DISTRIBUTION NETWORK AUTOMATION FOR MULTI- …

DISTRIBUTION NETWORK

AUTOMATION FOR MULTI-

OBJECTIVE OPTIMISATION

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

Doctor of Philosophy

in the Faculty of Science and Engineering

2018

BOYI ZHANG

SCHOOL OF ELECTRICAL AND ELECTRONIC ENGINEERING

Page | 2

List of Contents

List of Contents 2

List of Figures 7

List of Tables 10

List of Abbreviations 14

Abstract 16

Declaration 17

Copyright Statement 18

Acknowledgements 19

CHAPTER 1 20

INTRODUCTION 20

11 Motivation 20

12 Objectives 22

13 Contribution of the work 23

14 Structure of the thesis 25

CHAPTER 2 28

DISTRIBUTION AUTOMATION 28

21 Introduction 28

22 Distribution Network Configurations 29

23 Switchgear for Distribution Network 30

231 Reclosers 30

232 Sectionalising Switches 31

233 Tie-switches 31

24 Transformer Economic Operation 31

241 Basic Concepts 31

242 Literatures on Transformer Economic Operation 33

25 Distribution Network Reconfiguration 35


252 Literatures on Distribution Network Reconfiguration 36

26 Placement of Sectionalising Switches 38


262 Literatures on Sectionalising Switch Placement 41

Page | 3

27 Transformer Loss Assessment 42

271 Operating Principles 42

272 Transformer Quantities Measurement 43

273 Integrated Transformer Loss 46

28 Feeder Loss Assessment 47

29 Reliability Evaluation 48

291 Reliability Indices 48

292 Reliability Evaluation Methods 50

210 Multi-objective Optimisation 53

2101 Single Objective Function 54

2102 Single Fuzzy Satisfaction Objective Function 54

2103 Multi-objective Formulation in the Pareto Optimality Framework 56

211 Summary 58

CHAPTER 3 60

OPTIMISATION TECHNIQUES 60

31 Introduction 60

32 Monte Carlo Method 61

33 Ant Colony Optimisation 62

34 AIS-ACO Hybrid Algorithm 65

341 Artificial Immune Systems 65

342 Proposed AIS-ACO Hybrid Algorithm 66

35 Summary 68

CHAPTER 4 70

TRANSFORMER ECONOMIC OPERATION amp DISTRIBUTION NETWORK

RECONFIGURATION FOR TRANSFORMER LOSS REDUCTION 70

41 Introduction 70

42 Load Model 72

43 Problem Formulation 73

44 Methodology 73



45 Application Studies 77

451 Test Case 1 77

452 Test Case 2 85

Page | 4

46 Summary 90

CHAPTER 5 92

DISTRIBUTION NETWORK RECONFIGURATION amp DG ALLOCATION FOR

FEEDER LOSS REDUCTION 92

51 Introduction 92


53 Solution Method 94


532 Applying ACO to DNR and DGs Placement 95


541 33-bus System 99


55 Summary 109

CHAPTER 6 111

DISTRIBUTION NETWORK RECONFIGURATION amp TRANSFORMER

ECONOMIC OPERATION FOR NETWORK LOSS REDUCTION 111

61 Introduction 111

62 Time-varying Load Model 112


64 Applying ACO to DNR and TEO 114


651 Test Case 1 122

652 Test Case 2 123

653 Test Case 3 124

66 Summary 126

CHAPTER 7 128

OPTIMAL PLACEMENT OF SECTIONALISING SWITCHES FOR

RELIABILITY IMPROVEMENT 128

71 Introduction 128


721 Weighted Aggregation 129

722 Single Fuzzy Satisfaction Objective Function with Two Parameters 130

723 Single Fuzzy Satisfaction Objective Function with Three Parameters 131

Page | 5

724 Evaluation of ECOST 132

725 Evaluation of SAIDI 133

726 Evaluation of Switch Costs 133

73 Applying ACO to Sectionalising Switch Placement Problem 134

74 Benefit-to-cost Analysis 135


751 Test Case 1 138

752 Test Case 2 147

753 Test Case 3 147

76 Summary 148

CHAPTER 8 150

DISTRIBUTION NETWORK RECONFIGURATION FOR LOSS REDUCTION amp


81 Introduction 150


821 Multi-objective Reconfiguration Problem 152

822 Best Compromise Solution 153

83 Solution Methodology 154

831 Applying MOACO to Multi-objective DNR Problem 154

832 Applying AIS-ACO to Multi-objective DNR Problem 158



86 Summary 164

CHAPTER 9 166

MULTI-OBJECTIVE DISTRIBUTION NETWORK RECONFIGURATION amp DG

ALLOCATION CONSIDERING LOSS VOLTAGE DEVIATION AND LOAD

BALANCING 166

91 Introduction 166



922 Multi-objective Reconfiguration Problem Using Pareto Optimality 170

93 Solution methodology 171

931 Applying ACO to DNR and DG Allocation in the Fuzzy Domain 171

932 Applying AIS-ACO to Multi-objective DNR and DG Allocation Using

Pareto Optimality 171

Page | 6




95 Summary 187

CHAPTER 10 189

CONCLUSION amp FUTURE WORK 189

101 Conclusion 189

102 Future Work 193

References 195

APPENDIX A Network Model Data 204

APPENDIX B Simulation Results 209

APPENDIX C Control Parameters of Algorithms 221

APPENDIX D List of Publications 224

Word count 51012

Page | 7

List of Figures

Fig 2-1 Typical Distribution network [27] 29

Fig 2-2 Recloser operation 30

Fig 2-3 Transformer loss versus transformer load 32

Fig 2-4 Daily load curve of a typical substation before and after load smoothing [38]

34

Fig 2-5 Radial test system 35

Fig 2-6 Fully automated distribution feeder 40

Fig 2-7 Partially automated distribution feeder 41

Fig 2-8 Elements of a single phase transformer [33] 43

Fig 2-9 Construction of a three-phase transformer [33] 43

Fig 2-10 The open-circuit test [33] 44

Fig 2-11 The short-circuit test [33] 45

Fig 2-12 Simple two-bus network 47

Fig 2-13 Reliability model for static components 51

Fig 2-14 Procedure for reliability evaluation 52

Fig 2-15 Sample network 53

Fig 2-16 Linear membership function 54

Fig 3-1 Example of ant colony system [69] 63

Fig 3-2 Flowchart of the ant colony algorithm 65

Fig 3-3 Flowchart of the AIS-ACO algorithm 67

Fig 4-1 Procedure of domestic electricity demand profile generation 72

Fig 4-2 Monte Carlo simulation platform for three transformer operation modes

comparison 74

Fig 4-3 Flowchart of transformer loss assessment 75

Fig 4-4 Monte Carlo simulation platform for distribution network reconfiguration 76

Fig 4-5 Generic distribution network topology 78

Fig 4-6 Transformer load factor variation 79

Fig 4-7 Transformer loss variations in different scenarios 80

Fig 4-8 11 kV 4th

feeder voltage profiles in different scenarios 81

Fig 4-9 Voltage profiles of Load 4_1 in different scenarios 82


Page | 8

Fig 4-11 11 kV 4th

feeder mean voltage profile of various TCLFs 84

Fig 4-12 Test system 86

Fig 4-13 Daily load variations for different load groups 87

Fig 4-14 Mean voltage profiles in S1 S2 and S3 89


Fig 5-1 Search space of DNR and DGs Placement 95

Fig 5-2 Flowchart of the ACO applied to DNR and DGs placement 98

Fig 5-3 33-bus system 100

Fig 5-4 33-bus system for feeder loss minimisation Case II 101

Fig 5-5 33-bus system for feeder loss minimisation Case III 102

Fig 5-6 33-bus system for feeder loss minimisation Case IV 103

Fig 5-7 Comparison of feeder loss for different DG capacities before and after

simultaneous reconfiguration and DG allocation 104

Fig 5-8 Comparison of voltage profiles in different cases of 33-node system 104








Fig 6-1 The reconfiguration hours for a typical day 113

Fig 6-2 Search space of DNR and TEO 115

Fig 6-3 Sample network with three substations 116

Fig 6-4 Flowchart of the ACO applied to DNR and TEO for a specific type of day

117

Fig 6-5 Distribution feeder connected to RBTS Bus 4 118

Fig 6-6 Daily load profile of residential consumers 119

Fig 6-7 Daily load profile of commercial consumers 120

Fig 6-8 Daily load profile of industrial consumers 120

Fig 6-9 Daily load profile (MW) of the main feeder 120

Fig 6-10 Annual energy loss with different DG capacities 123

Fig 6-11 Annual energy loss in uncoordinated charging strategy 125

Fig 6-12 Annual energy loss in coordinated charging strategy 126

Page | 9

Fig 7-1 Membership function for SAIDI and switch cost reduction 131

Fig 7-2 Membership function for ECOST reduction 132

Fig 7-3 Search space of sectionalising switch placement 134

Fig 7-4 Distribution feeder connected to RBTS Bus 4 with 6 sectionalising switches

136

Fig 7-5 Optimal relocation of sectionalising switches in Test Case 11 139

Fig 7-6 Optimal installation of sectionalising switches in Test Case 12 141

Fig 7-7 Optimal installation and relocation of sectionalising switches in Test Case

13 142

Fig 7-8 BCR versus years 143

Fig 7-9 Variation of cost versus change in CDF 144

Fig 7-10 Number of installed sectionalising switches versus change in CDF 145

Fig 8-1 Flowchart of the MOACO algorithm applied to multi-objective DNR

problem 157

Fig 8-2 Flowchart of the AIS-ACO algorithm applied to multi-objective DNR

problem 158


Fig 8-4 Pareto solutions obtained (minimisation of feeder loss ECOST and SAIDI)

162

Fig 9-1 Membership function for feeder loss reduction 168

Fig 9-2 Membership function for maximum node voltage deviation reduction 169

Fig 9-3 Membership function for load balancing index reduction 170

Fig 9-4 33 bus-system for fuzzy multi-objective optimisation Case II 173

Fig 9-5 Pareto front obtained for 33-bus system in Case II 174

Fig 9-6 33 bus-system for fuzzy multi-objective optimisation Case III 175

Fig 9-7 Pareto front obtained for 33-bus system in Case III 176

Fig 9-8 33 bus-system for fuzzy multi-objective optimisation Case IV 178

Fig 9-9 Pareto front obtained for 33-bus system in Case IV 178

Fig 9-10 69 bus system for fuzzy multi-objective optimisation Case II 180


Fig 9-12 69-bus system for fuzzy multi-objective optimisation Case III 183


Fig 9-14 69-bus system for fuzzy multi-objective optimisation Case IV 185


Page | 10

List of Tables

Table 2-1 Transformer economic operation area 33

Table 2-2 Transformer technical specifications and costs 35

Table 3-1 Relationship of 119911 lowast and 119862 62

Table 4-1 Household size by number of people in household as a proportion [103] 72

Table 4-2 Parameters of a typical 3311 kV two-winding transformer [106] 78

Table 4-3 Daily transformer loss in different scenarios 80

Table 4-4 Transformer loss with different TCLF 85

Table 4-5 Average number of switching operations with different TCLF 85

Table 4-6 Transformer loss in Test Case 2 88

Table 5-1 Results of different cases for the 33-bus system 100

Table 5-2 Comparison of simulation results for 33-bus system in Case II 101

Table 5-3 Comparison of ACO with CGA and CSA for the 33-bus system in Case II

102



Table 6-1 Revised customer data (peak load) 119

Table 6-2 The distribution of load types for a whole year 121

Table 6-3 Results of DNR and TEO with different load types in Test Case 1 122

Table 6-4 Characteristics of EV 124

Table 7-1 Customer data (Average load) 137

Table 7-2 Sector interruption cost estimation ($kW) 138

Table 7-3 Results of sectionalising switches relocation in Test Case 11 140

Table 7-4 Results of sectionalising switches installation in Test Case 12 141

Table 7-5 Results of sectionalising switches relocation and installation in Test Case

13 143

Table 7-6 Impacts of 120588 variation on objective function 119869 146

Table 7-7 Impacts of variation in number of ants on objective function 119869 146


2 147

Table 7-9 Results of sectionalising switches installation and relocation in Test Case

3 148

Page | 11

Table 8-1 Revised customer data (Average load) 162

Table 8-2 Mean and standard deviation of Pareto Front (loss ECOST and SAIDI)

163

Table 8-3 Minimum solutions along each objective (loss ECOST and SAIDI) 163

Table 8-4 Best compromise solutions (loss ECOST and SAIDI) 164

Table 9-1 Results of DNR in fuzzy multi-objective formulation for 33-bus system in

Case II 173

Table 9-2 Mean and standard deviations of Pareto Front for 33-bus system in Case II

174

Table 9-3 Minimum solutions along each objective for 33-bus system in Case II 175


Case III 176

Table 9-5 Mean and standard deviations of Pareto Front for 33-bus system in Case

III 176

Table 9-6 Minimum solutions along each objective for 33-bus system in Case III 177

Table 9-7 Results of DNR and DG allocation in fuzzy multi-objective formulation

for 33-bus system in Case IV 178


IV 179

Table 9-9 Minimum solutions along each objective for 33-bus system in Case IV 179

Table 9-10 Results of DNR in fuzzy multi-objective formulation for 69-bus system

in Case II 181


II 181



in Case III 183


III 184

Table 9-15 Minimum solutions along each objective for 69-bus system in Case III

184

Table 9-16 Results of DNR and DGs allocation in fuzzy multi-objective formulation


Page | 12


IV 186

Table 9-18 Minimum solutions along each objective for 69-bus system in Case IV

187

Table A-1 Typical configurations and parameters of 11 kV triplex cables in the UK

204

Table A-2 Line and load data of 33-bus system 205


Table A-4 Feeder data of RBTS Bus 4 207

Table A-5 Reliability Data for RBTS Bus 4 208

Table B-1 The locations of tie-switch in Scenario 9 209

Table B-2 Mean voltage profiles at each node in the linked feeder 210

Table B-3 95th

voltage profiles at each node in the linked feeder 210

Table B-4 Network losses in each branch of 33-bus system 211


Table B-6 Pareto optimal solutions of multi-objective DNR (loss ECOST and

SAIDI) 214

Table B-7 Pareto optimal solutions of multi-objective DNR (loss maximum node

voltage deviation feeder load balancing index) for 33-bus system in Case II 215


voltage deviation feeder load balancing index) for 33-bus system in Case III 215


voltage deviation feeder load balancing index) for 33-bus system in Case IV 216







Table C-1 ACO parameters for distribution network reconfiguration and DG

allocation in Test Case 2amp3 221


allocation in Test Case 4 221

Page | 13

Table C-3 ACO parameters for distribution network reconfiguration and transformer

economic operation 221

Table C-4 ACO parameters for sectionalising switch placement in Test Case 1 222

Table C-5 ACO parameters for sectionalising switch placement in Test Case 2amp3222

Table C-6 MOACO parameters for multi-objective distribution network

reconfiguration (loss ECOST and SAIDI) 222

Table C-7 AIS-ACO parameters for multi-objective distribution network


Table C-8 ACO parameters for multi-objective DNR (loss maximum node voltage

deviation feeder load balancing index) 223

Table C-9 AIS-ACO parameters for multi-objective DNR (loss maximum node

voltage deviation feeder load balancing index) 223

Page | 14

List of Abbreviations

Abbreviations Definition

ACO Ant Colony Optimisation

ACS Ant Colony System

AENS Average Energy Not Supplied

AIS Artificial Immune Systems

AIS-ACO Artificial Immune Systems-Ant Colony Optimisation

ANN Artificial Neutral Network

ASP Active Server Pages

BCR Benefit-to-cost Ratio

BEM Branch Exchange Method

BPSO Binary Particle Swarm Optimisation

CDF Customer Damage Function

CGA Continuous Genetic Algorithm

CSA Cuckoo Search Algorithm

DA Distribution Automation

DNO Distribution Network Operator

DNR Distribution Network Reconfiguration

DG Distributed Generation

DPSO Discrete Particle Swarm Optimisation

ECOST Expected Customer Damaged Cost

EDNS Expected Demand Not Supplied

ENS Energy not supplied

EV Electric Vehicle

FMEA Failure-mode-and-effect Analysis

FWA Firework Algorithm

FRTU Feeder Remote Terminal Unit

GA Genetic Algorithm

HC Hyper Cube

HSA Harmony Search Algorithm

HV High Voltage

Page | 15

IWO Invasive Weed Optimisation

LV Low Voltage

MDC Maximum Driving Capability

MILP Mixed Integer Linear Programming

MOACO Multi-objective Ant Colony Optimisation

MV Medium Voltage

PSO Particle Swarm Optimisation

RBTS Roy Billinton Test System

RGA Refined Genetic Algorithm

SA Simulated Annealing

SAIDI System Average Interruption Duration Index

SAIFI System Average Interruption Frequency Index

SCADA Supervisory Control and Data Acquisition

SSP Sectionalising Switch Placement

TS Tabu Search

TCLF Transformer Critical Load Factor

TEO Transformer Economic Operation

TOM Transformer Operation Mode

VML Vector Markup Language

Page | 16

Abstract

The University of Manchester

Submitted by Boyi Zhang

for the degree of Doctor of Philosophy

Distribution Network Automation for Multi-objective Optimisation

December 2017

Asset management and automation are acknowledged by distribution utilities as a

useful strategy to improve service quality and reliability However the major

challenge faced by decision makers in distribution utilities is how to achieve long-

term return on the projects while minimising investment and operation costs

Distribution automation (DA) in terms of transformer economic operation (TEO)

distribution network reconfiguration (DNR) and sectionalising switch placement

(SSP) is recognised as the most effective way for distribution network operators

(DNOs) to increase operation efficiency and reliability Automated tie-switches and

sectionalising switches play a fundamental role in distribution networks

A method based on the Monte Carlo simulation is discussed for transformer loss

reduction which comprises of profile generators of residential demand and a

distribution network model The ant colony optimisation (ACO) algorithm is then

developed for optimal DNR and TEO to minimise network loss An ACO algorithm

based on a fuzzy multi-objective approach is proposed to solve SSP problem which

considers reliability indices and switch costs Finally a multi-objective ant colony

optimisation (MOACO) and an artificial immune systems-ant colony optimisation

(AIS-ACO) algorithm are developed to solve the reconfiguration problem which is

formulated within a multi-objective framework using the concept of Pareto

optimality The performance of the optimisation techniques has been assessed and

illustrated by various case studies on three distribution networks The obtained

optimum network configurations indicate the effectiveness of the proposed methods

for optimal DA

Page | 17

Declaration

No portion of the work referred to in the thesis has been submitted in support of an

application for another degree or qualification of this or any other university or other

institute of learning

Page | 18

Copyright Statement

i The author of this thesis (including any appendices andor schedules to this

thesis) owns certain copyright or related rights in in (the ldquoCopyrightrdquo) she

has given The University of Manchester certain rights to use such Copyright

including for administrative purposes

ii Copies of this thesis either in full or in extracts and whether in hard or

electronic copy may be made only in accordance with the Copyright

Designs and Patents Act 1988 (as amended) and regulations issued under it

or where appropriate in accordance with licensing agreements which the

University has from time to time This page must form part of any such

copies made

iii The ownership of certain Copyright patents designs trademarks and other

intellectual property (the ldquoIntellectual Propertyrdquo) and any reproductions of

copyright works in the thesis for example graphs and tables

(ldquoReproductionsrdquo) which may be described in this thesis may not be owned

by the author and may be owned by third parties Such Intellectual Property

and Reproductions cannot and must not be made available for use without the

prior written permission of the owner(s) of the relevant Intellectual Property

andor Reproductions

iv Further information on the conditions under which disclosure publication

and commercialisation of this thesis the Copyright and any Intellectual

Property andor Reproductions described in it may take place is available in

the University IP Policy (see

httpdocumentsmanchesteracukDocuInfoaspxDocID=24420) in any

relevant Thesis restriction declarations deposited in the University Library

The University Libraryrsquos regulations (see

httpwwwlibrarymanchesteracukaboutregulations) and in The

Universityrsquos policy on Presentation of Theses

Page | 19

Acknowledgements

First and foremost I would like to express my deepest gratitude to my supervisor

Prof Peter Crossley for his invaluable guidance and continuous encouragement

throughout the project

I would like to thank my friends and colleagues in the Ferranti Building at The

University of Manchester Prof Zhongdong Wang and Dr Qiang Liu for the fruitful

research discussions and their encouragement throughout the period of my PhD

I wish to thank North China Electric Power University PR China for the 2+2

course and also to Prof Chunming Duan and Prof Sangao Hu for their help and

encouragement

I also wish to thank Prof Bo Zhang Prof Jianguo Zhao and Prof Li Zhang from

Shandong University PR China who continued to support my research with their

valuable feedback and advice

Finally I would like to express my gratitude to my parents for their encouragement

and support

Page | 20

CHAPTER 1

INTRODUCTION

11 Motivation

The electricity ldquoutilityrdquo distribution network is part of a power system that carries

electricity from a high voltage transmission grid to industrial commercial and

residential customers [1] In England and Wales the voltage level of distribution

networks ranges from 132 kV to 230 V [2] Generally most distribution networks

operating at voltages below 25 kV are designed in closed loop but are operated

radially due to the simplicity of operation the ease of protection coordination and

the minimisation of overall economics [3] [4]

The electric power generation transmission and distribution companies are not only

energy producers but also significant power consumers Power loss occurs when

electricity is supplied to customers In 2013 the total distribution losses of GBrsquos

networks were estimated to be 196 TWh which indicates that about 6 of the total

power generation is wasted in the form of losses at distribution level [5] Utility

statistics also indicate that distribution transformers account for approximately 22

of these losses and the line and cable losses make up the remaining 78 Reduction

in active power loss can help distribution network operators (DNOs) save costs and

increase profits

The expression ldquoPower quality = Voltage qualityrdquo has been widely accepted as the

wave shape and magnitude of voltage that strongly influences the power quality

Chapter 1 Introduction

Page | 21

received by customers [6] According to the EN50160 standard [7] under normal

conditions at least 95 of the mean 10 minutes average rms voltage magnitudes in

an 11 kV electricity distribution network should be within the range 09 pu to 11 pu

during one week

Distribution network reliability has proved to be another fundamental attribute for

the safe operation of any modern power system [8] Data show that about 80 of

customer outages are due to distribution system failures [9] Based on the resource

from [10] in 2011 the average number of minutes of lost supply per customer in GB

is 70 minutes According to [11] electricity breakdowns cost the United States

around $80 billion per year With improved reliability the DNOs can save expenses

that are spent on networkrsquos maintenances after a failure [12]

The major challenge faced by DNOs is how to distribute the power in a low-cost

reliable and efficient way Distribution automation (DA) is recognised as the most

effective method for DNOs to increase operation efficiency and reliability The three

main parts of DA are transformer economic operation (TEO) distribution network

reconfiguration (DNR) and sectionalising switch placement (SSP) TEO refers to the

optimum selection of the transformers needed to supply each feeder This is related

to the economic evaluation of network performance and the resilience of the

network DNR is a process that involves changing the network topology by altering

the openclose status of sectionalising (normally closed) and tie (normally open)

switches [13] [14] Installation of new sectionalising switches and relocation of

existing sectionalising switches are defined as SSP

Mathematically DA is a discrete non-linear constrained combinational optimisation

problem that is subject to operating constraints As it is not a practical solution to

investigate all possible network configurations ant colony optimisation (ACO)-

based heuristic search algorithms have been developed

To build a cleaner climate-friendly community the European Union has set a target

on carbon emissions for a 40 60 and 80 below 1990 levels by 2030 2040

and 2050 respectively [15] Therefore a large number of renewable distributed

generations (DGs) are deployed DG is a small electric generation unit that is

connected directly to the distribution network or appears on side of the meter

accessed by the customer [16] Since the number of DGs has increased in recent


Page | 22

years this has resulted in bidirectional power flows and locally looped networks [17]

The integration of high numbers of DGs strongly affects network operation and

planning Therefore optimal placement and sizing of DGs strongly improve

distribution network performance

12 Objectives

The aim of this research is to improve service quality and efficiency based on the

results of DA To achieve this aim the objectives of this thesis are as follows

To review distribution networks DA loss and reliability assessment and

optimisation functions

To propose three optimisation techniques namely the Monte Carlo Method the

ACO algorithm and the artificial immune systems-ant colony optimisation (AIS-

ACO) algorithm

To develop an optimal strategy consisting of TEO and DNR for transformer loss

reduction Statistic models of customer electrical demands should be established

to evaluate their impact from the perspective of probability

To assess the DNR and DG placement problems simultaneously in terms of

distribution feeder loss minimisation

To assess the TEO and DNR problem simultaneously in terms of distribution

network loss minimisation including transformer loss and feeder loss under

different load scenarios

To assess the SSP problem simultaneously based on three objectives namely

reduction of unserved energy cost decrease in the average time that a customer is

interrupted and minimisation of switch costs and using the fuzzy set theory

To propose a benefit-to-cost analysis to justify whether the benefits of installing

and relocating sectionalising switches can justify the cost or not

To formulate the optimal network reconfiguration problem within a multi-

objective framework using the Pareto optimality concept where network loss

and reliability indices are simultaneously optimised


Page | 23

To assess the DNR and DG allocation problem in terms of three conflicting

objectives optimisation network loss maximum node voltage deviation and

load balancing index in order to obtain a set of non-dominated solutions

13 Contribution of the work

This thesis has presented three methodologies of DA All of them are designed to

achieve service quality and efficiency improvement

The contributions of this thesis are summarised below

Load profiles In most literatures the load variations are ignored in their studies

which could underestimate the total energy loss for the utility [18] The

stochastic nature associated with load variety is considered in Chapter 4 In this

chapter the value of the load associated with domestic demand profiles are

obtained from the research described in [19] this can produce a random 1-min

resolution model for UK households A pool of load profiles is randomly

generated by this model in MATLAB Following this each node in the feeders

from the system is assigned with residential demand profiles from the pool based

on the Monte Carlo methodology

In Chapter 6 the distribution loads experience daily and seasonal variations The

study considers the daily load curves of different types of consumers (residential

commercial and industrial) In addition the days are divided into eight types

spring weekdays spring weekends summer weekdays summer weekends

autumn weekdays autumn weekends winter weekdays and winter weekends

Optimisation problems Previously it was observed that sufficient work has

been completed in terms of examining the TEO and the DNR problems

separately In Chapter 4 and 6 both the TEO and network reconfiguration

problems are integrated to benefit the whole distribution network effectively

Different combinations of locations of tie-switches in the network and operation

modes of all transformers in the substations represent different network

configurations Network reconfiguration and transformer operation modes

variation are dealt simultaneously using the ACO algorithm with an objective of

network loss minimisation as presented in Chapter 6


Page | 24

Most research projects have focused only on the optimisation of either the DNR

or the DG allocation problem An ACO algorithm is proposed in Chapter 5 to

deal with the DNR and DG allocation problems simultaneously in terms of

feeder loss minimisation In Chapter 9 the study aims to determine the optimum

network configurations and DG locations that minimise the active power loss

maximum node voltage deviation and feeder load balancing simultaneously

Multi-objective optimisation framework When there are multiple and

conflicting objectives that need to be satisfied all objective can be converted into

a single objective function which reflects a compromise among all objectives

The single objective function has two forms weighted aggregation and fuzzy

satisfaction objective function The selection of the form depends on the number

of objectives as well as their units and dimensions In Chapter 7 the system

expected outage cost to customers (ECOST) and switch costs can be converted

into a single objective function by aggregating these objectives in a weighted

function However as system interruption duration index (SAIDI) and switch

costs have different dimensions and units the two conflicting objectives are

modelled with fuzzy sets and then combined into a single objective function

Also a fuzzy membership function based on max-min principle is presented for

optimising ECOST SAIDI and switch costs simultaneously In Chapter 9 a new

operator called lsquomax-geometric meanrsquo has been introduced to determine the

degree of overall fuzzy satisfaction

However the above simple optimisation processes only obtain a compromise

solution It is no longer suitable if the DNO wishes to obtain all possible optimal

solutions for all the conflicting objectives at the same time [20] Therefore a set

of Pareto optimal solutions is introduced in this study And the corresponding

objective values constitute the Pareto front It allows decision makers to select

the most suitable topology from the Pareto optimal solutions for implementation

depending on the utilitiesrsquo priorities In Chapter 8 the study formulates the

optimal network reconfiguration problem within a multi-objective framework

using the concept of Pareto optimality where network loss and reliability indices

are simultaneously optimised In Chapter 9 active power loss maximum node

voltage deviation and feeder load balancing are optimised simultaneously

After obtaining the Pareto optimal solutions the best compromise solution

among the multiple objectives can be selected by comparing the fitness value of


Page | 25

each member in the Pareto front The best compromise solution is varied by

changing the values of weighting factors based on the tendencies of the network

decision makers A set of best compromise solutions can be obtained by varying

the weighing factors of each objective function and this is presented in Chapter 8

Proposal of ACO-based algorithms for assessment of optimisation problems

The ACO algorithm is a population-based approach based on the behaviour of

real ants [14] The proposed algorithm is not only used for assessment of the

TEO problem but also with DNR DG allocation and SSP problems The ACO

control parameters are different for each test case The selection of parameters is

a balance between the convergence rate and the global search ability of the

algorithm They are set experimentally using information from several trial runs

The results obtained by the ACO algorithm have been compared to those from

other algorithms in Chapter 5 and the ACO parameter sensitivity analysis is

provided in Chapter 7

In Chapter 8 the multi-objective ant colony optimisation (MOACO) and AIS-

ACO algorithms have been proposed and compared for assessment of multi-

objective DNR problems Both algorithms focus on problems in terms of Pareto

optimality where the objective functions are multidimensional and not scalar

A full list of publications resulting from this thesis is included in Appendix D

14 Structure of the thesis

The thesis is organised as follows

Chapter 2 introduces the distribution network configurations and associated

equipment It also gives a comprehensive literature survey which reviews the

existing knowledge and research activities in the distribution automation (DA)

including transformer economic operation (TEO) distribution network

reconfiguration (DNR) and sectionalising switch placement (SSP) The assessment

of transformer loss feeder loss and reliability indices as well as the multi-objective

optimisation functions are also described in this chapter

Chapter 3 summarises the optimisation techniques for assessment of the multi-

objective problem The Monte Carlo Method ACO algorithm and AIS-ACO hybrid

algorithm are described in detail


Page | 26

Chapter 4 proposes two methodologies for transformer loss reduction whilst

maintaining satisfactory voltages which are TEO and DNR The demand profiles are

randomly generated by the profile generators in MATLAB Following this each

node in the feeders from the system is assigned with demand profiles based on the

