Probabilistic Low Voltage Distribution Network Design for Aggregated Light Industrial Loads

COPYRIGHT AND CITATION CONSIDERATIONS FOR THIS THESIS/ DISSERTATION

o Attribution — You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.

o NonCommercial — You may not use the material for commercial purposes.

o ShareAlike — If you remix, transform, or build upon the material, you must distribute your contributions under the same license as the original.

How to cite this thesis

Surname, Initial(s). (2012) Title of the thesis or dissertation. PhD. (Chemistry)/ M.Sc. (Physics)/ M.A. (Philosophy)/M.Com. (Finance) etc. [Unpublished]: University of Johannesburg. Retrieved from: https://ujdigispace.uj.ac.za (Accessed: Date).

http://www.uj.ac.za/

https://ujdigispace.uj.ac.za/

PROBABILISTIC LOW VOLTAGE DISTRIBUTION NETWORK DESIGN FOR

AGGREGATED LIGHT INDUSTRIAL LOADS

By

"

PIERRE VAN RHYN

THESIS

presented in partial fulfilment ofthe requirements for the degree

DOCTOR INGENERIAE

(D. Ing)

in the

FACULTY OF ENGINEERING

of the

UNIVERSITY OF JOHANNESBURG

SUPERVISOR: PROF. JHC PRETORIUS

CO-SUPERVISOR: DR. RON HERMAN

FEBRUARY 2011

III'~IIIIIIII~11111I11IlI3010266824 UJ LIe

1

Declaration

I, the undersigned, hereby declare that the work contained in this dissertation is my own original

work and has not been previously in its entirety or in part been submitted at any university for a

degree.

'.

5 April 2011

Signature Date

2

Acknowledgements

I wish to express my sincere appreciation to:

• My supervisor, Prof. Jan-Harm Pretorius, for his constant encouragement and

dedication.

• My co-supervisor, Dr Ron Herman, for his superb guidance and assistance with the

statistical load modelling ofconsumer loads.

• My family for their moral support and particularly my wife, Richi, who has been

supporting me with unequalled love and understanding.

• My Lord, for the wisdom provided in all my endeavours.

!.

3

Synopsis

This thesis initially reviews current empirical and probabilistic electrical load models available to

distribution design engineers today to calculate voltage regulation levels in low voltage

residential, commercial and light industrial consumer networks. Although both empirical and

probabilistic techniques have extensively been used for residential consumers in recent years, it

has been concluded that commercial and light industrial consumer loads have not been a focus

area of probabilistic load study for purposes of low voltage feeder design. However, traditional

empirical techniques, which include adjustments for diversity to accommodate non-coincidental

electrical loading conditions, have generally been found to be applied using in-house design

directives with only a few international publications attempting to address the problem.

This work defines the light industrial group of consumers in accordance with its international

Standard Industrial Classification (SIC) and presents case studies on a small group of three

different types of light industrial sub-classes, It is proposed and proved that the electrical load

models can satisfactorily be described as beta-distributed load current models at the instant of

group or individual maximum power demand on typical characteristic 24-hour load cycles.

Characteristic mean load profiles were obtained by recording repetitive daily loading of different

sub-classes, ensuring adequate sample size at all times. Probabilistic modelling of light industrial

loads using beta-distributed load current at maximum demand is a new innovation in the

modelling oflight industrial loads.

This work is further -complemented by the development of a new probabilistic summation

algorithm in spreadsheet format. This algorithm adds any selected number of characteristic load

current profiles, adjusted for scale, power factor, and load current imbalance, and identifies the

combined instant of group ~r system maximum demand. This spreadsheet also calculates the

characteristic beta pdf parameters per phase describing the spread and profile of the combined

system loading at maximum demand. These parameters are then conveniently used as input

values to existing probabilistic voltage regulation algorithms to calculate voltage regulation in

single-, bi- and three-phase low voltage distribution networks. The new probabilistic summation

4

\'

algorithm eliminates the need for any load and diversity approximation for groups of light

industrial consumers for which load data exists in the spreadsheet library. A specific level of

confidence is associated with probabilistic voltage regulation design to obtain usable distribution

component sizing for networks.

The usefulness of the developed methodology is illustrated by way of a direct comparison

between practical voltage regulation measurements in existing networks versus predicted voltage

regulation utilising the new statistical techniques involving beta load current models. The results

are also compared with the traditional empirical approach.

Lastly, a comparison is presented of a greenfield, light industrially-zoned development using

traditional empirical techniques with known stand sizes, but undefined tenant mix, to design

general-purpose low voltage networks as compared to pre-specified tenant mixes with known

statistical loading as per the work presented in this thesis.

It is believed that the findings will benefit both the academic and the practising engineering

fraternity.

5

a.c.aa*~,QI"ll\,

pPPa,f3b,PeX

2

()

P(J'

ifCDFN

ejeE(VconJE(Vcon/JE(V·conJIeII a

I b

t,I aI

I bI

I cl

InI nI

Ie,IefJ

i(t)I eH

leI

ih(t)I HkLllLI2LI3LI4LFnOJ

p(x)PPFQ

List of symbols used

Alternating electrical currentAlpha parameter for beta pdfAlpha parameter for beta pdf ofconsumer voltageAlpha parameters for beta load currents ofphases a, b and c.Beta parameter for beta pdfBeta parameter for beta pdfof consumer voltageBeta parameters for beta pdf load currents ofphases a, band cChi Square test statistic indicating goodness-of-fitPhase angle between load current and phase voltageMean value of data setStandard deviation ofdata setVariance ofdata setCircuit breaker valueDiversity factor for N consumersExpected frequency using a mathematical functionAcceptable error based on mean value of data setFirst statistical moment ofbeta pdf of consumer voltageSecond statistical moment of beta pdf of consumer voltageQuantile value for chosen value of confidence for consumer voltageEffective load current phasor as per IEEE defmitionRMS value ofload currentRMS value of load current in phase a of three phase networkRMS value of load current in phase b of three phase networkRMS value of load current in phase c of three phase networkFundamental RMS value of load current in phase aFundamental RMS value ofload current in phase bFundamentalRMS value.of load current in phase cRMS value of neutral current in 3 phase 4 wire systemFundamental RMS value ofneutral current in 3 phase 4 wire systemRMS value of effective load current as per IEEE definitionTime-dependent load currentRMS value of effective harmonic load currentRMS value of effective fundamental load currentTime-dependant harmonic load currentRMS harmonic currentNumber of classes in histogramAutomobile service workshop sub-class of light industrial consumersManufacturers ofbakery product sub-class of light industrial consumersCold storage warehouses as sub-class of light industrial consumersAuto body repairs/painting sub-class of light industrial consumersLoad factorNumber of samplesObserved frequency obtained from a histogram of field dataProbability functionActive power [W]Power factorReactive power [VARI

6

Rp

Rn

SSesTv(t)Va

Vb

Ve

Val

Vbl

Vc/Vabl

Vbcl

Veal

YesV.VCO II

V eon

AVVeon(eomp)

Veon(HB)

Vmax:

Vmin

VeR

Vel

"V.ftnal

Vbalaneed

XYYma

Zz

Phase conductorresistance [Q]Neutral conductorresistance [0]Apparentpower [VA]Effectiveapparentpower as per IEEEdefinitionSlendernessfactor of a data distributionPeriod offundamental componentTime dependant voltageRMS value ofphase a-neutral voltageRMS value ofphase b-neutral voltageRMS value ofphase c-neutral voltageFundamentalRMS phase a-neutralvoltageFundamentalRMS phase b-neutralvoltageFundamentalRMS phase c-neutralvoltageFundamentalRMS line-linevoltage (phase a / phase b)FundamentalRMS line-linevoltage (phase b / phase c)FundamentalRMS line-linevoltage (phase c / phase a)RMS value of effective supply voltageas per IEEEdefinitionSupplyvoltagephasorConsumervoltage phasorRMS value of consumer voltageFeeder voltagedrop phasorRMS value of consumer voltage using complex load.RMS value of consumer voltage assuming resistiveload by HB methodMaximumvalue ofconsumer voltageMinimumvalue ofconsumer voltageRMS value of effective harmonicphase-neutral voltageRMS value of effective phase-neutral fundamental voltage.Voltage drop in LV feeder after applyingcorrectionfactorsVoltage drop in LV feeder using ADMDand balancednetworkIndependentrandom variableIndependentrandom variableRandomvariable for node m on phase a drawnfrom a beta pdfIndependentrandom variableGaussianweight for given level of confidence

7

ADMD

AMEU

ESKOMCuDBDCF(N)DFsFARHBHVACLVLSMMVNAICSNRSpdfp.u.RMURMSSICTHDUCF(N)

Abbreviations

After Diversity Maximum Demand

Association of Municipal Electrical Undertakings

Electricity Supply Commission (South Africa)CopperDistribution panelDiversity Correction Factor for N consumersDiversity FactorsFloor area ratio - maximum allowable floor area on a development siteHerman-Beta statistical voltage regulation algorithm

.Heating, Ventilation and Air ConditioningLow VoltageLiving Standard Measurement of group ofconsumersMedium VoltageNorth American Industrial Classification ofconsumersNational Rationalised StandardsProbability density functionPer unitRing Main UnitRoot Mean SquareStandard Industrial Classification of consumersTotal Harmonic DistortionUnbalance Voltage Correction Factor for N consumers

!.

8

List of Figures

Figure 3.1: Histogram (columns) and pdf of load current of an automotive service workshop (L11)

....................................................................................................................................................... 36

Figure 3.2: Examples of bounded pdfs 37

Figure 3.3: Properties ofthe beta pdf 38

Figure 3.4: Actual demand for power created by 1 kW of each of the three types of load versus

voltage 40

Figure 3.5: A 50150 mixture ofconstant power and constant impedance 41;.

Figure 3.6: Graphical representation ofLI 2 average daily load curve and distribution ofload data

at maximum demand 45

Figure 3.7: Mean load current and standard deviation - LI 1 consumer 54



Figure 3.10: Fit of beta pdf to LI 1 (Small) including histogram - maximum demand at 14:47

(Figure 3.7) X-axis: Amps 56

Figure 3.11: Fit of beta pdf to LI 2 (Medium) - maximum demand at 06:47 (Figure 3.8) X-axis:

Amps : 56

Figure 3.12: Beta distributed current of constant power load class LI 3 (Medium) (Figure 3.9)

maximum demand at 10:47 X-axis: Amps PF = 0.86 57

Figure 4.1: Aggregated electrical load behaviour (mean load current) 61

Figure 4.2: Aggregated electri~al10ad behaviour (SD) 61

Figure 4.3: Histogram and beta pdf fit of the summation of LI 1, LI 2 and LI 3 at combined

maximum demand (also refer to Figure 4.1) 64

9

t·

Figure 404: Flow diagram of new algorithm to establish beta parameters at summated load

maximum demand 67

Figure 4.5: Measurement arrangement for aggregated load study 68

Figure 4.6: Measured aggregated load profile 70

Figure 4.7: Algorithm calculated load profile 70

Figure 5.1: Network of a single section distribution feeder 76

Figure 5.2: Examples offeeder configurations for two light industrial applications : 79

Figure 5.3: Phasor diagram indicating the magnitude ofthe consumer voltage 81

Figure 504: Per phase circuit diagram ofa simple feeder arrangement 81

Figure 5.5: Daily mean load and associated standard deviation profile for selected group (LI 1 +

L12) 85

Figure 6.1: A single line representation of the service workshop (class LI 1) fed from a miniature

substation via 50/70 mm', four-core copper cable (power logging instrumentation indicated) .... 93

Figure 7.1: Section of new township in Veldspaat Street, Polokwane, South Africa with industrial

zoning indicating the proposed MY and LV reticulation 100

Figure 7.2: Reticmaster simulation of LV feeder network for new development-empirical method

(MSA7) 103

Figure 7.3: Reticmaster simulation of LV feeder. network for new development using the

empirical method (MSA8) 104

Figure 704: LV feeder network for the miniature substation zone (MSA7) 107

Figure 7.5: LV feeder network for the miniature substation zone (MSA8) 108

Figure 7.6: Profile of effective balanced load current ofaggregated load at unity PF (MSA7).. 111

Figure 7.7: Profile of effective balanced load current ofaggregated load at unity PF (MSA8) .. 114

10

Figure D.l: Characteristic load profile of an 11 1 (small) light industrial consumer describing the

practical feeder (PF = 0.95) 132

11

!.

List of Tables

Table 2.1: Consumptionclass 28

Table 2.2: Domesticdensityclassification 28

Table 2.3: Typical design classification of consumer loads - income in 2005 ZAR (extraction

from NRS 034-1:2007) 29

Table 3.1: Light industrial consumer categories 34

Table 3.2: Selectedpilot group oflight industrialconsumers for load study 35

Table 3.3: Parametricapproximationof selectedsub-classes oflight industrialconsumers ........ 41

Table 3.4: Goodness-of-fit results for light industrial sub-classes-Ll 1 to LI 3 57

Table 4.1: Extract of typical five minute load data recorded 62

Table 4.2: Beta goodnessof fit summary for aggregated groups of light industrial sub-classes .. 64

Table 4.3: Descriptiveparameters of selected light industrial sub-classes at maximum demand for

a beta distributionof data 71

Table 5.1: Conformanceof light industrial pilot group load model to Herman-Betapre-conditions

....................................................................................................................................................... 83

Table 5.2: A sample input/output sheet which calculates design load parameters for the Herman-

Beta mode1- balanced three-phase load scenario 84

Table 5.3: TypicalHerman-Beta spreadsheet for a balanced three-phase load 86

Table 5.4: Input parameters for the Herman-Betamodel.. 87

Table 5.5: OutputparametersofHerman-Betamodel 87

Table 5.6: A sample input/output sheet which calculates design load parameters for the Herman-

Beta model for a 10% unbalancedthree-phaseload scenario 88

Table 5.7: TypicalHerman-Betaspreadsheet for 10% unbalancedthree-phase load ; 89

Table 5.8: Input parameters for Herman-Betamodel.. 90

12

Table 5.9: Output parameters ofHerman-Beta model 90

Table 6.1: Input parameters for new algorithm 94

Table 6.2: Output parameters ofthe new algorithm 94

Table 6.3: Summarised spreadsheet comparing actual voltage regulation measurements with

predicted voltage regulation using the statistical model for service workshop (LI 1 - small) ...... 95

Table 7.1: Schedule indicating stands to be developed under phase 1 with associated sizes and

required circuit breaker values for light industrial consumers 101

Table 7.2: Typical DFs usually applied to light industrial consumer loads 102

Table 7.3: Results for the empirical method - miniature substation selection 105

Table 7.4: Results for the empirical method - conductor specification and voltage regulation.. 105

Table 7.5: Schedule indicating stands to be developed under phase 1 with associated tenants .. 106

Table 7.6: Consumer sub-class and beta parameter assignment to nodes 107

Table 7.7: Input parameters for miniature substation zone MSA7 summation algorithm ......... 109

Table 7.8: New algorithm establishing aggregated demand for miniature substation MSA7 ..... 110

Table 7.9: New algorithm establishing aggregated demand and feeder design guidelines for node

A7.4 112

Table 7.10: Input parameters for miniature substation zone MSA8 - summation algorithm (shown

in blue below). Input parameters for other nodes also shown 113

Table 7.11: New algorithm establishing aggregated demand for miniature substation MSA8 e., 113

Table 7.12: Statistical load parameters of MSA7 and MSA8 to be applied to LV feeder design 115

Table 7.13: Herman-Beta voltage regulation calculation at node 7.4 with 90% level of confidence

................................................_ 116

Table 7.14: Schedule summarising required transformer capacity utilising new probabilistic

methods : 116

13

Table 7.15: Schedule summarising LV feeder component sizing utilising new probabilistic

methods 117

Table 7.16: Probabilistic/empirical feeder component sizing comparison for greenfield

development 118

Table A.1:Example of data library ofautomobile service workshop 125

Table A.2: Example of calculation sheet in new algorithm 126

Table 0.1: Spreadsheet of actual measurements recorded on the supply (miniature sub-station)

and consumer sides of the selected service workshop LV feeder (LI 1 [small] consumer) ........ 132

Table 0.2: New algorithm calculating the beta parameters at maximum demand 132

Table 0.3: Herman-Beta algorithm calculating voltage drop of the practical feeder 133

Table E.1: Table representing demographic data of different automotive workshop

dealerships .134

14

I'

This thesis is dedicated to my wife, Richi,

my son, Rickard-Pierre, and

my daughter, Leonet,

I-

15

Table of Contents

1. INTRODUCTION 19

1.1 GLOBAL PERSPECTIVE ON ENERGY 19

1.2 OPPORTUNITillS FOR INDUSTRIAL ENERGY EFFICIENCY 20

1.3 LIGHT INDUSTRIAL CONSUMERS OR ZONES 21

1.4 DESCRIPTION OF THE PROBLEM 23

1.5 APPRoACH USED IN DERIVING NEW ALGORITHM TO DESIGN LV FEEDERS FOR INDIVIDUAL OR

GROUPS OF LIGHT INDUSTRIAL CONSUMERS 24

2. STANDARDS AND NORMS FOR LOW VOLTAGE FEEDER DISTRIBUTION DESIGN ... 26

2.1 INTRODUCTION 26"

2.2 RESIDENTIAL CONSUMER LOADS ; 26

2.2.1 The deterministic (empirical) approach 26

2.2.2 The probabilistic approach 28

2.3 COMMERCIAL LOAD MODELLING 30

2.3.1 Background 30

2.3.2 Utility standards and norms 30

2.4 LIGHT INDUSTRIAL LOAD MODELLING 31

2.4.1 Background _ 31

2.4.2 Available standards and norms 32

3. STATISTICAL MODELLING OF LIGHT INDUSTRIAL CONSUMER LOADS 33

3.1

3.2

3.3

3.4

3.5

3.5.1

3.5.2

3.5.3

3.5.4

3.6

3.6.1

INTRODUCTION 33

DEFINITION OF A LIGHT INDUSTRIAL CONSUMER 33

STANDARD INDUSTRIAL CLASSIFICATION 34

SELECTION OF PILOT GROUP OF LIGHT INDUSTRIAL CONSUMERS FOR LOAD STUDy 34

MODELLING OF STOCHASTIC LIGHT INDUSTRIAL LOADS 35

Probabilistic approach 35

Pdfs to describe a set ofdata 36

Goodness-of-jit techniques 38

Parametric description oflight industrial loads 39

FIELD MEASUREMENTS 42

Coincidental measurement, sample frequency and sample size 42

16

3.6.2

3.6.3

3.6.4

3.6.5

3.6.6

3.7

Modem data loggingequipment 44

Loggingof24-hourloadprofilesfor individualconsumers 45

IEEE electricalpower measurementfundamentals undersinusoidalunbalancedconditions46

Ligh~ industrial grouppilot load survey 49

Fitting an appropriate distribution function at maximum demand 53

CONCLUDING REMARKS ON THE MODELLING OF LIGHT INDUSTRIAL LOADS 57

4. SUMMATION OF PDFS TO ESTABLISH AGGREGATED ELECTRICAL LOAD

BEHAVIOUR 59

4.1

4.2

4.3

4.4

4.4.1

4.4.2

4.4.3

4.4.4

4.4.5

4.4.6

4.4.7

INTRODUCTION 59

FUNDAMENTAL CONCEPTS ON THE SUMMATION OF PDFS 59

AGGREGATED ELECTRICAL LOAD BEHAVIOUR OF PILOT GROUP OF CONSUMERS 60

DEVELOPMENT OF AN ELECTRICAL LOAD SUMMATION ALGORITHM WHICH CAN IDENTIFY THE

INSTANT OF MAXIMUM DEMAND :: 62

Processingoffield data 62

Analysestatisticsofaggregatedload current at maximum demandandselect suitablepdf. 63

Calculating thedescriptiveparameters ofthe betapdfat maximum demand 64

Flow diagram ofthe new algorithm 65

Field measurements ofaggregatedloadprofile versusforecast loadprofile utilisingnew

algorithm 68

Suggestedstatisticaldescription ofselectedgroup oflight industrial consumersat intervalof

maximum demand 71

Concluding remarks on new algorithm 71

5. APPLYING THE HERMAN-BETA VOLTAGE REGULATION MODEL TO LIGHT

INDUSTRIAL CONSUMERS 73

5.1

5.2

5.2.1

5.2.2

5.2.3

5.2.4

5.3

5.3.1

INTRODUCTION 73

SUITABILITY OF THE HERMAN-BETA MODEL FOR LIGHT INDUSTRIAL LV FEEDER DESIGN 75

Summaryofthefundamental conceptsofthe Herman-Beta model ~ : 75

Modellingoflight industrialconsumersas beta-distributedconstantcurrent loads 78

Effect ofnon-unityPF on Herman-Beta calculations 80

Concluding remarks on the application ofthe Herman-Beta algorithm to beta modelled

constantcurrent light industrialconsumer loads 83

APPLYING DESCRIPTIVE PARAMETERS OF THE NEW ALGORITHM TO DERIVE PRACTICAL, USABLE

DISTRIBUTION COMPONENT SIZING FOR THE PILOT GROUP OF LIGHT INDUSTRIAL CONSUMERS 83

Input/outputparametersofthe new algorithm 83

17

5.3.2

5.4

Guidelines to the calculationofconductorsizing 85

CONCLUDING REMARKS ON THE PROBABILISTIC MODELLING OF AGGREGATED LIGHT INDUSTRIAL

LOADS TO CALCULATE VOLTAGE REGULATION IN LV FEEDERS .•••••••..•••.•.•.•••.••.•••.•...•...•...••.•.•••.. 90

6. APPLICATION EXAMPLE 1: COMPARING ACTUAL VOLTAGE REGULATION WITH

EXPECTED VOLTAGE REGULATION USING PROBABILISTIC TECHNIQUES FOR

EXISTING LIGHT INDUSTRIAL INSTALLATION 92

6.1

6.2

6.2.1

6.2.2

6.2.3

INTRODUCTION ••••••••.••..•..•.••••....•••••••••••..•••••.••.••••..••••••..•••••.....••.••••..•.•••••..••••••..••.••.••.•..•••.•.••••..•. 92

DEFINING TIlE NETWORK ••••••••••••••..•••....•......•..•••••.••••••....•...•••••.•••••••..•••..........•.•.••••••..••..•••••..••••• 92

Statisticalmodelling 93

Empiricalmodelling 95

Concluding remarks regardingcomparison between newprobabilistic techniques, empirical

techniquesandactual voltageregulation as measuredin a practicalnetwork 97:.

7. APPLICATION EXAMPLE 2: GREENFIELD INDUSTRIAL PARK DEVELOPMENT: NEW

ALGORITHM VERSUS CONVENTIONAL ADMD TECHNIQUES 99

7.1

7.2

7.2.1

7.2.2

7.3

INTRODUCTION .....•....•..•••••••••••.••••••••••••••.•••..••.••••..••••••..••••...•••.•••.......•••••...•••••..•....•.•...•..•..•......•. 99

TOWNSHIP TO BE STUDIED 100

Empiricaldesign methodoftownshipwith unknown tenantmix 100

Probabilisticdesignmethod oftownshipwith prior information oftypicaltenant mix using

new summation algorithm and beta-distributed load currents 106

CONCLUDING REMARKS: GREENFIELD DEVELOPMENT PROBABILISTIC VERSUS EMPIRICAL DESIGN

............................................................................................................... .117

8. CONCLUSION 119

8.1 SUMMARY OF WORK PRESENTED IN THE THESIS 119

8.2 EVALUATION 123

8.3 FUTURE WORK 124

ANNEXURE A ....•..•••.••......•.•.••••.•.~ 125

ANNEXURE B 129

ANNEXURE C 131

ANNEXURE D : 132

ANNEXURE E 135

REFERENCES 137

18

!.

1. INTRODUCTION

1.1 Global perspective on energy

Worldwide, nations are beginning to face up to the challenge of sustainable energy. People are

changing the way in which energy is utilised to enable the support of social, environmental and

economic objectives required for sustainable global development. The emission of greenhouse

gasses and the efficient utilisation of all forms of energy have become topics of discussion in all

sectors of the world economy'. Various countries have already started addressing energy efficient

best practices by dictating maximum allowable carbon emission levels and setting long term

targets for energy efficiency improvement.

The National Energy Efficiency Strategy for the Republic of South Africa' was published on 22

May 2009, Government Gazette no 32249, and sets a national long-term target for energy

efficiency improvement of 12% by 2015. It details expectations per sector of the economy and

also per energy carrier. As could be expected from a sub-Saharan African country, the combined

industrial and mining sectors are the largest users of energy in South Africa. A potential

theoretical energy saving of approximately 50% of the current consumption exists, which is in

line with international best practices.

Various primary energy carriers exist and can be divided into the following mediums: electricity,

petroleum products, gas, coal and renewable energy. Electrical energy is the most convenient

ready-to-use form of energy which is transformed from primary energy sources like fossil fuels,

nuclear fuels, renewable sources etcetera.

South Africa's main electricity utility, Eskom, has underwritten the new Energy Efficiency

Strategy by including a new separate addendum to all new electricity applications in support of

sustained energy savings. In this addendum, all new consumers or existing consumers wishing to

obtain an extension to an existing electrical supply are encouraged to continually use energy

accounting practices and methodologies to ensure sustained energy savings. Such consumers are

also required to adhere to all relevant South African Energy Efficiency Codes and Standards of

best practices, together with therelevant building regulations, health and safety legislation and all

other pertinent statutory requirements. The addendum to the new Energy Efficiency Strategy even

goes to the extent of requiring an energy efficiency compliance certificate by a Certified Energy

Manager or Professional Energy Consultant.

19

Electrical utilities have traditionally distinguished between consumers based on the type of

economic activity associated with each consumer. The three main categories that were identified

are residential, commercial and industrial consumers and can usually be broken down into

different sub-classes. In an attempt to implement energy efficient best practices amongst these

consumer groups, sufficient knowledge of the energy consumption and behavioural load patterns

of these consumer classes are a prerequisite. Although the behaviour of residential load has been

the topic ofcountless research programmes and publications in the past, very little is known about

the energy consumption and behavioural load profiles of commercial loads and even less of

industrial loads. This is mainly as a result of the diverse network of producers, technologies and

processes found in the industrial world.

1.2 Opportunities for industrial energy efficiency

Industrial activity can broadly be divided into two main classes:

• Heavy industrial or energy intensive industry, for example the iron, steel, chemical,

cement etcetera industries.

• Light industrial sector, for example the food processing, textile, printing etcetera

industries.

Industrial Energy Efficiency is the energy used to produce one unit of a commodity and is

determined by the type of process used to produce a commodity or provide a service, the nature

of the equipment used and the efficiency of the production process. However, the efficiency of

the distribution process of electricity from the power utility to the consumer is often overlooked.

The Northwest Energy Efficiency Alliance (NEEA) reported in their Distribution Efficiency

Initiative project'' 4 that was completed during 2007 that "distribution system efficiency is one of

the most energized subjects in the electric utility industry today". One could further add that it is

also one of the most overlooked resources of energy saving as most of the attention is usually

focussed towards the optimisation ofenergy flow within operations.

The modelling of the heavy industrial or energy intensive industry has been the subject of a vast

amount of publications and university research programmes in the past. Efficient distribution

systems to energise such loads are designed for specific needs and optimised by way of

commercially available load flow software to ensure optimum quality of electrical supply. Such.quality standards of electrical supply differ from country to country. South Africa's National

Electrical Quality of Supply Guidelines', NRS 048-2:2008, clearly outline acceptable levels of

20

Harmonic Distortion, Voltage Regulation and other power quality guidelines to be adhered to

when specifying new electrical supply to these consumers.

Unlike the heavy industrial consumer, the studying of the light industrial consumer and

specifically its behavioural load profile has traditionally been neglected due to the vast spread of

consumer sub-classes within this group. The design of energy efficient distribution systems to

energise the various types of light industrial load classes would therefore require extensive

knowledge of individual sub-classes.

1.3 Light industrial consumers or zones

The trend towards the creation of light industrial development nodes has become a general

phenomenon in the developing countries and various examples of successful and newly

developed industrial parks are found in the property market. The tabling of the National

Assembly Statement on the South African Industrial Policy Plan6 by Dr Rob Davies for the

period 2010/11 to 2012/13 re-emphasises the scaling up of efforts to promote long term

industrialisation and industrial diversification and it refers to the automotive and components,

plastic, clothing and other light industrial sectors. Light industrial zones are designed to provide

locations for those essential uses of property not allowed for within residential and commercial

sectors to reduce environmental and social impacts usually associated with heavy industry

(energy-intensive) activity. Light industrial consumers or zones would therefore exclude industry

activity which usually creates obnoxious, corrosive or offensive noise, gas odour, smoke, dust

and fume emissions-",

The Standard Industrial Classification (SIC) system is used by many countries, amongst others

the United States of America (USA) and South Africa, to classify different industries by way of

three to six digit codes. It is used by statistical agencies, universities and other research forums to

classify business establishments for purposes of collecting, analysing and publishing data related

to the business economy of the country. The North American Industry Classification System"

(NAICS) was released in 1997 and consists of a six-digit code. The South African SIC system10 is

published by Statistics South Africa and is a national five-digit classification of various industry

classifications which includes, amongst others, the light industrial group as defined above.

