω, 5 Ω, 10 Ω, 25


135 |

Ω, and 50 Ω. The difference between calculated and measured phase residual voltages

is shown in Figure 6-1 by means of box plots, one for every bus. On each box, the

central mark represents the median, the lower and upper edges of the box indicate the

25th

and the 75th

percentile, respectively, and the whiskers extend to the most extreme

data points not considered outliers. The calculated residual voltages correspond to faults

simulated at the fault locations estimated by each monitor. Measured voltages are the

ones corresponding to the actual fault location. Results for the 24 buses are included but

outliers have been neglected for the sake of clarity.

Table 6-3 Ratio between Negative-Sequence and Zero-Sequence Residual Voltages at Bus 12 for the

Fault Location Estimates of Table 6-2

Estimate (2)

12V (0)

12V (2) (0)

12 12/V V

1 0.0873 - j0.0763 0.0152 + j0.0038 4.2282 - j6.0791

2 0.0934 - j0.0777 0.0158 + j0.0044 4.2282 - j6.0791

3 0.0920 - j0.0783 0.0158 + j0.0042 4.2282 - j6.0791

4 0.0932 - j0.0284 0.0103 + j0.0081 4.2282 - j6.0791

5 0.1209 - j0.0344 0.0131 + j0.0108 4.2282 - j6.0791

6 0.1130 - j0.0358 0.0127 + j0.0098 4.2282 - j6.0791

7 0.1464 - j0.0487 0.0167 + j0.0125 4.2282 - j6.0791

8 0.1154 - j0.0376 0.0131 + j0.0099 4.2282 - j6.0791

9 0.1354 - j0.0465 0.0156 + j0.0114 4.2282 - j6.0791

10 0.2638 - j0.1212 0.0338 + j0.0199 4.2282 - j6.0791

11 0.2113 - j0.0476 0.0216 + j0.0198 4.2282 - j6.0791

12 0.1101 - j0.0608 0.0152 + j0.0075 4.2282 - j6.0791

13 0.1095 - j0.0607 0.0152 + j0.0075 4.2282 - j6.0791

14 0.1095 - j0.0607 0.0152 + j0.0075 4.2282 - j6.0791

Figure 6-1 Difference between calculated and real phase residual voltages of line to line to ground faults

on the IEEE-RTS.

As can be seen from Figure 6-1, differences between calculated and real residual

voltages occur in all buses of the IEEE-RTS. The highest dispersion in voltage

discrepancy is observed at buses 14 to 17. The voltage difference at these buses can be

higher than 0.45 p.u. For example, the lowest value, the median, the 75th

percentile, and

the highest value of bus 16 is 0.0 p.u., 0.1 p.u., 0.2 p.u., and 0.49 p.u., respectively,

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Buses

0

0.4

0.2

0.1

0.15

0.05

0.3

0.25

0.35

0.45

Dif

fere

nc

e in

vo

lta

ge

s (

p.u

.)

0.5


136 |

which means that half of the discrepancies are lie between 0 and 0.1 p.u., an additional

25% of the discrepancies range from 0.1 p.u. to 0.2 p.u., and the remaining differences

are between 0.2 p.u. and 0.49 p.u. The box plots of buses 1, 2, and 7 can be interpreted

in a similar way. It can thus be seen that these buses show the lowest variation in

voltage differences, typically below 0.1 p.u.

6.1.1.3 Most Probable Fault Location of Line to Line and Three-phase

Faults

The absence of the ratio between negative- and zero- sequence residual voltages in the

fault location formulation of line to line and three-phase faults gives rise to the

estimation of potential fault locations with practically equal residual voltages. The

negligible differences among voltages were confirmed by calculations. Therefore, the

selection of the most probable fault location is simply limited to the one presenting the

minimum difference between calculated and measured voltages at all monitors.

The most probable location of 6600 faults (1650 for each type of fault including fault

impedance values of 0, 5, 10, 25, and 50 Ω) was determined using the residual voltages

at bus 12. It was found that with the proposed approach 100% of line to ground and line

to line to ground faults and 62% of line to line and three-phase faults are correctly

localized. Figure 6-2 shows the difference between calculated and real magnitude of the

sags caused by the faults that were not correctly localized (38%). It can be seen that

75% of the errors in sag magnitude estimation lie below 0.08 p.u. and the remaining

estimation errors are less than 0.19 p.u. As stated in Chapter 4 (section 4.3.2), the

addition of one more monitor in the network suffices the correct location of all faults in

the IEEE-RTS and consequently the elimination of sag estimation errors.

Figure 6-2 Difference between calculated and real magnitude of sags caused by line to line and three-

phase faults not correctly localized using the residual voltages from bus 12.


137 |

6.1.2 Hybrid Monitor Placement Method

The approach proposed in this chapter combines the monitor placement methods for sag

estimation and for fault location reviewed in Chapter 3 and Chapter 4 , respectively.

Given that now the selection of the most probable fault location is based solely on the

attributes of fault location estimates, rather than on triangulation by multiple monitors

(like existing methods for sag estimation and fault location), the only constraint for

determining the proposed monitoring program is to ensure that all faults are detected by

at least one monitor, as an optimal sag monitoring program determined by the MRA

method. However, the detection of faults must be accomplished using the EFL method.

The new and simplified monitor placement problem is an integer linear programming

problem formulated as:

1

MinimizeN

x

x

M

1

Subject to : , 1, ,N

x

x x y x y

M MLA (6.3)

where MLA is the monitor location area defined for the generic formulation of the

optimal fault location monitoring problem in Chapter 4 . In this new formulation

though, MLA has the same size as the monitor reach area MRA defined in Chapter 3

since no combination of monitors are considered.

MLA matrices are built for each type of fault using the respective fault location

equations. There is no need to have a unique fault location estimate in an MLA because

only single monitors are taken into account.

The use of the row-reduced version instead of both, the original MLA matrix and the

MRA matrix, offers significant advantages over the last two; it is not affected by

different voltage thresholds and it indicates the areas of the network where faults can be

located. Both features along with the algorithm for cutting down the number of fault

location estimates can increase the accuracy of sag performance estimation and reduce

the number of monitors required for such purpose.

The sag monitoring program obtained by this approach is the minimum set of monitors

that not only can detect voltage sags throughout the network but can also pinpoint the

location of the faults that cause those sags regardless of their magnitude. Although


138 |

faults are not located uniquely, the actual fault location is selected correctly from a list

of possible estimates in the vast majority of cases and when it is not, the sag magnitude

estimation error incurred is negligible.

6.1.3 Simplified Voltage Sag Estimation

The system sag performance is estimated by determining the most probable fault

location from the set of potential fault locations for every fault detected and according

to the type of fault. For line to ground faults, the potential fault location having the

minimum value of the imaginary part is considered as the actual fault location.

For line to line, line to line to ground, and three-phase faults, faults are simulated at the

potential locations and with the estimated fault resistance. The most probable fault

location is the one which has the closest calculated residual voltages to the measured

voltages by all voltage measurement devices of the monitoring program. Although this

can result in the incorrect selection of the fault location, the error incurred in the sag

performance estimation is tolerable in large majority of the cases (as previously shown).

Distinctions should be made at this point between the proposed approach and the fault

location observability analysis and the associated monitor placement for fault location

presented in [53]. Even though both approaches aim to find a unique location estimate

for all faults, the method introduced in [53] chooses the most probable fault location

from the intersection of sets of potential locations of several monitors, whereas with the

proposed method such estimate is selected by evaluating the difference between

calculated voltages and measured voltages and the imaginary component of the fault

location estimate.

The dissimilarity in the procedure of each method leads to the most significant

difference between the two which is the total number of monitors required. The

proposed method utilizes only a fraction of the number of monitors demanded by the

method developed in [53] as it is shown in the next section.

6.2 Case Study 1: Assessment of Voltage Sag Events

The first case study has been performed to corroborate the sag event estimation

accuracy of the hybrid monitor placement method through stochastic simulation. The

cost-effectiveness of the hybrid method is also demonstrated with a comparison of the


139 |

number of voltage measurement devices required by the proposed and existing

approaches. The study was carried out in the 295-bus generic distribution system with a

pre-defined set of six fault positions distributed uniformly along all lines and taking into

account all types of faults.

6.2.1 Size of Monitoring Programs

The minimum number of monitors required to estimate the voltage sags caused by the

aforesaid set of faults and the minimum required to locate them was determined in

Chapter 3 and Chapter 5 , respectively. In addition, the number of voltage

measurements for full observability of the system (in the state estimation sense) has

been obtained using the topology-based method proposed in [117].

The size of each monitoring scheme is shown in Table 6-4. It can be seen that full

observability of the system for state estimation requires the greatest number of monitors

(68) followed by the optimal fault location monitoring program (28). As previously

determined in Chapter 3 (see Section 3.1.4), the size of the optimal sag monitoring

programs developed with the MRA method ranges from 7 to 45. The number of

monitors required for sag estimation using the proposed hybrid method is 8, equivalent

to the monitoring scheme required to locate all line to ground faults determined in

Chapter 5 (see Figure 5-6).

Table 6-4 Number of Voltage Measurement Devices Required for Distinct Functions in the 295-bus

GDS

Function Number of monitors

Voltage sag estimation Between 7 and 45

Unique fault location 28

State estimation 68

Sag estimation with non-unique fault location (Hybrid approach) 8

6.2.2 Sag Event Estimation

The sag monitoring program determined with the MRA method for a voltage threshold

of 0.7 p.u., consisting of 16 monitors and the 8 monitors obtained with the proposed

approach have been tested and compared through Monte Carlo simulation. In each

simulation a random number of faults is generated from the Poisson distribution and

based on the system fault statistics shown in Table 6-5. For faults simulated on lines the

fault point along the line is also randomly selected from a uniform distribution. This

ensures that the location of every fault simulated on a line is different from the six fault


140 |

positions used to determine the monitoring programs. The fault resistance of each fault

is randomly assigned. It is assumed that the fault resistances follow a normal

distribution with mean μ = 15 Ω and standard deviation δ = 4.5 Ω [90].

Three loading profiles have been considered during the simulations [80]. The

probability distribution and loading factors of these loading profiles are shown in Table

6-6. The pre-fault voltages corresponding to each loading profile were determined using

Matpower. For each simulated fault the loading profile and the associated pre-fault

voltage profile were assigned according to Table 6-6. A fourth loading profile

equivalent to 105% of the base loading profile was used in all calculations to test the

robustness of the method when pre-fault voltages are estimated.

Table 6-5 System Fault Statistics (adopted from [90])

Fault location Fault rate/year Fault distribution according to fault type

LG (73%) LL (6%) LLG (17%) LLL (4%)

Bus 0.08 0.0584 0.0048 0.0136 0.0032

132 kV line 0.6 0.438 0.036 0.102 0.024

33 kV line 3.7 2.701 0.222 0.629 0.148

11 kV line 8.7 6.351 0.522 1.479 0.348

11 kV cable 4.9 3.577 0.294 0.833 0.196

Table 6-6 Probability of Occurrence of Loading Profiles (adopted from [80])

Loading profile Load factor Probability

High load 110% 0.1250

Base load 100% 0.5417

Low load 90% 0.3333

A total of 100 simulations, each representing one year of system performance, were

executed. The residual voltages of all the faults simulated were calculated and the

voltages at monitored buses were used as pseudo-measurements to identify the most

probable fault locations and the number of sags was estimated based on these estimates.

The difference between the actual number of sags at all buses and the number estimated

using the voltage measurements of each monitoring program is shown in Table 6-7 for

two types of sags; voltage sags falling in the region of undervoltage conditions of the

ITIC curve are presented in the second and third columns and sags with magnitude of

0.9 p.u. or less of the nominal voltage (SARFI-90%) are shown in the fourth and fifth

columns. Results are presented in percentiles, each indicating the percent of buses in

which the difference between real and estimated number of sag events falls below a

certain value, for example, the fourth row of Table 6-7 (shaded in green) indicates that

for 80% of the buses the difference between the real sag incidence and the sag incidence

estimated using the MRA method can be as high as 1588 for ITIC events and as high as

http://en.wikipedia.org/wiki/Percentage


141 |

1615.5 for SARFI-90 events. With the hybrid approach these differences are 3 and 7

events, respectively.

The data of Table 6-7 illustrate significant improvement in accuracy of sag estimation

when a more robust fault location method is implemented. The monitoring program

determined with the proposed hybrid method estimated correctly the incidence of sags

below the ITIC Curve for half of the buses, whereas the optimal sag monitoring

program (OSMP) failed to register up to 91 events in one single bus over the simulation

period. More importantly, the maximum difference between the actual number of sags

and sags estimated by the new monitoring program was less than 6 for 95% of the

system buses. On the other hand, the OSMP entailed an error of up to 1618 missed sags

over the entire simulation period (100 years), i.e. an average of 16 sags per year

affecting a bus were not identified.

Similar results were obtained for voltage sags with magnitude less than 0.9 p.u. For half

of the buses of the network, the new monitoring program did not overlook any event,

while there were buses where the OSMP failed to detect 1438 events. Considering 95%

of the network, 14 sags at most were not detected by the proposed monitoring program

during the 100 years simulation period, i.e. less than 0.14 per year. In the same portion

of the network, monitors of the OSMP missed up to 1813 sags in a single bus in 100

simulations, an average of 18.13 per year. A moderate impact of the inaccuracy in

estimation of the pre-fault voltage values (introduced by using the aforesaid fourth

loading profile) on the proposed approach is evidenced by the marginal errors in sag

estimation shown in Table 6-7.

Table 6-7 Difference between Estimated and Actual Number of Sag Events

Percentile

ITIC SARFI-90

MRA method

(16 monitors)

Hybrid method

(8 monitors)

MRA method

(16 monitors)

Hybrid method

(8 monitors)

10% 40 0 106 0

20% 68 0 117 1

50% 91 0 1438 4

80% 1588 3 1615.5 7

90% 1595 4 1772 10

95% 1618 5.75 1813.8 14


142 |

6.3 Risk-Based Assessment of Financial Losses due to

Voltage Sags

The methodology for analysis of financial losses caused by voltage sags proposed in

[118] is implemented here due to its comprehensive risk-based approach. The

methodology is focused on losses suffered by industrial plants and includes a

probabilistic modeling of the main elements involved in the assessment of process-

disruptive sags and the associated financial losses. The financial loss incurred by an

industrial plant due to each sag event is given by (6.4) [118].

ProcessFinancial Loss due to

failure loss process trip

risk

(6.4)

It can be seen from (6.4) that the two most important factors that determine the

magnitude of financial loss are the failure risk of the industrial process and the losses

incurred due to process trip. The main factors that influence industrial process failure

risk are the sensitivity of customer equipment and processes and number and

characteristics of sags at the customer site. The financial losses entailed by a process

trip depend on the type of the process and the variation in process activity due to the

process cycle and the plant’s load profile.

For voltage sag financial analysis, the stochastic net present value (SNPV) method is

incorporated in the methodology. SNPV is a modification of conventional net present

value (NPV) method that includes risk representation in the analysis. This characteristic

allows taking into account the non-deterministic nature of several components included

in the analysis, such as process sensitivity and voltage sag profile.

The financial losses incurred by the industrial plant due to voltage sags can be

calculated using the following equations [118]:

1

SCFSNPV

1+

Yy

yy

Ir

(6.5)

1

SCFS

y y s s

s

T p L

(6.6)


143 |

where

ySCF stochastic net cash flow at year y ;

Y

project lifetime in years;

y year number;

I

initial investment (if applicable);

r

discount rate;

S

total number of sags in year y ;

s

sag number;

p process failure risk, obtained from (6.4)

yT

operation and maintenance cost of investment in year y (if applicable);

L

loss due to process trip, obtained from (6.4).

Although (6.5) and (6.6) were originally formulated to calculate the stochastic net

present value of a sag mitigation option, they can be used to determine how much

money could be lost without mitigation [118].

6.4 Case Study 2: Assessment of Financial Losses

Caused by Voltage Sags

Assessment of financial losses due to sags has been undertaken using various

monitoring schemes. The studies were performed on the 295-bus generic distribution

system (GDS) simulating four types of power system short circuit faults, i.e., line to

ground (LG), line to line (LL), line to line to ground (LLG), and three-phase faults

(LLL).

6.4.1 Conventional and Optimal Monitoring Schemes

Five sag monitoring schemes have been used to perform the financial loss assessment.

Two of them represent the current practice in most parts of the world, where power

quality monitoring takes place at HV/MV substations. These two monitoring schemes

have been termed “eng1” and “eng2”. eng1 consists of 9 monitors placed at 132/33kV

substations and 2 monitors located at 132/11kV substations (11 monitors in total). These

substations are indicated in Figure 6-3 by Roman numerals contained in red squares.

eng2 comprises 8 monitors installed at 33/11kV substations, 2 monitors measuring the

primary and secondary sides of 11/3.3kV transformers, and 2 monitors placed at 132/11


144 |

kV substations (12 monitors in total). Green squares with capital letters indicate the

location of these substations in Figure 6-3. The remaining three monitoring schemes,

termed “opt8”, “opt10”, and “opt6”, correspond respectively to the eight monitors

required to cover all line to ground faults plus and minus two monitors taken from the

25 required to pinpoint the location of all types of fault (see Table 5-5 in Chapter 5 ).

These schemes are depicted in Figure 6-3 with encircled Arabic numbers.

6.4.2 Assessment of Financial Losses

The methodology developed in [118] and summarized in Section 6.3 has been used to

calculate the financial losses incurred by 9 different types of customer plants due to

voltage sags. The plants’ characteristics used in the assessment are shown in Table 6-8.

The plants have financial loss specific to business type (ranging from less than £4.4k to

more than £3M), different numbers of sensitive processes in each plant (from 1 to 8),

and different types of sensitive equipment type.

Table 6-8 Customer Plant Characteristics, adopted from [119]

Customer Business Financial loss

(£/event)

Number of

sensitive

processes

Sensitive

equipment

1 Pulp and paper integrated 18300 5 AC contactors, ASD

2 Metal works 152500 4 ASD, PLC

3 Food processing 4366 3 ASD, PLC, AC contactors

4 Textile 15250 4 ASD, PLC, AC contactors

5 Semiconductor fabrication 3344000 8 ASD, PLC

6 Automotive assembly 45750 5 ASD, PLC, AC contactors,

PC

7 Chemical 30500 2 ASD, PLC

8 Equipment manufacturing 61000 4 ASD, AC Contactors

9 Plastic extrusion 18300 1 ASD

Eight different locations of customer plants have been considered in the assessment of

financial losses. Plants are either located close to (locations a, c, f, and g) or far away

from (locations b, d, e, and h) bulk supply substations (33/11kV), as depicted in Figure

6-3. Monte Carlo simulation of 1000 trials has been run for a one-year assessment

period. The steps involved in the simulation are as follows [118]:

Step 1) Generate the annual number of faults using the data of Table 6-5.

Step 2) For each fault, select the most probable fault location applying the

algorithms proposed in Section 6.1.1 and using the five monitoring

schemes described above.


145 |

Step 3) For each fault located, estimate sag characteristics at locations a – h

according to the simplified approach of Section 6.1.3.

Step 4) Run the sensitivity assessment for the 9 plants with the estimated sags

as input. Obtain process failure for each sag, as required by (6.6).

Step 5) Calculate the loss due to process trip ( )L using (6.4), with the data of

Table 6-8.

Step 6) Calculate SNPV using (6.5) and ignore investment costs.

Step 7) Repeats Steps 1) - 6) for 1000 trials.

The distribution of financial losses due to voltage sags for all customers’ plants attached

to location h is shown in Figure 6-4. Six graphs are plotted in each subfigure, five

corresponding to the losses estimated using the aforesaid monitoring schemes and the

sixth one representing the real losses; i.e., losses calculated assuming that a monitor is

present at the customer busbar (location h).

As the overlapping of the blue (real losses), black (losses estimated using opt10

scheme), and magenta (losses estimated using opt8 scheme) graphs shows, 8 and 10

optimally placed monitors provide the most accurate results. The 10 monitors measuring

voltages at both 33 kV and 11 kV voltage levels (eng2 scheme represented by green

graphs) estimate the real amount of losses fairly accurately although they overestimate

the probability of occurrence in most cases. Less accurate are the estimates derived from

the first 6 monitors of the optimal sag monitoring scheme (opt6 scheme represented by

cyan graphs), since the financial losses determined by this set of monitors tend to be

lower than the real losses.

Finally, the least accurate results, represented by red graphs, came from the set of

monitors installed at the 132 kV and 33 kV levels (eng1 scheme). The financial losses

estimated by this monitoring scheme are practically nil for all customers. This is

explained by the fact that 9 of the 11 monitors of eng1 scheme are situated at

transformers with delta-wye connections, which hinders the location of line to ground

and line to line to ground faults and these two types of fault constitute 90% of the total

as indicated by Table 6-5.


146 |

Figure 6-3 Monitoring schemes and customer’s plant locations in the generic distribution system.

Engineering monitoring sites are indicated through color squares with Roman numerals and uppercase

letters; optimal monitoring locations (25) are numbered with color circles; the eight plant locations

analyzed are symbolized and represented with minuscule letters.

24

46

17

28

16

14

12

26

21

19

23

22

22

2

18

15

54

52

53

22

9

50

75

22

7

74

22

8

20

22

0

51

76

13

26

7

87

48

47

49

22

1

43

42

41

40

39

38

37

26

8

23

42

35

23

0

78 79

80

81

85

88

28

5

82

83

84

28

6

90

91

92

94

93

95

96

97

10

09

8 99

10

1

10

21

03

10

4

10

51

06

10

7

10

8

10

9

11

0

11

1

11

2

11

31

14

11

5

12

0

12

1

12

21

23

12

4

12

5

12

6

12

7

11

6

11

7

11

81

19

86

11

10

8

97654

55

1

65

64

63

57

22

52

26

58

14

8

14

6

15

3

15

4

14

91

52

15

5

14

71

45

14

4

14

0

14

2

14

1

14

3

13

9

13

8

12

8

12

91

32

13

0

13

4

13

61

35

13

7

13

3

15

6

16

0

15

7

18

5

18

3

13

1

15

9

16

4

16

1

16

2

16

3

16

5

16

6

16

71

68

16

9

17

9

18

0

18

11

82

18

4

18

6

18

7

18

8

18

91

90

19

1

19

2

19

3

19

6

19

7

19

91

98

20

0

20

1

20

22

03

20

4

20

5

20

6

20

72

08

15

0

15

1

22

3

23

1

77

15

8

22

4

21

4

21

5

21

0

21

12

09

21

2

21

3

21

6

21

71

70

21

8

21

9

17

1

17

2

17

3

17

4

17

5

17

6

17

7

62

60

59

61

2

3

72

70

17

8

25

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147 |

Figure 6-4 Distribution of SNPV from 1000 trials for all customers’ plants at location h estimated using

all monitoring schemes.

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148 |

However, both of the remaining monitors of eng1 scheme are placed at wye-wye

transformers (substations IX and X) and thus they can locate all types of faults

occurring in this zone of the network (downstream of substations IX and X), accounting

for all the losses greater than zero estimated by eng1 scheme. Similar results were found

for the rest of the plant locations and these are presented in Appendix D.

Figure 6-4 also shows that for most of the 1000 trials, the SNPV for customers 1, 2, and

3 is centered around £200k, £150k, and £30k, respectively. This means that these plants

will lose every year an average present worth of £200k, £150k, and £30k, respectively,

due to voltage sags. Similarly, the assessment of financial losses for customers 4, 5, and

6 shows that they will lose an annual average present worth of £9k, £6M, and £275k,

respectively. The annual losses for customers 7 and 9 will average around £200k, and

for customer 8 £160k.

The distribution of financial losses due to voltage sags for customer 5 (semiconductor

factory) at every location (a to h) is shown in Figure 6-5. The first box plot in the

subfigures represents the actual losses and the other five the losses determined using a

specific monitoring scheme. For example, 25%, 50%, and 75% of the calculations of

real losses at location “a” are lower than £1.8M (lower edge of the blue box), £3.8M

(red central mark), and £6M (upper edge of the blue box). All the estimates lie between

£0 (lower whisker) and £13M (upper whisker).

A comparison between monitoring schemes shows that opt6 and eng1 provide the least

accurate financial loss estimation and among the two, eng1 entails the biggest

discrepancy between actual and estimated losses. This is due to the better fault location

observability of the first six optimal sag monitoring locations (three 11kV buses and

three 33 kV buses) than the eleven monitored substations (nine 132/33 kV and two

132/11kV) of scheme eng1.

Regarding the financial losses incurred by the semiconductor fabrication plant, which

suffers the highest financial loss per event, the median annual losses range from less

than £1 M to almost £10 M. It can be seen from Figure 6-5 that locating the plant close

to bulk supply substations (location a, c, f, g) entails lower financial losses than at the

end of feeders (location b, d, e, h). (Please note difference in ordinate scale in Figure

6-5). The estimation of financial losses for the rest of the customers shows similar

results as can be seen in Appendix E.


149 |

Figure 6-5 Distribution of SNPV from 1000 trials for a semiconductor factory at all locations (a-h)

estimated using all monitoring schemes.

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Chapter 6 •Techno-Economic Assessment of Voltage Sags Using Optimal Monitoring Programs

150 |

6.5 Summary

A new methodology for monitoring and estimation of voltage sags in power systems has

been developed in this chapter. The proposed methodology encompasses a hybrid

monitor placement method and a simplified technique for fault location that allows

network sag characterization. Two optimal monitor placement methods, one for voltage

sag detection and studied in Chapter 3 , and one for fault location and presented in

Chapter 4 , were combined to overcome the main limitations of both, i.e. the use of

triggering thresholds to detect the occurrence of voltage sags and the high

computational memory usage entailed by the optimal monitor placement for fault

location problem. The voltage measurements from the buses selected by this hybrid

monitor placement are used to determine the most probable location of faults and

estimate their impact throughout the network.

The sag monitoring schemes obtained with the proposed methodology were tested in

two case studies utilizing Monte Carlo simulation. First the characteristics of voltage

sags were estimated to quantify the number of ITIC and SARFI-90 events occurring in

the network. Secondly, the financial losses incurred by different sensitive customers due

to voltage sags were assessed using a risk-based methodology. This assessment was

carried out by estimating voltage sag profiles at customer busbars based on the

simplified approach for fault localization. Results of both studies support the following:

High accuracy in both sag event estimation and assessment of financial losses

due to voltage sags can be achieved when monitoring power quality in sites

other that substations and with sag monitoring schemes partly deployed.