Monte Carlo Method The effectiveness of the two investigated methods

implemented either alone or together are presented and discussed

Chapter 5 describes an ACO algorithm to assess the network reconfiguration and

DG placement problems simultaneously in terms of distribution feeder loss

minimisation The results of four scenarios carried out on two standard IEEE 33-

node and 69-node systems are presented to show the effectiveness of the proposed

approach The effect of DG capacities on DNR for feeder loss reduction is also

discussed Moreover the results obtained by ACO algorithm have been compared to

those from other algorithms in the literature

Chapter 6 presents the ACO algorithm for minimisation of the losses associated

with a network loss including transformer loss and feeder loss under different load

scenarios This is achieved by the optimum selection of which transformers need to

supply each feeder and by determining the optimal locations of the tie-switches The

performance of this approach to minimise power loss is assessed and illustrated by

various case studies on a typical UK distribution network The impact of DGs and

electrical vehicles (EVs) in reducing the loss is also discussed

Chapter 7 explores an ACO-based methodology for the placement of sectionalising

switches in distribution networks The objectives of the proposed sectionalising

switch placement problem are reduction of unserved energy costs decrease in the

average time that a customer is interrupted and minimisation of switch costs These

objectives are formulated in either a single objective function or a fuzzy satisfaction

objective function The performance of the proposed methodology is assessed and

illustrated by various test cases on a well-known reliability test system

Chapter 8 formulates the optimal network reconfiguration problem within a multi-

objective framework using the Pareto optimality concept where network loss and

reliability indices are simultaneously optimised The MOACO algorithm and AIS-

ACO algorithm are proposed and compared for assessment of DNR problems The


Page | 27

proposed approaches are tested on Bus 4 of the RBTS and a set of high quality non-

dominated solutions are obtained

Chapter 9 addresses two algorithms to assess the DNR and DG allocation problems

in terms of the three conflicting objectives minimisation network loss maximum

node voltage deviation and load balancing index The ACO algorithm is used to

solve the problem in the fuzzy domain and the AIS-ACO algorithm is adopted to

obtain a set of non-dominated solutions using the concept of Pareto optimality The

effectiveness and the efficiency of the proposed methods are implemented on two

standard test systems as case studies

Chapter 10 concludes the thesis by summarising the main findings of the work

Finally possible future research ideas associated with this thesis are proposed

All the network models are built in OpenDSS and all the algorithms are coded in

MATLAB They are carried on a 340-GHz processor with 16 GBs of RAM memory

for all studies

Page | 28

CHAPTER 2

DISTRIBUTION AUTOMATION

21 Introduction

Distribution automation (DA) is an important part of a Smart Grid [21] It enables a

distribution network operator (DNO) to monitor coordinate and operate distribution

components in real-time from a remote control centre [22] [23] This improves the

reliability performance and operational efficiency of the electrical distribution

system and helps increase the market penetration of distributed generations (DGs)

and electrical vehicles (EVs) [24]ndash[26]

The remainder of this chapter is structured as follows Sections 22-23 introduce the

network configurations and associated equipment Sections 24-26 present the three

main parts of DA namely transformer economic operation (TEO) distribution

network reconfiguration (DNR) and sectionalising switch placement (SSP)

Transformer loss feeder loss and reliability indices assessments are described in

Sections 27-29 Three methods for assessment of multi-objective optimisation

problems are reviewed in Section 210 A summary of the main conclusions in this

chapter is given in Section 211

Chapter 2 Distribution Automation

Page | 29

Tie-switch

Sectionalising switch

22 Distribution Network Configurations

In England and Wales the voltage level of distribution networks ranges from 132 kV

to 230 V [2] Generally most distribution networks are designed in closed loop but

are operated radially due to the simplicity of operation the ease of protection

coordination and the minimisation of overall economics [3] [4]

There are three typical system configurations shown in Fig 2-1 [27] The radial

system in Fig 2-1 (a) is common in rural areas but does not include any backup

supplies Consequently the lack of feeder interconnections means a short-circuit

fault will interrupt power to all the downstream customers and power will not be

restored until the faulted equipment is repaired The tie-switches (normally open) in

Fig 2-1 (b) connect two feeders and make the system radial in a primary loop There

are multiple tie-switches between multiple feeders in distribution systems Fig 2-1 (c)

describes a link arrangement and during normal conditions the systems are operated

radially However when a fault occurs the part affected by the fault is isolated by

tripping the breakers The unaffected areas can then be restored from a different

busbar by closing the tie-switches and feeding the supply

(a) Radial system (b) Primary loop (c) Link Arrangement

Fig 2-1 Typical Distribution network [27]


Page | 30

23 Switchgear for Distribution Network

There is a large variety of switchgears used in distribution networks this includes

reclosers sectionalising switches tie-switches fuses and circuit breakers This

section mainly focuses on reclosers sectionalising switches and tie-switches

231 Reclosers

Reclosers are automatic self-contained protection devices installed on main feeders

and operate as a part of the protection schemes [28] [29] They are a type of circuit

breakers with control measurement and automatic re-closing functions Most faults

on distribution feeders are temporary ie they last from a few cycles to a few

seconds and are cleared by protection tripping a circuit breaker [1] Reclosers

normally count the number of overcurrent pulses followed by the line de-

energisation sequences [1] They always coordinate with other types of protection

equipment These include such as fuses and sectionalising switches for the purpose

of fault isolation and system restoration The process of recloser operation is shown

in Fig 2-2 The time between reclosures and the time of the reclose can be

programmed If the fault is transient the recloser will operate 1-3 times and then

restore service quickly If the fault is permanent after a pre-set number of trip-

reclose operations the recloser is locked and the recloser interrupter triggers a final

trip

Fig 2-2 Recloser operation

Time between reclosures

Time of the reclose Fault current

Recloser locks

out on 2nd

reclose

as programmed

Recloser opens

Recloser recloses

fault still present

Recloser recloses

fault still present

Recloser re-opens

fault still present

Load current


Page | 31

232 Sectionalising Switches

Sectionalising switches are the protective devices that operate in conjunction with

backup circuit breakers or reclosers [25] They are isolating devices that

automatically isolate the faulted sections from a distribution network after a

permanent fault has occurred and after the line is de-energised by the feeder breaker

[1] This is because sectionalising switches are not designed to interrupt the fault

current and must be used with the feeder breaker that can break and reclose a circuit

under all conditions ie normal or faulty operating conditions [25] [30] A detailed

operation of sectionalising switches is presented in Section 26

233 Tie-switches

Tie-switches refer to the normally open switches of the network By closing the

opened tie-switch the load is transferred from one feeder to another but this requires

an appropriate sectionalising switch to be opened to restore the radial topology [31]

The tie-switch placement should follow certain principles ie all the loads are

energised and the network is operated in radial configurations The tie-switches are

designed to operate in normal condition but are not suitable for the interruption of

fault currents They are designed to operate after a switching device (circuit breaker

of fuse) has interrupted the fault current

24 Transformer Economic Operation

241 Basic Concepts

Power transformers are the interface between the generators and the transmission

lines and between lines operating at different voltage levels [32] They are a critical

part of an electric power system and transform the ac voltage based on the principle

of electromagnetic induction A step-up transformer ensures the efficient

transmission of power ie high voltage-low current and a step-down transformer

permits the transmitted power to be used at a lower and safer voltage [33]

Distribution transformers are used to reduce the primary system voltages to the


Page | 32

Tran

sfo

rme

r Lo

ss

Transformer Load Factor

1 Transformer

2 Transformers

utilisation voltages [25] normally 132 kV for high voltage (HV) 11 kV-33 kV for

medium voltage (MV) and 400 V for low voltage (LV) in UK distribution networks

For transformers currently in operation developing a new strategy for transformer

loss reduction is required rather than replacing them with high efficiency

transformers [34] Transformer economic operation refers to the optimum selection

of transformers needed to supply each feeder This is related to the economic

evaluation of network performance and the resilience of the network

In order to meet reliability requirements the load factor of each transformer should

not go beyond 50 when two transformers are operated in parallel In other words

the transformer load factor must be within 100 in separate operation modes

The integrated power loss curves of onetwo transformers in operations are shown in

Fig 2-3 The intersection of the two curves is 119878119871 which is called the transformer

critical load factor (TCLF) Therefore it can be concluded that

When the total load 119878 lt 119878119871 a single transformer produces less integrated

power loss than parallel transformers

When 119878 gt 119878119871 parallel operation of transformer is more economical

When 119878 = 119878119871 the losses in single or parallel operation modes are identical

Fig 2-3 Transformer loss versus transformer load

119878119871

Core loss for 2 transformers

Core loss for 1 transformer


Page | 33

As a result Table 2-1 presents the transformer commercial operation area

Table 2-1 Transformer economic operation area

Operation modes Single Transformer Two Parallel Transformers

Economic operation area 0 ~ 119878119871 119878119871 ~ 119878

242 Literatures on Transformer Economic Operation

Several papers that discuss research on transformer economic operation not only

focuse on transformer loss reduction but also discuss cost reduction and reliability

improvement

The papers concerned with transformer economic operation based on loss reduction

were presented in [35]ndash[37] Wang and Liu [35] used the ASP (Active Server Pages)

language as a foundation to analyse transformer economic operation on-line The

operation curves and interval graph of commercial operation were achieved from the

VML (Vector Markup Language) and the simulation results In the interest of the

economical and profitable operation of transformer real-time data was obtained

using the SCADA (Supervisory Control and Data Acquisition) and this included the

measurement of active power load and voltage [36] [37] Then the transformers

were monitored in real-time and the methods used to ensure their economical and

profitable operation were suggested online

However if the active power loss of transformers was measured based on the real-

time load data transformers would frequently be switched to a new state associated

with instantaneous economical and profitable operation As the number of switching

operations increases the lifetime of the transformers decreases As a result Song and

Zhang [38] developed a load smoothing algorithm to reduce the number of switching

operations of the transformer effectively The curves of transformer loads before and

after smoothing are presented in Fig 2-4 Table 2-2 and 2-3 illustrate the transformer

operation mode variation before and after smoothing respectively The results show

that the active loss achieved when using the load smoothing algorithm was a little

higher than when smoothing was not used However the total number of switching

operations of transformers with load smoothing was reduced from 6 to 2 which

would expand the transformer life cycle


Page | 34

(a) Before load smoothing (b) After load smoothing


Table 2-2 Transformer operation mode variation before load smoothing

Time Transformer operation mode The sum of active power loss

(Kw)

000-300 1 transformer in operation 12363

300-1600 2 transformer in operation

1600-2100 Parallel operation




(Kw)




Generally the cost of the energy loss of a transformer over its service life is much

higher than its initial capital price As a result the transformer selection decision is

based not only on the purchase price but also includes the cost of installation

maintenance and loss over the lifetime of the equipment [39]

Amoiralis etc [40] have investigated the cost of two transformers that have the same

capacity but different specifications The transformers were loaded at 50 of full

load and with an increase of 37 for each year The technical characteristics and the

costs associated with the two transformers are presented in Table 2-4 The total cost

is the summation of loss and capital cost of a transformer over 30 years Purchasing a


Page | 35

transformer with low efficiency (Transformer A) reduced the initial cost but resulted

in higher energy costs during the transformer lifetime in comparison with

Transformer B The economic approach in [41] and [42] were used to determine the

suitable size of transformers in Thailand The choice of a high capacity transformer

could improve voltage profiles and provide extra room for emergency conditions and

load increments in the future

Table 2-4 Transformer technical specifications and costs [40]

Transformer Size

(kVA)

No load loss

(kW)

Load loss

(kW)

Capital

price (euro)

Cost of loss

(euro)

Total cost

(euro)

A 1000 11 9 9074 34211 43285

B 1000 094 76 11362 28986 40348

25 Distribution Network Reconfiguration

251 Basic Concepts

DNR refers to a process that involves changing the network topology at normal and

abnormal operating conditions by altering the openclose status of sectionalising

(normally closed) and tie (normally open) switches [13] [14] In fact DNR can be

used as a tool for distribution network planning and real-time operation [14]

As presented in Fig 2-5 the openclosed status of the tie switches and sectionalising

switches determines the structure of the system To achieve a new system

configuration the tie-switch 3 is closed which will create a new loop In order to

restore the network back to a radial structure a switch from 1 2 4 and 5 is selected

and opened

Fig 2-5 Radial test system


Page | 36

Since there are various combinations of switching DNR is treated as a discrete and

constrained optimisation problem Recently optimal DNR strategies discussed in

many literatures have been implemented to achieve active power loss reduction and

system reliability improvement

252 Literatures on Distribution Network Reconfiguration

Network reconfiguration was first introduced by Merlin and Back [43] using a

discrete branch and bound optimisation method to reduce network loss Firstly all

the switches were closed to build a meshed network and then in each step one

branch was removed until the radial configuration was found

Another early study on loss reduction through network reconfiguration was

presented in [44] which discussed how to achieve minimum power loss in

distribution feeders through feeder reconfiguration It is possible to determine loss

variation by analysing the load flow results This involved simulating the system

configuration before and after the feeder was reconfigured [44] It was based on a

single pair switch operation per iteration The relevant results showed that the loss

was reduced only if the voltage across the tie-switch was significant and if the loads

connected at the lower voltage side were transferred to the other side [44] This

criterion was developed to eliminate undesirable switching options The best

switching option was then obtained from the results of load flow studies simulating

all feasible feeder configurations

Zehra etc [31] have proposed a branch exchange algorithm based on two stages of

the solution methodology It started with a feasible network operating in a radial

configuration The first step determined the loop that achieved maximum loss

reduction by comparing the circle sizes for each loop The largest circle indicated the

maximum loss reduction The second phase determined the switching options to be

operated in that loop to provide maximum loss reduction The smallest circle was

identified for the best solution In comparison with [44] the introduction of the

branch exchange method allowed the number of load flow solutions related to the

computation time to be greatly reduced However the results were strongly related to

the initial configuration of the electrical network [45] The above methodologies [31]

[43] [44] were able to obtain the global optimal solution but were only applied to

simplified network models


Page | 37

Later on the artificial intelligent and modern heuristic optimisation algorithms such

as genetic algorithm (GA) [46]ndash[49] simulated annealing (SA) [50] [51] tabu

search (TS) [52]ndash[54] and particle swarm optimisation (PSO) [55] etc were

developed with minor computational effort These intelligent techniques which are

affected by the selection of parameters are able to obtain the optimum solution of

good quality The GA based network reconfiguration method was presented and

tested in a real 136-bus distribution network in [13] Various radial topologies were

generated after the implementation of the genetic operators and the search space was

enlarged by a local improvement method The results show that after network

reconfiguration the power loss is reduced from 3203 kW to 2801 kW which

amounts to a 1255 reduction

Other important objectives including reliability improvement and service restoration

by DNR were mentioned in [56]ndash[58] An intelligent binary particle swarm

optimisation (BPSO) based search method was presented in [57] for assessment of

the DNR problem in terms of reliability improvement The failure of all distribution

equipment such as transformers feeders breakers etc was considered In this paper

the reliability index was in the form of expected demand not supplied (EDNS) The

EDNS of the original configuration is 1008 kW and after reconfiguration the best

result is reached with 849 kW

Network reconfiguration can be formulated not only as a single objective problem

but also as a multi-objective problem that considers various parameters

simultaneously [45] [59]ndash[62] In [59] the objective function was to minimise the

combination of loss cost and consumer interruption cost thus the multiple objectives

were aggregated into an single objective function In order to achieve optimal DNR

a new method was proposed in [60] using a fuzzy multi-objective function to

balance feeder loads and reduce power loss of the distribution systems Depending

on the operatorrsquos preferences the weighting factors of each of the variables could be

varied Das [61] introduced another fuzzy membership formulation to handle the

multiple objectives In this work the degree of overall satisfaction was the minimum

of all the above membership values and the final optimal solution was the maximum

of all such overall degrees of satisfaction [61] Mendoza etc [62] introduced a

micro-genetic algorithm to deal with the trade-offs between the power loss and

reliability indices in order to obtain a set of optimal network configurations using


Page | 38

the concept of Pareto optimality Andervazh etc [45] have presented another Pareto-

based multi-objective DNR method using discrete PSO The objectives were the

minimisation of power loss bus voltage deviations and number of switching

operations

In addition an optimal planning strategy based on network reconfiguration and DGs

placement was presented in [16] The primary objective was power loss reduction

and voltage stability improvement The performance of the methodology was tested

on a 33-bus network and three DGs were installed The power loss was reduced by

3093 by DNR 5624 by DG installation and 6689 by employing

reconfiguration and DG installation simultaneously

26 Placement of Sectionalising Switches

261 Basic Concepts

The implementation of DA requires the installation of various new devices [63]

Among other things DA involves the placement of sectionalising switches ie the

installation of new switches and relocation of existing switches DA in terms of

automatic and remote controlled sectionalising switch placement brings major

benefits to distribution network operators (DNOs) [64] [65] The duration and

number of outages per year determines the annual interruption time of customers

[66] It is possible to shorten outage duration by decreasing the restoration time and

to reduce the number of outages by improving failure rates [67] SSP is useful for the

reduction of the time required to detect and locate a fault and the improvement of

the speed of isolating the faulty sections in the primary distribution network [64]

The effectiveness of these objectives depends on the number and location of

sectionalising switches

In a distribution feeder the section is defined as a group of line segments between

adjacent sectionalising switches [68] And the equivalent load of the section is the

sum of the individual load points in this section [69] When a permanent fault occurs

the switch actions need to respond as follows


Page | 39

1 Detect and locate the fault and initiate tripping to clear the fault A transient

fault is normally cleared by two or three trips and reclose cycles

2 However if the fault persists beyond the predefined cycles reclosure will be

inhibited and the protection will initiate a final trip The load breaker will open and

all the downstream loads will be de-energised

3 The faulty section is then isolated by opening the upstream and downstream

sectionalising switches located next to the fault

4 Restore the loads in the healthy area by closing the upstream and downstream

circuit breakers automatically

5 Repair the faulty section of the feeder and manually restore the loads (ie

reconnect loads to the supply)

A fully and a partially automated distribution feeder are shown in Fig 2-6 and Fig

2-7 respectively The fault occurs on line section 4 It can be clearly seen in Fig 2-6

that all loads are restored after the faulty area is isolated and the total outage time is

the same as the switching time of circuit breakers and sectionalising switches [64]

However as shown in Fig 2-7 only Loads LP1 LP5 LP6 are restored after the

isolation of the faulty section the outage duration of other loads is equal to the repair

time ie significantly longer than the switching time As a result the installation of

sectionalising switches could increase the network reliability as well as the

investment and operation cost of automation [64]


Page | 40

LP1 LP2 LP3 LP4 LP5 LP6

1 2 3 4 5 6 7


1 2 3 4 5 6 7


1 2 3 4 5 6 7


1 2 3 4 5 6 7

Fault occurred on line section 4

CB1 opened

Sectionalising switches adjacent to the faulted area are opened

Energy restored to un-faulted area by closing CB1 and CB2

CB1 CB2

CB1CB2

CB1 CB2

CB1 CB2

Normally closed circuit breaker

Normally open circuit breaker

Closed sectionalising switch

Open sectionalising switch

Interrupted

load

Fig 2-6 Fully automated distribution feeder


Page | 41


1 2 3 4 5 6 7


1 2 3 4 5 6 7


1 2 3 4 5 6 7


1 2 3 4 5 6 7


CB1 opened



CB1 CB2

CB1CB2

CB1 CB2

CB1 CB2





Interrupted

load

Fig 2-7 Partially automated distribution feeder

262 Literatures on Sectionalising Switch Placement

The earliest work that discussed SSP in distribution networks was presented by

Miranda [70] A fuzzy-logic-based optimisation technique has been used to

determine the location of sectionalising switches

In [69] the optimum sectionalising switch relocation problem has been solved by

using the ant colony system (ACS) based method to reduce feeder interruption costs


Page | 42

after a fault In this work it is assumed that there were no additional capital

investments brought by switch relocation However the investment and operation

cost of a sectionalising switch is an important issue which cannot be ignored when

considering the problem of unsupplied energy costs minimisation since they conflict

with each other Therefore the information provided by the multi-objective model is

more valuable than the traditional mono-objective model Abiri-Jahromi etc [64]

have developed a mixed-integer linear programming (MILP) to deal with the new

sectionalising switch installation problem which considers customer outage costs as

well as switch capital operation and maintenance costs After the placement of

sectionalising switches the total system cost over the life period of the switches was

greatly reduced [64] In addition the impacts of customer damage function and load

density variations on SSP were also investigated through sensitivity analysis

The impacts of DG on the optimal number and location of sectionalising switches

were discussed in [71] The introduction of DGs connects a mono-source distribution

network to a multi-source one [66] This potentially improves network reliability

since it reduces the duration and restoration time of interruptions Many loads can be

restored through DGs when operating in islanding mode A mathematical

optimisation methodology has been proposed to minimise the reliability cost when

operating with a minimum number of sectionalising switches The results indicate

the reliability indices of distribution networks are affected by the number and

location of sectionalising switches

27 Transformer Loss Assessment

271 Operating Principles

A transformer has three essential elements a primary winding a secondary winding

and a core [33] As shown in Fig 2-8 the winding connected to the electrical source

is called the primary winding and the secondary winding is linked with the loads All

the windings are connected by the common magnetic flux in the core


Page | 43

Fig 2-8 Elements of a single phase transformer [33]

Usually the power is generated and distributed in a three-phase system Therefore it

is necessary to use a three-phase transformer to increasedecrease the voltage The

structure of the three-phase transformer is presented in Fig 2-9

Fig 2-9 Construction of a three-phase transformer [33]

272 Transformer Quantities Measurement

The transformer quantities present the self-loss during power transmission which

consists of active power loss together with increase in the reactive power of the

network unit [72]

Open-circuit test

The equivalent circuit for the open-circuit test is shown in Fig 2-10 The test is made

on the low-voltage side by applying rated voltage at rated frequency with the high-

voltage winding open [33] The input power and current are measured which are

named no-load loss 119875119874119862 and no-load current 119868119874119862


Page | 44

(a) Test circuit

(b) Equivalent circuit

Fig 2-10 The open-circuit test [33]

As the secondary is open the primary current is equal to the no-load current The no-

load current is used to produce the primary magnetic flux when the transformer is in

no-load operation which is also called the exciting current The voltage drops in the

primary winding can be ignored so the no-load loss is the summation of hysteresis

and eddy current losses [33] The input power is practically equal to the no-load loss

at rated voltage and frequency

119875119874119862 = 119875ℎ+119890 =119880119874119862

2

119877119888119871119881= 119880119874119862119868ℎ+119890 (2-1)

where 119877119888119871119881 is the resistance referred to the low-voltage side 119868ℎ+119890 is the core loss

current

Short-circuit test

The short-circuit test is used to measure the equivalent resistance and reactance of

the winding [6] As shown in Fig 2-11 the low-voltage terminal is shorted together

and the high-voltage side of the transformer is connected to a low-voltage high-

119880119900119888

119868ℎ+119890 119868120601

119868119900119888 119885119890119902 119871119881

119877119888 119871119881 119883119898 119871119881


Page | 45

current source at rated frequency [33] The source voltage is increased until the short

circuit current reaches the rated value At this time value of the source voltage is

known as the short-circuit source voltage 119880119878119862

(a) Test circuit


Fig 2-11 The short-circuit test [33]

As the secondary side is shorted the voltage applied to the full load current is low

compared to the rated voltage and the exciting current 119868119890119909 is negligible during this

test [33] Since the rated current is used the input power is equal to the full-load loss

and expressed as

119875119878119862 = 1198681198781198622 119877119890119902119867119881 (2-2)

where 119877119890119902119867119881 is the winding resistance referred to the high voltage side

As the full-load loss depends on the value of the full load current the loss in the

winding resistance is varied under different loading conditions

119880119904119888

119868119890119909

119868119904119888 119877119890119902 119867119881 119883119890119902 119867119881

(119899119890119892119897119890119888119905)


Page | 46

Active power loss

The active power loss ∆119875 of a two-winding transformer is decided by the no-load

loss 119875119874119862 full-load loss 119875119878119862 and the transformer load factor [73]

∆119875 = 119875119874119862 + 1205732119875119878119862 (2-3)

where 120573 =119878119871

119878119873 represents the transformer load factor 119878119871 is the transformer actual

loading (kVA) 119878119873 is the transformer rated capacity (kVA) Assuming the voltages

are held constant at 10 pu

Reactive power loss

The no-load current 119868119900119888 and short-circuit source voltage 119880119878119862 represent the change of

reactive power ∆119876 in other words the reactive power loss which can be simplified

as

∆119876 = 119876119874119862 + 1205732119876119878119862 (2-4)

119876119874119862 = 119878119874119862 =119868119874119862

119868119873∙ 119878119873 (2-5)

119876119878119862 = 119878119878119862 = 119880119878119862

119880119873∙ 119878119873 (2-6)

273 Integrated Transformer Loss

In general the power loss of a transformer is related to the active power [74]

However if a transformer draws reactive power (it takes current) this causes real

power loss in the network The integrated power loss refers to the sum of active

power loss of the transformer and the increased active power loss contributed by the

reactive power of the transformer [72]

The integrated power loss of a two-winding transformer is calculated by

1198791198711 = 11988002119875119885119874119862 +

1205732

11988002 119875119885119878119862 (2-7)

119875119885119874119862 = 119875119874119862 + 119870119876119876119874119862 (2-8)


Page | 47

119875119885119878119862 = 119875119878119862 + 119870119876119876119878119862 (2-9)

where 119875119885119874119862 and 119875119885119878119862 are the integrated no-load loss (kW) and the full-load loss (kW)

120573 =119878119871

119878119873 represents the transformer load factor 119878119871 is the transformer actual loading

(kVA) 119878119873 is the rated capacity of the transformer (kVA) 119875119874119862 and 119876119874119862 are the no-

load active power loss (kW) and no-load reactive power loss (kVAr) 119875119878119862 and 119876119878119862

are the full load active power loss (kW) and full load reactive power loss (kVAr) 119870119876

represents the reactive equivalent which is the ratio of increased active power loss to

the change of the node reactive power (kWkVAr) [72] 1198800 is the operational voltage

of the transformer low voltage side in per unit

The no-load and full-load power losses are obtained from the open-circuit and short-

circuit test separately

For two transformers operating in parallel with the same capacity the current

flowing through each transformer is reduced by half Thus the full-load loss of each

transformer becomes a quarter of the previous case The total integrated power loss

is twice the no-load loss and half (2 times1

4) of the full-load loss of one transformer

1198791198712 = 211988002119875119885119874119862 +

1

2

1205732

11988002 119875119885119878119862 (2-10)

28 Feeder Loss Assessment

The distribution network power loss is mainly due to resistive loss in distribution

feeders which is obtained through a power flow study [75] The calculation of

power loss is explained using a two-bus network as shown in Fig 2-12

Fig 2-12 Simple two-bus network


Page | 48

Assume there is no capacitance on either the sending or receiving bus and 119868119887119904 =

119868119887119903 = 119868119887 As a result the current flowing through branch b and the real power loss

are derived using the following equations

119875119887119877 + 119895119876119887119877 = 119887119877 times 119868lowast (2-11)

119875119887 = 1198681198872 times 119877119887 (2-12)

From (2-11) and (2-12) it is calculated as

119875119887 =119875119887119877

2 +1198761198871198772

1198811198871198772 times 119877119887 (2-13)

where 119875119887 is the real power loss of branch b (W) 119875119887119877 and 119876119887119877 are the real power (W)

and reactive power (VAr) at the receiving end of branch b 119881119887119877 represents the rms

voltage at the receiving end of branch b (V) 119868119887 is the rms current through branch b

(A) and 119877119887 is the resistance of branch b (Ω)

The real power losses in the other branches are evaluated similarly and the network

real loss is the sum of the power losses in all branches as presented in (2-14)

119864119871 = sum 119875119887119899119873119887119899 (2-14)

where 119873119887 is the set of all the distribution network branches

29 Reliability Evaluation

291 Reliability Indices

Reliability is a fundamental attribute for the safe operation of any modern power

system [8] A distribution network which is directly connected to customers has a

large impact on power reliability Distribution reliability primarily relates to

equipment outages and customer interruptions [76] The reliability indices of

distribution network can be classified into two groups ie load point reliability

indices and system reliability indices [77]


Page | 49

The three primary load point reliability indices average failure rate (120582) average

annual outage time (119880) and average outage time (119903) are calculated by [73]

120582 = sum 120582119895119895 (2-15)

119880 = sum 120582119895119895 119903119895 (2-16)

119903 =119880

120582 (2-17)

where 120582119895 and 119903119895 are the failure rate and outage time of contingency j for this load

point

The system reliability indices mainly include system average interruption frequency

index (SAIFI) system average interruption duration index (SAIDI) average energy

not supplied (AENS) and expected customer damaged cost (ECOST) [78] The

Formulae for these reliability indicators are presented in (2-18) to (2-21) [78]

119878119860119868119865119868 =sum 120582119894119873119894119894

sum 119873119894119894 (2-18)

119878119860119868119863119868 =sum 119880119894119873119894119894

sum 119873119894119894 (2-19)

119860119864119873119878 =sum 119880119894119871119894119894

sum 119873119894119894 (2-20)

119864119862119874119878119879 = sum 119888119898(119889119898)119891119898119871119898119872119898=1 (2-21)

where 119873119894 is the total number of customers of load point 119894 120582119894 119880119894 and 119871119894is the failure

rate outage time and average load connected to load point i 119872 is quantity of load

outage events 119871119898 is load curtailed (kW) due to outage event m 119891119898 and 119889119898 are the

frequency and duration of outage event m 119888119898(119889119898) is the outage cost (poundkW) of

outage duration 119889119898 using the customer damage function (CDF)

SAIFI is a measure of the number of outages an average customer will experience

SAIDI states the average interruption hours for a customer in the system AENS

presents the effect of interruptions on the energy that is not supplied to the customers

during failures [79] ECOST is the index that connects reliability with economics


Page | 50

292 Reliability Evaluation Methods

The methods used to calculate reliability indicators for distribution network are

classified into two groups namely the simulation method and analytical method

Simulation method

The simulation method has better scalability and flexibility when incorporating

complex considerations in comparison with the analytical technique And it is more

capable of dealing with large-scale power systems and the variation of load points

[77] The Monte Carlo method is a typical example of a simulation method and

takes into account the time varying and stochastic nature of load models in

evaluating the power system reliability [80] Vitorino etc [12] proposed a non-

sequential Monte Carlo method based on branch reliability to estimate energy not

supplied (ENS) index Contingencies were simulated by randomly selecting a faulty

branch from a candidate network pool based on failure probabilities [12] However

although the Monte Carlo method can simulate the behaviour of a complex system

with a high degree of accuracy it requires a considerable amount of CPU time and

memory

Analytical method

The first step of an analytical technique is to build a reliability probabilistic model

for the system according to network topology as well as the relationships between

the system and components [77] The model is then solved by calculating the

reliability indices in iterations [77] The most common analytical methods are

minimal path method minimal cutset method and failure-mode-and-effect analysis

(FMEA)

In [81] the minimal path method which identifies the shortest paths from a node to

a source and between any two nodes was described The minimal path of the source

node to the load points was obtained by searching for the upstream node from the

load points [82] As the distribution network was radial each node had only one

upstream node The sections out of service after a fault occurred were identified and

separate subsystems were formed The nodes were classified in terms of the effect of

a failure on them Using the node class and amount of load shedding data the

reliability indexes could then be evaluated [81]


Page | 51

FMEA is a classical analytical algorithm for distribution network reliability

evaluation based on the analysis of all the failure modes of each static component

[82] As shown in Fig 2-13 there are four failure modes which are 1) active failure

2) transient failure 3) passive failure and 4) maintenance The active and transient

failures can cause the operation of breakers and hence the healthy components can

be removed from service [75] The passive failures are similar to maintenance outage

and have no effect on the protection system and remaining heathy zone [82]