Examples of the more common classes of light industrial consumers found in both South Africa.and other countries and which are included in light industrial estates or parks include the

following:

21

..

;,

• automotive service workshops,

• manufacturing of bakery products,

• cold storage warehouses,

• auto body repairs,

• general storage warehousing,

• machinery workshops, and

• wooden furniture manufacturing etcetera.

A more comprehensive list of light industrial consumers as a sub-section of Standard Industrial

Classifications is presented in chapter 3.

Energy efficient distribution design for the above group of consumers would require a detailed

understanding and characterisation of the utilisation of electrical energy for the various types of

light industrial end-users. The electrical distribution system associated with these consumers

would typically comprise of two sub-systems: medium voltage:(MV) distribution and low voltage

(LV) distribution. In South Africa, MY networks having a nominal voltage level of IkV up to

and including 33kV, have traditionally been designed utilising commercially available load flow

software with estimates of design loads Forecasts for the electrical load of large groups of

consumers have been the subject ofnumerous research literatures in the past.

Similarly, in accordance with the South African quality of supply guidelines, LV networks are

used to distribute electricity to the consumer and has an upper limit of a.c. voltage being lOOOV.

The standard voltage is defined as a phase to neutral voltage equal to 230V and a phase to phase

voltage for multi phase systems of J3 x 230V."

Although LV distribution system design has been studied in detail for residential" and, to a lesser

extent, for commercial application, light industrial loading seems to have been neglected

throughout the world with very few publications and research reports available. This is also

understandable as the phenomenon of groups of this category of industrial consumers, for

example light industrial parks, have only become popular in recent years and as a result so too the

importance of grouped electrical loading of light industrial consumers. Similar to the residential

loading profile, the light industrial consumer's load is also stochastic of nature and a thorough

knowledge of the statistical properties ofthe different types of loads is required.

22

1.4 Description of the problem

The design of LV distribution networks for residential consumers has been the topic of many a

research project in the pasez, 13. Evidence of this work is seen worldwide and usually focuses

around the modelling of the loads either by means of empirical or probabilistic methodsv'.The

probabilistic method for residential design as developed by Dr Ron Herman in association with

the University of Stellenbosch, South Africa during 1993, has been accepted as the preferred

voltage regulation algorithm by South Africa's electricity utility, Eskom, and is widely used by

students and network designers. It is referred to as the Herman-Beta algorithm. Due to the spread

of load data usually associated with a probabilistic method, a level of confidence has been

introduced with success. Usable design parameters are available for residential low voltage feeder

design, be it empirical After Diversity Maximum Demand (ADMD) guidelines or statistical

parameters based on probability density functions (Pdfs).

Unfortunately, similar design parameters are not available for light industrial consumers, as

defmed in paragraph 1.3, resulting in oversized distribution component specification in an effort

to create greater reliability and leave room for future expansion. The uncertainty in the load not

only ties up constrained utility capacity, but also results in uneconomical designs and energy

wastage as a result of larger than required distribution components. A detailed investigation into

the specification of design guidelines for light industrial consumers has yielded only a few

pointers from different parts of the world. Energex, the South East Queensland electricity utility

in Australia", has published general design guidelines for developers. They refer to standard size

low voltage underground conductors but characterise the industrial load as a generalised complex

load of 30 kVA p~r lot with a standard deviation of 0 and a power factor (PF) of 0.8. The

Tshwane Metropolitan Council, South Africa, refers to an ADMD of 80 kVA per hectare for light

industrial development". Pilot measurements taken in Polokwane, South Africa, during 2006

have also confirmed the above ADMD of 80 kVA per hectare measured at substation level'". This

was a group ADMD incorporating 200 light industrial consumers comprising of different sub

classes. Although this characterises the loading of these consumers on a macro level and is useful

for MV distribution network design, no information is available for LV regulation design for

individual sub-classes where all diversity advantages disappear.

A closer study of the load pro.files of different types of light industrial consumers has revealed

that each sub-class has a unique 24-hour load profile and that the instant of maximum demand

can vary depending on the day of the week. The popular characterisation ofa "one size fits all" as

published by the various distribution authorities is therefore a simplified approach which do not

support modem energy efficiency design objectives.

23

\.

It has been further found that by analysing data statistically, mean load profiles and associated

variances of different sub-classes can be summated to obtain aggregated models for groups of

different light industrial consumers. The combined instant of maximum demand can then be

derived and appropriate parameters calculated for a representative pdf. By proving that these

loads can be parametrically described as beta distributed constant current loads at maximum

demand, the existing Herman-Beta algorithm can be utilised to calculate the voltage regulation in

distribution networks statistically.

1.5 Approach used in deriving new algorithm to design LV feeders for individual or

groups of light industrial consumers

This research focuses on the studying of the load profiles of a selected group of light industrial

consumers and the development of a summation algorithm that can identify individual or

combined instances of maximum demand for purposes of ~y feeder design. Similar to the

residential pilot studies conducted by Dr Ron Herman during 198818, sufficient load power data

was captured for each sub-class to ensure representative statistical samples of the populations.

Power networks feeding this consumer group are usually three-phase, four-wire systems and are

mostly unbalanced. For the purposes of generalising the measured parameters, total three-phase

apparent power was calculated as per the latest power definitions reported by the IEEE task

group 19, followed by the calculation of the effective balanced load currents (Ieff) for the

equivalently (virtual) balanced three-phase systems with the same total apparent power as the

unbalanced system. By using statistical techniques, mean values and variances were calculated at

five minute averaging intervals over repetitive 24-hour daily load cycles for each sub-class. This

was followed by the summation of the means and variances of the load profiles and the

establishment of the combined instant of maximum demand (the system maximum demand as

defmed in Chapter 4) utilising look-up tables in Excel spreadsheet format. The statistics at the

instant of system maximum demand for the individual sub-classes could then be arranged in the

form of a histogram, followed by the selection of an appropriate mathematical description to

continuously describe the load data as a function of the probability of its occurrence. It has been

established that these statistics can adequately be described by way of a beta pdf, similar to that of

the stochastic residential load behaviour", The Chi-Square goodness-of-fit program" was

employed to confirm adequacy of the particular pdf. The beta pdf parameters, namely alpha, beta

and an upper limit of the load data (load current or power), could easily be derived from the mean

and variance values of the statistics at maximum demand as described in Chapter 4.

24

The choice ofparametric description of light industrial loads is analysed in Chapter 3. It has been

established that light industrial loads are usually combinations of constant power and constant

impedance loads as reported by Willis22• This is mainly attributable to the widespread application

of induction motors used in the processes of heating and cooling (HVAC) whilst constant

impedance loads are found in resistive heating equipment and lighting. According to Willis, loads

consisting of a combination of constant power and constant impedance components, can

conveniently be modelled as constant current loads within a specific range of error. This has

allowed the beta pdfs to be described in terms of Effective Balanced Load Currents (L), This is

particularly useful as the Herman-Beta probabilistic voltage regulation algorithm, as applied for

residential consumers, could then also be employed to calculate the voltage regulation and LV

feeder component sizing for individual light industrial loads or aggregated groups of light

industrial consumers within industrial zones/parks. During the application of the Herman-Beta

algorithm, the PF of load currents at maximum demand had to be normalised to unity from actual

values experienced at maximum demand and it has been shown that this adjustment yields

acceptable results for purposes of LV feeder design.

The new algorithm automatically calculates the beta pdf parameters of the effective balanced load

current at maximum demand for any combination of light industrial sub-classes having different

individual load profiles and which can parametrically be described as constant current or constant

power loads. A load current imbalance correction factor has also been incorporated which

calculates different combinations of three-phase load currents including neutral current at

maximum demand having the same _effective apparent power as per IEEE defmition. Beta pdf

parameters are then calculated for the different phase currents and applied to the standard

Herman-Beta algorithm. PF correction for specific needs other than unity can also be selected in

the algorithm followed by the updated calculation ofbeta pdfparameters per phase.

This research is intended to contribute towards the present vacuum which exists in available LV

feeder design guidelines for groups of individual light industrial consumers using probabilistic

techniques. It will be proposed in the final chapter that similar pilot programmes be conducted on

all major categories of light industrial consumers and that the field data of these groups is

included in the new algorithm.

25

2. STANDARDS AND NORMS FOR LOW VOLTAGE FEEDERDISTRIBUTION DESIGN

2.1 Introduction

In this chapter a general overview is provided of global LV distribution engineering design

practice with specific reference to practical design guidelines for the residential, commercial and

light industrial consumer groups.

2.2 Residential consumer loads

Residential loads may electrically be represented as a combination of constant resistance and

constant power loads and have been the topic of numerous publications in recent years". It has

been found that the representation of residential load as a constant current "sink" provides the

best compromise and that this model is also consistent with the observed behaviour of residential

load. This parametric description of residential load behaviour has become the basis for the

following two approaches in low voltage feeder design:

• Deterministic approach specifying ADMD associated with a diversity factor (DF).

• Probabilistic approach where the load current is described in terms of a pdf.

2.2.1 The deterministic (empirical) approach

2.2.1.1 Background

Traditional design procedures in most countries utilise the average value of the stochastic load

demand for residential consumers and is described as prevalent engineering practise (PEP) by

McQueen and Watsonr'.The average value ofthe load demand at system peak is often referred to

as the ADMD. The ADMD can be specified as a load current at rated voltage or as an apparent

power at a specific PF.

ADMD is calculated using the collective peak load for a large group of homogenous residential

consumers divided by the number of consumers. The characteristic ADMD is normally based on

1000 consumers and is sometimes referred to as ADMD IOOO• As the number of consumers (N)

reduce to a single connectiori; the stochastic load nature of the individual consumer becomes

more evident and the ADMD has to be corrected by means of a diversity correction factor,

namely DCF(N). A second correction factor, the unbalanced voltage correction factor UCF(N), is

26

usually introduced to provide for additional voltage drop in the neutral conductor of a four-wire

three-phase system. The fmal voltage drop is therefore corrected as shown in Equation 2.1. The

ADMD for less than 1000 consumers is calculated as shown in Equation 2.2.

Vfina.=Vba.anced UCF(N) DCF(N)

ADMDN= ADMDlOoo x DCF(N)

(2-1)

(2-2)

The correction factors as adopted in the United Kingdom (UK.) and South Africa are shown

below":

United Kingdom

UCF(N) = 1+ 4.14.IN

and (2-3)

or

DCF(N)= 1+ 8 for ADMD ::5 5 [ADMD=ADMDlOoolADMD.N

DCF(N) = 1+ 12 for ADMD > 5 [ADMD=ADMDlOoolADMD.N

(2-4)

(2-5)

South Africa (AMEU)

UCF(N)= 1+ 2.8IN

2DCF(N)= 1+-

N

(2-6)

(2-7)

Energy sales forecasts for specific consumer groups are sometimes used to derive an ADMD

figure. In these cases a load factor at suburb level is estimated, usually between 25-45%. The

equation for the calculation of the ADMD based on the energy load factor method is shown as

Equation 2.8 below. During the late 1980s Kritzinger" proved that there is a weak correlation

between energy consumption and ADMD for residential consumers.

kWhADMD=--

LF.h

Where:

kWh = Energy consumption over a period of h hours

!.

(2-8)

27

h =period in hours

LF = Load factor

2.2.1.2 South African standards and norms

The South African guidelines for human settlement planning and design provide guidance for

ADMD figures according to broad categories of consumption class. These guidelines are obtained

from the National Rationalised Specifications, NRS 034-Part 127, and are summarised in tables

2.1 and 2.2.

Consumption Class Approx. Final Loading Approx. Annual Approx. kWh per

(See 4.3.3.2 ofNRS 034-1) and Design ADMD (kVA) Load Factor (%) Annum

Very High >6 >42 >22000

High 3 to6 :. 35 to 42 9200 to 22 000

Medium 1.Sto 3 31 to 35 4100 to 9200

Low 0.5 to 1.5 29 to 31 1200 to 4100Very Low <0.5 28 to 29 <1300

Table 2.1: Consumption class

Domestic Density Stand Size Average Load Density

Classification (m2) (kW Ikm2

)

URBAN ADMDmil1- 0.5 kVA

ADMDmax =4.5 kVA

High density (HD) < I 000 500 to 30 000

Medium density (MD) 1000·4000 300 - 5000

Low density (LD) 4000 ·20 000 100 to I 500

Rural > 20000 0.5 to 250

Table 2.2: Domestic density classification

2.2.2 The probabilistic approach

2.2.2.1 Background

The Statistical Approach to residential load modelling has proven itself to be the superior model

for stochastic loads as it describes consumer loads with diversity more accurately'"

28

Davies and Paterson in 1962 started a process of statistical load modelling of residential loads,

which was later (during the early 1980s) further developed by the UK. Electricity Industry". They

adopted the statistical approach based on a normal distribution of load power at the instant of

maximum demand. This was commercialised in a software package referred to as the "Debut

Program". The UK. Electricity Industry related their peak demand to annual energy consumption.

As a result, during the late 1980s, Herman and Gaunr8 initiated the residential load monitoring

research programme in South Africa to synchronously measure a representative sample of a

homogeneous residential consumer group. It was found that the distribution of load data at the

instant of system maximum demand could conveniently be represented by means of a beta pdf.

This pdf accounted for the skewness of the dispersion and was a more accurate model for

stochastic residential loads. These loads are now classified into several load classes, each with

different beta parameters, namely alpha, beta and C, (the circuit breaker size).

Using the beta model, a probabilistic LV feeder analysis method was developed by Ron Herman

as a PhD dissertation'! at the University of Stellenbosch, South Africa. This model was later

accepted by the Association of Municipal Electrical Undertakings (AMEU) in 1993 and today

endorsed as the preferred design method in the NRS-034 rationalised user specification for

domestic and residential feeder design in South Africa.

2.2.2.2 South African standards and norms

An income-based statistical load estimation model is used for South African residential low

voltage feeder design and is outlined in the rationalised user specification NRS 034-1:2007.

Load parameters - 7 years Load parameters - 15 years

Consumer LS,,,1 Income Alpha Beta Cb ADMD Alpha Beta Cb ADMD

Cia", Range (A) (kVA) (A) (kVA)

Rural LSMI Q.600 03 2.98 20 0.42 0.35 2.88 20 O.SSettlement (low)

Rural Villaoc LSM 1&2 400-900 0.43 2.52 20 0.67 0.48 2.13 20 0.85

Informal LSM 800-1500 0.77 9.88 60 I 0.91 8.8 60 1.29

Settlement 3&4

Townshin area LSM5&6 1500-3000 1.0S 7.81 60 1.64 1.21 5.86 60 2.38

Urban LSM 3000-5500 1.23 5.56 60 2.5 1.25 3.55 60 4.59

residential l 7

Urban LSM 5500-8500 1.45 6.07 80 3.54 1.42 4.1 80 4.73

residential Z 7&8

Urban LSM 8500 to 1.45 5.75 80 3.7 1.42 4.13 80 4.71

townhouses 8 12000

Urban LSM8 1200010 1.43 4.41 80 4.5 1.37 3.39 80 5.3multistorev (Ill2h) 24000

Table 2.3: Typical design classification of consumer loads - income in 2005 ZAR (extraction fromNRS 034-1:2007)

29

2.3 Commercial load modelling

2.3.1 Background

Comparatively few publications are available on the modelling of commercial load. However, it

has been found that such design guidelines are mostly guarded in-house by utilities and

consulting institutions. The documents are retained as internal directives and are seldom

published.

Commercial loads include such loads as corporate offices, shopping centres, hospitals etcetera.

These loads are normally a combination of constant impedance and constant power loads.

Empirical design techniques are normally involved and loads are usually modelled as bulk loads

with no diversity adjustments for purposes of low voltage feeder design. Various commercial

feeder design software packages are available in the marketplace today. A product which is often

used by the South African electricity utility, Eskom, is Reticmaster", This program conveniently

models the load as a constant current load, or as a constant power load in kVA at a specified PF

by using iterative processes to calculate voltage drop in LV feeders.

2.3.2 Utility standards and norms

Various utility and internal directives for business zoning according to diversified maximum

demands have been located both in South Africa and abroad.

Energex, the South East Queensland electricity Utility in Australia", provides ADMD design

guidelines for commercial consumers. This is specified as a once-off 30 kVA per erf with a

standard deviation of 0 and a PF of 0.8, which reminds of a constant power load as there is no

dispersion around the ADMD.

The Tshwane Metropolitan Council" in South Africa specifies in their Supply of Electricity

Guideline Part 2 an authorised maximum demand of 7 kVA per 100 m2 ofpotential building floor

area (FAR) for business/corporate offices and for instances of "special" use. A study of the

general design norm of consultants in South Africa for the design of electrical distribution

networks for large commercial shopping centres has revealed that an average ADMD of 12-14

kVA per 100 m2 of potential building floor area is used as a guideline. This is due to provision

having to be made for a consumer mix which includes substantial Heating, Ventilation and

Cooling (HVAC) systems, as well as provision for significant energy consumption by restaurants

and supermarkets.

30

2.4 Light industrial load modelling

2.4.1 Background

Light industrial loads, as defined in Chapter 3, can electrically be modelled as a combination of

different constant power and constant impedance loads22. Constant power loads are mainly due to

the extensive use ofelectrical induction motors in the various processes, for example compressors

for refrigeration plants, machining tools for engineering workshops and many more. Constant

impedance loads are attributable to heating equipment and incandescent lighting, which are

presently being phased out globally due to the low energy efficiency of conventional lighting.

The studying of typical daily load profiles of light industrial consumers has revealed that different

classes of light industrial consumers have different daily load profiles, each with its own unique

instant of peak demand (kVA or A). The behaviour of the light industrial group of consumers has

only been studied by a few institutions in the world. Research conducted by Jardini" at the

Utilities of Electrical Energy of Sao Paulo State, Brazil, has confirmed that characteristic 24-hour

load curves can be obtained for residential, commercial and industrial consumers and that due to

the behavioural differences of the consumers, the time of maximum demand differs from

consumer to consumer. The simple addition of the individual maximum demands required to

obtain a grouped demand for load forecasting would therefore over-simplify the calculation and

yield the wrong result. Due to the stochastic behaviour of individual classes of light industrial

consumers, a statistical approach has also been adopted by Jardini. Although this author

suggested the summation of the means and variances of the apparent power (kVA) of groups of

different types of consumers, the spread of the load data at the instant of maximum demand was

not studied to derive a mathematical probability density function which could be characterised by

simple parameters and applied to probabilistic LV feeder design methods with specific levels of

confidence.

This research work attempts to characterise the load profiles of three sub-classes of light

industrial users, uniquely identified by way of SIC codes. By performing field measurements and

developing a complete practical statistical load model to combine any number or combination of

users, a representative aggregated 24-hour load curve can be obtained with the associated spread

in data at each selected averaging interval. It will be shown that the existing statistically-based

Herman-Beta low voltage feeder design algorithm is perfectly suited for the application.

31

2.4.2 Available standards and norms

Reference has been made to ADMD design guidelines for genera11ight industrial application in

Chapter 1. These guidelines are useful for MY load forecasting and substation capacity planning

where a large group of industrial consumers are combined to obtain an average estimate of

maximum demand. Contact with various low voltage distribution design consultants in the

engineering field has confirmed that, when required, tailor-made design parameters have to be

generated for each light industrial sub-class user, or group of users, by performing field

measurements of similar installations to establish individual instances of maximum demand.

These measurements are usually performed over only a few 24-hour cycles, which usually results

in an unmanageable spread of data around the instant of maximum demand. This typically leads

to an over-estimation of the maximum demand, which reflects back to non-economical

distribution component design.

This research project will show that a detailed statistical study of selected classes of light

industrial consumers, or any other type of consumer, can result in the mathematical description of

the spread of the load data at the daily instant of maximum demand, referred to as a pdf. By

applying the characteristic parameters of the pdf to a statistical voltage regulation algorithm and

assigning a level of risk to the calculation, specific values for distribution feeder components, for

example conductor size, transformer capacity etcetera, can be obtained.

It is the intention to expand the selected list of light industrial users to a more comprehensive list

in future and to apply the new statistical design guidelines to any mixture of sub-classes to derive

a practical, useful design tool for distribution consultants.

32

\.

3. STATISTICAL MODELLING OF LIGHT INDUSTRIALCONSUMER LOADS

3.1 Introduction

In this chapter the light industrial consumer group will be defined and classified in terms of a

Standard Industrial Classification (SIC) system. A pilot group of light industrial consumers will

be selected for the load study and its electrical modelling possibilities examined. Due to the

stochastic nature ofthese loads, statistical techniques will be used to derive a mathematical model

to describe behavioural electrical load patterns at the instant of maximum demand of

representative 24-hour load profiles. Data acquisition and the identification of the correct load

parametric description will also be examined. Lastly, the latest IEEE electrical power

measurement fundamentals will be reviewed.

3.2 Definition of a light industrial consumer

Although reference is made to the light industrial consumer group in municipal planning and

zoning guidelines in various countries around the world, only a few guidelines provide definitions

for this consumer group. Mariposa County and the City of Temecula in California, USA7, 8, define

a light industrial district as a zone which provides locations for those essential uses not allowed

within the residential or commercial classification to promote the development of attractive,

comprehensively planned industrial activity. It is intended to reduce the environmental and social

impacts usually associated with industrial activity.

In South Africa, light industrial activity is usually found within the so-called "industrial park" or

"industrial estate" type of developments. According to South Africa's New Regional Industrial

Development Strategy", industrial parks and estates are usually located close to transport

facilities, especially where more than one transport modality coincides, such as highways,

railroads, airports and navigable rivers. Offices and light industry, rather than heavy industry, are

usually accommodated within these areas .During the developmental planning stage of projects,

care should be taken to ensure that the correct mix of light industrial industries are combined

within these parks and estates to ensure compatibility with one another. This knowledge of

specific mixes of industries within these industrial parks can allow engineering planners to

optimise LV distribution feeder design, as presented in Chapter 7, for groups of consumers.utilising the developed statistical models presented in this work.

33

3.3 Standard Industrial Classification

The Standard Industrial Classification (SIC) system is used by many countries around the world

to classify different industries by using four to six digit codes.

Although light industrial consumers are uniquely defined as in paragraph 3.2, no separate

mention within the SIC systems could be found for this sub-category. However, the above

mentioned and other municipal planning and zoning guidelines refer to specific light industrial

industries which can conveniently be cross-referenced to standard SIC codes. A few of the more

popular light industrial industries found within light industrially-zoned areas with corresponding

South African and North American SIC codes have been summarised in Table 3.1.

Number Llght Industrial sector South African North AmericanSIC SIC

I Automotive Service workshop 63201 44112 Manufacturers ofBakery products 3041 31183 Cold storage warehouses 7412 49314 Auto Body Renairs/naintinz 63204 81115 Machining workshops 3541 33276 Boiler Shops 3542 23827 Wooden Furniture manufacturing 3221 33718 Jewellery related manufacturing 3921 33999 Newspaper printing 3242 323110 Pottery and related 3421 326011 Freight handling 7123 484212 Processing of fruit& vegetables 3013 311413 Leather goods manufacturing 3162 316914 Renting of construction equipment 5050 238915 Electrical/Plumbing contracting 5032 238216 Bulk plants for storage of petroleum 6141 424717 Marine facilities: boat repairs etc. 3841 541318 Dairy products 3020 112119 Beverage bottling plants Not available 312120 Laboratory services Not available 5417

Table 3.1: Light industrial consumer categories

3.4 Selection of pilot group of light industrial consumers for load study

Although it will be a final objective to group the comprehensive list oflight industrial sub-classes

above into a smaller group ofmain sub-classes after having studied the behavioural electrical load

pattems of all individual sectors, it has been decided to select the following four sub-classes for

34

the load pilot study and to document all the associated demographic data associated with these

consumer groups. The proposed new sub-class category identification has been included in Table

3.2.

Number Light Industrial sector Sub-Class South Africancategory SIC

1 Automotive Service workshop LIl 632012 Manufacturers of Bakery products LI2 30413 Cold storage warehouses LI3 74124 Auto Bodv Repairs/painting LI4 63204

Table 3.2: Selected pilot group of light industrial consumers for load study

3.5 Modelling of stochastic light industrial loads

3.5.1 Probabilistic approach

Similar to domestic electrical loads reported on earlier, the electrical loading of light industrial

consumers is also stochastic by nature and grouped loading also requires modelling by using

probabilistic methods at a given time of occurrence. The stochastic nature of consumer loads

refers to the random variation in time of certain variables such as load current.

The traditional description of variables at a given time of occurrence has been by way of

frequency tables or histograms, indicating frequencies of occurrence of a specific electrical

loading condition of a homogeneous group of consumers, which is the so-called discrete

representation of the frequency of occurrence of a set of data. By calculating the mean value of

these distributions at the instant of maximum demand, the previously referred to ADMD is found,

which has traditionally been used in association with "diversity adjustments to model such loads

for purposes of voltage regulation calculations. The stochastic nature of the data has conveniently

been ignored and replaced with a diversity correction factor.

By identifying a continuous mathematical function that follows the profile of the histogram and in

the case of the variable being a description of electrical load, a usable model can be found which

can be applied to statistical voltage regulation algorithms such as the Herman-Beta model", As

already mentioned in chapter 1, 'such continuous mathematical functions that are used to describe

a set of data are referred to as pdfs, of which a vast selection of standardised mathematically

described functions is available in the industry today.

35

Figure 3.1 represents a typical histogram for a light industrial consumer's load current with its

corresponding pdf describingthe histogram mathematically at the instant ofmaximum demand.

EasyFit - Evaluation VersionProbabilityDensityFunction

35 40 45 50x

55 60 65

IEJ Histogram - Beta

Figure 3.1: Histogram (columns) and pdf of load current of an automotive service workshop (LIt)

3.5.2 Pdfs to describe a set of data

Pdfs conveniently describe the probability that a variable, such as load current, will take on a

value between an upper and lower limit by establishing the corresponding area under the pdf

curve.

Electrical loads, such as light industrial loads, are supported on a finite base with a minimum

loading of zero and a maximum loading determined by the distribution feeder protection level, be

it a circuit breaker, fuse or relay setting. Some of the standard bounded pdfs that can be

considered to describe a set of light industrial load data at a specific interval in time are

summarised in Figure 3.2.

36

100

EasyFitXL- Evaluation VersionProbabilityDensity Function

150x

E1a Histogram - Beta- Kumaraswamy - Pert- Power Function - Reciprocal-Uniform

-Johnson SB- Power Function- Triangular

Figure 3.2: Examples of bounded p,dfs

It will be shown later that the beta pdf, being the "flex-curve" of pdfs, can adequately describe the

distribution of the load data at the instant of maximum demand for the four main selected sub

classes, namely LIl to LI4. This distribution function makes provision for the load data

boundaries of zero and the maximum and can accommodate symmetrical or skewed current

distributions.

Beta pdfparameters can easily be derived from a set of field data by calculating the mean (u) and

variance (J2) of the data using standard statistical formulae followed by the calculation of the

three descriptive parameters for the beta pdf, namely n, pand C, where:

a = I1(CI1-Il/\2-a"2)

Ca"2

{3= (C -11)(CI1-I1"2 - a"2)Ca"2

(3-1)

(3-2)

C = Scaling factor for variable.measured for example the circuit breaker value for load current.

The beta pdf can be described as follows:

37

p(x) = (x"-1(1_x)1l-1) / B(a,~) (O<x<l)

1

where B(a,~) = Ju"-l(l_u)~-l duo

(3-3)

(3-4)

Subsequent properties of the beta pdf are presented in various publications and journals". The

flexibility ofthe beta pdf is clearly shown in Figure 3.3 for various combinations of a and B.

Properties of the Beta pdf

Parameters: lX, ~ and scalingfactor,C

Can accommodate a varietyof shapes

(a) alpha < beta

(b) alpha> beta (c) alpha = beta

p{x)

o 0,5

Figure 3.3: Properties ofthe beta pdf

3.5.3 Goodness-of-fit techniques

Goodness-of-fit tests are performed to establish the appropriateness of the fit of a mathematical

function (such as the beta pdf) to the observed frequency distribution as found in a histogram of

the load data at the instant ofmaximum demand.