The main factor influencing the effectiveness of sag monitoring schemes is the

extent of their fault location observability area, which is greatly determined by

the presence of transformers with delta connections.

The number of voltage measurement devices entailed by the proposed hybrid

methodology is considerably less than the generic formulation of the monitor

placement for fault location (see Chapter 4 ), and can be implemented when

resources are limited or as the first stage of a measurement device deployment,

without significant impact on the accuracy of techno-economic assessment of

voltage sags.

Chapter 7 • Conclusions and Future Work

151 |

Chapter 7

Conclusions and Future

Work

7.1 Conclusions

The thesis developed a methodology for strategical monitor placement for the

estimation of voltage sags in power systems based on robust fault localization.

A review of past literature showed that voltage sags are currently one of the most

critical power quality disturbances. The economic losses entailed by the extensive

disruption of commercial and industrial processes caused by sags have been estimated

in the range of hundreds of millions of funds per year in developed countries alone. The

continuous proliferation of sensitive equipment in households, business and industry

threatens to exacerbate the economic impact of voltage sags.

The evaluation of voltage sags (as any other power quality problem) starts with the

correct identification and accurate characterization by means of measurement and data

collection. While monitoring the power quality at a single site is a relatively simple way

to obtain the data required to quantify and qualify the occurrence of sags at that site, the

sag performance characterization of an entire network becomes increasingly complex

and requires significant investment in measurement equipment and in data collection

and processing. Alternatively limited monitoring programs capable of estimating the

incidence and characteristics of sags at every bus of the network can be developed. A

strategic selection of monitoring locations is required to specify this such a

measurement scheme.

A thorough review of past power quality surveys conducted around the world revealed a

lack of consensus in the criteria for selection of monitoring locations and monitoring


152 |

periods, as well as great heterogeneity in the monitoring data obtained. Only in very few

instances are monitors placed at locations other than substations and there have been no

major efforts aimed at deploying monitors to estimate the sag performance of an entire

network. Despite the surge in monitoring of power quality in electric power systems in

recent years, there are no specific guidelines prescribed in current standards in power

quality for selecting strategic monitoring locations and for the number of monitors

required to characterize the overall sag performance of the network.

Academic research has not fully addressed the optimal monitor placement for sag

estimation either, and the leading (most cited) method proposed to date has important

limitations. This monitor reach area (MRA) method is particularly sensitive to pre-fault

voltage, fault impedance, fault position, and voltage sag thresholds; so that the

minimum number of monitors required to cover the network varies significantly with

changes in any of these parameters. A recently developed fault location algorithm is

incorporated as a part of this research into the MRA method to enhance its robustness to

variation in pre-fault voltage and to provide virtual immunity to voltage sag thresholds,

fault impedance and fault position. The improvement of the MRA method leads to a

fixed minimum number of monitors regardless of variation in any of the aforesaid

influencing factors and with no additional data requirements. The development of the

enhanced monitor reach area (EMRA) algorithm is the first original contribution of this

thesis.

The vast majority of sags causing process disruptions originate from short-circuit faults.

If these faults are pinpointed, an accurate estimation of the induced sags throughout the

network can be achieved. Therefore, a set of monitors optimally deployed to locate

faults is equivalent to an optimal sag monitoring program. A recently proposed optimal

monitor placement method for fault location is extended and generalized in this thesis

for its implementation in large power networks. Adapting concepts from the MRA

method the monitor location area (MLA) is developed as the centerpiece of this

generalization. The MLA is introduced as the area of the network where up to two

monitors are able to pinpoint a fault to simplify and reduce the number of constraints in

the problem. The formulation of generic framework for the optimal monitor placement

for fault location is the second original contribution of this thesis.


153 |

In some cases finding optimal fault location monitoring programs using linear

programming can be impeded when an immense number of combinations of monitors

needs to be analyzed. A heuristic search algorithm, which is much less memory

demanding, is developed in this research to find “sub-optimal” monitoring programs as

a trade-off between problem solvability and number of monitors considered. Custom

objective functions are also developed to guide the monitor deployment consistent with

maximization of fault location observability and minimization of sag magnitude

estimation error (SMEE) and sag event estimation error (SEEE); the latter being a user-

defined measure of sag estimation accuracy. In this thesis different benchmarking

criteria, such as sag immunity curves, ITIC and SEMI F47, performance indices,

SARFI, generalized sag table and voltage quality standards, EN 50160, are used to

define the SEEE. The heuristic monitor placement method unifies two monitoring

objectives, namely estimation of sag characteristics and indices and fault localization.

The proposed unified approach to sag and fault monitoring represents the third original

contribution of this thesis.

The use of monitoring data for sag estimation and fault location is intrinsically related.

Sag estimation at non-monitored buses is performed by means of fault location, while

short-circuit faults can be located using the voltage sags measured at monitored buses.

Sag estimation and fault location algorithms are further combined to create a synergistic

method that performs both sag estimation and fault location using fewer monitors than

optimal fault location monitoring programs. With the novel approach, the actual

location of faults is identified from several estimates with the aid of validity analysis of

measured voltages rather than triangulation of multiple monitors. This results in a

reduction of the number of monitors required while preserving the robustness of fault

location and accuracy of sag estimation. Case studies demonstrate that the proposed

technique provides accurate data for techno-economic assessment of voltage sags from

both strategically or conventionally deployed monitors. The flexible, cost-effective, and

scalable methodology for monitor placement and sag estimation constitutes the fourth

original contribution of this thesis.


154 |

7.2 Future Work

Although all initially defined goals of this research have been fulfilled and its

contributions can help to develop guidelines for the deployment of power quality

monitoring devices and sag performance estimation at non-monitored sites, some

assumptions had to be made throughout the research to ensure that research goals are

met within prescribed time frame, while at the same time providing technically sound

and robust results and conclusions.

The approach taken in this thesis to locate faults utilizes impedance matrix techniques.

A core assumption is that the network data including negative-, positive- and zero-

sequence parameters are known, and thus the bus impedance matrix of the network can

be readily built. The suitability of alternative fault location algorithms that employ local

data, such as superimposed components, travelling waves, and synchronized or

unsynchronized measurements from one or more terminals, needs to be determined in

the future for systems where the bus impedance matrix cannot be constructed.

The considered fault location methods in this thesis include one-terminal and two-

terminal algorithms. Only the former, however, has been pursued since it is better suited

for minimization of monitoring costs. The two-terminal algorithm simplifies greatly the

fault location procedure at expense of an increase in number of monitors. If it is deemed

affordable, the optimal monitor placement problem for fault location and sag estimation

based on the two-terminal algorithm can be performed. The corresponding optimization

problem however has yet to be formulated. The hybrid approach, i.e., combination of

one- and two-terminal algorithms, to solving the monitor placement problem could also

be addressed in the future.

Throughout this thesis it was assumed that all transmission lines in the test systems are

fully transposed and that they can be represented by single circuits with lumped

parameters using π-equivalent model. The fault location algorithms used could be

further extended and adjusted to handle the changes in line impedance introduced by

non-transposed and double-circuit lines. Furthermore, if distributed parameter line

models are to be used, the iterative solution methods would need to be considered.

The impact of measurement errors and errors in network parameters, e.g., line

parameters, transformer parameters, source impedances, etc., on fault location accuracy


155 |

and thus sag estimation accuracy has not been directly assessed in this research. A

probabilistic tool might be the most suitable approach to handle all these uncertainties.

Some initial work in this area has been carried out though and it showed promising

results [F12].

Since zero-sequence components are required to locate the most common type of faults,

line-to-ground faults, monitors connected phase-to-ground are considered better suited

for estimation of voltage sags based on fault location. If monitors connected phase-to-

phase are to be used, sag estimation can still be completed but not through fault

location. The problem of strategic placement of monitors connected phase-to-phase, or a

combination of these and monitors connected phase-to-ground, needs further research.

This would be very practical extension of present research as it is very likely that in real

networks a mix of monitors would be deployed.

It is proved in this thesis that voltage sag triggering thresholds, like 0.9 p.u. of nominal

voltage, are not required to perform both fault location and sag estimation at non-

monitored buses. Therefore, the occurrence of faults has to be detected even when the

voltage drop measured at monitored locations remains above 0.9 p.u. This can be

achieved using parametric methods, where a signal model is used [120]. The residuals

or models errors are calculated as the difference between the original waveform and the

waveform estimated by the model. Residual values are small as long as the signal is

quasi-stationary but they become large in the presence of sudden changes in the signal.

Residuals can therefore be used to detect the occurrence of short-circuit faults and

voltage sags without the use of sag triggering thresholds. The detailed application of

these methods in power quality monitoring programs requires further research.

Although this research has been focused on the monitoring and estimation of one of the

most pressing power quality problems, i.e. voltage sags, a comprehensive power quality

monitoring scheme needs to be developed in the future. The number and optimal

locations of monitoring devices required for simultaneous detection and estimation of

several, if not all, power quality disturbances (e.g. harmonic distortion, flicker,

unbalance, voltage transients, etc) needs to be determined in the future as this would be

the most cost-effective way of monitoring the power quality of the network.

Chapter 8 • References

156 |

Chapter 8

References

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Interruptions, Piscataway, NJ, 1999.

[2] R.C. Dugan, M.F. McGranaghan, S. Santoso, H.W. Beaty, Electrical Power Systems

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[3] R. Targosz, J. Manson, Pan European LPQI power quality survey, in: 19th

International Conference on Electricity Distribution (CIRED), Vienna, 2007.

[4] CIGRE/CIRED C4.107 Economic Framework For Power Quality, in, Paris, 2011.

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[6] W.W. Carter, Control of power quality in modern industry, in: IEEE Annual Textile

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[10] IEC 61000-2-8, Electromagnetic compatibility (EMC) - Part 2-8: Environment -

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[11] CIGRE TF C4.102 Voltage dip evaluation and prediction tools, (2009).

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2001.


157 |

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[14] M.H.J. Bollen, I.Y.H. Gu, Signal Processing of Power Quality Disturbances,

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[15] M.H.J. Bollen, Characterisation of voltage sags experienced by three-phase

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pp. 34-41.

[17] S.Z. Djokic, J.V. Milanovic, Advanced voltage sag characterisation. Part I: Phase

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Brumsickle, A. McEachern, J.R. Gordon, G. Ethier, R. Neumann,

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Appendix A • Network Data of Test Systems

167 |

Appendix A Network Data of Test

Systems

Table A-1 Generator impedances of the 10-bus 500 kV power system

Generator bus number Positive sequence (p.u.) Zero sequence (p.u.)

1 0.001006 + j0.016521 0.0018296 + j0.013763

6 0.00016441 + j0.0046618 0.00017024 + j0.0028855

7 0.0016382 + j0.024301 0.0056571 + j0.03134 9 0.0014553 + j0.023504 0.0026958 + j0.022641

10 0.00020591 + j0.004648 0.00052175 + j0.0047921

Table A-2 Transmission line parameters of the 10-bus 500 kV power system

Line (from bus-to bus) Length (mile) Positive sequence (p.u.) Zero sequence (p.u.)

1-2 52.58 0.0008 + j0.012 0.0087 + j0.0309 2-3 33.20 0.0005 + j0.0076 0.0083 + j0.0252 3-4 47.90 0.0007 + j0.0109 0.012 + j0.0366 4-2 56.88 0.0009 + j0.013 0.0143 + j0.0427 2-7 45.45 0.0007 + j0.0097 0.0106 + j0.031 4-5 27.99 0.0004 + j0.0064 0.0074 + j0.0215 5-8 63.51 0.001 + j0.0142 0.0169 + j0.0498

8-10 62.77 0.001 + j0.0143 0.0166 + j0.0484 5-6 86.81 0.0014 + j0.0197 0.0181 + j0.0555 4-9 27.72 0.0004 + j0.0063 0.0075 + j0.0192

Table A-3 Bus data of the IEEE Reliability Test System (RTS)

Bus number Type Pd Qd Gs Bs Area Vm Va Base kV Zone Vmax Vmin

1 2 108.00 22.00 0 0 1 1.035 -7.2064 138 1 1.06 0.94 2 2 97.00 20.00 0 0 1 1.035 -7.3084 138 1 1.06 0.94 3 1 180.00 37.00 0 0 1 0.9864 -5.431 138 1 1.06 0.94 4 1 74.00 15.00 0 0 1 1.0007 -9.7563 138 1 1.06 0.94 5 1 71.00 14.00 0 0 1 1.0318 -10.021 138 1 1.06 0.94 6 1 136.00 28.00 0 0 1 1.0856 -13.000 138 1 1.06 0.94 7 2 125.00 25.00 0 0 1 1.0250 -7.3282 138 1 1.06 0.94 8 1 171.00 35.00 0 0 1 0.9997 -11.109 138 1 1.06 0.94 9 1 175.00 36.00 0 0 1 1.0064 -7.6215 138 1 1.06 0.94

10 1 195.00 40.00 0 0 1 1.0553 -9.7312 138 1 1.06 0.94 11 1 0.00 0.00 0 0 1 1.0001 -3.0003 230 1 1.06 0.94 12 1 0.00 0.00 0 0 1 1.0089 -1.4634 230 1 1.06 0.94 13 3 265.00 54.00 0 0 1 1.0200 0 230 1 1.06 0.94 14 2 194.00 39.00 0 0 1 0.9881 0.1628 230 1 1.06 0.94 15 2 317.00 64.00 0 0 1 1.0140 11.8605 230 1 1.06 0.94 16 2 100.00 20.00 0 0 1 1.0170 10.9874 230 1 1.06 0.94 17 1 0.00 0.00 0 0 1 1.0401 14.7403 230 1 1.06 0.94 18 2 333.00 68.00 0 0 1 1.0500 16.1978 230 1 1.06 0.94 19 1 181.00 37.00 0 0 1 1.0230 9.7628 230 1 1.06 0.94 20 1 128.00 26.00 0 0 1 1.0381 10.6403 230 1 1.06 0.94 21 2 0.00 0.00 0 0 1 1.0500 17.1449 230 1 1.06 0.94 22 2 0.00 0.00 0 0 1 1.0500 22.7139 230 1 1.06 0.94 23 2 0.00 0.00 0 0 1 1.0500 11.8366 230 1 1.06 0.94 24 1 0.00 0.00 0 0 1 0.9812 5.4794 230 1 1.06 0.94


168 |

Table A-4 Generator data of the IEEE Reliability Test System (RTS) Bus Pg Qg Qmax Qmin Vg Rate Status Pmax Pmin R1 X1 R0 X0

1 15 3.31 10 0 1.035 24 1 20 16 0.001 0.32 0.001 0.1406 1 15 3.31 10 0 1.035 24 1 20 16 0.001 0.32 0.001 0.1406

1 75 3.31 30 -25 1.035 89 1 76 15.2 0.001 0.30 0.001 0.0379

1 75 3.31 30 -25 1.035 89 1 76 15.2 0.001 0.30 0.001 0.0379 2 15 0 10 0 1.035 24 1 20 16 0.001 0.32 0.001 0.1406

2 15 0 10 0 1.035 24 1 20 16 0.001 0.32 0.001 0.1406

2 75 -9.02 30 -25 1.035 89 1 76 15.2 0.001 0.30 0.001 0.0379 2 75 -9.03 30 -25 1.035 89 1 76 15.2 0.001 0.30 0.001 0.0379

7 80 14.64 60 0 1.025 118 1 100 25 0.001 0.32 0.001 0.0286

7 80 14.64 60 0 1.025 118 1 100 25 0.001 0.32 0.001 0.0286 7 80 14.64 60 0 1.025 118 1 100 25 0.001 0.32 0.001 0.0286

13 32.44 28.68 80 0 1.02 232 1 197 68.95 0.001 0.32 0.001 0.0145

13 32.44 28.68 80 0 1.02 232 1 197 68.95 0.001 0.32 0.001 0.0145 13 32.44 28.68 80 0 1.02 232 1 197 5 0.001 0.32 0.001 0.0145

15 9 0 6 0 1.014 14 1 12 2.4 0.001 0.32 0.001 0.2411

15 9 0 6 0 1.014 14 1 12 2.4 0.001 0.32 0.001 0.2411 15 9 0 6 0 1.014 14 1 12 2.4 0.001 0.32 0.001 0.2411

15 9 0 6 0 1.014 14 1 12 2.4 0.001 0.32 0.001 0.2411

15 9 0 6 0 1.014 14 1 12 2.4 0.001 0.32 0.001 0.2411 15 155 -14.72 80 -50 1.014 182 1 155 54.25 0.001 0.30 0.001 0.0185

16 155 34.44 80 0.02 1.017 182 1 155 54.25 0.001 0.30 0.001 0.0185

18 400 141.8 200 -50 1.05 471 1 400 100 0.01 0.40 0.01 0.0072 21 400 113.6 200 -50 1.05 471 1 400 100 0.001 0.40 0.001 0.0072

22 50 -6.09 16 -10 1.05 53 1 50 10 0.001 0.28 0.001 0.1061

22 50 -6.09 16 -10 1.05 53 1 50 10 0.001 0.28 0.001 0.1061 22 50 -6.09 16 -10 1.05 53 1 50 10 0.001 0.28 0.001 0.1061

22 50 -6.09 16 -10 1.05 53 1 50 10 0.001 0.28 0.001 0.1061

22 50 -6.09 16 -10 1.05 53 1 50 10 0.001 0.28 0.001 0.1061 22 50 -6.09 16 -10 1.05 53 1 50 10 0.001 0.28 0.001 0.1061

23 149.59 50.14 80 -50 1.05 182 1 155 54.25 0.001 0.30 0.001 0.0185

23 149.59 50.14 80 -50 1.05 182 1 155 54.25 0.001 0.30 0.001 0.0185 23 350 80 150 -25 1.05 412 1 350 140 0.001 0.30 0.001 0.0082

Table A-5 Line data of the IEEE Reliability Test System (RTS)

From

bus

To

bus R1 X1 B1 R0 X0 B0

Rating Length Type Status

A B C (miles)

1 2 0.0007 0.0012 0.0007 0.0026 0.0011 0.0007 175 200 193 0.95 C 1

1 3 0.0542 0.2111 0.0613 0.1595 0.7628 0.0319 175 220 208 55 OL 1 1 5 0.0224 0.0849 0.0244 0.0649 0.3064 0.0127 175 220 208 22 OL 1

2 4 0.0336 0.1273 0.0366 0.0972 0.4593 0.0191 175 220 208 33 OL 1

2 6 0.0506 0.1920 0.0557 0.1466 0.6939 0.0290 175 220 208 50 OL 1 3 9 0.0315 0.1192 0.0343 0.0911 0.4301 0.0179 175 220 208 30.9 OL 1

4 9 0.0269 0.1078 0.0279 0.0767 0.3577 0.0154 175 220 208 26.5 OL 1

5 10 0.0233 0.0884 0.0254 0.0676 0.3189 0.0132 175 220 208 22.9 OL 1 6 10 0.0226 0.0333 0.1303 0.0521 0.0218 0.1303 175 200 193 16 C 1

7 8 0.0161 0.0610 0.0179 0.0471 0.2222 0.0093 175 220 208 16 OL 1

8 9 0.0423 0.1648 0.0478 0.1248 0.5959 0.0249 175 220 208 42.9 OL 1 8 10 0.0423 0.1648 0.0478 0.1248 0.5959 0.0249 175 220 208 42.9 OL 1

11 13 0.0058 0.0475 0.0959 0.0321 0.1483 0.0590 500 625 600 33 OL 1

11 14 0.0051 0.0417 0.0843 0.0282 0.1304 0.0518 500 625 600 29 OL 1 12 13 0.0058 0.0476 0.0959 0.0321 0.1483 0.0590 500 625 600 33 OL 1

12 23 0.0122 0.0964 0.1984 0.0547 0.3131 0.1095 500 625 600 67 OL 1

13 23 0.0106 0.0864 0.1752 0.0581 0.2697 0.1078 500 625 600 60.2 OL 1 14 16 0.0048 0.0388 0.0785 0.0263 0.1241 0.0483 500 625 600 27 OL 1

15 16 0.0021 0.0173 0.0349 0.0117 0.0540 0.0214 500 625 600 12 OL 1

15 21 0.0061 0.0490 0.1006 0.0278 0.1595 0.0555 500 625 600 34 OL 1 15 21 0.0061 0.0490 0.1006 0.0278 0.1595 0.0555 500 625 600 34 OL 1

15 24 0.0064 0.0519 0.1066 0.0295 0.1688 0.0587 500 625 600 36 OL 1

16 17 0.0032 0.0259 0.0523 0.0175 0.0810 0.0322 500 625 600 18 OL 1 16 19 0.0028 0.0230 0.0465 0.0156 0.0720 0.0286 500 625 600 16 OL 1

17 18 0.0018 0.0144 0.0291 0.0097 0.0450 0.0179 500 625 600 10 OL 1

17 22 0.0123 0.1053 0.2116 0.0489 0.3427 0.1110 500 625 600 73 OL 1 18 21 0.0033 0.0260 0.0533 0.0149 0.0845 0.0293 500 625 600 18 OL 1

18 21 0.0033 0.0260 0.0533 0.0149 0.0845 0.0293 500 625 600 18 OL 1

19 20 0.0051 0.0396 0.0814 0.0227 0.1290 0.0448 500 625 600 27.5 OL 1 19 20 0.0051 0.0396 0.0814 0.0227 0.1290 0.0448 500 625 600 27.5 OL 1

20 23 0.0028 0.0216 0.0444 0.0124 0.0704 0.0245 500 625 600 15 OL 1

20 23 0.0028 0.0216 0.0444 0.0124 0.0704 0.0245 500 625 600 15 OL 1 21 22 0.0083 0.0677 0.1367 0.0321 0.2215 0.0715 500 625 600 47.1 OL 1


169 |

Table A-6 Transformer data of the IEEE Reliability Test System (RTS)

From bus To bus R1 X1 B1 From winding To winding Tap Shift Rating

Status A B C

3 24 0.0023 0.0839 0.0000 Wye Wye 1 0 400 600 510 1

9 11 0.0023 0.0839 0.0000 Wye Wye 1 0 400 600 510 1

9 12 0.0023 0.0839 0.0000 Wye Wye 1 0 400 600 510 1 10 11 0.0023 0.0839 0.0000 Wye Wye 1 0 400 600 510 1

10 12 0.0023 0.0839 0.0000 Wye Wye 1 0 400 600 510 1

Table A-7 Bus data of the IEEE 118-bus Test System

Bus

number Type Pd Qd Gs Bs Area Vm Va

Base

kV Zone Vmax Vmin

1 2 51.00 27.00 0 0 1 0.955 10.67 138 1 1.06 0.94 2 1 20.00 9.00 0 0 1 0.971 11.22 138 1 1.06 0.94

3 1 39.00 10.00 0 0 1 0.968 11.56 138 1 1.06 0.94

4 2 39.00 12.00 0 0 1 0.998 15.28 138 1 1.06 0.94 5 1 0.00 0.00 0 -40 1 1.002 15.73 138 1 1.06 0.94

6 2 52.00 22.00 0 0 1 0.9900 13 138 1 1.06 0.94 7 1 19.00 2.00 0 0 1 0.9890 12.56 138 1 1.06 0.94

8 2 28.00 0.00 0 0 1 1.0150 20.77 345 1 1.06 0.94

9 1 0.00 0.00 0 0 1 1.0430 28.02 345 1 1.06 0.94 10 2 0.00 0.00 0 0 1 1.0500 35.61 345 1 1.06 0.94

11 1 70.00 23.00 0 0 1 0.9850 12.72 138 1 1.06 0.94

12 2 47.00 10.00 0 0 1 0.9900 12.2 138 1 1.06 0.94 13 1 34.00 16.00 0 0 1 0.9680 11.35 138 1 1.06 0.94

14 1 14.00 1.00 0 0 1 0.9840 11.5 138 1 1.06 0.94

15 2 90.00 30.00 0 0 1 0.9700 11.23 138 1 1.06 0.94 16 1 25.00 10.00 0 0 1 0.9840 11.91 138 1 1.06 0.94

17 1 11.00 3.00 0 0 1 0.9950 13.74 138 1 1.06 0.94

18 2 60.00 34.00 0 0 1 0.9730 11.53 138 1 1.06 0.94 19 2 45.00 25.00 0 0 1 0.9630 11.05 138 1 1.06 0.94

20 1 18.00 3.00 0 0 1 0.9580 11.93 138 1 1.06 0.94

21 1 14.00 8.00 0 0 1 0.9590 13.52 138 1 1.06 0.94 22 1 10.00 5.00 0 0 1 0.9700 16.08 138 1 1.06 0.94

23 1 7.00 3.00 0 0 1 1.0000 21 138 1 1.06 0.94

24 2 13.00 0.00 0 0 1 0.9920 20.89 138 1 1.06 0.94 25 2 0.00 0.00 0 0 1 1.0500 27.93 138 1 1.06 0.94

26 2 0.00 0.00 0 0 1 1.0150 29.71 345 1 1.06 0.94

27 2 71.00 13.00 0 0 1 0.9680 15.35 138 1 1.06 0.94 28 1 17.00 7.00 0 0 1 0.9620 13.62 138 1 1.06 0.94

29 1 24.00 4.00 0 0 1 0.9630 12.63 138 1 1.06 0.94

30 1 0.00 0.00 0 0 1 0.9680 18.79 345 1 1.06 0.94 31 2 43.00 27.00 0 0 1 0.9670 12.75 138 1 1.06 0.94

32 2 59.00 23.00 0 0 1 0.9640 14.8 138 1 1.06 0.94

33 1 23.00 9.00 0 0 1 0.9720 10.63 138 1 1.06 0.94 34 2 59 26 0 14 1 0.986 11.3 138 1 1.06 0.94

35 1 33 9 0 0 1 0.981 10.87 138 1 1.06 0.94

36 2 31 17 0 0 1 0.98 10.87 138 1 1.06 0.94 37 1 0 0 0 -25 1 0.992 11.77 138 1 1.06 0.94

38 1 0 0 0 0 1 0.962 16.91 345 1 1.06 0.94

39 1 27 11 0 0 1 0.97 8.41 138 1 1.06 0.94 40 2 66 23 0 0 1 0.97 7.35 138 1 1.06 0.94

41 1 37 10 0 0 1 0.967 6.92 138 1 1.06 0.94

42 2 96 23 0 0 1 0.985 8.53 138 1 1.06 0.94 43 1 18 7 0 0 1 0.978 11.28 138 1 1.06 0.94