Fig 2-13 Reliability model for static components

The proposed reliability evaluation method is based on the N-1 criterion and its

computation procedure is demonstrated in Fig 2-14

Normal operation

Active

failure

Transient

failure

Passive

failure

Maintenance

120582119860 120582119879 120582119875 120582119872

120583119860 120583119879 120583119875

120583119872


Page | 52

Start

Read system topology load

data and reliability parameters

Initialise failure number i=1

All failures are considered

Search for the upstream feeder breaker

Search for the upstream and downstream

sectionalising switches and tie-switch

The load points are classified into three categories

Evaluate the reliability of load points

and whole system when fault at line i

Next failure i=i+1

Calculate the reliability of the whole system

End

No

Yes

Fig 2-14 Procedure for reliability evaluation

The system failure events are enumerated first For a failure event the scope of the

failure is determined by searching for the adjacent circuit breaker or tie switch The

isolation zone is then confirmed by the location of the upstream and downstream

sectionalising switches and the appropriate tie-switch Subsequently all the load

points are classified based on their interruption times Finally the consequence of

each contingency and a value for total system reliability are evaluated

When a fault occurs all the load points can be categorised as follows

Healthy points are load points not affected by the fault and refer to upstream

nodes of the upstream circuit breaker or downstream nodes of the


Page | 53

downstream circuit breaker or tie-switch For example when a fault occurs at

L2 in Fig 2-15 LP1 and LP5 are healthy points

Temporary damaged points when the protection systems are in operation

they cause the load points to be interrupted but the load points can be

restored by isolating the faulty area and by using a supply through another

path When a fault occurs at L2 in Fig 2-15 LP2 and LP4 are isolated by

opening the sectionalising switches S1 and S2 LP2 is restored by closing B1

and LP4 is supplied by closing the tie-switch As a result LP2 and LP4 are

temporary damaged points The interruption time is 119879119878 which is the average

switching time after failure

Permanent damaged points are load points that are interrupted by the

operation of protection devices and cannot be restored until the fault is

cleared [82] When a fault occurs at L2 in Fig 2-15 LP3 is the permanent

damaged point The interruption time is 119879119877 which is the average repair time

after failure

Fig 2-15 Sample network

Overall the analytical method which is based on a reliability model of each

component evaluates system reliability by enumeration of all failure states However

the increasing number of devices in a complex system results in an increase in the

quantity of failure states and the complexity of calculation As such the scale of the

network might be limited

210 Multi-objective Optimisation

The aim of this section is to provide fundamental information in order to assess

multi-objective optimisation problems The objectives are conflicting and can be


Page | 54

0

1

converted into three forms which are 1) single objective function 2) single fuzzy

satisfaction objective function and 3) Pareto front

2101 Single Objective Function

The single objective function is generally done by simply aggregating the objectives

with the same dimension and transforming others into constraints [83] It can be

solved by traditionally scalar-valued optimisation techniques However this function

has several limits 1) it results in only one solution 2) the analysis of the objectives

that are converted into constraints is limited

In [64] a sectionalising switch placement strategy was proposed to minimise the

sum of ECOST and sectionalising switch costs The above mentioned objectives

were simply aggregated and calculated in US dollars Other objectives such as the

number of available switches were converted into constraints

2102 Single Fuzzy Satisfaction Objective Function

In the fuzzy domain each variable is associated with a membership function varying

from zero to unity which indicates the satisfaction level of the objective [84] The

higher the membership value is the better the solution is Generally the linear

membership function is formulated as given in (2-22) and is presented in Fig 2-16

120572 =

1 119883 le 119883119898119894119899119883119898119886119909minus119883

119883119898119886119909minus119883119898119894119899119883119898119894119899 lt 119883 lt 119883119898119886119909

0 119883 ge 119883119898119886119909

(2-22)

Fig 2-16 Linear membership function

If 119883 is equal or less than 119883119898119894119899 the membership value is one As 119883 becomes greater

than 119883119898119894119899 the degree of satisfaction decreases This decrease is continued until 119883

reaches 119883119898119886119909 and the membership function becomes zero

120572

119883119898119894119899 119883119898119886119909 119883


Page | 55

The fuzzy-based optimisation procedure is used for handling multiple conflicting

objectives with different dimensions and units [66] The degrees of satisfaction level

can be formulated into a single objective function in three methods which are 1)

weighted aggregation 2) max-min method 3) max-geometric-mean method The

objective is to maximise such degree of satisfaction

Weighted aggregation

In this method the degree of satisfaction level is the weighted aggregation of the

membership values of all objectives [85] Thus the final compromise solution for

multi-objective functions is described as follows

119872119886119909 119869 = 12059611205721 + 12059621205722 + ⋯ + 120596119899120572119899 (2-23)

where 120596119894 is the constant weighting factor for each of the membership values and

they should meet the condition sum 120596119894119894 = 1

The weighting factors are decided by the decision makers and a higher weighting

factor indicates that this parameter is more important However the disadvantage of

this technique is that DNOs may have difficulty in obtaining enough information

about the relative importance of each objective to determine the trade-offs among the

selected objectives

Saffar etc [60] have developed a network reconfiguration technique to reduce power

loss and equal load balancing of feeders As these objectives had different

dimensions and units they were transformed into a single objective function with

fuzzy variables A set of compromised solutions was obtained by varying the

weighting factors of each element

Max-min method

In this technique the degree of overall satisfaction is the minimal value among the



119872119886119909 119869 = min 1205721 1205722 hellip 120572119899 (2-24)

The solution is optimised by maximising the overall satisfaction of all objectives

However the max-min method might not predict the best compromise solution


Page | 56

because even if one membership value is weak it does not necessarily mean that

other membership values are also weak [86]

The max-min principle was adopted in [84] for the multi-objective optimisation with

fuzzy sets The aim was to minimise real power loss and the absolute value of branch

current as well as to minimise nodes voltage deviation Finally an optimal solution

was obtained which indicated a concession among all the objectives The results also

revealed that although network reconfiguration resulted in a significant reduction in

total system loss the loss allocated to a certain number of customers increased [84]

It is important to change the tariff structure for these consumers so that they are not

obliged to pay more for the increase in loss allocation as a result of network

reconfiguration

Max-geometric-mean method

Like the above max-min method the geometric-mean function is also used to

evaluate the degree of overall fuzzy satisfaction but in different forms The objective

is computed as follows

119872119886119909 119869 = (1205721 ∙ 1205722 ∙ hellip ∙ 120572119873)1 119899frasl (2-25)

In [86] firstly all the variables (real power loss branch current loading maximum

voltage deviation and switching numbers) were assigned by truncated sinusoidal

fuzzy membership functions The overall degree of satisfaction was the geometric

mean of all fuzzy membership values [86] The best compromise solution was then

obtained by maximising this satisfaction level

2103 Multi-objective Formulation in the Pareto Optimality

Framework

All the studies mentioned above are solved by a single-objective optimisation

technique In contrast a Pareto optimal solution is provided for the treatment of

multi-objective problems This produces a range of solutions rather than just one

which represents a compromise that goes some way to optimise objective functions

[87] [88] The Pareto optimal solution is based on a dominance concept The

solution 119883 dominates 119884 means that 119865(119883) is no worse than 119865(119884) for all objectives


Page | 57

and there is at least one objective for which 119865(119883) is better than 119865(119884) as expressed in

(2-26) and (2-27) The following conditions should be satisfied concurrently

forall 119894 = 12 hellip 119873119900119887119895 119865119894(119883) le 119865119894(119884) (2-26)

exist 119894 = 12 hellip 119873119900119887119895 119865119894(119883) lt 119865119894(119884) (2-27)

where 119873119900119887119895 is the number of objective functions

If a solution 119883 and solution 119884 do not dominate each other these two solutions are

incomparable For example the objective is to minimise 1198911 and 1198912 and there are

three solutions whose objective function values are 119865(119883) = (24) 119865(119884) = (44)

119865(119885) = (52) It can be seen that 119883 dominates 119884 as 1198911(119883) lt 1198911(119884) and 1198912(119883) le

1198912(119884) And the solution 119883 and 119885 are incomparable because 1198911(119883) lt 1198911(119885) and

1198912(119883) gt 1198912(119885) Similarly solutions 119884 and 119885 are also incomparable

A solution belongs to Pareto optimal solutions if there is no other solution that can

improve at least one objective without degradation of any other objectives [83] In

other words there is no another solution that dominates it The Pareto set is the set of

all non-dominated solutions and its corresponding objective values constitute the

Pareto front [88] The goal of the multi-objective optimisation is to select the most

suitable one from the Pareto set for implementation according to decision makersrsquo

preferences

In [45] the study proposed a Pareto-based multi-objective DNR method using a

discrete PSO algorithm It aims to reduce power loss voltage deviations and the

number of switching operations Firstly each objective function was optimised

separately and the best results were found All objectives were then optimised

simultaneously and the Pareto optimal set was obtained The best results for each

objective were included in the Pareto front and the corresponding solutions were

stored in the Pareto optimal set Finally the best compromise solutions among the

multiple objectives were derived Different scenarios were modelled by assigning

different weighting factors based on the preferences of the decision makers


Page | 58

211 Summary

Generally most distribution networks are designed in closed loop but are operated

radially There are three typical distribution network topologies which are the radial

system primary loop and link arrangement The descriptions of three switchgears ie

recloser sectionalising switch and tie-switch are also included in this chapter

TEO DNR and SSP are the three main parts of DA In this chapter there are several

reviews of these techniques TEO which refers to optimum selection of which

transformers need to supply each feeder can not only reduce loss but also reduce

total costs and improve network reliability DNR is defined as a process that

involves changing the network topology under normal and abnormal operating

conditions by relocation of tie-switches [13] [14] The methodologies from a branch

and bound optimisation method to modern heuristic optimisation algorithms

designed for loss reduction are reviewed In addition DNR is also able to improve

service quality and efficiency at the same time The placement of sectionalising

switches refers to the installation of new switches and relocation of existing switches

It is used for distribution network reliability improvement and service restoration

However so far few studies have been carried out that consider the combination of

the above three techniques

The major challenge facing DNOs is how to distribute the power in a low-cost

reliable and efficient way Thus the assessments of transformer loss feeder loss and

reliability indices are proposed in Section 27-29 The integrated transformer loss

consists of not only real power loss but also reactive power loss The transformer

quantities such as no-load loss and full-load loss are obtained from open-circuit test

and short-circuit test The distribution network power loss is achieved through power

flow study The reliability indices can be calculated through reliability evaluation

methods namely simulation methods and analytical methods The most common one

is FMEA which is also used for reliability evaluation in this thesis Although there

are many research projects that consider feeder loss and reliability simultaneously

few consider transformer loss and feeder loss at the same time

Three objective functions for optimising multiple conflicting objectives are 1) single

objective function 2) single fuzzy satisfaction objective function and 3) Pareto front


Page | 59

The single objective function is generally done by simply aggregating some

objectives and transforming others into constraints In the fuzzy objective function

each variable is associated with a membership function and then aggregated into a

single objective function [84] The first two functions only obtain a single solution

However Pareto optimal solutions can obtain a set of non-dominated solutions

rather than one which represents a compromise that goes some way to optimising

objective functions In this thesis all three objectives functions will be studied and

results will be presented in the following chapters

This thesis will deal with single objective and multiple objectives through different

methods of DA based on various algorithms The next chapter will introduce the

Monte Carlo method and modern heuristic optimisation algorithms such as ant

colony optimisation (ACO) and artificial immune systems (AIS)

Page | 60

CHAPTER 3

OPTIMISATION TECHNIQUES

31 Introduction

Mathematically distribution automation (DA) is categorised as a discrete non-linear

constrained and combinational optimisation problem since the problem is to

determine the status of all transformers and switches In general the optimisation

techniques for assessment of this problem can be divided into two large groups 1)

simulation methods and 2) analytical methods

The Monte Carlo method is a typical example of a simulation method which will be

discussed in Section 32 in detail It can handle uncertainties and solve the

probabilistic optimal power flow [89] In a complex system with hundreds of

switches although the Monte Carlo method can find the best solution with a high

degree of accuracy it is generally not practical to carry out an extensive search of all

possible configurations as it consumes a great deal of CPU time and memory [88]

Therefore most DA problems are solved by analytical methods

The analytical methods can obtain a solution of good quality or even the global

optimal solution of the problem [13] It can be classified into four types 1) branch

and bound 2) optimal flow pattern 3) branch exchange and 4) metaheuristic

techniques Recently the last type has become the most popular

Chapter 3 Optimisation Techniques

Page | 61

The metaheuristic method is a process that attempts to find a solution to the problem

beginning from a starting point or a set of starting points and exploring all the search

space [13] It also includes a strategy to explore the search space and provide an

escape from the local optimal This process does not guarantee a globally optimal

solution but can offer near optimal solutions with a reasonable computational effort

This includes genetic algorithm (GA) ant colony optimisation (ACO) particle

swarm optimisation (PSO) and artificial immune systems (AIS) Different

metaheuristic techniques use different strategies that pass through and explore the

search space [13]

As for the remainder of the chapter the Monte Carlo method is discussed in Section

32 Section 33 presents the proposed ACO algorithm Section 34 discusses a new

hybrid AIS-ACO framework and the summary of this chapter is provided in Section

35

32 Monte Carlo Method

The Monte Carlo method is a simulation algorithm that can be carried out many

times to produce numerical samples that accurately reflect the probability

distribution of the real results [90] [91] This method is always used to solve power

system issues involving uncertain parameters [92] The uncertainties are allocated

randomly and each simulation is operated numerous times In theory the more

simulations are running the less deviation error between actual mean value and

sample mean value Therefore it is important to determine the overall running times

of the Monte Carlo simulation The convergence or stopping criteria is used to

determine the simulation times required to obtain acceptable accurate results

The confidence interval acts as a good estimate of the unknown parameters The

probability that the true parameter remains in the confidence interval is calculated as

follows [93]

119862 = 119875(119883 minus 119871 le 120583 le 119883 + 119871) = int 119866(119883)119889119909119883+119871

119883minus119871 (3-1)

119871 = 119911lowast 120590

radic119899 (3-2)


Page | 62

where 119862 is the degree of confidence is the estimated mean value 119871 is the

confidence interval which provides an estimate range of values which probably

contains an unknown population parameter 120583 is the true population mean value

119866(119883) is the Gaussian distribution 120590 is the sample standard deviation and 119899 is the

number of samples the estimation of 119911lowast is based on the degree of confidence 119862 as

presented in Table 3-1 The most common 119911lowast is 196 and the corresponding 119862 is

095

Table 3-1 Relationship of 119911lowast and 119862

119862 09 095 099 0999

119911lowast 1645 1960 2576 3291

The required number of samples could be expressed as

119899 = (119911lowast120590

119871)2 (3-3)

There are several methods used to determine the sample size and to obtain results

with acceptable accuracy One is by predefining the maximum sample size 119873 when

119899 reaches 119873 the simulation is stopped Another one is by using the degree of

confidence 119862 The confidence interval 119871 is calculated and compared with the

predefined 119871 for each sample and the simulation reaches the stopping criteria when

the confidence interval is less than the critical value

33 Ant Colony Optimisation

The ant colony optimisation method is one of the metaheuristic techniques that has

been employed for the solution of combinational optimisation problems in recent

years [60] The ant colony system (ACS) simulates the behaviour of real ants [94]

[95] The moving paths of artificial ants construct the candidate solutions to a

problem [96] The ants communicate with other ants by a chemical substance called

pheromones [97] Originally all the ants start from their nest and search for their

food in a random manner When the food source is found the ants leave a chemical


Page | 63

substance trail on the way home The pheromone deposited by the ants is used as the

primary guide function for the other ants The pheromones will then evaporate after a

period of time As all of the ants travel approximately at the same speed the shortest

path has the largest probability to contain more pheromones because more ants

choose this one The ants tend to follow the path that has more pheromones than

others After a brief period the shortest path with the most intensity of pheromones

could attract more and more ants providing feedback to the system that promotes the

use of best paths [98] Fig 3-1 represents the behaviours of real ants [69]

Fig 3-1 Example of ant colony system [69]

As shown in Fig 3-1 (a) all the ants are travelling in the same path which connects

point A and point B by a straight line The environment is changed due to the

occurrence of an obstacle in Fig 3-1 (b) and (c) At first all the ants choose the left

or right path randomly because they have no guide It is assumed that they move

through path C or D with the same probability Later on the ants that choose path C

will move faster than that choose path D As a result the pheromones deposited on

path C accumulate faster than those on the path D and this attracts more ants to

choose path C Finally all the ants tend to choose the shortest path (path C) as this

contains the most pheromones

The flowchart of ACO algorithm is shown in Fig 3-2 and the main stages of the

algorithm are presented as follows [69] [94] [95] [97] [98]

Initialisation In this stage the trail intensity on each edge in the search

space is initialised to a constant positive value and all the ants are located in


Page | 64

the nest

Ant Dispatch In this step each ant begins its tour at the starting point and

chooses the next node to move to according to a probabilistic selection rule

which involves the intensity of pheromones deposited on each node by other

ants [88] [99] The ants prefer to choose the path with a higher pheromones

This process is repeated until all the ants have reached the food source

Quality Function Evaluation After all the ants have completed a tour the

relevant quality function of the optimisation problem is calculated to evaluate

the performance of each ant If any constraint is violated the configuration is

discarded Otherwise the objective function is evaluated

Trail Intensity Update There are two pheromone updating rules applied in

this step One is called the global pheromone update It accumulates the

pheromone values on the high-quality solution path to improve convergence

However the pheromone intensity of each edge evaporates over time due to

another rule called the local pheromone update This update is used to

enlarge the search space and to avoid premature convergence for local

minima Ants travelling between two nodes update the relevant pheromone

intensity in the corresponding edge

Convergence Determination This process is operated until the maximum

iteration number is reached or all the ants choose the same path between their

home colony and food source


Page | 65

Start

Set Iteration n=1

Maximum iteration

reached

End

No

Yes

Initialise the parameters for ACO algorithm

searching space and build graph of the tours

Dispatch ants based on the

amount of pheromones on edges

Quality function evaluation

Trail intensity update

Record the high quality solutions of this

iteration and empty all location lists

n=n+1

Fig 3-2 Flowchart of the ant colony algorithm

The above procedure should be modified to a computational procedure to solve

different optimisation problems and this is discussed in the following chapters

Several factors need to be taken into account when designing an ACO algorithm

such as search space transition probability etc

34 AIS-ACO Hybrid Algorithm

341 Artificial Immune Systems

The immune system acts as a defensive barrier to recognise and eliminate foreign

antigens ie bacteria virus etc B lymphocytes are the main immune cells in the

biological immune system and originate in the bone marrow Being exposed to an


Page | 66

antigen a specific antibody is produced on the surfaces of B cells and an immune

response is elicited to make antibodies recognise and bind the antigen [88] [100]

Those B cells whose antibodies best match the antigen are activated and cloned

several times [88] This process is called cloning To identify the most suitable

antibodies for the antigen it is necessary to cause the antibody and the antigen to

interact more closely with each other This is achieved through a process call

hypermutation in which random changes are introduced into the genes of the cloned

B cells [88] One such change might lead to an increase or decrease in the closeness

between antibody and antigen [88] The new B cells can only survive if they are

closely related to the antigen and therefore the B cells that are closely related are

then chosen to enter the pool of memory cells [100] These cloning hypermutation

and selection processes are called the clonal selection principle [101] By repeating

this principle a number of times the immune system learns to respond more

efficiently for the same antigen

Several computational models of the AIS have been developed recently as the

immune system is an adaptive learning system that has the following specifications

learning memory recognition of foreigners and pattern recognition [102]

342 Proposed AIS-ACO Hybrid Algorithm

The proposed AIS-ACO hybrid algorithm combines the advantages of AIS and ACO

The hypermutation developed from the AIS is used as a random operator by

adopting random changes to perturb a solution and hence to enlarge the search space

However the pheromones provided by the ACO can store information about the

quality of solution components for improving the objective functions [88] In

addition the information obtained from pheromone updating guides the algorithm in

its search and improves the convergence rate [88]

The limitation of ACO is that the algorithm can easily fall into a local optimum

which might be due to an insufficient range of candidate solutions This can be made

up by the random changes of solutions in AIS through hypermutation Also the

weakness of the global searching ability in AIS is improved by the pheromone tables

in ACO Thus the new hybrid AIS-ACO framework based on the pheromone-based

hypermutation method has better diversity and convergence in comparison with

either the AIS or ACO algorithms


Page | 67

Start

Cloning

Maximum iteration

reached

End

No

Yes

Initialise and set iteration number n=1

Hypermutation

Fitness evaluation

Non-dominated solutions extraction

Pheromone updating

n=n+1

Record the Pareto front and

Pareto optimal solutions

In this thesis the AIS-ACO hybrid approach is used to generate a set of non-

dominated solutions The antigen is the multi-objective function and the antibody is

the solution to the problem The affinity between the antibody and the antigen is the

Pareto dominance among solutions which indicates the quality of the solution [88]

All the non-dominated solutions experience cloning hypermutation and selection

until the maximum number of iterations is reached The flowchart of the AIS-ACO

algorithm for Pareto optimality is presented in Fig 3-3

Fig 3-3 Flowchart of the AIS-ACO algorithm


Page | 68

The key parts of the algorithm are explained as follows

Initialisation At the beginning of this algorithm a set of initial solutions is

generated These solutions should meet the condition of constraints The

information related to each objective is represented by an individual

pheromone table Each pheromone value represents the probability of

selection of the corresponding edge in the network model [88] All

pheromone values are initially set as the same value

Cloning The number of clones for each non-dominated solution should be

the same as the number of objectives and also as the number of pheromone

tables [88]

Hypermutation The selection of an edge in each cloned solution for

hypermutation is dependent on its pheromone values [88] A higher

pheromone value of a cell in the table indicates that the corresponding edge

in the network is more likely to be selected

Non-dominated solutions extraction This is the process of selecting non-

dominated solutions according to their affinity value [99] All the solutions

are compared as presented in Section 2103 and all the non-dominated

solutions are then extracted for the next iteration

Pheromone updating The aim of this stage is to accumulate the pheromone

values on the edges that belong to a part of the non-dominated solutions and

this is called the global pheromone update However the pheromone

intensity of all edges will evaporate over time by the local pheromone update

This update is used to explore the entire search space

Termination This process is operated until the maximum iteration number

is reached The set of final non-dominated solutions is called the Pareto set

which is used to solve the problem [88]

35 Summary

This chapter introduces the techniques for assessment of mono-objectivemulti-

objective optimisation problems The optimisation techniques are categorised into

two groups simulation methods and analytical methods


Page | 69

The Monte Carlo method is a typical simulation technique and is generally used to

handle uncertain parameters It can find the best solution with a high degree of

accuracy but requires a considerable amount of CPU time and memory The

application of this methodology is discussed in Chapter 4 In that chapter an

efficient methodology based on the Monte Carlo Method is proposed for finding

transformer economic operation modes and optimal tie-switch placement strategies

to minimise transformer loss

The ACO algorithm is one of the metaheuristic techniques designed for assessment

of distribution automation (DA) problems It simulates the behaviour of artificial

ants with positive feedback and distributed computation The positive feedback

enhances the search speed in order to find the global solution and the distributed

computation explores the search space The ACO algorithm is able to find the global

solution in a reasonable computation time It is used for either loss reduction or

reliability improvement as discussed in Chapter 5-7 In addition a new multi-

objective ACO (MOACO) algorithm for assessment of multi-objective DNR

problems in terms of Pareto optimality is provided in Chapter 8

The AIS-ACO hybrid algorithm is a combination of AIS and ACO Hypermutation

is used in AIS as a random operator by using random changes to perturb a solution to

maintain the diversity of the solutions avoiding premature convergence for local

minima The pheromone tables used in the ACO are used to direct the algorithm

towards high quality solutions [88] The AIS-ACO hybrid algorithm is always used

for assessing the DA problem in terms of multiple objectives optimisation in order

to obtain a set of non-dominated solutions In addition the advantages of the AIS-

ACO algorithm over the MOACO algorithm for the assessment of multi-objective

optimisation problems are also discussed in Chapter 8

Page | 70

CHAPTER 4

TRANSFORMER ECONOMIC

OPERATION amp DISTRIBUTION

NETWORK RECONFIGURATION FOR

TRANSFORMER LOSS REDUCTION

41 Introduction

The electrical power generation transmission and distribution companies are not

only energy producers but also significant power consumers Energy loss occurs in

the process of power transfer and takes place in all electrical equipment including

generators power lines and transformers The large number and power capacity of

transformers used in a transformer and distribution network means transformer loss

is a significant component in energy loss The lifetime cost of energy loss in a

transformer is significant especially when one considers rising electricity demand

and the cost of the energy supplied For this reason it is important to tackle the

causes of transformer loss and the problems which then ensue so that energy

consumption can be reduced To support this statement several research projects

that have focused on transformer loss reduction are discussed in Section 242

Chapter 4 Transformer Economic Operation amp Distribution Network

Reconfiguration for Transformer Loss Reduction

Page | 71

An efficient methodology based on the Monte Carlo Method for the 3311 kV

transformer loss reduction with consideration of the voltage issues observed on a

distribution network is proposed in this chapter For a substation with two

transformers there are three operation modes that can occur 1) single transformer in

separate operation 2) two transformers in parallel operation 3) transformer

economic operation (TEO) as mentioned in Section 24 With regard to the load

models which are also discussed in this chapter a database containing numerous

domestic electricity demand profiles is imported into MATLAB to work as the

profile generators A Monte Carlo simulation platform is established by combining

the residential demand profiles with a 3311 kV distribution network model built in

OpenDSS Based on this platform the impacts of three operation modes of

transformers on transformer loss minimisation are investigated and compared

In addition an enumeration approach used for the optimum relocation of tie-switches

in a linked 11 kV distribution network is also suggested The process that involves

changing the distribution network topology by relocation of tie-switches is called

distribution network reconfiguration (DNR) [13] [14] The control centre can

change the location of tie-switches and the transformer operation modes (TOMs) in

each substation based on load data and simulated power loss from the test system at

each time interval The proposed approach is applied to the test system and the

effectiveness of an optimal planning strategy using TEO and DNR to achieve

minimum transformer loss is demonstrated through the results obtained

The remainder of this chapter is structured as follows Section 42 explains the load

models Section 43 describes the mathematical formulation of transformer loss

Section 44 analyses the methodology used to minimise transformer loss whilst

maintaining satisfactory voltages and the case studies and the results are presented

and discussed in Section 45 Finally the main conclusions are summarised in

Section 46



Page | 72

42 Load Model

In order to access the performance of the distribution feeders with different operation

modes of transformers in the substation the time-series behaviour of loads has to be

modelled

The value of the load associated with domestic electricity demand customers has

been obtained from the research described in [19] this can produce a random 1-min

resolution model for UK households There are six steps for creating a domestic

electricity demand model as shown in Fig 4-1 Table 4-1 presents the proportion of

household sizes based on UK statistics [103]

Fig 4-1 Procedure of domestic electricity demand profile generation

Table 4-1 Household size by number of people in household as a proportion [103]

Number of people

in household

1 2 3 4 ge5

Percentage () 3058 341 1557 1288 686

A pool of 10000 different load profiles covering 24 hours in a typical February

weekday are generated by this model For computation reasons the 1440 1-min

time-step load profiles are integrated as 144 10-min resolution profiles in this study

Specify the number of residents in the house from 1 to 5

Specify either a weekday or

weekend

Select the month of the year from 1 to

12

Random allocate appliances to the

dwelling

Run the active occupancy model

Run the electricity demand simulation



Page | 73

(active power is recorded for each minute and then averaged at intervals of 10

minutes) The power factors of all the loads are set to 095

43 Problem Formulation

The objective of this study is to minimise transformer loss through TEO and optimal

DNR The energy loss of the transformer is related to active power However as a

transformer draws reactive power (it takes current) it causes real power loss in the

network The integrated power loss refers to the sum of active power loss of the

transformer itself and the increased active power loss contributed by reactive power

loss of the transformer [73] The mathematical formulation can be expressed as

follows

Minimise 119891 = 1198800

2119875119885119874119862 +1205732

11988002 119875119885119878119862 119905119903119886119899119904119891119900119903119898119890119903 119894119899 119904119894119899119892119897119890 119900119901119890119903119886119905119894119900119899

211988002119875119885119874119862 +

1

2

1205732

11988002 119875119885119878119862 119905119903119886119899119904119891119900119903119898119890119903119904 119894119899 119901119886119903119886119897119897119890119897 119900119901119890119903119886119905119894119900119899

(4-1)


120573 =119878119871

119878119873 represents the transformer load factor S is the transformer actual loading

(kVA) 119878119873 is the transformer rated capacity (kVA) 1198800 is the operational voltage of

the transformer secondary side in per unit

44 Methodology

In this study there are two methodologies used for transformer loss reduction which

are called TEO and DNR


In this section a Monte Carlo simulation platform for three TOMs comparison is

established as shown in Fig 4-2 and the flowchart of the transformer loss assessment

is presented in Fig 4-3



Page | 74

Fig 4-2 Monte Carlo simulation platform for three transformer operation modes comparison

Firstly a pool of 10000 10-min daily domestic electricity demand profiles is


node in the feeders from the system is assigned with residential demand profiles

from the pool using the Monte Carlo Method Theses profiles and one of the TOMs

are then imported into the distribution network model built in OpenDSS After this a

sequential load flow calculation is performed and the simulation results are returned

including voltage profiles and transformer losses to MATLAB The obtained

results are then analysed and compared with the system constraints for each time

step In this study for each TOM the calculation is set to be repeated 10000 times

in order to satisfy the convergence criteria When the losses of all TOMs are

calculated the minimum transformer loss and its associated operation mode are

obtained

Profile

generator of

domestic

electricity

demand profiles

Transformer

operation

modes

MATLAB

Distribution

network

model built

in OpenDSS

Analyse and

compare

simulation

results in

MATLAB

Load flow calculation



Page | 75

Start

Monte Carlo trail number N=1

All transformer operation

modes considered

End

No

Yes

Select demand profiles to each

customer randomly

Select transformer operation

mode

Sequentially run power flow

calculation for 144 10-minute time step

Record results

Change

transformer

operation

mode

N=N+1

Maximum iteration reached

Minimum transformer loss and its associated

transformer operation mode are obtained

No

Yes

Load and aggregate the domestic

electricity demand profiles pool

(144 10-minute time steps)