Chi-square is a statistical test commonly used to compare observed data with data one would

expect to obtain according to a'specific hypothesis, for example that a beta pdf fits a set of data. A

test statistic referred to as i indicates the goodness-of-fit, with a low value indicating a good fit.

Karl Pearson" derived the following equation to calculate the test statistic:

38

with i = k-I (3-5)

where OJ= observed frequency, ej= calculated (expected) frequency for example for beta model

and with k classes in the histogram with (k-l) degrees of freedom.

The statistical package, EasyFit 5.3 Professional by MathWave, can conveniently be used to fit a

specific distribution, for example,a beta pdf, to a set of observed data by calculating the Chi

square test statistic and referring to the standard table to obtain the critical values of l for

specific degrees of freedom and levels of confidence. The probability levels indicated in

published X2 tables refer to the probability that X2 (as calculated by the statistical software package

also referred to as the test statistic) will be larger than t critical as indicated in the statistical table

corresponding to the said probability and degrees of freedom found from the number ofhistogram

classes. If the test statistic is lower than i critical it implies a satisfactory fit of a particular pdf.

3.5.4 Parametric description of light industrial loads

Electrical loads are usually grouped into three categories, depending on the load demand

sensitivity to supply voltage variation. Light industrial load classes have to be classified in terms

of specific parametric load models to establish the type of statistical variable that is to be used in

the appropriate pdffor further analysis.

3.5.4.1 Constant power (P) loads

A constant power load is represented by electrical motors, regulated power supplies and any other

load where demand remains constant regardless ofthe supply voltage. It typically compensates by

demanding increased load current as supply voltage reduces to maintain the power level. The

opposite in the case of increased supply voltage is also true.

3.5.4.2 Constant impedance (Z) loads

A constant impedance load is usually represented by resistive water heaters, resistive baking

ovens, incandescent lighting and other loads where the demand is proportional to the supply

voltage squared.

3.5.4.3 Constant current (I) loads

A smaller number of devices are considered as pure constant current loads where the demand is

directly proportional to the supply voltage. Electrical welding machines and purely inductive

loads are examples of constant current loads. Constant current load approximations are widely

39

used in distribution studies as it results in linear calculations for voltage regulation. Constant

current loads generally represent the aggregate behaviour of a mixture of constant impedance and

constant power loads as reported by Willis22 earlier. Figure 3.4 shows the load versus voltage

characteristics of a 1W load at 1 per unit (p.u.) supply voltage for all three types. The load

behaviour as a result of supply voltage fluctuation need only be studied over the range 0.9 p.u. to

1.1 p.u. corresponding to South Africa's National Electrical Quality of Supply Guidelines", NRS

048-2:2008.

p vs V for constant P,I,Z loads

1.4

1.2

0.8

j...0.6

0.4

0.2

o0.9 0.92 0.94 0.96 0.98 1 1.02 1.04 1.06 1.08 1.1

Supply voltage (p.u.)

Figure 3.4: Power versus supply voltage for constant P,I,Z loads

A 50150 mixture of constant impedance and constant power with an equivalent power of 0.5W at

rated voltage is shown in Figure 3.5. According to Willis, this mixture of power and impedance

load looks very much like, and can be modelled as, constant current loads. On closer analysis of

the combined effect as outlined above, a constant current load within 1% is found over the range

of0.9 p.u. to 1.1 p.u:

40

Constant Current Approx. of 50/50 P-Z load

1.2

0.8

:;~ 0.6...

0.4

0.2

o0.9 0.92 0.94 0.96 0.98 1 1.02 1.04 1.06 1.08 1.1

Supply voltage (p.u.)

Figure 3.5: A 50/50 mixture of constant power and constant impedance

3.5.4.4 Analysis of light industrial load

The selected group of light industrial sub-classes as outlined in Table 3.2 has to be studied to

establish individual parametric descriptions. Although the modelling of the voltage sensitivity of

the individual load types would be the recommended option to follow, the adjustment of supply

voltage to monitor demand behaviour on an existing operational feeder arrangement from a

miniature substation is not practical. It was therefore decided to study the load behaviour of

individual electrical appliances within the sub-classes to establish representative models for these

loads.

Willis further highlights the fact that in his experience, all loads, except special ones, are

designated as a default mixture of power and impedance loads. By using basic electrical formulae

for P, V and Z, the accuracy of specific parametric descriptions of the loads can be calculated.

The following conclusions have been drawn for sub-classes LIl to 114 over the supply voltage

range of0.9 p.u. to 1 p.u. by analysing the type of electrical appliance utilised within each class.

Category Light Industrial sector Constant Constant Parametric AccuracyPOWel" Impedance Description

LIl Automotive Service workshop 60% 40% Constant I 2%LI2 Manufacturers ofBakery products 30% 70% Constant I 4%LI3 Cold storage warehouses 95% 5% Constant P 1%LI4 Auto Body Repairs/painting 60% 40% Constant I 2%

Table 3.3: Parametric approximation of selected sub-classes of light industrial consumers

41

The accuracy of the above constant current/constant power approximations over the sensitive

supply voltage range of 0.9 p.u. to I p.u. for voltage regulation purposes at the lower end falls

within a 0-4% accuracy margin.

Current load models are used in many of the South African design methodologiesi'.Using the

constant current representation reduces the voltage regulation calculations to linear relationships.

Earlier work done by Herman and Heunis'" during 2002 reported that constant power loads can

also be represented by way of beta distributed load currents with an associated level of

confidence.

3.6 Field measurements

Field measurements used to obtain relevant load data are required for probabilistic load modelling

techniques. These data must meet the following criteria:

• The data must be representative of the sampled group.

• The sample must be large enough to be statistically valid.

• The sample group must fit into an identifiable class of consumer.

• The identification of the group must be related to predictable practical demographic

parameters.

3.6.1 Coincidental measurement, s.ample frequency and sample size

The repetitive daily sampling of selected homogeneous groups of consumer loads require

accurate synchronisation of measured parameters to allow the statistic manipulation of data at

each sampling interval. The coincidentally monitored signals are temporarily stored and

recursively averaged over a selected sampling .interval. These average values are then

sequentially stored in the on-board Random Access Memory (RAM) ofmeasuring equipment.

Averaging of sampled load data is obtained by effectively determining the area under the

measured parameter as a function of time divided by the duration of the measurement. Other than

for utility billing purposes, which have been set at an averaging interval of 30 minutes for the

South African consumer, integration for purposes of quality of supply measurement and voltage

regulation models must match statutory voltage specifications. The specification of the voltage

characteristics, compatibility levels, limits and assessment methods are contained in the South

African Standards document NRS 048-2:20085•

42

According to NRS 048 the deviation from the standard or declared voltage of -J3 x 230V phase

to phase voltage in three phase LV networks shall be ± 10%. The assessment period for the above

limits is defined as a minimum of seven consecutive days for voltage quality assessment. During

the assessment period, for 95% of the time, the highest and lowest 10 minute RMS values shall be

determined. For compliance, not more than two consecutive 10 minute RMS values shall exceed

the higher compatibility value of declared voltage +10%. Similarly, not more than two

consecutive 10 minute RMS values shall be less than the lower compatibility level of the declared

voltage -lO%.According to the Nyquist criterion, the sampling rate should always be at least

double the frequency of the highest fluctuation under consideration. In this case the averaging

interval's duration can conveniently be dictated by the Nyquist criterion and therefore be set at 5

minutes.

When considering the sampling frequency of the raw data, provision has to be made for the

highest fluctuation rate of the data. Seeing that modern data logging equipment can measure

harmonic components as high as the 40th harmonic, which is u~~ful for power quality work, then,

based on a 50 Hz fundamental and the above criteria, the sampling frequency should be at least 4

kHz.

The statistical validity of sampled data depends on sample size. The correct number of samples

should be taken to establish a representative sample of the selected consumer class's primary

population, for example the sampling of daily load curves of manufacturers of bakery products

should be representative of the industry. Required sample size can be derived from pilot surveys

measuring a small number of consumer load profiles and establishing the standard deviation (0-)

of data (statistics) at a specific instant in time (that is at maximum demand) from these

measurements.

According to Cochran's 1977 sample size formula", the number of samples (daily load profiles)

required can be calculated using Equation 3.6:

(3-6)

Where:

n = number of samples required (daily load profiles)

0- = Standard deviation ofpilot sample

z = Gaussian weight for given level ofconfidence

43

e = Acceptable error based on mean value Il

The value of z (obtained from the normal distribution's standard statistical table) is an indication

of the probability that the calculation of n will lead to the required accuracy. Typical values of

confidence are 90% or 95%, which correspond to a Gaussian weight of 1.64 or 1.96 respectively

and refer to the confidence levels at which the variables (that is the load current) will fall between

the mean value (u) plus/minus the Gaussian weight multiplied by 036•

3.6.2 Modern data logging equipment

The availability of off-the-shelf modem data logging. equipment has simplified the data

acquisition process considerably in recent years. During the 1990s, data acquisition systems still

had to be developed for specific needs to ensure real-time recordings with adequate memory

capacity, sampling rates and battery back-up for data protection':'.

Modem data acquisition requirements for electrical supply quality analysis, where harmonic

frequencies of up to the 40th harmonic can be studied, have necessitated the increase in sampling

rates to values of 12 kHz and more. Typical on-board memory size is 4 MB and the duration of

selected averaging intervals determines the duration of the logging period in days. Typical

interfacing with personal computers is achieved via RS232 ports and data is usually exportable to

modem spreadsheet software for further manipulation, especially power calculations in

accordance with the latest IEEE guidelines. Finally, flexible current probes simplify its

installation into existing equipment and can be set up within minutes.

Typical logging equipment requirements for load study purposes are:

• Sufficient memory to store data at typical five minute averaging intervals for at least

two weeks.

• Sampling rate at least double the harmonic frequency to be recorded (Nyquist).

• Error margin for~S voltage and currentS 1%.

• Battery back-up of eight hours to ensure continued recording after power failures.

• External power supply for extended recordings.

• Accurate onboard real-time clock to ensure time-tagged data for future reference.

• Instrument compact enough to ensure its installation within distribution panels,

metering kiosks or miniature substations.

• Recorded data exportable to personal computers and compatible with modem

spreadsheet software.

44

• Confirmation of correct electrical power theory (mathematics) used by

instruments/loggers to define active, reactive and apparent power, especially under

unbalanced and non-sinusoidal conditions.

• Economically priced.

3.6.3 Logging of 24-hour load proflles for individual consumers

The development of statistical load models for the selected light industrial sub-classes requires an

extensive pilot study to establish typical daily load profiles for each sub-class and to extract

statistical load data at the instants of maximum demand. The load data will be analysed in

paragraph 3.6,6 to fit an appropriate distribution function to the data for further manipulation.

Sufficient 24-hour load profiles have to be recorded for each sub-class to ensure a statistically

representative sample of the primary population as explained in paragraph 3.6.1. Each daily load

profile represents only one sample as only one load value will b~ used at the aggregated instant of

maximum demand for each daily load profile per homogeneous group of consumer. Measured

data is time-stamped at each averaging interval of five minutes to enable the synchronised

summation of data and calculation of statistical parameters, for example means and variances at

each interval. Figure 3.6 shows a graphical representation of mean values and standard deviation

of a set of daily load curves for a typical LI 2 sub-class consumer.

Effective Load Current andSO

140.00

120.00

i 100.00

!~ 80.00c~

<3 60.00

~40.00

20.00

0.00'" en w CI.I r/)s s s .§.§~ ~ ~ ~ ~

g~i:j ti~s s s gjgj

'" ..E Eo 0

~ ~r.; N... 0

~ ~Time

Figure 3.6: Graphical representation of LI 2 average daily load curve and distribution of load data atmaximum demand

45

3.6.4 IEEE electrical power measurement fundamentals under sinusoidal unbalanced

conditions

The measurement of energy flow and power in electrical circuits still remains the topic of

numerous publications and discussions. The definitions for active, reactive and apparent powers

in three phase circuits, which are currently used throughout the world, are based on the

knowledge developed and verified during the 1940s. These defmitions have served the industry

well as long as the systems were balanced and voltage and current waveforms remained nearly

sinusoidal.

Significant development in industry technology over the past 50 years has necessitated the

revisiting of fundamental definitions of electrical power to accommodate both non-sinusoidal and

three-phase circuit unbalanced conditions. Fundamental definitions of apparent power as

proposed in 1922 by the German engineer F. Buchholz'? and explained by the American engineer

W.M. Goodhue38 during 1933, as well as subsequent updatespublished as various standards by

the IEEE, have now been reworked by the IEEE workgroup under the chairmanship ofAlexander

Eigeles Emanuel" and published as a new IEEE standard, namely Standard 1459-201039, during

March 2010.

3.6.4.1 Usable electrical power definitions

Usable, practical definitions arising from the latest work as outlined above are available for use in

the proposed load study of the selected light industrial consumer classes. Some useful alternatives

in power flow phenomena in large industrial plant have also been reported by Pretorius, van Wyk

and Swart'" during July 2000. Power definitions and the physical mechanism of power flow have

extensively been addressed by Emanuel" in a new reference book published during 2010.

Light industrial loads, as will be shown later, are mostly unbalanced and, to a lesser extent, non

sinusoidal. Although the definitions to be presented below also make provision for the harmonic

components associated with non-sinusoidal load current behaviour, the measurement of RMS

values of voltage and current fundamentals and subsequent harmonic components are not always

available, although these components are measured internally by instruments for purposes of on

board power calculations. The measured RMS quantities that are to be applied to the IEEE

defmitions presented below for the pilot group of light industrial consumers refer to the

fundamental component as a THD of less than 3% was generally experienced with the particular

group.

Note": Worcester Polytechnic Institute, USA

46

I'

The basic formulas for RMS voltage and current as used by typical recording instrumentation are

provided by equations 3.7 and 3.8:

(1 f ·2IRMs = 'iT 1 dt

where v = time dependant voltage

where i = time dependant current

(3-7)

(3-8)

The power formulas derived below are extracts of the latest IEEE standard referred to above and

are applicable to unbalanced three-phase, four-wire systems where neutral load current can be

measured or calculated from the phase currents.

An effective line current, L" is presented which assumes a virtual balanced circuit that has exactly

the same power losses as the actual unbalanced circuit. For applications where supply voltage is

not balanced, a further definition is presented for the effective line-neutral voltage Ve• The

following equations provide definitions for the calculation of L" Ve and ultimately effective

apparent power, S; L, and Ve are further presented as a function of both the fundamental and the

harmonic components. Using effective line currents to create equivalent virtual balanced circuits

assists with the per phase modelling of three phase loads as is required for the study of the light

industrial consumer load profiles:

(3-9)

where IeH equals the RMS value of the effective harmonic line currents, and lei equals the RMS

value ofthe effective fundamental line current.

(3-10)

where V eH equals the RMS value of the effective harmonic phase voltage, and Vel equals the

RMS value of the effective fundamental phase voltage..

47

The effective line current at the fundamental frequency (lei) of an unbalanced three-phase circuit

can be conveniently calculated using measurable quantities of RMS phase and neutral currents:

(3-11)

\

where la" Ibh lei and Inl denote fundamental RMS line and neutral currents, and if IeH is ignored

for sinusoidal approximation then Ie = lei ,and I, = la" Ib= ~I , Ie = lei , In = Inl

The effective line voltage at the fundamental frequency 01el) of a supply voltage unbalanced

three phase circuit can be conveniently calculated using measurable quantities of RMS phase and

neutral currents:

( 3-12)

where v., v., Vel,Vab" Vbcl, Veal denote fundamental RMS voltages.

If the supply voltage is balanced then Vel=Val=Vbl=Vel and for sinusoidal approximation Ve=Vel.

Finally, the effective apparent power, Se, is presented in Equation 3.13 for a fundamental

approximation of a three-phase unbalanced system as would typically be experienced with

industrial consumers such as the LI 1 to LI 4 consumer categories being studied.

(3-13)

Ve and Ie as defined above.

48

3.6.5 Light industrial group pilot load survey

Selected light industrial consumer load data was collected between 2006 and 2010 as part of a

University of Johannesburg, South Africa, research programme to study electrical load

behavioural patterns of the identified group of consumers. Approximately 1700 hours of five

minute samples were collected and stored in a database for each of the following four consumer

classes:

• Automotive service workshops (LI 1),

• Manufacturers of bakery products (LI 2),

• Cold storage warehouses (LI 3), and

• Auto body repairs/painting (LI 4).

The forth consumer, Auto body repairs/painting (LI 4), was monitored on a smaller scale as it was

included in a group of consumers fed from a miniature substation in an existing industrial park on

which grouped behaviour was studied.

A Fluke 1735 Power Quality Recorder was utilised to record RMS load current, RMS supply

voltage and PF per phase of the above consumer groups. The recorder had a sample rate of 10.24

kHz, 4 ME onboard memory and a real-time clock. The operating error on voltage was < 0.5%,

whilst the operating error on current was < 1%. Although the recorder had the facility of internal

power calculations, it was decided -to export the voltage, current and PF data to an Excel

spreadsheet on a personal computer to perform calculations as per the latest power definitions

outlined in paragraph 3.6.4.1. Annexure A shows a snapshot of a typical spreadsheet for an

automotive workshop, which is included as a data library in the new algorithm to be discussed in

later chapters.

The following demographic features are proposed on the respective homogeneous groups that

will typify it as prospective load types in further/future distribution studies:

49

LI 1: AUTOMOTIVE SERVICE WORKSHOPS

SA SIC CODE: 6320

Description:

Sales, maintenance and repair of motor vehicles and motorcycles. The electrical load

specifications for automotive service workshops are based on the number of vehicles serviced per

day as a near-linear relationship which has been noted between number of vehicles serviced per

day and monthly electrical energy consumption. A summary of a field survey conducted amongst

10 major automotive dealerships in key metropolitan areas in South Africa is presented in

Annexure E. As field measurements were only performed on the first sub-class, which has

conveniently been defined below as the "small" category, a scaling factor has been introduced to

derive practical load data for subsequent larger sub-classes based on a practically derived energy

consumption indicator per vehicle serviced. Annual electrical energy consumption indicators

have been used previously by Jardini" to scale characteristic.load curves for various types of

consumers. It is worth noting that no relationship between energy consumption and maximum

demand is drawn during the scaling process. Two additional sub-class categories are defmed

below based on the maximum number of vehicles serviced per day. The maximum demand

obtained from the scaled mean load curves for each of the three categories was compared with

utility maximum demands (kVA) indicated on monthly electrical energy consumption bills and

found to correlate satisfactory as shown in the summarised table in Annexure E.

Separate provision has to be made for the power consumption of showrooms and associated

administration and sales building infrastructure.

Sub-classes

Small: A workshop with administrative support, sales function and a daily service throughput of

0-20 sedan, LDV and SUV vehicles. The typical amount of hydraulic lifts installed for this sub

class is between 5 and 10.

Electrical supply requirements: 400V Three-phase with 100A supply circuit breaker.

Estimated NMD: 35 kVA

Typical energy consumption per annum: 0-150,000 kWh [0-12,000 kWh/month]

Typical workshop floor area: < 1000 m2

Medium: A workshop with administrative support, sales function and a daily throughput of 0-50

light sedan, LDV and SUV vehicles. The typical amount of hydraulic lifts installed for this sub


50

Electrical supply requirements: 400V, Three-phase with 200A supply circuit breaker.



Typical workshop floor area: 1000-2000 m2

Large: A workshop with administrative support, sales function and a daily throughput of 0-75

light sedan, LDV and SUV vehicles. The typical amount of hydraulic lifts installed for this sub


Electrical supply requirements: 400V, Three-phase with 300A supply circuit breaker.



Typical workshop floor area: >2000 m2

LI 2: MANUFACTURERS OF BAKERY PRODUCTS

SA SIC CODE: 3041

Description:

Baking systems incorporating rotary rack ovens, deck ovens, convection ovens and associated

equipment such as proofers and mixers that are used to bake bread, roles etcetera. Light industrial

systems do not include large tunnel ovens meant for major baking operations, for example

operations producing 6000 loaves of bread per hour. These systems would use combinations of

electricity and oil, gas, paraffin or diesel.

Sub-classes

Small: A rotary rack or deck oven with associated equipment to bake standard bread (600-900g)

and rolls at a rate of up to 120 loaves of bread pe~ hour. Electrical supply is utilised for most light

industrial application due to safety policies applicable within modem municipal areas for fuel

such as diesel, paraffin, oil, gas etcetera. For fuel application, refer to the manufacturers' data

sheets. For multiple installations,of 120 loaves per hour systems (for example two similar ovens)

the design criteria can be increased pro-rata.


Typical electrical power requirements: 35 kW

Required minimum building floor area: 150 m2

51

Medium: A rotary rack or deck oven with associated equipment to bake standard bread (600

900g) and rolls at a rate of up to 240 loaves of bread per hour. Electrical supply is utilised for

most light industrial application due to safety policies applicable within modem municipal areas

for fuel such as diesel, paraffin, oil; gas etcetera. For fuel application, refer to the manufacturers'

data sheets. For multiple installations of 240 loaves per hour systems (for example two similar

ovens) the design criteria can be increased pro-rata.




Large: A rotary rack or deck oven with associated equipment to bake standard bread (600-900g)

and rolls at a rate ofup to 480 loaves ofbread per hour. Electrical supply is utilised for most light

industrial application due to safety policies applicable within modem municipal areas for fuel

such as diesel, paraffm, oil, gas etcetera. For fuel application, refer to the manufacturers' data

sheets. For multiple installations of 480 loaves per hour systems (for example two similar ovens)

the design criteria can be increased pro-rata.




LI 3: COLD STORAGE WAREHOUSES

SA SIC CODE: 7412

Description:

Cold storage warehouses are storage facilities which incorporate refrigeration systems to cool

down large areas to either freezing or sub-zero temperature levels. Ice-making plants are also

included in this category as all these systems use compressor systems utilising the basic vapour

compression cycle. Characteristic loads are for complete warehouses including associated

administration functions.

Sub-classes

Small: A refrigeration plant with an installed compressor having electrical power requirements of

up to 60 kW. Power requirements are usually specified by appointed mechanical consultants or

suppliers of cooling equipment.

52

Electrical supply requirements: 400V three-phase with 150A supply circuit breaker

Typical warehouse floor area: 750 m2

Medium: A refrigeration plant with an installed compressor having electrical power requirements

of up to 120 kW. Power requirements are usually specified by appointed mechanical consultants

or suppliers of cooling equipment.



Large: A refrigeration plant with an installed compressor having electrical power requirements of

up to 240 kW. Power requirements are usually specified by appointed mechanical consultants or

suppliers of cooling equipment.



3.6.6 Fitting an appropriate distribution function at maximum demand

Daily representative load profiles for the above-mentioned light industrial consumer classes were

prepared by calculating the effective average load current (L) as defined in paragraph 3.6.4.1

above from five minute averaging interval RMS phase currents. Corresponding supply voltage

and PF per phase were also recorded. Sample size was confirmed to ensure that there is a 90%

chance that the values of the mean. effective load current of the sample will fall within 1.64

standard deviations from the mean value of the population's effective load current within an error

margin of 5%. Annexure A summarises a typical spreadsheet. By summating the various daily

load curves (effective load current profiles) per phase, or alternatively by calculating the mean

value of the load current at each five minute interval, a new representative load profile of

effective phase current over a 24-hour day can be found. Furthermore, the standard deviation of

the data (the spread of the data) at each interval can also be calculated and is shown in Figures 3.7

to 3.9. The light industrial consumer groups LI 1 to LI 3 have been included in the above

mentioned representations.

53

"!"l Load Current [Amps) "!"l!is' ....

8~ A

(fCl

= 0 ~ ~en co '" = Load Current [Amps]., 0 p p p .,

tD 0 0 0 0 0 is 0 0 <0 '" w ... '" en0 0 0 0 0 0 0 tD P P 0 P ~ P

~ 06:02:16 Oms ~0 0 8 0 0 80 0 0 0 0

~ 06:47:16 Oms ;;J 06:02:16 Oms

s= 07:32:16 Oms s= 06:47:16 Oms

tD tD 07:32:16 Oms

= 08:17:16 Oms == = 06:17:160ms- 09:02:16 Oms QQ 09:02:16 Oms

= 09:47:16 Oms =Q. Q. 09:47:16 Oms

n 10:32:160ms n 10:32: 16 Oms= m =., 11:17:160ms if .,11:17:16 Oms., .., m

tD 12:02:16 Oms !l tD if= :;r = 12:02:16 Oms.... 12:47:16 Oms

CD .... ~= r- = 12:47:16 Oms

= 13:32:160ms0 =I» 13:32:16 Oms •Q. ... Q. 0

'" 14:17:16 Oms 0 '" 14:17:16 OmsI».... .... c .... ...

= 3" 15:02:160ms ; = .... (')

= CD = 3' 15:02:16 Oms S;Q. 15:47:160ms' a Q.

CD iil

= I» = 15:47:16 Oms a.,16:32:16 Oms :::s .,

16:32:16 Oms I»Q. Q. Q. ::::I

Q. 17:17:16 Oms(I)

Q. 17:17:16 Oms...

C (I)

~. 18:02:16 Oms "E ~ 18:02:16 OmsC.... "E= 18:47:16 Oms

... =- :0: ::t. 18:47:160ms -S· 0

19:32:16 OmsCD Q 19:32:16 Oms

(I)

= ... = 3

I 20:17:160msc' I 20:17:16 Oms .5a.

~ 21 :02:16 Oms ~ 21:02:160ms.. ..N 21:47:160ms .... 21:47:16 Omsn n 22:32:16 OmsQ 22:32:16 Oms Q

= = 23:17:16 Oms'" 23:17:160ms '"= =51 51tD tD., .,

VI.j::o.

·_·_~c~~"",,;c.,~ Si?", c_- -?=:-" ~.• -. ~'··"":::·;;2;,'.:·~¥~"""'·';'·7-' ~-'Y-,""j.,.·"

EffectiveLoadCurrentandSO (LI 3Medium)

300.00

250.00

1200.00

C~ 150.00::Io..,IV.3 100.00

50.00

<II <II .. <II~ ~ ~E E E E

0 0 0 0 0 0 0<D <D ~ <D ~ <D ~;: N N ~ N ~ N

0 '.'l <;:! ~ '":t ~ '" 0 N N ~- '"Time

Figure 3.9: Mean load current and standard deviation - LI 3 consumer:.

If required, the spread of data at each five minute sampling interval can be arranged in the form

of a histogram, but as explained in earlier chapters, the fitting of a continuous pdf to describe the

statistics of the data at any chosen interval results in a useful practical mathematical tool. As the

intention of this research work is ultimately the development ofa statistical model to calculate the

voltage regulation in LV distribution systems feeding the selected industrial group of consumers,

the behaviour of the daily load profiles at their respective instants of maximum demand have

been analysed to make provision for the worst case scenario in feeder voltage regulation. A beta

pdf has successfully been fitted to the data at the various instances of maximum demand as

confirmed by a goodness-of-fit test for the distribution. Figures 3.10 to 3.12 depict the fit of beta

pdfs at the specified intervals of maximum demand followed by the goodness-of-fit results

summarised in Table 3.4.

55

EasyFil- Evaluation VersionProbability Density Function

i!

)655550x

454035

, , • I I , ,I , I I I I I

0.3& -1--------------t-------------~~-------------i-------- - ----r ------ ---- -- -!-- -- ----- - ---- !

0.32 +-------------\------------- :------------+-----------+-------------10.28- -j--------------[------------- -------------~--------------[--------------[

0.24 +------------i-·------ ---- -----+------------1--------------1~ 0, +----------- !--------------!--.--.--------j

I I :0.16 -~------------ -----------+--------------1

1 ! !0.12 +----------- ' ,

!0.08 -j--------- ---0.04- -i---- -------.