44 1 16 8 0 10 1 0.985 13.82 138 1 1.06 0.94

45 1 53 22 0 10 1 0.987 15.67 138 1 1.06 0.94 46 2 28 10 0 10 1 1.005 18.49 138 1 1.06 0.94

47 1 34 0 0 0 1 1.017 20.73 138 1 1.06 0.94

48 1 20 11 0 15 1 1.021 19.93 138 1 1.06 0.94 49 2 87 30 0 0 1 1.025 20.94 138 1 1.06 0.94

50 1 17 4 0 0 1 1.001 18.9 138 1 1.06 0.94

51 1 17 8 0 0 1 0.967 16.28 138 1 1.06 0.94 52 1 18 5 0 0 1 0.957 15.32 138 1 1.06 0.94

53 1 23 11 0 0 1 0.946 14.35 138 1 1.06 0.94

54 2 113 32 0 0 1 0.955 15.26 138 1 1.06 0.94 55 2 63 22 0 0 1 0.952 14.97 138 1 1.06 0.94

56 2 84 18 0 0 1 0.954 15.16 138 1 1.06 0.94 57 1 12 3 0 0 1 0.971 16.36 138 1 1.06 0.94

58 1 12 3 0 0 1 0.959 15.51 138 1 1.06 0.94

59 2 277 113 0 0 1 0.985 19.37 138 1 1.06 0.94 60 1 78 3 0 0 1 0.993 23.15 138 1 1.06 0.94


170 |

61 2 0 0 0 0 1 0.995 24.04 138 1 1.06 0.94

62 2 77 14 0 0 1 0.998 23.43 138 1 1.06 0.94 63 1 0 0 0 0 1 0.969 22.75 345 1 1.06 0.94

64 1 0 0 0 0 1 0.984 24.52 345 1 1.06 0.94 65 2 0 0 0 0 1 1.005 27.65 345 1 1.06 0.94

66 2 39 18 0 0 1 1.05 27.48 138 1 1.06 0.94

67 1 28 7 0 0 1 1.02 24.84 138 1 1.06 0.94 68 1 0 0 0 0 1 1.003 27.55 345 1 1.06 0.94

69 3 0 0 0 0 1 1.035 30 138 1 1.06 0.94

70 2 66 20 0 0 1 0.984 22.58 138 1 1.06 0.94 71 1 0 0 0 0 1 0.987 22.15 138 1 1.06 0.94

72 2 12 0 0 0 1 0.98 20.98 138 1 1.06 0.94

73 2 6 0 0 0 1 0.991 21.94 138 1 1.06 0.94 74 2 68 27 0 12 1 0.958 21.64 138 1 1.06 0.94

75 1 47 11 0 0 1 0.967 22.91 138 1 1.06 0.94

76 2 68 36 0 0 1 0.943 21.77 138 1 1.06 0.94 77 2 61 28 0 0 1 1.006 26.72 138 1 1.06 0.94

78 1 71 26 0 0 1 1.003 26.42 138 1 1.06 0.94

79 1 39 32 0 20 1 1.009 26.72 138 1 1.06 0.94 80 2 130 26 0 0 1 1.04 28.96 138 1 1.06 0.94

81 1 0 0 0 0 1 0.997 28.1 345 1 1.06 0.94

82 1 54 27 0 20 1 0.989 27.24 138 1 1.06 0.94 83 1 20 10 0 10 1 0.985 28.42 138 1 1.06 0.94

84 1 11 7 0 0 1 0.98 30.95 138 1 1.06 0.94

85 2 24 15 0 0 1 0.985 32.51 138 1 1.06 0.94 86 1 21 10 0 0 1 0.987 31.14 138 1 1.06 0.94

87 2 0 0 0 0 1 1.015 31.4 161 1 1.06 0.94

88 1 48 10 0 0 1 0.987 35.64 138 1 1.06 0.94 89 2 0 0 0 0 1 1.005 39.69 138 1 1.06 0.94

90 2 163 42 0 0 1 0.985 33.29 138 1 1.06 0.94

91 2 10 0 0 0 1 0.98 33.31 138 1 1.06 0.94 92 2 65 10 0 0 1 0.993 33.8 138 1 1.06 0.94

93 1 12 7 0 0 1 0.987 30.79 138 1 1.06 0.94

94 1 30 16 0 0 1 0.991 28.64 138 1 1.06 0.94 95 1 42 31 0 0 1 0.981 27.67 138 1 1.06 0.94

96 1 38 15 0 0 1 0.993 27.51 138 1 1.06 0.94

97 1 15 9 0 0 1 1.011 27.88 138 1 1.06 0.94 98 1 34 8 0 0 1 1.024 27.4 138 1 1.06 0.94

99 2 42 0 0 0 1 1.01 27.04 138 1 1.06 0.94

100 2 37 18 0 0 1 1.017 28.03 138 1 1.06 0.94 101 1 22 15 0 0 1 0.993 29.61 138 1 1.06 0.94

102 1 5 3 0 0 1 0.991 32.3 138 1 1.06 0.94

103 2 23 16 0 0 1 1.001 24.44 138 1 1.06 0.94 104 2 38 25 0 0 1 0.971 21.69 138 1 1.06 0.94

105 2 31 26 0 20 1 0.965 20.57 138 1 1.06 0.94

106 1 43 16 0 0 1 0.962 20.32 138 1 1.06 0.94 107 2 50 12 0 6 1 0.952 17.53 138 1 1.06 0.94

108 1 2 1 0 0 1 0.967 19.38 138 1 1.06 0.94

109 1 8 3 0 0 1 0.967 18.93 138 1 1.06 0.94 110 2 39 30 0 6 1 0.973 18.09 138 1 1.06 0.94

111 2 0 0 0 0 1 0.98 19.74 138 1 1.06 0.94

112 2 68 13 0 0 1 0.975 14.99 138 1 1.06 0.94 113 2 6 0 0 0 1 0.993 13.74 138 1 1.06 0.94

114 1 8 3 0 0 1 0.96 14.46 138 1 1.06 0.94 115 1 22 7 0 0 1 0.96 14.46 138 1 1.06 0.94

116 2 184 0 0 0 1 1.005 27.12 138 1 1.06 0.94

117 1 20 8 0 0 1 0.974 10.67 138 1 1.06 0.94 118 1 33 15 0 0 1 0.949 21.92 138 1 1.06 0.94

Table A-8 Generator data of the IEEE 118-bus Test System

Bus Pg Qg Qmax Qmin Vg Rate Status Pmax Pmin R1 X1 R0 X0

1 0 0.00 15 -5 0.955 100 1 100 0 0 0.30 0 0.05

4 0 0.00 300 -300 0.998 100 1 100 0 0 0.30 0 0.05

6 0 0.00 50 -13 0.99 100 1 100 0 0 0.30 0 0.05 8 0 0.00 300 -300 1.015 100 1 100 0 0 0.30 0 0.05

10 450 0.00 200 -147 1.05 100 1 550 0 0 0.30 0 0.05

12 85 0.00 120 -35 0.99 100 1 185 0 0 0.30 0 0.05 15 0 0.00 30 -10 0.97 100 1 100 0 0 0.30 0 0.05

18 0 0.00 50 -16 0.973 100 1 100 0 0 0.30 0 0.05

19 0 0.00 24 -8 0.962 100 1 100 0 0 0.30 0 0.05 24 0 0.00 300 -300 0.992 100 1 100 0 0 0.30 0 0.05

25 220 0.00 140 -47 1.05 100 1 320 0 0 0.30 0 0.05

26 314 0.00 1000 -1000 1.015 100 1 414 0 0 0.30 0 0.05


171 |

27 0 0.00 300 -300 0.968 100 1 100 0 0 0.30 0 0.05

31 7 0.00 300 -300 0.967 100 1 107 0 0 0.30 0 0.05 32 0 0.00 42 -14 0.963 100 1 100 0 0 0.30 0 0.05

34 0 0.00 24 -8 0.984 100 1 100 0 0 0.30 0 0.05 36 0 0.00 24 -8 0.98 100 1 100 0 0 0.30 0 0.05

40 0 0.00 300 -300 0.97 100 1 100 0 0 0.30 0 0.05

42 0 0.00 300 -300 0.985 100 1 100 0 0 0.30 0 0.05 46 19 0.00 100 -100 1.005 100 1 119 0 0 0.30 0 0.05

49 204 0.00 210 -85 1.025 100 1 304 0 0 0.30 0 0.05

54 48 0.00 300 -300 0.955 100 1 148 0 0 0.30 0 0.05 55 0 0.00 23 -8 0.952 100 1 100 0 0 0.30 0 0.05

56 0 0.00 15 -8 0.954 100 1 100 0 0 0.30 0 0.05

59 155 0.00 180 -60 0.985 100 1 255 0 0 0.30 0 0.05 61 160 0.00 300 -100 0.995 100 1 260 0 0 0.30 0 0.05

62 0 0.00 20 -20 0.998 100 1 100 0 0 0.30 0 0.05

65 391 0.00 200 -67 1.005 100 1 491 0 0 0.30 0 0.05 66 392 0.00 200 -67 1.05 100 1 492 0 0 0.30 0 0.05

69 516.4 0.00 300 -300 1.035 100 1 805.2 0 0 0.30 0 0.05

70 0 0.00 32 -10 0.984 100 1 100 0 0 0.30 0 0.05 72 0 0.00 100 -100 0.98 100 1 100 0 0 0.30 0 0.05

73 0 0.00 100 -100 0.991 100 1 100 0 0 0.30 0 0.05

74 0 0 9 -6 0.958 100 1 100 0 0 0.30 0 0.05 76 0 0 23 -8 0.943 100 1 100 0 0 0.30 0 0.05

77 0 0 70 -20 1.006 100 1 100 0 0 0.30 0 0.05

80 477 0 280 -165 1.04 100 1 577 0 0 0.30 0 0.05 85 0 0 23 -8 0.985 100 1 100 0 0 0.30 0 0.05

87 4 0 1000 -100 1.015 100 1 104 0 0 0.30 0 0.05

89 607 0 300 -210 1.005 100 1 707 0 0 0.30 0 0.05 90 0 0 300 -300 0.985 100 1 100 0 0 0.30 0 0.05

91 0 0 100 -100 0.98 100 1 100 0 0 0.30 0 0.05

92 0 0 9 -3 0.99 100 1 100 0 0 0.30 0 0.05 99 0 0 100 -100 1.01 100 1 100 0 0 0.30 0 0.05

100 252 0 155 -50 1.017 100 1 352 0 0 0.30 0 0.05

103 40 0 40 -15 1.01 100 1 140 0 0 0.30 0 0.05 104 0 0 23 -8 0.971 100 1 100 0 0 0.30 0 0.05

105 0 0 23 -8 0.965 100 1 100 0 0 0.30 0 0.05

107 0 0 200 -200 0.952 100 1 100 0 0 0.30 0 0.05 110 0 0 23 -8 0.973 100 1 100 0 0 0.30 0 0.05

111 36 0 1000 -100 0.98 100 1 136 0 0 0.30 0 0.05

112 0 0 1000 -100 0.975 100 1 100 0 0 0.30 0 0.05 113 0 0 200 -100 0.993 100 1 100 0 0 0.30 0 0.05

116 0 0 1000 -1000 1.005 100 1 100 0 0 0.30 0 0.05

Table A-9 Line data of the IEEE Reliability the IEEE 118-bus Test System

From

bus

To


Rating Status

A B C

1 2 0.0303 0.0999 0.0254 0.0909 0.2997 0.0127 9900 0 0 1

1 3 0.0129 0.0424 0.0108 0.0387 0.1272 0.0054 9900 0 0 1 4 5 0.0018 0.0080 0.0021 0.0053 0.0239 0.0011 9900 0 0 1

3 5 0.0241 0.1080 0.0284 0.0723 0.3240 0.0142 9900 0 0 1

5 6 0.0119 0.0540 0.0143 0.0357 0.1620 0.0071 9900 0 0 1 6 7 0.0046 0.0208 0.0055 0.0138 0.0624 0.0028 9900 0 0 1

8 9 0.0024 0.0305 1.1620 0.0073 0.0915 0.5810 9900 0 0 1

9 10 0.0026 0.0322 1.2300 0.0077 0.0966 0.6150 9900 0 0 1 4 11 0.0209 0.0688 0.0175 0.0627 0.2064 0.0087 9900 0 0 1

5 11 0.0203 0.0682 0.0174 0.0609 0.2046 0.0087 9900 0 0 1

11 12 0.0060 0.0196 0.0050 0.0179 0.0588 0.0025 9900 0 0 1 2 12 0.0187 0.0616 0.0157 0.0561 0.1848 0.0079 9900 0 0 1

3 12 0.0484 0.1600 0.0406 0.1452 0.4800 0.0203 9900 0 0 1

7 12 0.0086 0.0340 0.0087 0.0259 0.1020 0.0044 9900 0 0 1 11 13 0.0223 0.0731 0.0188 0.0668 0.2193 0.0094 9900 0 0 1

12 14 0.0215 0.0707 0.0182 0.0645 0.2121 0.0091 9900 0 0 1

13 15 0.0744 0.2444 0.0627 0.2232 0.7332 0.0313 9900 0 0 1 14 15 0.0595 0.1950 0.0502 0.1785 0.5850 0.0251 9900 0 0 1

12 16 0.0212 0.0834 0.0214 0.0636 0.2502 0.0107 9900 0 0 1

15 17 0.0132 0.0437 0.0444 0.0396 0.1311 0.0222 9900 0 0 1 16 17 0.0454 0.1801 0.0466 0.1362 0.5403 0.0233 9900 0 0 1

17 18 0.0123 0.0505 0.0130 0.0369 0.1515 0.0065 9900 0 0 1 18 19 0.0112 0.0493 0.0114 0.0336 0.1479 0.0057 9900 0 0 1

19 20 0.0252 0.1170 0.0298 0.0756 0.3510 0.0149 9900 0 0 1

15 19 0.0120 0.0394 0.0101 0.0360 0.1182 0.0051 9900 0 0 1 20 21 0.0183 0.0849 0.0216 0.0549 0.2547 0.0108 9900 0 0 1


172 |

21 22 0.0209 0.0970 0.0246 0.0627 0.2910 0.0123 9900 0 0 1

22 23 0.0342 0.1590 0.0404 0.1026 0.4770 0.0202 9900 0 0 1 23 24 0.0135 0.0492 0.0498 0.0405 0.1476 0.0249 9900 0 0 1

23 25 0.0156 0.0800 0.0864 0.0468 0.2400 0.0432 9900 0 0 1 25 27 0.0318 0.1630 0.1764 0.0954 0.4890 0.0882 9900 0 0 1

27 28 0.0191 0.0855 0.0216 0.0574 0.2565 0.0108 9900 0 0 1

28 29 0.0237 0.0943 0.0238 0.0711 0.2829 0.0119 9900 0 0 1 8 30 0.0043 0.0504 0.5140 0.0129 0.1512 0.2570 9900 0 0 1

26 30 0.0080 0.0860 0.9080 0.0240 0.2580 0.4540 9900 0 0 1

17 31 0.0474 0.1563 0.0399 0.1422 0.4689 0.0200 9900 0 0 1 29 31 0.0108 0.0331 0.0083 0.0324 0.0993 0.0042 9900 0 0 1

23 32 0.0317 0.1153 0.1173 0.0951 0.3459 0.0587 9900 0 0 1

31 32 0.0298 0.0985 0.0251 0.0894 0.2955 0.0126 9900 0 0 1 27 32 0.0229 0.0755 0.0193 0.0687 0.2265 0.0096 9900 0 0 1

15 33 0.0380 0.1244 0.0319 0.1140 0.3732 0.0160 9900 0 0 1

19 34 0.0752 0.2470 0.0632 0.2256 0.7410 0.0316 9900 0 0 1 35 36 0.0022 0.0102 0.0027 0.0067 0.0306 0.0013 9900 0 0 1

35 37 0.0110 0.0497 0.0132 0.0330 0.1491 0.0066 9900 0 0 1

33 37 0.0415 0.1420 0.0366 0.1245 0.4260 0.0183 9900 0 0 1 34 36 0.0087 0.0268 0.0057 0.0261 0.0804 0.0028 9900 0 0 1

34 37 0.0026 0.0094 0.0098 0.0077 0.0282 0.0049 9900 0 0 1

37 39 0.0321 0.1060 0.0270 0.0963 0.3180 0.0135 9900 0 0 1 37 40 0.0593 0.1680 0.0420 0.1779 0.5040 0.0210 9900 0 0 1

30 38 0.0046 0.0540 0.4220 0.0139 0.1620 0.2110 9900 0 0 1

39 40 0.0184 0.0605 0.0155 0.0552 0.1815 0.0078 9900 0 0 1 40 41 0.0145 0.0487 0.0122 0.0435 0.1461 0.0061 9900 0 0 1

40 42 0.0555 0.1830 0.0466 0.1665 0.5490 0.0233 9900 0 0 1

41 42 0.0410 0.1350 0.0344 0.1230 0.4050 0.0172 9900 0 0 1 43 44 0.0608 0.2454 0.0607 0.1824 0.7362 0.0303 9900 0 0 1

34 43 0.0413 0.1681 0.0423 0.1239 0.5043 0.0211 9900 0 0 1

44 45 0.0224 0.0901 0.0224 0.0672 0.2703 0.0112 9900 0 0 1 45 46 0.0400 0.1356 0.0332 0.1200 0.4068 0.0166 9900 0 0 1

46 47 0.0380 0.1270 0.0316 0.1140 0.3810 0.0158 9900 0 0 1

46 48 0.0601 0.1890 0.0472 0.1803 0.5670 0.0236 9900 0 0 1 47 49 0.0191 0.0625 0.0160 0.0573 0.1875 0.0080 9900 0 0 1

42 49 0.0715 0.3230 0.0860 0.2145 0.9690 0.0430 9900 0 0 1

42 49 0.0715 0.3230 0.0860 0.2145 0.9690 0.0430 9900 0 0 1 45 49 0.0684 0.1860 0.0444 0.2052 0.5580 0.0222 9900 0 0 1

48 49 0.0179 0.0505 0.0126 0.0537 0.1515 0.0063 9900 0 0 1

49 50 0.0267 0.0752 0.0187 0.0801 0.2256 0.0094 9900 0 0 1 49 51 0.0486 0.1370 0.0342 0.1458 0.4110 0.0171 9900 0 0 1

51 52 0.0203 0.0588 0.0140 0.0609 0.1764 0.0070 9900 0 0 1

52 53 0.0405 0.1635 0.0406 0.1215 0.4905 0.0203 9900 0 0 1 53 54 0.0263 0.1220 0.0310 0.0789 0.3660 0.0155 9900 0 0 1

49 54 0.0730 0.2890 0.0738 0.2190 0.8670 0.0369 9900 0 0 1

49 54 0.0869 0.2910 0.0730 0.2607 0.8730 0.0365 9900 0 0 1 54 55 0.0169 0.0707 0.0202 0.0507 0.2121 0.0101 9900 0 0 1

54 56 0.0028 0.0096 0.0073 0.0083 0.0287 0.0037 9900 0 0 1

55 56 0.0049 0.0151 0.0037 0.0146 0.0453 0.0019 9900 0 0 1 56 57 0.0343 0.0966 0.0242 0.1029 0.2898 0.0121 9900 0 0 1

50 57 0.0474 0.1340 0.0332 0.1422 0.4020 0.0166 9900 0 0 1

56 58 0.0343 0.0966 0.0242 0.1029 0.2898 0.0121 9900 0 0 1 51 58 0.0255 0.0719 0.0179 0.0765 0.2157 0.0089 9900 0 0 1

54 59 0.0503 0.2293 0.0598 0.1509 0.6879 0.0299 9900 0 0 1 56 59 0.0825 0.2510 0.0569 0.2475 0.7530 0.0285 9900 0 0 1

56 59 0.0803 0.2390 0.0536 0.2409 0.7170 0.0268 9900 0 0 1

55 59 0.0474 0.2158 0.0565 0.1422 0.6474 0.0282 9900 0 0 1 59 60 0.0317 0.1450 0.0376 0.0951 0.4350 0.0188 9900 0 0 1

59 61 0.0328 0.1500 0.0388 0.0984 0.4500 0.0194 9900 0 0 1

60 61 0.0026 0.0135 0.0146 0.0079 0.0405 0.0073 9900 0 0 1 60 62 0.0123 0.0561 0.0147 0.0369 0.1683 0.0073 9900 0 0 1

61 62 0.0082 0.0376 0.0098 0.0247 0.1128 0.0049 9900 0 0 1

63 64 0.0017 0.0200 0.2160 0.0052 0.0600 0.1080 9900 0 0 1 38 65 0.0090 0.0986 1.0460 0.0270 0.2958 0.5230 9900 0 0 1

64 65 0.0027 0.0302 0.3800 0.0081 0.0906 0.1900 9900 0 0 1

49 66 0.0180 0.0919 0.0248 0.0540 0.2757 0.0124 9900 0 0 1 49 66 0.0180 0.0919 0.0248 0.0540 0.2757 0.0124 9900 0 0 1

62 66 0.0482 0.2180 0.0578 0.1446 0.6540 0.0289 9900 0 0 1

62 67 0.0258 0.1170 0.0310 0.0774 0.3510 0.0155 9900 0 0 1 66 67 0.0224 0.1015 0.0268 0.0672 0.3045 0.0134 9900 0 0 1

65 68 0.0014 0.0160 0.6380 0.0041 0.0480 0.3190 9900 0 0 1

47 69 0.0844 0.2778 0.0709 0.2532 0.8334 0.0355 9900 0 0 1 49 69 0.0985 0.3240 0.0828 0.2955 0.9720 0.0414 9900 0 0 1

69 70 0.0300 0.1270 0.1220 0.0900 0.3810 0.0610 9900 0 0 1

24 70 0.0022 0.4115 0.1020 0.0066 1.2345 0.0510 9900 0 0 1


173 |

70 71 0.0088 0.0355 0.0088 0.0265 0.1065 0.0044 9900 0 0 1

24 72 0.0488 0.1960 0.0488 0.1464 0.5880 0.0244 9900 0 0 1 71 72 0.0446 0.1800 0.0444 0.1338 0.5400 0.0222 9900 0 0 1

71 73 0.0087 0.0454 0.0118 0.0260 0.1362 0.0059 9900 0 0 1 70 74 0.0401 0.1323 0.0337 0.1203 0.3969 0.0168 9900 0 0 1

70 75 0.0428 0.1410 0.0360 0.1284 0.4230 0.0180 9900 0 0 1

69 75 0.0405 0.1220 0.1240 0.1215 0.3660 0.0620 9900 0 0 1 74 75 0.0123 0.0406 0.0103 0.0369 0.1218 0.0052 9900 0 0 1

76 77 0.0444 0.1480 0.0368 0.1332 0.4440 0.0184 9900 0 0 1

69 77 0.0309 0.1010 0.1038 0.0927 0.3030 0.0519 9900 0 0 1 75 77 0.0601 0.1999 0.0498 0.1803 0.5997 0.0249 9900 0 0 1

77 78 0.0038 0.0124 0.0126 0.0113 0.0372 0.0063 9900 0 0 1

78 79 0.0055 0.0244 0.0065 0.0164 0.0732 0.0032 9900 0 0 1 77 80 0.0170 0.0485 0.0472 0.0510 0.1455 0.0236 9900 0 0 1

77 80 0.0294 0.1050 0.0228 0.0882 0.3150 0.0114 9900 0 0 1

79 80 0.0156 0.0704 0.0187 0.0468 0.2112 0.0094 9900 0 0 1 68 81 0.0018 0.0202 0.8080 0.0053 0.0606 0.4040 9900 0 0 1

77 82 0.0298 0.0853 0.0817 0.0894 0.2559 0.0409 9900 0 0 1

82 83 0.0112 0.0367 0.0380 0.0336 0.1100 0.0190 9900 0 0 1 83 84 0.0625 0.1320 0.0258 0.1875 0.3960 0.0129 9900 0 0 1

83 85 0.0430 0.1480 0.0348 0.1290 0.4440 0.0174 9900 0 0 1

84 85 0.0302 0.0641 0.0123 0.0906 0.1923 0.0062 9900 0 0 1 85 86 0.0350 0.1230 0.0276 0.1050 0.3690 0.0138 9900 0 0 1

86 87 0.0283 0.2074 0.0445 0.0848 0.6222 0.0223 9900 0 0 1

85 88 0.0200 0.1020 0.0276 0.0600 0.3060 0.0138 9900 0 0 1 85 89 0.0239 0.1730 0.0470 0.0717 0.5190 0.0235 9900 0 0 1

88 89 0.0139 0.0712 0.0193 0.0417 0.2136 0.0097 9900 0 0 1

89 90 0.0518 0.1880 0.0528 0.1554 0.5640 0.0264 9900 0 0 1 89 90 0.0238 0.0997 0.1060 0.0714 0.2991 0.0530 9900 0 0 1

90 91 0.0254 0.0836 0.0214 0.0762 0.2508 0.0107 9900 0 0 1

89 92 0.0099 0.0505 0.0548 0.0297 0.1515 0.0274 9900 0 0 1 89 92 0.0393 0.1581 0.0414 0.1179 0.4743 0.0207 9900 0 0 1

91 92 0.0387 0.1272 0.0327 0.1161 0.3816 0.0163 9900 0 0 1

92 93 0.0258 0.0848 0.0218 0.0774 0.2544 0.0109 9900 0 0 1 92 94 0.0481 0.1580 0.0406 0.1443 0.4740 0.0203 9900 0 0 1

93 94 0.0223 0.0732 0.0188 0.0669 0.2196 0.0094 9900 0 0 1

94 95 0.0132 0.0434 0.0111 0.0396 0.1302 0.0056 9900 0 0 1 80 96 0.0356 0.1820 0.0494 0.1068 0.5460 0.0247 9900 0 0 1

82 96 0.0162 0.0530 0.0544 0.0486 0.1590 0.0272 9900 0 0 1

94 96 0.0269 0.0869 0.0230 0.0807 0.2607 0.0115 9900 0 0 1 80 97 0.0183 0.0934 0.0254 0.0549 0.2802 0.0127 9900 0 0 1

80 98 0.0238 0.1080 0.0286 0.0714 0.3240 0.0143 9900 0 0 1

80 99 0.0454 0.2060 0.0546 0.1362 0.6180 0.0273 9900 0 0 1 92 100 0.0648 0.2950 0.0472 0.1944 0.8850 0.0236 9900 0 0 1