Fig 4-3 Flowchart of transformer loss assessment



Page | 76


Reconfiguration of radial distribution system is achieved by local control of tie-

switches located in linked feeders The Monte Carlo simulation platform through

DNR is presented in Fig 4-4

Fig 4-4 Monte Carlo simulation platform for distribution network reconfiguration

In the proposed strategy the tie-switch status is modified by the control centre and

the detailed control algorithm is discussed below

Step 1 Random load profiles are first selected

Step 2 When the load profiles have been imported into the network model a

sequential load flow calculation is performed to calculate and compare the

transformer loss under different network configurations (different tie-switches

location) at each time interval

Step 3 Minimum transformer loss and its associated network configuration are

obtained

Step 4 Location of tie-switches based on minimum transformer loss over a whole

day is recorded

Step 5 Optimal DNR strategy is obtained

Profile

generator of

domestic

electricity

demand profiles

Tie-switch

status

MATLAB

Distribution

network

model built

in OpenDSS

Analyse and

compare

simulation

results in

MATLAB




Page | 77

45 Application Studies

To demonstrate the impact of TOMs and DNR on transformer loss the proposed

methodologies are applied to two test networks Several scenarios are tested and the

results are analysed and reported

451 Test Case 1

The single line diagram of the network shown in Fig 4-5 is developed from the UK

generic distribution network [104] The network model is built to incorporate a 3311

kV substation supplying the downstream loads in the OpenDSS software

environment The two transformers have the same specifications and their

characteristics are presented in Table 4-2 The corresponding TCLF is calculated as

5244 The 11 kV network is represented by four outgoing feeders from a single

busbar For computation reasons three of the feeders are simplified lumped loads

whilst the 4th

feeder is modelled in detail The 4th

11 kV feeder consists of eight

nodes which represents a small system with a total of 252 domestic single phase

house loads connected on each node A Monte Carlo simulation approach is

implemented to select these load profiles randomly from a pool of domestic

electricity demand profiles Each house in the 4th

feeder is then assigned with a

residential demand profile The loads in the other three feeders are then lumped with

the same daily profile of the 4th

feeder All the values of the network components are

based on a broad collection from [104] [105] and are recorded in Appendix A1

In this test a comparison of the three TOM methods for transformer loss

minimisation is provided A time-series load flow algorithm is implemented to

quantify the changes in feeder voltage and transformer loss in the previous described

3311 kV UK distribution network for different TOMs In this test three scenarios

are studied and summarised as follows

Scenario 1 Single transformer in separate operation

Scenario 2 Two transformers in parallel operation

Scenario 3 Transformer economic operation in this mode if the transformer load

factor is less than TCLF only one transformer remains in service if the transformer

load factor is higher than TCLF two transformers are operated in parallel



Page | 78

A

A

A

A

B

B

B

B

Load1Load2Load3Load4_1

Load4_2

Load4_3

Load4_4

Load4_5

Load4_6

Load4_7

Load4_8

75 MVA

33 kV

11 kV

33 kV

Voltage

Source

75 MVA

Fig 4-5 Generic distribution network topology

Table 4-2 Parameters of a typical 3311 kV two-winding transformer [106]

Sub-

sector

Transf

Rating

(kVA)

Conn Tapping

Range

Load

Losses

at

75

(kW)

No-

Load

Losses

(kW)

Impedance voltage

at rated current for

the principle

tapping

()

Reference

standard

Urban 7500 YY0 plusmn75

6 steps of 25

Each

50

75

835 BS 171 amp

IEC 60076

1) Test 1-1 Base Case

The simulation results of transformer load factor variation are shown in Fig 4-6 and

the transformer loss variation curves are presented in Fig 4-7 It is observed that the

transformer loss in Scenario 3 is the same as in Scenario 1 between 000 to 630 and



Page | 79

0

10

20

30

40

50

60

70

80

90

100

0 2 4 6 8 10 12 14 16 18 20 22

Tran

sfo

rme

r Lo

ad F

acto

r

Time (h)

0

10

20

30

40

50

60

70

0 2 4 6 8 10 12 14 16 18 20 22

Tran

sfo

rme

r Lo

sse

s (k

W)

Time (h)

0

10

20

30

40

50

60

70

0 2 4 6 8 10 12 14 16 18 20 22

Tran

sfo

rme

r Lo

sse

s (k

W)

Time (h)

the same in Scenario 2 from 1800 to 2200 With the introduction of Scenario 3 the

minimum loss is around 9 kW at 000 which is below the 18 kW of Scenario 2 The

maximum loss of Scenario 3 is nearly 40 kW at 1900 which is far below the 60 kW

of Scenario 1

Fig 4-6 Transformer load factor variation

(a) Scenario 1

(b) Scenario 2



Page | 80

0

10

20

30

40

50

60

70

0 2 4 6 8 10 12 14 16 18 20 22

Tran

sfo

rme

r Lo

sse

s (k

W)

Time (h)

(c) Scenario 3

Fig 4-7 Transformer loss variations in different scenarios

The mean values of 3311 kV transformer energy loss during one day under different

scenarios are presented in Table 4-3 As shown in Fig 4-6 the average transformer

load factor during a whole day is slightly below the TCLF (5244 in this test) This

situation is more suitable for a single transformer than two transformers The loss in

Scenario 3 reaches the lowest value and results in a reduction of 1133 and 1441

in comparison with Scenario 1 and Scenario 2

Table 4-3 Daily transformer loss in different scenarios

Scenario 1 Scenario 2 Scenario 3

Transformer losses (kWh) 53982 55922 47865

According to the EN50160 standard [7] under normal conditions at least 95 of the

10-min average mean rms voltage magnitude in the 11 kV electricity distribution

network should be within the range 09 pu to 11 pu over one week In other words

the 95th

percentile voltage profile is compared with the allowed voltage range to

check the networkrsquos reliability

The mean and 95th

percentile voltage profiles at each node in the fourth feeder are

presented in Fig 4-8 It can be seen that the voltage level at each node can change

considerably after the scenario changes It also appears that the nodes in Scenario 1

experience the most severe voltage drop in comparison with the other two scenarios

The worst 95 voltage value of the node lsquoLoad4_8rsquo at the end of the studied feeder

in Scenario 1 is around 098 pu which is not as satisfactory as the results of 0987 pu

and 0984 pu observed in Scenario 2 and Scenario 3



Page | 81

0976

0978

098

0982

0984

0986

0988

099

0992

Load4_1 Load4_2 Load4_3 Load4_4 Load4_5 Load4_6 Load4_7 Load4_8

Vo

ltag

e (

pu

)

Scenario1

Scenario2

Scenario3

0974

0976

0978

098

0982

0984

0986

0988

099


Vo

ltag

e (

pu

)

Scenario1

Scenario2

Scenario3

(a) Mean value

(b) 95th

value

Fig 4-8 11 kV 4th

feeder voltage profiles in different scenarios

To show in detail the voltage profiles affected by different TOMs the load at the

start of the 4th

feeder lsquoLoad4_1rsquo and the end one lsquoLoad4_8rsquo have been selected

Since the Monte Carlo method produces many loss and voltage values it is

preferable to present the averages of all these values and their deviations

As shown in the charts from Fig 4-9 and Fig 4-10 the voltage drops severely from

1800 to 2000 which is also the maximum daily demand period It also appears that

the voltage profile in Scenario 3 is the same as in Scenario 1 between 000 to 630

and the same as in Scenario 2 from 1800 to 2200 With the introduction of Scenario



Page | 82

088

09

092

094

096

098

1

0 2 4 6 8 10 12 14 16 18 20 22

Bu

s V

olt

age

(p

u)

Time (h)

088

09

092

094

096

098

1

0 2 4 6 8 10 12 14 16 18 20 22

Bu

s V

olt

age

(p

u)

Time (h)

088

09

092

094

096

098

1

0 2 4 6 8 10 12 14 16 18 20 22

Bu

s V

olt

age

(p

u)

Time (h)

3 the lowest voltage of lsquoLoad4_8rsquo is around 097 pu which is significantly above

the lower limit 090 pu

(a) Scenario 1

(b) Scenario 2

(c) Scenario 3

Fig 4-9 Voltage profiles of Load 4_1 in different scenarios

Lower Limit

Lower Limit

Lower Limit



Page | 83

088

09

092

094

096

098

1

0 2 4 6 8 10 12 14 16 18 20 22

Bu

s V

olt

age

(p

u)

Time (h)

088

09

092

094

096

098

1

0 2 4 6 8 10 12 14 16 18 20 22

Bu

s V

olt

age

(p

u)

Time (h)

088

09

092

094

096

098

1

0 2 4 6 8 10 12 14 16 18 20 22

Bu

s V

olt

age

(p

u)

Time (h)

(a) Scenario 1

(b) Scenario 2

(c) Scenario 3


Lower Limit

Lower Limit

Lower Limit



Page | 84

0976

0978

098

0982

0984

0986

0988

099

0992


0 25

5244 75

100

As most people are sleeping late at night and the transformer load factor is less than

the TCLF transformers are in individual operation mode When most people are at

home again from 1800 the transformer load factor increases beyond the TCLF As a

result the voltage profiles are improved when transformers are operated in parallel

In conclusion when the transformer load factor is less than the TCLF transformers

in a separate service result in less loss but more voltage dips however transformers

operating in parallel cause lower voltage drops but more loss When the transformer

load factor is higher than the TCLF transformers in parallel operation cause less loss

and lower voltage drops As a result based on the economic operation theory the

transformer in Scenario 3 significantly reduces transformer loss and maintains the

voltages at a satisfactory level

2) Test 1-2 TCLF Sensitivity Analysis

In this test the value of TCLF used to distinguish whether the transformer should be

in separate or parallel operation is discussed The complete process presented

previously is carried out again but takes into account the effect of different critical

values 0 25 5244 75 and 100

Fig 4-11 shows the effect on the mean voltage magnitudes of various TCLFs The

results indicate that the voltage profile is closely related to the TCLF and the TCLF

should be decreased to increase the region in which transformers operate in parallel

This will improve the voltage profiles

Fig 4-11 11 kV 4th

feeder mean voltage profile of various TCLFs



Page | 85

Table 4-4 describes the effect on the transformer loss when TCLF is changed It

reaches the lowest value when TCLF is 5244 If the TCLF is decreased or

increased above this value the loss increases Overall the TCLF should be set to

5244 in order to minimise transformer loss

Table 4-4 Transformer loss with different TCLF

TCLF () 0 25 5244 75 100

Transformer loss

(kWh)

55922 50783 47865 49414 53982

As presented in Table 4-5 the average number of switching operations is increased

as the TCLF is approached to its optimum value

Table 4-5 Average number of switching operations with different TCLF

TCLF () 0 25 5244 75 100

Average number of

switching operations

0 2 4 2 0

452 Test Case 2

The impacts of TOMs and DNR on transformer loss are evaluated in this section As

presented in Fig 4-12 the model of the test system is developed from the

duplication of the generic distribution network shown in Fig 4-5 All the values of

the network parameters are obtained from [104]ndash[106] The system is supplied by

two 3311 kV substations and each bus has four feeders There is one linked feeder

with nine tie-switches Tie-switches refer to the switches of the network that are

normally open The function of the tie-switches is to alter the network topology to

provide various routes for supplying loads In order to feed all loads and keep the

systemrsquos radial topology only one tie-switch is open and all the others are closed



Page | 86

0

02

04

06

08

1

12

14

16

0 2 4 6 8 10 12 14 16 18 20 22

Act

ive

Po

we

r (k

W)

Time (h)

TW1 TW2 TW3 TW4 TW5

A1

A2

A3

A4_1 A4_2 A4_3 A4_4 A4_5 A4_6 A4_7 A4_8 B4_8 B4_7 B4_6 B4_5 B4_4 B4_3 B4_2 B4_1

B1

B2

B3

EndA EndB

TW9TW8TW7TW6

Tie-Switch (close) Tie-Switch (open)

Fig 4-12 Test system

For simplicity the daily load variations in each feeder are the same and the load

profiles of each node in the linked feeder are also the same Therefore the loads

could be categorised into two groups

Group 1 A1 A2 A3 B1 B2 B3

Group 2 A4_1 A4_2 A4_3 A4_4 A4_5 A4_6 A4_7 A4_8 B4_1 B4_2

B4_3 B4_4 B4_5 B4_6 B4_7 B4_8

On the basis of transformer load factor variation shown in Fig 4-6 the relevant 10-

min resolution load models of the two groups are presented in Fig 4-13 The power

factors of all the loads are set to 095

(a) Group 1



Page | 87

0

002

004

006

008

01

012

014

016

018

02

0 2 4 6 8 10 12 14 16 18 20 22

Act

ive

Po

we

r (k

W)

Time (h)

(b) Group 2

Fig 4-13 Daily load variations for different load groups

As this test system is developed from the duplication of the generic distribution

network and all the loads have the same profiles the position of the tie-switch is

selected from lsquoTW1rsquo to lsquoTW5rsquo For example the tie-switch located in lsquoTW1rsquo has the

same effect as lsquoTW9rsquo The control strategy is used to quantify the changes in feeder

voltage and transformer loss in the previously described test system under different

scenarios which could be categorised as

Scenario 1 each end has one transformer in operation and the tie-switch is located

at TW1 ie entire feeder supplied from end B


in TW5 ie feeder split at mid-point

Scenario 3 each end has one transformer in operation and the location of the tie-

switch is based on minimum transformer loss operation

Scenario 4 each end has two transformers in operation and the tie-switch is located

at TW1


at TW5

Scenario 6 each end has two transformers in operation and the location of the tie-




Page | 88

Scenario 7 each end has onetwo transformers in operation based on the transformer

load factor and the tie-switch is located at TW1




load factor and the location of the tie-switch is based on minimum transformer loss

operation

Table 4-6 indicates the mean value of 3311 kV transformer loss during one day

under different scenarios As can be seen from the table when the tie-switches have

the same location TW1 transformer loss in Scenario 7 results in a reduction of

1396 and 1456 in comparison with Scenario 1 and Scenario 4 In conclusion

the mode introducing a flexible number of transformers in operation based on TCLF

reduces the loss In addition the transformer loss in Scenario 9 is 9528 kWh per day

which is 217 and 014 lower than Scenario 7 and Scenario 8 As a result the

variation of tie-switch locations could reduce transformer loss The detailed location

of the tie-switch in Scenario 9 is included in Appendix B1

Table 4-6 Transformer loss in Test Case 2

Scenarios S1 S2 S3 S4 S5 S6 S7 S8 S9

Loss

(kWhday)

11319 10848 10848 11399 11162 11162 9739 9572 9528

The graph presented in Fig 4-14 illustrates the voltage variation caused by the tie-

switch relocation The node voltages in Scenario 1 experience the worst profile

which increases to a peak of 09749 pu from 09675 pu along the linked feeder In

order to reduce the loss the tie-switch is always located in the middle of the feeder

TW5 in Scenario 3 As a result the voltage profiles of Scenario 2 and Scenario 3 are

the same It should be noted that Scenario 2 experiences a slight drop from 09787 pu

to 0972 pu and then climbs back to 09827 pu It can also be clearly seen that the

voltage reaches the lowest value where the tie-switch is located The further away

the nodes are from the tie-switch the better the voltage profiles that can be obtained

In addition when the tie-switch moves closer to the middle of the linked feeder the



Page | 89

096

0962

0964

0966

0968

097

0972

0974

0976

0978

098

A4_1A4_2A4_3A4_4A4_5A4_6A4_7A4_8B4_8B4_7B4_6B4_5B4_4B4_3B4_2B4_1

Vo

ltag

e (

pu

)

Scenario1

Scenario2

Scenario3

0955

096

0965

097

0975

098

0985

099


Vo

ltag

e (

pu

)

Scenario1

Scenario4

Scenario7

voltage performance is improved And the detailed voltage values at each node in the

linked feeder for different scenarios are presented in Appendix B1

Fig 4-14 Mean voltage profiles in S1 S2 and S3

As shown in Fig 4-15 the voltage variation is due to a change in TOMs


As in the case of the tie-switch located in lsquoTW1rsquo all the node voltages experience a

rise along the linked feeder from lsquoEndArsquo to lsquoEndBrsquo It should be noted that the node

voltages in Scenario 4 achieve the best profile which increase to a peak of 0984 pu

from 0976 pu As discussed in Test Case 1 the transformers in parallel operation

could improve the voltage profiles In addition the flexible number of transformers



Page | 90

in operation based on TCLF (Scenario 7) shows a slight difference in voltage from

that in Scenario 4

As discussed above the location of the tie-switch and the change of TOMs have an

impact on the feeder voltage variation The tie-switch located in the middle of the

feeder and transformers with parallel operation defines the best voltage profiles

46 Summary

This chapter illustrates why transformer economic operation (TEO) is an economical

solution to reduce transformer loss The substation composed of two transformers

with the same characteristics has been used as an example to introduce the general

approach of determining the TCLF and TEO area A Monte Carlo simulation

platform was established to tackle load uncertainties A methodology to prove that

the TOM variation affects the performance of the 11kV distribution network is

discussed and analysed The TEO mode with minimum loss and satisfactory voltages

is achieved depending on the the transformer load factors by operating with either

one or two transformers and can be summarised as when the transformer load factor

is less than the TCLF transformers should be in separate operation when the

transformer load factor is higher than the TCLF transformers are recommended to

operate in parallel This results in a reduction of 1441 over the conventional

transformer loss ie when two transformers are in parallel operation However

simulation studies also indicate voltage profiles are improved when transformers

operate in parallel Therefore a slight reduction in TCLF results in an increased loss

but an improvement in voltage performance

The effectiveness of a DNR strategy has also been proposed through the results

obtained The presented results illustrate the impact of different TOMs in each

substation and tie-switch statuses on transformer loss and the voltages measured

along the feeder during a 24 hour operating period The optimal economic operation

strategy with TEO and DNR have successfully reduced the transformer loss and

improved the voltage profiles The further away the nodes are from the tie-switch

the better the voltage profiles obtained In addition when the tie-switch moves closer

to the middle of the linked feeder the voltage performance is improved



Page | 91

In normal operating conditions transformers operate in parallel and the tie-switch is

located in the middle of the linked feeder As indicated by Table 46 the daily

energy loss in Scenario 5 is 11162 kWh After the introduction of Scenario 9 the

annual saving energy could be 59641 kWh

Page | 92

CHAPTER 5


RECONFIGURATION amp DG ALLOCATION

FOR FEEDER LOSS REDUCTION

51 Introduction

Distribution networks generally operate in radial configuration to ease protection

coordination and to reduce short circuit current [107] Distribution feeders can be

reconfigured to alter the network topology at normal and abnormal operating

conditions by changing the openclose status of switches to satisfy the operatorrsquos

objectives [13] [14]

DG is a small electric generation unit that is connected directly to the distribution

network or appears on side of the meter accessed by the customer [16] With the

increasing number of DGs bidirectional power flows have appeared and locally

looped networks have become inevitable [17] Therefore the type size and location

of DGs in the distribution networks strongly affect power system operation and

planning

The studies in [5] indicate that about 5 of the total power generation is wasted in

the form of feeder loss at the distribution level Reduction in active power loss can

help distribution network operators (DNOs) save costs and increase profits The

Chapter 5 Distribution Network Reconfiguration amp DG Allocation for Feeder Loss

Reduction

Page | 93

optimal distribution network reconfiguration (DNR) placement and sizing of DGs

strategies should be used to reduce feeder loss while satisfying the operating

constraints

The ant colony optimisation (ACO) developed by M Dorigo is a metaheuristic

algorithm for the assessment of optimisation problems [94] It is based on the

pheromones deposited by ants as a guide for finding the shortest path between a food

source and their home colony The detailed description of ACO algorithm has been

presented in Section 33 In this chapter an ACO algorithm is proposed to solve the

network reconfiguration and DG placement problems simultaneously based on

distribution feeder loss minimisation The proposed technique is tested on two

standard IEEE 33-node and 69-node systems and the simulation results show the

performance and effectiveness of the proposed method Four scenarios are

considered during network reconfiguration and DG allocation The impacts of DG

capacity on assessing the DNR and DG allocation problems in terms of feeder loss

reduction are also studied Moreover the results obtained by ACO algorithm have

been compared to those from other algorithms in the literature

As for the remainder of this chapter the mathematical formulation of the objective

function and its constraints are explained in Section 52 Section 53 discusses the

application of ACO algorithms in order to solve the problem Section 54 provides a

detailed analysis of the numerical results and Section 55 provides the final

conclusions


The proposed objective function (F) of the problem is formulated to minimise the

feeder loss of a distribution network which is described as follows

119872119894119899119894119898119894119904119890 119891 = sum 119896119894119877119894(119875119894

2+1198761198942

1198801198942 )

119873119887119894=1 (5-1)

where 119877119894 is the resistance of the ith branch 119875119894 and 119876119894 are the real power (W) and

reactive power (VAr) at the receiving end of branch i 119880119894 represents the rms voltage

at the receiving end of branch i (V) 119896119894 is a binary variable 119896119894 = 0 indicates that


Reduction

Page | 94

branch 119894 is open and 119896119894 = 1 indicates that branch 119894 is closed The detailed feeder loss

assessment has been given in Section 28

Subject to

∆119881119899 le ∆119881119898119886119909 for all load points (5-2)

119868119887 le 119868119898119886119909 for all branches (5-3)

119875119894 le 119875119894119898119886119909 (5-4)

det(119860) = 1 119900119903 minus 1 (5-5)

Constraints (5-2) ndash (5-3) represent the computed voltages and currents and should be

in their permissible range Constraint (5-4) indicates that the power flow at all

branches should be within the limits defined for each branch Constraint (5-5)

ensures the radial topology of the network [32] The branch to node incidence matrix

Arsquo has one row for each branch and one column for each node 119886119894119895 represents the

coefficient in row i and column j 119886119894119895 = 0 if branch i is not connected with node j

119886119894119895 = 1 if branch i is directed away from node j and 119886119894119895 = minus1 if branch i is directed

towards node j When the column corresponding to the reference node and the rows

of open branches are deleted from matrix Arsquo a new square branch-to-node matrix A

is obtained Then the determinant of A is calculated If det(A) is 1 or -1 the system is

radial Otherwise the system is not radial

53 Solution Method


With regard to the DNR problem each solution is represented by a string of integers

which indicates the location of tie-switches As the number of tie-switches that keep

the network radial is always constant the number of the solutionrsquos elements is equal

to the number of tie-switches in the network


Reduction

Page | 95

Home

1 2 NP1NP1-1

1 2 NP1-1 NP1

1 2 NP1NP1-1

1 2 NP2-1 NP2

1 2 NP2NP2-1

1 2 NP2-1 NP2

1 2 NP2NP2-1

1 2 NP2-1 NP2

Food

Stage

1

2

NT-1

NT

NT+1

NT+2

NT+NDG-1

NT+NDG

Part 1 Number of

existing tie-switches

Part 2 Number

of DGs

532 Applying ACO to DNR and DGs Placement

In this chapter an ACO algorithm is adopted to find the optimum locations of tie-

switches and sites of DGs placement in the network in terms of feeder loss

minimisation When the locations of tie-switches and DGs are changed a new

network configuration will be formed For each network configuration the feeder

loss is evaluated by using the approach presented in Section 52

Fig 5-1 Search space of DNR and DGs Placement


Reduction

Page | 96

The search space of the DNR and DG allocation problems is modelled as a directed

graph as shown in Fig 5-1 In Part I the states signify the location of tie switches

and the sites for DGs installation are represented by states in Part II The number of

stages in this graph is the sum of the amount of existing tie-switches 119873119905 and the

number of installed DGs 119873119863119866 1198731199011is the number of possible locations for the tie-

switches relocation and 1198731199012 is the number of candidate buses for DGs installation

Artificial ants start their tours at home moving along the paths in the graph and end

at the food source Each location list consists of a string of integers and represents a

solution to the problem Different orders of the solutionrsquos elements indicate different

routes However several routes might indicate a certain solution as the order of the

solutionrsquos elements makes no difference to the network configuration For example

the solution vector (1 2 3) represents the same network configuration as the solution

vector (3 2 1) And the objective functions of these two routes are the same In this

study the first route that the ants found will be chosen as the feasible solution The

flowchart of the proposed ACO algorithm is presented in Fig 5-2 and is expressed in

five steps

Step 1 Initialisation First of all all the ants are initially located at home The

pheromone values of the edges in the search space are all set to a small positive

constant value

Step 2 Ant Dispatch All the ants are sent in parallel from the home colony and one

of the states is chosen in the next stage according to a probabilistic selection rule

which involves the intensity of pheromones deposited on the states [66] The

locations of the tie-switches are determined first and the sites for the DGs

installation are then selected The probability of an ant choosing state j of the next

stage y is

119875119895119910(119873) =

120591119895119910

(119873)

sum 120591119895119910

(119873)ℎisin∆119910

(5-6)

where 120591119895119910

(119873) is the pheromone value of state j of stage y at iteration N ∆119910 is the set

of available states which an ant can choose at stage y


Reduction

Page | 97

Step 3 Objective Function Evaluation After all the ants have completed their tour

the location list and corresponding objective function in (5-1) for each ant are

evaluated If any constraint in (5-2) - (5-5) is violated the corresponding solution is

assigned with a huge value and is discarded If not all the objective functions are

assessed and the best configuration of the Nth iteration with minimum objective

function 119891119887119890119904119905(119873) is recorded This should be compared to the best configuration

obtained so far 119891119887119890119904119905 if 119891119887119890119904119905(119873) lt 119891119887119890119904119905 the best solution should be updated such

that 119891119887119890119904119905 = 119891119887119890119904119905(119873) [14] If not the best configuration found in the previous

iteration is retained After this the location list is emptied and all the ants are free to

choose a new trail

Step 4 Pheromone Updating The aim of this step is to favour transitions towards

states involving high quality solutions with greater pheromones There are two rules

of pheromone updating the local rule and global rule

Local rule The amount of pheromone deposited in the search space should be

evaporated to make paths less attractive The local pheromone update rule is

calculated as following

120591119895119910

(119873) = (1 minus 120588)120591119895119910

(119873 minus 1) + 120591119888 (5-7)

where 120588 is the pheromone evaporation rate which is set between 0 and 1 120591119888 is a

small positive constant value Even if the amount of pheromone deposited on an

edge is at the lowest value of 120591119888 there is a slight chance that an ant will still choose

this edge

Global rule The global pheromone updating rule involves ants depositing large

amounts of pheromone to the edges that belong to the highest quality solution per

iteration This rule is to guide the search to find the global optimal solution The

pheromones of those edges can be modified by

120591119895119910(119873) = 120591119895

119910(119873) + 120588119891119887119890119904119905

119891119887119890119904119905(119873) (5-8)

After applying the local and global pheromone updating rules the method Max-Min

ACO algorithm is integrated into the proposed approach

120591119895119910(119873) = 120591119898119886119909 119894119891 120591119895

119910(119873) ge 120591119898119886119909 (5-9)

120591119895119910(119873) = 120591119898119894119899 119894119891 120591119895

119910(119873) le 120591119898119894119899 (5-10)


Reduction

Page | 98

Start

Set Iteration n=1

Maximum iteration

reached

Output best

configuration and end

No

Yes





Relocate tie-switches and DGs by location lists

Calculate the objective function for each ant

The pheromones are updated according

to local and global rules

n=n+1

Record the best solution so far and empty

all location lists

Read system topology

and load data

where 120591119898119886119909and 120591119898119894119899 are the higher and lower bound of the pheromone level on each

edge respectively The trail limit of the pheromone ensures the probabilities of all

the edges are greater than zero which maintains the diversity of the solutions and

avoids premature convergence for local minima

Step 5 Termination The computation continues until the predefined maximum

number iterations is reached The best tour selected among all iterations implies the

optimal solution

Fig 5-2 Flowchart of the ACO applied to DNR and DGs placement


Reduction

Page | 99


To demonstrate the performance and effectiveness of the proposed technique in

assessing the network reconfiguration and placement of DG problems

simultaneously the proposed ACO is implemented on two 1266 kV test systems

consisting of 33 and 69 buses The network models are built in OpenDSS and the

solution algorithm is developed in MATLAB For both test systems the substation

voltage is assumed to be 10 pu and all the branches and buses are considered as

candidate locations for tie-switches and DG placement respectively In this study

for simplicity the number of installed DGs is three All the DGs are synchronous

generators and are represented as PQ models with a 100 kVA capability and a

power factor equal to 10 For the purpose of better illustration and comparison four

cases are considered to analyse the superiority and performance of the proposed

method

Case I System is without reconfiguration and has no DGs (base case)

Case II System is optimally reconfigured and has no DGs

Case III System is optimally reconfigured after DGs are placed at certain buses

Case IV System is optimally reconfigured and DGs are optimally placed

simultaneously

It is to be noted that the ACO control parameters are different for each test case

They are set experimentally using information from several trial runs The final

combinations that provide the best results for all of the above tests are given in

Appendix C1

541 33-bus System

In this section the proposed procedure is implemented on a 33-bus 1266 kV radial

distribution system with 37 branches and 5 tie-switches whose single-line diagram

is shown in Fig 5-3 The tie-switches are located at L33 to L37 represented by red

dotted lines The data of line and load are taken from [108] and summarised in

Appendix A2 The total real and reactive power loads of the system are 3715 kW

and 2300 kVAr respectively The performance of the presented method for the four


Reduction

Page | 100

10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

18 19 20 21

22 23 24

25 26 27 28 29 30 31 32

L1 L2 L3 L4 L5 L6 L7 L8 L9 L10 L11 L12 L13 L14 L15 L16 L17

L18

L19 L20 L21

L22

L23 L24

L25

L26 L27 L28 L29 L30 L31 L32

L33

L34

L35

L36

L37

cases is given in Table 5-1 The network losses in each branch for all test cases are

listed in Appendix B2

Fig 5-3 33-bus system

Table 5-1 Results of different cases for the 33-bus system

Case Active feeder

loss (kW)

Minimum voltage

(pu)

(Bus No)

Location of tie-switches

on Fig 53

DG location

Case I 20314 09116 (B17) L33 L34 L35 L36 L37 NA

Case II 13981 09361 (B31) L7 L9 L14 L32 L37 NA

Case III 11753 09357 (B31) L7 L9 L14 L28 L31 B17 B21 B24

Case IV 10844 09462 (B32) L7 L9 L14 L32 L37 B30 B31 B31

Case I base case

For the base case without reconfiguration and DGs the initial active feeder loss of

this system is 20314 kW The lowest bus voltage is 09116 pu and this occurs at

Bus 17

Case II with reconfiguration only (no DGs)

In this case only reconfiguration is considered and no DGs are installed The

network configuration after DNR is shown in Fig 5-4 The number of the solutionrsquos

elements for this case is 5 which is the number of tie-switches After DNR the total

feeder loss is 13981 kW which corresponds to a 3118 reduction in loss In

addition the minimum voltage also increases from 09116 pu to 09361 pu


Reduction

Page | 101

10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

18 19 20 21

22 23 24

25 26 27 28 29 30 31 32


L18

L19 L20 L21

L22

L23 L24

L25

L26 L27 L28 L29 L30 L31 L32

L33

L34

L35

L36

L37

Fig 5-4 33-bus system for feeder loss minimisation Case II

To illustrate the performance of the proposed ACO the results are compared with

the results obtained using the branch exchange method (BEM) [109] harmony

search algorithm (HSA) [110] fireworks algorithm (FWA) [16] particle swarm

optimisation (PSO) [55] and invasive weed optimisation (IWO) [111] these are all

described in the literature and are presented in Table 5-2 It is observed that the

results obtained from the ACO are identical to those from the HAS PSO and IWO

but better than the results from the BEM and FWA This is because that BEM and

FWA have plunged into a local optimal solution and they lack the ability to escape

from it

Table 5-2 Comparison of simulation results for 33-bus system in Case II

Method Feeder loss

(kW)

Loss reduction

()

Tie-switches location Minimum

voltage (pu)