Figure 3.10: Fit of beta pdf to LI 1 (Small) including histogram - maximum demand at 14:47 (Figure3.7) X-axis: Amps

EasyFd - Evaluation VersionProbability Density Function

0.01 i -------l-------l--------~-------L_------~----..-: ------: : : : : : : ,

0.00 ~ -------t-------+-------+-------+-------+- ·_--+--------t--- ---t--------r--------t0.008 : ------+-----+----+-----+---- -r------+------+----- 1-------+-------[0,007 : ------+----+----+-----+- --+-----+-------i--------; ------i--------i

~ 0008 i------+-----+----+-------; ------+-----+-------t--------j--- --+-------j~ 0.005" ~ -------+-------t-------+---- -t-------+-------+--------t--------t----- --t--------i

: : : : : : : l 1 i 10.004 I -------+-------+--------1-- -----}.-------~----.---~-------.+--------}------- }--------}

: : : : : : : :: :o.coa ~------.-~--------~------ : --------~-------~--------~------·~t--------t--------~ -------t0.002! --------~------:~-- ----~------)--------l--------l------..\--------i--------~-- -----I0.001! --------l------ -~--------~----.)--------l--------l--------i--------\--------l---- .]

o i .~ .l l j. L l L_. j L io 20 40 60 80 100 120 140 160 reo

x

Figure 3.11: Fit of beta pdf to LI 2 (Medium) - maximum demand at 06:47 (Figure 3.8) X-axis: Amps

56

EasyF~ - Evaluation VersionProbability Density Function

0.03&. ------.-- ----- ----- ------ -----.------ ••-- --~ --- - .-.-- ------••---- ------ ----- -----------10.032· ---------------------------,------------ --j----- --------------------------------------[0.02ll· ------------------------------------- ----j-------- ------------------------------------t0.024. -----------._----------------'-.---- -··---f------·--- ----------------------------------t-

: 1

~ 0.02·. --------------------------------- --------!------------ --------------------------------!-~ i i

::"=:::=-:::-F:::-::===:I0.00 --------------------------- ---------------1------------------ -------------------------1

0.004· ----------------------- ------------------j---------------------- ----------------------1-

o· -------------------------- 1 ----------------------------- :250

X

Bela (255.5; 255.5; 0; 503.54) I

Figure 3.12: Beta distributed current of constant power load class LI 3 (Medium) (Figure 3.9)maximum demand at 10:47 X-axis: Amps'pF =0.86

Goodness of Fit for Beta probability density function-Easy Fit 5.3

Light Industrial -l Dearees of Probability Chi-Squared Successfu

SUb-Class critical freedom 112> 12 critical X Fit

L11 11.07 5 5% 1.4538 Yes

L12 12.592 6 5% 4.8369 Yes

L131 N/A N/A N/A N/A Yes

1- Betapdf loadcurrentequivalent for constant power load

Table 3.4: Goodness-of-fit results for light Industrial sub-classes LI 1 to LI 3

3.7 Concluding remarks on the modelling of light industrial loads

The selected sub-classes have been typified in terms of its demographic features.

It has been shown that by averaging several repetitive 24-hour load profiles of the selected light

industrial classes at each averaging interval of five minutes, an interval of sub-class maximum

demand can be identified. By analysing the statistics at this interval, it has been found that these

sets of data can conveniently be represented by way of a beta distribution. The Chi-square.goodness-of-fit test has confirmed the acceptability of a beta pdf fit to the data. By analysing the

composition of these loads in terms of constant power and constant impedance parametric

characteristics, it has been shown that all can conveniently be modelled as constant current loads

57

within 4% accuracy over the target supply voltage range, including the constant power load,

which can be modelled in terms of an equivalent beta distributed load current.

The latest IEEE definitions of electrical power have been reviewed and the convenience of the

use of an equivalent balanced load current for unbalanced systems have been suggested.

Modelling has been restricted to the measurement of fundamental components as THD of less

than 3% has been observed with the particular pilot group.

The beta distributed effective phase currents at maximum demand can now conveniently be

applied to statistical voltage regulation techniques in LV feeders.

58

4. SUMMATION OFPDFs TO ESTABLISH AGGREGATEDELECTRICAL LOAD HEHAVIOUR

4.1 Introduction

In this chapter the summation of the previously established electrical load profiles of the light

industrial sub-classes will be examined. The aggregated behaviour of groups of consumers as

typically found in industrial parks is of critical importance as this will enable the final

development of a statistical model which can mathematically describe the load characteristics at

the combined instant of maximum demand. The spread of data at this combined instant of

maximum demand will once again be studied to confirm the acceptability of a beta distribution fit

to the data as before. It will also be shown that an algorithm containing libraries of field data of

target groups of consumers can be developed, which can automatically identify an instant of

maximum demand for any combination of sub-classes with data availability in the libraries. Such

an algorithm can provide usable, practical statistical design parameters for voltage regulation

calculations in LV feeder networks.

4.2 Fundamental concepts on the summation of pdfs

Pdfs are used to describe sets of variables which can be represented as X, Y, Z etcetera. A useful

set of characteristics of statistical distributions are their moments.

The mean value of a set of data associated with X, Y or Z can be obtained by calculating the first

moment of a pdf about the origin (J.1), whilst the variance, (a2) of a set of data can be obtained by

calculating the second moment about its mean.

These moments can mathematically be described as follows, with the first moment of a pdf f(x)

given by:

~ = Ix!(x)dx'

The second moment of a pdf f(x) is given by:

ci= Jx2 f(x)dx

(4-1)

(4-2)

The first moment and the second moments are linear in the sense that if X and Yare independent

random variables", then:

59

!l (X + Y) = !leX)+ !leY)

and

var(X + Y)=var(X) + var(Y)

where var = variance =02

(4-3)

(4-4)

The above-mentioned independent variables X, Y and Z can be assigned to the sets of data

obtained at the instant of maximum demand for the LI 1 to LI 3 characteristic daily load profiles.

This implies that the individual means and variances of X, Y and Z can be summated to obtain a

new summated distribution with known mean and variance, but with unknown distribution type.

Unfortunately the summation of similar distribution functions does not necessarily yield a similar

distribution function. For example, the fact that the beta pdf has been confirmed as an acceptable

continuous description for LI 1 to LI 3 at maximum demand does not automatically imply a beta

pdf end result. Annis43 explained that, as an example, when one considers X and Y to have

uniform distributions over the interval (0,1), the distribution of their sum is a triangular

distribution over the interval (0,2). However, the summation of certain distributions remains

unchanged, for example Gaussian distributions remains Gaussian. The aggregated load behaviour

of the selected group of consumers is studied in the next paragraph.

4.3 Aggregated electrical load beliaviour of pilot group of consumers

It has been established that means and variances of independent variables like the data sets of LI

1, LI 2 and LI 3 at maximum demand can simply be summated to derive an aggregated set of

electrical load statistics for the combined group. These variables will eventually be increased to

as many as 10 or 15 to accommodate all the selected light industrial consumer sub-classes. In

general, means and variances of daily load profiles for different sub-classes (LI Ito LI 3) can be

calculated for each averaging interval of five minutes, including the interval ofmaximum demand

as referred to above. Figures 4.1 and 4.2 show the aggregated load behaviour of (LI 1 + LI 2 + LI

3).

60

Individual and composite effective load current (L11 +L12 +L13)450.00

400.00

350.00

300.00

~ 250.00enc.~ 200.00

150.00

100.00

50.00

0.00en Ul en en en en en en en '" '" en '" en '" '" en '" '" en '" enE E E E E E E E E E E E E E E E E E E E E E0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0<0 co <0 ~ <0 <0 ~ <0 <0 ~ <0 ~ <0 ~ ~ ~ <0 <0 ~ <0 ~ <0-e- ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

N N N N N N N N N N N N N N N N N N N N N N0 10 "" (') N ~ c::! If! "" '" N ~ 0 Ii> "" '" N ~ c::! If! "" (')

<0 i.O i-:. cD 0; 0 ~ ~ N M :t Iii <0 <0 i-:. cD 0; 0 N N N M0 0 0 0 0 ~ ~ ~ -e- ~ ... ... ... e- ... ... N N N

Time

Figure 4.1: Aggregated electrical load behaviour (mean load current)

Individual and composite standard deviation (L11 + LI2+ L13)

__Ulsmall

-<>-L12modium

=c=··U3medium

0.00en '" '" rIJ rIJ en en en '" rIJ rIJ '" '" en '" '" en '" en '" '" '" '" enE E E E E E E E E E E E E E E E E E E E E E E E0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0<0 CO ~ <0 <0 <0 <0 <0 ~ <0 CO (l) <0 <0 (l) <0 <0 (l) <0 (l) (l) <0 (l) <0~ ~ ... ... ... ... ... e- ~ ~ ... ... ~ ... ... ... ... ... ... ... ... ...N ;..:. N i-:. N i-:. N ;..:. N t: (-oj ;..:. N i-:. N i-:. N ;..:. N ;..:. N ;..:. N ~0 ""

(') ... 0 "" '" ... 0 "'f '" ~ 0 "" '" -e- 0 ""(') e- ':=! ~ '"<0 cO ;..:. cD 0; 0; 0 e- N N M ~ Iii Iii cO t-: cD CO 0; 0 N ... N M

0 0 0 0 0 0 ... ... ... ~ ~ ~ ... ... ~ -e- ... ... ... N N N N

Time

Figure 4.2: Aggregated electrical load behaviour (SD)

20.00

40.00

10.00

60.00

50.00

c~III 30.00a.E-c

61

4.4 Development of an electrical load summation algorithm which can identify the

instant of maximum demand

4.4.1 Processing of field data

The pilot field survey which was conducted for the selected sub-groups of light industrial

consumers resulted in the creation of three different libraries of relevant electrical load data for

the above consumer groups at five minute integration intervals over repetitive 24-hour load

cycles. Table 4.1 is an extract of a typical LI 2 library spreadsheet for three measurement

intervals on the same day. The table indicates the measured electrical parameters.

Date . 1/8/2009 1/8/2009 1/8/2009Time 09:12:16 Oms 09:17:16 Oms 09:22:16 OmsVa 236.126 235.913 235.51Vb 237.074 237.121 236.339Ve 237.666 237.974 237.335la 88.227 63.409 82.773Ib 98.318 66.136 95.591Ie 138.955 93.682 128.591PF 0.981 0.905 0.985

PF2 0.96 0.82 0.97

Self 81.21 55.32 76.02

lelf 113.90 77.48 106.77

lei 12973.09 6003.66 11399.67

Table 4.1: Extract of typical five minute load data recorded

Where:

Va, Vb, Vc= Phase to neutral voltages (Volts)

la, lb, Ie = Load currents (Amps)

PF = Average power factor of all phases

Seff=Se = Effective apparent power (as defined in paragraph 3.6.4.1)

leff= I, = Effective balanced load current (as defined in paragraph 3.6.4.1)

In = Neutral current - calculated and used in Equation C-2.

By utilising an Excel spreadsheet for the above recordings and calculations (separate sheets for

each sub-class have been used), mean and variance values for effective. load current (balanced

equivalent as discussed previously) and PF could be obtained for each five minute interval per

62

!.

sub-class by using fundamental statistical principles. A simple routine, which adds means and

variances for selected combinations of sub-classes at each interval, was introduced with an option

of selecting a scaling factor for larger' or smaller installations as per the previously defined

demographic parameters. By utilising Excel look-up tables, the interval of maximum demand

(maximum mean effective load current) could be selected automatically for any combination or

quantity of sub-classes for LI 1 to LI 3. A PF calculation which combines individual sub-class

PFs at maximum demand has also been introduced in the algorithm. This calculation resolves

individual apparent powers (S) into its components of active (P) and reactive (Q) power; adds

active and reactive power of the selected combination of sub-classes and re-calculates the

aggregated PFtot as mathematically described by Equation 4-1 and further explained in Annexure

A:

PFtot = CosfI'an' LQILP) .. (4-1)

In an attempt to provide a "normalised" maximum demand at unity PF, the identified values of

the aggregated effective load current at this interval is adjusted for PF = 1.

Finally, the algorithm also has an option to select an unbalanced load current percentage at

maximum demand, which has the same effective apparent power as the balanced equivalent (Se).

4.4.2 Analyse statistics of aggregated load current at maximum demand and select suitable

pdf

In an attempt to describe the load current at the instant of maximum demand (as identified in

paragraph 4.4.1) mathematically, a suitable load current distribution (pdf) must once again be

found to describe the summated loads as accurately as possible. Due to the versatility of the beta

pdf and its appropriateness to the description of load current of individual sub-classes at

maximum demand, it has been decided to test its validity for all combinations of LI 1 to LI 3 by

generating beta-distributed random numbers with the same mean and variance as the individual

distributions. The Easy Fit 5.3 software package was again utilised to generate 500 beta

distributed load currents for each sub-class and to summate various combinations of sub-classes

to derive new sets ofdata for: (LI 1 + LI 2), (LI 1 + LI 3), (LI 2 + LI 3) and (LI 1 + LI 2 + Ll3).

The new sets of data were all tested for goodness-of-fit against a beta pdf and found to be an

acceptable fit. Figure 4.3 indicates a histogram and beta pdf fit for the summation ofLl 1 to LI 3.

63

EasyFit·Evaluation VersionProbabnfiy Den_tty Function

0.22: -------T----------------------------------f----------------------------------r------------0.2' -------+----------------------------- ---------------------------f------------

0.18' --------~--------------------- -----------------f------------: :

0.1B -------+------------------ -----------------r------------0.1 -------+--------------- -- - -------------+-----------

_ 0.12 --------f----------- -------!------------~ 0.1 ------.-l------- -------L-----------

I :

0.08' -------+----- --- ----·f------------0.06 --------~ ----- L _0.04 J

350 400X

450

Figure 4.3: Histogram and beta pdf fit of the summation of LI 1, LI 2 and LI 3 at combinedmaximum demand (also refer to Figure 4.1)

Table 4.2 summarises the results of the statistical parameters associated with various

combinations of the sub-groups at the specific intervals ofmaximum demand. It also provides the

results ofthe Chi-square goodness-of-fit test.

Aggrtp1Jd50__

IIl1tMI of max. dtrmmd a p C P rl SUM Betapdfteststatistic SuccessfuCalculated Random numbel$ ChI-5quared Belaflt

u rI- u rI- liCritical lc.knl>lOl

lI1 35.36 80.49 150 45.78 40.94 (k09) (k09)

U1+lI2 822 153.88 546.36 153.51 538.44 15.5 8.26 YeslI2 10.08 8.57 200 108.1 505.42

lI1 36.15 76.306 150 48.22 4327Ul+lI3 12:42 299.52 188.97 299.5 179 15.5 10.212 Yes

lI3 255.5 255.5 502.67 251.3 123.7

lI2 10.08 8.57 200 108.1 505.42U2+lI3 822 356.55 625.98 356 635 15.5 9.815 Yes

lI3 255.5 255.5 496.9 24845 12056

lI1 35.36 80.49 150 45.78 40.94Lll+lI2+U3 822 lI2 10.08 8.57 200 1081 505.42 402.33 886.92 401.9 672 155 8.8.4 Yes

lI3 255.5 255.5 496.9 248.45 ·120.56

Table 4.2: Beta goodness of fit summary for aggregated groups of light industrial sub-classes

The results displayed in Table 4.2 also confirm the linear relationship of the first and second

moments as indicated by equations 4.3 and 4.4. The specific intervals of maximum demand were

located by utilising the algorithm as described in paragraph 4.4.4.

4.4.3 Calculating the descriptive parameters of the beta pdf at maximum demand

It has been confirmed that combinations of beta-distributed load currents of LI 1 to LI 3 at

maximum demand results in a distribution which can also adequately be described in terms of a

beta distribution (pdf) as summarised in Table 4.2.

64

It

Beta pdfs can be described in terms of three parameters, namely (1, ~ and C as defined by way of

equations 3.1 and 3.2. The new algorithm, which is to be explained by way of a flow diagram in

the next paragraph, calculates the above parameters automatically after identifying the effective

mean balanced load current at maximum demand, as well as its associated spread (variance). The

scaling factor, C, usually corresponds to the value of the installed feeder circuit breaker for a

specific sub-class as identified in paragraph 3.6.5.

The beta pdf presented in Figure 4.3 can be presented using the following parameters:

J.l = 402.33 Amps

ci = 666.92 Amps'

o = 25.82 Amps

C = 600 Amps (Circuit breaker values ofLl 1+ Ll 2 + Ll 3) See paragraph 3.6.5

a = Il(CIl-Il/\2-a/\2) = 79.29Ca/\2

p= (C-Il)(Cfl-f.l/\2-a/\2) =38.95Ca/\2

A similar procedure can be followed for any beta-distributed data set (load current at maximum

demand) to obtain the descriptive parameters for the mathematical function if the above statistical

parameters are available.

4.4.4 Flow diagram of the new algorithm

The data flow of the new algorithm is outlined in Figure 4.4. The input/output parameters of the

algorithm can be summarised as follows:

Input parameters:

• Select any combination ofLl 1, Ll 2 and LI 3.

• Select small, medium or large installations as per demographic descriptions.

• Select repetition of Ll 1 or Ll 2 or LI3 within the specific group.o

• Select the percentage imbalance of load current, for example 0%, 10% etcetera.

• Select required combined PF.

65

Output parameters:

• Effective mean load current at maximum demand for combined group.

• Time interval of selected aggregated group maximum demand.

• Standard deviation of effective mean load current at maximum demand.

• Mean total PF at maximum demand.

• a, ~ and C values at maximum demand per phase.

• Calculation of required transformer size to feed the selected combined load with a 10%

associated risk.

• A 24-hour effective mean load current profile with associated standard deviation on

five minute intervals ofthe combined load selection in graphical format.

66

Comments

Figure 4.4: Flow diagram of new algorithm to establish beta parameters at summated load maximumdemand

67

4.4.5 Field measurements of aggregated load profile versus forecast load profile utilising

new algorithm

In an attempt to prove the validity of the summation function of the new algorithm in the field, it

was necessary to locate an existing LV feeder installation, comprising of a combination of the

researched group of light industrial consumers, on which separate and combined load profiles

could be recorded.

An LV feeder arrangement was located in an industrial zone in Polokwane, South Africa, which

comprised of one of each of the following combination of light industrial consumers fed from a

315 kVA miniature substation:

• LI 1- Automotive Service workshop (small) (field data available)

• LI 4 - Auto Body repairs / painting workshop (new field data recorded)

• LI I - Auto Tuning workshop (very small) (field data available by scaling)

Figure 4.5 depicts the measurement arrangement for the LV feeder.

12

100 A

'3

1

verySII1111

serviceWarkshap

14

§Logger

#1(A1llII"8ll11tBd

dlIlIllndI

VIndependent Measurements

(time stampedl

Figure 4.5: Measurement arrangement for aggregated load study

68

Data loggers one to four represent typical connection positions of the data logging equipment.

The four measurements were not synchronised but were independently recorded to obtain

individual representative 24-hour mean and standard deviation load profiles at time-stamped five

minute intervals. The recorded data allowed the algorithm to summate means and variances (as

before) for each sub-class to calculate an aggregated load profile. Data logger number one

recorded the actual aggregated load current representing the combined effect of the three sub

classes.

Load profiles for the measured and calculated combinations of light industrial consumers are

shown in figures 4.6 and 4.7. A satisfactory correlation is seen in mean values and variances,

whilst the differences in maximum demand amounts to approximately 4%, with a slightly higher

predicted maximum demand calculated by the algorithm using statistical techniques. The wider

spread of data as observed on the standard deviation (SD) profile of the measured load profile

possibly indicates the necessity for a larger sampling size, but as LI 4 (Auto panel beater

workshop) is not included in the primary study field ofthe research, the sampling size will not be

expanded at this stage:

69

:clQii1

lQ

~Q.

rDIQ.

"0a::!Iii''i

CD

IIIc:iila

Amps.... ... :t:f\) .... en en 0 N

P 0 P 0 0 0 00 0 0 0 0 0 00 0 0 0 0 0 0

ooo06:02:16 Oms

06:57:16 Oms

07:52:16 Oms

08:47:16 Oms

09:42:16 Oms

10:37:16 Oms

11:32:16 Oms

12:27:16 Oms

13:22:16 Oms

-I 14:17:16 Oms

~. 15:12:16 Oms

16:07:16 Oms

17:02:16 Oms

17:57:16 Oms

18:52:16 Oms

19:47:16 Oms

20:42:16 Oms

21:37:16 Oms

22:32:16Oms

23:27:16 Oms

~1iQ.

="'ltD....~

i'"="'ltD=-Jg

i=0'=="'Cl"'lo=;-

Amps ... ... ...'" .... 0> CD 0 '" ....

0 0 0 p 0 0 0 p0 0 0 0 0 0 0 00 0 0 0 0 0 0 0

06:02:16 Oms

06:57:16 Oms~

liS· . 07:52:16 Oms

='"l 08:47:16 OmstD.... 09:42:16 Oms~

10:37:16 Oms ):-

~lQ

11:32:16 OmslQ...

0 CD'"l 12:27:16 Oms lQ::;: DICI" ....

13:22:16 Oms CDa Q.

n -I 14:17:16 Oms r-= 0- ~. 15:12:16 OmsDIn Q.=£;" 16:07:16 Oms "0.... ...

tD 0

=- 17:02:16 Oms :=0' ij)

17:57:16 Oms ......= ~=-"'Cl 18:52:16 Oms lQ"'l 00 19:47:16 Oms 3:= :TtD 20:42: 16Oms ].

21:37:16 Oms

22:32:16 Oms

23:27:16 Oms

'Io

4.4.6 Suggested statistical description of selected group of light industrial consumers at

interval of maximum demand

The new algorithm can conveniently be used to establish beta parameters at maximum demand

for individual or combined groups of the selected sub-classes. Table 4.3 summarises the

individual descriptive parameters for the researched groups of light industrial sub-classes. For

combinations of these sub-classes, the special algorithm, containing the original libraries of

electrical load data, has to be used. The standard deviation values for LI 3 has been approximated

as zero. For accurate values, the algorithm can be utilised.

Light industrial consumer descriptive parameters at max. demand for PF=l

and balanced 3-phase load conditions

Mean SO AOMOSub-Class Category a 13 C II C1 (kVA).

L11' Small 25.74 31.01 100 45.3 6.5 31L11 Medium 20.19 15.42 200 113 16.4 78L11 Larqe 20.19 15.42 300 170 24.57 117

L12' Small 3.9 2.6 100 60 17.9 41L12 Medium 3.9 2.6 200 120 35.8 83L12 Large 1.45 0.36 300 240 71.6 165

LI 3' Small 255.5 255.5 217.69 108.8 0 75L13 Medium 255.5 255.5 435.38 218 0 150L13 Large 255.5 255.5 870.76 435 0 300

Notes. (1) Forunbalancedsystemsreler to algomhm (2) Forcombinations 01SUb-classes relerto algonthm

Table 4.3: Descriptive parameters of selected light industrial sub-classes at maximum demand for abeta distribution of data

4.4.7 Concluding remarks on new algorithm

The fundamental concepts of the summation of pdfs have been reviewed before being applied

within the new algorithm in order to add daily mean load profiles of any number or combination

of light industrial sub-classes at the instant of maximum demand. The algorithm consists of

libraries of electrical field data describing the selected sub-classes, namely LI 1 - LI 3, over

repetitive 24-hour cycles and calculating mean values of data with its associated statistical spread

at five minute time intervals for each sub-class. By adding means and variances of selected sub

classes, aggregated load profiles are developed.

. A look-up table facility in Excel establishes an interval of maximum mean effective load current

(as previously defined) for the aggregated behaviour of a selected group within a 24-hour load

cycle. The typical distribution of load data at various combinations of sub-classes was studied to

confirm the appropriateness of a beta pdf description of the data at maximum demand. It was also

shown in Table 4.2 that intervals of maximum demand vary for different combinations of sub-

71

classes. A Chi-square goodness-of-fit test was performed on various combinations/summations of

LI 1 - LI 3 and it found the beta pdf to be a representative description of the data in all cases.

The usefulness of the algorithm was further expanded by making provision for the selection of

different PF levels for combined groups of sub-classes as well as the introduction of a load

current imbalance factor to simulate typical unbalanced three-phase, four-wire, LV feeder

arrangements found in industry today. Adjustments in load current per phase (L, lb, L: and In) are

done around the value of the mean effective load current (L) to always ensure a constant effective

apparent power at maximum demand as previously defined. Finally, the algorithm calculates the

typical sizing of transformers to supply these aggregated light industrial loads with electrical

power.

The algorithm provides as an output useable beta pdf paraineters per phase, which can be

exported to a statistical voltage regulation algorithm, as will be studied in the next chapter, to

design MY and LV feeders for the selected groups (or individuals) of light industrial consumers.

By adding additional libraries of field data for other light industrial consumers to the algorithm, a

holistic model can be found for use in future greenfield light industrial park load forecasting or

where refurbishment of existing industrial areas with known groups of consumers is required.

72

5. APPLYING THE HERMAN-BETA VOLTAGE REGULATIONMODEL TO LIGHT INDUSTRIAL CONSUMERS

5.1 Introduction

The significance of the establishment of the usable descriptive parameters of the selected

industrial consumers at the instant of maximum demand lies in the fact that it can be used in a

statistical model to design the components of LV feeders to supply such loads from a power

source which can include, amongst others, transformers, generators and renewable power sources.

LV feeders are usually designed for worst case electrical loading conditions to ensure acceptable

voltage regulation at the furthest supply point from the energy source.

The selection of the correct load model and subsequent calculation of voltage drop in feeders is

extremely important as a poor correlation of predicted versus actual network performance can

result in over- or under-investment in capital and energy. In previous chapters it has been shown

that the selected group of light industrial consumers can adequately be described as stochastic

constant current loads with a beta distribution of load current at maximum demand. The statistical

description of these loads calls for a statistical method to analyse voltage regulation and to design

the LV and MY feeder components in distribution networks.

Various voltage regulation algorithms are available in the world today which can broadly be

divided into deterministic algebraic approaches and probabilistic models. Research done by

Sellick and Gaunt" has shown that the following six models are presently being used in South

Africa and the UK:

1) Monte Carlo Simulation developed by Dekenah".

2) A British method" based on a normal load distribution, which includes loss of

diversity and an unbalance factor using empirical formulas, but treats all the

consumers along a feeder as a lumped load. Therefore no information is available at

the various cascaded sections. Empirical formulas are based on a 90% confidence

level and standard deviation is undefined.

3) DT Volt Drop47 incorporates the British method, as stated above, but adapted to

South African conditions, known as the AMEU method. The formulas have been

defined in equations 2.6 and 2.7. ADMD is used with no dispersion of the load at

maximum demand.

4) The Loss of Diversity method developed by Gaunt" was derived from Monte Carlo

simulations using load models defined as normal distributions with different levels of

I,73

dispersion around the mean (ADMD), which is referred to as the slenderness factor

(s, and s = lila). This method utilises a series of tables to calculate loss of diversity,

which results in a complicated algorithm when calculating voltage drop in feeder

arrangements. This method also solves the problem of a feeder with distributed loads

in a single step.

5) The Unbalanced Voltage Drop method was developed by Dekenah'" and is based on

real load distribution of a typical consumer with adjustment for the number of

consumers. The factors used for the adjustment are based on loads being balanced as

far as possible at each node.

6) The Herman-Beta algorithm" is a statistical voltage drop algorithm which uses a beta

distribution of the load current at maximum demand. This model is currently

applicable to single-phase, bi-phase and three-phase distribution networks where the.«

load behaviour is of the constant current type, beta distributed at maximum demand

and with a unity PF. Characteristic beta distributed design parameters are available

for the South African residential consumer group and have been published

extensively. This method utilises a specified level of confidence (or inversely a risk

factor) to derive a single value of voltage drop on a specific feeder section per phase

or for a total feeder. This method calculates neutral load current in unbalanced

systems automatically and adjusts voltage drop levels accordingly.

Sellick and Gaunr'' have concluded their comparative work on the different models by classifying

the Herman-Beta algorithm as the most consistently reliable for voltage drop calculations of the

alternatives considered. These comparisons were made between the different models and a

standard Monte Carlo base case simulation yielding"inaccuracies of up to 40% of the base case.

The Herman-Beta algorithm provided voltage drops within 10% of the base case. This method is

presently accepted as the only valid design algorithm in South Africa and has been published in

the, NRS-034-l 27 standards document.

In the past, the application of the Herman-Beta algorithm has mainly focussed on the statistical

voltage regulation studies of residential consumers and to a lesser extent to constant power loads,

for example water pump installations, which can also be described in terms of beta-distributed

load currents that are associated with specific levels of confidence as reported before. The light

industrial load study has now provided another unique application opportunity for the Herman

Beta model to enable the accurate specification of, and economical feeder component sizing in,

three-phase distribution networks.

74

The statistical summation algorithm as developed for the light industrial consumers (LI I - LI 3)

in chapter 4 provides usable, practical input design parameters for the Herman-Beta voltage

regulation model.