94 100 0.0178 0.0580 0.0604 0.0534 0.1740 0.0302 9900 0 0 1

95 96 0.0171 0.0547 0.0147 0.0513 0.1641 0.0074 9900 0 0 1 96 97 0.0173 0.0885 0.0240 0.0519 0.2655 0.0120 9900 0 0 1

98 100 0.0397 0.1790 0.0476 0.1191 0.5370 0.0238 9900 0 0 1

99 100 0.0180 0.0813 0.0216 0.0540 0.2439 0.0108 9900 0 0 1 100 101 0.0277 0.1262 0.0328 0.0831 0.3786 0.0164 9900 0 0 1

92 102 0.0123 0.0559 0.0146 0.0369 0.1677 0.0073 9900 0 0 1

101 102 0.0246 0.1120 0.0294 0.0738 0.3360 0.0147 9900 0 0 1 100 103 0.0160 0.0525 0.0536 0.0480 0.1575 0.0268 9900 0 0 1

100 104 0.0451 0.2040 0.0541 0.1353 0.6120 0.0271 9900 0 0 1 103 104 0.0466 0.1584 0.0407 0.1398 0.4752 0.0204 9900 0 0 1

103 105 0.0535 0.1625 0.0408 0.1605 0.4875 0.0204 9900 0 0 1

100 106 0.0605 0.2290 0.0620 0.1815 0.6870 0.0310 9900 0 0 1 104 105 0.0099 0.0378 0.0099 0.0298 0.1134 0.0049 9900 0 0 1

105 106 0.0140 0.0547 0.0143 0.0420 0.1641 0.0072 9900 0 0 1

105 107 0.0530 0.1830 0.0472 0.1590 0.5490 0.0236 9900 0 0 1 105 108 0.0261 0.0703 0.0184 0.0783 0.2109 0.0092 9900 0 0 1

106 107 0.0530 0.1830 0.0472 0.1590 0.5490 0.0236 9900 0 0 1

108 109 0.0105 0.0288 0.0076 0.0315 0.0864 0.0038 9900 0 0 1 103 110 0.0391 0.1813 0.0461 0.1172 0.5439 0.0231 9900 0 0 1

109 110 0.0278 0.0762 0.0202 0.0834 0.2286 0.0101 9900 0 0 1

110 111 0.0220 0.0755 0.0200 0.0660 0.2265 0.0100 9900 0 0 1 110 112 0.0247 0.0640 0.0620 0.0741 0.1920 0.0310 9900 0 0 1

17 113 0.0091 0.0301 0.0077 0.0274 0.0903 0.0038 9900 0 0 1

32 113 0.0615 0.2030 0.0518 0.1845 0.6090 0.0259 9900 0 0 1 32 114 0.0135 0.0612 0.0163 0.0405 0.1836 0.0081 9900 0 0 1

27 115 0.0164 0.0741 0.0197 0.0492 0.2223 0.0099 9900 0 0 1

114 115 0.0023 0.0104 0.0028 0.0069 0.0312 0.0014 9900 0 0 1 68 116 0.0003 0.0041 0.1640 0.0010 0.0122 0.0820 9900 0 0 1

12 117 0.0329 0.1400 0.0358 0.0987 0.4200 0.0179 9900 0 0 1

75 118 0.0145 0.0481 0.0120 0.0435 0.1443 0.0060 9900 0 0 1


174 |

76 118 0.0164 0.0544 0.0136 0.0492 0.1632 0.0068 9900 0 0 1

Table A-10 Transformer data of the IEEE Reliability the IEEE 118-bus Test System


Status A B C

8 5 0 0.0267 0 Wye Wye 0.985 0 9900 0 0 1 26 25 0 0.0382 0 Wye Wye 0.960 0 9900 0 0 1

30 17 0 0.0388 0 Wye Wye 0.960 0 9900 0 0 1

38 37 0 0.0375 0 Wye Wye 0.935 0 9900 0 0 1 63 59 0 0.0386 0 Wye Wye 0.960 0 9900 0 0 1

64 61 0 0.0268 0 Wye Wye 0.985 0 9900 0 0 1

65 66 0 0.0370 0 Wye Wye 0.935 0 9900 0 0 1 68 69 0 0.0370 0 Wye Wye 0.935 0 9900 0 0 1

81 80 0 0.0370 0 Wye Wye 0.935 0 9900 0 0 1

Table A-11 Bus data of the 295-bus Generic Distribution System (GDS)

Bus number

Type Pd Qd Gs Bs Area Vm Va Base kV

Zone Vmax Vmin

1 1 0.2407 0.0392 0 0 1 0.9659 -5.49 11 1 1.06 0.94

2 1 0.1033 0.0149 0 0 1 0.9645 -5.52 11 1 1.06 0.94

3 1 0.0000 0.0000 0 0 1 0.9622 -5.55 11 1 1.06 0.94 4 1 0.8932 0.0130 0 0 1 0.9646 -5.51 11 1 1.06 0.94

5 1 0.1699 0.0279 0 0 1 0.9637 -5.52 11 1 1.06 0.94

6 1 0.0473 0.0121 0 0 1 0.9632 -5.53 11 1 1.06 0.94 7 1 0.1474 0.0213 0 0 1 0.9630 -5.53 11 1 1.06 0.94

8 1 0.0000 0.0000 0 0 1 0.9629 -5.53 11 1 1.06 0.94

9 1 0.0111 0.0019 0 0 1 0.9629 -5.53 11 1 1.06 0.94 10 1 0.0000 0.0000 0 0 1 0.9628 -5.53 11 1 1.06 0.94

11 1 0.1066 0.0185 0 0 1 0.9628 -5.53 11 1 1.06 0.94

12 1 0.1020 0.0159 0 0 1 0.9953 -8.58 11 1 1.06 0.94 13 1 0.0872 0.0127 0 0 1 0.9896 -8.63 11 1 1.06 0.94

14 1 0.1731 0.0298 0 0 1 0.9975 -8.56 11 1 1.06 0.94

15 1 0.0000 0.0000 0 0 1 0.9991 -8.55 11 1 1.06 0.94 16 1 0.0299 0.0080 0 0 1 0.9988 -8.55 11 1 1.06 0.94

17 1 0.0160 0.0050 0 0 1 0.9989 -8.55 11 1 1.06 0.94

18 1 0.0000 0.0000 0 0 1 0.9990 -8.55 11 1 1.06 0.94 19 1 0.0361 0.0050 0 0 1 1.0018 -8.52 11 1 1.06 0.94

20 1 0.0000 0.0000 0 0 1 1.0063 -8.48 11 1 1.06 0.94

21 1 0.0152 0.0020 0 0 1 1.0062 -8.49 11 1 1.06 0.94 22 1 0.4105 0.0819 0 0 1 1.0118 -8.43 11 1 1.06 0.94

23 1 0.0000 0.0000 0 0 1 0.9804 -8.70 11 1 1.06 0.94

24 1 0.7024 0.1576 0 0 1 0.9803 -8.70 11 1 1.06 0.94 25 1 0.0000 0.0000 0 0 1 0.9597 -5.57 11 1 1.06 0.94

26 1 0.0000 0.0000 0 0 1 0.9757 -8.76 11 1 1.06 0.94

27 1 0.0000 0.0000 0 0 1 0.9594 -5.58 11 1 1.06 0.94 28 1 0.0000 0.0000 0 0 1 0.9750 -8.77 11 1 1.06 0.94

29 1 0.5936 0.1395 0 0 1 0.9579 -5.58 11 1 1.06 0.94

30 1 0.0786 0.0256 0 0 1 0.9559 -5.58 11 1 1.06 0.94 31 1 0.4062 0.0881 0 0 1 0.9532 -5.57 11 1 1.06 0.94

32 1 0.0000 0.0000 0 0 1 0.9534 -5.57 11 1 1.06 0.94

33 1 0.0000 0.0000 0 0 1 0.9534 -5.57 11 1 1.06 0.94 34 1 0.6605 0.1490 0 0 1 0.9531 -5.57 11 1 1.06 0.94

35 1 0.1326 0.0327 0 0 1 0.9531 -5.57 11 1 1.06 0.94

36 1 0.0391 0.0127 0 0 1 0.9531 -5.57 11 1 1.06 0.94 37 1 0.3897 0.0974 0 0 1 0.9542 -9.20 11 1 1.06 0.94

38 1 0.1095 0.0219 0 0 1 0.9554 -9.21 11 1 1.06 0.94 39 1 0.6730 0.2149 0 0 1 0.9563 -9.21 11 1 1.06 0.94

40 1 0.7774 0.2500 0 0 1 0.9569 -9.18 11 1 1.06 0.94

41 1 0.2059 0.0506 0 0 1 0.9588 -9.18 11 1 1.06 0.94 42 1 0.1184 0.0268 0 0 1 0.9617 -9.19 11 1 1.06 0.94

43 1 0.3977 0.0957 0 0 1 0.9639 -9.19 11 1 1.06 0.94

44 1 0.3127 0.0576 0 0 1 0.9719 -8.77 11 1 1.06 0.94 45 1 0.4198 0.0946 0 0 1 0.9724 -8.77 11 1 1.06 0.94

46 1 0.0000 0.0000 0 0 1 0.9710 -8.82 11 1 1.06 0.94

47 1 0.0000 0.0000 0 0 1 0.9710 -8.82 11 1 1.06 0.94 48 1 0.2733 0.0603 0 0 1 0.9708 -8.82 11 1 1.06 0.94

49 1 0.4437 0.1055 0 0 1 0.9706 -8.82 11 1 1.06 0.94

50 1 0.2681 0.0424 0 0 1 1.0175 -8.39 11 1 1.06 0.94 51 1 0.4793 0.0878 0 0 1 1.0164 -8.42 11 1 1.06 0.94

52 1 0.0000 0.0000 0 0 1 1.0171 -8.43 11 1 1.06 0.94

53 1 0.4992 0.0806 0 0 1 1.0167 -8.44 11 1 1.06 0.94


175 |

54 1 0.6236 0.1264 0 0 1 1.0178 -8.34 11 1 1.06 0.94

55 1 0.3901 0.0812 0 0 1 0.9660 -5.49 11 1 1.06 0.94 56 1 0.1188 0.0187 0 0 1 0.9674 -5.47 11 1 1.06 0.94

57 1 0.1646 0.0273 0 0 1 0.9698 -5.42 11 1 1.06 0.94 58 1 0.5276 0.1371 0 0 1 0.9724 -5.38 11 1 1.06 0.94

59 1 0.6552 0.1307 0 0 1 0.9730 -5.48 11 1 1.06 0.94

60 1 0.7942 0.1471 0 0 1 0.9741 -5.33 11 1 1.06 0.94 61 1 0.2830 0.0492 0 0 1 0.9729 -5.48 11 1 1.06 0.94

62 1 0.1565 0.0245 0 0 1 0.9711 -5.40 11 1 1.06 0.94

63 1 0.4096 0.0733 0 0 1 0.9693 -5.43 11 1 1.06 0.94 64 1 0.2411 0.0413 0 0 1 0.9686 -5.44 11 1 1.06 0.94

65 1 0.4400 0.0758 0 0 1 0.9676 -5.44 11 1 1.06 0.94

66 1 0.8287 0.1574 0 0 1 0.9650 -5.43 11 1 1.06 0.94 67 1 0.0000 0.0000 0 0 1 0.9619 -5.56 11 1 1.06 0.94

68 1 0.0000 0.0000 0 0 1 0.9619 -5.56 11 1 1.06 0.94

69 1 0.0167 0.0028 0 0 1 0.9618 -5.56 11 1 1.06 0.94 70 1 0.0000 0.0000 0 0 1 0.9619 -5.56 11 1 1.06 0.94

71 1 0.1628 0.0314 0 0 1 0.9617 -5.56 11 1 1.06 0.94

72 1 0.0000 0.0000 0 0 1 0.9619 -5.56 11 1 1.06 0.94 73 1 0.0231 0.0037 0 0 1 0.9619 -5.56 11 1 1.06 0.94

74 1 0.0000 0.0000 0 0 1 1.0148 -8.46 11 1 1.06 0.94

75 1 0.4166 0.0669 0 0 1 1.0142 -8.47 11 1 1.06 0.94 76 1 0.7046 0.1391 0 0 1 1.0150 -8.45 11 1 1.06 0.94

77 1 0.0000 0.0000 0 0 1 1.0130 -6.64 11 1 1.06 0.94

78 1 0.1007 0.0147 0 0 1 1.0244 -7.60 11 1 1.06 0.94 79 1 0.4065 0.0721 0 0 1 1.0222 -7.64 11 1 1.06 0.94

80 1 0.7890 0.2540 0 0 1 1.0203 -7.67 11 1 1.06 0.94

81 1 0.0000 0.0000 0 0 1 1.0139 -7.61 11 1 1.06 0.94 82 1 0.0000 0.0000 0 0 1 1.0138 -7.62 11 1 1.06 0.94

83 1 0.0370 0.0051 0 0 1 1.0134 -7.63 11 1 1.06 0.94

84 1 0.0308 0.0041 0 0 1 1.0132 -7.63 11 1 1.06 0.94 85 1 0.0000 0.0000 0 0 1 1.0129 -7.64 11 1 1.06 0.94

86 1 0.1251 0.0236 0 0 1 1.0126 -7.65 11 1 1.06 0.94

87 1 0.9032 0.1630 0 0 1 1.0254 -7.66 11 1 1.06 0.94 88 1 0.0000 0.0000 0 0 1 1.0130 -7.62 11 1 1.06 0.94

89 1 1.1915 0.3914 0 0 1 1.0122 -7.63 11 1 1.06 0.94

90 1 0.0000 0.0000 0 0 1 1.0123 -7.64 11 1 1.06 0.94 91 1 0.0000 0.0000 0 0 1 1.0116 -7.68 11 1 1.06 0.94

92 1 0.0440 0.0072 0 0 1 1.0115 -7.68 11 1 1.06 0.94

93 1 0.0000 0.0000 0 0 1 1.0114 -7.70 11 1 1.06 0.94 94 1 0.0082 0.0010 0 0 1 1.0110 -7.70 11 1 1.06 0.94

95 1 0.0000 0.0000 0 0 1 1.0103 -7.71 11 1 1.06 0.94

96 1 0.0367 0.0061 0 0 1 1.0103 -7.72 11 1 1.06 0.94 97 1 0.0000 0.0000 0 0 1 1.0099 -7.72 11 1 1.06 0.94

98 1 0.0163 0.0020 0 0 1 1.0097 -7.72 11 1 1.06 0.94

99 1 0.0825 0.0163 0 0 1 1.0094 -7.73 11 1 1.06 0.94 100 1 0.0734 0.0143 0 0 1 1.0097 -7.73 11 1 1.06 0.94

101 1 0.0000 0.0000 0 0 1 1.0106 -7.74 11 1 1.06 0.94

102 1 0.0663 0.0112 0 0 1 1.0103 -7.74 11 1 1.06 0.94 103 1 0.0092 0.0010 0 0 1 1.0103 -7.75 11 1 1.06 0.94

104 1 0.0000 0.0000 0 0 1 1.0099 -7.77 11 1 1.06 0.94

105 1 0.0235 0.0031 0 0 1 1.0099 -7.77 11 1 1.06 0.94 106 1 0.0387 0.0061 0 0 1 1.0095 -7.78 11 1 1.06 0.94

107 1 0.0183 0.0031 0 0 1 1.0090 -7.80 11 1 1.06 0.94 108 1 0.0000 0.0000 0 0 1 1.0087 -7.81 11 1 1.06 0.94

109 1 0.0000 0.0000 0 0 1 1.0086 -7.81 11 1 1.06 0.94

110 1 0.1291 0.0315 0 0 1 1.0083 -7.81 11 1 1.06 0.94 111 1 0.0203 0.0031 0 0 1 1.0085 -7.82 11 1 1.06 0.94

112 1 0.0000 0.0000 0 0 1 1.0084 -7.82 11 1 1.06 0.94

113 1 0.0061 0.0009 0 0 1 1.0083 -7.82 11 1 1.06 0.94 114 1 0.0102 0.0010 0 0 1 1.0083 -7.83 11 1 1.06 0.94

115 1 0.0000 0.0000 0 0 1 1.0079 -7.84 11 1 1.06 0.94

116 1 0.0061 0.0009 0 0 1 1.0078 -7.84 11 1 1.06 0.94 117 1 0.0000 0.0000 0 0 1 1.0078 -7.84 11 1 1.06 0.94

118 1 0.0051 0.0007 0 0 1 1.0078 -7.84 11 1 1.06 0.94

119 1 0.0081 0.0010 0 0 1 1.0078 -7.84 11 1 1.06 0.94 120 1 0.0000 0.0000 0 0 1 1.0078 -7.84 11 1 1.06 0.94

121 1 0.0000 0.0000 0 0 1 1.0078 -7.84 11 1 1.06 0.94

122 1 0.0000 0.0000 0 0 1 1.0078 -7.84 11 1 1.06 0.94 123 1 0.0000 0.0000 0 0 1 1.0078 -7.84 11 1 1.06 0.94

124 1 0.0091 0.0010 0 0 1 1.0076 -7.84 11 1 1.06 0.94

125 1 0.0233 0.0071 0 0 1 1.0074 -7.84 11 1 1.06 0.94 126 1 0.0071 0.0010 0 0 1 1.0073 -7.84 11 1 1.06 0.94

127 1 0.0203 0.0030 0 0 1 1.0073 -7.85 11 1 1.06 0.94

128 1 0.0000 0.0000 0 0 1 0.9791 -7.67 11 1 1.06 0.94


176 |

129 1 0.0431 0.0077 0 0 1 0.9791 -7.67 11 1 1.06 0.94

130 1 0.0000 0.0000 0 0 1 0.9792 -7.67 11 1 1.06 0.94 131 1 0.0353 0.0048 0 0 1 0.9767 -7.71 11 1 1.06 0.94

132 1 0.0180 0.0028 0 0 1 0.9744 -7.75 11 1 1.06 0.94 133 1 0.0170 0.0028 0 0 1 0.9710 -7.81 11 1 1.06 0.94

134 1 0.0000 0.0000 0 0 1 0.9699 -7.84 11 1 1.06 0.94

135 1 0.0094 0.0009 0 0 1 0.9699 -7.84 11 1 1.06 0.94 136 1 0.8682 0.2853 0 0 1 0.9657 -7.96 11 1 1.06 0.94

137 1 0.0000 0.0000 0 0 1 0.9657 -7.96 11 1 1.06 0.94

138 1 0.0000 0.0000 0 0 1 0.9808 -7.64 11 1 1.06 0.94 139 1 0.0096 0.0019 0 0 1 0.9808 -7.64 11 1 1.06 0.94

140 1 0.0000 0.0000 0 0 1 0.9841 -7.58 11 1 1.06 0.94

141 1 0.0213 0.0068 0 0 1 0.9840 -7.58 11 1 1.06 0.94 142 1 0.0000 0.0000 0 0 1 0.9871 -7.53 11 1 1.06 0.94

143 1 0.0029 0.0004 0 0 1 0.9871 -7.53 11 1 1.06 0.94

144 1 0.0029 0.0004 0 0 1 0.9896 -7.48 11 1 1.06 0.94 145 1 0.0000 0.0000 0 0 1 0.9935 -7.42 11 1 1.06 0.94

146 1 0.0000 0.0000 0 0 1 0.9966 -7.35 11 1 1.06 0.94

147 1 0.0189 0.0030 0 0 1 0.9965 -7.35 11 1 1.06 0.94 148 1 0.0000 0.0000 0 0 1 1.0029 -7.21 11 1 1.06 0.94

149 1 0.0201 0.0030 0 0 1 1.0028 -7.21 11 1 1.06 0.94

150 1 0.0000 0.0000 0 0 1 1.0083 -7.03 11 1 1.06 0.94 151 1 0.0091 0.0010 0 0 1 1.0083 -7.03 11 1 1.06 0.94

152 1 0.0000 0.0000 0 0 1 0.9903 -7.48 11 1 1.06 0.94

153 1 0.0206 0.0039 0 0 1 0.9902 -7.48 11 1 1.06 0.94 154 1 0.0000 0.0000 0 0 1 0.9865 -7.55 11 1 1.06 0.94

155 1 0.0127 0.0019 0 0 1 0.9865 -7.55 11 1 1.06 0.94

156 1 0.0000 0.0000 0 0 1 0.9837 -7.59 11 1 1.06 0.94 157 1 0.0348 0.0058 0 0 1 0.9835 -7.59 11 1 1.06 0.94

158 1 0.0203 0.0029 0 0 1 0.9834 -7.59 11 1 1.06 0.94

159 1 0.0183 0.0029 0 0 1 0.9825 -7.62 11 1 1.06 0.94 160 1 0.0000 0.0000 0 0 1 0.9791 -7.70 11 1 1.06 0.94

161 1 0.0345 0.0048 0 0 1 0.9788 -7.71 11 1 1.06 0.94

162 1 0.1312 0.0316 0 0 1 0.9785 -7.71 11 1 1.06 0.94 163 1 0.0048 0.0007 0 0 1 0.9785 -7.71 11 1 1.06 0.94

164 1 0.0076 0.0010 0 0 1 0.9764 -7.78 11 1 1.06 0.94

165 1 0.0000 0.0000 0 0 1 0.9754 -7.81 11 1 1.06 0.94 166 1 0.0000 0.0000 0 0 1 0.9752 -7.81 11 1 1.06 0.94

167 1 0.0200 0.0029 0 0 1 0.9752 -7.81 11 1 1.06 0.94

168 1 0.0390 0.0076 0 0 1 0.9749 -7.81 11 1 1.06 0.94 169 1 0.0000 0.0000 0 0 1 0.9747 -7.81 11 1 1.06 0.94

170 1 0.0000 0.0000 0 0 1 0.9691 -8.01 11 1 1.06 0.94

171 1 0.0000 0.0000 0 0 1 0.9689 -8.01 11 1 1.06 0.94 172 1 0.1116 0.0225 0 0 1 0.9684 -8.02 11 1 1.06 0.94

173 1 0.0000 0.0000 0 0 1 0.9683 -8.02 11 1 1.06 0.94

174 1 0.0347 0.0047 0 0 1 0.9683 -8.02 11 1 1.06 0.94 175 1 0.0000 0.0000 0 0 1 0.9682 -8.02 11 1 1.06 0.94

176 1 0.0356 0.0066 0 0 1 0.9681 -8.03 11 1 1.06 0.94

177 1 0.0000 0.0000 0 0 1 0.9681 -8.03 11 1 1.06 0.94 178 1 0.0000 0.0000 0 0 1 0.9597 -5.57 11 1 1.06 0.94

179 1 0.0000 0.0000 0 0 1 0.9746 -7.81 11 1 1.06 0.94

180 1 0.0000 0.0000 0 0 1 0.9745 -7.82 11 1 1.06 0.94 181 1 0.0085 0.0009 0 0 1 0.9744 -7.82 11 1 1.06 0.94

182 1 0.0000 0.0000 0 0 1 0.9742 -7.82 11 1 1.06 0.94 183 1 0.0114 0.0209 0 0 1 0.9741 -7.81 11 1 1.06 0.94

184 1 0.0000 0.0000 0 0 1 0.9740 -7.82 11 1 1.06 0.94

185 1 0.0190 0.0028 0 0 1 0.9739 -7.82 11 1 1.06 0.94 186 1 0.0398 0.0085 0 0 1 0.9737 -7.82 11 1 1.06 0.94

187 1 0.0000 0.0000 0 0 1 0.9743 -7.84 11 1 1.06 0.94

188 1 0.0000 0.0000 0 0 1 0.9743 -7.84 11 1 1.06 0.94 189 1 0.0047 0.0065 0 0 1 0.9743 -7.84 11 1 1.06 0.94

190 1 0.0047 0.0007 0 0 1 0.9743 -7.84 11 1 1.06 0.94

191 1 0.0047 0.0007 0 0 1 0.9743 -7.84 11 1 1.06 0.94 192 1 0.0180 0.0028 0 0 1 0.9726 -7.90 11 1 1.06 0.94

193 1 0.0000 0.0000 0 0 1 0.9719 -7.91 11 1 1.06 0.94

194 1 0.0085 0.0009 0 0 1 0.9719 -7.91 11 1 1.06 0.94 195 1 0.0085 0.0009 0 0 1 0.9718 -7.91 11 1 1.06 0.94

196 1 0.0151 0.0028 0 0 1 0.9717 -7.91 11 1 1.06 0.94

197 1 0.0000 0.0000 0 0 1 0.9713 -7.92 11 1 1.06 0.94 198 1 0.0160 0.0019 0 0 1 0.9713 -7.92 11 1 1.06 0.94

199 1 0.0170 0.0028 0 0 1 0.9711 -7.93 11 1 1.06 0.94

200 1 0.0226 0.0047 0 0 1 0.9708 -7.93 11 1 1.06 0.94 201 1 0.0000 0.0000 0 0 1 0.9706 -7.94 11 1 1.06 0.94

202 1 0.0198 0.0028 0 0 1 0.9705 -7.94 11 1 1.06 0.94

203 1 0.0075 0.0009 0 0 1 0.9703 -7.94 11 1 1.06 0.94


177 |

204 1 0.0000 0.0000 0 0 1 0.9702 -7.95 11 1 1.06 0.94

205 1 0.0000 0.0000 0 0 1 0.9701 -7.95 11 1 1.06 0.94 206 1 0.0000 0.0000 0 0 1 0.9700 -7.95 11 1 1.06 0.94

207 1 0.0075 0.0009 0 0 1 0.9700 -7.95 11 1 1.06 0.94 208 1 0.0442 0.0094 0 0 1 0.9698 -7.95 11 1 1.06 0.94

209 1 0.0000 0.0000 0 0 1 0.9715 -7.93 11 1 1.06 0.94

210 1 0.0000 0.0000 0 0 1 0.9710 -7.95 11 1 1.06 0.94 211 1 0.0000 0.0000 0 0 1 0.9710 -7.95 11 1 1.06 0.94

212 1 0.0000 0.0000 0 0 1 0.9709 -7.95 11 1 1.06 0.94

213 1 0.0320 0.0047 0 0 1 0.9707 -7.95 11 1 1.06 0.94 214 1 0.0000 0.0000 0 0 1 0.9703 -7.97 11 1 1.06 0.94

215 1 0.0000 0.0000 0 0 1 0.9703 -7.97 11 1 1.06 0.94

216 1 0.0000 0.0000 0 0 1 0.9696 -7.99 11 1 1.06 0.94 217 1 0.0789 0.0197 0 0 1 0.9691 -8.00 11 1 1.06 0.94