The proposed ACO 13981 3118 L7 L9 L14 L32 L37 09361

BEM [109] 14054 3082 L7 L10 L14 L32 L37 09361

HSA [110] 13981 3118 L7 L9 L14 L32 L37 09361

FWA [16] 14026 3095 L7 L9 L14 L28 L32 09396

PSO [55] 13981 3118 L7 L9 L14 L32 L37 09361

IWO [111] 13981 3118 L7 L9 L14 L32 L37 09361

Moreover both the continuous genetic algorithm (CGA) [112] and cuckoo search

algorithm (CSA) [113] are implemented to further investigate the performance of the

proposed ACO It is important to note that the performance of the ACO CGA and

CSA depends on the selection of their control parameters All three algorithms are

solved 100 times The average maximum minimum and standard deviation of the

100 runs are compared and shown in Table 5-3 The convergence number is defined


Reduction

Page | 102

10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

18 19 20 21

22 23 24

25 26 27 28 29 30 31 32


L18

L19 L20 L21

L22

L23 L24

L25

L26 L27 L28 L29 L30 L31 L32

L33

L34

L35

L36

L37

DG2

DG1

DG3

as the number of the iterations when the objective function is convergence It can be

seen that all three algorithms have obtained the same minimum loss However the

proposed ACO method has a higher probability in finding the global optimum

solution as the mean and standard deviation of the fitness values of the ACO

algorithm are less than those obtained by the other algorithms Furthermore as the

average value of convergence number of the ACO is less than that of the other two

algorithms this means the proposed algorithm has a higher convergence rate In

terms of the computation times the proposed ACO runs faster when compared with

CGA and CSA


Method Feeder loss (kW) Convergence number Average

computation

times

(second)

AVG MAX MIN STD AVG STD

ACO 13981 13981 13981 0 228 821 1448

CGA [112] 14002 14619 13981 12121 5463 2986 3926

CSA [113] 13986 14028 13981 01328 8363 3425 7258

AVG MAX MIN and STD mean the average maximum minimum and standard deviation of the 100 runs

Case III with reconfiguration only (with DGs)

In this case the three DGs are located at the end of the feeders ie Bus 17 21 24

The network configuration after DNR is illustrated in Fig 5-5 As shown in Table 5-

1 the network reconfiguration results in a reduction of 4214 in feeder loss in

comparison with the original network without DGs and a reduction of 1594 in

comparison with the reconfigured system without DGs

Fig 5-5 33-bus system for feeder loss minimisation Case III


Reduction

Page | 103

10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

18 19 20 21

22 23 24

25 26 27 28 29 30 31 32


L18

L19 L20 L21

L22

L23 L24

L25

L26 L27 L28 L29 L30 L31 L32

L33

L34

L35

L36

L37

DG2DG1

DG3

Case IV with reconfiguration and DG allocation

Fig 5-6 illustrates the optimal network configuration and DG locations The network

is reconfigured and DGs are allocated simultaneously in this case Therefore the

number of the solutionrsquos elements for this case becomes 8 which is the sum of the

number of tie-switches and DGs The results show the final configuration with a

feeder loss of 10844 kW with 4662 2244 and 773 reduction in comparison

with that in Case I Case II and Case III respectively

Fig 5-6 33-bus system for feeder loss minimisation Case IV

In this case the impacts of DG capacity on assessing the DNR and DG allocation

problems in terms of feeder loss reduction are also studied The capacity of each DG

is set as 100 400 700 and 1000 kVA respectively The feeder losses for different

DG capacities are shown in Fig 5-7 Before simultaneous reconfiguration and DG

allocation the feeder loss decreases from 1783 kW to 1023 kW when the capacity

of DG is increased from 100 kVA to 700 kVA However the feeder loss increases to

1042 kW if the capacity of DG continuously grows to 1000 kVA The inappropriate

network configuration and DG location might result in loss increment when the size

of the DG is increased However with the introduction of network reconfiguration

and DG allocation feeder loss is reduced no matter what the capacity of DG is This

proves that the proposed methodology can reduce the total feeder loss by

determining the most suitable network topology and DG locations in comparison

with the original configuration


Reduction

Page | 104

086

088

09

092

094

096

098

1

102

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32

Vo

ltag

e (

pu

)

Bus No

Case I

Case II

Case III

Case IV

0

20

40

60

80

100

120

140

160

180

200

100 400 700 1000

Fee

de

r lo

ss (

kW)

DG Capacity (kVA)

Before simultaneousreconfiguration and DG allocation

After simultaneous reconfigurationand DG allocation

Fig 5-7 Comparison of feeder loss for different DG capacities before and after simultaneous

reconfiguration and DG allocation

The voltage profiles of four cases are compared and shown in Fig 5-8 It can be seen

that the voltage profiles at most buses in Case IV have been improved in comparison

with the other three cases In terms of Case III and Case IV the buses which inject

DGs show the improvement in voltage profiles ie the voltage of Bus 31 is

improved from 09357 pu in Case III to 09537 pu in Case IV In Case IV as Bus 32

is the furthest bus being supplied its voltage is the lowest value among all buses In

conclusion the systemrsquos voltage profiles are improved by optimal DNR and DG

allocation

Fig 5-8 Comparison of voltage profiles in different cases of 33-node system


Reduction

Page | 105

10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

27

28

29

30

31 32 33 34

35

36

37

38 39 40 41 42 43 44 45

46 47 48 49

50

51

52

53 54 55 56 57 58 59 60 61 62 63 64

65 66

67 68

L1 L2 L3 L4 L5 L6 L7 L8 L9 L10 L11 L12 L13 L14 L15 L16 L17 L18 L19 L20 L21 L22 L23 L24 L25 L26

L27

L28

L29

L30

L31 L32 L33 L34

L35

L36

L37

L38 L39 L40 L41 L42 L43 L44 L45

L46

L47 L48 L49

L50

L51

L52

L53 L54 L55 L56 L57 L58 L59 L60 L61 L62 L63 L64

L65

L66

L67

L68

L69

L70

L71

L72L73

542 69-bus System

This is a large-scale radial distribution system consisting of 73 branches and 5 tie-

switches whose single-line diagram is shown in Fig 5-9 The tie-switches are

located at L69 to L73 represented by red dotted lines The line and load data of the

system are taken from [84] and summarised in Appendix A3 The total power loads

are 379589 kW and 26891 kVAr respectively Similar to 33-bus system this

system is also simulated for four cases and the results are given in Table 5-4 The

network losses in each branch for all test cases are listed in Appendix B2



Case Active feeder

loss (kW)

Minimum voltage

(pu)

(Bus No)

Tie-switches location DG location

Case I 22562 09072 (B64) L69 L70 L71 L72 L73 NA

Case II 9885 09476 (B60) L14 L55 L61 L71 L72 NA



Case I base case

Base case active feeder loss in the system is 22562 kW The lowest bus voltage is

09072 pu and occurs at bus 64


Reduction

Page | 106

10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

27

28

29

30

31 32 33 34

35

36

37

38 39 40 41 42 43 44 45

46 47 48 49

50

51

52

53 54 55 56 57 58 59 60 61 62 63 64

65 66

67 68


L27

L28

L29

L30

L31 L32 L33 L34

L35

L36

L37

L38 L39 L40 L41 L42 L43 L44 L45

L46

L47 L48 L49

L50

L51

L52

L53 L54 L55 L56 L57 L58 L59 L60 L61 L62 L63 L64

L65

L66

L67

L68

L69

L70

L71

L72L73


After DNR switches at L14 L55 L61 L71 and L72 are opened as shown in Fig 5-

10 The total feeder loss is reduced by 5619 and the minimum voltage is

increased to 09476 pu in comparison with the base case


The comparisons of results among the proposed ACO with FWA [16] HSA [110]

and genetic algorithm (GA) [110] are presented in Table 5-5 It is observed that the

results obtained from the ACO are better than those from the FWA HSA and GA

as these algorithms are trapped into the local optimal solution


Method Feeder loss

(kW)

Loss reduction

()


voltage (pu)


FWA [16] 9886 5618 L14 L56 L61 L71 L72 09476

HSA [110] 10546 5326 L13 L18 L56 L61 L72 09475

GA [110] 10242 5461 L14 L53 L61 L71 L72 09462



The network configuration after DNR is illustrated in Fig 5-11 As shown in Table


Reduction

Page | 107

10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

27

28

29

30

31 32 33 34

35

36

37

38 39 40 41 42 43 44 45

46 47 48 49

50

51

52

53 54 55 56 57 58 59 60 61 62 63 64

65 66

67 68


L27

L28

L29

L30

L31 L32 L33 L34

L35

L36

L37

L38 L39 L40 L41 L42 L43 L44 L45

L46

L47 L48 L49

L50

L51

L52

L53 L54 L55 L56 L57 L58 L59 L60 L61 L62 L63 L64

L65

L66

L67

L68

L69

L70

L71

L72L73

DG3

DG1

DG2

10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

27

28

29

30

31 32 33 34

35

36

37

38 39 40 41 42 43 44 45

46 47 48 49

50

51

52

53 54 55 56 57 58 59 60 61 62 63 64

65 66

67 68


L27

L28

L29

L30

L31 L32 L33 L34

L35

L36

L37

L38 L39 L40 L41 L42 L43 L44 L45

L46

L47 L48 L49

L50

L51

L52

L53 L54 L55 L56 L57 L58 L59 L60 L61 L62 L63 L64

L65

L66

L67

L68

L69

L70

L71

L72L73

DG3DG1

DG2

5-5 the network reconfiguration results in a reduction of 6118 in feeder losses as

compared with the original network without DGs and a reduction of 1140 in




Fig 5-12 illustrates the optimal network configuration and DG locations In this case

the results show the final configuration with a feeder loss of 7397 kW with 6721

2517 and 1554 reduction in comparison with that in Case I Case II and Case

III respectively



Reduction

Page | 108

0

50

100

150

200

250

100 400 700 1000

Fee

de

r lo

ss (

kW)

DG Capacity (kVA)





is set as 100 500 900 and 1300 kVA respectively The feeder loss curves for

different DG capacities are shown in Fig 5-13 After simultaneous reconfiguration

and DG allocation the feeder loss decreases from 7397 kW to 873 kW when the

DG capacity is increased from 100 kVA to 900 kVA However the loss bounces

back to 114 kW if the DG capacity continues to increase to 1300 kVA This means

that the capability of network reconfiguration and DG allocation on feeder loss

reduction is limited when the size of DGs is large But the proposed methodology

can still reduce the total feeder loss for all DG capacities by determining the most

suitable network topology and DG locations in comparison with the original

configuration



Fig 5-14 shows the voltage profile of the 69-bus system It can be seen that the

voltage profiles at most buses in Case IV have been improved in comparison with

the other three cases Compared with Case III and Case IV the buses which inject

DGs show improvement in voltage profiles ie the voltage of Bus 60 is improved

from 09477 pu in Case III to 09571 pu in Case IV In Case IV although there are

three DGs connected as Bus 60 as the value of load connected at this bus is the

largest (1244 kW) this bus voltage is the lowest among all buses In conclusion the

systemrsquos voltage profiles are improved by optimal DNR and DG allocation


Reduction

Page | 109

086

088

09

092

094

096

098

1

102

0 5 10 15 20 25 30 35 40 45 50 55 60 65

Vo

ltag

e (

pu

)

Bus No

Case I

Case II

Case III

Case IV


55 Summary

In this chapter the application of optimal planning using DNR and DG allocation for

the problem of distribution feeder loss minimisation has been implemented The

method based on ACO has been successfully applied to the 1266 kV 33-bus and 69-

bus systems to find the optimum system configuration and DG locations

There are four cases used to analyse the superiority and performance of the proposed

method The proposed ACO is capable of finding the optimal solutions in all cases

In Case IV the feeder losses are reduced by 4662 and 6721 for the 33-bus and

69-bus system respectively in comparison with the base case Therefore Case IV is

found to be more effective in minimising the total loss and improving voltage

profiles compared to the other cases The numerical results show that for best

performance the existing tie-switches are relocated and the DGs are optimally

placed in comparison with the original network In addition the impacts of DG


reduction are also studied The inappropriate network configuration and DG location

might result in loss increment when the size of DG is increased The proposed

methodology has successfully reduced the total feeder loss for different capacities of

DG by determining the most suitable network topology and the DG locations


Reduction

Page | 110

compared to the original configuration The minimum loss obtained by DNR and DG

allocation decreases as the capacities of DGs are increased However this decrease

stops when DGs can supply all the loads without the main supply After that the

minimum loss increases as the capacities of DGs are increased

Moreover the simulation results have been compared with other classical methods in

literature and the proposed ACO is more efficient and is more likely to obtain the

global optimum solution

Page | 111

CHAPTER 6


RECONFIGURATION amp TRANSFORMER

ECONOMIC OPERATION FOR NETWORK

LOSS REDUCTION

61 Introduction

Rapid increases in electricity demand have forced electric power utilities throughout

the world into major reconstructing processes As a significant proportion of electric

energy is dissipated in the operation of a distribution network the reduction of loss

should be considered an important problem for the economic operation of the overall

system [82]

Load variations have been disregarded in most studies on distribution automation

(DA) problems ie average loads were used in their reconfiguration schemes In this

chapter distribution loads experience daily and seasonal variations The study

considers the daily load curves of different types of consumers (residential

commercial and industrial) and in addition the days are divided into eight types

spring weekdays spring weekends summer weekdays summer weekends autumn

Chapter 6 Distribution Network Reconfiguration amp Transformer Economic

Operation for Network Loss Reduction

Page | 112

weekdays autumn weekends winter weekdays and winter weekends The best

reconfiguration hours during each of these typical days are then selected

The objective function for finding the best configuration of the network when

considering feeder loss and transformer loss will be studied in this chapter Different

combinations of locations of tie-switches in the network and operation modes of all

transformers in the substations represent different network configurations An Ant

colony optimisation (ACO) algorithm is adopted on an 11 kV distribution network

developed from Bus 4 of the Roy Billinton Test System (RBTS) to determine the

optimal network configuration during each type of day Furthermore the effects of

DGs and EVs in solving distribution network reconfiguration (DNR) and

transformer economic operation (TEO) based on network loss reduction are also

investigated

This chapter is organised as follows the next section discusses the variation of loads

and the reconfiguration hours Section 63 presents the objective function and

constraints for DNR Section 64 describes the application of ACO algorithms to the

problem Numerical studies are presented and discussed in Section 65 and finally

Section 66 summarises the main conclusions

62 Time-varying Load Model

As distribution loads experience daily and seasonal variations the optimum network

configuration constantly changes [82] However it is not reasonable to reconfigure a

network frequently ie based on hourly schedule since each switch has a maximum

number of allowable switching operations during its lifetime and frequent switching

actions will increase its maintenance costs [82]

However infrequent actions cause the system to work well below its optimum state

In order to determine the best reconfiguration time during a day the daily load

profiles should be smoothed In other words the daily load curves are divided into a

number of periods As the maintenance cost of a switch increases with the increasing

number of switching actions the number of intervals is a trade-off between the

optimum reconfiguration and switch cost As there is a peak and a valley of network



Page | 113

Actual daily load curve

Smoothed daily load curve

load variations during a day it is appropriate to divide the 24 hours daily load curves

into two periods Increasing the number of intervals will not change the nature of the

problem but will increase its complexity

Fig 6-1 The reconfiguration hours for a typical day

As the difference between 1198751 and 1198752 is increased the effect of DNR on loss

reduction increases where 1198751 and 1198752 are the average active power of the loads

during the first and second time periods respectively As shown in Fig 6-1 hours

1199051and 1199052 are calculated to maximise |1198751 minus 1198752| It should also be noted that the above

load smoothing methodology is only used to determine the reconfiguration intervals

and the active power loss during each interval is calculated based on the actual daily

load curve [82]


In this study the 24 hours of a typical day is divided into two periods The first time

period is 0000 to 1199051 and 1199052 to 2400 and the second time period is between 1199051 and 1199052

The following objective function is calculated for all possible network configurations

during each time interval and the one that minimises the total power loss and

satisfies all constraints is selected The energy losses of the distribution network over

the first and second time interval are presented in (6-1) and (6-2) the objective

function (6-3) is to minimise f the sum of f1 and f2

P1

P2

1199051 1199052 Time (h)



Page | 114

1198911 = sum (119864119871119905 + 119879119871119905)1199051minus1119905=1 + sum (119864119871119905 + 119879119871119905) 1199051

24119905=1199052 isin 1 2 hellip 24 (6-1)

1198912 = sum (119864119871119905 + 119879119871119905)1199052minus1119905=1199051 1199052 isin 1 2 hellip 24 (6-2)

Min 119891 = 1198911 + 1198912 (6-3)

where 119864119871119905 is the feeder loss of the distribution network during hour t (kWh) 119879119871119905

represents the transformer loss during hour t (kWh) The detailed calculation of

transformer loss and feeder loss are presented in Section 27 and 28 respectively

The computed voltages currents and the power flow at all branches should be kept

in their permissible range and the network should be operated in radial The

configurations that violate any constraint are assigned with huge objective functions

and are disregarded

64 Applying ACO to DNR and TEO

In this chapter the objective of simultaneous reconfiguring network and changing

transformer operation modes is to deal with energy loss minimisation including

transformer loss and feeder loss To implement the optimisation problem the

developed ACO algorithm is adopted to find the optimum location of tie-switches

and transformer operation modes in the network When the location of tie-switches

and operation modes of transformers are changed a new network configuration will

be formed For each network configuration the objective function is evaluated by

using the approach presented in Section 63

The search space of the DNR and TEO problems is modelled as a directed graph as

shown in Fig 6-2 Each solution is represented by a string of integers which

indicates the transformer operation modes and the location of tie-switches The

number of the solutionrsquos elements is equal to the number of stages in this graph

which is the sum of the amount of main feeders (the number of transformer pairs 119873119904)

and the number of existing tie-switches 119873119905



Page | 115

Home

0 1

0 1

0 1

0 1

1 2 NPNP-1

1 2 NP-1 NP

1 2 NPNP-1

1 2 NP-1 NP

Food

Stage

1

2

Ns-1

Ns

Ns+1

Ns+2

Ns+Nt-1

Ns+Nt

Part 1

Number of

substations

Ns

Part 2 Number

of existing tie-

switches Nt

Number of candidate locations for the tie-switches NP

Fig 6-2 Search space of DNR and TEO

As shown in Fig 6-3 the number of transformer pairs is 3 and the number of

existing tie-switches is 4 Therefore the number of the solutionrsquos elements for this

system is 7 In addition the possible branches for tie-switch placement are 4



Page | 116

Tie-switch

Transformer

Fig 6-3 Sample network with three substations

For transformer operation mode selection in Part I the ACO algorithm is applied to

assign each bit of the front part of the solution vector to the status of substations and

hence the number of transformers in operation in each substation can be represented

as a binary vector

State 0 this substation has one transformer in operation

State 1 this substation has two transformers in operation

However for the relocation of existing tie-switches in Part II the states indicate the

location of switches Artificial ants will start their tours at home move along the

paths in the graph and end at the food source

The 24 hour load curve is divided into two time intervals for all load types in terms

of the principle presented in Section 62 Fig 6-4 demonstrates the computation

procedure for the transformer operation mode selection and tie-switches relocation

problem at each of the time interval The application of the ACO algorithm to the

TEO and DNR problem is similar to that in Section 532 For each time interval the

operation modes of the transformers are selected first and the locations of tie-

switches are then determined



Page | 117

Start

Set time interval T=1

Maximum iteration

reached

Output best


No

Yes

Divide the 24-h daily load curve into two

intervals using the technique in Section 62

Iteration N=1

Initialise the parameters for ACO

algorithm searching space

Dispatch ants based on the amount

of pheromone on edges

Relocate tie-switches and select the

number of transformers to be operated in

all substations by location lists

N=N+1

Calculate the objective function

for each ant at this time interval


and load data

The pheromones are updates

according to local and global rules

Record the best solution so far

and empty all location lists

T=T+1

Tgt2

Yes

t=t+1

No




Page | 118

LP11 LP12 LP13 LP14 LP15 LP16 LP17

LP8 LP9 LP10



LP29 LP30 LP31

LP26 LP27 LP28

LP18 LP19 LP20 LP21 LP22 LP23 LP24 LP25

19

20

21

22

23

24

26

25 27

28

29 30

71

13 15

14 16

17

18

69

1 3

2

5

4

7

6 8

10

9

68

11 12

56

57

58 60

59 61 62

65

64 66 67

50 52

51

54

53 55

44

45

46

47

48

49

70

31

32

33

34

36

35

39

37 38 40

41

42 43

63

F3

F2

F1

F7

F6

F5

F4

Normally Open Circuit BreakerNormally Closed Circuit Breaker

Subbus1

Subbus2

Subbus3

T1

T3

T5

Main

feeder

Main

feeder

Main

feeder

T2

T4

T6


In this study the proposed methodology is applied to an 11 kV distribution network

developed from Bus 4 of the RBTS a single-line diagram of the network is shown in

Fig 6-5 The network consists of 38 load points and 4 tie-switches the associated

data can be found in [114] The types and lengths of 11 kV feeders are listed in

Appendix A4 The network built in OpenDSS incorporates three 3311 kV double

transformer substations supplying the downstream loads

Fig 6-5 Distribution feeder connected to RBTS Bus 4

This typical urban distribution network supplies residential commercial and

industrial consumers The maximum value of active and reactive power and the



Page | 119

customer type of each node are modified from the original values and the new values

are listed in Table 6-1

Table 6-1 Revised customer data (peak load)

Number

of load

points

Load points Customer type P

(kW)

Q

(kVAr)

Number of

customers

4 1-2 9-10 residential 8869 8426 220

6 3-5 13-15 residential 8137 7731 200

12 6-7 16-17 23-25 28

30-31 37-38

commercial 6714 6378 10

6 8 11 18 26 32-33 industrial 2445 23228 1

10 12 19-22 27 29 34-

36

industrial 1630 15485 1

The days of the year are divided into eight categories spring weekdays spring

weekends summer weekdays summer weekends autumn weekdays autumn

weekends winter weekdays and winter weekends Typical loads profiles for

different consumer types are shown in Fig 6-6-6-8 which are multiplied by the

values of Table 6-1 to obtain the real demand of each node [82] In order to find the

reconfiguration hours for each day type the aggregated load profiles of the main

feeder shown in Fig 6-9 are used

Fig 6-6 Daily load profile of residential consumers



Page | 120

Fig 6-7 Daily load profile of commercial consumers

Fig 6-8 Daily load profile of industrial consumers

Fig 6-9 Daily load profile (MW) of the main feeder



Page | 121

In this case eight types of day and two time intervals for each of them are

considered As a result the optimisation problem has to be solved 16 times to obtain

a yearly reconfiguration scheme The distribution of load types for a whole year is

shown in Table 6-2

Table 6-2 The distribution of load types for a whole year

Load Types Number of days Total days

Spring

(Mar Apr May)

Weekdays 66 92

Weekends 26

Summer

(Jun Jul Aug)

Weekdays 66 92

Weekends 26

Autumn

(Sep Oct Nov)

Weekdays 65 91

Weekends 26

Winter

(Dec Jan Feb)

Weekdays 64 90

Weekends 26

Year 365 Days

For the purpose of better illustration and comparison three test cases are considered

to analyse the superiority and performance of the proposed method

Test Case 1 The system is optimally reconfigured and has no DGs and EVs

Test Case 2 The system is optimally reconfigured after DGs are placed at certain

buses

Test Case 3 The system is optimally reconfigured after integration of EVs

The proposed ACO algorithm is coded in the MATLAB to obtain the location of tie-

switches and operation modes of transformers for the optimum configuration The

settings of the ACO parameters that provided the optimum solution for these three

cases are presented in Appendix C2 The selection of parameters is a balance

between the convergence rate and the global search ability of the algorithm



Page | 122

651 Test Case 1

In this test the tie-switches are relocated and the operation modes of transformers in

all substations are changed to obtain the best network configuration with minimum

network loss

Table 6-3 Results of DNR and TEO with different load types in Test Case 1

As shown in Fig 6-5 the tie-switches are located in L68-71 and each substation has

two transformers operating in parallel for the base network configuration The test

results with different load conditions are presented in Table 6-3 Reconfiguration of

the network and changes in the operation modes of transformers in all substations

using the proposed algorithm result in a reduction of loss for all load conditions As

a result the annual energy loss is reduced from 4337150 kWh to 4117681 kWh

which amounts to a 506 reduction Both transformer loss and feeder loss are

reduced through this optimal planning using DNR and TEO It can be noted that on

winter weekdays the loading of the main feeders is very high from 800 to 2100

Spring

weekday

Spring

weekend

Summer

weekday

Summer

weekend

Autumn

weekday

Autumn

weekend

Winter

weekday

Winter

weekend

Before

Reconfiguration

Whole Day Open branches L68L69

L70L71

L68L69

L70L71

L68L69

L70L71

L68L69

L70L71

L68L69

L70L71

L68L69

L70L71

L68L69

L70L71

L68L69

L70L71

Number of operated

transformers

1st substation 2 2 2 2 2 2 2 2

2nd substation 2 2 2 2 2 2 2 2

3rd substation 2 2 2 2 2 2 2 2

Loss

(kWh)

Cable 9233 3498 8050 3151 9660 3665 11009 4080

Transformer 4301 3410 4109 3350 4372 3437 4597 3507

Total 13534 6908 12159 6501 14032 7102 15606 7587

After

Reconfiguration

1st interval Time (h) 0-7

23-24

0-6 0-7

23

0-7 0-7

22-23

0-6

0-7

22-23

0-6

Open branches L48L68

L69L71

L68L69

L70L71

L17L68

L70L71

L17L68

L70L71

L17L68

L70L71

L68L69

L70L71

L17L68

L70L71

L68L69

L70L71

Number of operated

transformers




2nd interval Time (h) 8-22 7-23 8-22 8-23 8-21 7-23 8-21 7-23


L65L70

L68L69

L70L71

L41L48

L65L69

L68L69

L70L71

L17L41

L65L70

L68L69

L70L71

L17L41

L65L70

L68L69

L70L71

Number of operated

transformers




Loss

(kWh)

Cable 9043 3516 7851 3169 9519 3685 10845 4103

Transformer 3955 2616 3759 2517 4036 2656 4264 2755

Total 12998 6132 11610 5686 13479 6341 15109 6858



Page | 123

0

05

1

15

2

25

3

35

4

45

05 1 15 2 25 3

Before reconfiguration

After reconfiguration

Thus transformers in all substations are operated in parallel However during spring

weekends from 000 to 700 as the loadings supplied by all feeders are lower than

the critical transformer load factor (TCLF) and hence transformers in all substations

are operated in single In addition the loadings supplied by Feeder 4 are much larger

than that of Feeder 3 in summer weekdays between 800 to 2200 Thus the tie-

switch is moved from L71 to L41 and LP24amp25 are moved from Feeder 4 to Feeder

3 This ensures balancing of the loads between the two feeders

652 Test Case 2

In this test the presence of three DG units is taken into consideration The effect of

DGs on assessing the DNR and TEO problems in terms of loss minimisation is

studied The introduction of DGs converts a mono-source distribution network to a

multi-source one [66] The three DGs are located at the end of the feeders ie Bus

17 41 and 65 All the DGs are synchronous generators and considered as PQ models

The capacity of DG is assumed to be 05 1 15 2 25 and 3 MVA respectively

The results are shown in Fig 6-10 and show that the proposed methodology has

successfully reduced the total energy loss for different capacities of DG by

determining the most suitable network topology

Fig 6-10 Annual energy loss with different DG capacities

To

tal

loss

(G

Wh

)

DG Capacity (MW)



Page | 124

653 Test Case 3

The objective of this section is to illustrate the behaviour of the proposed

optimisation process when EVs are integrated into the existing distribution network

The impacts of EV penetration levels and charging strategies are studied This

section utilises the optimal planning using DNR and TEO as a technique to decrease

network loss whilst respecting the operation constraints It is assumed that the

battery starts charging once the EV is connected to the charger at home

The charging duration can be calculated according to the following formula [89]

119905119888 =119862119864119881times(1minus119878119874119862)times119863119874119863

120578times119875119862 (6-4)

where 119862119864119881 is the battery capacity In this section EVs are divided into four types

with different market shares and batteries as in Table 6-4 [115] 119863119874119863 and 120578 are

depth of discharge and charger efficiency (assumed to be 80 and 90 separately)

Two types of chargers with different charging rates (119875119862) are commonly used for

consumer EVs at home charging points this study assumes that 80 of EVs are

charged at 3kW (13A) and 20 at 7kW (30A) [92] SOC is state-of-charge and is

defined as the ratio of available energy to maximum battery capacity [89] It is

determined by the distance covered by the EV in terms of number of miles during

the day

Table 6-4 Characteristics of EV

Types 119862119864119881 (kWh) Maximum driving

capability (mile)

Market share ()

Micro car 12 50 20

Economy car 14 53 30

Mid-size car 18 56 30

Light truck SUV 23 60 20

According to [116] the average number of miles covered by a vehicle was reported

to be 2164 milesday in 2014 Then the SOC for an EV is calculated based on

number of miles (m) and the maximum driving capability (MDC) as follows



Page | 125

4

42

44

46

48

5

30 60 90



119878119874119862 = 0 119898 gt 119872119863119862

119872119863119862minus119898

119872119863119862 119898 le 119872119863119862 (6-5)

As mentioned before the EVs are distributed over all the residential load points The

number of customers of residential loads is given in Table 6-1 It is reported that

each customer has 15 vehicles [92] The problem is solved for three different

penetration levels of EVs in the test network 30 60 and 90 respectively In

addition two charging strategies are introduced (1) uncoordinated charging and (2)

coordinated charging The thermal problems of cables which caused by high

penetration levels of EVs are ignored in this study

1) Uncoordinated Charging Strategy

In this part all EVs are plugged in and immediately start charging when they arrive

home In most cases the EV plug-in time is modelled by normal distribution which

increases uncertainty However in order to simplify the discussion the charging start

time is assumed to be 1800 when most people are back home from work The total

losses in the network for the different penetration levels of EVs are compared in Fig

6-11 It can be seen that as the penetration of EVs is increased the total loss also

increases But the total loss for all penetration levels decreases by implementing the

optimal planning strategy in comparison with the original network

Fig 6-11 Annual energy loss in uncoordinated charging strategy

To

tal

loss

(G

Wh

)

Penetration level ()



Page | 126

4

42

44

46

48

5

30 60 90



2) Coordinated Charging Strategy

In this case the DNOs tend to charge the EVs during off-peak hours to avoid a clash

with the evening peak hours As a result the charging start time is delayed to 0100

when most people are sleeping The total network loss for different EV penetrations

is compared in Fig 6-12 The results show that the postponement of charging time

and optimal planning strategy has been successful in reducing the total energy loss in

comparison with the uncoordinated charging method

Fig 6-12 Annual energy loss in coordinated charging strategy

66 Summary

This study has presented a new optimal planning strategy using DNR and TEO for

distribution network loss minimisation including transformer loss and feeder loss In

this study the distribution loads experience daily and seasonal variations The day is

divided into two periods The proposed ACO algorithm has been successfully

applied to the modified Bus 4 of the RBTS to find the optimum network

configuration and economic operation mode of transformers in all substations during

each time interval Using the results obtained for reconfiguration the existing tie-

switches are relocated and the transformer operation modes are changed

Furthermore the simulation results obtained with numerical studies further

demonstrate the capability of applying the ACO algorithm to distribution network

planning including networks with DGs and EVs The proposed methodology has

successfully reduced the total network loss for different capacities of DG and

To

tal

loss

(G

Wh

)