5.2 Suitability of the Herman-Beta model for light industrial LV feeder design

5.2.1 Summary ofthe fundamental concepts ofthe Herman-Beta model

The Herman-Beta model was developed during 1990 by Dr Ron Herman" when it was noticed

that the spread of residential load data at the instant of maximum demand for the South African

consumer displayed a skewed dispersion and not a normal distribution as was previously

reported. A need also arose for a .model that could conveniently accommodate statistical risk

factors in the design as well as instances of unbalanced load conditions in single-phase, bi-phase

and three-phase networks. A risk factor of zero would imply a worst case feeder design condition

utilising the maximum load current recorded during a field survey whilst a risk factor ofbetween

, zero and 50% would result in more conservative LV feeder design or lower voltage regulation

levels. Typical risk factors would be between 10%and 20%.

The analysis of the field data of the residential consumer loads yielded beta distributed load

currents at the instant of system maximum demand, established at 12 noon on a Sunday afternoon

for the South African scenario. A detailed study of the development of the Herman-Beta model

which includes the derivation of statistical voltage regulation mathematical tools is presented in

the PhD dissertation of Ron Herman!' previously referred to. However, some of the relevant

fundamental concepts are revisited below.

The beta description of the load data has the following benefits as opposed to previous statistical

models:

• It is constrained to a finite base in the same way that load currents are confined

between zero and the circuit breaker limit.

• It can be negatively.and positively skewed.

• Its parameters a and ~ can easily be calculated from field data.

• The use of a beta pdf with associated risk factor eliminates the need for diversity

correction curves.

75

It was further established that residential loads can parametrically be represented as constant

current loads at instances of maximum demand as this was the best representation of the mixture

of constant power and constant impedance loads usually found in the residential sector. This

allowed for a linear description of the voltage drop calculation in feeder networks, which

simplified calculations considerably. It was also established that residential loads could be

approximated as resistive loads with unity PF at maximum demand.

In developing the Herman-Beta model, the following assumptions were made and remain a pre

requisite for the voltage regulation modelling of other feeder networks incorporating different

types ofload models:

• Maximum voltage drop occurs at interval ofmaximum demand.

• Loads are represented as currents at unity PF.

• At any specified interval, the collective loads may be represented as statistics whose

description fits the beta pdf.

• At this interval, load currents are assumed to be independently distributed.

• LV feeder impedance is regarded as resistive at a specified temperature.

The basic voltage regulation relationships were developed for a single section of a distribution

feeder. Such a network is shown in Figure 5.1:

r--------II

eLoad

IIIII8denctt

Figure 5.1: Network of a single section distribution feeder

Impedances of feeder conductors are shown as resistive because inductive and capacitive

reactances are usually negligible under modem residential underground reticulation conditions.

76

With reference to Figure 5.1, R, and Rn represents phase conductor and neutral return conductor

resistances respectively. In practical networks, Rn is usually equal to R, and is therefore indicated

accordingly in Figure 5.1. The load current phasors are la, Ib, and I; The neutral current (In) is the

phasor sum of the phase currents.

If there are lIla, II1b and m, consumers with beta distributed load currents, then their probable

combined current may be expressed by:

I. = C[ YI +.....+ Yma]

I, = C[YI +....+ Yme]

where C = scaling factor

and Y = random variable O<Y<1 drawn from beta pdfwith parameters a. and B,

(5-1)

(5-2)

(5-3)

It can be shown that the voltage drop across R, is also beta distributed similar to the consumer

voltage Veon' By calculating the beta parameters a.* and ~* of the consumer voltage from the first

and second statistical moments of the beta pdf of the consumer voltage, E(V* can t) and E(V*can ?)respectively, a quantile" value, E(V*eon t), can be obtained corresponding to a chosen value of

confidence. This value may be extracted from the consumer voltage pdf using the inverse beta

function available in most spreadsheets.

The actual consumer voltage for this quantile value, Veon, is finally given by:

Vcan = E(V* can t)(Vmax-Vmin) + Vmin (5-4)

Where Vmax and Vmin are maximum and minimum values of the consumer voltage Vcan 1.

A modem spreadsheet program has been developed by Ron Herman which incorporates the

tedious algebra into a practical easy to use voltage regulation model. The following input and

output parameters are found in the Herman-Beta algorithm:

Inputs:

• Select line typology,

• Choose load type: u, ~ and C (Circuit breaker value) for each node,

• Assign customers to phases and nodes,

77

• Select conductor size: Rp and Rn,

• Select operating temperature of feeder cables,

• Select feeder lengths between nodes,

• Select supply voltage per phase, and

• Select level of confidence or risk.

Outputs:

• Consumer voltage per phase at selected nodes,

• Voltage regulation per phase,

• Transformer size,

• Mean summated load current (ADMD), and

• Standard deviation of summated load current at maximum demand.

5.2.2 Modelling of light industrial consumers as beta-distributed constant current loads

It has been shown in chapter 4 that individual or aggregated groups of light industrial consumers,

as selected for the pilot study, can adequately be described in terms of beta-distributed load

currents at their respective varied instances of maximum demand. Tables 4.2 and 4.3 have

summarised the descriptive parameters of these loads at maximum demand. It is intended to

further expand the study of the load characteristics of light industrial consumers by also including

other typical sub-classes as summarised in Table 3.1. The subsequent work will follow this initial

work on the behaviour of the pilot group of light industrial consumers. Due to the typical constant

impedance or constant power behaviour of most industrial loads, its likely inclusion into the

present statistical models is expected.

By including the descriptive electrical load parameters of the selected sub-classes into an LV or

MY feeder arrangement for a specific scenario, the Herman-Beta algorithm can conveniently be

used to calculate the consumer voltage at selected nodes. Figure 5.2 presents examples of single

line diagrams of two applications of different light industrial load configurations in preparation

for a Herman-Beta voltage regulation calculation.

78

Feeder #1

eo40 50x

EasyFil~ EvaluationVersionProbability DensityFunction0.3sr-~,..--':"'-...----n

MV/LVTransformer

Node 1 LI 110 Histogram - Beta

Feeder '2

EasyF~ - Evaluation VersionProbabnily Dansily Function

250 300x

ID Histogram - Beta

MV/LVTrensformer

Node 1 LIt

Ie (a.,tJ •• C.1

~ 200 250

Node 2 LI3 ID Histogram - Beta

Figure 5.2: Examples of feeder configurations for two light industrial applications

Feeder number 1 represents a three-phase, four-wire system feeding a single light industrial

consumer (node 1) of sub-class LI 1 (small). The effective load current, as previously defined, is

represented as a beta distribution at maximum demand, which would typically occur at 14:47,

with parameters u\, ~\, and Cl. Figure 3.7 and Table 4.3 are relevant to this example.

Feeder number 2 represents a similar arrangement, but has two light industrial consumers

connected to the network. Consumer LI 1 (small) is connected to node 1, whilst a consumer of

sub-class LI 3 (medium) is connected to node 2. The effective load current at maximum demand

and time of occurrence differs for the feeder sections connected to node 1 and node 2. The

descriptive beta parameters of the effective load current in the feeder connected to node 2 is uz,

~z, and Cz at maximum demand, which would typically occur at 10:47. Figure 3.12 and Table 4.3

are relevant. The descriptive parameters of the effective load current in the feeder connected to

79

node 1 are an aggregated load current distribution consisting of the sum of LI 1 and LI 3. As can

be seen from Table 4.2, the instant of maximum demand for this first feeder section typically

occurs at 12:42. The unique beta parameters for the first section are 113, ~3' and C3 at maximum

demand.

5.2.3 Effect of non-unity PF on Herman-Beta calculations

The Herman-Beta voltage regulation algorithm has been developed with certain assumptions

regarding the required statistical load model, parametric description of the load, feeder impedance

and PF of the load. The algorithm has initially been developed to accommodate the residential

consumer group, which has traditionally been associated with a close-to-unity PF, especially at

the instant of system maximum demand. The algorithm was therefore originally developed to

model non-complex loads which simplified voltage drop calculations, preventing the use of

complex algebra in these calculations.

The study of the behavioural electrical load profiles of the selected group of light industrial

consumers has revealed, as expected, that industrial consumer loads are generally complex of

nature with PFs smaller than unity, typically in the range of 0.8 to 0.98. The field measurements

of the pilot group that were recorded at five minute intervals (as reported in previous chapters),

therefore also included PF measurements. The mean PF values at each time interval per sub-class

are utilised by the new summation algorithm to calculate the aggregated PF required to adjust the

effective balanced load current at the instant of maximum demand to an equivalent load current at

unity PF. By establishing the beta parameters of the effective (balanced) load current at unity PF,

the Herman-Beta algorithm can conveniently be applied to voltage regulation calculations. As

complex electrical loads are usually intentionally compensated to adjust the PF to close to unity,

thereby reducing peak load current, the voltage regulation calculations using the Herman-Beta

algorithm should normally yield satisfactory results.

However, the new summation algorithm has also been developed to select non-unity PF scenarios

to statistically simulate these non-ideal conditions where additional voltage drop can be expected.

In order to prevent the complete re-engineering of the Herman-Beta model, it has been decided to

.calculate the error in voltage regulation calculations by using mathematical formulae and phasor

diagrams.

Figure 5.3 shows the phasor diagram of one phase of a three-phase system with the supply

voltage (Vs) equal to the phase to neutral voltage as a reference phasor. The load current I, is also

represented as a phasor. Figure 5.4 is a simple per phase circuit diagram representation of a feeder

80\'

network, indicating a resistive (R) conductor and a complex load Z. Veon is the consumer voltage

and AV is the voltage drop across the conductor.

Figure 5.3: Phasor diagram indicating the magnitude ofthe consumer voltage

I-AV--fR Ie

YS i Yean

Figure 5.4: Per phase circuit diagram of a simple feeder arrangement

The complex load current can be represented as follows:

I, = Iecosf +j I, sinS

PF = cosS

(where I, is a scalar value) (5-5)

(5-6)

With reference to the phasor diagram in Figure 5.3 and circuit diagram in Figure 5.4, the scalar

value of the consumer voltage phasor can be represented as follows:

Venn = .J(Vs - ~V cos'0)"'2 + (ilV sin 0)"'2 (5-7)

The scalar value of the voltage drop across R with constant load current has the following linear

relationship:

81

Ii.V = I. .R and

Veon = V s - Ie-R

Therefore:

Veon(eompl.x) = ~(VS - Ie.R cos (})"'2 + (Ie.R sin (})"'2

(5-8)

(5-9)

(5-10)

The Herman-Beta model, on the other hand, will assume that the load current Ie feeds a resistive

load with unity power, which will result in a consumer voltage as shown by the following

equation:

V eon(HB) = V S - I e-R (Herman-Beta linear relationship) (5-11)

The error margin when applying the Herman-Beta algorithm to non-unity PF feeder arrangements

is therefore provided by the following ratio:

Error ratio =Veon(eomplex)Neon(HB)

If this ratio is solved for a typical feeder configuration where:

Vs = 230 V, Ie = 200A, R = 0.050, cosu= 0.8, sinS = 0.6

then it can be shown that:

Vcon(compl.x)Neon(HB) [Typical] = 1.009

(5-12)

(5-13)

This implies an error margin of less than 1%, suggesting that the Herman-Beta algorithm can

comfortably be applied to non-unity PF applications for purposes of voltage regulation

calculations when PFs are between 0.8 and 1.0.

82

5.2.4 Concluding remarks on the application of the Herman-Beta algorithm to beta

modelled constant current light industrial consumer loads

With reference to earlier pre-conditions for the application of the Herman-Beta model, Table 5.1

outlines conformance ofthe pilot group oflight industrial consumers to the above conditions.

Conformance of light industrial pilot group load model to HB pre-conditions

Condition Conformance

1 At any specified interval, collective loads may be Yesrepresented as statistics whose description fits theBeta probability density function (pdf)

2 Loads are represented as constant current "drains" Yesat unity power factor.

3 Maximum voltage drop occurs at interval of Yesmaximum demand

4 At interval of maximum demand, load currents are Yesassumed to be indeoendently distributed.

5 LVfeeder impedance is regarded as resistive at a Yesspecified temperature.

Table 5.1: Conformance of light industrial pilot group load model to Herman-Beta pre-conditions

5.3 Applying descriptive parameters of the new algorithm to derive practical, usable

distribution component sizing for the pilot group oflight industrial consumers

5.3.1 Input/output parameters of the new algorithm

The flow diagram of the new algorithm has been discussed in paragraph 4.4.4 and is

diagrammatically represented in Figure 4.4. Table 5.2 represents the Input/Output sheet for a

specific load condition where input parameter options have been indicated in blue font, whilst

output design parameters are depicted in red font. The total algorithm consists of field data sheets,

look-up tables, beta parameter calculators and an aggregated load current profile.

83

21.79 0.00% 0.805TD Am s PhaseCurrent Imbalence Power Factor Correct

Inputs in Blue

27.24

a·Phase123.72 kVA

STDPF 0.80

23.37

546.35 08:22:16 OmsVAR (Amps2) Time

STD Am s0.93

179.30

Mean PF

leffIa 179.30Ib 179.30le 179.14C 300.00

300

16.6311.35

300.00

Ic

200

.»

16.8411.33

300.00

1 100

Ib

Class/Scale "C"

11.3316.84

300.00

la

"C" Inputs in blue

PER NODELJ·1

LJ·3

MIXURE OF LOADS

LJ·2

123.72147.78

kVAkVA

Table 5.2: A sample input/output sheet which calculates design load parameters for the Herman-Betamodel- balanced three-phase load scenario

The algorithm starts with the identification ofthe selected load's (LI l+LI 2) instant of maximum

demand and records both mean effective load current and standard deviation at this specific

instant. The PF at the same interval is recorded and a new balanced mean effective load current is

calculated for the unity PF.

Thereafter a new PF can be selected, which adjusts the value of the mean effective load current

accordingly (for example 0.8). A phase current imbalance adjustment option also exists, which

adjusts the load current around the balanced mean by adding a percentage to the mean load and

calculating the third load and neutral currents in order to ensure a constant value of the effective

84

apparent power at maximum demand. Annexure C summarises mathematical formulae applied to

perform the above calculations.

Beta pdf parameters are automatically calculated per phase, which will be similar for balanced

three-phase systems and different for unbalanced systems. Figure 5.5 is an automatically

generated daily load profile provided by the new algorithm for any selected load condition.

EffectiveLoad CurrentandSO (L11+L12)

180.00

160.00

i 140.00

!1: 120.00eJ 100.00

] BO.OO

"~ BO.OOEEiii 40.00

20.00

Time

Figure 5.5: Daily mean load and associated standard deviation profile for selected group (LI 1 + LI2)

Lastly, the new algorithm calculates the required effective apparent power transformer rating as

outlined in Equation 3.13. By assuming a normal distribution at transformer level and adding a

10% uncertainty factor to the mean effective load current (mean + 1.28.a), a conservative design

specification can be obtained for a suitable distribution transformer.

5.3.2 Guidelines to' the calculation of conductor sizing

The Herman-Beta model has traditionally been applied to single-phase residential consumers with

unique beta parameters for specific residential load classes. In the case of three-phase loads,

balanced conditions with similar beta parameters per phase are usually modelled. It will be shown

that unbalanced three-phase loads. can be modelled by distributing phases over different nodes

with feeder lengths between nodes approximating zero. The required input parameters to the

Herman-Beta model were presented in paragraph 5.2.1.

85

5.3.2.1 Balanced three phase load scenario

Table 5.3 represents a typical Herman-Beta spreadsheet, where a single node balanced load

condition has been taken to establish the voltage regulation at the furthest point from the

transformer for a specific confidence level and conductor size. The conductor length between the

transformer and the load node has been taken as 100 m. The aggregated load as calculated in

Table 5.2 has been incorporatedinto the example.

VS 2Ju.OnORiskl\t Yll)

HOOe Number Red White 81ue Alpha 8eta Cb lenath k cableCOnsumers rna mb me =Rn/rp code

1 lYYYt I'Y11·"'·1 16.84 11..33 300 T W(<fJS- 0.7 3 60 50 1 AllCl5

- 0.7 3 60 50 1 A8C3S155 255 43.48 1 1 AllCJ5

- 0.7 3 60 50 1 AllC350.7 3 60 50 1 AIlC35

- 0.126 1.997 60 50 1 A8CJ5- 0.126 1.997 60 50 1 AllC35

0,126 1.997 60 SO 1 A8C35- 0.116 1.997 60 SO 1 A8m

0.126 1.997 60 50 1 A8050.126 1.997 60 50 1 A8C35

- - 0.126 1.99] 60 50 1 AIlCl5- - 0.126 1.997 60 50 1 AIlC35- 0.116 1.997 60 50 1 A805

- 0.116 1.997 60 50 1 ABClS- 0.126 l.997 60 50 1 A8CJ5

- - 0.126 1.997 60 50 1 AB05- - 0.116 1.997 60 50 1 A8CJ5- 0.126 1.997 60 50 1 ABC35

- 0.126 1.997 60 50 1 AllCJ5- 0.116 1.997 60 50 1 A8CJ5- 0.126 l.997 60 50 1 A8C35- - 0.126 1.997 60 50 1 AIlCJ5

- - 0.126 1.997 60 50 1 A8C350.126 l.997 60 50 1 A8CJ5

- - - 0.126 1.997 60 50 1 A805

ITHREE.PHASE H·BVOLTDROPS>ii'j>\:'~1Input Blue Cells Only· Results inRedResulis Red White Blue%-t1leVcoo 22m m.7a 223.1& v%Voltdrop 2.71 yy· ......2.11 ·.·.··y .•·..·.2.11 'IoV%-t1leIsurn 214.15 214.15 214.15 AMeanIsum 179.34 179.34 179.34 AstdevIsurn 21.14 27.24 27.24 ACons Count 1 1 1Nodes 1 1 1

Code Rlkm@t2f'VC<)5 ·0.246AB05 0.868000 0.641ABClO 0.443

5 0.320ABCIX9S 0.160PVCl10 0.201tl35USERJUSER4

228228m228

0.15 m0.20 m

mm228

Rlkm Rp

0.245 0.0250.868 0.0430.868 0.0430.868 0.0010.868 0.0430.868 0.0430.868 0.11430.868 0.0430.868 0.0430.868 0.0430.868 0.0430.868 0.0430.868 0,1)430.868 0.0430.868 0.0430.868 0.0430.868 0.0430.868 0.0430.868 0.0430.868 0.0430.868 0.0430.868 0.0430.868 0.0430.868 0.0430.868 0.0430.868 0.0430.868 0.043

Table 5.3: Typical Herman-Beta spreadsheet for a balanced three-phase load

86

:.

Table 5.4 summarises the input parameters.

Input parameters for HB model

parameter tvatue

~ (Mean I.) 179.3 A

a (STD) 27.24 A

C 300A

a (All phases) 16.84

13 (All phases) 11.33

PF 0.8 (Design)

Conductor size 95mm" PVC/SWAJPVC

Load L11+L12Risk factor 10%Supply voltaoe (phase-neutral) 230VFeeder Lenath 100mDesign temperature of conductor 20 DegC

Table 5.4: Input parameters for the Herman-Beta model

Table 5.5 summarises the output parameters.

Output parameters of HB method

arameter vaiue :;A :;landard(231V+/-100/0)

V. (Phase-neutral) 223.76 V 208V

v; (Phase-neutral) 223.76 V 208V

V0 (phase-neutral) 223.76 V 208VV. (% voltage drop) 2.71% 10%

Vb(% voltage drop) 2.71% 10%

Vo (% voltage drop) 2.71% 10%

Table 5.5: Output parameters of Herman-Beta model

If the output parameters indicate voltage regulation or voltage drop in excess of any utility's

quality of supply standards, for example as specified in NRS 0485 for South African standards,

the selection of the conductor size must be adjusted iteratively on the Herman-Beta spreadsheet

until acceptable voltage regulation levels are obtained at the furthest point of the feeder.

5.3.2.2 Unbalanced three-phase load scenario

Table 5.6 represents a sample spreadsheet of the new summation algorithm for the same

combination of light industrial consumer sub-classes, but for a load current imbalance oflO%.

87

Phage Current Imbalance PowerFactor CorrectInputs in Blue

10.00% 0.80

27.24

3-Phase123.72 kVA

STOF'F 0.80179.30leffla 197.23Ib 179.30Iec

154.93300.00

1 100

200

Class/Scale "C"

300

15.1314.17

300.00

Ie16.8411.33

300.00

Inputs in blue

Ib

9.0217.30

300.00

la

SCALING FACTORS

Transfonner Size

Mean laa<ling size:Corrected for 10% risk

123.72147.78

kVAkVA

Table 5.6: A sample input/output sheet which calculates design load parameters for the Herman-Beta

model for a 10% unbalanced three-phase load scenario

Table 5.6 shows the different sets of beta parameters for each phase due to the selected unbalance

of 10%. The PF is still set at. 0.8. Table 5.7 shows the Herman-Beta spreadsheet for the above

condition. A different node was created for each feeder, with the distance between the

transformer and the first feeder (phase a) being 100 m, and the distances between the feeders for

phases band c, one metre each.

88

-Ys 230.00

DR~k% ··>;.;;;JO

Node Number Red White Blue AIDha Beta Cb lenath k CableConsumers rna mb me =Rn/rp code

•••• » ;;. I) •••• •· ;1 ·.i>···....· ............. •••••• '.17.3' ••••••••.•••9.02. i>300 i;m I>i »; .·>n Ii> ••• . ;; ; I·· ••••• ;.;.;; •• •· ·.• ·;i··...·.,.;... jg~A 1.'.;;.11.33 ;U.300 I;;;·'.;' I;;,.; ......;.;; I> ;. ; .••. >•• i; I;··.·.·.····u··.... , ;;1 I;;\~1l Itl1 300 1··•••······;\>:.·. ;;

····.u ..- 255 zss 43.48 1 1 ABC35

0.1 3 60 50 1 ABC3S- . 0.7 3 60 50 1 AB05

0.126 1.991 60 50 1 ABOS0.126 1.997 60 50 1 AOC35

- 0.126 1.991 liO 50 1 ABC35- 0.126 1.997 60 50 1 AB05

- 0.126 1.997 60 50 1 AB05- 0.126 VJ91 60 50 1 ABC35

- - - 0.126 1.997 liO 50 1 ABC35-- 0.126 l.997 60 50 1 AB05

- - 0.126 1.997 60 50 1 AB05- - - 0.126 1.991 60 50 1 AOC35

- 0.126 1.4191 60 50 1ABC35- - 0.126 1.997 60 50 1 ABOS- - 0.126 1.991 60 50 1 ABC35- - 0.126 1.991 60 50 1 ABC15- - - 0.126 1.991 60 50 1 ABC35

0.126 1.991 60 50 1 AllOS- - 0.126 1.991 60 50 1 ABC35- - 0.126 1.997 liO 50 1 ABOS

0.126 1.991 60 50 1 AllC35- 0.126 1.991 60 50 1 Allf,35- - 0.126 l.991 60 50 1 ABC35

ITHREE-PHASE H·BVOLTORQPS <~~;'z~1Input Blue Cells Only· Results in RedResults Red Whne BluelI/o·tileYcoo 222.14 223.&0' 225.01 VII/oYoltdrop UQ 1.·.··);•• 2.18 ·);··.·.··••·•••• 2.11 %VII/o-tilelsum 231.63 214.15 190.13 AMean Isum 197.19 119.34 154.&1 AStdev Isum 27.24 27.24 27.24 ACons Count 1 1 1Nodes 3 3 3

228m228228228

0.20 2282282lSm

R/km Rp

0.246 0.0250.246 0.0000.246 0.0000.868 0.0010.868 0.0430.868 0.0430.868 0.0430.868 0.0430.868 0.0430.868 0.0430.868 0.0430.868 0.0430.868 0.0430.868 0.0430.868 0.0430.868 0.0430.868 0.0430.868 0.0430.868 0.0430.868 0.0430.868 0.0430.868 0.0430.868 0,1)430.868 0.0430.868 0.0430.868 0.0430.868 0.043

Table 5.7: Typical Herman-Beta spreadsheet for 10% unbalanced three-phase load

89

Table 5.8 summarises the input parameters.

Input parameters for HB model10% Load unbalance

Parameter Value

Il (Mean I.) 179.3Ae rsro: 27.24 AC 300ACa. abo Qe 17.3 .16.84 , 15.13

13.,l3b.l3. 9.02.11.33,14.17

I., lb. I. 197.23A, 179.3A. 154.93APF 0.8 Oesian

Conductor size 95mm' PVC/SWNPVCLoad L11+L12Risk factor 10%Suoolvvoltaae (phase-neutral) 230VFeeder l.enqth 100mOesiQntemoerature of conductor 20 DeQC

Table 5.8: Input parameters for Herman-Beta model

Table 5.9 summarises the output parameters.

Output parameters of HB method10% load unbalance

Parameter Value SA Standard(231 V+/.10%)

V. (Phase-neutral) 222.64 208V

v, (Phase-neutral) 223.6 208V

Vc (Phase-neutral) 225.01 208V

V. (% voltage drop) 3.20% 10%

Vb(% voltage drop) 2.78% 10%

v,(% voltage drop) 2.17% 10%

Table 5.9: Output parameters of Herman-Beta model

5.4 Concluding remarks on the probabilistic modelling of aggregated light industrial

loads to calculate voltage regulation in LV feeders

It has been established that light industrial consumer loads are, like residential consumers,

.stochastic of nature and that probabilistic techniques are required to characterise the load at the

instant of maximum demand. The appropriateness of a beta-distributed load current model for

individual or combined sub-classes of the pilot group of light industrial consumers at maximum

demand was verified. A new spreadsheet-based algorithm has been developed which can add

individual sub-classes, identify instances of maximum demand and calculate beta parameters per

phase for purposes of LV feeder design. Provision has been made in the new algorithm to adjust

load current to accommodate three-phase load unbalance as well as different selectable PFs.

90

It was confmned that the light industrial load model provide output design parameters that are

compatible with the existing Herman-Beta voltage regulation algorithm - an algorithm which has

been the preferred statistical model for voltage regulation calculations in South Africa for the past

20 years. The approximation of non-unity PF loads as resistive loads for purposes of voltage drop

calculation by the Herman-Beta algorithm has been shown to provide suitable results.

91

6. APPLICATION EXAMPLE 1: COMPARING ACTUALVOLTAGE REGULATION WITH EXPECTED VOLTAGE

REGULATION USING PROBABILISTIC TECHNIQUES FOREXISTING LIGHT INDUSTRIAL INSTALLATION

6.1 Introduction

The primary objective of this research project is to develop probabilistic electrical load models

for the selected group of light industrial consumers and to introduce statistical techniques to

summate any selected combination of light industrial consumers in.order to derive an aggregated

model of the combined load. A new spreadsheet-type algorithm has been developed to perform

the above-mentioned statistical functions and to locate the daily intervals of maximum demand

for purposes of voltage regulation calculation in LV and MY feeder arrangements. It has been

suggested and motivated that the Herman-Beta statistical voltage regulation algorithm can

conveniently be utilised by using the alphalbeta load model parameters obtained from the new

algorithm. By assigning a level of confidence to the Herman-Beta model, specific voltage

regulation calculations canbe performed for selected feeder component sizes.

This chapter will evaluate a case study of an existing light industrial installation in Polokwane,

South Africa, with known supply voltage, feeder conductor sizing, conductor length and

statistical load model at maximum demand as discussed in previous chapters. It is the intention to

compare the actual voltage regulation measured at the consumer terminals with the expected

voltage regulation as forecasted by the newly developed load model at maximum demand and

voltage regulation as calculated by the Herman-Beta model.

The actual voltage regulation as measured will also be compared with conventional ADMD and

diversity adjustment methods based on installed circuit breaker size.

6.2 Defining the network

An existing three-phase, four-wire distribution system has been selected for evaluation purposes.

A 315 kVA miniature substation transforms the medium voltage supply from 11 kV to 400 V for

distribution purposes. The miniature substation is connected to a few different classes of light

industrial consumers, one of which is a class LI 1 (small) consumer as defined in chapter 3. The

light industrial consumer is an automotive service workshop with a maximum demand of 30 kVA

as measured by the local supply utility. The service workshop distribution board (DB) is supplied

from an external metering kiosk via a 50 mnr', four-core PVC/SWAJPVC (40 m long)"

92

underground copper conductor. The metering kiosk is supplied from the miniature substation via

an 80 m long, 70 mrrr', four-core PVC/SWNPVC underground copper conductor as shown in

Figure 6.1.

eII

L~~~:rl==========:J)

#1

~SyncI1rintsad

Date 1==========$Logger

M1Il1c1psl Supplyl1kV

M1n1stlrs Substation.l1kV/400V. 31!ikVASl1 VIlI' Street PolokWBnS

#2 COOSUIIIlI'DB

Class U1 (SIIalll

Figure 6.1: A single line representation of the service workshop (class LI 1) fed from a miniature

substation via 50170 mm2, four-core copper cable (power logging instrumentation indicated)

6.2.1 Statistical modelling

By using the new summation/maximum demand algorithm, statistical design parameters can be

obtained for the LI 1 (small) consumer at the interval of maximum demand. Although the

intention.of this exercise is the practical confirmation of the probabilistic prediction of voltage

regulation at the selected service workshop distribution board (single consumer), the basic

principle for summated consumers remains unchanged.