218 1 0.0000 0.0000 0 0 1 0.9688 -8.01 11 1 1.06 0.94

219 1 0.0619 0.0094 0 0 1 0.9687 -8.01 11 1 1.06 0.94 220 1 0.0000 0.0000 0 0 1 1.0166 -8.41 11 1 1.06 0.94

221 1 0.0000 0.0000 0 0 1 0.9678 -9.19 11 1 1.06 0.94

222 1 0.9151 0.1797 0 0 1 1.0192 -8.36 11 1 1.06 0.94 223 1 0.0000 0.0000 0 0 1 1.0121 -6.66 11 1 1.06 0.94

224 1 0.6706 0.1313 0 0 1 1.0126 -6.68 11 1 1.06 0.94

225 1 17.0941 3.0690 0 0 1 0.9761 -5.30 11 1 1.06 0.94 226 1 0.0000 0.0000 0 0 1 0.9761 -5.30 11 1 1.06 0.94

227 1 2.4472 0.4207 0 0 1 1.0205 -8.32 11 1 1.06 0.94

228 1 0.0000 0.0000 0 0 1 1.0205 -8.32 11 1 1.06 0.94 229 1 0.0000 0.0000 0 0 1 1.0273 -7.53 11 1 1.06 0.94

230 1 1.8787 0.3504 0 0 1 1.0273 -7.53 11 1 1.06 0.94

231 1 0.9612 0.1756 0 0 1 1.0134 -6.62 11 1 1.06 0.94 232 1 68.8649 14.4206 0 0 1 0.9880 -2.12 132 1 1.10 0.90

233 1 0.0000 0.0000 0 0 1 0.9880 -2.12 132 1 1.10 0.90

234 1 0.0000 0.0000 0 0 1 1.0343 23.78 33 1 1.06 0.94 235 1 0.0000 0.0000 0 0 1 1.0343 23.78 33 1 1.06 0.94

236 1 0.0000 0.0000 0 0 1 1.0112 24.49 33 1 1.06 0.94

237 1 0.0000 0.0000 0 0 1 1.0343 23.78 33 1 1.06 0.94 238 1 0.0000 0.0000 0 0 1 1.0343 23.78 33 1 1.06 0.94

239 1 3.4953 0.7065 0 0 1 0.9751 25.45 33 1 1.06 0.94

240 1 0.0000 0.0000 0 0 1 1.0125 25.17 33 1 1.06 0.94 241 1 31.7830 8.8286 0 0 1 1.0323 23.69 33 1 1.06 0.94

242 1 28.0839 5.4088 0 0 1 1.0088 24.62 33 1 1.06 0.94

243 1 0.0000 0.0000 0 0 1 1.0088 24.62 33 1 1.06 0.94 244 1 14.6242 2.3698 0 0 1 1.0144 24.72 33 1 1.06 0.94

245 1 0.0000 0.0000 0 0 1 1.0144 24.72 33 1 1.06 0.94

246 1 40.7015 8.7496 0 0 1 0.9719 24.23 33 1 1.06 0.94 247 1 0.0000 0.0000 0 0 1 0.9719 24.23 33 1 1.06 0.94

248 1 26.1959 5.3742 0 0 1 1.0358 23.82 33 1 1.06 0.94

249 1 0.0000 0.0000 0 0 1 1.0358 23.82 33 1 1.06 0.94 250 1 0.0000 0.0000 0 0 1 1.0157 24.73 33 1 1.06 0.94

251 1 0.0000 0.0000 0 0 1 1.0191 24.35 33 1 1.06 0.94

252 1 0.0000 0.0000 0 0 1 0.9906 -1.92 132 1 1.10 0.90 253 1 68.3597 12.1889 0 0 1 0.9874 -2.30 132 1 1.10 0.90

254 1 0.0000 0.0000 0 0 1 0.9874 -2.30 132 1 1.10 0.90

255 1 0.0000 0.0000 0 0 1 0.9910 -1.86 132 1 1.10 0.90 256 1 0.0000 0.0000 0 0 1 0.9910 -1.86 132 1 1.10 0.90

257 1 42.9038 9.1610 0 0 1 0.9860 -2.10 132 1 1.10 0.90 258 1 0.0000 0.0000 0 0 1 0.9860 -2.10 132 1 1.10 0.90

259 1 0.0000 0.0000 0 0 1 1.0173 24.54 33 1 1.06 0.94

260 1 0.0000 0.0000 0 0 1 1.0173 24.54 33 1 1.06 0.94 261 1 0.0000 0.0000 0 0 1 0.9872 -2.25 132 1 1.10 0.90

262 1 0.0000 0.0000 0 0 1 0.9901 -1.89 132 1 1.10 0.90

263 1 0.0000 0.0000 0 0 1 0.9901 -1.89 132 1 1.10 0.90 264 1 0.0000 0.0000 0 0 1 0.9727 25.20 33 1 1.06 0.94

265 1 0.0000 0.0000 0 0 1 1.0341 23.78 33 1 1.06 0.94

266 1 0.0000 0.0000 0 0 1 1.0341 23.78 33 1 1.06 0.94 267 1 0.0000 0.0000 0 0 1 1.0294 23.68 33 1 1.06 0.94

268 1 0.0000 0.0000 0 0 1 1.0294 23.68 33 1 1.06 0.94

269 1 0.0000 0.0000 0 0 1 0.9814 -2.16 132 1 1.10 0.90 270 1 0.0000 0.0000 0 0 1 0.9865 -2.18 132 1 1.10 0.90

271 1 0.0000 0.0000 0 0 1 0.9812 -2.16 132 1 1.10 0.90

272 1 0.0000 0.0000 0 0 1 0.9850 -2.18 132 1 1.10 0.90 273 1 0.0000 0.0000 0 0 1 0.9907 -1.90 132 1 1.10 0.90

274 1 0.0000 0.0000 0 0 1 0.9909 -2.03 132 1 1.10 0.90

275 1 0.0000 0.0000 0 0 1 0.9864 -2.18 132 1 1.10 0.90 276 1 0.0000 0.0000 0 0 1 0.9892 -2.15 132 1 1.10 0.90

277 1 0.0000 0.0000 0 0 1 0.9892 -2.15 132 1 1.10 0.90

278 1 0.0000 0.0000 0 0 1 0.9900 -2.04 132 1 1.10 0.90


178 |

279 1 0.0000 0.0000 0 0 1 0.9900 -2.04 132 1 1.10 0.90

280 1 0.0000 0.0000 0 0 1 1.0126 22.37 0.4 1 1.06 0.94 281 1 0.0000 0.0000 0 0 1 1.0126 22.37 0.4 1 1.06 0.94

282 1 0.0000 0.0000 0 0 1 0.9826 53.78 0.4 1 1.06 0.94 283 1 0.0000 0.0000 0 0 1 0.9826 53.78 0.4 1 1.06 0.94

284 1 0.0000 0.0000 0 0 1 1.0173 54.54 0.4 1 1.06 0.94

285 1 0.0000 0.0000 0 0 1 1.0126 -7.63 11 1 1.06 0.94 286 1 0.0000 0.0000 0 0 1 1.0126 -7.63 11 1 1.06 0.94

287 1 0.0000 0.0000 0 0 1 0.9987 -0.19 400 1 1.10 0.90

288 1 0.0000 0.0000 0 0 1 0.9987 -0.19 400 1 1.10 0.90 289 1 0.0000 0.0000 0 0 1 0.9987 -0.50 275 1 1.10 0.90

290 1 0.0000 0.0000 0 0 1 0.9996 -0.08 275 1 1.10 0.90

291 1 0.0000 0.0000 0 0 1 0.9993 -0.12 275 1 1.10 0.90 292 1 0.0000 0.0000 0 0 1 0.9993 -0.12 275 1 1.10 0.90

293 1 0.0000 0.0000 0 0 1 0.9992 -0.13 400 1 1.10 0.90

294 1 0.0000 0.0000 0 0 1 0.9992 -0.13 400 1 1.10 0.90 295 3 0.0000 0.0000 0 0 1 1.0000 0.00 400 1 1.10 0.90

Table A-12 Generator data of the Generic Distribution System (GDS)

Bus Pg Qg Qmax Qmin Vg Rate Status Pmax Pmin R1 X1 R0 X0

300 0 0 99999 -99999 1 1200 1 99999 0 0.0000 0.0208 0.0006 0.0063

Table A-13 Line data of the Generic Distribution System (GDS)

From bus To


Rating Type Status

A B C

232 233 0.00001 0.00001 0.00000 0.00006 0.00003 0.00000 99 0 0 OL 1

232 278 0.00840 0.00598 0.00136 0.05040 0.01794 0.00045 99 0 0 C 1

278 256 0.00103 0.00736 0.00167 0.00167 0.02208 0.00056 99 0 0 C 1 233 279 0.00840 0.00598 0.00136 0.05040 0.01794 0.00045 99 0 0 C 1

279 255 0.00103 0.00736 0.00167 0.00617 0.00221 0.00056 99 0 0 C 1

256 255 0.00001 0.00001 0.00000 0.00006 0.00001 0.00000 99 0 0 OL 1

279 276 0.00139 0.00989 0.00225 0.00834 0.02967 0.00075 99 0 0 C 1

278 277 0.00139 0.00989 0.00225 0.00834 0.02967 0.00075 99 0 0 C 1

247 246 0.00001 0.00001 0.00000 0.00006 0.00003 0.00000 99 0 0 OL 1 253 254 0.00001 0.00001 0.00000 0.00006 0.00003 0.00000 99 0 0 OL 1

233 253 0.00388 0.02760 0.00627 0.02328 0.08280 0.00209 99 0 0 C 1

232 254 0.00388 0.02760 0.00627 0.02328 0.08280 0.00209 99 0 0 C 1 256 263 0.00588 0.00441 0.03391 0.03528 0.01323 0.01130 99 0 0 C 1

255 262 0.00588 0.00441 0.03391 0.03528 0.01323 0.01130 99 0 0 C 1

226 225 0.00001 0.00001 0.00000 0.00006 0.00003 0.00000 99 0 0 OL 1 226 58 0.12491 0.07400 0.00025 0.74946 0.22200 0.00008 99 0 0 C 1

58 62 0.05640 0.02157 0.00005 0.33840 0.06471 0.00002 99 0 0 C 1 62 63 0.08474 0.04121 0.00012 0.50844 0.12363 0.00004 99 0 0 C 1

61 59 0.02940 0.01983 0.00007 0.17640 0.05949 0.00002 99 0 0 C 1

59 60 0.06000 0.27600 0.00008 0.36000 0.82800 0.00003 99 0 0 C 1 60 226 0.10500 0.04831 0.00014 0.63000 0.14493 0.00005 99 0 0 C 1

63 64 0.04237 0.02060 0.00006 0.25422 0.06180 0.00002 99 0 0 C 1

225 57 0.12712 0.06181 0.00019 0.76272 0.18543 0.00006 99 0 0 C 1 57 56 0.04943 0.02404 0.00007 0.29658 0.07212 0.00002 99 0 0 C 1

56 55 0.02825 0.01374 0.00004 0.16950 0.04122 0.00001 99 0 0 C 1

64 65 0.21795 0.03210 0.00005 1.30770 0.09630 0.00002 99 0 0 C 1 64 66 0.40866 0.06019 0.00010 2.45196 0.18057 0.00003 99 0 0 C 1

67 68 0.09174 0.16264 0.00000 0.55044 0.48792 0.00000 99 0 0 OL 1

68 69 0.07521 0.02876 0.00007 0.45126 0.08628 0.00002 99 0 0 C 1 68 70 0.07645 0.13554 0.00000 0.45870 0.40662 0.00000 99 0 0 OL 1

70 71 0.11281 0.04314 0.00011 0.67686 0.12942 0.00004 99 0 0 C 1

70 72 0.03431 0.02314 0.00008 0.20586 0.06942 0.00003 99 0 0 C 1 72 73 0.08405 0.14909 0.00000 0.50430 0.44727 0.00000 99 0 0 OL 1

72 3 0.12000 0.05521 0.00016 0.72000 0.16563 0.00005 99 0 0 C 1

3 2 0.09750 0.04486 0.00013 0.58500 0.13458 0.00004 99 0 0 C 1 2 55 0.06000 0.02760 0.00008 0.36000 0.08280 0.00003 99 0 0 C 1

55 1 0.05449 0.00802 0.00001 0.32694 0.02406 0.00000 99 0 0 C 1

74 75 0.13161 0.05033 0.00130 0.78966 0.15099 0.00043 99 0 0 C 1 74 76 0.05650 0.02747 0.00008 0.33900 0.08241 0.00003 99 0 0 C 1

3 178 0.11281 0.04314 0.00011 0.67686 0.12942 0.00004 99 0 0 C 1

178 25 0.00001 0.00001 0.00000 0.00006 0.00003 0.00000 99 0 0 OL 1

25 27 0.01470 0.00992 0.00004 0.08820 0.02976 0.00001 99 0 0 C 1

26 28 0.01470 0.00992 0.00004 0.08820 0.02976 0.00001 99 0 0 C 1

55 4 0.10248 0.02641 0.00006 0.61488 0.07923 0.00002 99 0 0 C 1 4 5 0.17569 0.04527 0.00009 1.05414 0.13581 0.00003 99 0 0 C 1


179 |

5 6 0.14640 0.03773 0.00008 0.87840 0.11319 0.00003 99 0 0 C 1

6 7 0.07521 0.02876 0.00007 0.45126 0.08628 0.00002 99 0 0 C 1 7 8 0.05640 0.02157 0.00005 0.33840 0.06471 0.00002 99 0 0 C 1

8 9 0.07521 0.02876 0.00007 0.45126 0.08628 0.00002 99 0 0 C 1 8 10 0.04700 0.01798 0.00005 0.28200 0.05394 0.00002 99 0 0 C 1

10 11 0.01880 0.00792 0.00002 0.11280 0.02338 0.00001 99 0 0 C 1

12 14 0.03760 0.01438 0.00004 0.22560 0.04314 0.00001 99 0 0 C 1 12 13 0.10341 0.03955 0.00100 0.62046 0.11865 0.00033 99 0 0 C 1

13 23 0.16921 0.06471 0.00016 1.01526 0.19413 0.00005 99 0 0 C 1

24 23 0.01880 0.00719 0.00002 0.11280 0.02157 0.00001 99 0 0 C 1 23 26 0.09887 0.04807 0.00015 0.59322 0.14421 0.00005 99 0 0 C 1

27 29 0.07320 0.01886 0.00004 0.43920 0.05658 0.00001 99 0 0 C 1

29 30 0.13622 0.02006 0.00003 0.81732 0.06018 0.00001 99 0 0 C 1 30 32 0.19071 0.02809 0.00004 1.14426 0.08427 0.00001 99 0 0 C 1

32 31 0.02820 0.01079 0.00003 0.16920 0.06474 0.00001 99 0 0 C 1

32 33 0.00001 0.00001 0.00000 0.00006 0.00003 0.00000 99 0 0 OL 1 33 34 0.02820 0.01079 0.00003 0.16920 0.03237 0.00001 99 0 0 C 1

33 35 0.11712 0.03018 0.00006 0.70272 0.09054 0.00002 99 0 0 C 1

35 36 0.10898 0.01605 0.00003 0.65388 0.04815 0.00001 99 0 0 C 1 37 38 0.27244 0.04012 0.00006 1.63464 0.12036 0.00002 99 0 0 C 1

38 39 0.16346 0.02407 0.00004 0.98076 0.07221 0.00001 99 0 0 C 1

28 46 0.09887 0.04807 0.00015 0.59322 0.14421 0.00005 99 0 0 C 1 46 48 0.08173 0.01204 0.00002 0.49038 0.03612 0.00001 99 0 0 C 1

47 46 0.00001 0.00001 0.00000 0.00006 0.00003 0.00000 99 0 0 OL 1

47 49 0.08173 0.01204 0.00002 0.49038 0.03612 0.00001 99 0 0 C 1 28 45 0.32693 0.04815 0.00008 1.96158 0.14445 0.00003 99 0 0 C 1

45 44 0.14640 0.03773 0.00008 0.87840 0.11319 0.00003 99 0 0 C 1

221 47 0.04943 0.24010 0.00007 0.29658 0.07203 0.00002 99 0 0 C 1 221 43 0.13176 0.03395 0.00007 0.79056 0.10185 0.00002 99 0 0 C 1

43 42 0.08748 0.02264 0.00005 0.52488 0.06792 0.00002 99 0 0 C 1

42 41 0.11712 0.03018 0.00006 0.70272 0.09054 0.00002 99 0 0 C 1 41 40 0.08784 0.02264 0.00005 0.52704 0.06792 0.00002 99 0 0 C 1

40 39 0.03814 0.05617 0.00009 0.22884 0.16851 0.00003 99 0 0 C 1

227 228 0.00001 0.00001 0.00000 0.00006 0.00003 0.00000 99 0 0 OL 1 76 220 0.14124 0.06868 0.00021 0.72744 0.20604 0.00007 99 0 0 C 1

220 50 0.05650 0.02747 0.00008 0.33900 0.08241 0.00003 99 0 0 C 1

50 228 0.15536 0.07555 0.00023 0.93216 0.22665 0.00008 99 0 0 C 1 220 51 0.04411 0.02975 0.00011 0.26466 0.08925 0.00004 99 0 0 C 1

52 53 0.07521 0.02876 0.00007 0.45126 0.08628 0.00002 99 0 0 C 1

52 54 0.09401 0.35950 0.00009 0.56406 1.07850 0.00003 99 0 0 C 1 54 228 0.23425 0.06036 0.00013 1.40550 0.18108 0.00004 99 0 0 C 1

14 15 0.02820 0.01079 0.00003 0.16920 0.03237 0.00001 99 0 0 C 1

15 18 0.27870 0.09107 0.00000 1.24722 0.27321 0.00000 99 0 0 OL 1 18 16 0.55431 0.24284 0.00000 0.32586 0.72856 0.00000 99 0 0 OL 1

18 17 0.48502 0.21249 0.00000 2.91012 0.63747 0.00000 99 0 0 OL 1

15 19 0.04700 0.01798 0.00005 0.28200 0.05394 0.00002 99 0 0 C 1 19 20 0.07521 0.02876 0.00001 0.45126 0.08628 0.00000 99 0 0 C 1

20 21 0.13161 0.05033 0.00013 0.78966 0.15099 0.00004 99 0 0 C 1

20 22 0.09401 0.03595 0.00009 0.56406 0.10785 0.00003 99 0 0 C 1 22 227 0.13500 0.06211 0.00018 0.81000 0.18633 0.00006 99 0 0 C 1

255 273 0.00282 0.00298 0.02927 0.01692 0.00894 0.00976 99 0 0 C 1

256 252 0.00282 0.00298 0.02927 0.01692 0.00894 0.00976 99 0 0 C 1 243 242 0.00001 0.00001 0.00000 0.00006 0.00003 0.00000 99 0 0 OL 1

243 236 0.01274 0.01633 0.00293 0.07644 0.04899 0.00098 99 0 0 C 1 236 251 0.00952 0.05048 0.00006 0.05712 0.15144 0.00002 99 0 0 C 1

251 259 0.00504 0.02673 0.00003 0.03024 0.08019 0.00001 99 0 0 C 1

250 260 0.00585 0.02700 0.00003 0.03510 0.08100 0.00001 99 0 0 C 1 251 241 0.01776 0.06236 0.00007 0.07056 0.18708 0.00002 99 0 0 C 1

240 250 0.01176 0.06236 0.00007 0.07056 0.18708 0.00002 99 0 0 C 1

250 244 0.02414 0.08624 0.00009 0.14484 0.25872 0.00003 99 0 0 C 1 244 245 0.00001 0.00001 0.00000 0.00006 0.00003 0.00000 99 0 0 OL 1

274 252 0.00348 0.01608 0.00350 0.02088 0.04824 0.00117 99 0 0 C 1

258 257 0.00001 0.00001 0.00000 0.00006 0.00003 0.00000 99 0 0 OL 1 255 257 0.00399 0.02622 0.00596 0.02394 0.07866 0.00199 99 0 0 C 1

256 258 0.00399 0.02622 0.05960 0.02394 0.07866 0.01987 99 0 0 C 1

259 260 0.00001 0.00001 0.00000 0.00006 0.00003 0.00000 99 0 0 OL 1 275 257 0.00276 0.01272 0.00277 0.01656 0.03816 0.00092 99 0 0 C 1

270 258 0.00197 0.01104 0.00251 0.01182 0.03312 0.00084 99 0 0 C 1

269 257 0.00197 0.01104 0.00251 0.01182 0.03312 0.00084 99 0 0 C 1 257 261 0.00137 0.00897 0.00204 0.00822 0.02691 0.00068 99 0 0 C 1

258 271 0.00137 0.00897 0.00204 0.00822 0.02691 0.00068 99 0 0 C 1

248 249 0.00001 0.00001 0.00000 0.00006 0.00003 0.00000 99 0 0 OL 1 248 241 0.02324 0.08624 0.00009 0.13944 0.25872 0.00003 99 0 0 C 1

248 234 0.02324 0.01372 0.00153 0.13944 0.04116 0.00051 99 0 0 C 1

234 267 0.07471 0.04409 0.00493 0.44826 0.13227 0.00164 99 0 0 C 1


180 |

249 235 0.02324 0.01372 0.00153 0.13944 0.04116 0.00051 99 0 0 C 1

235 268 0.07471 0.04409 0.00493 0.44826 0.13227 0.00164 99 0 0 C 1 261 253 0.00305 0.02001 0.00455 0.01830 0.06003 0.00152 99 0 0 C 1

248 266 0.05313 0.03135 0.00350 0.31878 0.09405 0.00117 99 0 0 C 1 249 265 0.05313 0.03135 0.00350 0.31878 0.09406 0.00117 99 0 0 C 1

229 230 0.00001 0.00001 0.00000 0.00006 0.00003 0.00000 99 0 0 OL 1

230 78 0.07841 0.05289 0.00190 0.47046 0.15867 0.00063 99 0 0 C 1 78 79 0.05881 0.03967 0.00014 0.35286 0.11901 0.00005 99 0 0 C 1

222 227 0.12742 0.08595 0.00031 0.76452 0.25785 0.00010 99 0 0 C 1

79 80 0.06050 0.03388 0.00011 0.36300 0.10164 0.00004 99 0 0 C 1 80 81 0.30600 0.02760 0.00008 1.83600 0.08280 0.00003 99 0 0 C 1

81 88 0.04500 0.02070 0.00006 0.27000 0.06210 0.00002 99 0 0 C 1

88 89 0.06000 0.02807 0.00008 0.36000 0.84210 0.00003 99 0 0 C 1 88 286 0.06000 0.02807 0.00008 0.36000 0.08421 0.00003 99 0 0 C 1

285 286 0.00001 0.00001 0.00000 0.00006 0.00003 0.00000 99 0 0 OL 1

285 90 0.04500 0.02070 0.00006 0.27000 0.06210 0.00002 99 0 0 C 1 90 91 0.07645 0.13554 0.00000 0.45870 0.40662 0.00000 99 0 0 OL 1

91 92 0.14750 0.07500 0.00000 0.88500 0.22500 0.00000 99 0 0 OL 1

91 93 0.03058 0.05421 0.00000 0.18348 0.16263 0.00000 99 0 0 OL 1 93 101 0.16430 0.19791 0.00000 0.98580 0.59373 0.00000 99 0 0 OL 1

101 102 0.38350 0.19500 0.00000 2.30100 0.58500 0.00000 99 0 0 OL 1

101 103 0.05868 0.07068 0.00000 0.35208 0.21204 0.00000 99 0 0 OL 1 103 104 0.10562 0.12723 0.00000 0.63372 0.38169 0.00000 99 0 0 OL 1

104 105 0.14750 0.07500 0.00000 0.88500 0.22500 0.00000 99 0 0 OL 1

104 106 0.10500 0.10150 0.00000 0.63000 0.30450 0.00000 99 0 0 OL 1 106 107 0.18000 0.17400 0.00000 1.08000 0.52200 0.00000 99 0 0 OL 1

107 108 0.09000 0.08700 0.00000 0.54000 0.26100 0.00000 99 0 0 OL 1

108 109 0.11800 0.06000 0.00000 0.70800 0.06300 0.00000 99 0 0 OL 1 109 110 0.21211 0.02603 0.00003 1.27266 0.07809 0.00001 99 0 0 C 1

108 111 0.15085 0.13090 0.00000 0.90510 0.39270 0.00000 99 0 0 OL 1

111 112 0.17240 0.11782 0.00000 1.03440 0.35346 0.00000 99 0 0 OL 1 112 113 0.14750 0.08120 0.00000 0.88500 0.24360 0.00000 99 0 0 OL 1

112 114 0.08620 0.05891 0.00000 0.51720 0.17673 0.00000 99 0 0 OL 1

114 115 0.38789 0.26509 0.00000 2.32734 0.79527 0.00000 99 0 0 OL 1 115 116 0.47200 0.24000 0.00000 2.83200 0.72000 0.00000 99 0 0 OL 1

116 117 0.23600 0.12000 0.00000 1.41600 0.36000 0.00000 99 0 0 OL 1

117 118 0.23600 0.12000 0.00000 1.41600 0.36000 0.00000 99 0 0 OL 1 117 119 0.17700 0.09000 0.00000 1.06200 0.27000 0.00000 99 0 0 OL 1

115 120 0.17240 0.11782 0.00000 1.03440 0.35346 0.00000 99 0 0 OL 1

120 121 0.05449 0.00802 0.00001 0.32694 0.02406 0.00000 99 0 0 C 1 121 122 0.05449 0.00802 0.00001 0.32694 0.02406 0.00000 99 0 0 C 1

121 123 0.05449 0.00802 0.00001 0.32694 0.02406 0.00000 99 0 0 C 1

123 124 0.20650 0.10500 0.00000 1.23900 0.31500 0.00000 99 0 0 OL 1 124 125 0.41300 0.21000 0.00000 2.47800 0.63000 0.00000 99 0 0 OL 1

125 126 0.17700 0.09000 0.00000 1.06200 0.27000 0.00000 99 0 0 OL 1

126 127 0.20680 0.10500 0.00000 1.23900 0.31500 0.00000 99 0 0 OL 1 81 82 0.03760 0.01438 0.00004 0.22560 0.04314 0.00001 99 0 0 C 1