Page | 127

different penetration levels of EVs by determining the most suitable network

topology compared to the original configuration The benefits associated with the

increasing capacity of DGs and increasing penetration levels of EVs are also

presented Comparative results show that coordinated charging of EVs results in less

energy loss compared to uncoordinated charging plan with the same EV penetration

level This is due to the postponement of charging time which avoids a clash with

the peak power demand times

The proposed ACO algorithm is suitable for planning a future network based on the

load estimation results Hence there is no limitation on the calculation time An

additional interesting point about DNR and TEO is that although the opening and

closing of switches and transformers result in the life reduction of plants the

additional costs for utilities is insignificant in comparison with the benefits they

bring All the results have proved that a distribution network can be reconfigured and

the operation modes of transformers can be changed to reduce network power loss

which can increase the profits of the distribution utilities

Page | 128

CHAPTER 7

OPTIMAL PLACEMENT OF

SECTIONALISING SWITCHES FOR

RELIABILITY IMPROVEMENT

71 Introduction

Failures in the distribution network cause the majority of service interruptions [78]

And reliability improvement becomes a motivation for distribution utilities to launch

research and demonstration projects [64] An effective method to reduce customer

minutes lost is the greater and more effective use of automated and remote controlled

sectionalising switches and feeder breaker automation This approach will reduce

customer restoration time and minimise the region of a network affected by a short-

circuit fault The effectiveness depends on the number location and type of

sectionalising switches and feeder breakers

Reliability improvement by reduction of expected customer damaged cost (ECOST)

and system interruption duration index (SAIDI) as well as the minimisation of

switch costs are considered in formulating the objective function used in this study

When there are multiple objectives to be considered a compromise solution has to

be made to obtain the best solution ECOST and switch costs can be converted into a

single objective function by aggregating these objectives in a weighted function

Chapter 7 Optimal Placement of Sectionalising Switches for Reliability

Improvement

Page | 129

However as SAIDI and switch costs have different dimensions and units a single

fuzzy satisfaction objective function is used to transform the two conflicting

objectives into fuzzy memberships and then finally to combine them into a single

objective function Also a fuzzy membership function based on the max-min

principle is presented for optimising ECOST SAIDI and switch costs

simultaneously These are achieved by the optimal installation of new switches and

the relocation of existing switches Therefore identifying the number and location of

switches becomes an optimisation problem The ant colony optimisation (ACO) is

adopted which has the ability to find near optimal solutions close to the global

minimum in a finite number of steps This algorithm is proposed for the assessing

the sectionalising switch placement (SSP) problem based on reliability improvement

and switch costs minimisation using a multi-objective function with fuzzy variables

The impact of benefit-to-cost analysis is then investigated to justify investment

expenses Furthermore the importance of the customer damage function (CDF)

variation in determining the SSP is investigated through sensitivity analysis And the

ACO parameter sensitivity analysis is also provided in this study

The mathematical formulation of the objective function is presented in Section 72

and in Section 73 the applied ACO algorithm used to address the problems of SSP

is discussed Section 74 describes the benefit-cost analysis and the numerical case

studies are presented and discussed in Section 75 The main conclusions of the study

are summarised in Section 76


The primary objective of this study is to resolve the three conflicting objectives

reduction of unserved energy cost decrease in the average time a customer is

interrupted and minimisation of switch costs Three formulations of objective

functions are presented and the solution is a trade-off between each objective

721 Weighted Aggregation

As ECOST and switch costs have the same units and dimensions they are

transformed into a single objective function by aggregating all the objectives in a

weighted function


Improvement

Page | 130

119872119894119899 119869 = micro1 ∙ 119864119862119874119878119879 + micro2 ∙ 119878119862 (7-1)

where ECOST is the system expected outage cost to customers ($) and SC is the cost

of sectionalising switches ($) micro1and micro2 are the weighting factors given to the

reliability index and the cost of switches

722 Single Fuzzy Satisfaction Objective Function with Two

Parameters

SAIDI and switch costs are associated with a membership function in a fuzzy

domain due to different dimensions The satisfaction level of each objective is

represented by the membership function [66] The higher the membership value is

the better the solution is The two objectives are combined into a fuzzy environment

and a final objective function is formulated as follows

119872119886119909 119870 = 1205961 ∙ 120572119878119860 + 1205962 ∙ 120572119878119862 (7-2)

where 120572119878119860 is the membership function value to distribution reliability improvement

by SAIDI reduction 120572119878119862 is the value of membership function for a decrease in the

switch costs 1205961and 1205962 are the constant weighting factors for each of the parameters

The optimisation process can be changed for different purposes by varying the

values of weighting factors which should satisfy the condition 1205961 + 1205962 = 1 A

higher weighting factor indicates that this parameter is more important [66] In the

fuzzy domain each objective has a membership value varying from zero to unity

[66] The proposed membership function for each objective is described below

Membership function for SAIDI reduction

The basic purpose of this membership function is to improve reliability or obtain the

minimum SAIDI Therefore the placement of sectionalising switches with a lower

SAIDI value obtains a higher membership value The membership function for

reliability improvement is formulated in (7-3) and presented in Fig 7-1 (a) As

SAIDI becomes greater than 119878119860119868119863119868119898119894119899 the degree of satisfaction is decreased This

reduction is continued until SAIDI reaches 119878119860119868119863119868119900119903119894


Improvement

Page | 131

0

1

0

1

120572119878119860 =

1 119878119860119868119863119868 le 119878119860119868119863119868119898119894119899119878119860119868119863119868119900119903119894minus119878119860119868119863119868

119878119860119868119863119868119900119903119894minus119878119860119868119863119868119898119894119899119878119860119868119863119868119898119894119899 lt 119878119860119868119863119868 lt 119878119860119868119863119868119900119903119894

0 119878119860119868119863119868 ge 119878119860119868119863119868119900119903119894

(7-3)

where 119878119860119868119863119868119900119903119894 is the SAIDI of the original network 119878119860119868119863119868119898119894119899 is the minimum

value of SAIDI which is obtained by placing sectionalising switches in all candidate

locations As it is not appropriate for decision makers to obtain a combination of

sectionalising switches which reduces reliability after switch placement the

minimum value of 120572119878119860 is selected as 0 if SAIDI is greater than or equal to 119878119860119868119863119868119900119903119894

(a) SAIDI reduction (b) SC reduction

Fig 7-1 Membership function for SAIDI and switch cost reduction

Membership function for switch cost reduction

The membership function for switch costs reduction is shown in Fig 7-1(b) The

mathematical equation is presented below

120572119878119862 =

1 119878119862 le 119878119862119900119903119894119878119862119898119886119909minus119878119862

119878119862119898119886119909minus119878119862119900119903119894119878119862119900119903119894 lt 119878119862 lt 119878119862119898119886119909

0 119878119862 ge 119878119862119898119886119909

(7-4)

where 119878119862119900119903119894 and 119878119862119898119886119909 are the original and maximum value of switch costs

respectively The maximum switch costs are obtained by installing sectionalising

switches in all candidate sites

723 Single Fuzzy Satisfaction Objective Function with Three

Parameters

When there are more than two objectives with different dimensions and units to be

satisfied simultaneously a single fuzzy satisfaction objective function based on the

120572119878119860

119878119860119868119863119868119898119894119899 119878119860119868119863119868119900119903119894 119878119860119868119863119868

120572119878119862

119878119862119900119903119894 119878119862119898119886119909 119878119862


Improvement

Page | 132

0

1

max-min principle is considered The three conflicting objectives to be optimised are

ECOST SAIDI and switch costs The membership functions for SAIDI and switch

costs are presented in the previous section The function for ECOST is shown in Fig

7-2 and expressed as

120572119864119862 =

1 119864119862119874119878119879 le 119864119862119874119878119879119898119894119899119864119862119874119878119879119900119903119894minus119864119862119874119878119879

119864119862119874119878119879119900119903119894minus119864119862119874119878119879119898119894119899119864119862119874119878119879119898119894119899 lt 119864119862119874119878119879 lt 119864119862119874119878119879119900119903119894

0 119864119862119874119878119879 ge 119864119862119874119878119879119900119903119894

(7-5)

where 119864119862119874119878119879119900119903119894 and 119864119862119874119878119879119898119894119899 are the original and minimum value of ECOST

respectively The minimum ECOST is obtained by installing sectionalising switches

in all candidate locations

Fig 7-2 Membership function for ECOST reduction

The degree of overall satisfaction for these objective functions is the minimum value

of all the membership functions [85] The fuzzy decision for a final compromised

solution is the maximum degree of overall satisfaction and is formulated in (7-6)

Max 119871 = min (120572119878119860 120572119878119862 120572119864119862) (7-6)

724 Evaluation of ECOST

ECOST is an index that combines reliability with economics The best way to

present customer interruption costs is in the form of CDF A CDF provides the

interruption cost versus interruption duration for a various class of customers and

can be aggregated to produce a composite CDF at any particular load point [67] [69]

Generally ECOST is used to represent the customer outage costs since it not only

considers the effects of the system configuration interruption durations load

variations and equipment failure probability but also accounts for the various

customer types and their damage functions [52]

120572119864119862

119864119862119874119878119879119898119894119899 119864119862119874119878119879119900119903119894 119864119862119874119878119879


Improvement

Page | 133

The calculation of ECOST of the total system over T years is based on failure-mode-

and-effect analysis (FMEA) and can be quantified as follows

1 ( 1)

1 1 1 1 1 1

( ) ( ) ( ) ( ) (1 ) (1 )b b b b bN CT NR CT NST

t t

b b k R k s

t b k j k j

ECOST L P k j C d P k j C d IR DR

(7-7)

where T is time period (year) 119873119887 is the total number of branches 120582119887and 119871119887 are the

average failure rate (failurekm-year) and length (km) of branch b 119862119879119887 119873119877119887 and

119873119878119887 are the total number of customer types permanent damaged and temporary

damaged load points when the fault is at branch b P(k j) is the average load of the

kth-type customers at the jth load point (kW) 119862119896(119889) is the CDF for kth-type

customer lasting d hours ($kW) 119889119877 and 119889119878 are the average repair time and the

switch time after failure IR and DR are the annual load increase rate and discount

rate

725 Evaluation of SAIDI

The SAIDI which represents the average outage duration time of each customer

over T years can be expressed as

119878119860119868119863119868 = sum sum 120582119887∙119871119887[sum 119889119877

119873119862119877(119887)119899=1 +sum 119889119878

119873119862119878(119887)119899=1 ]

119873119887119887=1

119873119862119905119900119905119886119897119879

119905=1 (7-8)

where 119873119862119877(119887) and 119873119862119878(119887) are the number of permanent damaged and temporary

damaged customers when the fault is at branch b 119873119862119905119900119905119886119897 is the total number of

served customers SAIDI is measured in hours

726 Evaluation of Switch Costs

In this study reliability is improved by the installation of new sectionalising

switches and relocation of existing switches Thus the total cost of switches can be

determined as following

119878119862 = 119862119868119878 ∙ 119873119899119890119908 + 119862119877119878 ∙ 119873119903119890119897 + sum 119872119862119879119905=1 ∙ (119873119899119890119908 + 119873119890119909119894119904) ∙ (1 + 119863119877)minus(119905minus1) (7-9)

where CIS is the investment and installation cost of a new sectionalising switch ($)

119873119899119890119908 119873119903119890119897 and 119873119890119909119894119904 are the number of newly installed relocated and existing

sectionalising switches respectively CRS is the relocation cost of an existing


Improvement

Page | 134

Home

0

1

0

1

0

1

0

1

Food

Number of candidate locations for sectionalising switches

sectionalising switch ($) and MC is the maintenance and operation cost of a

sectionalising switch ($)

73 Applying ACO to Sectionalising Switch Placement

Problem

This study uses ACO algorithm for distribution automation in terms of the

installation of new sectionalising switches and relocation of existing switches When

the locations of sectionalising switches are changed a new network configuration

will be formed The search method is used for finding the optimal value of objective

functions as presented in Section 721-723

The search space of the automation problem in terms of SSP is modelled as a

directed graph as shown in Fig 7-3 The number of stages is the candidate locations

for all the sectionalising switches 119873119878 For this problem the switch status can be

represented as a binary vector in each stage State 0 ldquono sectionalising switch in this

locationrdquo State 1 is ldquoa sectionalising switch in this locationrdquo The artificial ant

searches for the values of the bits and produces a solution to the problem after it

completes a tour between the home and food source which is similar to the process

described in Section 532

Fig 7-3 Search space of sectionalising switch placement


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Page | 135

74 Benefit-to-cost Analysis

The benefit-to-cost analysis is a financial term that describes the expected balance of

benefits made from the investment and costs incurred during the production process

It helps predict if an investmentdecision is feasible and whether its benefits

outweigh the costs during a predefined time interval [82]

In this study the benefit-to-cost ratio (BCR) offers a comparison between ECOST

and SC The benefit to the distribution network operator (DNO) is the reduction of

ECOST which is equal to

119887119890119899119890119891119894119905 = sum119864119862119874119878119879119887119886119904119890

119905 minus119864119862119874119878119879119900119901119905119905

(1+119863119877)119905119879119905=1 (7-10)

where 119864119862119874119878119879119887119886119904119890119905 and 119864119862119874119878119879119900119901119905

119905 are the value of ECOST of year t before and after

the placement of switches ($)DR is the annual discount rate

The cost for the DNO is the total switching cost including investment maintenance

and operation cost as presented in (7-9) and BCR is defined as

119861119862119877 =119887119890119899119890119891119894119905

119878119862 (7-11)

A higher value for BCR indicates that the benefits relative to the costs are greater

The investment return time refers to the time when BCR starts to exceed 10 If the

investment return time is less than the lifetime of a switch adding a switch will bring

benefits to the investors


Improvement

Page | 136


LP8 LP9 LP10



LP29 LP30 LP31

LP26 LP27 LP28


9 10 11 12 13 33

6 7 8 31

1 2 3 4 5 30

25 26 27 29

22 23 24

19 20 21

32

14 15 16 17 18

28

F3

F2

F1

F7

F6

F5

F4


Subbus1

Subbus2

Subbus3

T1

T3

T5

Main

feeder

Main

feeder

Main

feeder

T2

T4

T6



developed from Bus 4 of the Roy Billinton Test System (RBTS) The single-line

diagram of the network with 6 existing sectionalising switches is shown in Fig 7-4


In this study there are 51 locations considered as candidates for switch placement

[114] All the values of the required data ie feeder type and length as well as

component failure rate are available in [114] and summarised in Appendix A4 The

failure rate of the feeders is proportional to their physical length and all other


Improvement

Page | 137

components ie transformers buses and breakers are assumed to be completely

reliable This typical urban distribution network supplies residential commercial and

industrial consumers The average value of active power and the customer type of

each node were also found in [114] and listed in Table 7-1 The power factors of all

the loads are set to 10

Table 7-1 Customer data (Average load)

Number

of load

points


(kW)

Number of

customers

15 1-4 11-13 18-21 32-35 residential 545 220

7 5 14 15 22 23 36 37 residential 500 200

7 8 10 26-30 industrial 1000 1

2 9 31 industrial 1500 1

7 6 7 16 17 24 25 38 commercial 415 10

The relocation cost of a sectionalising switch is US $ 500 The investment and

installation cost of a sectionalising switch is US $ 4700 [64] The annual

maintenance and operation cost is considered to be 2 of the investment cost [64]

All the sectionalising switches and circuit breakers are remotely controlled The

costs of the feeder terminal unit which is used for data acquisition of the switch

status and communication equipment have also been added to the automated

sectionalising switches The overall switching time of sectionalising switch and

circuit breakers for temporary damage load points in other words the time between

the occurrence of a fault and the restoration of energy to unaffected areas is set to 10

minutes [64] And the average repair time of the permanent faulty section is assumed

to be 5 hours The lifetime of a switch depends on various factors such as the

maximum number of allowable switching operations the number of annual

switching operations of the switch etc Based on these factors the life period of the

switches is calculated to be 15 years The load growth rate and the annual interest

rate are set to 3 and 8 respectively The CDF data are extracted from [64] and

summarised in Table 7-2


Improvement

Page | 138

Table 7-2 Sector interruption cost estimation ($kW)

User Sector Interruption Duration

10 min 1 hour 2 hour 4 hour 5 hour 10 hour

Residential 006 11 16 26 316 5

Industrial 288 806 95 124 1387 276

Commercial 205 96 125 185 2151 6306

The proposed ACO algorithm was coded in the MATLAB to obtain the location of

the sectionalising switches In this study three cases with different objective

functions are considered to analyse the superiority and performance of the proposed

method

Test Case 1 Minimisation of ECOST and switch costs

Test Case 2 Minimisation of SAIDI and switch costs

Test Case 3 Minimisation of ECOST SAIDI and switch costs

The final combinations of the ACO control parameters that provide the best results

for all the above tests are given in Appendix C3

751 Test Case 1

In this test the minimisation of ECOST and switch costs are considered in the

formulation of a single objective function this involves aggregating the objective

functions as presented in Section 721 For simplicity both weighting factors micro1

and micro2 are set to 1 ie these two objectives are assumed to be equally important

Three cases are studied as follows

Case 11 Optimal relocation of existing sectionalising switches

Case 12 Optimal installation of new sectionalising switches

Case 13 Optimal installation of new sectionalising switches and relocation of

existing sectionalising switches


Improvement

Page | 139


LP8 LP9 LP10



LP29 LP30 LP31

LP26 LP27 LP28


9 10 11 12 13 33

6 7 8 31

1 2 3 4 5 30

25 26 27 29

22 23 24

19 20 21

32

14 15 16 17 18

28

F3

F2

F1

F7

F6

F5

F4


Subbus1

Subbus2

Subbus3

T1

T3

T5

Main

feeder

Main

feeder

Main

feeder

T2

T4

T6


The objective of this case is to investigate the optimum sectionalising switch

relocation problem The optimal locations of sectionalising devices are shown in Fig

7-5 Before relocation the total cost including ECOST operation and maintenance

cost of existing switches over 15 years is US $ 477090 After relocation the total

cost including the addition of relocation cost obtained by the ACO approach is US

$ 343620 which amounts to a reduction of 2798

Fig 7-5 Optimal relocation of sectionalising switches in Test Case 11


Improvement

Page | 140

In comparison with the original configuration 4 switches change their locations The

optimal locations of sectionalising switches and the number and types of loads

adjacent to each switch are presented in Table 7-3 The results indicate that each

feeder attempts to have at least one switch As there are 6 switches and 7 feeders

and the total load level of Feeder 5 is 3000 kW which is the lowest value for all the

feeders no switch is placed on Feeder 5 It should also be noted that the load

density and customer types play an important role in determining the locations of

sectionalising switches For instance the adjacent load of Switch 1 is LP6 and LP7

which has the highest CDF value (commercial load) and relatively high load levels

In addition Switch 2 is placed on 7D whose adjacent load is LP9 and this has the

largest load density

Table 7-3 Results of sectionalising switches relocation in Test Case 11

Switch

No

Feeder Location Total Feeder

Load (kW)

Adjacent Load Adjacent Load Levels (kW) and

Type

1 1 5D 3510 LP6 LP7 415 (commercial) 415 (commercial)

2 2 7D 3500 LP9 1500 (industrial)



5 6 23D 3500 LP30 1000 (industrial)

6 7 28D 3595 LP36 500 (commercial)

( Each section has two candidate locations for sectionalising switch placement U means upstream side of the section and D

means downstream side of the section)


In this case the effect of installing new sectionalising switches without relocating

the existing switches is studied As shown in Fig 7-6 there are 11 new

sectionalising switches installed

The detailed results of ECOST capital and installation as well as the operation and

maintenance cost of sectionalising switches over 15 years are shown in Table 7-4

After the installation of sectionalising switches the total system cost is decreased

from US $ 477090 to US $ 286980 ie a reduction of 3984


Improvement

Page | 141


LP8 LP9 LP10



LP29 LP30 LP31

LP26 LP27 LP28


9 10 11 12 13 33

6 7 8 31

1 2 3 4 5 30

25 26 27 29

22 23 24

19 20 21

32

14 15 16 17 18

28

F3

F2

F1

F7

F6

F5

F4


Subbus1

Subbus2

Subbus3

T1

T3

T5

Main

feeder

Main

feeder

Main

feeder

T2

T4

T6

Fig 7-6 Optimal installation of sectionalising switches in Test Case 12

Table 7-4 Results of sectionalising switches installation in Test Case 12

ECOST

($)

Number of

installed

switches

Capital and

installation cost

($)

Maintenance

and operation

cost ($)

Total system

cost ($)

Before switches

installation

472260 0 0 4830 477090

After switches

installation

221610 11 51700 13670 286980


Improvement

Page | 142


LP8 LP9 LP10



LP29 LP30 LP31

LP26 LP27 LP28


9 10 11 12 13 33

6 7 8 31

1 2 3 4 5 30

25 26 27 29

22 23 24

19 20 21

32

14 15 16 17 18

28

F3

F2

F1

F7

F6

F5

F4


Subbus1

Subbus2

Subbus3

T1

T3

T5

Main

feeder

Main

feeder

Main

feeder

T2

T4

T6

Case 13 Optimal relocation and installation of sectionalising switches

A Base case

The main objective of this test is to reduce the total system cost including ECOST

and switch costs by the relocation of existing sectionalising switches and the

installation of new ones The switch locations are presented in Fig 7-7

Fig 7-7 Optimal installation and relocation of sectionalising switches in Test Case 13

In comparison with the original configuration there are 8 new sectionalising

switches installed and 5 existing switches relocated As expected the sectionalising

switches are placed adjacent to the load centres with either the highest load density


Improvement

Page | 143

0

1

2

3

4

5

6

7

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

BC

R

Years

or the highest CDF For example the adjacent load of switch 13D is LP6 and LP7

which has the highest CDF value (commercial loads) In addition switch 7D is

placed adjacent to LP9 which has the largest load density The detailed results for

ECOST and switch costs are shown in Table 7-5 After the installation and relocation

of the switches the total system cost is decreased from US $ 477090 to US

$ 272480 ie a reduction of 4289

Table 7-5 Results of sectionalising switches relocation and installation in Test Case 13

ECOST

($)

Number of

relocated

switches

Relocation

cost ($)

Number of

installed

switches

Capital and

installation

cost ($)

Maintenance

and operation

cost ($)

Total

system

cost ($)

Before switch

placement

472260 0 0 0 0 4830 477090

After switch

placement

221120 5 2500 8 37600 11260 272480

B Benefit-to-Cost analysis

BCR analysis is used to verify the benefits and costs of sectionalising switch

placement for distribution operators The results are presented in Fig 7-8 The

benefits and costs are accumulated during the predefined life period There is no

return on investment for the first year as the BCR for Year 1 is 055 However the

BCR for Year 2 is 108 which means the investors start to get benefits in Year 2 In

addition switch placement proved to be a feasible investment since the BCR is

increased to 620 when the switch achieves its service life 15 years in this study

Fig 7-8 BCR versus years


Improvement

Page | 144

0

20

40

60

80

100

120

140

160

05 1 15 2 25 3 35 4 45 5 55 6 65 7 75 8

Co

st (

th

ou

san

d $

)

CDF multiplier

ECOST

Switch costs

Total costs

C Sensitivity analysis

To demonstrate the impact of changing the values of different parameters on the

corresponding results several sensitivity analysis studies are discussed

CDF variation sensitivity analysis

The main objective of this test is to assess the behaviour of the proposed approach

when the CDF (customer damage function) is varied The CDF is increased from 50

to 800 of its initial value in 50 increments The original value of the CDF

multiplier is 100 The effect of variation in the CDF on the ECOST switching

costs and the total system cost is plotted in Fig 7-9 Switch costs include

sectionalising switch installation relocation operation and maintenance cost The

ECOST and switching costs increase as the CDF is increased However the

difference between ECOST and switching costs is also increased

Fig 7-9 Variation of cost versus change in CDF

Variations of the optimal number of installed sectionalising switches versus the CDF

are presented in Fig 7-10 The optimal number of newly installed switches increases

from 7 to 34 as the CDG multiplier is increased from 05 to 8 This indicates the

network needs to be more automated especially if the consequence of customer

damage becomes more serious However the growth in the optimal number of

sectionalising switches is slowing down As shown in Fig 7-10 when the CDF

multiplier increases above 3 the number of sectionalising switches remains at 32 as


Improvement

Page | 145

0

5

10

15

20

25

30

35

40

05 1 15 2 25 3 35 4 45 5 55 6 65 7 75 8

Nu

mb

er

of

swit

che

s

CDF multiplier

the reduction of ECOST brought by installing a sectionalising switch is small

compared to the increase in switch costs Only when the CDF multiplier reaches 55

does the reduction of ECOST outweigh the installation cost of a switch and hence

acquiring a sectionalising switch is a cost-effective investment This is due to the fact

that the installation of the first sectionalising switch has the largest effect on

reducing the total system cost and the impact of sectionalising switch installation on

ECOST decreases as the network becomes more automated

Fig 7-10 Number of installed sectionalising switches versus change in CDF

ACO parameters sensitivity analysis

The ACO parameter analysis is provided in this section In each test only one

parameter is changed whilst the others remain constant The convergence number is

defined as the number of the iterations when the objective function is convergence

The assessment of the impact of the pheromone evaporation rate ρ on the proposed

algorithm is presented in Table 7-6 The number of ants is 200 and the iteration time

is 400 Parameter ρ is varied from 01 to 06 with an increment of 01 For each ρ the

test is run 100 times Table 7-6 shows the impacts of the ρ variation on the objective

function J It can be seen the evaporation rate ρ has a considerable impact on the

convergence performance of the ACO algorithm When ρ is small the residual

pheromone on the path is dominant and the positive feedback of pheromone is weak

This results in an increment in the stochastic performance and global search ability


Improvement

Page | 146

of the ACO algorithm but a reduction in the convergence rate When ρ is large the

positive feedback of the pheromone is dominant which results in an improvement in

the convergence rate but a reduction in the search ability of the algorithm In other

words the algorithm is more easily trapped into a local optimal solution In summary

the selection of ρ is based on two factors of the algorithm 1) convergence rate 2)

global search ability As shown in the table the best value of ρ for this case is 04

which results in the minimum average value and has a suitable convergence rate

Table 7-6 Impacts of 120588 variation on objective function 119869

120588 Objective function value Average convergence

number Average Maximum Minimum

01 273120 274810 272480 223

02 273400 275960 272480 175

03 273480 274810 272480 132

04 273100 274810 272480 110

05 273550 274810 272480 94

06 273440 274810 272480 81

Table 7-7 presents the impacts of the variation in the number of ants on objective

function J The evaporation rate is 04 and the iteration number is 400 The number

of ants is changed from 100 to 500 with an increment of 100 The greater the

number of ants the more likely the global optimum value is achieved This is due to

the growth in global search capability However the convergence rate decreases To

balance the global search ability and convergence rate the number of ants is set to

400

Table 7-7 Impacts of variation in number of ants on objective function 119869

Number of ants Objective function value Average convergence


100 273865 276120 272480 91

200 273100 274810 272480 110

300 273030 274370 272480 135

400 272820 274230 272480 168

500 273170 274230 272480 245


Improvement

Page | 147

However in this study the proposed approach is used for planning a future network

Thus the computation time is not an issue The number of ants and iteration should

be large enough for the ACO algorithm to find the global optimum solution

752 Test Case 2

The objective of this test is to minimise SAIDI and switch costs by maximising the

fuzzy bi-objective function as presented in Section 722 The results of the

membership values of objectives SAIDI as well as switch costs are listed in Table

7-8 The weighting factors of the system objectives can be changed by the network

operator which make it possible to give preference to one over the other Three

cases are studied in which the weighting factors 1205961and 1205962vary from 01 to 09

As shown in the table as the weighing factor of SAIDI 1205961 is increased more

sectionalising switches are installed and reliability is improved The results show the

algorithm can adapt itself to the variation of the weighting factors For decision

making appropriate weighting factors for each objective are selected and a

compromised switch placement plan is obtained using the proposed approach


Test Cases 1205961 1205962 120572119878119860 120572119878119862 Objective

Function

SAIDI

(hrscustomer)

Switch costs ($)

Case 21 01 09 04909 09970 09464 1157 68275

Case 22 05 05 08456 09061 08758 556 67378

Case 23 09 01 09384 07761 09221 39936 153950



753 Test Case 3

In this test the three objective functions of the problem to be optimised are ECOST

SAIDI and switch costs The detailed test results before and after switch placement

are listed in Table 7-9 The placement of sectionalising switches results in a

reduction of 60 in ECOST and 7148 in SAIDI It is observed that the

installation and relocation of sectionalising switches has obtained a compromise

solution of three objectives optimisation


Improvement

Page | 148

Table 7-9 Results of sectionalising switches installation and relocation in Test Case 3

Objective

Function

120572119864119862 120572119878119860 120572119878119862 ECOST

($)

SAIDI

(hrscustomer)

Switch costs

($)

Before

switch

placement

0 0 0 1 472260 1989 4830

After switch

placement

08327 08327 08392 08384 188950 56723 112410

76 Summary

This study has presented an ACO algorithm for assessing the SSP problem in terms

of three conflicting objectives optimisation reduction of unserved energy cost

decrease in the average time that a customer is interrupted and minimisation of

switch costs The proposed model has been successfully applied on Bus 4 of the

RBTS In comparison with the original system the existing sectionalising switches

are relocated and new automatic switches are installed The effectiveness of the

proposed approach has been demonstrated through the results obtained which

indicates switch placement using the ACO algorithm reduces the customer outage

costs and interruption duration times during fault contingencies Furthermore the

importance of the CDF variation in determining the SSP is investigated through

sensitivity analysis The impact of installing sectionalising switches on reducing the

total system costs decreases as the number of sectionalising switches is increased As

the parameters of ACO algorithm affect the performance of the proposed method an

ACO parameter sensitivity analysis is also provided in this study The selection of

pheromone evaporation rate and number of ants is a trade-off between the global

search ability and convergence rate of the algorithm In addition a benefit-to-cost

analysis is implemented and used to prove switch investment is profitable The

procedure is used for system planning and is applied off-line so there is no

limitation in calculation times

The main contribution of this study is the conversion of all the multiple objectives

into a single objective function in two forms weighted aggregation and fuzzy

satisfaction objective function considering ECOST SAIDI and cost of

sectionalising switches simultaneously The selection of each form depends on the


Improvement

Page | 149

number of objectives as well as their units and dimensions Another contribution is

the incorporation of FMEA to evaluate the impact on distribution system reliability

of increased automation

Page | 150

CHAPTER 8


RECONFIGURATION FOR LOSS

REDUCTION amp RELIABILITY

IMPROVEMENT

81 Introduction

Optimal distribution network reconfiguration (DNR) can not only solve a single

objective function such as feeder loss minimisation but can also deal with multiple

objectives The presence of multiple objectives raises the issue of how to consider

them simultaneously [117] In the previous section the multiple objectives are

transformed into a single equation using fuzzy logic based approaches The

optimisation is then formulated either as the weighted sum of the fuzzy membership

functions or with the application of the max-min principle

However the above simple optimisation processes only find a compromise solution

It is no longer acceptable for a system with multiple conflicting objectives if the

distribution network operator (DNO) desires to know all possible optimal solutions

for all the objectives simultaneously [20] Therefore a set of trade-off solutions

using the Pareto optimality concept is now proposed These solutions can be

Chapter 8 Distribution Network Reconfiguration for Loss Reduction amp Reliability