The input and output parameters for the selection of the statistical load parameters for the service

workshop (LI 1) are summarised in Table 6.1.

93

Input parameters for new algorithm

Parameter Value

Mixure of loads LI 1 x 1Scaling factor SmallCircuit breaker -C 100APower Factor 0.95Phase current imbalance 0%

Table 6.1: Input parameters for new algorithm

Output parameters of new algorithm

Parameter, Value

Effective Phase Current @ max. demand 47.74 APhase currents for selected imbalance 47.74 AStandard deviation @ max. demand 6.9AAlpha-Beta load parameters per phase a (24.57), 13 (26.89)Effective Apparent power at max. demand 32.94 kVAC parameter 100

Table 6.2: Output parameters of the new algorithm

The statistical load parameters, a, ~ and C, as summarised in tables 6.1 and 6.2, characterise the

spread and mean value of the service workshop's load current at maximum demand. With the

network configuration classified as three-phase four-wire, the feeder conductor length and size

known and with a selected confidence level of 90%, the only outstanding parameter required to

calculate the expected voltage regulation on the consumer side, is the supply voltage (Vs) at the

miniature substation. As voltage regulation is usually calculated for the worst case condition and

therefore at the interval of maximum demand, supply voltage measurements were recorded in

synchronisation with consumer voltage levels on five minute averaging intervals (as before) to

accurately calculate the voltage regulation per phase at the interval of maximum demand. This

interval is conveniently provided as an output value by the new algorithm. Two separate power

logging devices were simultaneously connected to the feeder arrangement as indicated in Figure

6.1. Annexure D summarises actual simultaneous RMS values of load current and phase voltage

on both the supply side (miniature substation) and the consumer side of the service workshop that

were used to extract the information as summarised in Table 6.3. For purposes of voltage

regulation comparison, the phase with the highest loading was selected, namely phase B. The

actual voltage regulation calculations, as measured, are also shown bei'ow.

94

Measured parameters at maximum demand Statistical ModelMinisub Consumer Voltaae Voltaae Voltaae Voltaae

Vb Ib Vb Ib drop regulation drop regulation(Volt) (Amp) (Volt) (Amp) (Volt) (%) (Volt) (%)232.90 40.42 229.73 40.36 3.17 1.36% 3.03 1.30%233.10 36.58 232.19 36.27 0.91 0.39% 3.03 1.30%232.70 37.51 229.82 35.46 2.88 1.24% 3.03 1.30%233.60 40.39 229.61 39.55 3.99 1.71% 3.04 1.30%233.00 50.40 230.72 51.96 2.28 0.98% 3.03 1.30%234.00 47.00 228.43 47.18 5.57 2.38% 3.04 1.30%234.30 50.91 227.22 52.91 7.08 3.02% 3.05 1.30%235.00 56.74 230.35 55.91 4.66 1.98% 3.06 1.30%235.30 47.34 228.43 47.46 6.87 2.92% 3.06 1.30%235.80 36.11 231.84 39.68 3.96 1.68% 3.07 1.30%235.40 45.39 229.45 45.55 5.96 2.53% 3.06 1.30%236.00 38.13 231.60 41.05 4.40 1.86% 3.07 1.30%231.20 48.55 228.43 47.18 2.77 1.20% 3.01 1.30%231.30 54.19 227.50 53.73 3.80 1.64% . 3.01 1.30%232.60 62.02 227.08 . 62.59 5.53 2.38% 3.02 1.30%233.70 41.61 231.65 43.36 2.05 0.88% 3.04 1.30%

Mean 46.11 229.63 46.45 4.25 1.76% 3.04 1.30%

Table 6.3: Summarised spreadsheet comparing actual voltage regulation measurements withpredicted voltage regulation using the statistical model for service workshop (LI 1 - small)

Judging from the above results, the accuracy of the statistical model (measured against voltage

regulation of the practical network) derived for a light industrial automobile service workshop, as

described by the beta load parameters summarised in Table 6.2, has been found to be within 1%

of actual measurements recorded with a selected level of confidence of 90%. The PF has been

adjusted in the new summation algorithm to actual values observed, at an average of 0.95. It is

also worth noting that the mean load current measured during the comparative study was 46.45A,

whilst the new model predicted a loading of 47.74A at maximum demand and a PF of 0.95.

Relevant statistical spreadsheets are also shown in Annexure D.

6.2.2 Empirical modelling

In South Africa, based on research done in major metropolitan areas'", empirical modelling of

groups of light industrial consumers is based on a typical apparent power density (ADMD) of 80

kVA per hectare as reported earlier. The electrical power requirements for LV feeder design for a

single user are mostly calculated on the installed circuit breaker value to ensure acceptable

voltage regulation when maximum demand is experienced. When two or more users are

cascaded, in-house derived diversity adjustments are usually made to calculate overall loading

based on specific stand sizes. Typical diversity factors (DFs) as found in the South African

industry for light industrial consumers will be summarised in the next chapter.

The LI 1 (small) service workshop is typically found on a stand size of 0-3500 m2 as per the

researched demographic data summarised in paragraph 3.6.5 with typical LV feeder circuit

95

breaker values of 100 A three-phase (refer to paragraph 6.2.1). This implies that traditional design

techniques would assume a bulk constant power load of 70 kVA at 400 V, which has

conveniently been modelled using Reticmaster 20045°.Figure 6.2 shows a Reticmaster simulation

of the load with its associated expected voltage regulation.

Munic96.00%Source ; IY1unic

fcJ~:53'"%sti-eeLMini~b315kVA 11kVl400V Star Dyn11(30+)

N299.85%400VConsumer DBTotal =70. O(Q.95)kVA

Figure 6.2: Reticmaster simulation of existing feeder network using empirical modelling with bulkload of 70 kVA

In this specific scenario, due to oversized conductors, it can be seen that traditional ADMD

modelling techniques yield similar results to that of the statistical model if the conductor size is

fixed (as is the case with the practical network). Voltage regulation is simulated at 1.68%

(101.53% - 99.85%), which compares favourably with both the statistical forecast and the actual

measurements as summarised in Table 6.3. However, with statistical modelling being a more

exact description of the statistical loading conditions of a specific load, an opportunity is offered

to the design engineer to optimise distribution components and forecast maximum demand more

accurately.

It can be shown that if the above LV network was considered for refurbishment, the following

results could be expected for both (1) empirical design, and (2) statistical design.

96

(1) Empirical design:

• ADMD of load: 70 kVA

• Feeder conductor size: 35 mm2 x four-core

• Mean load current: 100 A

• Voltage regulation at consumer DB: 2.9%

(2) Statistical design:

• ADMD ofload: 33 kVA

• Feeder conductor size: 25 mm2x four-core

• Mean load current: 47.7 A

• Voltage regulation at consumer DB: 3%

• Transformer capacity: 40 kVA

"

6.2.3 Concluding remarks regarding comparison between new probabilistic techniques,

empirical techniques and actual voltage regulation as measured in a practical network

The newly developed statistical load model for an automobile service workshop, sub-class LI I

(small), was practically evaluated utilising an existing MV/LV feeder network in the industrial

area ofPolokwane, South Africa.

Synchronised power measurements were taken on both sides of the feeder network to calculate

actual voltage regulation per phase at the daily intervals ofmaximum demand. The new algorithm

was utilised to identify the relevant intervals that could be extracted selectively from the

synchronised data.

The network was then statistically modelled using the new descriptive beta parameters for an LI I

(small) sub-class consumer. These design parameters were obtained from the new algorithm and

they identify the mean load current at maximum demand (adjusted for actual PF as measured in

the network). The existing feeder components, namely the miniature substation and underground

conductor sizing, were used as inputs to the Herman-Beta voltage regulation spreadsheet and

calculations ofvoltage drop were done for each of the measured supply voltages at the miniature

substation. Table 6.3 compared the mean voltage regulation as measured in the practical network

with the statistically calculated voltage regulation using the beta-distributed load current model

for LI I (small).

97

The results obtained from the statistical modelling procedure were found to correlate to within

1% of the practically measured voltage regulation level. This analysis confirmed the validity of

the proposed new load model and associated statistical design spreadsheets.

An empirical analysis was also performed on the same network (by using Reticrnaster) and a bulk

load with no diversity was defined as the feeder only supplies a single consumer. This network is

a typical example where oversized components are found in industry today due to the lack of

accurate design information available to design engineers.

With the existing oversized conductor, very little difference in voltage regulation was observed.

However, once optimised using the proposed statistical model. a reduction of 30% in required

copper could be achieved for the same load with voltage regulation increasing to 3%, which is

well within the generally accepted quality of supply limits.

Finally, the reduction in forecast demand of almost 30% as opposed to empirical ADMD

approximations for non-residential consumers confirms the importance of accurate (probabilistic)

load models to define overall energy requirements.

98

7. APPLICATION EXAMPLE 2: GREENFIELD INDUSTRIALPARK DEVELOPMENT: NEW ALGORITHM VERSUS

CONVENTIONAL ADMD TECHNIQUES

7.1 Introduction

Chapter 6 detailed an application of the new algorithm where the specific sub-class has been

modelled as a beta distributed load current at maximum demand and where the load was

connected to a transformer supplying energy via an underground feeder cable. The modelled

voltage regulation of the feeder arrangement was compared with. actual mean voltage drop levels

that were measured in the installation at the daily instances of maximum demand and they were

found to correlate to within I% of the practically measured voltage regulation level.

The ultimate application of the newly developed statistical load model and LV feeder design

algorithm would typically be found in a planning and design example of a greenfield, light

industrially-zoned township development. According to the American heritage dictionary of the

English language, greenfield development refers to a piece of semi-rural property that is

underdeveloped except for agricultural use, and which is being considered for urban expansion.

The new design guidelines can assist with both overall load forecasting for a mixed sub-class

development, as well as the internal distribution component sizing of conductors, miniature

substations (transformers) and other distribution switchgear (RMUs).

This chapter will review an example of a township development, correctly zoned for light

industrial development, with unknown tenant description and provision for distribution networks

based on ADMD and Diversity Factors (DFs) for light industrial consumers in general. These

design guidelines, in which typical data has been summarised, are normally not published

externally and are only available as in-house design directives for distribution design engineers.

By applying empirical design guidelines for empty stands destined for light industrial end-users

and based on specific stand sizes, a comparison is presented with a scenario where a tenant mix is

pre-specified by the developer and the distribution network specifically designed for light

industrial sub-classes with known load models using probabilistic design techniques.

The availability of a preferred tenant mix prior to the design of bulk services for industrial park

developments is of the utmost importance if cost and energy efficient forecasting, as well as

accurate load forecasting for purposes of specifying external electrical link service (and

99

ultimately the internal LV feeder design), is to be achieved by using the new probabilistic load

models.

Lastly, the upgrading of LV distribution networks of any existing industrial area where tenant

information or light industrial consumer types are already known would also be simplified

considerably by using the newly developed statistical design tools.

7.2 Township to be studied

A section of a newly developed township in the light industrially-zoned area of Polokwane, South

Africa is shown in Figure 7.1. ;.

§] I ~I r-

II

r-- I

.~~MiBWB.2 ~- lilt.. AS. 1

2.110 ~I 2xlse ~AB.I 0A9.~="~9.3 AB.~ .~

~7.2K',3 0

...~ ~A7

LEGEND ~ [31 i1J

Iij;JIx110

MINIATURE SUBSTATION

r! AS.2~ AS. 1

~S~DISTRIBUTION KIOSK a--95nm2 XLPE llkV CABLE 0 ~--LV ClPER CONDUCTOR 3~

0 I'HllSl'MT S1lIEEi -STAND NUMBER

PROm:

NEW LIGHT INDUSTRIAL DEVELOPMENT, Polokwane - South Africa

Figure 7.1: Section of new township in Veldspaat Street, Polokwane, South Africa with industrialzoning indicating the proposed MV and LV reticulation

7.2.1 Empirical design method of township with unknown tenant mix

The above township has been subdivided into a variety of different stand sizes by a town planner

following its rezoning from residential or agricultural property. For the purposes of the

comparative study in LVfeeder design and load forecasting, it has beendecided to concentrate on

100

the development of the following stands only, which will be referred to as phase 1 of the

development:

Note. ADMD"refers to the characterislic ADMDforeach standsize category

Stand number Size Approved Circuit breaker ADMOm2 FAR. size 1(80kVAlHect

(Utility Specification ADMOx

1 2000-3500 30% BOA 2BkVAOpen 3500-6000 30% 100A 35kVA

2 6000-7000 30% 150A 52kVA3 6000-7000 30% 150A 52kVA4 6000-7000 30% 150A 52kVA5 6000-7000 30% 150A 52kVA

Open 7000-9000 30% 200A 70kVA6 9000-13000 30% 300A 104 kVA7 9000-13000 30% 300A ;. 104 kVAB 18000-26000 30% 600A 208 kVA

..

Table 7.1: Schedule indicating stands to be developed under phase 1 with associated sizes andrequired circuit breaker values for light industrial consumers

The various stand sizes as indicated in Table 7.1 can each be associated with unique ADMD

values, similar to those of the LSM groups as specified in NRS-034 for residential consumers.

These ADMD values are easily derived from the power density information of 80 kVA per

hectare for large groups of light industrial consumers traditionally found on the above-mentioned

stand sizes and can conveniently be referred to as ADMDx, where x = 1 refers to the characteristic

ADMD of the first stand size (2000 - 3500 rn'), x = 2 refers to the second stand size (3500 - 6000

m2) and so forth. The available area for development on each stand is obtained by multiplying the

area ofthe stand with the Floor Area Ratio (FAR) value as regulated by the local municipality. As

an example, stand 2 has a maximum area of 7000 m2 but the limit on allowable building floor

area is only 7000 x 30% (FAR=30%) = 2100 m2.The research referred to in paragraph 6.2.2 has

further revealed that specific circuit breaker sizes are usually associated with each stand size,

which ultimately indicates the allowable maximum demand of any single user in an LV feeder

arrangement.

One of the most controversial subjects amongst distribution designers today is that of the

diversity assumptions to be applied to non-coincidental light industrial loads in LV feeder design.

These assumptions vary from no diversity at all for a design catering for worst case simultaneous

demand for all consumers on a specific feeder arrangement (resulting in an over-designed

network), to optimistically high DFs where the available transformer capacity is limited resulting

in under designed distribution components. Table 7.2 summarises typical DFs obtained from

selected design houses in South Africa usually applied to light industrial groups of consumers.

101

These DFs will be used in the comparative study between the empirical electrical design and the

probabilistic approach to LV feeder component specification.

Diversity Factor Consumers Diversity Factor(DFN) (N) (DFN)

DF1 1 2DF2 2 1.5DF3 3 1.3DF4 4 t.1DFs 5 1.08DFe 6 1DF7 7 1DFs 8 1

Note: ADMDN =DFN x r (ADMDX)

Table 7.2: Typical DFs usually applied to light industrial consumer loads

Figure 7.2 shows the LV distribution network and node connections for the miniature substation

zone, MS A7, where an empirical. distribution component sizing has been modelled using

Reticmaster. The characteristic ADMDs (ADMDX) were applied for each stand size and the DFs,

summarised in Table 7.2, were used to calculate effective bulk loads for each feeder section. The

PF has been selected as unity for purposes ofthe comparative study.

With reference to Figure 7.2, the following nodes have been allocated to the stand numbers and

sizes as summarised in Table 7.1:

• NodeA7.2:

• NodeA7.3:

• NodeA7.4:

• NodeA7.5:

• NodeA7.6:

Stand size: 6000-7000~ (ADMDA7.2 = 52 kVA) [Stand 3, Figure 7.1]

Stand size: 6000-7000~ (ADMDA7.3 = 52 kVA) [Stand 2]

Stand size: 6000-7000 m2 (ADMDA7.4 = 52 kVA) [Stand 5]

Stand size: 6000-7000 m2 (ADMDA7.5 = 52 kVA) [Stand 4]

Stand size: 2000-3500 m2 (ADMD A7.6 = 28 kVA) [Stand 1]

Examples:

Bulk load as seen at Node A7.2 including load of Node A7.3:

Bulk load =DF2 (ADMDA7.2 +ADMDA7

.3) = 1.5 (104) = 156 kVA

102

Bulk load as seen at Node A7.3:

Bulk load =DF 1 (ADMDA7.3) = 2 (52) = 104 kVA

M.rie

~m.1lO'1.SOllee: MJnie

P=17.6A -490.2A

~. MSA7 :.

98.53%Diversified load =SUM CFDlVERSIFIED BllK LOADS:158+173=331 kVATalal=334.6ItOOL]kVA

svJ.cH4 .2A

A7395.89'1.400VADMD=52kVAI8OkV~1Tetal aJk=l04.qtOOlkVA

185 LV2 A A74

97.56'1.400vADMD=52 kVA Load=DF(~x 132 kVATalai Bulk=173.711.00lkVA

LV

A759611%400VADMD=52 kVA Load=DF[2]x 80kVATalal Bulk=12O.~l(lO)kVA

LVAA76

94.62%400vADMJ:28 kVAI8OkVM-1ectlTalai Bulk=5&Ql00LlkVA

Figure 7.2: Reticmaster simulation of LV feeder network for new development-empirical method(MSA7)

Figure 7.3 shows the LV distribution network and node connections for the miniature substation

zone, MS A8, where an empirical distribution component sizing has been modelled using

Reticmaster. The characteristic ADMDs (ADMDX) were applied for each stand size and the DFs

summarised in Table 7-2 were used to calculate effective bulk loads for each feeder section.

103

Mlnic100.00'1.Source: Munic

P=44.M =123kA

MSABTolalload =ACM) (Tolal) XDF(3) =416 x13=540 kVATolal=836.~100..1kVA

TRF BUSBAR1IIIIIIIIII • 1mm497.6'3%400V0000..

AS 397.31%400VADMD=104 kVA [80 kVAtlect)TolaIBulk=20B.q1.00lkVA

2m2x1&l VClV

61 OA

AS 297.32%400vADMD=20S kVA (80kVAJHect)Total eJk=416.0(10mkVA

3185P elV

.5AAB197.31%400VADt-ID:104 kVA (SOkVAJHect)Total8Uk=208.~100lkVA

Figure 7.3: Reticmaster simulation of LV feeder network for new development using the empiricalmethod (MSA8)

With reference to Figure 7.3, the following nodes have been allocated to the stand numbers and

sizes as summarised in Table 7.1:

• Node A8.1: Stand size: 9000-13000 m2 (ADMDA8.1 = 104 kVA) [Stand 6, Figure 7.1]

• Node A8.2: Stand size: 18000-26000 m2 (ADMDA8.2 = 208 kVA) [Stand 8A and 8B]

• Node A8.3: Stand size: 9000-13000 m2 (ADMDA8.3 = 104 kVA) [Stand 7]

. The bulk loads as shown in the above node diagram have all been derived from the characteristic

ADMDs with adjustment in accordance with the DF for a single user DF1 = 2 (refer to Table 7.2).

With reference to the LV networks above, the following observations regarding the selection of

conductor sizes and transformer capacity are worth noting:

• Conductor sizes were firstly' selected to ensure conformance with thermal constraints

after applying a derating factor of 0.85 to the published current rating as a result of

possible increased ground temperature and increased soil resistivity conditions.

104

• Conductor sizes were further adjusted upwards (where necessary) if voltage regulation

in feeder sections exceeded the 10% limit at the furthest feeder point as per NRS 048

for South-African conditions.

• The simulation software, Reticmaster, do not adjust summated bulk. power loads for

diversity. Specific pre-calculated loads were therefore added at each node as discussed

above and as typically found in industry. It is for this reason that total apparent power

ratings of transformers MSA7 and MSA8 do not reflect diversified load and have been

re-calculated as indicated on the diagrams in figures 7.2 and 7.3.

Tables 7.3 and 7.4 summarise the results of the LV network design for a greenfield development

with industrially zoned sub-divided stands of known size but unknown tenants of light industrial..sub-classes. These results reflect the most commonly found empirically-based design

methodology used by distribution engineers in South Africa today in the absence of exact load

models, be it statistical or empirical.

Schedule summarizing mmiature su station specifications with empincal methodMiniature Most probable Installed Maximum Maximum

Substation Engineer's capacity diversified non-diversifiedTransformer selection demand demand

MSA7 11kV/400V. 500 kVA 500 kVA 331 kVA 472 kVA

MSA8 11kV/400V. 750 kVA 750 kVA 540 kVA 836 kVA

Table 7.3: Results for the empirical method - miniature substation selection

Schedule summarizing design results with empirical methodNode Feeder Feeder Mean load Voltage Node

Length Size current Regulation Voltage(Cu)

A7.2 25m 95 rnm" x 4 core 233A 2.10% 226V

A7.3 100m 70 mm2 x 4 core 156A 4.11% 221V

A7.4 60m 185 rnrrr' x 4 core 257A 2.44% 225V

A7.5 75m 95 mm2 x 4 core 181A 3.89% 222V

A7.6 50m 25 mm2 x 4 core 85A 5.38% 218V

A8.1 30m' 185 mm2 x 4 core 308A 2.69% 224V

A8.2 25m 2 x 150 mm2 x 4 core 617A 2.68% 225V

A8.3 30m 185 mm2 x 4 core 308A 2.69% 224V

Table 7.4: Results for the empirical method - conductor specification and voltage regulation

105

7.2.2 Probabilistic design method of township with prior information of typical tenant mix

using new snmmation algorithm and beta-distributed load currents

The main objective of this research project was firstly to develop statistical load models for a

selected group of light industrial consumers and secondly to develop an easy-to-use summation

spreadsheet by using characteristic load data to establish specific design parameters for

aggregated loads at instances of combined maximum demand. Adjustments for phase imbalance

and non-unity PFs have been incorporated in the spreadsheet program and have already been

discussed in earlier chapters.

Due to the limited range of light industrial consumers studied, a selection of typical tenants which

conform to the demographic description of the three sub-classes, namely LI 1 to LI 3, has been

chosen as the occupants of the stands in the township that is being studied. Table 7.5 summarises

an allocation of specific sub-classes of light industrial consumers to the stands as selected

previously for the greenfield development, Suitability of selected tenants can be verified by

adjusting stand sizes in accordance with an FAR of 30% to derive the floor areas specified in the

demographic descriptions. Utility specified circuit breakers will initially remain unchanged.

Stand number Size Approved Circuit breaker Consumer Tenant

m2 F.A.R. size sub-class description(Utility)

1 2000-3500 30% aOA L12 (small) Small bakeryOpen 350G-6000 30% 100A Open Open

2 600D-7000 30% 150A L11 small x2 Auto service workshoos3 6000-7000 30% 150A U3 small x2 Ice producinQplants4 600D-7000 30% 150A L11 small x2 Auto service workshoos5 6000-7000 30% 150A L13 small x2 Ice cream storaqe

Ooen 700D-9000 30% 200A Ooen Ooen6 9000-13000 30% 300A 1I1 (medium) Auto service workshop7 9000-13000 30% 300A LI 3 (medium) x 2 Frozen sea food warehouses8 1800D-26000 30% GOOA L11 (large) x 2 Laroe auto service workshops

Table 7.5: Schedule indicating stands to be developed under phase 1 with associated tenants

The previously proposed node connection sequence and LV feeder designs for MSA7 and MSA8

will also remain unchanged to ensure a direct and clear comparison between the empirical design

procedure (as summarised in Table 7.4) and the probabilistic procedure to follow.

The following allocation of light industrial consumer sub-classes, which would ultimately be the

tenants, has been assigned to the different nodes as shown in Table 7-6 below. Characteristic beta

parameters are conveniently associated with each node which will be established by using the

new summationlbeta parameter algorithm. The Herman-Beta model will then be utilised to

106

establish the voltage regulation in each feeder section, assigning a 90% level of confidence to

prepare similar result tables to that oftables 7.3 and 7.4.

Stand number Size Node Consumer Tenant Beta parameters

m2 Description sub-class Description a 13 C

1 2000-3500 A7.6 L12 (small) Small Bakery a1 (31 C1

Open 3500-6000 Open Open Open

2 6000-7000 A7.3 LI 1 (small) x 2 Auto Service Workshop 02 (32 C2

3 6000-7000 A7.2 LI 3 (small) x 2 Ice producing plant 03 (33 C3

4 6000-7000 A7.5 LI 1 (small) x 2 Auto Service Workshop ~ (34 C4

5 6000-7000 A7.4 LI 3 (small) x 2 Ice Cream storage Os (35 c,Open 7000-9000 Open Open Open

6 9000-13000 Aa.1 LI 1 (medium) Auto Service Workshop 06 (36 C6

7 9000-13000 A8.3 LI 3 (medium) x 2 Frozen sea food warehouse 07 l3r C7

8 18000-26000 A8.2 LI 1 (large) x 2 Large Auto Service workshop Os (3s C6

Table 7.6: Consumer sub-class and beta parameter assignment to nodes

A schematic representation of the LV feeder networks indicating nodes, consumer sub-classes

and beta parameter allocation for MSA7 and MSA8 are shown in figures 7.4 and 7.5 respectively:

e Ml.I11c1pel S\4lPlY.- 100.001! 11kV

MSA7HkV/400V

I t cs, /3s. CSI

IID•••••••••••~ TRF BUSBAR

A7.2LI3ISII8IlI

A7.3LIS(s1I8111

1-2511I Ia3, 133. C31

1.7.4LI3ISIIe111

A7.5LIS(sslll

A7.6LI2(SIIs111

1-6011I I a5, 135, C51

Figure 7.4: LV feeder network for the miniature substation zone (MSA7)

107

MlI1:1c

e 100.001, SO\Fce MlI11cI l1kY

IMSIoBl1kY/400V

I I «ro, !S10, CI01

,.•••••••••I11III TfF BUSBAR

1-301l1 1-2511 1-3OIlI Ias, !Ss, CSI I Ias, (3S, Cal I t ar, !S7, cn

loB.2LIl[largel

loB. 3LI3Illsd:lUll)

Figure 7.5: LV feeder network for the miniature substation zone (MSA8)

It must be noted that the above feeder network diagrams only indicate the particular sub-class

assigned to each node and not the number of sub-classes connected to each node. Table 7.6

provides detailed information.

Prior to embarking on any feeder size and voltage regulation calculations, the new summation

algorithm will be utilised to calculate the beta-distributed load currents and associated design

parameters (beta parameters) for each node. In the case of the feeder network supplied from

MSA7, the aggregated load current parameters will be established for nodes A7.2, A7.4 and

A7.5. Nodes A7.3 and A7.6 are single nodes with no aggregation of further nodes. The instances

ofmaximum demand for the combinations of consumers will be identified with its associated beta

parameters at the specific intervals for purposes of conductor design, which would be a worst

case scenario. It is worth noting that time intervals of maximum demand might differ from node

to node due to the different sub-classes and tenants being combined in the same feeder or same

feeder transformer.

The new algorithm will also ~onvenient1y be used to establish the aggregated load behaviour of

all consumers fed from the same transformer (MSA7 and MSA8) to establish the required

transformer specifications.

108

Only a sample spreadsheet of the application of the summation algorithm will be shown for each

of the miniature sub-station zones, but the probabilistic forecast as well as the sample spreadsheet

of transformer sizing will be shown.

7.2.2.1 Miniature substation zone MSA7

The input parameters for the summation algorithm for all nodes have been summarised in Table

7.7 and it includes the parameters required for the calculation of the transformer size (MSA7).

Node Mixure Input Power Imbalanceof loads (per node) factor selection

(As seen at each node) (Connections)

MSA7 L11 small 4 . 1 0%L12 small 1 1 0%L13 small 4 1 0%

A7.2 LI 3 (small) 2 1 0%LI 1 (small 2 1 0%

A7.3 Lit small 2 1 0%A7.4 L13 small 2 1 0%

L11 small 2 1 0%L12 (small 1 1 0%

A7.5 L11 (small 2 1 0%L12 {small 1 1 0%

A7.6 L12 (small 1 1 0%.

Table 7.7: Input parameters for miniature substation zone MSA7 summation algorithm (shown inblue below). Input parameters of other nodes also shown.