82 83 0.21550 0.14727 0.00000 1.29300 0.44181 0.00000 99 0 0 OL 1

83 84 0.12930 0.08836 0.00000 0.77580 0.26508 0.00000 99 0 0 OL 1 84 85 0.21550 0.14727 0.00000 1.29300 0.44181 0.00000 99 0 0 OL 1

85 86 0.17240 0.11782 0.00000 1.03440 0.35346 0.00000 99 0 0 OL 1

87 229 0.16818 0.29818 0.00000 1.00908 0.89454 0.00000 99 0 0 OL 1 93 94 0.14750 0.07500 0.00000 0.88500 0.22500 0.00000 99 0 0 OL 1

94 95 0.29500 0.15000 0.00000 1.77000 0.45000 0.00000 99 0 0 OL 1 95 96 0.11800 0.06000 0.00000 0.70800 0.18000 0.00000 99 0 0 OL 1

95 97 0.23600 0.12000 0.00000 1.41600 0.36000 0.00000 99 0 0 OL 1

97 100 0.26550 0.13500 0.00000 1.59300 0.40500 0.00000 99 0 0 OL 1 97 98 0.17700 0.09000 0.00000 1.06200 0.27000 0.00000 99 0 0 OL 1

98 99 0.29500 0.15000 0.00000 1.77000 0.45000 0.00000 99 0 0 OL 1

258 272 0.00879 0.02175 0.00455 0.05274 0.06525 0.00152 99 0 0 C 1 239 264 0.04180 0.11780 0.00120 0.25080 0.35340 0.00040 99 0 0 C 1

231 223 0.04879 0.05058 0.00024 0.29274 0.15174 0.00008 99 0 0 C 1

223 150 0.09755 0.33284 0.00000 0.58530 0.99852 0.00000 99 0 0 OL 1 150 151 0.17322 0.07589 0.00000 1.03932 0.22767 0.00000 99 0 0 OL 1

150 148 0.21000 0.20300 0.00000 1.26000 0.60900 0.00000 99 0 0 OL 1

148 149 0.24510 0.10624 0.00000 1.47060 0.31872 0.00000 99 0 0 OL 1 148 146 0.25860 0.17673 0.00000 1.55160 0.53019 0.00000 99 0 0 OL 1

146 147 0.34645 0.15178 0.00000 2.07870 0.45534 0.00000 99 0 0 OL 1

146 145 0.12930 0.08836 0.00000 0.77580 0.26508 0.00000 99 0 0 OL 1 145 152 0.29500 0.15000 0.00000 1.77000 0.45000 0.00000 99 0 0 OL 1

145 144 0.30169 0.20618 0.00000 1.80140 0.61854 0.00000 99 0 0 OL 1

144 142 0.19395 0.13255 0.00000 1.16370 0.39765 0.00000 99 0 0 OL 1 142 143 0.17322 0.07589 0.00000 1.03932 0.22767 0.00000 99 0 0 OL 1

142 140 0.23705 0.16200 0.00000 1.42230 0.48600 0.00000 99 0 0 OL 1

140 141 0.20787 0.09107 0.00000 1.24722 0.27321 0.00000 99 0 0 OL 1


181 |

140 138 0.25860 0.17673 0.00000 1.55160 0.53019 0.00000 99 0 0 OL 1

138 139 0.13858 0.06071 0.00000 0.83148 0.18213 0.00000 99 0 0 OL 1 138 130 0.12930 0.08836 0.00000 0.77580 0.26508 0.00000 99 0 0 OL 1

130 131 0.21550 0.14727 0.00000 1.29300 0.44181 0.00000 99 0 0 OL 1 130 128 0.17240 0.11782 0.00000 1.03440 0.35346 0.00000 99 0 0 OL 1

128 129 0.10775 0.07364 0.00000 0.64650 0.22092 0.00000 99 0 0 OL 1

231 77 0.05489 0.05690 0.00270 0.32934 0.17070 0.00090 99 0 0 C 1 77 224 0.03881 0.10400 0.00000 0.23286 0.31200 0.00000 99 0 0 OL 1

214 215 0.12930 0.08836 0.00000 0.77580 0.26508 0.00000 99 0 0 OL 1

215 216 0.19395 0.13255 0.00000 1.16370 0.39765 0.00000 99 0 0 OL 1 216 170 0.25860 0.17673 0.00000 1.55160 0.53019 0.00000 99 0 0 OL 1

170 171 0.06465 0.04418 0.00000 0.38790 0.13254 0.00000 99 0 0 OL 1

171 172 0.27244 0.04012 0.00006 1.63464 0.12036 0.00002 99 0 0 C 1 172 173 0.16346 0.02407 0.00000 0.98076 0.07221 0.00000 99 0 0 OL 1

173 174 0.08620 0.05891 0.00000 0.51720 0.17673 0.00000 99 0 0 OL 1

174 175 0.15085 0.10309 0.00000 0.90510 0.30927 0.00000 99 0 0 OL 1 175 176 0.27244 0.04012 0.00006 1.63464 0.12036 0.00002 99 0 0 C 1

216 217 0.27716 0.12142 0.00000 1.66296 0.36429 0.00000 99 0 0 OL 1

217 218 0.48502 0.21249 0.00000 2.91012 1.27494 0.00000 99 0 0 OL 1 218 219 0.22621 0.04686 0.00009 1.35726 0.14058 0.00003 99 0 0 C 1

152 153 0.20787 0.09107 0.00000 1.24722 0.27321 0.00000 99 0 0 OL 1

152 154 0.35400 0.18000 0.00000 2.12400 0.54000 0.00000 99 0 0 OL 1 154 155 0.24251 0.10624 0.00000 1.45506 0.31872 0.00000 99 0 0 OL 1

154 156 0.27716 0.12142 0.00000 1.66296 0.36426 0.00000 99 0 0 OL 1

156 157 0.25860 0.17673 0.00000 1.55160 0.53019 0.00000 99 0 0 OL 1 157 158 0.31180 0.13660 0.00000 1.87080 0.40980 0.00000 99 0 0 OL 1

156 159 0.11149 0.07376 0.00000 0.66894 0.22128 0.00000 99 0 0 OL 1

159 160 0.34612 0.20653 0.00000 2.07672 0.61959 0.00000 99 0 0 OL 1 160 161 0.15608 0.10326 0.00000 0.93648 0.30978 0.00000 99 0 0 OL 1

161 162 0.22298 0.14752 0.00000 1.33788 0.44256 0.00000 99 0 0 OL 1

162 163 0.21350 0.09126 0.00000 1.28100 0.27378 0.00000 99 0 0 OL 1 160 164 0.34479 0.23564 0.00000 2.06874 0.70692 0.00000 99 0 0 OL 1

164 165 0.12930 0.08836 0.00000 0.77580 0.26508 0.00000 99 0 0 OL 1

165 166 0.11800 0.06000 0.00000 0.70800 0.18000 0.00000 99 0 0 OL 1 166 167 0.20787 0.09107 0.00000 1.24722 0.27321 0.00000 99 0 0 OL 1

166 168 0.23600 0.12000 0.00000 1.41600 0.36000 0.00000 99 0 0 OL 1

168 169 0.17700 0.09000 0.00000 1.06200 0.27000 0.00000 99 0 0 OL 1 169 179 0.09401 0.03595 0.00009 0.56406 0.10785 0.00003 99 0 0 C 1

179 180 0.17700 0.09000 0.00000 1.06200 0.27000 0.00000 99 0 0 OL 1

180 181 0.23600 0.12000 0.00000 1.41600 0.36000 0.00000 99 0 0 OL 1 180 182 0.35400 0.18000 0.00000 2.12400 0.54000 0.00000 99 0 0 OL 1

182 183 0.35400 0.18000 0.00000 2.12400 0.54000 0.00000 99 0 0 OL 1

182 184 0.27716 0.12142 0.00000 1.66296 0.36426 0.00000 99 0 0 OL 1 184 185 0.21350 0.09126 0.00000 1.28100 0.27378 0.00000 99 0 0 OL 1

184 186 0.53374 0.22816 0.00000 3.20244 0.68448 0.00000 99 0 0 OL 1

131 132 0.19395 0.13255 0.00000 1.16370 0.39765 0.00000 99 0 0 OL 1 132 133 0.30169 0.20618 0.00000 1.81014 0.61854 0.00000 99 0 0 OL 1

133 134 0.09000 0.08700 0.00000 0.54000 0.26100 0.00000 99 0 0 OL 1

134 135 0.13161 0.05033 0.00000 0.78966 0.15099 0.00000 99 0 0 OL 1 134 136 0.36000 0.34800 0.00000 2.16000 1.04400 0.00000 99 0 0 OL 1

136 137 0.12000 0.11600 0.00000 0.72000 0.34800 0.00000 99 0 0 OL 1

165 187 0.17240 0.11782 0.00000 0.03440 0.35346 0.00000 99 0 0 OL 1 187 188 0.20787 0.09107 0.00000 1.24722 0.27321 0.00000 99 0 0 OL 1

188 189 0.27716 0.12142 0.00000 1.66296 0.36426 0.00000 99 0 0 OL 1 188 190 0.41574 0.18213 0.00000 2.49440 0.54639 0.00000 99 0 0 OL 1

190 191 0.27716 0.12142 0.00000 1.66296 0.36426 0.00000 99 0 0 OL 1

187 192 0.30169 0.20618 0.00000 1.81014 0.61854 0.00000 99 0 0 OL 1 192 209 0.25860 0.17673 0.00000 1.55160 0.53019 0.00000 99 0 0 OL 1

209 210 0.12930 0.08836 0.00000 0.77580 0.26508 0.00000 99 0 0 OL 1

210 215 0.21550 0.14727 0.00000 1.29300 0.44181 0.00000 99 0 0 OL 1 210 211 0.18258 0.07622 0.00000 1.09548 0.22866 0.00000 99 0 0 OL 1

211 212 0.29213 0.12195 0.00000 1.75278 0.36585 0.00000 99 0 0 OL 1

212 213 0.43820 0.17673 0.00000 2.62920 0.53019 0.00000 99 0 0 OL 1 192 193 0.36517 0.15244 0.00000 2.19102 0.45732 0.00000 99 0 0 OL 1

193 196 0.14607 0.06098 0.00000 0.87642 0.18294 0.00000 99 0 0 OL 1

193 194 0.17322 0.07589 0.00000 1.03932 0.22767 0.00000 99 0 0 OL 1 194 195 0.31180 0.13660 0.00000 1.87080 0.40980 0.00000 99 0 0 OL 1

196 197 0.25562 0.10671 0.00000 1.53372 0.32013 0.00000 99 0 0 OL 1

197 198 0.20787 0.09107 0.00000 1.24722 0.27321 0.00000 99 0 0 OL 1 197 199 0.18258 0.07622 0.00000 1.09548 0.22866 0.00000 99 0 0 OL 1

201 202 0.09401 0.03595 0.00009 0.56406 0.10785 0.00003 99 0 0 C 1

201 203 0.43820 0.18293 0.00000 2.62920 0.54879 0.00000 99 0 0 OL 1 203 204 0.21910 0.09146 0.00000 1.31460 0.27447 0.00000 99 0 0 OL 1

204 205 0.07521 0.02876 0.00007 0.45126 0.08628 0.00002 99 0 0 C 1

205 206 0.14607 0.06098 0.00000 0.87642 0.18294 0.00000 99 0 0 OL 1


182 |

206 207 0.29213 0.12195 0.00000 1.75278 0.36585 0.00000 99 0 0 OL 1

206 208 0.40168 0.16768 0.00000 2.41008 0.50304 0.00000 99 0 0 OL 1 245 249 0.04356 0.20100 0.00022 0.26136 0.60300 0.00007 99 0 0 C 1

199 200 0.29213 0.12195 0.00000 1.75278 0.36585 0.00000 99 0 0 OL 1 200 201 0.25562 0.10671 0.00000 1.53372 0.32013 0.00000 99 0 0 OL 1

234 237 0.03600 0.38510 0.00004 0.21600 1.15530 0.00001 99 0 0 C 1

235 238 0.36300 0.03851 0.00004 0.21780 0.11553 0.00001 99 0 0 C 1 176 177 0.49039 0.07222 0.00012 2.94234 0.21666 0.00004 99 0 0 C 1

Table A-14 Transformer data of the Generic Distribution System (GDS)


Status A B C

294 295 0.00010 0.01000 0.00000 Wye Wye 1.00 0 99 0 0 1

234 294 0.00330 0.14660 0.00000 Wye Wye 1.00 0 99 0 0 1

293 295 0.00010 0.01000 0.00000 Wye Wye 1.00 0 99 0 0 1 235 293 0.00333 0.14667 0.00000 Wye Wye 1.00 0 99 0 0 1

248 278 0.00833 0.30000 0.00000 Delta Wye 1.00 30 99 0 0 1

249 279 0.00833 0.30000 0.00000 Delta Wye 1.00 30 99 0 0 1 255 292 0.00417 0.18333 0.00000 Wye Wye 1.00 0 99 0 0 1

292 295 0.00010 0.01000 0.00000 Wye Wye 1.00 0 99 0 0 1

256 291 0.00417 0.18333 0.00000 Wye Wye 1.00 0 99 0 0 1 291 295 0.00010 0.01000 0.00000 Wye Wye 1.00 0 99 0 0 1

257 290 0.00556 0.22222 0.00000 Wye Wye 1.00 0 99 0 0 1

290 295 0.00010 0.01000 0.00000 Wye Wye 1.00 0 99 0 0 1 258 289 0.00278 0.01380 0.00000 Wye Wye 1.00 0 99 0 0 1

289 295 0.00005 0.00500 0.00000 Wye Wye 1.00 0 99 0 0 1

228 265 0.01587 0.44440 0.00000 Wye Wye 1.00 0 99 0 0 1 227 264 0.01587 0.44440 0.00000 Wye Wye 1.00 0 99 0 0 1

245 254 0.01250 0.40000 0.00000 Delta Wye 1.00 30 99 0 0 1 244 275 0.01250 0.40000 0.00000 Delta Wye 1.00 30 99 0 0 1

243 271 0.01250 0.40000 0.00000 Delta Wye 1.25 30 99 0 0 1


247 277 0.02500 0.55000 0.00000 Delta Wye 1.00 30 99 0 0 1

288 295 0.00010 0.01000 0.00000 Wye Wye 1.00 0 99 0 0 1 259 288 0.00208 0.10000 0.00000 Wye Wye 1.00 0 99 0 0 1

287 295 0.00005 0.00500 0.00000 Wye Wye 1.00 0 99 0 0 1

260 287 0.00104 0.05000 0.00000 Wye Wye 1.00 0 99 0 0 1 250 273 0.00833 0.30000 0.00000 Delta Wye 1.25 30 99 0 0 1

251 263 0.00833 0.30000 0.00000 Delta Wye 1.00 30 99 0 0 1

229 269 0.03333 0.60000 0.00000 Wye Delta 1.00 -30 99 0 0 1 230 270 0.03333 0.60000 0.00000 Wye Delta 1.00 -30 99 0 0 1

232 268 0.06667 0.80000 0.00000 Wye Delta 1.00 -30 99 0 0 1

231 267 0.06667 0.80000 0.00000 Wye Delta 1.00 -30 99 0 0 1 241 274 0.02500 0.55000 0.00000 Delta Wye 1.00 30 99 0 0 1

233 266 0.06667 0.80000 0.00000 Wye Delta 1.05 -30 99 0 0 1


282 240 0.02142 0.17143 0.00000 Delta Wye 0.95 30 99 0 0 1


Appendix B • Minimization of SMEE by greedy monitor placement

183 |

Appendix B Minimization of SMEE by

greedy monitor placement


184 |

Nu

m.

Bu

ses

SM

EE

A

SM

EE

B

SM

EE

C

SM

EE

AB

C

Std

. d

ev.

A

Std

. d

ev.

B

Std

. d

ev.

C

Std

. d

ev.

AB

C

Max

.

A

Max

.

B

Max

.

C

Max

.

AB

C

Over

all

net

work

cover

age

(%)

LG

fau

lts

net

work

cover

age

(%)

LL

fau

lts

net

work

cover

age

(%)

LL

G f

ault

s

net

work

cover

age

(%)

LL

L f

ault

s

net

work

cover

age

(%)

1

223

49.0

9

51.7

0

51.8

0

50.8

7

4.9

5

5.4

4

5.9

6

5.4

0

60.2

5

66.4

2

64.9

3

62.8

5

9.5

3

33.0

9

2.2

8

0.4

8

2.2

8

2

229

39.2

9

40.8

8

40.4

6

40.2

1

1.9

5

3.4

2

3.0

3

2.7

8

42.6

3

47.5

9

46.2

3

45.4

5

26.2

0

52.1

6

26.0

2

0.6

0

26.0

2

3

290

32.7

7

35.1

9

34.6

0

34.1

9

2.0

1

3.6

1

3.2

6

2.9

4

36.2

9

41.4

8

40.1

0

39.2

6

32.6

7

76.2

6

26.3

8

1.6

8

26.3

8

4

16

27.2

8

29.8

9

29.2

3

28.8

0

2.3

4

3.8

8

3.5

2

3.2

4

32.0

2

36.7

3

35.2

6

34.6

5

39.6

9

90.6

5

33.2

1

1.6

8

33.2

1

5

238

13.6

5

15.9

6

15.4

2

15.0

1

3.0

6

3.8

6

3.4

7

3.4

1

22.0

6

22.7

8

21.3

4

22.0

4

41.7

6

98.2

0

33.2

1

2.4

0

33.2

1

6

246

9.9

3

12.1

3

11.5

9

11.2

2

3.3

2

3.8

7

3.4

8

3.4

9

19.4

8

18.9

6

17.5

3

18.6

4

41.9

4

98.5

6

33.2

1

2.7

6

33.2

1

7

239

3.7

9

5.8

1

5.2

7

4.9

5

3.7

6

3.8

8

3.4

9

3.6

1

15.2

4

12.6

5

11.2

2

13.0

2

42.1

2

98.9

2

33.2

1

3.1

2

33.2

1

8

214

2.7

3

4.5

4

4.2

2

3.8

3

3.1

2

3.7

6

3.4

3

3.3

3

19.8

6

16.1

1

14.2

7

15.9

5

56.5

9

99.2

8

52.2

8

22.4

2

52.4

0

9

67

1.8

9

2.9

0

2.8

7

2.5

6

2.7

5

2.8

4

2.7

8

2.5

5

26.9

4

11.5

2

11.2

9

11.2

9

65.7

4

99.6

4

61.5

1

40.1

7

61.6

3

10

126

1.3

1

2.2

9

2.4

0

2.0

0

2.4

4

2.2

5

2.1

0

1.9

4

27.8

1

9.1

1

8.5

0

12.5

4

76.3

8

99.6

4

74.3

4

57.0

7

74.4

6

11

75

1.1

7

1.7

5

2.1

2

1.6

8

2.5

0

1.7

0

1.7

0

1.7

3

28.1

0

6.1

5

6.4

3

13.1

0

79.8

3

99.6

4

77.1

0

65.3

5

77.2

2

12

236

1.1

3

1.7

1

1.7

8

1.5

4

2.5

1

1.9

4

1.9

9

1.9

2

28.0

8

6.6

6

6.9

2

13.3

9

81.5

3

99.6

4

77.1

0

72.1

8

77.2

2

13

137

0.8

4

1.6

9

1.7

4

1.4

2

1.0

6

2.0

9

2.1

3

1.7

5

4.2

4

7.5

6

7.8

3

6.5

4

84.1

7

100

.00

80.3

4

75.9

0

80.4

6

14

65

0.7

6

1.5

3

1.6

5

1.3

1

1.1

9

2.3

0

2.3

8

1.9

4

4.8

5

8.5

1

8.8

3

7.3

9

86.1

8

100

.00

83.0

9

78.4

2

83.2

1

15

42

0.7

3

1.3

8

1.4

7

1.1

9

1.3

8

2.6

0

2.7

5

2.2

4

5.7

1

10.7

6

11.2

0

9.2

2

88.9

7

100

.00

85.6

1

84.5

3

85.7

3

16

186

0.6

6

1.2

5

1.3

5

1.0

9

1.4

0

2.6

3

2.7

8

2.2

7

6.2

4

11.8

6

12.2

3

10.1

1

90.8

6

100

.00

88.1

3

87.0

5

88.2

5

17

208

0.5

7

1.1

1

1.2

1

0.9

7

1.3

1

2.5

1

2.6

6

2.1

6

6.5

2

12.5

4

13.4

1

10.7

2

93.2

0

100

.00

91.2

5

90.1

7

91.3

7

18

176

0.5

0

0.9

0

1.0

1

0.8

0

1.2

2

2.2

9

2.4

1

1.9

7

6.2

2

11.8

5

12.4

4

10.1

7

95.8

6

100

.00

94.6

0

94.2

4

94.6

0

19

189

0.4

3

0.8

1

0.8

8

0.7

1

1.3

6

2.5

5

2.6

8

2.2

0

7.0

0

13.2

8

13.9

4

11.4

1

96.3

1

100

.00

95.2

0

94.8

4

95.2

0

20

35

0.4

1

0.7

7

0.8

5

0.6

7

1.3

2

2.4

2

2.5

6

2.1

0

8.2

5

15.7

2

16.4

9

13.4

8

97.2

1

100

.00

96.4

0

96.0

4

96.4

0

21

69

0.4

1

0.7

5

0.8

3

0.6

6

1.3

2

2.4

6

2.6

0

2.1

2

8.2

4

16.1

0

16.8

7

13.7

3

97.2

7

100

.00

96.4

0

96.2

8

96.4

0

22

119

0.4

4

0.7

9

0.8

9

0.7

1

1.5

4

2.8

8

3.0

6

2.4

9

9.8

9

19.6

3

20.5

9

16.7

0

97.7

5

100

.00

97.0

0

97.0

0

97.0

0

23

99

0.6

0

1.0

4

1.2

0

0.9

4

2.3

3

4.3

6

4.7

2

3.8

0

19.0

0

36.4

2

38.1

3

31.1

7

98.8

0

100

.00

98.4

4

98.3

2

98.4

4

24

1

2.8

9

4.6

7

4.6

2

4.0

6

3.4

5

5.4

1

5.5

5

4.7

8

27.8

1

48.6

0

48.3

1

41.5

7

99.0

7

100

.00

98.8

0

98.6

8

98.8

0

25

9

0.0

0

0.0

0

0.0

0

0.0

0

0.0

0

0.0

0

0.0

0

0.0

0

0.0

0

0.0

0

0.0

0

0.0

0

100

.00

100

.00

100

.00

100

.00

100

.00

Tab

le B

-1

Gre

edy

mon

ito

r p

lace

men

t w

ith

min

imiz

atio

n o

f sa

g m

agn

itu

de

esti

mat

ion

err

or

(SM

EE

) fo

r al

l ty

pes

of

fau

lts


185 |

Nu

m.

Buse

s S

ME

E

A

SM

EE

B

SM

EE

C

SM

EE

AB

C

Std

.

dev

.

A

Std

.

dev

.

B

Std

.

dev

.

C

Std

.

dev

.

AB

C

Max

.

A

Max

.

B

Max

.

C

Max

.

AB

C

Net

wo

rk

cover

age

(%)

1

66

0.3

0

9.1

1

10

.08

6.4

9

0.4

7

5.2

4

5.9

6

3.0

5

3.9

6

48

.66

19

.47

18

.17

0.9

6

2

16

0.0

2

1.8

9

0.7

9

0.9

0

0.0

6

1.6

0

0.5

9

0.7

2

0.4

2

5.1

0

1.8

5

2.2

8

34

.53

3

20

7

0.0

2

1.1

7

0.5

4

0.5

8

0.0

8

1.1

9

0.5

1

0.5

5

0.6

2

6.2

3

1.9

3

2.3

9

56

.12

4

35

0.0

2

0.8

2

0.3

4

0.3

9

0.0

8

1.0

9

0.4

0

0.4

9

0.6

7

7.2

0

1.3

7

2.7

4

62

.83

5

98

0.0

1

0.3

5

0.1

9

0.1

8

0.0

2

0.3

5

0.1

9

0.1

8

0.1

5

2.1

7

0.9

3

1.0

0

72

.78

6

74

0.0

0

0.2

4

0.1

3

0.1

2

0.0

1

0.1

9

0.1

0

0.1

0

0.0

7

0.8

7

0.4

4

0.4

2

75

.54

7

39

0.0

0

0.2

0

0.1

1

0.1

0

0.0

1

0.2

1

0.1

1

0.1

1

0.0

7

0.9

4

0.4

9

0.4

4

78

.06

8

17

7

0.0

0

0.1

7

0.0

9

0.0

9

0.0

1

0.2

2

0.1

1

0.1

1

0.1

0

1.2

2

0.5

2

0.5

8

83

.21

9

11

9

0.0

0

0.1

1

0.0

8

0.0

6

0.0

0

0.1

4

0.1

1

0.0

8

0.0

2

0.5

2

0.5

5

0.3

3

89

.57

10

67

0.0

0

0.0

9

0.0

6

0.0

5

0.0

0

0.1

2

0.1

0

0.0

7

0.0

1

0.5

4

0.4

8

0.3

4

91

.37

11

13

5

0.0

0

0.0

6

0.0

5

0.0

4

0.0

0

0.1

0

0.0

9

0.0

6

0.0

1

0.5

5

0.4

9

0.3

5

94

.60

12

19

1

0.0

0

0.0

7

0.0

6

0.0

4

0.0

0

0.1

1

0.1

0

0.0

7

0.0

1

0.6

2

0.5

5

0.3

9

95

.20

13

12

3

0.0

0

0.0

8

0.0

6

0.0

5

0.0

0

0.1

3

0.1

2

0.0

8

0.0

1

0.7

3

0.6

5

0.4

6

95

.92

14

18

6

0.0

0

0.1

2

0.1

1

0.0

8

0.0

0

0.2

9

0.2

8

0.1

9

0.0

3

1.9

1

1.6

9

1.2

0

98

.44

15

1

0.0

9

2.4

0

2.0

7

1.5

2

0.2

9

0.6

8

0.6

7

0.2

5

2.3

3

4.3

7

2.6

0

1.8

9

98

.80

16

11

0.0

0

0.0

0

0.0

0

0.0

0

0.0

0

0.0

0

0.0

0

0.0

0

0.0

0

0.0

0

0.0

0

0.0

0

10

0.0

0

Tab

le B

-2

Gre

edy

mon

ito

r p

lace

men

t w

ith

min

imiz

atio

n o

f sa

g m

agn

itu

de

esti

mat

ion

err

or

(SM

EE

) fo

r li

ne

to l

ine

fau

lts


186 |

Nu

m.