Improvement

Page | 151

compared by using the concept of dominance [88] In this concept a solution is non-

dominated when no other solution exists with better values for all the individual

objectives The Pareto set is the set of all non-dominated solutions and the

corresponding objective values constitute the Pareto front [88] This allows the

DNOs to select the most suitable one for implementation depending on the utilitiesrsquo

priorities Pareto analysis is suitable for addressing problems whose conflicting

solutions cannot be addressed using a single solution [117]

This study formulates the optimal network reconfiguration problem within a Pareto

optimal framework where feeder loss and system reliability indices are

simultaneously optimised Two types of reliability indices are considered system

expected outage costs to customers (ECOST) and system interruption duration index

(SAIDI) The multi-objective ant colony optimisation (MOACO) and artificial

immune systems-ant colony optimisation (AIS-ACO) algorithms are proposed and

compared for the assessment of DNR problems Both algorithms focus on problems

in terms of Pareto optimality where the objective functions are multidimensional In

MOACO each objective function is assigned with a pheromone matrix and all

values from multiple pheromone matrices are aggregated into a single pheromone

value by a weighted sum [96] In AIS-ACO the quality of elements that make up the

solution to the problem is represented by the pheromones developed from the ACO

And the hypermutation from the AIS is used as a random operator to enlarge the

search space [88] To verify the suitability of the proposed algorithms they have

been tested on Bus 4 of the Roy Billinton Test System (RBTS) system and the Pareto

set is obtained

The remaining parts of this chapter are organised as follows Section 82 deals with

the framework of multi-objective optimisation and DNR problem formulation The

implementation details of the MOACO and AIS-ACO algorithms to the problem are

discussed in Section 83 The simulation results and the best compromise solutions

are presented and discussed in Section 84 and 85 Section 86 summarises the main

conclusions


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This section formulates the DNR problems in the Pareto optimal framework

821 Multi-objective Reconfiguration Problem

In this study three objectives are considered and they are feeder loss unserved

energy cost and the average time that a customer is interrupted Therefore the multi-

objective DNR problem can be defined as the minimisation of the vector

119865(119866) = [1198911(119866)1198912(119866)1198913(119866)]119879 (8-3)

where 1198911(119866) 1198912(119866) and 1198913(119866) are described below for a given network

configuration G

8211 Minimisation of feeder loss

The total feeder loss of the network is formulated as

1198911(119866) = sum 119896119894119877119894(119875119894

2+1198761198942

1198801198942 )

119873119887119894=1 (8-4)





assessment is presented in Section 28

8212 Minimisation of ECOST

The ECOST represents the unserved energy cost and is described as

1 ( 1)

1 1 1 1 1 1


t t

b b k R k s

t b k j k j


(8-5)





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kth-type customers at the jth load point (kW) 119862119896(119889) is the customer damage

function for kth-type customer lasting d hours ($kW) 119889119877 and 119889119878 are the average

repair time and the switch time after failure IR and DR are the annual load increase

rate and discount rate

8213 Minimisation of SAIDI

The average time that a customer is interrupted is represented by a reliability index

SAIDI and is defined as

119878119860119868119863119868 = sum sum 120582119887∙119871119887[sum 119889119877

119873119862119877(119887)119899=1 +sum 119889119878

119873119862119878(119887)119899=1 ]

119873119887119887=1

119873119862119905119900119905119886119897119879

119905=1 (8-6)




8214 Constraints



configurations that violate any constraint should be disregarded

822 Best Compromise Solution

After obtaining the Pareto set the best compromise solution among the multiple

objectives can be selected by comparing the fitness value of each member in the

Pareto front as follows [45]

119891119901119904(119894) = sum 120596119895max(119900119891119895)minus119900119891119895(119875119878119894)

max(119900119891119895)minusmin (119900119891119895)

119873119900119887119895

119895=1 (8-7)

where 119873119900119887119895 is the number of objectives which is three in this study max(119900119891119895) and

min(119900119891119895) are the maximum and minimum value of the jth objective function

obtained by all the members in the Pareto front respectively 1205961 1205962 and 1205963 are the

weighting factor for feeder loss ECOST and SAIDI respectively

The best compromise solution is varied by changing the values of the weighting

factors based on the tendencies of the decision makers


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Page | 154

83 Solution Methodology

In this study there are two methodologies proposed for generating the Pareto set to

the multi-objective DNR problem which are MOACO and AIS-ACO algorithm

Each solution is represented by a string of integers which indicates the locations of

tie-switches

831 Applying MOACO to Multi-objective DNR Problem

Generally ACO algorithm is developed for the assessment of a single objective

optimisation problem However a MOACO algorithm is proposed for assessing

multiple objective functions in the Pareto optimality framework which can generate

diverse solutions rather than just one The flowchart of the MOACO algorithm is

presented in Fig 8-1 and is divided into six steps


number of pheromone matrices is equal to the number of objectives Each

pheromone matrix has 33 rowsstates (candidate locations for tie-switches) and 4

columnsstages (number of tie-switches) The pheromone values of the edges in the

search space are all initialised at an equal value which is a small positive constant

number

Step 2 Pheromone matrix generation and ant dispatch As there are multiple

pheromone matrices 1205911 1205912 and 1205913 are associated with feeder loss ECOST and

SAIDI respectively All matrices are aggregated into a single pheromone matrix by

weighted sum as

120591119894119909 = 1199011 ∙ 1205911198941199091 + |1199011 minus 1199012| ∙ 120591119894119909

2 + (1 minus 1199012) ∙ 1205911198941199093 (8-8)

where 1205911198941199091 120591119894119909

2 and 1205911198941199093 are the levels of pheromone deposited on state i of stage x for

feeder loss ECOST and SAIDI respectively where 1199011 and 1199012 are uniform random

numbers between 0 and 1 and 1199011 is less than 1199012 This ensures the selection of the

three pheromone matrices all have the same probability and can be used to build the

new matrix

All the ants begin their tours from the home colony and choose the next node to

move to based on the intensity of pheromones from a new pheromone matrix They


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Page | 155

experience different pheromone matrices according to the random variation of

weights The probability of an ant choosing state i of stage x is

119875119894119909(119873) =120591119894119909(119873)

sum 120591119894119909(119873)ℎisin∆119909

(8-9)

where 120591119894119909(119873) is the level of pheromone deposited on state i of stage x at iteration

N ∆119909 is the set of available states which an ant can choose at stage x


the location list and corresponding objective functions in (8-3) for each ant are

evaluated If any constraint is violated the corresponding solutions are discarded

Step 4 Non-dominated Solutions Extraction and Diversity Measure The non-

dominated solutions extraction extracts solutions from a pool based on the concept

of dominance as presented in Section 821 The crowding distance is used to

measure the extent to which non-dominated solutions are spread over the objective

space [20] As there are three objectives to be optimised the crowding distance of a

solution is equal to the side length of the cuboid which is built by two adjacent

solutions [88] Regarding the boundary solutions (the corner solutions) they are

assigned with an infinite distance The solutions are assigned with a small distance

value if they are located in a crowded area The decision makers tend to choose the

solutions from less crowded regions of the search space (with higher crowding

distance) if the maximum number of non-dominated solutions is restricted to a

certain number [88]


states by non-dominated solutions with greater pheromone values There are two

rules of pheromone updating the local rule and global rule

Local rule The pheromones deposited in the search space should be evaporated to

make the paths less attractive The local pheromone update rule is calculated as

follow

120591119894119909119899 (119873) = (1 minus 120588)120591119894119909

119899 (119873 minus 1) + 120591119888 (8-10)

where 120588 is the pheromone evaporation rate which is set between 0 and 1 120591119894119909119899 (119873 minus

1) is pheromone value deposited on state i of stage x of matrix n at iteration N-1 120591119888


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Page | 156

is a small positive constant value Even if the amount of pheromone deposited on an


this edge


amounts of pheromone to the edges that belong to the corner non-dominated

solutions which are the solutions that have minimum values along each objective

The pheromones of those edges can be updated by

120591119894119909119899 (119873) = 120591119894119909

119899 (119873) + 120588119891119887119890119904119905

119899 (119873)

119891119887119890119904119905119899 (119873minus1)

(8-11)

where 119891119887119890119904119905119899 (119873 minus 1) and 119891119887119890119904119905

119899 (119873) are the minimum values of objective function n

obtained by the non-dominated solutions at iteration N-1 and N respectively



120591119894119909119899 (119873) = 120591119898119886119909 119894119891 120591119894119909

119899 (119873) ge 120591119898119886119909 (8-12)

120591119894119909119899 (119873) = 120591119898119894119899 119894119891 120591119894119909

119899 (119873) le 120591119898119894119899 (8-13)

where 120591119898119886119909and 120591119898119894119899 are the higher and lower bound of pheromone level on each

edge respectively Even if the amount of pheromone deposited to a path is at the

lowest value 120591119898119894119899 there is a slight chance that an ant will still choose this path This

enlarges the search space and prevents convergence from occurring too rapidly

After this the non-dominated solutions with their location lists and corresponding

fitness values in the current iteration are retained and all the ants are free to choose a

new path for the next iteration


number of iterations is reached The final non-dominated solutions are considered as

the Pareto set to the multi-objective DNR problem


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Page | 157

Start

Iteration N=1

Maximum ant number

reaches

Output Pareto

optimal set and end

No

Yes

Initialise the parameters for MOACO

algorithm search space

Ant number m=1

Random select weights and

aggregate multiple pheromone

matrices into one

Dispatch the ant based on the

amount of pheromone on edges

Calculate the multiple objective functions

for this ant

N=N+1


and load data

Diversity measure and extract non-

dominated solutions

Maximum iteration

reaches

Yes

m=m+1

No



Fig 8-1 Flowchart of the MOACO algorithm applied to multi-objective DNR problem


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Page | 158

Start

Cloning

Maximum iteration

reached

Output Pareto

optimal set and end

No

Yes

Initialise and set iteration n=1

Pheromone based hypermutation


dominated solutions

The pheromones are updated according to

local and global rules

n=n+1

832 Applying AIS-ACO to Multi-objective DNR Problem

The general description of AIS-ACO algorithm is presented in Section 34 In this

study the AIS-ACO hybrid approach is used to handle multi-objective formulation

using the Pareto optimality concept The antigen is the multi-objective function and

the antibody is the solution to the problem The affinity between the antibody and the

antigen is the Pareto dominance among solutions which indicates the quality of the

solution [88] The information related to each objective is represented by an

individual pheromone table All the non-dominated solutions experience cloning

hypermutation selection and updating until the maximum number of iterations is

reached The flowchart of the AIS-ACO algorithm for Pareto optimality is presented

in Fig 8-2

Fig 8-2 Flowchart of the AIS-ACO algorithm applied to multi-objective DNR problem


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Page | 159


Step 1 Initialisation At the beginning of this algorithm a set of initial solutions is

generated These solutions should satisfy the constraints An individual pheromone

table is also built for each objective Each pheromone table has 33 cells (candidate

locations for tie-switches) The pheromone value of each cell represents the

probability of selecting the corresponding switch to be opened in the network model

The pheromone values of all cells are initially set at the same value

Step 2 Cloning All the non-dominated solutions are subjected to cloning In this

study as there are three objectives to be optimised the number of clones for each

non-dominated solution is three

Step 3 Hypermutation The selection of a cell in each clone for hypermutation is

obtained by applying a roulette wheel on its pheromone table [88] The probability of

selecting a cell is dependent on its pheromone intensity A higher pheromone value

of a cell in the table indicates that the corresponding edge in the network is more

likely to be selected The probability of selection cell i in table n is given by

119901119894119899 =

120591119894119899

sum 120591119895119899

119895 (8-14)

where 120591119894119899 is the pheromone value of cell i in table n sum 120591119895

119899119895 represents the sum of

pheromone values of all cells in table n

Step 4 Non-dominated Solutions Extraction and Diversity Measure This step is

same to the step which has been discussed in Section 831

Step 5 Pheromone Updating The aim of this step is to favour transitions toward

non-dominated solutions with great pheromone values There are two rules of

pheromone updating the local rule and global rule

Local rule Pheromones deposited in the search space should be evaporated to make

the paths less attractive The local pheromone update rule is calculated as follows

120591119894119899(119873) = 119898119886119909 (1 minus 120588)120591119894

119899(119873 minus 1) 120591119898119894119899 (8-15)

where 120588 is the pheromone evaporation rate which is set between 0 and 1 120591119894119899(119873 minus 1)

is pheromone value deposited on cell i of table n at iteration N-1 120591119898119894119899 is the lower


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bound of pheromone level on each edge Even if the amount of pheromone deposited

to a path is at the lowest value 120591119898119894119899 there is a slight chance that an ant will still

choose this path This enlarges the entire search space

Global rule The global pheromone updating rule involves depositing large amounts

of pheromone to the edges that are a part of all the non-dominated solutions in the

current iteration [88] At iteration N the edges of the non-dominated solutions can be

updated as

120591119894119899(119873) = 119898119894119899120591119894

119899(119873) + 120588min (119891119899(119866))

119891119899(119866) 120591119898119886119909 (8-16)

where each 119894 isin edge set of G 119899 isin objective set and 119866 isin non-dominated solutions set

119891119899(119866) is the value of objective function n obtained by the non-dominated solution G

120591119898119886119909 is the higher bound of pheromone level on each edge

After this the non-dominated solutions with their location lists and fitness values in

the current iteration are retained and all the ants are free to choose a new path for the

next iteration


number iteration is reached The final non-dominated solutions are considered as the

Pareto set to the multi-objective DNR problem


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LP8 LP9 LP10



LP29 LP30 LP31

LP26 LP27 LP28


19

20

21

22

23

24

26

25 27

28

29 30

71

13 15

14 16

17

18

69

1 3

2

5

4

7

6 8

10

9

68

11 12

56

57

58 60

59 61 62

65

64 66 67

50 52

51

54

53 55

44

45

46

47

48

49

70

31

32

33

34

36

35

39

37 38 40

41

42 43

63

F3

F2

F1

F7

F6

F5

F4


Subbus1

Subbus2

Subbus3

T1

T3

T5

Main

feeder

Main

feeder

Main

feeder

T2

T4

T6


The proposed MOACO and AIS-ACO algorithms have been tested on an 11 kV

distribution network developed from Bus 4 of the Roy Billinton Test System (RBTS)

a single-line diagram of the network is shown in Fig 8-3 The network consists of 38

load points and 4 tie-switches the associated data can be found in [114] The types

and lengths of 11 kV feeders are listed in Appendix A4 The network built in

OpenDSS incorporates three 3311 kV double transformer substations supplying the

downstream loads



industrial consumers The average value of active and reactive power and the




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300

350

400

450

4

45

5

55

6

x 104

08

09

1

11

12

13

14

15

Feeder loss (kW)ECOST ($yr)

SA

IDI

(hrs

custo

mer

yr)

Table 8-1 Revised customer data (Average load)

Number

of load

points


(kW)

Q

(kVAr)

Number of

customers

4 1-2 9-10 residential 545 51775 220

6 3-5 13-15 residential 500 475 200

12 6-7 16-17 23-25 28 30-

31 37-38


6 8 11 18 26 32-33 industrial 1500 1425 1

10 12 19-22 27 29 34-36 industrial 1000 950 1

The proposed MOACO and AIS-ACO algorithms are coded in the MATLAB to

obtain the location of tie-switches for the optimum configuration The settings of the

algorithm parameters that provided the optimum solution for these two cases are

presented in Appendix C4

The number of Pareto optimal solutions obtained by the two algorithms is 26 and its

Pareto front is presented in Fig 8-4 in three dimensions The Pareto set is listed in

Appendix B3 in detail These solutions provide the network operator with various

configurations for the system to choose from Both algorithms have obtained the

same results However for 100 runs the average computation time of AIS-ACO

algorithm is 402s which is significantly lower than the MOCAO algorithm 1053s



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Table 8-2 presents the mean and standard deviation of the Pareto front


Feeder loss (kW) ECOST ($yr) SAIDI (hrscustomeryr)

Mean

38074 48139 09975

Standard deviation

3431 5291 01165

The corner non-dominated solutions representing minimum feeder loss minimum

ECOST and minimum SAIDI are marked by the red circle yellow circle and green

circle respectively as shown in Fig 8-4 The objective values of these solutions and

relevant tie-switches locations are presented in Table 8-3 It is obvious that the three

objectives are conflicting with each other and the algorithm is able to find the global

optimal solution for each objective function The minimum loss configuration is the

base configuration of RBTS-Bus4 In minimum ECOST solution the unserved

energy cost is reduced by 1133 in comparison with that in the original network

The minimum SAIDI solution shows a reduction of 3695 in the average time that

a customer is interrupted

Table 8-3 Minimum solutions along each objective (loss ECOST and SAIDI)

Feeder loss (kW) ECOST ($yr) SAIDI

(hrscustomeryr)

Tie-switches location

Minimum Loss

32142 46404 13090 68 69 70 71

Minimum ECOST

35409 41145 10586 10 17 41 70

Minimum SAIDI

43523 57891 08253 7 26 54 69


After obtaining the Pareto set the best compromise solution is the member which

has the largest fitness value as calculated in Eq (8-7) The results are presented in

Table 8-4 The importance of each objective function is represented by its weighting


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factor which ranges from 1 to 10 A higher weighing factor indicates this objective

function is more important It can be seen that the solutions are different if the

weighing factors of each objective function are varied based on the tendencies of

DNO For example as shown in the table Case 2 (1205961 = 10 1205962 = 1 1205963 = 1)

indicates that the importance of feeder loss reduction is higher than the other two

objectives and hence the best compromise solution for this case obtains the

minimum loss among all the solutions which is the same as the results obtained

from Table 8-3 In comparison of Case 5 with Case 2 as the importance of ECOST

reduction is increased the network is reconfigured and its feeder loss increases by

588 to compensate for a 1045 decrease in the ECOST If there is no preferred

objective the best solution is obtained by setting 1205961 = 1205962 = 1205963 (Case 1)

Table 8-4 Best compromise solutions (loss ECOST and SAIDI)

Case No Weighting factors Best

compromise

solution

Feeder

loss

(kW)

ECOST

($yr)

SAIDI

(hrscustomeryr) 1205961 1205962 1205963

1 10 10 10 10 41 69 70 34033 41553 10996

2 10 1 1 68 69 70 71 32142 46404 13090

3 1 10 1 10 17 41 70 35409 41145 10586

4 1 1 10 7 26 54 69 43523 57891 08253

5 10 10 1 10 41 69 70 34033 41553 10996

6 10 1 10 10 54 69 71 34759 46644 10217

7 1 10 10 7 17 41 70 40368 43329 09570

86 Summary

The MOACO and AIS-ACO algorithms have been presented in this study for the

assessment of the multi-objective DNR problem using the Pareto optimality concept

The proposed DNR problem is formulated taking into account three objectives to be

minimised feeder loss ECOST and SAIDI The algorithms have been successfully

tested in an RBTS-Bus 4 network The results illustrate that the proposed algorithm

is able to generate a set of non-dominated solutions with high quality and great

diversity This set of solutions represent different trade-offs among the objective

functions And the corner non-dominated solutions which represent the minimum


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value of each objective function are presented in the Pareto front chart By varying

the weighting factors for the parameters the decision makers can select the best

compromise strategy among the three objectives for implementation depending on

the utilitiesrsquo priorities

According to the obtained results both algorithms have obtained the same Pareto

optimal solutions but the AIS-ACO algorithm performs better in comparison with

the MOACO algorithm in terms of computation time The pheromone tables in AIS-

ACO algorithm are used to guide the search process and improve the solution quality

In addition the hypermutation is used as a random operator to enlarge the search

space and to prevent the algorithm from easily falling into the local optimum Future

work could include the assessment of the DNR problem with other objectives such

as balancing loads on feeders and minimising the maximum node voltage deviation

The AIS-ACO algorithm can also be applied to larger systems

Page | 166

CHAPTER 9

MULTI-OBJECTIVE DISTRIBUTION

NETWORK RECONFIGURATION amp DG

ALLOCATION CONSIDERING LOSS

VOLTAGE DEVIATION AND LOAD

BALANCING

91 Introduction

As discussed in the previous chapters distribution network reconfiguration (DNR)

can not only be used for single objective optimisation but also multi-objective

optimisation The study aims to determine a system topology that simultaneously

minimises feeder loss maximum node voltage deviation and feeder load balancing

This is achieved by optimal DNR and DG allocation

There are two methods presented in this chapter that tackle these objectives a single

fuzzy satisfaction objective function is used to transform the three conflicting


function The ultimate goal is to find a solution that maximises this single objective

while maintaining the constraints of the network [20] In Chapter 7 the degree of

Chapter 9 Multi-objective Distribution Network Reconfiguration amp DG Allocation

Considering Loss Voltage Deviation and Load Balancing

Page | 167

overall fuzzy satisfaction is determined by the max-min principle However there is

no guarantee that if one membership value is weaker than the other membership

values then for the same option the optimised single function will also be weak [86]

Therefore the max-min principle may not predict the best compromise solution In

this study a new operator called lsquomax-geometric meanrsquo has been introduced to

determine the degree of overall fuzzy satisfaction

Another methodology used for assessing the multi-objective DNR and DG allocation

problem is based on the Pareto optimality concept The proposed method provides a

set of non-dominated solutions with high quality and great diversity This constructs

a full Pareto front which represents different trade-offs among the objective

functions It allows the decision makers to select the most suitable one from all the

non-dominated solutions and use this for implementation which depends on the

utilitiesrsquo priorities

The optimisation algorithms for DNR and DG allocation can be classified into two

groups

Ant colony optimisation (ACO) algorithm which is used to solve the

problem in the fuzzy domain

Artificial immune systems-ant colony optimisation (AIS-ACO) algorithm

which is adopted to formulate the optimal network reconfiguration problem

within a multi-objective framework based on the Pareto optimality concept

The effectiveness and the efficiency of the proposed methods are implemented on

two standard IEEE 33-node and 69-node systems as case studies

The remainder of this chapter is organised as follows in Section 92 the

mathematical models of the problem are developed Then the solution procedures

are presented in Section 93 Numerical studies are presented and discussed in

Section 94 and finally Section 95 summarises the main conclusions



Page | 168

0

1


The primary objective of this study is to minimise the three conflicting objectives

feeder loss maximum node voltage deviation and the feeder load balancing index

Two formulations of objective functions are presented as follow


In this study the three conflicting objectives are transformed into a single objective

function in the fuzzy domain The best compromise solution is obtained using a

lsquomax-geometric meanrsquo principle and is formulated as follows

Max 119871 = (120572119871 times 120572119881 times 120572119861)1 3frasl (9-1)

where 120572119871 120572119881 120572119861 represents the value of the membership functions for the feeder loss

the maximum node voltage deviation and the feeder load balancing index

respectively

The membership functions used to describe the three objectives of the DNR and DG

allocation problem are presented in the following sections

Membership function for feeder loss reduction

The calculation of feeder loss has been discussed in Section 28 The basic purpose

of this membership function is to reduce feeder loss Therefore the network

topology with a lower loss value obtains a higher membership value The

membership function for loss reduction is formulated in (9-2) and presented in Fig

9-1

Fig 9-1 Membership function for feeder loss reduction

As feeder loss becomes greater than 119871119874119878119878119898119894119899 the degree of satisfaction decreases

This reduction is continued until feeder loss reaches 119871119874119878119878119900119903119894

120572119871

119871119874119878119878119898119894119899 119871119874119878119878119900119903119894 119871119874119878119878



Page | 169

0

1

120572119871 =

1 119871119874119878119878 le 119871119874119878119878119898119894119899119871119874119878119878119900119903119894minus119871119874119878119878

119871119874119878119878119900119903119894minus119871119874119878119878119898119894119899119871119874119878119878119898119894119899 lt 119871119874119878119878 lt 119871119874119878119878119900119903119894

0 119871119874119878119878 ge 119871119874119878119878119900119903119894

(9-2)

where 119871119874119878119878119900119903119894 is the loss of the original network 119871119874119878119878119898119894119899 is the minimum loss that

a network can achieve As it is not appropriate for decision makers to obtain a

network topology which increases loss after DNR and DG allocation the minimum

value of 120572119871 is selected as 0 if the loss is greater than or equal to 119871119874119878119878119900119903119894

Membership function for maximum node voltage deviation reduction

The maximum deviation of bus voltages from their rated values is formulated as

119881119863 = max|119881119903119890119891 minus 119898119894119899(119881119894)| |119881119903119890119891 minus 119898119886119909(119881119894)| 119894 120598 1 2 hellip 119873119887 (9-2)

where 119881119903119890119891 is the reference value for the node voltage which is the substation voltage

it is assumed to be 10 per unit in this study 119881119894 is the voltage at the ith node and 119873119887

is the number of nodes

The membership function for maximum node voltage deviation is shown in Fig 9-2

Fig 9-2 Membership function for maximum node voltage deviation reduction

The mathematical equation is presented below

120572119881 =

1 119881119863 le 119881119863119898119894119899119881119863119900119903119894minus119881119863

119881119863119900119903119894minus119881119863119898119894119899119881119863119898119894119899 lt 119881119863 lt 119881119863119900119903119894

0 119881119863 ge 119881119863119900119903119894

(9-3)

where 119881119863119900119903119894 and 119881119863119898119894119899 are the original and minimum values of the maximum node

voltage deviation respectively

120572119881

119881119863119898119894119899 119881119863119900119903119894 119881119863



Page | 170

0

1

Membership function for feeder load balancing index reduction

The feeder load balancing index is calculated as

119871119861119868 = 119881119886119903[1198681

1198681119898119886119909

1198682

1198682119898119886119909 hellip

119868119894

119868119894119898119886119909 hellip

119868119899

119868119899119898119886119909] (9-4)

where 119868119894 is the current flowing through branch 119894 119868119894119898119886119909 represents the maximum

current limit of branch 119894

The function for feeder load balancing index is shown in Fig 9-3 and expressed as

120572119861 =

1 119871119861119868 le 119871119861119868119898119894119899119871119861119868119900119903119894minus119871119861119868

119871119861119868119900119903119894minus119871119861119868119898119894119899119871119861119868119898119894119899 lt 119871119861119868 lt 119871119861119868119900119903119894

0 119871119861119868 ge 119871119861119868119900119903119894

(9-5)

where 119871119861119868119900119903119894 and 119871119861119868119898119894119899 are the original and minimum values of the feeder load

balancing index respectively

Fig 9-3 Membership function for load balancing index reduction

922 Multi-objective Reconfiguration Problem Using Pareto

Optimality

In this study the multi-objective DNR problem can be defined as the minimisation

of the vector

119865(119866) = [1198911(119866)1198912(119866)1198913(119866)]119879 (9-6)

where 1198911(119866) 1198912(119866) and 1198913(119866) are feeder loss maximum node voltage deviation and

feeder load balancing index respectively The calculation of these three parameters

is discussed in Section 921

120572119861

119871119861119868119898119894119899 119871119861119868119900119903119894 119871119861119868



Page | 171

93 Solution methodology

931 Applying ACO to DNR and DG Allocation in the Fuzzy

Domain

In this study the objective of reconfiguring the network and allocating DGs

simultaneously is to deal with the single fuzzy satisfaction objective function In

order to tackle this optimisation problem an ACO algorithm is adopted to find the

optimum configuration of tie-switches and the location of DGs in the network When

the locations of tie-switches and DGs are changed a new network configuration will

be formed For each network configuration the overall satisfaction of the plan is

calculated using Eq (9-1) The search space of the DNR and DG allocation problems

is modelled as a directed graph as shown in Fig 5-1 The flowchart of the proposed

ACO algorithm is presented in Fig 5-2

932 Applying AIS-ACO to Multi-objective DNR and DG

Allocation Using Pareto Optimality

The application of the AIS-ACO algorithm to the multi-objective DNR and DG

allocation problem using the concept of Pareto optimality is similar to that in Section

832 with an additional process for DG allocation


To demonstrate the performance and effectiveness of the proposed techniques in

solving the network reconfiguration and placement of DG problems simultaneously

the proposed ACO and AIS-ACO are implemented on two 1266 kV test systems


solution algorithms are developed in MATLAB For both test systems the substation

voltage is assumed to be 10 pu and all the sections and buses are considered as



generators and are represented as PQ models with a 100 kVA and a power factor



Page | 172

equal to 10 However the proposed methodology can be implemented for any

number of DGs For the purpose of better illustration and comparison four cases are

considered to analyse the superiority and performance of the proposed methods





simultaneously

It is to be noted that the ACO and AIS-ACO control parameters are different for

each test case They are set experimentally using information from several trial runs

The final combinations that provide the best results for all of the above tests are

given in Appendix C5 And the Pareto sets for all test cases are listed in Appendix

B4 in detail

941 33-bus System


distribution system with 37 branches and 5 tie-switches whose single line diagram is

shown in Fig 5-3 The tie-switches are located at L33 to L37 represented by red

dotted lines The data of lines and loads are taken from [108] and summarised in

Appendix A2 The current carrying capacity of all branches is 255A The total real

and reactive power loads of the system are 3715 kW and 2300 kVAr respectively

Case I base case

For the base case without reconfiguration and DGs the initial active feeder loss

maximum node voltage deviation and feeder load balancing index of this system are

20314 kW 00884 pu and 00419 respectively



Page | 173

10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

18 19 20 21

22 23 24

25 26 27 28 29 30 31 32


L18

L19 L20 L21

L22

L23 L24

L25

L26 L27 L28 L29 L30 L31 L32

L33

L34

L35

L36

L37


In this case only reconfiguration is considered and no DGs are installed

After DNR the best compromise solution obtained using ACO algorithm in a single

fuzzy satisfaction objective function is presented in Table 9-1 It can be seen that the

DNR has resulted in a reduction of 2956 in feeder loss 2930 in maximum node

voltage deviation and 3556 in feeder load balancing index compared to the base

case This solution is one of the Pareto optimal solutions which are obtained by

using AIS-ACO algorithm And the network configuration after DNR is shown in

Fig 9-4

Table 9-1 Results of DNR in fuzzy multi-objective formulation for 33-bus system in Case II

Objective function Feeder loss

(kW)

Maximum node

voltage deviation

(pu)

Feeder Load

balancing index

Tie-switches

location

08734 14310 00625 00270 6 9 14 32 37

Fig 9-4 33 bus-system for fuzzy multi-objective optimisation Case II

The number of Pareto optimal solutions obtained using AIS-ACO algorithm is 21

and its Pareto front is presented in Fig 9-5 in three dimensions Table 9-2 presents

the mean and standard deviations of the objective values of the Pareto solutions



Page | 174

120140

160180

200220

006

008

01

012

014

016

0022

0024

0026

0028

003

0032

0034

0036

Feeder loss (kW)Maximum node voltage deviation (pu)