109

Phase Current Imbalance Power Factor CorractInputs in Blue

0.00% 1.00

33.88

3-Phase447.68 kVA

STOPF 1.00648.81leftla 648.81Ib 648.81tec

648.241384.83

MIXURE OF LOADSPER NODE

L1-1L1-2L1-3

Inputs in blueClass/Scale "C"

1 100

0.5 100

0.5 150

Al halBeta des' n ramaters la Ib IeAlpha 194.42 194.42 194.22Betac

220.551384.83

220.551384.83

220.701384.83

Transformer Size

447.68477.61

kVAkVA

Table 7.8: New algorithm establishing aggregated demand for miniature substation MSA7

The profile of the aggregated mean load current as seen by transformer MSA7 is shown in Figure

7.6. The suggested transformer size, corrected for 90% confidence, is 478 kVA (refer to Table

7.8). The Author's selection of a transformer size is 500 kVA. The beta load current parameters

for the aggregated load on the transformer LV busbar are (19 = 194.42, P9 = 220.55 and C9 =

1384.83 per phase as calculated by the new algorithm (Table 7.8). A 750A three phase 25kA

circuit breaker will most probably be used to feed this arrangement.

110!.

Effective Load Current and SO (MS A7•PF=1)

700.00

600.00

i 500.00

!.. 400.00

~"o 300.00

!200.00

100.00

0.00" <II <II

8 8 8~ ~ ~N t..:. No '<l" M

s 8 ~

<II <II <II <IIE 8 E E0 0 0CD ~ CD

~,:..: N ,:..: N-e- 0 "I" M

~ 2 ~ -g

" <II " " .. <II <II .. <II .. .. .. .. ..8 E E E E 8 E E E E E E E E

0 0 0 0 0 0 0 0 0 0 0 0

~ ~CD

~CD

~CD ~ CD

~CD

~ ~ CDe- e-- e-- e- e- -e-

;.:.~

,:..: N ~ ~;.:.

~ ~. ~ i-: N ;.:. N"I" r 0 r '? ~ M

~.;;

~ ~ ~ ~ ~ ~ iri en 0 N N Nr r N N

Time

Figure 7.6: ProfIle of effective balanced load current of aggregated load at unity PF (MS A7)

The beta-distributed load parameters for node A7.4 are shown in Table 7.9, which includes the

loads at nodes A7.5 and A7.6 at the combined instant of maximum demand. The mean effective

load current is calculated as 348A at .unity PF. The beta parameters for the aggregated load are U5

= 199.97, ~5 = 224.31 and C5 = 739.58. If supply voltage is known and a confidence level

selected the voltage regulation can be calculated by using the Herman-Beta statistical model.

111

PhaseCurrent Imbalance Power FactorCorrectInputs in Blue

0.00% 1.00

17.90

3·Phase240.52 kVA

STDPF 1.00348.57leff1£1 348.57Ib 348.57Ie 348.26C 739.58

1 100Class/Scale "e"

"C· Inputs in blue

o.

0.5

100

150

AI haiBela desl n ematere la Ib IcAlpha 199.97 199.97 199.77Beta 224.31 224.31 224.46c 739.58 739.58 739.58

Transformer Size

Mean loadi size: 240.52 kVACorrected for 10% risk 256.33 kVA

Table 7.9: New algorithm establishing aggregated demand and feeder design guidelines for node A7.4

7.2.2.2 Miniature substation zone MSA8

The input parameters for the summation algorithm for the three nodes (A8.l, A8.2 and A8.3)

have been summarised in Table 7.10. This includes the parameters required for the calculation of

the transformer size (MSA8).

112

Node Mixure Input Power Imbalanceof loads (per node) factor selection

(As seen at each node) (Connections)

MSA8 LI 1 (large) 2 1 0%LI 1 (medium) 1 1 0%LI 3 (medium) 2 1 0%

A8.1 LI 1 (medium) 1 1 0%A8.2 LI 1 (larue) 2 1 0%A8.3 LI 3 (medium) 2 1 0%

Table 7.10: Input parameters for miniature substation zone MSA8- summation algorithm (shown inblue below). Input parameters for other nodes also shown.

Phasa Current Imbalance Power Factor CorrectInputs in Blue

0.00% 1.00

67.99

3-Phase607.59 kVA

STDPF 1.00

0.89

880.57leff

MAXIMUM PHASE AMPS

Mean PF Max Demand

DESIGN

994.21 Am s

la 880.57Ib 880.57Ic 879.78C 1685.22

10 800

"C" Inputs in blueClass/Scale "C"

0.5

1

100

300

I haJ8eta desi n aramaters la Ib lcAI na 79.57 79.57 79.51Beta 72.71 72.71 72.79c 1685.22 168522 1685.22

Transformer Size

Mean loadin size: 607.59 kVACorrected for 10% risk 667.64 kVA

Table 7.11: New algorithm establishing aggregated demand for miniature substation MSA8

113

With reference to Table 7.11, the overall scaling factor for the group of11 1 consumers has been

derived as follows:

LI 1 (large) x 2 =3.75 x 2 =7.5

LI 1 (medium) x 1 = 2.5

Total LI 1 scaling = 10

The profile of the aggregated mean load current as seen by transformer MSA8 is shown in Figure

7.7. The suggested transformer size, corrected for 90% confidence, is 667 kVA (as shown in

Table 7.11) although a 630 kVA (standard size) would comfortably satisfy the need as most

transformers can be overloaded by 10% of its rated capacity. This would also be the Author's

selection for a transformer size. The beta load current paramet~rs for the aggregated load on the

transformer LV busbar are (l1O = 79.57, ~IO =72.71 and CIO = 1685.22 per phase as calculated by

the new algorithm. A 1000A 3 phase 25kA circuit breaker would most probably be specified for

the LV feeder arrangement.

Effective Load Current andSO (MS AS •PF=1)

1000.00

900.00

800.00

'u; 700.00Q.

E~ 600.00C.,

500.00~0'll 400.00l'Il

.3300.00

200.00

100.00

0.00In In In In InE E E E E0 0 0 0 0CD CD CD CD CD~ e- ~ rN t: N ;.; N0 't '" ~ '"co 8 -: iD 00 0 0 e-

Time

Figure 7.7: Profile of effective balanced load current of aggregated load at unity PF (MSA8)

114

7.2.2.3 Calculation of the probabilistic voltage regulation

A complete summary of the statistical load parameters for all the nodes associated with MSA7

and MSA8 is presented in Table 7.12 (this can be verified by utilising the new algorithm).

Stand Size Node Consumer Tenant Beta parameters

number mZ Description sub-class Description a p C

1 2000-3500 A7.6 L12 (small) Small Bakery 01=3.9 131=2.6 C1=100Open 3500-6000 Open Open Open

2 6000-7000 A7.3 LI 1 (small) x 2 Auto Service Workshop or25.74 132=31.01 C2=2003 6000-7000 A7.2 LI 3 (small) x 2 Ice producing plant or187.51 (3,-204.13 Cr637.034 6000-7000 A7.5 L11 (small) x 2 Auto Service Workshop 0.=43.75 13.-52.96 C.-300

5 6000-7000 A7A Ll3 (small) x 2 Ice Cream storage 05=199.97 135=224.31 C5=739.58Open 7000-9000 Open Open Open

6 9000-13000 A8.1 L11 (medium) Auto Service Workshop 06=20.19 136=15.42 C6=200

7 9000-13000 A8.3 LI 3 (medium) x 2 Frozen sea food warehouse or255.5 137=255.5 C7=870.768 18000-26000 AB.2 L11 (large) x 2 Large Auto Service workshop 08- 20.19 138-15.42 C8-600

Table 7.12: Statistical load parameters of MSA7 and MSA8 to be applied to LV feeder design

Table 7.13 illustrates, as an example, how the Herman-Beta voltage regulation algorithm can be

used to develop the specifications for the feeder section from MSA7 to node A7.4 and to

calculate the voltage regulation to within a 90% level of confidence. The supply voltage is taken

as the output voltage of the miniature substation MSA7.

Once the voltage regulation for the first feeder section has been calculated, a new supply voltage

is obtainedfor the nextfeeder section from node A7.5 to node A7.6. This process continues until

all feeder sections have been specified.

115

11'HREE!PHA$EHH~VO~;rOltOP$r

InputBlueCelisunly· Hesults In soaResults Rea White 81ue%·tlleVcon 226.57 226.57 225.57 VC/oVolt drop 1.49 1.49 1.49 %VC/o·tlie Isum 371.56 371.56 371.56 AMeanIsum 348.58 348.58 348.58 Astde.I.um 17.90 17.90 17,90 ACon.COunt 1 1 1Nodes 1 1 1

e R m

Vs 230,01)DRIs %He Numr R

Consumers maWilemb

Hueme

Beta

1.997

C Len

0.144

Cacode

ABC35

R/km Rp

0.144 0.0090.868 0.0430.868 0.0430.868 0.0010.868 0.0430.868 0.0430.868 0.0430.868 0.0430.868 0.0430.868 0.0430.868 0.0430.868 0.0430.868 0.0430.868 0.0430.868 0.0430.868 0.0430.868 0.0430.868 0.0430.868 0.0430.868 0.0430.868 0.0430.868 0.0430.868 0.0430.868 0.0430.868 0.0430.868 0.0430.868 0.043

Table 7.13: Herman-Beta voltage regulation calculation at node A7.4 with 90% level of confidence

Tables 7.14 and 7.15 summarise the results of the LV network design for a greenfield

development with industrially zoned sub-divided stands of known size and end-use. Probabilistic

techniques utilising the newly developed beta-distributed current models have been used to

specify the distribution components.

Schedule summarizing miniature substation specifications with statistical methodMiniature Specification Installed Minimum Transformer Most

Substation capacity Transformer utilization probablecapacity upsize

MSA7 11kV/400V, 500 kVA 500 kVA 478 kVA 95% N/A

MSA8 11kV/400V, 630 kVA 630 kVA 667 kVA 106% N/A

Table 7.14: Schedule summarising required transformer capacity utilising new probabilistic methods

'. 116

Schedule summarizing design results with statistical methodNode Feeder Feeder Mean load Voltage Node

Length Size current Regulation Voltage(Cu)

A7.2 25m 150 mrrr' x 4 core 305A 0.64% 228.53

A7.3 100m 35 mm 2 x 4 core 90A 4.15% 220.52

A7.4 60m 185 mrrr' x 4 core 348A 1.49% 226.57

A7.5 75m 70 mm 2 x 4 core 135A 3.43% 222.16

A7.6 Sam 25 rnrrr' x 4 core 60A 5.58% 217.37

A8.1 30m 70 mrrr' x 4 core 113A 0.68% 228.44

A8.2 25m 2 x 95 mm2 x 4 core 340A 0.63% 228.54

A8.3 30m 2 x 95 mm2 x 4 core 435A 0.78% 228.21.Table 7.15: Schedule summarising LV feeder component sizing utilising new probabilistic methods

7.3 Concluding remarks: greenfield development probabilistic versus empirical design

This final chapter focussed on an actual case study of a light industrially-zoned township

development consisting of a number of stands of specific sizes with and without end-user

information.

A proposed MY and LV layout design, including miniature substation selection, has been shown

and the feeder component sizing has been designed by using both the conventional empirical

(ADMD) design method for unknown tenant types and the newly developed probabilistic

summation, modelling and voltage regulation algorithms with tenant information. During the

probabilistic process allocations of consumers to empty stands have been done to occupy each

stand to its full capability in available floor area where in practise less dense developments would

usually be found. This would result in improved results for the probabilistic method as compared

with the empirical method.

It was concluded that tenant mix information during the' design stage of bulk infrastructure is of

the utmost importance if cost- and energy-efficient distribution component design and load

forecasting are to be achieved.

Table 7.16 shows the fma1 comparison in feeder component sizing as well as the fma1 load

forecasting of the development using the two above-mentioned design approaches.

117

Stand number Node Consumer Feeder EmpiricalDesi n Probabilistic DesignDescription Class lennth Conductor Mean load Voltage Conductor Mean load Voltage

Size current Regulation Size current Regulation(40<:ore) (40<:0re)

1 A7.B L12 (small) 50m 25mm'Cu 85A 5.38% 25mm'Cu BOA 5.58%2 A7.3 L11 (small\ 100m 70mm'Cu 156A 4.11% 35mm'Cu 90A 4.15%3 A7.2 L13 (small) 25m 95mm'Cu 233A 2.10% l50mm Cu 305A 0.64%

4 A7.5 L11 (small) 75m 95mm'Cu 181A 3.89% 70mm'Cu 135A 3.43%5 A7.4 L13 (small) 60m 185mm'Cu 257A 2.44% l85mm'Cu 348A 1.49%

6 AS.l L11(medium) 30m 185mm'Cu 30M 2.69% 70mm'Cu 113A 0.68%7 A8.3 LI 3 (medium\ 30m 185mm'Cu 308A 2.69% 2x95mm'Cu 435A 0.78%

8 AS.2 L11 (large) 25m 2x150mm'Cu 617A 2.68% 2x95mm'Cu 340A 0.63%

Specification Specification

MSA7 llkV/400V 500 kVA 11kVl400V 500 kVAMSA8 l1kV/400V 750 kVA 11kV/400V 630 kVA

Table 7.16: Probabilistic/empirical feeder component sizing comparlson for greenfield development

The close correlation in estimated maximum demand between the empirical and the probabilistic

methods indicates the validity of the assigned ADMDs per stand as well as the selected circuit

breaker sizes installed on empty stands of specific sizes as per Municipal or Local Authority

guidelines. The introduction of the typical DFs as used on the empty stands for prospective light

industrial application also seem to have yielded acceptable results when compared with the

statistical results derived after assigning specific sub-classes to the stands. With reference to

Table 7.16, it is worth noting that virtually all conductor sizes (except for one feeder) has been

reduced in size due to the incorporation of the new statistical load models. In the case of the LV

feeder supplied from MSA8, a reduction of almost 20% was achieved in the estimated

transformer load specification.

In the absence of accurate load models, continuous uncertainty with regards to whether accurate

provision has been made for future electrical load would exist. It has been established that

distribution engineers in South Africa usually overcome this problem by ensuring that adequate

surplus capacity exists in MV networks to service future "surprises" in load. The results reflected

in Table 7.16 confirms that the electric load assumptions provided for during this empirical

design example was, in this case, a reasonable guess. If the sizes of installed circuit breaker

values were increased or faulty ,ADMD forecasts 'made, conductor sizes and estimated

transformer capacity utilising the empirical method would have been even larger with its

associated increaseindevelopmentcost.

The newly developed probabilistic load models and summation algorithm for the selected group

of light industrial consumers will allow distribution engineers to predict group electrical loading

more accurately in future and design conductor sizes in LV feeders with confidence.

118

8. CONCLUSION

8.1 Summary of work presented in the thesis

Chapter 1 provides a global perspective on energy and outlines the huge potential for energy

savings in the industrial and mining sectors in, amongst others, sub-Saharan African countries.

Industrial energy efficiency is defined and reference is made to international publications

addressing the importance of efficient distribution system design.

Light industrial consumer groups, and specifically its incorporation into modem industrial parks,

are defined and categorised in terms ofboth the NAICS and the South African SIC system.

The fundamental problem of the non-availability of practical design guidelines for LV feeder

networks supplying stochastic light industrial loads is addressed. The absence of proper

mathematical, statistical load models at instances of maximum demand for the various sub

classes has been found to lead to the over-estimation of distribution component sizing and load

forecasting, which results in expensive designs.

The usefulness of a new summation algorithm, which can summate means and variances of any

combination of light industrial users in order to obtain aggregated design parameters for LV

feeders at the instant of maximum demand, is discussed.

Chapter 2 provides a general overview of distribution engineering design and focuses on

available design guidelines for residential, commercial and light industrial consumer loads. Both

the empirical and probabilistic techniques are reviewed and the superiority of statistical methods

is discussed. Earlier work by the UK Electrical Industry is reviewed, followed by South African

research, which lead to the development of the beta pdf load current model and the statistical LV

feeder design model by Dr. Ron Herman for local residential consumers.

Load estimation guidelines, based on income levels forresidential consumers, are presented for

both empirical and probabilistic design techniques. The unavailability of published design criteria

for both commercial and light industrial loads is addressed. Reference is made to some empirical

load estimation guidelines in power density format, both in South Africa and in Australia. Some

practical findings of in-house design guidelines by distribution consultants are also presented.

Reference is made to the unique daily load profiles for the different classes of light industrial

consumers, as observed during the extensive pilot load study conveyed during this research

119

programme. Similar research conducted by the electricity utility of Brazil is been presented and

its limited findings are reviewed.

Global and local definitions of light industrial consumer groups are reviewed in chapter 3, with

reference to the standard lists contained in both the South African and North American SIC

classifications. A list of typical light industrial industries is proposed and a set of four sub-classes

is selected for the pilot research survey.

This chapter further examines the modelling of light industrial loads. It is concluded that the

stochastic nature of these loads necessitates the use of probabilistic techniques. An overview is

presented of the suitability of pdfs to continuously describe the 'nature of a set of data, which is

later referred back to in terms of data sets obtained from daily load profiles at specific time

intervals. Various bounded pdfs are reviewed but only the flexibility of the beta pdf to describe

most distributions is shown. It is further shown that the selected group of light industrial sub

classes can be parametrically described as constant current loads within an acceptable range of

error. The requirements for the field survey data logging equipment are discussed and the actual

survey is reported on. Demographic features used to typify the selected sub-classes are defined to

be used in future prospective load type distribution studies. It is also concluded that the spread of

data of the individual representative daily load current profiles can be adequately described by

means ofbeta pdfs at the individual instances ofmaximum demand.

Finally, the chapter reviews some practical electrical power definitions as published in the latest

IEEE standard 1459-2010 of March 2010. The concept of the use of the fundamental effective

load current for a virtual balanced circuit is discussed and applied in the pilot survey conducted.

Chapter 4 reviews the fundamental concepts of the summation of pdfs to establish aggregated

electrical load behaviour, which is then applied within a new practical summation algorithm. This

algorithm consists of libraries of electrical load data of the selected groups of sub-classes to

enable the summation of means and variances for any combination thereof. Due to the unique

load profiles of the individual sub-classes, instances of combined maximum demand varies over a

24-hour period and it is explained how the new algorithm conveniently identifies such intervals.

This chapter also analyses the combined spread of load data at identified intervals of maximum

demand and successfully tests the statistical spread of data against a standard beta distribution. A

flow diagram of the new algorithm is presented and it highlights the adjustment options for a non

unity power factor and phase current imbalance scenario for any selected combination of the sub

classes contained in the data library.

120

An aggregated load current profile (as generated by the new algorithm) is also tested against a

physical LV feeder network using the data logging device, which is positioned at the summation

node of the network, with excellent correlation reported.

Finally, a schedule summarising the proposed new statistical parameters for the selected group of

light industrial consumers is presented. It is recommended that the new algorithm be used to

obtain descriptive parameters for combinations of the selected group of light industrial

consumers. These results can conveniently be applied to existing statistical LV feeder design

models to derive practical distribution component sizing.

Chapter 5 addresses the application of the previously referred to Herman-Beta voltage regulation'

model to the pilot group of light industrial consumers. A summary is presented of a selection of

well-known voltage regulation algorithms presently used by distribution engineers both locally

and in the UK. It is concluded that the statistically-based Herman-Beta algorithm proves to be the

most consistently reliable model for LV feeder network design. A brief description of the

fundamentals of the Herman-Beta model is provided and it is shown that the pilot group of light

industrial consumers conforms to the pre-conditions for load parametric description and load

current distribution required by the Herman-Beta model.

This chapter also shows how the aggregated power factor is calculated. The aggregated power

factor is generally found to be smaller than unity for the industrial loads. The influence of these

complex loads on the accuracy of voltage regulation calculations, utilising the Herman-Beta

model, has been shown to be negligible. An example of the application of the new summation

algorithm for grouped loading is demonstrated for both balanced and unbalanced scenarios.

Finally, it is shown how the beta output parameters per phase can be applied to the Herman-Beta

model to provide usable, practical distribution component sizing for LV distribution networks.

Chapter 6 reviews the fIrst case study of an existing LV feeder which supplies a small automobile

service workshop in South Africa. The feeder network is firstly utilised to calculate the expected

probabilistic voltage regulation at the consumer terminals using the new summation and

maximum demand algorithm in conjunction with the Herman-Beta voltage regulation model.

These results are then compared to the actual mean voltage regulation obtained by performing

practical synchronous voltage measurements on the consumer and supply sides at five minute

intervals over a period of time. Mean voltage regulation was calculated by extracting information

at the characteristic intervals of maximum demand (as forecast by the new algorithm) for

consecutive days. The expected and actual results correlated to within an error margin of 1%.

121

This chapter concludes with a useful demonstration of the typical over-estimated distribution

component sizing as found in industry today. It is shown that the existing network can be

upgraded using both empirical techniques, based on the installed circuit breaker value and bulk

loading with no diversity, and probabilistic techniques using the accurate load model and

statistical spreadsheets as developed in this thesis. A reduction of 60% in copper conductor sizing

and 30% in required transformer capacity has been demonstrated by using the new statistical

tools.

The final chapter demonstrates the ultimate application of the newly developed statistical load;.

models and summation algorithm for the selected group of light industrial consumers. An actual

light industrially-zoned township development, presently under development in Polokwane,

South Africa, has been selected to establish the positive contribution of the statistical tools

developed, as opposed to the use of conventional empirical design techniques as found in various

countries around the world.

A selection of sub-classes of light industrial consumers, as defined in the pilot research

programme, has been allocated to the various empty stands in the new development in accordance

with the required stand sizes derived from typical floor areas of consumers and a typical FAR

(Floor Area Ratio) of 30%. In an attempt to demonstrate the benefit of having access to usable

load model information, as opposed to specifying feeder networks based on installed municipal

sized circuit breakers per stand size, both empirical and probabilistic designs were created for the

proposed LV feeder networks.

The empirical method utilises installed circuit breaker sizes, ADMD/hectare for large groups of

light industrial consumers and DFs to adjust the group ADMD to that of single users. A table of

typical in-house DFs for light industrial consumers, as used by distribution engineers in South

Africa, is presented. Voltage regulation is modelled by using Reticmaster with bulk loads and

DFs. A set of distribution component sizes, including transformer capacity, is also summarised.

.The probabilistic approach summates the selected loads and utilises the new algorithm to

calculate beta parameters per phase for each feeder section in the network. The Herman-Beta

model is used to calculate node voltages with selected conductor sizes. An up-down approach is

demonstrated, whereby calculated node voltages become supply voltages for the subsequent

feeder sections.

Finally, a comprehensive comparison is presented between the distribution component sizing of

the empirical design method (with unknown tenant mix) and the probabilistic method using the

122

new design tools (with known tenant mix). It is shown how informed assumptions on ADMD and

the use of DFs can lead to acceptable results. A general reduction in conductor sizing

specification has been demonstrated utilising the new statistical approach. However, in the

absence of usable statistical load models and associated design tools, the specifying of

distribution component sizes using conventional empirical techniques in LV feeders would

continuously remain a guessing game.

8.2 Evaluation

The author is a practising distribution design engineer and has identified the pressing need to

develop usable, practical electrical design guidelines for LV feeders associated with light

industrial consumer loads as defined in this thesis. The non-availability of proper mathematical

load models to describe these consumer loads at instances of individual or grouped maximum

demand has traditionally lead to the overestimation of distribution component sizing as was

shown in the practical network in chapter 6. The statistical load model, which has been developed

in this work, was successfully evaluated for a specific sub-class by comparing the forecast

voltage regulation with that of a practical network and found it to correlate to within an error

margin of 1%. Optimisation of this network using the newly developed statistical tools has lead to

a reduction of 30% in the required transformer capacity and 60% in required copper conductor

cross sectional area.

Earlier work reported by researchers in Brazil suggested the summation of means and variances

of daily apparent power load profiles to obtain the aggregated behaviour of groups of light

industrial loads without studying the spread of data at the combined instant of maximum demand,

therefore making it difficult for further application, for example in LV feeder design.

By characterising the load data at the instant of maximum demand in terms of a beta probability

density function and by proving that the selected groups of light industrial consumers can

parametrically be described as constant current or constant power loads, the work presented in

this thesis has resulted in the development of an integrated summation/maximum demand

algorithm for groups of light industrial consumers. The algorithm provides practical mathematical

design parameters which can be used in conjunction with the existing statistical voltage

regulation algorithm for LV feeder design as developed by Dr Ron Herman.

The comparison of the traditional empirical design method to the ::t;lewly developed statistical

model in a greenfield development leads to the conclusion that the work in this thesis presents

usable results which, as in the case of the practical network studied, results in a considerable

123

reduction in distribution component sizing if sufficient information IS available regarding

proposed tenant mixes within these developments.

It is the opinion of the author that this work has.created new opportunities for improved cost and

energy effective load forecasting and LV feeder design for light industrial consumers, both in

South Africa and abroad.

Finally, it is anticipated that this research work will be the start of a process whereby statistical

design parameters, similar to those of the residential consumers, < will be incorporated into design

guidelines for the larger group of light industrial consumers, as extracted from local and

international SIC classifications, and used by the practising engineering fraternity.

8.3 Future work

The following research topics and follow-up work are proposed:

• By adding additional libraries of field data for other light industrial consumers to the

algorithm, a holistic model can be created for load forecasting in future greenfield, light

industrial parks or where refurbishment of existing industrial areas with known groups

ofconsumers is required.

• Subsequent field surveys could be conducted in other countries to establish specific or

generic load models for sub-classes of light industrial consumers in accordance with

international SIC classifications.

• A final evaluation could be conducted of the researched sub-classes in this thesis in

order to refine demographic descriptions before adding the balance of the light

industrial sub-classes to the algorithm. This work could then be made available to the

local distribution design fraternity.

• The field data of residential consumers could be included in the new algorithm's data

library to assist witlr load forecasting at sub-station level for local municipalities and

other utilities.

• The effect of non-sinusoidal load current behaviour on the developed models can be

investigated.

• It is suggested that in countries where different design standards and demographic

profiles are experienced, the newly developed design tool is refined to suit specific

requirements.