Buse

s S

ME

E

A

SM

EE

B

SM

EE

C

SM

EE

AB

C

Std

.

dev

.

A

Std

.

dev

.

B

Std

.

dev

.

C

Std

.

dev

.

AB

C

Max

.

A

Max

.

B

Max

.

C

Max

.

AB

C

Net

wo

rk

cover

age

(%)

1

13

5

66

.57

69

.73

69

.57

68

.62

0.4

3

5.5

8

5.3

0

3.7

7

67

.54

83

.02

81

.81

77

.42

0.1

2

2

25

7

43

.42

49

.85

49

.13

47

.47

0.4

6

6.5

3

6.0

7

4.3

2

44

.24

64

.53

61

.14

56

.58

0.8

4

3

87

25

.11

32

.22

31

.41

29

.58

1.4

7

6.0

0

5.6

3

4.0

3

29

.12

45

.39

41

.99

37

.44

0.8

4

4

74

10

.84

19

.08

18

.02

15

.98

1.4

8

5.3

8

5.0

9

3.6

0

14

.95

30

.99

27

.56

23

.02

0.8

4

5

23

8

3.3

2

11

.84

11

.23

8.8

0

1.5

1

5.2

6

4.9

8

3.5

4

7.4

9

23

.65

20

.29

15

.63

1.5

6

6

1

2.6

3

9.1

8

9.0

4

6.9

5

1.7

1

5.7

1

5.5

2

4.0

1

7.1

7

20

.54

19

.23

14

.07

13

.43

7

22

4

2.7

0

8.0

5

8.1

3

6.2

9

2.0

5

5.4

4

5.4

1

4.0

4

8.1

0

18

.17

18

.11

14

.26

23

.62

8

98

1.8

1

7.4

0

7.6

2

5.6

1

0.4

9

5.9

6

5.5

6

3.9

6

3.3

5

21

.03

19

.62

14

.59

35

.49

9

24

7

1.2

6

6.8

8

7.1

0

5.0

8

0.4

9

5.9

9

5.5

9

3.9

8

2.8

0

20

.59

19

.17

14

.11

35

.85

10

23

9

0.7

0

6.3

5

6.5

8

4.5

4

0.4

9

6.0

3

5.6

2

4.0

0

2.2

6

20

.14

18

.72

13

.62

36

.21

11

16

0.4

2

5.3

2

6.1

3

3.9

6

0.3

2

5.9

1

5.6

0

3.9

1

1.2

3

20

.28

19

.63

13

.65

44

.48

12

20

8

0.3

9

3.8

6

5.0

2

3.0

9

0.3

1

4.2

2

4.2

0

2.8

2

1.4

5

17

.47

15

.83

11

.42

58

.99

13

24

0

0.2

4

3.8

0

3.8

7

2.6

4

0.3

6

5.1

3

4.7

1

3.3

6

1.6

0

20

.67

17

.87

13

.37

65

.83

14

37

0.2

3

3.6

8

3.5

9

2.5

0

0.4

3

6.0

3

5.4

3

3.9

3

1.9

4

25

.13

21

.69

16

.24

71

.94

15

69

0.3

7

3.2

7

3.4

3

2.3

6

0.2

1

4.7

4

5.0

6

3.3

1

1.3

2

18

.08

19

.80

12

.46

78

.78

16

10

0.1

3

2.9

7

3.1

6

2.0

9

0.2

4

5.0

5

5.3

9

3.5

3

1.2

8

18

.84

20

.67

12

.90

80

.10

17

21

8

0.1

4

2.9

0

2.9

8

2.0

0

0.3

3

5.8

3

5.7

8

3.9

5

1.8

2

26

.73

26

.85

18

.24

85

.97

18

18

6

0.1

6

2.7

8

2.7

3

1.8

9

0.4

0

6.9

3

6.7

7

4.6

7

2.2

2

32

.57

32

.72

22

.23

88

.49

19

12

5

0.1

7

2.3

8

2.3

6

1.6

3

0.7

3

7.5

7

6.4

7

4.8

7

5.0

7

52

.08

38

.21

31

.45

94

.96

20

66

0.0

2

1.8

1

2.2

9

1.3

7

0.0

4

6.7

8

7.0

2

4.5

9

0.1

9

44

.82

45

.36

30

.08

97

.48

21

19

0

0.0

2

1.6

7

1.7

0

1.1

3

0.0

5

8.5

5

8.7

0

5.7

5

0.2

5

58

.83

59

.53

39

.48

98

.08

22

34

0.0

5

1.3

2

1.3

3

0.9

0

0.1

4

8.3

3

8.4

7

5.6

2

0.6

8

88

.34

89

.19

59

.36

99

.28

23

11

8

0.0

0

0.0

0

0.0

0

0.0

0

0.0

0

0.0

0

0.0

0

0.0

0

0.0

0

0.0

0

0.0

0

0.0

0

10

0.0

0

Tab

le B

-3

Gre

edy

mon

ito

r p

lace

men

t w

ith

min

imiz

atio

n o

f sa

g m

agn

itu

de

esti

mat

ion

err

or

(SM

EE

) fo

r li

ne

to l

ine

to g

rou

nd

fau

lts


187 |

Nu

m.

Buse

s S

ME

E

A

SM

EE

B

SM

EE

C

SM

EE

AB

C

Std

.

dev

.

A

Std

.

dev

.

B

Std

.

dev

.

C

Std

.

dev

.

AB

C

Max

.

A

Max

.

B

Max

.

C

Max

.

AB

C

Net

wo

rk

cover

age

(%)

1

98

30

.61

30

.61

30

.61

30

.61

11

.17

11

.17

11

.17

11

.17

5

7.2

4

57

.24

57

.24

57

.24

1.4

4

2

19

0

7.6

2

7.6

2

7.6

2

7.6

2

8.3

0

8.3

0

8.3

0

8.3

0

28

.22

28

.22

2

8.2

2

28

.22

47

.48

3

17

6.0

2

6.0

2

6.0

2

6.0

2

7.9

3

7.9

3

7.9

3

7.9

3

32

.18

32

.18

3

2.1

8

32

.18

54

.32

4

34

3.9

3

3.9

3

3.9

3

3.9

3

4.5

7

4.5

7

4.5

7

4.5

7

16

.39

16

.39

1

6.3

9

16

.39

63

.31

5

20

8

3.3

5

3.3

5

3.3

5

3.3

5

3.7

7

3.7

7

3.7

7

3.7

7

14

.65

14

.65

1

4.6

5

14

.65

70

.62

6

12

4

3.2

4

3.2

4

3.2

4

3.2

4

3.9

5

3.9

5

3.9

5

3.9

5

15

.57

15

.57

1

5.5

7

15

.57

77

.10

7

18

5

3.1

4

3.1

4

3.1

4

3.1

4

4.1

6

4.1

6

4.1

6

4.1

6

15

.83

15

.83

1

5.8

3

15

.83

79

.62

8

17

3

3.0

3

3.0

3

3.0

3

3.0

3

4.6

0

4.6

0

4.6

0

4.6

0

17

.94

17

.94

1

7.9

4

17

.94

84

.77

9

65

2.8

7

2.8

7

2.8

7

2.8

7

5.1

7

5.1

7

5.1

7

5.1

7

21

.78

21

.78

2

1.7

8

21

.78

87

.53

10

76

2.6

5

2.6

5

2.6

5

2.6

5

5.6

9

5.6

9

5.6

9

5.6

9

27

.91

27

.91

2

7.9

1

27

.91

90

.29

11

13

5

2.2

7

2.2

7

2.2

7

2.2

7

5.1

7

5.1

7

5.1

7

5.1

7

21

.77

21

.77

21

.77

21

.77

93

.53

12

49

1.7

5

1.7

5

1.7

5

1.7

5

5.7

0

5.7

0

5.7

0

5.7

0

34

.62

34

.62

3

4.6

2

34

.62

96

.04

13

11

8

1.9

0

1.9

0

1.9

0

1.9

0

6.6

0

6.6

0

6.6

0

6.6

0

40

.80

40

.80

4

0.8

0

40

.80

96

.64

14

67

2.3

6

2.3

6

2.3

6

2.3

6

9.2

2

9.2

2

9.2

2

9.2

2

74

.99

74

.99

7

4.9

9

74

.99

98

.44

15

1

6.1

9

6.1

9

6.1

9

6.1

9

9.6

7

9.6

7

9.6

7

9.6

7

89

.24

89

.24

8

9.2

4

89

.24

98

.80

16

10

0.0

0

0.0

0

0.0

0

0.0

0

0.0

0

0.0

0

0.0

0

0.0

0

0.0

0

0.0

0

0.0

0

0.0

0

10

0.0

0

Tab

le B

-4

Gre

edy

mon

ito

r p

lace

men

t w

ith

min

imiz

atio

n o

f sa

g m

agn

itu

de

esti

mat

ion

err

or

(SM

EE

) fo

r th

ree-p

has

e fa

ult

s

Appendix C • Minimization of SEEE by greedy monitor placement

188 |

Appendix C Minimization of SEEE by

greedy monitor placement


189 |

Tab

le C

-1

Min

imiz

atio

n o

f th

e O

ver

all

Sag

Ev

ent

Est

imat

ion

Err

or

(SE

EE

) in

th

e G

DS

Net

wo

rk w

ith

Gre

edy

Mo

nit

or

Pla

cem

ent

N

um

ber

of

buse

s

EN

50

160

ITI

Curv

e

Gen

eral

ized

Sag

Tab

le

SA

RF

I-9

0

SE

MI

F4

7 C

urv

e

SE

EE

S

td.

dev

.

Co

ver

age

(%)

SE

EE

S

td.

dev

.

Co

ver

age

(%)

SE

EE

S

td.

dev

.

Co

ver

age

(%)

SE

EE

S

td.

dev

.

Co

ver

age

(%)

SE

EE

S

td.

dev

.

Co

ver

age

(%)

1

12

3.0

3

57

.53

3.0

0

16

4.7

6

24

.35

9.5

3

26

.11

10

.38

9

.53

18

4.3

9

43

.06

9.5

3

16

2.0

6

22

.31

9.5

3

2

53

.51

28

.51

19

.24

9

5.2

6

5.9

6

26

.20

13

.38

6.4

1

27

.34

92

.93

5.0

1

26

.20

91

.08

8

.17

26

.20

3

36

.78

19

.75

32

.40

4

9.3

1

6.8

4

32

.67

8.2

4

7.2

3

44

.39

46

.81

4.3

7

32

.67

50

.16

7

.68

32

.67

4

25

.04

18

.69

38

.70

2

0.0

0

5.2

0

39

.69

6.1

9

5.7

7

54

.98

19

.56

6.2

0

38

.49

20

.74

6

.10

39

.69

5

16

.16

19

.12

47

.75

8

.09

4.7

1

41

.67

4.6

9

3.8

6

67

.18

6.2

2

4.2

1

40

.47

10

.13

5

.30

41

.76

6

8.6

1

7.6

1

53

.63

3

.60

4.2

4

50

.72

3.6

9

3.5

3

71

.43

2.4

7

3.4

9

46

.22

3.8

9

4.4

8

50

.81

7

5.6

2

4.0

5

64

.21

2

.52

2.8

1

61

.36

2.9

7

3.4

4

75

.96

1.4

7

2.1

8

56

.80

2.8

2

3.0

2

61

.45

8

3.7

4

2.8

3

66

.01

1

.77

2.8

1

61

.54

2.3

3

2.8

3

78

.03

0.6

3

0.6

2

63

.70

2.0

7

3.0

2

61

.63

9

2.1

2

1.9

9

72

.90

1.1

8

1.0

5

65

.14

1.2

1

2.6

8

79

.74

0.1

3

0.4

6

63

.88

1.4

7

1.2

7

65

.23

10

1.0

5

0.6

8

87

.65

0

.67

1.1

2

65

.32

0.6

0

1.1

3

83

.33

0.0

8

0.4

4

65

.68

0.9

6

1.1

4

66

.94

11

0.3

4

0.6

5

87

.83

0

.41

0.5

0

82

.37

0.1

3

0.2

5

85

.97

0.0

5

0.4

2

65

.86

0.4

5

1.1

6

67

.12

12

0.1

0

0.3

1

89

.84

0

.19

0.4

9

84

.17

0.0

5

0.1

2

87

.23

0.0

2

0.1

4

82

.91

0.1

9

0.4

9

84

.17

13

0.0

7

0.2

9

90

.38

0

.01

0.0

9

86

.18

0.0

2

0.0

9

89

.12

0.0

0

0.0

1

88

.31

0.0

1

0.0

9

86

.18

14

0.0

4

0.2

6

90

.53

0

.00

0.0

4

88

.82

0.0

1

0.0

6

91

.76

0.0

0

0.0

1

88

.85

0.0

0

0.0

4

88

.82

15

0.0

1

0.0

5

91

.37

0

.00

0.0

2

89

.72

0.0

0

0.0

2

91

.94

0.0

0

0.0

1

88

.91

0.0

0

0.0

2

89

.72

16

0.0

0

0.0

3

93

.71

0

.00

0.0

0

91

.61

0.0

0

0.0

1

94

.00

0.0

0

0.0

1

89

.36

0.0

0

0.0

0

91

.61

17

0.0

0

0.0

1

94

.60

0

.00

0.0

0

92

.06

0.0

0

0.0

0

96

.34

0.0

0

0.0

1

90

.26

0.0

0

0.0

0

92

.06

18

0.0

0

0.0

1

95

.14

0

.00

0.0

0

94

.39

0.0

0

0.0

0

96

.88

0.0

0

0.0

1

92

.60

0.0

0

0.0

0

94

.39

19

0.0

0

0.0

1

95

.59

0

.00

0.0

0

95

.44

0.0

0

0.0

0

97

.33

0.0

0

0.0

1

93

.65

0.0

0

0.0

0

95

.44

20

0.0

0

0.0

1

96

.64

0

.00

0.0

0

95

.92

0.0

0

0.0

0

98

.38

0.0

0

0.0

1

95

.53

0.0

0

0.0

0

95

.92

21

0.0

0

0.0

1

98

.53

0

.00

0.0

0

98

.56

0.0

0

0.0

0

98

.56

0.0

0

0.0

1

96

.07

0.0

0

0.0

0

98

.56

22

0.0

0

0.0

1

98

.71

0

.00

0.0

0

98

.65

0.0

0

0.0

0

98

.65

0.0

0

0.0

1

98

.71

0.0

0

0.0

0

98

.65

23

0.0

0

0.0

1

98

.80

0

.00

0.0

0

98

.80

0.0

0

0.0

0

98

.80

0.0

0

0.0

1

98

.80

0.0

0

0.0

0

98

.80

24

0.8

6

0.2

9

99

.07

0

.67

0.3

0

99

.07

0.0

3

0.0

8

99

.07

0.8

5

0.3

5

99

.07

0.4

0

0.2

9

99

.07

25

0.0

0

0.0

0

10

0.0

0

0.0

0

0.0

0

10

0.0

0

0.0

0

0.0

0

10

0.0

0

0.0

0

0.0

0

10

0.0

0

0.0

0

0.0

0

10

0.0

0


190 |

Table C-2 Minimization of the Sag Event Estimation Error (SEEE)for Sags as Classified by EN 50160

Num. Buses SEEE Std.

dev. Max.

Network coverage (%)

LG LL LLG LLL All

1 236 123.03 57.53 232.75 7.55 2.04 0.36 2.04 3.00

2 75 53.51 28.51 138.25 21.94 27.10 0.84 27.10 19.24

3 137 36.78 19.75 82.25 55.40 36.57 0.96 36.69 32.40

4 290 25.04 18.69 74.25 79.50 36.57 2.04 36.69 38.70

5 69 16.16 19.12 66.00 79.50 45.68 20.02 45.80 47.75

6 229 8.61 7.61 27.00 98.56 47.84 20.14 47.96 53.63

7 119 5.62 4.05 22.00 98.56 60.55 37.05 60.67 64.21

8 238 3.74 2.83 18.00 98.56 60.55 44.24 60.67 66.01

9 42 2.12 1.99 9.00 98.56 67.75 57.43 67.87 72.90

10 176 1.05 0.68 4.75 98.56 85.25 81.53 85.25 87.65

11 246 0.34 0.65 4.00 98.92 85.25 81.89 85.25 87.83

12 65 0.10 0.31 2.25 98.92 88.01 84.41 88.01 89.84

13 16 0.07 0.29 2.25 98.92 88.73 85.13 88.73 90.38

14 67 0.04 0.26 2.25 99.28 88.85 85.13 88.85 90.53

15 223 0.01 0.05 0.50 99.28 88.85 88.49 88.85 91.37

16 208 0.00 0.03 0.25 99.28 91.97 91.61 91.97 93.71

17 35 0.00 0.01 0.25 99.28 93.17 92.81 93.17 94.60

18 126 0.00 0.01 0.25 99.28 93.88 93.53 93.88 95.14

19 189 0.00 0.01 0.25 99.28 94.48 94.12 94.48 95.59

20 99 0.00 0.01 0.25 99.28 95.92 95.44 95.92 96.64

21 186 0.00 0.01 0.25 99.28 98.44 97.96 98.44 98.53

22 239 0.00 0.01 0.25 99.64 98.44 98.32 98.44 98.71

23 214 0.00 0.01 0.25 100.00 98.44 98.32 98.44 98.80

24 1 0.86 0.29 1.00 100.00 98.80 98.68 98.80 99.07

25 9 0.00 0.00 0.00 100.00 100.00 100.00 100.00 100.00

Table C-3 Minimization of the Sag Event Estimation Error (SEEE) for Sags as Classified by ITIC Curve


dev. Max.


LG LL LLG LLL All

1 223 164.76 24.35 217.75 33.09 2.28 0.48 2.28 9.53

2 229 95.26 5.96 112.25 52.16 26.02 0.60 26.02 26.20

3 290 49.31 6.84 70.75 76.26 26.38 1.68 26.38 32.67

4 16 20.00 5.20 40.00 90.65 33.21 1.68 33.21 39.69

5 236 8.09 4.71 24.25 98.20 33.21 2.04 33.21 41.67

6 69 3.60 4.24 18.50 98.20 42.33 20.02 42.33 50.72

7 126 2.52 2.81 15.25 98.20 55.16 36.93 55.16 61.36

8 246 1.77 2.81 14.50 98.56 55.16 37.29 55.16 61.54

9 42 1.18 1.05 8.25 98.56 57.67 46.64 57.67 65.14

10 239 0.67 1.12 8.25 98.92 57.67 47.00 57.67 65.32

11 176 0.41 0.50 2.00 98.92 80.10 70.38 80.10 82.37

12 238 0.19 0.49 2.00 98.92 80.10 77.58 80.10 84.17

13 65 0.01 0.09 1.00 98.92 82.85 80.10 82.85 86.18

14 75 0.00 0.04 0.50 98.92 85.61 85.13 85.61 88.82

15 35 0.00 0.02 0.25 98.92 86.81 86.33 86.81 89.72

16 186 0.00 0.00 0.00 98.92 89.33 88.85 89.33 91.61

17 189 0.00 0.00 0.00 98.92 89.93 89.45 89.93 92.06

18 208 0.00 0.00 0.00 98.92 93.05 92.57 93.05 94.39

19 99 0.00 0.00 0.00 98.92 94.48 93.88 94.48 95.44

20 119 0.00 0.00 0.00 98.92 95.08 94.60 95.08 95.92

21 137 0.00 0.00 0.00 99.28 98.32 98.32 98.32 98.56

22 214 0.00 0.00 0.00 99.64 98.32 98.32 98.32 98.65

23 67 0.00 0.00 0.00 100.00 98.44 98.32 98.44 98.80

24 1 0.67 0.30 1.00 100.00 98.80 98.68 98.80 99.07

25 9 0.00 0.00 0.00 100.00 100.00 100.00 100.00 100.00


191 |

Table C-4 Minimization of the Sag Event Estimation Error (SEEE) for Sags as Classified by Generalized Sag Table


dev. Max.


LG LL LLG LLL All

1 223 26.11 10.38 63.50 33.09 2.28 0.48 2.28 9.53

2 16 13.38 6.41 25.50 47.48 30.70 0.48 30.70 27.34

3 176 8.24 7.23 25.50 47.48 53.12 23.86 53.12 44.39

4 35 6.19 5.77 25.50 71.58 62.11 24.10 62.11 54.98

5 119 4.69 3.86 17.75 90.65 76.98 24.10 76.98 67.18

6 229 3.69 3.53 17.75 90.65 76.98 41.13 76.98 71.43

7 65 2.97 3.44 17.75 90.65 79.74 53.72 79.74 75.96

8 238 2.33 2.83 10.75 98.20 79.74 54.44 79.74 78.03

9 236 1.21 2.68 10.75 98.20 79.74 61.27 79.74 79.74

10 42 0.60 1.13 5.75 98.20 82.25 70.62 82.25 83.33

11 75 0.13 0.25 1.00 98.20 85.01 75.66 85.01 85.97

12 69 0.05 0.12 0.75 98.20 86.69 77.34 86.69 87.23

13 186 0.02 0.09 0.75 98.20 89.21 79.86 89.21 89.12

14 137 0.01 0.06 0.75 98.56 92.45 83.57 92.45 91.76

15 246 0.00 0.02 0.25 98.92 92.45 83.93 92.45 91.94

16 290 0.00 0.01 0.25 98.92 92.45 92.21 92.45 94.00

17 208 0.00 0.00 0.00 98.92 95.56 95.32 95.56 96.34

18 126 0.00 0.00 0.00 98.92 96.28 96.04 96.28 96.88

19 189 0.00 0.00 0.00 98.92 96.88 96.64 96.88 97.33

20 99 0.00 0.00 0.00 98.92 98.32 97.96 98.32 98.38

21 239 0.00 0.00 0.00 99.28 98.32 98.32 98.32 98.56

22 214 0.00 0.00 0.00 99.64 98.32 98.32 98.32 98.65

23 67 0.00 0.00 0.00 100.00 98.44 98.32 98.44 98.80

24 1 0.03 0.08 0.25 100.00 98.80 98.68 98.80 99.07

25 9 0.00 0.00 0.00 100.00 100.00 100.00 100.00 100.00

Table C-5 Minimization of the Sag Event Estimation Error (SEEE) for Sags as Classified by SARFI90


dev. Max.


LG LL LLG LLL All

1 223 184.39 43.06 247.00 33.09 2.28 0.48 2.28 9.53

2 229 92.93 5.01 111.50 52.16 26.02 0.60 26.02 26.20

3 290 46.81 4.37 64.25 76.26 26.38 1.68 26.38 32.67

4 75 19.56 6.20 40.50 90.65 30.58 2.16 30.58 38.49

5 236 6.22 4.21 24.75 98.20 30.58 2.52 30.58 40.47

6 65 2.47 3.49 19.50 98.20 35.25 16.19 35.25 46.22

7 119 1.47 2.18 16.25 98.20 47.96 33.09 47.96 56.80

8 42 0.63 0.62 7.50 98.20 55.16 46.28 55.16 63.70

9 239 0.13 0.46 6.75 98.56 55.16 46.64 55.16 63.88

10 238 0.08 0.44 6.75 98.56 55.16 53.84 55.16 65.68

11 246 0.05 0.42 6.75 98.92 55.16 54.20 55.16 65.86

12 176 0.02 0.14 1.25 98.92 77.58 77.58 77.58 82.91

13 67 0.00 0.01 0.25 99.28 84.89 84.17 84.89 88.31

14 126 0.00 0.01 0.25 99.28 85.61 84.89 85.61 88.85

15 69 0.00 0.01 0.25 99.28 85.61 85.13 85.61 88.91

16 189 0.00 0.01 0.25 99.28 86.21 85.73 86.21 89.36

17 35 0.00 0.01 0.25 99.28 87.41 86.93 87.41 90.26

18 208 0.00 0.01 0.25 99.28 90.53 90.05 90.53 92.60

19 99 0.00 0.01 0.25 99.28 91.97 91.37 91.97 93.65

20 186 0.00 0.01 0.25 99.28 94.48 93.88 94.48 95.53

21 16 0.00 0.01 0.25 99.28 95.20 94.60 95.20 96.07

22 137 0.00 0.01 0.25 99.64 98.44 98.32 98.44 98.71

23 214 0.00 0.01 0.25 100.00 98.44 98.32 98.44 98.80

24 1 0.85 0.35 1.00 100.00 98.80 98.68 98.80 99.07

25 9 0.00 0.00 0.00 100.00 100.00 100.00 100.00 100.00


192 |

Table C-6 Minimization of the Sag Event Estimation Error (SEEE) for Sags as Classified by SEMI F47 Curve


dev. Max.


LG LL LLG LLL All

1 223 162.06 22.31 212.50 33.09 2.28 0.48 2.28 9.53

2 229 91.08 8.17 111.50 52.16 26.02 0.60 26.02 26.20

3 290 50.16 7.68 71.00 76.26 26.38 1.68 26.38 32.67

4 16 20.74 6.10 40.25 90.65 33.21 1.68 33.21 39.69

5 238 10.13 5.30 25.75 98.20 33.21 2.40 33.21 41.76

6 69 3.89 4.48 19.00 98.20 42.33 20.38 42.33 50.81

7 126 2.82 3.02 16.00 98.20 55.16 37.29 55.16 61.45

8 246 2.07 3.02 15.25 98.56 55.16 37.65 55.16 61.63

9 42 1.47 1.27 8.25 98.56 57.67 47.00 57.67 65.23

10 236 0.96 1.14 8.25 98.56 57.67 53.84 57.67 66.94

11 239 0.45 1.16 8.25 98.92 57.67 54.20 57.67 67.12

12 176 0.19 0.49 2.00 98.92 80.10 77.58 80.10 84.17

13 65 0.01 0.09 1.00 98.92 82.85 80.10 82.85 86.18

14 75 0.00 0.04 0.50 98.92 85.61 85.13 85.61 88.82

15 35 0.00 0.02 0.25 98.92 86.81 86.33 86.81 89.72

16 186 0.00 0.00 0.00 98.92 89.33 88.85 89.33 91.61

17 189 0.00 0.00 0.00 98.92 89.93 89.45 89.93 92.06

18 208 0.00 0.00 0.00 98.92 93.05 92.57 93.05 94.39

19 99 0.00 0.00 0.00 98.92 94.48 93.88 94.48 95.44

20 119 0.00 0.00 0.00 98.92 95.08 94.60 95.08 95.92

21 137 0.00 0.00 0.00 99.28 98.32 98.32 98.32 98.56

22 214 0.00 0.00 0.00 99.64 98.32 98.32 98.32 98.65

23 67 0.00 0.00 0.00 100.00 98.44 98.32 98.44 98.80

24 1 0.40 0.29 1.00 100.00 98.80 98.68 98.80 99.07

25 9 0.00 0.00 0.00 100.00 100.00 100.00 100.00 100.00

Appendix D • Distribution of SNPV from 1000 trials for all customer’s plants at different locations

193 |

Appendix D Distribution of SNPV from

1000 trials for all

customers’ plants at

different locations


194 |

Figure D-1 Distribution of SNPV from 1000 trials for all customers’ plants at location a estimated using


-50

510

15

x 1

05

02468x 1

0-6

Real

Eng1

Eng2

Opt1

0O

pt8

Opt6

-20

24

68

10

x 1

05

0123456x 1

0-6

Pulp

and p

aper

inte

gra

ted

Probability Density

-10

12

34

56

7

x 1

06

01234567x 1

0-7

Meta

l m

anufa

ctu

ring

-20

24

68

10

12

14

16

x 1

04

0

0.51

1.52

2.53

x 1

0-5

Food p

rocessin

g

-0.5

00

.51

1.5

22

.53

x 1

04

0123456x 1

0-4

Textile

Probability Density

-0.5

00

.51

1.5

22

.5

x 1

07

0

0.51

1.52

x 1

0-7

Sem

iconducto

r fa

brication

-20

24

68

10

x 1

05

01234x 1

0-6

Auto

motive a

ssem

bly

-10

12

34

56

78

x 1

05

0123456x 1

0-6

Chem

ical

Probability Density

Sto

ch

astic N

et P

rese

nt V

alu

e

-0.5

00

.51

1.5

22

.53

3.5

x 1

05

0

0.2

0.4

0.6

0.81

1.2

1.4

x 1

0-5

Equip

ment

manufa

ctu

ring

Sto

ch

astic N

et P

rese

nt V

alu

e

-20

24

68

10

x 1

05

012345x 1

0-6

Pla

stic e

xtr

usio

n

Sto

ch

astic N

et P

rese

nt V

alu

e


195 |

Figure D-2 Distribution of SNPV from 1000 trials for all customers’ plants at location b estimated using


-50

510

15

x 1

05

02468x 1

0-6

Real

Eng1

Eng2

Opt1

0O

pt8

Opt6

-20

24

68

10

12

x 1

05

01234x 1

0-6

Pulp

and p

aper

inte

gra

ted

Probability Density

-20

24

68

10

x 1

06

012345x 1

0-7

Meta

l m

anufa

ctu

ring

-50

51

01

52

0

x 1

04

0

0.51

1.52

2.53

x 1

0-5

Food p

rocessin

g

-10

12

34

5

x 1

04

012

x 1

0-4

Textile

Probability Density

-0.5

00

.51

1.5

22

.53

3.5

4

x 1

07

0

0.51

1.52

x 1

0-7

Sem

iconducto

r fa

brication

-20

24

68

10

12

14

x 1

05

0

0.51

1.52

2.53

3.5

x 1

0-6

Auto

motive a

ssem

bly

-20

24

68

10

x 1

05

012345x 1

0-6

Chem

ical

Probability Density

Sto

ch

astic N

et P

rese

nt V

alu

e

-0.5

00

.51

1.5

22

.53

3.5

4

x 1

05

0

0.2

0.4

0.6

0.81

1.2

x 1

0-5

Equip

ment

manufa

ctu

ring

Sto

ch

astic N

et P

rese

nt V

alu

e

-20

24

68

10

12

x 1

05

0

0.51

1.52

2.53

3.5

x 1

0-6

Pla

stic e

xtr

usio

n

Sto

ch

astic N

et P

rese

nt V

alu

e


196 |

Figure D-3 Distribution of SNPV from 1000 trials for all customers’ plants at location c estimated using


-50

510

15

x 1

05

02468x 1

0-6

Real

Eng1

Eng2

Opt1

0O

pt8

Opt6

-20

24

68

10

12

x 1

05

01234x 1

0-6

Pulp

and p

aper

inte

gra

ted

Probability Density

-20

24

68

10

x 1

06

012345x 1

0-7

Meta

l m

anufa

ctu

ring

-50

51

01

52

0

x 1

04

0

0.51

1.52

2.5

x 1

0-5

Food p

rocessin

g

-10

12

34

56

78

x 1

04

0123456x 1

0-4

Textile

Probability Density

-10

12

34

5

x 1

07

0

0.2

0.4

0.6

0.81

1.2

1.4

x 1

0-7

Sem

iconducto

r fa

brication

-20

24

68

10

12

14

16

x 1

05

0

0.51

1.52

2.53

x 1

0-6

Auto

motive a

ssem

bly

-20

24

68

10

12

x 1

05

01234x 1

0-6

Chem

ical

Probability Density

Sto

ch

astic N

et P

rese

nt V

alu

e

-0.5

00

.51

1.5

22

.53

3.5

4

x 1

05

0

0.2

0.4

0.6

0.81

1.2

x 1

0-5

Equip

ment

manufa

ctu

ring

Sto

ch

astic N

et P

rese

nt V

alu

e

-20

24

68

10

12

x 1

05

0

0.51

1.52

2.53

3.5

x 1

0-6

Pla

stic e

xtr

usio

n

Sto

ch

astic N

et P

rese

nt V

alu

e


197 |

Figure D-4 Distribution of SNPV from 1000 trials for all customers’ plants at location d estimated using


-50

510

15

x 1

05

02468x 1

0-6

Real

Eng1

Eng2

Opt1

0O

pt8

Opt6

-20

24

68

10

12

x 1

05

0

0.51

1.52

2.53

3.5

x 1

0-6

Pulp

and p

aper

inte

gra

ted

Probability Density

-20

24

68

10

x 1

06

012345x 1

0-7

Meta

l m

anufa

ctu

ring

-0.5

00

.51

1.5

22

.5

x 1

05

0

0.51

1.52

x 1

0-5

Food p

rocessin

g

-10

12

34

56

78

x 1

04

0

0.2

0.4

0.6

0.81

1.2

1.4

x 1

0-4

Textile

Probability Density

-10

12

34

5

x 1

07

0

0.2

0.4

0.6

0.81

x 1

0-7

Sem

iconducto

r fa

brication

-20

24

68

10

12

14

16

x 1

05

0

0.51

1.52

2.5

x 1

0-6

Auto

motive a

ssem

bly

-20

24

68

10

12

x 1

05

0

0.51

1.52

2.53

3.5

x 1

0-6

Chem

ical

Probability Density

Sto

ch

astic N

et P

rese

nt V

alu

e

-10

12

34

5

x 1

05

02468x 1

0-6

Equip

ment

manufa

ctu

ring

Sto

ch

astic N

et P

rese

nt V

alu

e

-20

24

68

10

12

14

x 1

05

0

0.51

1.52

2.53

x 1

0-6

Pla

stic e

xtr

usio

n

Sto

ch

astic N

et P

rese

nt V

alu

e


198 |

Figure D-5 Distribution of SNPV from 1000 trials for all customers’ plants at location e estimated using


-50

510

15

x 1

05

02468x 1

0-6

Real

Eng1

Eng2

Opt1

0O

pt8

Opt6

-10

12

34

56

7

x 1

05

0

0.2

0.4

0.6

0.81

1.2

x 1

0-5

Pulp

and p

aper

inte

gra

ted

Probability Density

-10

12

34

5

x 1

06

0

0.2

0.4

0.6

0.81

1.2

1.4

x 1

0-6

Meta

l m

anufa

ctu

ring

-20

24

68

10

12

x 1

04

0

0.2

0.4

0.6

0.81

1.2

1.4

x 1

0-4

Food p

rocessin

g

-10

12

34

5

x 1

04

01234x 1

0-4

Textile

Probability Density

-0.5

00

.51

1.5

22

.53

x 1

07

012345x 1

0-7

Sem

iconducto

r fa

brication

-20

24

68

10

x 1

05

0

0.2

0.4

0.6

0.81

x 1

0-5

Auto

motive a

ssem

bly

-10

12

34

56

7

x 1

05

0

0.2

0.4

0.6

0.81

1.2

x 1

0-5

Chem

ical

Probability Density

Sto

ch

astic N

et P

rese

nt V

alu

e

-0.5

00

.51

1.5

22

.5

x 1

05

0

0.51

1.52

2.53

x 1

0-5

Equip

ment

manufa

ctu

ring

Sto

ch

astic N

et P

rese

nt V

alu

e

-10

12

34

56

7

x 1

05

0

0.2

0.4

0.6

0.81

x 1

0-5

Pla

stic e

xtr

usio

n

Sto

ch

astic N

et P

rese

nt V

alu

e


199 |

Figure D-6 Distribution of SNPV from 1000 trials for all customers’ plants at location f estimated using


-10

12

34

5

x 1

05

0

0.51

1.52

x 1

0-5

Pulp

and p

aper

inte

gra

ted

Probability Density

-0.5

00

.51

1.5

22

.53

3.5

4

x 1

06

0

0.51

1.52

2.5

x 1

0-6

Meta

l m

anufa

ctu

ring

-20

24

68

10

x 1

04

012

x 1

0-4

Food p

rocessin

g

-0.5

00

.51

1.5

22

.53

3.5

x 1

04

01234x 1

0-4

Textile

Probability Density

-50

51

01

52

0

x 1

06

02468x 1

0-7

Sem

iconducto

r fa

brication

-10

12

34

56

7

x 1

05

0

0.51

1.52

x 1

0-5

Auto

motive a

ssem

bly

-10

12

34

5

x 1

05

0

0.51

1.52

2.5

x 1

0-5

Chem

ical

Probability Density

Sto

ch

astic N

et P

rese

nt V

alu

e

-0.5

00

.51

1.5

22

.5

x 1

05

0123456x 1

0-5

Equip

ment

manufa

ctu

ring

Sto

ch

astic N

et P

rese

nt V

alu

e

-10

12

34

56

x 1

05

0

0.51

1.52

x 1

0-5

Pla

stic e

xtr

usio

n

Sto

ch

astic N

et P

rese

nt V

alu

e

-50

510

15

x 1

05

02468x 1

0-6

Real

Eng1

Eng2

Opt1

0O

pt8

Opt6


200 |

Figure D-7 Distribution of SNPV from 1000 trials for all customers’ plants at location g estimated using


-50

510

15

x 1

05

02468x 1

0-6

Real

Eng1

Eng2

Opt1

0O

pt8

Opt6

-10

12

34

56

x 1

05

0

0.51

1.52

2.53

x 1

0-5

Pulp

and p

aper

inte

gra

ted

Probability Density

-0.5

00

.51

1.5

22

.53

3.5

4

x 1

06

0

0.51

1.52

2.53

3.5

x 1

0-6

Meta

l m

anufa

ctu

ring

-10

12

34

56

78

x 1

04

01234x 1

0-4

Food p

rocessin

g

-0.5

00

.51

1.5

22

.53

3.5

4

x 1

04

012

x 1

0-4

Textile

Probability Density

-0.5

00

.51

1.5

22

.5

x 1

07

0

0.2

0.4

0.6

0.81

1.2

x 1

0-6

Sem

iconducto

r fa

brication

-10

12

34

56

x 1

05

0

0.51

1.52

2.5

x 1

0-5

Auto

motive a

ssem

bly

-10

12

34

5

x 1

05

0

0.51

1.52

2.53

x 1

0-5

Chem

ical

Probability Density

Sto

ch

astic N

et P

rese

nt V

alu

e

-0.5

00

.51

1.5

22

.5

x 1

05

02468x 1

0-5

Equip

ment

manufa

ctu

ring

Sto

ch

astic N

et P

rese

nt V

alu

e

-10

12

34

56

x 1

05

0

0.51

1.52

2.5

x 1

0-5

Pla

stic e

xtr

usio

n

Sto

ch

astic N

et P

rese

nt V

alu

e

Appendix E • Distribution of SNPV from 1000 trials at all locations for different types of customer plants

201 |

Appendix E Distribution of SNPV from

1000 trials at all locations

for different types of

customer plants


202 |

Figure E-1 Distribution of SNPV from 1000 trials for an integrated pulp and paper mill at all locations

(a-h) estimated using all monitoring schemes.

01234567

x 1

05

Real

Eng1

Eng2

Opt6

Opt8

Opt1

0

Pla

nt

location a


0123456789

x 1

05

Real

Eng1

Eng2

Opt6

Opt8

Opt1

0

Pla

nt

location b

0123456789

x 1

05

Real

Eng1

Eng2

Opt6

Opt8

Opt1

0

Pla

nt

location c

0123456789

10

x 1

05

Real

Eng1

Eng2

Opt6

Opt8

Opt1

0

Pla

nt

location d

0

0.51

1.52

2.53

3.54

4.55

x 1

05

Real

Eng1

Eng2

Opt6

Opt8

Opt1

0

Monitori

ng S

chem

e

Pla

nt

location e


0

0.51

1.52

2.53

3.54

4.5

x 1

05

Real

Eng1

Eng2

Opt6

Opt8

Opt1

0

Monitori

ng S

chem

e

Pla

nt

location f

0

0.51

1.52

2.53

3.54

4.5

x 1

05

Real

Eng1

Eng2

Opt6

Opt8

Opt1

0

Monitori

ng S

chem

e

Pla

nt

location g

0123456789

x 1

05

Real

Eng1

Eng2

Opt6

Opt8

Opt1

0

Monitori

ng S

chem

e

Pla

nt

location h


203 |

Figure E-2 Distribution of SNPV from 1000 trials for a metal manufacturing plant at all locations (a-h)


0123456

x 1

06

Real

Eng1

Eng2

Opt6

Opt8

Opt1

0

Pla

nt

location a


01234567

x 1

06

Real

Eng1

Eng2

Opt6

Opt8

Opt1

0

Pla

nt

location b

01234567

x 1

06

Real

Eng1

Eng2

Opt6

Opt8

Opt1

0

Pla

nt

location c

012345678x 1

06

Real

Eng1

Eng2

Opt6

Opt8

Opt1

0

Pla

nt

location d

0

0.51

1.52

2.53

3.54

x 1

06

Real

Eng1

Eng2

Opt6

Opt8

Opt1

0

Mo

nito

rin

g S

ch

em

e

Pla

nt

location e


0

0.51

1.52

2.53

3.5

x 1

06

Real

Eng1

Eng2

Opt6

Opt8

Opt1

0

Mo

nito

rin

g S

ch

em

e

Pla

nt

location f

0

0.51

1.52

2.53

3.5

x 1

06

Real

Eng1

Eng2

Opt6

Opt8

Opt1

0

Mo

nito

rin

g S

ch

em

e

Pla

nt

location g

01234567

x 1

06

Real

Eng1

Eng2

Opt6

Opt8

Opt1

0

Mo

nito

rin

g S

ch

em

e

Pla

nt

location h


204 |

Figure E-3 Distribution of SNPV from 1000 trials for a food processing plant at all locations (a-h)


02468

10

12

x 1

04

Real

Eng1

Eng2

Opt6

Opt8

Opt1

0

Pla

nt

location a


02468

10

12

14

16

x 1

04

Real

Eng1

Eng2

Opt6

Opt8

Opt1

0

Pla

nt

location b

02468

10

12

14

16

18

x 1

04

Real

Eng1

Eng2

Opt6

Opt8

Opt1

0

Pla

nt

location c

02468

10

12

14

16

18

x 1

04

Real

Eng1

Eng2

Opt6

Opt8

Opt1

0

Pla

nt

location d

0123456789

x 1

04

Real

Eng1

Eng2

Opt6

Opt8

Opt1

0

Mo

nito

rin

g S

ch

em

e

Pla

nt

location e


012345678

x 1

04

Real

Eng1

Eng2

Opt6

Opt8

Opt1

0

Mo

nito

rin

g S

ch

em

e

Pla

nt

location f

01234567

x 1

04

Real

Eng1

Eng2

Opt6

Opt8

Opt1

0

Mo

nito

rin

g S

ch

em

e

Pla

nt

location g

05

10

15

x 1

04

Real

Eng1

Eng2

Opt6

Opt8

Opt1

0

Mo

nito

rin

g S

ch

em

e

Pla

nt

location h


205 |

Figure E-4 Distribution of SNPV from 1000 trials for a textile mill at all locations (a-h) estimated using


0

0.51

1.52

2.5

x 1

04

Real

Eng1

Eng2

Opt6

Opt8

Opt1

0

Pla

nt

location a


0

0.51

1.52

2.53

3.54

x 1

04

Real

Eng1

Eng2

Opt6

Opt8

Opt1

0

Pla

nt

location b

0123456

x 1

04

Real

Eng1

Eng2

Opt6

Opt8

Opt1

0

Pla

nt

location c

01234567

x 1

04

Real

Eng1

Eng2

Opt6

Opt8

Opt1

0

Pla

nt

location d

0

0.51

1.52

2.53

3.54

x 1

04

Real

Eng1

Eng2

Opt6

Opt8

Opt1

0

Mo

nito

rin

g S

ch

em

e

Pla

nt

location e


0

0.51

1.52

2.53

x 1

04

Real

Eng1

Eng2

Opt6

Opt8

Opt1

0

Mo

nito

rin

g S

ch

em

e

Pla

nt

location f

0

0.51

1.52

2.53

3.5

x 1

04

Real

Eng1

Eng2

Opt6

Opt8

Opt1

0

Mo

nito

rin

g S

ch

em

e

Pla

nt

location g

01234567

x 1

04

Real

Eng1

Eng2

Opt6

Opt8

Opt1

0

Mo

nito

rin

g S

ch

em

e

Pla

nt

location h


206 |

Figure E-5 Distribution of SNPV from 1000 trials for an automotive assembly plant at all locations (a-h)


0123456789x 1

05

Real

Eng1

Eng2

Opt6

Opt8

Opt1

0

Pla

nt

location a


02468

10

12

x 1

05

Real

Eng1

Eng2

Opt6

Opt8

Opt1

0

Pla

nt

location b

02468

10

12

x 1

05

Real

Eng1

Eng2

Opt6

Opt8

Opt1

0

Pla

nt

location c

02468

10

12

14

x 1

05

Real

Eng1

Eng2

Opt6

Opt8

Opt1

0

Pla

nt

location d

01234567

x 1

05

Real

Eng1

Eng2

Opt6

Opt8

Opt1

0

Mo

nito

rin

g S

ch

em

e

Pla

nt

location e


0123456

x 1

05

Real

Eng1

Eng2

Opt6

Opt8

Opt1

0

Mo

nito

rin

g S

ch

em

e

Pla

nt

location f

012345

x 1

05

Real

Eng1

Eng2

Opt6

Opt8

Opt1

0

Mo

nito

rin

g S

ch

em

e

Pla

nt

location g

02468

10

12

x 1

05

Real

Eng1

Eng2

Opt6

Opt8

Opt1

0

Mo

nito

rin

g S

ch

em

e

Pla

nt

location h


207 |

Figure E-6 Distribution of SNPV from 1000 trials for a chemical plant at all locations (a-h) estimated

using all monitoring schemes.

01234567

x 1

05

Real

Eng1

Eng2

Opt6

Opt8

Opt1

0

Pla

nt

location a


012345678

x 1

05

Real

Eng1

Eng2

Opt6

Opt8

Opt1

0

Pla

nt

location b

0123456789

10

x 1

05

Real

Eng1

Eng2

Opt6

Opt8

Opt1

0

Pla

nt

location c

0123456789

10

x 1

05

Real

Eng1

Eng2

Opt6

Opt8

Opt1

0

Pla

nt

location d

012345

x 1

05

Real

Eng1

Eng2

Opt6

Opt8

Opt1

0

Mo

nito

rin

g S

ch

em

e

Pla

nt

location e


0

0.51

1.52

2.53

3.54

4.5

x 1

05

Real

Eng1

Eng2

Opt6

Opt8

Opt1

0

Mo

nito

rin

g S

ch

em

e

Pla

nt

location f

0

0.51

1.52

2.53

3.54

x 1

05

Real

Eng1

Eng2

Opt6

Opt8

Opt1

0

Mo

nito

rin

g S

ch

em

e

Pla

nt

location g

0123456789

x 1

05

Real

Eng1

Eng2

Opt6

Opt8

Opt1

0

Mo

nito

rin

g S

ch

em

e

Pla

nt

location h


208 |

Figure E-7 Distribution of SNPV from 1000 trials for an equipment manufacturing plant at all locations

(a-h) estimated using all monitoring schemes.

0

0.51

1.52

2.53

x 1

05

Real

Eng1

Eng2

Opt6

Opt8

Opt1

0

Pla

nt

location a


0

0.51

1.52

2.53

3.5

x 1

05

Real

Eng1

Eng2

Opt6

Opt8

Opt1

0

Pla

nt

location b

0

0.51

1.52

2.53

3.5

x 1

05

Real

Eng1

Eng2

Opt6

Opt8

Opt1

0

Pla

nt

location c

0

0.51

1.52

2.53

3.54

x 1

05

Real

Eng1

Eng2

Opt6

Opt8

Opt1

0

Pla

nt

location d

0

0.51

1.52

x 1

05

Real

Eng1

Eng2

Opt6

Opt8

Opt1

0

Mo

nito

rin

g S

ch

em

e

Pla

nt

location e


0

0.2

0.4

0.6

0.81

1.2

1.4

1.6

1.82

x 1

05

Real

Eng1

Eng2

Opt6

Opt8

Opt1

0

Mo

nito

rin

g S

ch

em

e

Pla

nt

location f

0

0.51

1.52

x 1

05

Real

Eng1

Eng2

Opt6

Opt8

Opt1

0

Mo

nito

rin

g S

ch

em

e

Pla

nt

location g

01234567

x 1

05

Real

Eng1

Eng2

Opt6

Opt8

Opt1

0

Mo

nito

rin

g S

ch

em

e

Pla

nt

location h


209 |

Figure E-8 Distribution of SNPV from 1000 trials for a plastic extrusion plant at all locations (a-h)


012345678

x 1

05

Real

Eng1

Eng2

Opt6

Opt8

Opt1

0

Pla

nt

location a


0123456789

10

x 1

05

Real

Eng1

Eng2

Opt6

Opt8

Opt1

0

Pla

nt

location b

0123456789

10

x 1

05

Real

Eng1

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Opt6

Opt8

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0

Pla

nt

location c

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10

x 1

05

Real

Eng1

Eng2

Opt6

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Opt1

0

Pla

nt

location d

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05

Real

Eng1

Eng2

Opt6

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0

Mo

nito

rin

g S

ch

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e

Pla

nt

location e


0

0.51

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Opt8

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0

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nito

rin

g S

ch

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e

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nt

location f

0

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2.53

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Opt6

Opt8

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0

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location g

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location h

Appendix F • List of Publications

210 |

Appendix F

List of Publications

Journal Papers

[F1] J. M. Avendano-Mora and J. V. Milanović, “Monitor Placement for Reliable

Estimation of Voltage Sags in Power Networks,” IEEE Transactions on Power

Delivery, Vol. 27, No 2, 2012, pp. 936-944.

[F2] J. M. Avendano-Mora and J. V. Milanović, “Generalized Formulation of the

Optimal Monitor Placement Problem for Fault Location," accepted for

publication in Elsevier Electric Power Systems Research, 2012.

[F3] N. C. Woolley, J. M. Avendano-Mora, J. V. Milanović, “Immune System

Inspired Methodology for Robust Monitoring of Voltage Sags Based on

Equipment Trip Probabilities,” accepted for publication in Elsevier Electric

Power Systems Research, 2012.

Submitted Journal Papers

[F4] N. C. Woolley, J. M. Avendano-Mora, J. V. Milanović, “Probabilistic voltage

sag performance estimation part I: localisation and voltage magnitude

estimation,” submitted to IEEE Transactions on Power Systems in 2012.

[F5] N. C. Woolley, J. M. Avendano-Mora, J. V. Milanović, “Probabilistic voltage

sag performance estimation part II: estimation of impacts on end users,”

submitted to IEEE Transactions on Power Systems in 2012.

Appendix F • List of Publications

211 |

International Conference Papers

[F6] J. M. Avendano-Mora, Y. Zhang, J. V. Milanović and B. Patel, "The influence

of model parameters and uncertainties on assessment of network wide costs of

voltage sags," 10th

IEEE International Conference Electric Power Quality and

Utilisation (EPQU), 15-17 September 2009.

[F7] J. M. Avendano-Mora, N. C. Woolley and J. V. Milanović, "On improvement

of accuracy of optimal voltage sag monitoring programmes," 14th

IEEE

International Conference on Harmonics and Quality of Power (ICHQP), 26-29

September 2010.

[F8] N. C. Woolley, J. M. Avendano-Mora, J. V. Milanović, “A Comparison of

Voltage Sag Estimation Algorithms Using Optimal Monitoring Locations”,

International Conference on Harmonics and Quality of Power (ICHQP), 26-29

September 2010.

[F9] J. M. Avendano-Mora and J.V. Milanović, "Methodology for flexible, cost-

effective monitoring of voltage sags," 21st International Conference on

Electricity Distribution CIRED 2011, 6-9 June 2011.

[F10] N. C. Woolley, J. M. Avendano-Mora, and J. V. Milanović, “Integration of

cost effective bus profiling in distribution networks”, International Federation

of Automatic Control (IFAC), 28 Aug – 02 Sept. 2011, Invited Conference

Paper

[F11] J. M. Avendano-Mora and J.V. Milanović, "A Heuristic Approach for Optimal

Monitor Placement for Fault Location," IEEE International Conference on

Smart Measurements for Future Grids (SMFG), 14-16 November 2011.

[F12] N. C. Woolley, J. M. Avendano-Mora, J. V. Milanović, “Probabilistic Fault

Location Using Erroneous Measurement Devices”, Smart Metering for Future

Grids (SMFG), 14-16 November 2011

[F13] J. M. Avendano-Mora, J.V. Milanović and M. Madrigal, “Assessment of

Financial Losses Due to Voltage Sags Using Optimal Monitoring Schemes,”

International Conference on Renewable Energies and Power Quality

(ICREPQ), 28-30 March 2012.

N.B.: Only publications F1, F2, F6, F7, F9, F11, and F13 are cited in the list of

contributions as they are directly based on the work embodied in this thesis.

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