124

ANNEXURE A

Example of a data library for small automobile service workshops asfound in the new summation/maximum demand algorithm

Field Deta for Light Industrial Class U 1 (small) [Automobile Service Workshops @l 0 ·20 vehicles per davlDate 3010312009 3010312009 3010312009 3010312009 30/0312009 30/03/2009 3010312009 3010312009 30/0312009 30/0312009Time 14:24:38 Oms 14:29:38 Oms 14:34:38 Oms 14:39:38 Oms 14:44:38 Oms 14:49:38 Oms 14:54:38 Oms 14:59:38 Oms 15:04:38 Oms 15:09:38 OmsVa 238.045 238.164 238.448 238.235 239.917 241.481 242.026 242.192 241.694 241.789Vb 233.307 233.33 235.013 236.339 236.387 236.292 237.311 235.723 235.937 236.079Ve 234.942 235.534 237.382 238.661 238.306 237.832 238.969 238.211 237.406 237.951la 31.459 27.736 35.414 47.373 40.759 28.35 32.577 21.205 23.809 24.805Ib 54.259 50.155 50.768 54.859 55.677 52.309 53.455 51.614 50.714 49.868Ie 55.445 49.668 47.005 50.482 55.445 55.405 56.032 49.473 54.518 52.582PF 0.915 0.928 0.938 0.93 0.925 0.923 0.928 0.902 0.914 0.905

PF2 0.837 0.861 0.880 0.865 0.856 0.852 0.861 0.814 0.836 0.819S.. 35.64 32.66 32.61 36.61 37.29 35.66 36.44 33.63 34.90 33.95

I.. 50.19 45.71 45.58 51.14 51.82 49.22 50.18 46.28 48:14 46.80

1..2 2518.71 2089.30 2077.70 2614.85 2684.84 2422.48 2518.20 2141.80 2317.22 2190.17

Date 31/0312009 3110312009 31/0312009 3110312009 31103/2009 31/0312009 31/03/2009 31/0312009 31/0312009 31/03/2009Time 14:24:38 Oms 14:29:38 Oms 14:34:38 Oms 14:39:38 Oms 14:44:38 Oms 14:49:38 Oms 14:54:38 Oms 14:59:38 Oms 15:04:38 Oms 15:09:38 OmsVa 237.287 238.448 238.093 237.737 238.14 238.401 237.737 237.192 237.382 237.524Vb 235.558 235.605 235.889 235.415 234.894 235.202 235.534 235.842 235.297 235.25Ve 237.382 237.714 237.998 237.121 237.737 237.098 237.287 237.785 237.098 238.282la 48.445 42.273 45.218 42.6 39.055 37.118 45.723 48.832 45.777 41.714Ib 54.982 56.032 56.4 53.414 55.568 52.527 53.645 52.459 54.995 51.995Ie 56.577 57.505 56.277 55.418 51.095 53.4 56.973 53.591 56.755 47.5PF 0.913 0.912 0.914 0.928 0.908 0.923 0.928 0.937 0.929 0.933

PF' 0.834 0.832 0.835 0.861 0.824 0.852 0.881 0.878 0.863 0.870S.. 37.84 37.95 38.06 36.56 35.58 35.13 37.55 36.90 37.78 33.99

I•• 53.14 53.06 53.26 51.26 49.61 49.13 52.64 51.73 53.06 47.55

1..2 2823.38 2815.05 2838.80 2627.20 2480.86 2413.35 2771.49 2875.68 2815.13 2261.42

Date 11412009 1/4/2009 11412009 114/2009 11412009 1/4/2009 1/4/2009 114/2009 1/4/2009 114/2009Time 14:24:38 Oms 14:29:38 Oms 14:34:36 Oms 14:39:38 Oms 14:44:38 Oms 14:49:36 Oms 14:54:38 Oms 14:59:38 Oms 15:04:38 Oms 15:09:38 OmsVa 237.05 236.932 237.524 239.728 238.661 239.325 239.206 239.183 240.652 240.628Vb 232.975 233.838 234.515 238.79 235.984 235.534 235.463 235.487 235.96 235.889Ve 238.742 236.15 237.264 239.609 238.993 239.017 239.988 239.017 238.851 239.372la 32.359 36.723 37.173 41.523 41.741 37.95 37.2 35.318 28.582 26.959Ib 54.409 54.259 52.8 57.791 55.562 56.55 56.973 54.873 53.973 52.064Ie 44.1 50.25 46.623 50.959 48.341 49.459 43.173 47.209 49.568 44.468PF 0.901 0.908 0.923 0.914 0.925 0.915 0.899 0.912 0.911 0.919

PF' 0.812 0.624 0.852 0.835 0.856 0.837 0.808 0.832 0.830 0.845S.. 32.63 34.51 33.24 36.81 35.40 35.53 34.28 34.11 34.22 32.05

I.tr 45.89 48.55 48.65 51.19 49.37 49.49 47.62 47.53 47.40 44.39

1..2 2105.74 2356.98 2176.38 2620.29 2437.40 2449.52 2267.29 2259.42 2246.41 1970.67

Date 21412009 2/4/2009 21412009 21412009 2/412009 214/2009 21412009 21412009 214/2009 214/2009Time 14:24:38 Oms 14:29:38 Oms 14:34:38 Oms 14:39:38 Oms 14:44:38 Oms 14:49:38 Oms 14:54:38 Oms 14:59:38 Oms 15:04:38 Oms 15:09:38 Omsv« 240.746 240.296 239.112 239.23 239.893 239.562 239.017 239.941 240.296 240.675Vb 235.392 235.344 235.605 235.747 235.297 234.871 234.326 235.202 235.415 235.913Ve 239.609 240.581 240.32 240.628 238.969 238,282 239.206 239.775 240.462 240.415la 26.905 27.845 33.682 35.059 37.132 34.35 29.386 27.45 28.8 27.436Ib 52.841 52.759 51.545 54.886 61.038 57.9 54.805 53.359 54.873 52.405Ie 40.895 33.027 33.286 35.373 50.277 48.968 36.218 35.877 35.959 37.895PF 0.894 0.879 0.89 0.899 0.872 0.855 0.869 0.877 0.874 0.886

PF' 0.799 0.773 0.792 0.808 0.760 0.731 0.755 0.769 0.764 0.785S.. 31.46 29.95 30.09 31.96 37.31 35.58 31.27 30.57 31.36 30.65

I•• 43.57 41.50 41.73 44.27 51.84 .49.51 43.58 42.47 43.50 42.45

1.tr2 1897.92 1722.47 1741.68 1959.72 2687.24 2451.36 1899.13 1803.75 1892.43 1802.12

Mean I." 48.19 47.20 46.81 49.46 50.71 49.34 48.51 47.00 48.02 45.30Variance 18.38 23.60 23.06 11.99 1.70 0.04 15.00 14.55 15.40 5.42SO 4.29 4.88 4.80 3.46 1.30 0.19 3.87 3.82 3.92 2.33MeanPF 0.91 0.91 0.92 0.92 0.91 0.90 0.91 0.91 0.91 0.91

Table A.l:Example of data library of automobile service workshop

Notes:

'.• Effectivebalanced load current(I.ff = Ie) and variancecalculated for eachaveraging intervalof 5 minutes.

• Note typicalloadcurrent imbalance.

125

AGGREGATED LOAD PROFILE (COMBINATIONS OFLI, L2. L3)

06:02:16 Oms 06:07:16 Oms 06:12:16 Oms 06:17:16 Oms 06:22:16 Oms 06:27:16 Oms 06:32:16 Oms 06:37:16 Oms 06:42:16 Oms

20B 20.34 20.21 2044 20.48 20.62 20.06 20.29 206411.99 lH7 "17.87 1633 13.93 12.82 10.43 12.96 13.040.87 0.87 0.87 0.87 0.87 0.87 0.87 087 0.87000 0002 0.004 0.002 0.001 0.002 0.002 0.002 00023.46 HI 4.23 4.04 3.73 358 3.23 3.60 3.610.50 0.50 0.50 0.50 0.49 0.49 0.50 0.50 0.48

14.84 24.82 37.46 5207 76.38 97.33 117.06 125.62 126.7592.69 617.91 1392.69 1686.46 2040.01 2450.99 236536 1589.58 1469.070.77 0.80 0.84 0.88 0.92 0.93 093 0.95 095

0.011 0011 0.011 0.007 0.005 0.004 0.004 0.004 00039.63 ·24.86 37.32 41.07 45.17 49.51 48.63 39.87 38.330.64 0.59 0.54 0.47 0.39 0.36 0.36 0.33 0.32

212.88 211.39 216.00 220.16 221.56 222.41 22257 224.20 221.1587.73 86.51 90.32 9384 95.03 95.76 95.90 97.31 94.680.81. 0.81 0.81 081 0.81 0.81 0.8'1 0.82 0820.00 0.00 000 000 000 0.00 0.00 000 0009.37 9.30 9.50 9.69 9.75 9.79 9.79 9.86 9.730.59 0.58 0.59 0.58 0.58 0.58 0.58 0.57 0.57

49.94 69.98 95.13 124.58 173.23 21528 25418 271.53 274.13382.73 2485.41 5588.65 6762.18 8173.96 9816.79 947185 6371.30 5889.33

19.56 49.85 74.76 82.23 90.41 99.08 9732 79.82 76.740.81 0.82 0.85 0.88 0.91 0.93 0.93 0.94 0.94

400.00

2

PERNODE1I·11I·21I·3 o o o

Table A.2: Example of calculation sheet in new algorithm

Notes:

• Example sheet shows selection of 1 offLI 1 (small) and I offLI 2 (large)

• Algorithm finds time interval where aggregated load current is atits maximum value.

• Load currents areadjusted for imbalance (if selected) as shown in Annexure C.

• Load currents arefurther adjusted for other PFs as discussed inearlier work.

• Key formulae usedin algorithm: :'

126

1) Aggregated selected effective load current at each time interval

=D6*D37*D58+D14*D42*D59+D22*D50*D60

D6= r,= Jeff [11 1]

D37= Scaling factor [LI 1]

D58= Consumers per node [LI 1]

D14= r,= Ieff [11 2]



D22= t, = Ieff [LI 3]



2) Variance of aggregated selected load current at each time interval

if (total) =D7*(D37*D58)"2+D15*(D42*D59)"2+D23*(D50*D60)"2

D7= Variance ofleff [LI 1]

D15= Variance ofieff [LI 2]

D23= Variance ofleff [LI 3]

3) Standard deviation of aggregated selected load current at specific time interval

= SQRT((32 (total))

4) Aggregated power factor of selected loads at specific time interval

=COS(ATAN«D6*D37*D58*Dll+D14*D42*D59*DI9+D22*D50*D60*D27)/(D6*D3

7*D5 8*D8+D 14*D42*D59*D16+D22 *D50*D60*D24)))

D11=SIN(ACOS(D8))

D19=5IN(ACOS(D16))

D27=SIN(ACOS(D24))

D8= Mean PFLI I

D16= Mean PFLI 2

D24= Mean PFLI 3

5) Aggregated I, (pF=l) = Aggregated I, * Aggregated PF

6) Calculation of la, Ib and I, as well as In for phase imbalance selection:

Refer to Annexure C :.

127

7) Calculation ofHerman-Beta parameters per phase

Refer to Herman-Beta model and spreadsheet subroutine"

8) Calculation of transformer size to supply aggregated load with power at 90%

confidence level.

=(B10+1.28*G10)*230*3/1000 kVA

B10= Aggregated Jeff following correctionfor PF

G10= Aggregated standard deviation followingcorrection for PF...

:.

128

ANNEXUREB

Operating instructions for new summation/maximum demandalgorithm

The new algorithm can be used following installation from the source compact disc (CD). The

algorithm consists of ten different Excel spreadsheets linked together with only a single

Input/Output sheet that is applicable to the user. The three load data libraries for the LI 1, LI 2

and LI 3 light industrial consumers are contained in the spreadsheets.

Minimum System Requirements

• Pentium I CPU at 2.6 GHz

• 10MB free hard drive space (At present with three libraries)

• 2.4GBRAM

• Windows Professional

• Microsoft Excel 2003

The algorithm is security protected and only specific fields can be changed in the input/output

sheet, defined as the input data.

The following sheets are found in the algorithm:

• Sheet 1: LI 1 (small) Load data of automobile service workshops

• Sheet 2: LI 2 (medium) Load data for manufacturers ofbakery products

• Sheet 3: LI 3 (medium) Cold storage wa~ehouses

• Sheet 4: Look-up sheet

• Sheet 5: Calculation sheet

• Sheet 6: Input/Output sheet - User Interface Sheet

• Sheet 7: AlphalBeta parameters Phase A

• Sheet 8: Alpha/Beta parameters Phase B

• Sheet 9: AlphalBeta parameters Phase C

• Sheet 10: Current imbalance calculator

:1

129

Inputting the data

Note:

The algorithm performs one calculation at a time and provides beta load current parameters (a, pand C values) per phase at the instant of maximum demand of a combination of the selected

loads. It also provides the user with the total apparent power of the load, as well as a

recommendation of the size of the energy source, for example a transformer. The PF is known at

any stage.

..Input data

• Step l: Select the load class and "C" value of the consumer loads to be summated

(Blue).The load class incorporates the scalingfactor.

• Step 2: Select the mixture ofloads, for example 1 xLII and 2 X LI 2 (Blue).

• Step 3: Select the target PF of the combined load (Blue).

• Step 4: Select the phase current imbalance percentage for example 0%, 5%, 10%

etcetera. (Blue).

• Step 5: Note the results in Red.

Output data

• AlphaJbeta design parameters for the beta-distributed load current per phase (Red).

• Effective balanced load current of summated load at maximum demand (Red).

• Individual phase currents at maximum demand if feeder is imbalanced (Red).

• Total apparent power loading at maximum demand (Red).

• Suggested transformer size to feed the summated load (Red).

• Graphical representation of summated mean effective daily load current and standard

deviation.

130

ANNEXUREC

Calculation of load phase currents in three-phase, four-wire systems forunbalanced electrical loads

Pilot load surveys for the selected group of light industrial consumers have revealed that

industrial loads are mostly unbalanced, either due to the random addition of single phase loads to

the three-phase systems, or due to a voltage imbalance on the supply side of a network.

With reference to the latest IEEE power definitions as discussed in chapter 3, balanced effective

three-phase load' currents were calculated for each five minute averaging interval logged by the

power measurement instrumentation.

A requirement, however, exists in industry to make provision for a slight imbalance in feeder

network loading, which normally leads to additional voltage drop both in the phase with the

highest load current and the neutral conductor which accommodates the unbalance at the neutral

point.

For purposes of this research project, it was decided to use the effective balanced load current Ie

at maximum demand as the first phase current (Ib = L) and to add a selected % (x) unbalance to

obtain the second phase current (I, = (1+x/lOO)*Ie). The 3rd phase current (Ie) has to satisfy

equations (C-2) and (C-3).

If In = I, + Ib + I, (three-phase four-wire) (C-l)

and In is set as the reference phasor, then it can be shown that the scalar value of I, can be

calculated from the following equations:

In = SQR[ (I, - O.5*Ib - O.5*Iei + (1.73*IJ2 - 1.73/2*Ici l (C-2)

laA2 + IbA2 + leA2 + InA2

3(IEEE defmition) (C-3)

with I = I dO I = I d l20 I = I _i240a a , b b 'e cl;;"

The key consideration with the selection of different combinations of load current and neutral

current is that the total effective apparent power / effective load curre,~t as per Equation C-3 must

at all times remain constant (Equation 3.13).

131

ANNEXURED

Actual spreadsheet of measured electrical parameters to establishvoltage regulation in practical feeder arrangement

CaylTIm& Minisub

Va laConsumer

Va Ia

MinI ub Consul ler

Vb Ib Vb lb

Minisub

Ve Ie

Consumer

Ve Ie PF

71161201014:45

71161201014:50

71161201014:55

233.50 41.69

233.80 24.51

233.30 33.93

230.20 40.91

230.91 23.73

23D.49 33.41

40.42

36.58

37.51

229.73 40.36. 232.19 36.27

. 35.46·

234.40 21.61

234.50 23.68

234.30 14.97

235.80 20.05

232.41 23.05

233.40 15.82

0.96

0.97

0.9671161201015:4071161201015:4571161201015:5071161201015:5571161201015:1071161201016:15

234.00 45.90233.50 47.74234.20 50.87234.70 51.79236.10 48.01236.00 48.80

232.17 45.96232.24 47.73228.59 50.46228.97 50.32228.26 48.27229.16 49.64

233.00234.00234.30235010235.00

40.3950.4047.0050.9156.6356.74

39.5551.96

I

I

227.76. 230.35

234.90 21.38234.20 26.30235.20 31.97235.50 32.70236.30 25.06236.20 28.04

233.38 22.64232.74 26.32232.90 30.96230.65 29.05233.35 25.77232.08 28.64

0.960.950.940.930.950.95

711612010 16:2071161201016:2571161201016:3071161201016:3571161201016:4071191201014:4571191201014:5071191201015:4071191201016:40

Mean Load Current

236.20 48.71236.70 38.69236.30 49.45236.80 43.17236.30 48.72231.90 36.50232.20 37.82233.10 53.06234.20 48.13

44.31

228.69 47.18232.98 36.14228.69 '49.77228.28 44.05232.24 47.73229.35 34.91229.61 37.09228.64 52.36228.95 46.77

43.69

235.30235.80235.40236.00235.70231.20231.30 .

232.60233.70

47.3436.1145.3938.1345.1448.5554.1962.0241.61

46.39

228.43231.84229.45231.60227.29228.43227,50227.08231.65

I

47.4639.6845.5541.0545.1447,18

53.7362.5943.3646,76

236.50 24.98237.10 18.01236.70 27.34237.30 20.39236.90 24.63232.40 25.40232.80 24.32234.20 24.88235.60 19.06

24.15

232.95 24.96231.81 19.23235.46 27.55233.26 20.59235.46 24.55233.38 26.05232.93 24.41234.94 25.50231.86 19.77

24.16

0.950.970.940.960.940.950.950.960.970.95

Table D.I: Spreadsheet of actual measurements recorded on the supply (miniature sub-station) andconsumer sides of the selected service workshop LV feeder (LI I [small] consumer)

With reference to the characteristic mean load curve of an LI I (small) consumer, as shown in

Figure D.I below, more than one interval of "high" demand can be observed and corresponding

supply and consumer phase voltages were used during all these intervals to calculate mean

voltage regulation.

Effective LoadCurrent andSO(L11 Small)

60.00

50.00

} 40.00

C~ 30.00::Jo-g.3 20.00

10.00

0.00

'" ~ '" .. '" '" ..E E E E E E0 0 0 0 0 0 0

~ ~ ;'? ~ '" '" ~

'" OJ OJ '" ~ ~ OJ

~ '" ~ '":!: ~ ~ N N ~Time

Figure D.I: Characteristic load profile of an LI I (small) light industrial consumer describing thepractical feeder (PF =0.95)

132

PhaseCurrentImbalance PowerFactorCorrect

Inputs in Blue

0.00% 0.95

6.90

3-Phase32.94 kVA

STDPF 0.9547.74

MeanPF

leffla 47.74Ib 47.74Ie 47.70C 100.00

1 1aOClass "C"

300

150

24.5426.91

100.00

Ie24.57

2

26.89100.00

Ib

0.5

26.8924.57

100.00

la

"C" Inputs in blue

PER NODE

L1-3L1-2L1-1

MIXUREOF LOADS

Transformer Size

Meanloadingsize:Correctedfor 10% fisk

32.9440.56

kVAkVA

Table D.2 : New algorithm calculating the beta parameters at maximum demand for PF = 0.95

133

ITHREE-PHASE H-B VOLTDROPS ft ; 'l]InputBlue Cells Only - Results inRed

'C RI RI @11 T1.1-0 tlS0.87 2280.64 22S0.44 1-28OJI- 2180,33 t4t0.47 241

tla228

R/km Rp

0.333 0.0270.470 0.0190.868 0.0430.868 0.0010.868 0.0430.868 0.0430.868 0.0430.868 0.0430.868 0.0430.868 0.0430.868 0.0430.868 0.0430.868 0.0430.868 0.0430.868 0.0430.868 0.0430.868 0.0430.868 0.0430.868 0.0430.868 0.0430.868 0.0430.868 0.0430.868 0.0430.868 0.0430.868 0.0430.868 0.0430.868 0.043

Red

231.9010

NumberConsumers

Node

VsDRisk%

e'SCl5

USER1IJSER4

Results Red White Blue%-tileVcon 229.88 229.88 229.88 V%VoItdrop 1.30 1.30 1.30 %V%-tllelsum 66.66 56.66 56.55 AMeanlsum 47.75 41.75 47.75 ASldevIsum 6.90 6.90 6.90 ACons Count 4 913 1Nodes 2 2 2

Table D.3 : Herman-Beta algorithm calculating voltage drop of the practical feeder utilizing the betaparameters as calculated by the new algorithm

:.

134

ANNEXUREE

Field survey conducted to establish automotive dealership demographicparameters

Dealership A B C D E F

Sub-elass Laroe tu Small[SJ Medium [MJ tame [Ll Small [Sl Small[SJ

Vehicles 70 15 50 65 20 22servicedlper day

Hydraulic 12 6 12 20 6 10lifts

Showroom 2768 500 2100 2500 0 800floor area

MD@ 83 kVA 15 kVA 63kVA 75 0 24 kVA30VAlm2

Energy· 21,573 kWh 4,000 kWh 26,000 kWh 22,000 kWh 0 7,000 kWhkWh

Workshop 3100 870 1800 3050 900 800floor area

MD@ 155 kVA 43 kVA 90kVA 175 kVA 45 kVA 40 kVA50VAlm2

Energy· 50000 kWh 14,000 kWh 29000 kWh 57000 kWh 14,600kWh 13000 kWhkWh

kWh/vehicle 714 933 580 876 730 590serviced

MD 228 kVA 57 kVA 150kVA 255 kVA 35 kVA 75kVAUtility Bill

Total kWh 80,000 kWh 20,000 kWh 50,000 kWh 90,000 kWh 7710kWh 28,000 kWhUtility Bill

* Monthly

Table E.1: Table representing demographic data of different automotive service workshop

dealerships

:.

135

Calculation of monthly energy consumption per proposed category

Average energy consumption per vehicle serviced: 740 kWh/vehicle/month

Small [S]: Defined as 0-20 vehicles per day implying an energy consumption of

14,800 kWh/month.

Medium [M]: Defined as 0-50 vehicles per day implying an energy consumption of37,000

kWh/month

Large [L]: Defined as 0-75 vehicles per day implying an energy consumption of 55,000

kWh per month .'

Scaling factor calculation:

Ratio [M] : [S] = 2.5

Ratio [L] : [8] = 3.75

The above scaling factors are used in the new summation algorithm.

:'

136

2

4

9

10

11

12

13

14

REFERENCES

Aimee McKane, Lynn Price, Stephanie de la Rue du Can, "Policies for promoting

industrial energy efficiency in developing countries and transition economies", Unido

Side Event on Sustainable Industrial Development, 8 May 2007.

National Energy Efficiency Strategy for the Republic of South Africa: First Review

October 2008, Government Gazette no 32249, May 2009.

K.C. Fagen, R.W.Beck,. Robert Fletcher, "Distribution systems get efficiency

upgrades" Transmission & Distribution World, Feb 2010. .,

Northwest Energy Efficiency Alliance (NEEA-USA), "Distribution efficiency initiativeI

(DEI)projecf', 2007.

NRS 048-2:2008: Electricity Supply-Quality of Supply, Part 2: Voltage characteristics,

compatibility levels, limits and assessment methods, South Africa.

Rob Davies, Minister of Trade and Industry South Africa: National Assembly

Statement on Industrial Policy Action Plan (IPAP2) 2010/11 to 2012/13. February 2010.

Mariposa County, California, Town Planning Area & Zoning Regulations: Light

Industrial and other zoning definitions. Website: http://ca

mariposacounty.civicplus.com/index.aspx

Temecula Development Code, California: Zoning classifications. Website:

www.cityoftcmecula.orgltemecula/govcmment/commdev/zoningclassification.htm

North American Industry Classification System: Website:

www.ccnsus.gov/cos/www/naics

Standard Industrial Classification of all Economic Activities, 5th edition, Statistics

South Africa, January 1993.

Ronald Herman, "Voltage regulation analysis for the design of low voltage networks

feeding stochastic domestic electrical loads", PhD Dissertation, University of

Stellenbosch, November 1993.

Ronald' Herman, "A practical probabilistic design procedure for LV residential

distribution systems", IEEE Transactions on Power Delivery.

Ronald Herman and J.J. Kritzinger, "The statistical description ofgrouped domestic

electrical load currents", Elect. Power Syst. Res. Vol 27, pp. 43-48, 1993.

Eskom Distribution Standard Part I-Planning guidelines: Section 23 & 28 - Load

forecasting and LV feeder voltage drop calculation methods, SCSASAB09 & P4, Feb.

2003. :.

137

15

16

17

18

19

20

21

22

23

24

25

26

27

28

Energex Limited, "General design parameters-developer design and construct estates

information handout", South East Queensland Electricity Utility in Australia, Version 8,

Page 9 of 17,5 May 2004.

Tshwane Metropolitan Council, South Africa-Supply of Electricity: Erf quota for the

design ofintemal network, Chapter A, Par.Ll (iv).

Pienaar and Erwee: " Internal report-measurement of ADMD of large group of light

industrial consumers in Polokwane, South Africa", 2006.

R.Herman: "Load data collection and forecasting" NEC Report, Project Elek. 17, South

Africa, 1990.

IEEE Power System' Instrumentation and Measurements Committee, "IEEE

Standard Definitions for the Measurement ofElectric Power Quantities under Sinusoidal,

Nonsinusoidal, Balanced, or Unbalanced Conditions", IEEE Std 1459™, 2010, IEEE

Power & Energy Society.

Ronald Herman, "A practical probabilistic design procedure for LV residential

distribution systems", IEEE Transactions on Power Delivery.

J.F. Kennedy, E.S. Keeping, "Mathematics ofstatistics" 3rd Edition, April 1954.

H. Lee Willis, "Power distribution planning reference book", 2nd Edition, Revised and

expanded, 2004.

R.L. Sellick, C.T. Gaunt: " Comparing Methods of Calculating Voltage Drop in Low

Voltage Feeders", Transactions of the S.A. Institute of Electrical Engineers,September

1995, pp. 96-110.

D.H.O. McQueen, P.R. Hyland and Simon J. Watson: "Monte Carlo Simulation of

Residential Electricity Demand for Forecasting Maximum Demand on Distribution

Networks", IEEE Trans. on power systems, 2004, pp. 1-5.

Eskom Distribution Standard: " Planning guidelines for LV feeder voltage drop

calculations", South African Electricity Utility Standard, February 2003

R. Herman, J.J. Kritzinger: " The Statistical description of grouped domestic electrical

load currents", Electric Power Systems Research, 27 (1993) pp. 43-48

NRS 034-1: Electricity Distribution-Guidelines For The Provision Of Electrical

Distribution Networks In Residential Areas, Part 1: Planning and Design of Distribution

Systems Standards South Africa. Pretoria, South Africa.

R.Herman, C.T. Gaunt, S.W. Heunis, "Benchmark tests andresults for the evaluation

ofLV distribution voltage drop calculation procedures", Trans SAIEE, vol. 90, no. 2, pp.

54-60, 1999.

138

29

30

31

32

33

34

35

36

37

38

39

40

41

42

J.A. Jardini, C.M.V. Tahan, S.U. Ahn, F.M. Figueiredo, "Daily load profiles for

residential, commercial and industrial low voltage consumers", IEEE Trans. On Power

Delivery, Vol 15, No 1, January 2000.

South Mrica's New Regional Industrial Development Strategy: June 2006, Website:

www.thedti.gov.za/publications/pdfrids/chapter8.pdf

Ronald Herman, "LV distribution system planning and design" Course notes, 2008.

NRS 048-2:2008: Electricity Supply-Quality of Supply, Part 2: Voltage characteristics,

compatibility levels, limits and assessment methods, South Africa."

D. J. Warren, "Cost effective calculation procedures in reticulation design", SAEE:

Workshop on electrification of developing communities: Innovation and standardization,

South Africa, 1991.

R. Herman, S.W. Heunis, "Load models for mixed-class domestic and fixed, constant

power loads for use in probabilistic LV feeder analysis", Electric Power Systems

Research 66 (2003) 149-153.

Bartlett, Kotrlik & Higgins, "Organizational research: determining appropriate sample

size in survey research", Information Technology, Learning and Performance Journal,

Vol. 19, No.1, Spring 2001.

David C. Howell, "Fundamental statistics for the behavioral sciences", 4th edition, 1994.

F. Buchholz, "Die Drehstrom-Scheinleistung bei Ungleichmassiger Belastung Der Drei

Zweige", Licht und Kraft, No.2, Jan.20,1922, pp 9-11.

W.M. Goodhue, "Discussion to reactive power concepts in need ofclarification", AlEE

Transactions, Vol.52, Sept. 1933, p787.

IEEE Std 1459™-2010: "IEEE standard definitions for the measurement of electric

power quantities under sinusoidal, non sinusoidal, balanced, or unbalanced conditions"

Power System Instrumentation and Measurements Committee of the IEEE Power &

Energy Society. 2 Feb. 2010.

Pretorius J.H.C., van Wyk J.D. and Swart P.H., "An evaluation ofsome alternative.methods ofpower resolutions in a large industrial plant", IEEE Transactions on Power

Delivery, vol. 15,no. 3, pp. 1052-1059, July 2000.

Alexander Eigeles Emanuel, "Power Definitions and the Physical Mechanism of

Powerflow", Worcester Polytechnic Institute, USA, IEEE Press 2010.

Ronald Herman, S.W. Heunis, "Load models for mixed-class domestic and fixed,

constant power loads for use in probabilistic LVfeeder analysis" Electric Power Systems

Research 66 (2003) 149-153.:.

139

43

44

45

46

47

48

49

50

Charles Annis, "Statistical Engineering.com" Sums of random variables, 1998-2008.

R.L. Sellick, C.T. Gaunt, "Comparing methods of calculating voltage drop in low

voltagefeeders", Transactions of the SA Institute ofElectrical Engineers, Sept. 1995.

M. Dekenah, "Calculation of volt drops on unbalanced radial feeders supplying

domestic consumers", University of Cape Town, 1991.

ACE Report No 13: "Design ofmedium voltage underground networksfor new housing

estates", British Electricity Boards, 1966.

F. Nortje, "DT Vdrop 5 (Low voltage simulation p.ackage)", Eskom Distribution

Technology.

C.T. Gaunt, "Parameters for the design of low voltage electricity distribution to

domestic consumers", Hill Kaplan Scott Inc., 1993.

M. Dekenah, "Calculation of Volt Drops on Unbalanced Radial Feeders Supplying

Domestic Consumers", University of Cape Town, 1991.

Reticmaster Version 2004.1: "Electrical Network Software for Distribution Systems",

Developed by Inspired Interfaces Limited-Quick reference guide.

.,

140

Probabilistic Low Voltage Distribution Network Design for Aggregated Light Industrial Loads

Documents

Transcript of Probabilistic Low Voltage Distribution Network Design for Aggregated Light Industrial Loads