Feeder

load b

ala

ncin

g index

Fig 9-5 Pareto front obtained for 33-bus system in Case II


Feeder loss (kW) Maximum node voltage

deviation (pu)

Feeder Load balancing index

Mean

15499 00815 00256

Standard deviation

1549 00194 00023

The corner non-dominated solutions which represent minimum feeder loss

minimum voltage deviation and minimum feeder load balancing index are marked

by the red circle yellow circle and green circle respectively as shown in Fig 9-5

The objective values of these solutions and relevant tie-switches locations are

presented in Table 9-3 In minimum loss solution the feeder loss is reduced by 3118

compared to the initial state If improving voltage profiles is the principle objective

the solution with maximum node voltage deviation of 00604 pu is optimum which

represents a 3167 improvement compared to the base case If balancing feeder



Page | 175

10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

18 19 20 21

22 23 24

25 26 27 28 29 30 31 32


L18

L19 L20 L21

L22

L23 L24

L25

L26 L27 L28 L29 L30 L31 L32

L33

L34

L35

L36

L37

DG2

DG1

DG3

load is the main objective the solution with load balancing index of 00223 is

optimum where the index decreases by 4678 in comparison with the initial case

Table 9-3 Minimum solutions along each objective for 33-bus system in Case II

Feeder loss (kW) Maximum node

voltage deviation (pu)

Feeder Load balancing

index


Minimum Loss

13981 00639 00280 7 9 14 32 37

Minimum Voltage Deviation

14026 00604 00310 7 9 14 28 32

Minimum Feeder Load Balancing Index

20248 01309 00223 7 30 34 35 37



The feeder loss maximum node voltage deviation and feeder load balancing of the

original network with DGs are 17831 kW 00823 pu and 00389 pu respectively


fuzzy satisfaction objective function is presented in Table 9-4 Compared to the Case

I feeder loss maximum node voltage deviation and feeder load balancing decrease

by 3893 3281 and 4511 respectively This solution belongs to the Pareto

set which are obtained by using AIS-ACO algorithm Fig 9-6 illustrates the optimal

network configuration

Fig 9-6 33 bus-system for fuzzy multi-objective optimisation Case III



Page | 176

110120

130140

150160

170

004

006

008

01

0120018

002

0022

0024

0026

0028

003


Feeder

load b

ala

ncin

g index

Table 9-4 Results of DNR in fuzzy multi-objective formulation for 33-bus system in Case III


(kW)

Maximum node

voltage deviation

(pu)

Feeder Load

balancing index

Tie-switches

location

08590 12405 00594 00230 6 8 14 32 37

Fig 9-7 shows the Pareto front obtained by the AIS-ACO method and the number

of Pareto optimal solutions for this case is 28 The mean and standard deviations of

the objective values of the Pareto solutions are listed in Table 9-5

Fig 9-7 Pareto front obtained for 33-bus system in Case III

Table 9-5 Mean and standard deviations of Pareto Front for 33-bus system in Case III


deviation (pu)

Feeder load balancing index

Mean

12850 00711 00231

Standard deviation

1003 00166 00029



Page | 177




Table 9-6 presents the objective values of these solutions and relevant tie-switches

locations In minimum loss solution the network reconfiguration results in a

reduction of 4214 in feeder loss compared to the original network and a

reduction of 1594 compared to the reconfigured network without DGs If

improving voltage profiles is the principle objective the solution with maximum

node voltage deviation of 00567 pu is optimum which represents a 3586 and

613 improvement compared to Case I and Case II If balancing feeder load is the

main objective the solution with load balancing index of 00189 is optimum where

the index decreases by 5489 and 1525 in comparison with Case I and Case II





index


Minimum Loss

11753 00643 00241 7 9 14 28 31


12592 00567 00265 6 8 14 28 32


16419 01139 00189 7 21 30 35 37


The network is reconfigured and DGs are allocated simultaneously in this case The

best compromise solution obtained using the proposed algorithm in a single fuzzy

satisfaction objective function after DNR and DG allocation is presented in Table 9-

7 Feeder loss maximum node voltage deviation and feeder load balancing decrease

by 4645 4355 and 4463 respectively in comparison with the base case

This solution is one of the Pareto optimal solutions which are obtained by using

AIS-ACO algorithm Fig 9-8 illustrates the optimal network configuration and DG

locations



Page | 178

10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

18 19 20 21

22 23 24

25 26 27 28 29 30 31 32


L18

L19 L20 L21

L22

L23 L24

L25

L26 L27 L28 L29 L30 L31 L32

L33

L34

L35

L36

L37

DG1

DG3

DG2

100110

120130

140150

160

004

006

008

01

012

0016

0018

002

0022

0024

0026

0028


Feeder

load b

ala

ncin

g index

Table 9-7 Results of DNR and DG allocation in fuzzy multi-objective formulation for 33-bus system

in Case IV

Objective

function

Feeder loss

(kW)

Maximum node

voltage

deviation (pu)

Feeder Load

balancing

index

Tie-switches

location

DGs location

08961 10878 00499 00232 7 9 14 36 37 B32 B32 B32

Fig 9-8 33 bus-system for fuzzy multi-objective optimisation Case IV

The number of non-dominated solutions obtained by the AIS-ACO algorithm is 295

However the maximum number for Pareto optimal solutions is restricted to 50

Therefore the solutions with a high value of crowding distance are selected Fig 9-9

shows the Pareto front obtained by the proposed method

Fig 9-9 Pareto front obtained for 33-bus system in Case IV



Page | 179

The mean and standard deviations of the Pareto front are listed in Table 9-8

Table 9-8 Mean and standard deviations of Pareto Front for 33-bus system in Case IV


deviation (pu)


Mean

13295 00873 00194

Standard deviation

1354 00179 00019





presented in Table 9-9 In minimum loss solution the network reconfiguration and

DG allocation result in a reduction of 4662 2244 and 773 in feeder loss

compared to Case I Case II and Case III respectively If improving voltage profiles

is the principle objective the solution with maximum node voltage deviation of

00490 pu is optimum which represents a 4457 1887 and 1358

improvement compared to Case I Case II and Case III respectively If balancing

feeder load is the main objective the solution with load balancing index of 00178 is

optimum where the index decreases by 5752 2018 and 582 in comparison

with Case I Case II and Case III respectively



voltage deviation

(pu)

Feeder Load

balancing index

Tie-switches

location

DGs location

Minimum Loss

10844 00538 00228 7 9 14 32 37 B30 B31 B31


11020 00490 00259 7 9 14 28 36 B31 B31 B32


15443 01090 00178 7 30 34 35 37 B8 B9 B12



Page | 180

10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

27

28

29

30

31 32 33 34

35

36

37

38 39 40 41 42 43 44 45

46 47 48 49

50

51

52

53 54 55 56 57 58 59 60 61 62 63 64

65 66

67 68


L27

L28

L29

L30

L31 L32 L33 L34

L35

L36

L37

L38 L39 L40 L41 L42 L43 L44 L45

L46

L47 L48 L49

L50

L51

L52

L53 L54 L55 L56 L57 L58 L59 L60 L61 L62 L63 L64

L65

L66

L67

L68

L69

L70

L71

L72L73

942 69-bus System




system are taken from [84] and summarised in Appendix A3 The current carrying

capacity of the branches 1-9 is 400 A 46-49 and 52-64 is 300 A and for all other

branches it is 200 A The total power loads are 379589 kW and 26891 kVAr

respectively

Case I base case





In this case only reconfiguration is considered and no DGs are installed After DNR

the best compromise solution obtained using ACO algorithm in a single fuzzy

satisfaction objective function is presented in Table 9-10 and the network

configuration is shown in Fig 9-10 Reconfiguring the network brings a reduction of

5619 4353 and 2355 in feeder loss maximum node voltage deviation and

feeder load balancing index respectively compared to the base case This solution

belongs to the Pareto set which are obtained by using AIS-ACO algorithm

Fig 9-10 69 bus system for fuzzy multi-objective optimisation Case II



Page | 181

80

100

120

140

160

005

006

007

0080016

0018

002

0022

0024

0026

0028


Feeder

load b

ala

ncin

g index



(kW)

Maximum node

voltage deviation

(pu)

Feeder Load

balancing index

Tie-switches

location

09676 9885 00524 00195 14 55 61 71 72

The number of Pareto optimal solutions obtained by the AIS-ACO algorithm is 12

and its Pareto front are presented in Fig 9-11 in three dimensions


The mean and standard deviations of the objective values of the Pareto solutions are

listed in Table 9-11



deviation (pu)


Mean

12535 00605 00192

Standard deviation

2458 00085 00028



Page | 182





presented in Table 9-12 In minimum loss solution the feeder loss is reduced by

5619 compared to the initial state If improving voltage profiles is the principle

objective the solution with maximum node voltage deviation of 00523 pu is

optimum which represents a 4364 improvement compared to the base case If

balancing feeder load is the main objective the solution with load balancing index of

00161 is optimum where the index decreases by 3784 in comparison with the

initial case




Feeder load balancing

index


Minimum Loss

9885 00524 00195 14 55 61 71 72


10535 00523 00242 9 14 55 61 71


15051 00701 00161 14 61 69 71 72





After DNR Table 9-13 presents the best compromise solution obtained using ACO

algorithm in a single fuzzy satisfaction objective function and the optimal network

configuration is shown in Fig 9-12 Compared to the base case feeder loss

maximum node voltage deviation and feeder load balancing decrease by 6118

4364 and 3282 respectively This solution is one of the Pareto optimal

solutions which are obtained by using AIS-ACO algorithm



Page | 183

10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

27

28

29

30

31 32 33 34

35

36

37

38 39 40 41 42 43 44 45

46 47 48 49

50

51

52

53 54 55 56 57 58 59 60 61 62 63 64

65 66

67 68


L27

L28

L29

L30

L31 L32 L33 L34

L35

L36

L37

L38 L39 L40 L41 L42 L43 L44 L45

L46

L47 L48 L49

L50

L51

L52

L53 L54 L55 L56 L57 L58 L59 L60 L61 L62 L63 L64

L65

L66

L67

L68

L69

L70

L71

L72L73

DG3

DG1

DG2

8090

100110

120130

140

005

006

007

008

0014

0016

0018

002

0022

0024


Feeder

load b

ala

ncin

g index



(kW)

Maximum node

voltage deviation

(pu)

Feeder Load

balancing index

Tie-switches

location

08829 8758 00523 00174 14 55 61 71 72

Fig 9-12 69-bus system for fuzzy multi-objective optimisation Case III


of Pareto optimal solutions for this case is 19




Page | 184





deviation (pu)


Mean

10707 00576 00183

Standard deviation

2042 00071 00029





locations are presented In minimum loss solution the network reconfiguration

results in a reduction of 6118 in feeder loss compared to the original network and

a reduction of 1140 compared to the reconfigured network without DGs If










index


Minimum Loss

8758 00523 00174 13 55 61 71 72


9729 00522 00226 7 12 55 61 71


13686 00681 00147 11 61 69 71 72



Page | 185

10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

27

28

29

30

31 32 33 34

35

36

37

38 39 40 41 42 43 44 45

46 47 48 49

50

51

52

53 54 55 56 57 58 59 60 61 62 63 64

65 66

67 68


L27

L28

L29

L30

L31 L32 L33 L34

L35

L36

L37

L38 L39 L40 L41 L42 L43 L44 L45

L46

L47 L48 L49

L50

L51

L52

L53 L54 L55 L56 L57 L58 L59 L60 L61 L62 L63 L64

L65

L66

L67

L68

L69

L70

L71

L72L73

DG3DG1

DG2

Case IV with reconfiguration and DGs allocation

In this case the network is reconfigured and DGs are allocated simultaneously

Table 9-16 presents the best compromise solution obtained using the ACO algorithm

in a single fuzzy satisfaction objective function after DNR and DGs allocation and

the optimal network configuration and DG locations are shown in Fig 9-14 Feeder

loss maximum node voltage deviation and feeder load balancing decrease by

6721 5377 and 3840 respectively in comparison with the base case This

solution is one of the Pareto optimal solutions which are obtained by using AIS-

ACO algorithm

Table 9-16 Results of DNR and DGs allocation in fuzzy multi-objective formulation for 69-bus

system in Case IV

Objective

function

Feeder loss

(kW)

Maximum

node voltage

deviation (pu)

Feeder Load

balancing

index

Tie-switches

location

DGs location

08882 7397 00429 00158 14 55 61 71 72 B60 B60 B60

Fig 9-14 69-bus system for fuzzy multi-objective optimisation Case IV


Fig 9-15 shows the Pareto front obtained by the proposed method The mean and

standard deviations of the objective values of the Pareto solutions are listed in Table

9-17



Page | 186

70

80

90

100

110

120

004

0045

005

0055

006

0012

0013

0014

0015

0016

0017

0018

0019


Feeder

load b

ala

ncin

g index




deviation (pu)


Mean

9872 00520 00147

Standard deviation

1491 00055 00013









00428 is optimum which represents a 5388 1816 and 1801 improvement

compared to Case I Case II and Case III respectively If balancing feeder load is the



Page | 187

main objective the solution with load balancing index of 00125 pu is optimum

where the index decreases by 5174 2236 and 1497 in comparison with Case

I Case II and Case III respectively



voltage deviation

(pu)

Feeder Load

balancing index

Tie-switches

location

DGs location

Minimum Loss

7397 00429 00158 14 55 61 71 72 B60 B60 B60


8032 00428 00183 11 55 61 71 72 B60 B60 B60


10962 00577 00125 14 63 69 71 72 B62 B62 B62

95 Summary

In this study the DNR and DG allocation problem is formulated either within a

fuzzy satisfaction objective function or within a multi-objective Pareto optimal

framework This formulation incorporates the minimisation of three conflicting

objectives feeder loss maximum node voltage deviation and feeder load balancing

index In the fuzzy multi-objective formulation all three objectives are transformed

into a single fuzzy satisfaction objective function and the ACO algorithm is used to

provide decision support The AIS-ACO algorithm has been presented in this study

for the assessment of the multi-objective DNR problem from a Pareto optimality

point of view The proposed methods have been successfully applied on a 33-bus and

a 69-bus radial distribution system The results illustrate that the proposed algorithm


diversity This allows the network operators to choose any one from the non-

dominated solutions for implementation based on utilitiesrsquo priorities And the corner

non-dominated solutions which represent the minimum value of each objective

function are presented in the Pareto front chart



Page | 188

Future work could include the assessment of the DNR and DG allocation problem

with more than three objectives These objectives may include balancing loads on

transformers minimising the number of switching operations etc The proposed

methodologies can be evaluated further by applying them to actual systems

Page | 189

CHAPTER 10

CONCLUSION amp FUTURE WORK

101 Conclusion

The aim of this thesis is to improve service efficiency and quality in distribution

networks Optimal distribution automation (DA) is one of the best solutions to

achieve this goal The multiple objectives are transformed into different forms based

on utilitiesrsquo priorities For this purpose the Monte Carlo method is used to solve

power system issues involving uncertain load values And a set of ant colony

optimisation (ACO)-based algorithms has been developed for objectives

optimisation This section summarises the conclusions drawn from the research

results

A comprehensive review of the network configurations switchgears DA

assessment of loss and reliability indices and different forms of multi-objective

functions was provided in Chapter 2 This has demonstrated the need for DA to

provide a reliable and high efficiency power supply to all customers with a minimum

cost

In Chapter 3 the thesis reviewed the techniques for the assessment of mono-

objectivemulti-objective optimisation problems which were categorised into two

groups simulation methods and analytical methods The Monte Carlo method is a

typical simulation technique and is generally used to deal with power system

calculations involving uncertain parameters It can find the best solution with a high

Chapter 10 Conclusion amp Future Work

Page | 190

degree of accuracy but requires a considerable amount of CPU time and memory

The ant colony optimisation (ACO) algorithm is one of the metaheuristic techniques

designed for assessing the DA problems It can find the global optimum solution in a

reasonable computation time The artificial immune systems (AIS)-ACO hybrid

algorithm was used for assessing the DA problems in order to obtain a set of non-

dominated solutions by using the concept of Pareto dominance

The thesis illustrates why transformer economic operation (TEO) is an economical

solution to reduce transformer loss The TEO mode with minimum loss and

satisfactory voltages is achieved by operating with one or two transformers This

can be summarised as when the transformer load factor is less than the TCLF

transformers should operate separately However when the transformer load factor is

higher than the TCLF it is recommended that transformers operate in parallel In

Chapter 4 a Monte Carlo simulation platform was established to tackle load

uncertainties A methodology based on TEO to reduce transformer loss was then

described This results in a reduction over the conventional transformer loss ie

when two transformers are in parallel operation However simulation studies also

indicate voltage profiles are improved when transformers operate in parallel

Therefore a slight reduction in TCLF results in an increased loss but an

improvement in voltage performance

In Chapter 4 the thesis also demonstrates why distribution network reconfiguration

(DNR) is an effective strategy for transformer loss reduction The presented results

illustrate the optimal locations of tie-switch statuses have successfully reduced the

transformer losses and improved the voltages profiles during a 24 hour operating

period The further away the nodes are from the tie-switch the better the voltage

profiles obtained In addition when the tie-switch moves closer to the middle of the

linked feeder the voltage performance is improved In this case the daily energy

loss in Scenario 5 is 11162 kWh After the introduction of Scenario 9 the annual

saving energy could be 59641 kWh

One conclusion of this thesis is that the network can be reconfigured and DGs can be

relocated simultaneously for feeder loss reduction In Chapter 5 an ACO algorithm

was used for assessing the DNR and DG allocation problems in terms of feeder loss

reduction The numerical results showed that for best performance the existing tie-


Page | 191

switches were relocated and DGs were optimally placed at the same time The feeder

losses are reduced by 4662 and 6721 for the 33-bus and 69-bus system

respectively The inappropriate network configuration and DG location might result

in loss increment when the size of DG is increased The proposed methodology has

also successfully reduced the total feeder loss and improved the voltage profiles for

different capacities of DG by determining the most suitable network topology and

the DG locations In addition the simulation results have been compared with other

classical methods in literature and it is demonstrated that the proposed ACO is more

efficient and is more likely to obtain the global optimum solution

Another conclusion of this thesis is that the distribution network loss including

transformer loss and feeder loss can be minimised by using a new optimal planning

strategy This strategy is a combination of TEO and network reconfiguration as

presented in Chapter 6 In this chapter the distribution loads experience daily and

seasonal variations and the day is divided into two periods The proposed ACO

algorithm has successfully found the optimum network configuration and economic

operation mode of transformers in all substations during each time interval The

annual energy loss is reduced by 506 compared to the original network Both

transformer loss and feeder loss are reduced through this optimal planning using

DNR and TEO Furthermore simulation results obtained with numerical studies

have demonstrated the capability of applying the ACO algorithm to distribution

network planning including networks with DGs and EVs The proposed

methodology has successfully reduced the total network loss for different capacities

of DG and different penetration levels of EVs by determining the most suitable

network topology compared to the original configuration Comparative results also

show that coordinated charging plan results in less energy loss compared to

uncoordinated charging strategy with the same EV penetration level This is due to

the postponement of charging time which avoids a clash with the peak power

demand times

The thesis develops an effective strategy of sectionalising switch placement (SSP)

for system reliability improvement This is achieved by installing new switches and

relocating existing switches In Chapter 7 an ACO algorithm was proposed for the

assessment of the SSP problem based on reliability improvement and switch costs

minimisation using either a single objective function with weighted aggregation of a


Page | 192

multi-objective function with fuzzy variables The selection of pheromone

evaporation rate and number of ants is a trade-off between the global search ability

and convergence rate of the ACO algorithm In comparison with the original system

existing sectionalising switches were relocated and new automatic switches were

installed For this practical system the total system costs are reduced by 4289

compared to the original network The impact of installing sectionalising switches on

reducing the total system costs decreases as the number of sectionalising switches is

increased Furthermore a benefit-to-cost analysis which offered a comparison

between ECOST and switch costs was implemented The analysis reveals that the

installing and relocating sectionalising switches is a profitable investment In

addition a set of compromise solutions was obtained by assessing the SSP problem

in terms of ECOST and SAIDI reduction during fault contingencies The placement

of sectionalising switches results in a reduction of 60 in ECOST and 7148 in

SAIDI

The thesis also proposes a strategy for assessing the DNR problems if the


for all the multiple conflicting objectives simultaneously This formulates the DNR

problem within a multi-objective formulation in the Pareto optimal framework In

Chapter 8 The MOACO and AIS-ACO algorithms were used for assessing this

problem in terms of loss reduction and reliability improvement Both algorithms

have obtained the same Pareto optimal solutions but the AIS-ACO algorithm

performs better in comparison with the MOACO algorithm in terms of computation

time Feeder loss maximum node voltage deviation and feeder load balancing were

simultaneous optimised in Chapter 9 A set of non-dominated solutions with high

quality and great diversity was obtained This set of solutions represent different

trade-offs among the objective functions And the corner non-dominated solutions

which represent the minimum value of each objective function are presented in the

Pareto front chart For IEEE 69-bus system compared to the base case the network

reconfiguration and DG allocation result in a reduction of 6721 in minimum loss

solution If improving the voltage profiles is the principle objective the best solution

represents a 5388 improvement of this index If balancing feeder load is the main

objective this index decreases by 5174 By varying the weighting factors for the


Page | 193

parameters the decision makers can select the best compromise among the three

objectives for implementation depending on the utilitiesrsquo priorities

102 Future Work

Based on the findings of this project the suggestions for future work are

In this thesis the transformers have the same characteristics In the future as the

cost of replacing an existing transformer with a new one is cheaper than

replacing both transformers the situation that two transformers with different

characteristics in a substation is not uncommon Therefore an optimisation

method for two transformers with different characteristics will be investigated

and four operation modes can occur

1) First transformer operates alone

2) Second transformer operates alone

3) Two transformers operate in parallel

4) Optimisation mode optimum selection of the transformers needed to

supply each feeder

At present in the UK customers pay for losses in the network In this thesis the

losses are analysed as a whole without allocating them to the users in the network

In the future a loss allocation scheme to customers in the distribution network

will be developed However after reconfiguration the total network loss is

reduced but the loss allocation to some customers may increase The customers

with more loss allocated will be dissatisfied with the network reconfiguration It

is therefore important to change the tariff structure for these customers so that

they are not obliged to pay more for the increase in loss allocation as a result of

network reconfiguration

In this thesis the maximum number of objectives to be optimised simultaneously

is three However the work could be extended to solve the DA problem with

more than three objectives These objectives may include balancing load on

transformers minimising the number of switch operations and maximising the

load on feeders


Page | 194

The optimal DNR DG allocation TEO and SSP will be combined together to

solve the multi-objective optimisation problem The proposed methodologies

could be tested in large-scale practical systems

In this thesis the evaluation of reliability indices only considers the faults in the

line sections And all the feeders are supposed to have the same parameters and

hence the same failure rates However historical data shows the failure rates of a

feeder vary with geographical location and the weather Therefore different

types of feeders and seasonal varying data of feeder section failure rates will be

considered in future work Moreover the impacts of contingencies on the system

such as faults in the transformers and protective devices could also be considered

The integration of large number of electric vehicles (EVs) into the distribution

network places an extra burden on the electricity grid such as increases in energy

loss overloading in feeders decrease in reliability and power quality Therefore

network reconfiguration techniques and smart charging strategies will be

proposed to moderate the charging effects of EVs In addition the vehicle-to-grid

(V2G) technique which returns electricity to the gird will also be studied The

bi-directional of EVs in the network can provide power to improve load

balancing by ldquovalley fillingrdquo (charging) and ldquopeak shavingrdquo (discharging) [118]

The simulation results show ACO-based algorithms could find a set of good

solutions within a reasonable computation time The ACO control parameters are

set experimentally using information from several trial runs More work is

needed to improve the performance of the proposed algorithms by determining

the optimum set of parameter values It is expected that new ACO-based

algorithms will outperform any existing ones or at worst match their results

In the future a multi-objective stochastic optimal flow problem with the

consideration of load DG EV uncertainties will be addressed The load DG

and EV models are obtained by using a Monte Carlo probabilistic power flow

The objectives are then optimised by using a suitable metaheuristic technique

Page | 195

References

[1] L M Faulkenberry Electrical power distribution and transmission Pearson

Education India 1996

[2] Parliamentary Office of Science and Technology ldquoUK Electricity Networksrdquo

2001

[3] R Das et al ldquoDistribution automation strategies evolution of technologies

and the business caserdquo IEEE Trans Smart Grid vol 6 no 4 pp 2166ndash2175

2015

[4] P Balakrishna K Rajagopal and K S Swarup ldquoApplication benefits of

Distribution Automation and AMI systems convergence methodology for

distribution power restoration analysisrdquo Sustain Energy Grids Networks vol

2 pp 15ndash22 2015

[5] ofgem ldquoEnergy Efficiency Directive An assessment of the energy efficiency

potential of Great Britainrsquos gas and electricity infrastructurerdquo 2015

[6] R C Dugan M F McGranaghan and H W Beaty ldquoElectrical power

systems qualityrdquo 1996

[7] British Standards Institution DECC UK Office for National Statistic and

Met Office UK ldquoVoltage characteristics of electricity supplied by public

distribution systemsrdquo Whether and Climate change no December pp 1ndash18

2010

[8] Y F Niu Z Y Gao and W H K Lam ldquoEvaluating the reliability of a

stochastic distribution network in terms of minimal cutsrdquo Transp Res Part E

Logist Transp Rev vol 100 pp 75ndash97 2017

[9] R Billinton and J E Billinton ldquoDistribution system reliability indicesrdquo

IEEE Trans Power Deliv vol 4 no 1 pp 561ndash568 1989

[10] Ofgem ldquoElectricity Distribution Annual Report for 2010-11rdquo 2012

[11] J Hamachi K Eto ldquoUnderstanding the Cost of Power Interruption to US

Electric Consumers LBNL-55718rdquo 2004

[12] R M Vitorino H M Jorge and L P Neves ldquoLoss and reliability

optimization for power distribution system operationrdquo Elsevier BV 2013

[13] E M Carreno R Romero and A Padilha-Feltrin ldquoAn efficient codification

to solve distribution network reconfiguration for loss reduction problemrdquo

IEEE Trans Power Syst vol 23 no 4 pp 1542ndash1551 2008

[14] A Y Abdelaziz R A Osama and S M El-Khodary ldquoReconfiguration of

distribution systems for loss reduction using the hyper-cube ant colony

optimisation algorithmrdquo IET Gener Transm Distrib vol 6 no 2 p 176

References

Page | 196

2012

[15] European commission ldquoRoadmap for moving to a low-carbon economy in

2050rdquo DG Clim Action portal pp 1ndash2 2011

[16] A Mohamed Imran M Kowsalya and D P Kothari ldquoA novel integration

technique for optimal network reconfiguration and distributed generation

placement in power distribution networksrdquo Int J Electr Power Energy Syst

vol 63 pp 461ndash472 2014

[17] W Guan Y Tan H Zhang and J Song ldquoDistribution system feeder

reconfiguration considering different model of DG sourcesrdquo Int J Electr

Power Energy Syst vol 68 pp 210ndash221 2015

[18] S A Yin and C N Lu ldquoDistribution feeder scheduling considering variable

load profile and outage costsrdquo IEEE Trans Power Syst vol 24 no 2 pp

652ndash660 2009

[19] I Richardson M Thomson D Infield and C Clifford ldquoDomestic electricity

use A high-resolution energy demand modelrdquo Energy Build vol 42 no 10

pp 1878ndash1887 2010

[20] K Deb A Pratap S Agarwal and T Meyarivan ldquoA fast and elitist

multiobjective genetic algorithm NSGA-IIrdquo IEEE Trans Evol Comput vol

6 no 2 pp 182ndash197 2002

[21] M E Elkhatib R El Shatshat and M M A Salama ldquoDecentralized reactive

power control for advanced distribution automation systemsrdquo IEEE Trans

Smart Grid vol 3 no 3 pp 1482ndash1490 2012

[22] C-L Su and J-H Teng ldquoOutage costs quantification for benefitndashcost

analysis of distribution automation systemsrdquo Int J Electr Power Energy

Syst vol 29 no 10 pp 767ndash774 2007

[23] I Goroohi Sardou M Banejad R Hooshmand and a Dastfan ldquoModified

shuffled frog leaping algorithm for optimal switch placement in distribution

automation system using a multi-objective fuzzy approachrdquo IET Gener

Transm Distrib vol 6 no 6 p 493 2012

[24] C L Smallwood and J Wennermark ldquoBenefits of distribution automationrdquo

IEEE Ind Appl Mag vol 16 no 1 pp 65ndash73 2010

[25] T Goumlnen Electric power distribution system engineering McGraw-Hill New

York 1986

[26] V Madani et al ldquoDistribution automation strategies challenges and

opportunities in a changing landscaperdquo IEEE Trans Smart Grid vol 6 no 4

pp 2157ndash2165 2015

[27] J J Burke ldquoPower distribution engineering fundamentals and applicationsrdquo

1994

[28] A Elmitwally E Gouda and S Eladawy ldquoRestoring recloser-fuse

coordination by optimal fault current limiters planning in DG-integrated

References

Page | 197

distribution systemsrdquo Int J Electr Power Energy Syst vol 77 pp 9ndash18

2016

[29] L He J R Mayor R G Harley H Liles G Zhang and Y Deng ldquoMulti-

physics modeling of the dynamic response of a circuit breaker recloser

Systemrdquo in IEEE International Electric Machines amp Dirves Conference 2013

vol 1 pp 1001ndash1008

[30] J M Gers and E J Holmes Protection of electricity distribution networks

vol 47 The Institution of Electrical Engineers 2004

[31] E-J-A Zehra M Moghavvemi M M I Hashim and M Kashem ldquoNetwork

reconfiguration using PSAT for loss reduction in distribution systemsrdquo in 1st

International Conference on Energy Power and Control (EPC-IQ) 2010 pp

62ndash66

[32] J J S Grainger W D J J Grainger and W D Stevenson Power system

analysis McGraw-Hill New York 1994

[33] R D Laramore An introduction to electrical machines and transformers

Wiley 1990

[34] D Borge-Diez A Colmenar-Santos M Castro-Gil and J Carpio-Ibaacutentildeez

ldquoParallel distribution transformer loss reductions A proposed method and

experimental validationrdquo Int J Electr Power Energy Syst vol 49 no 1 pp

170ndash180 2013

[35] Y Wang and hui chao Liu ldquoThe information system for economic operation

of transformer based on ASPrdquo in Intertational Power Engineering

Conference 2007 pp 1914ndash1917

[36] X Chen and Z Guo ldquoEconomic operation of power transformer based on real

time parameter checkingrdquo in Power Engineering Society General Meeting

2006 pp 4ndash6

[37] W Yuan and Y Zhang ldquoEconomic operation of transformers in the area

power network based on real-time analysis and controlrdquo in China

International Conference on Electricity Distribution 2008 pp 1ndash5

[38] R Song and X Zhang ldquoThe application research of load smoothing algorithm

in the transformer economic operationrdquo in International Conference on

Energy and Environment Technology 2009 vol 2 pp 328ndash331

[39] C Mamane ldquoTransformer loss evaluation user-manufacturer

communicationsrdquo IEEE Trans Ind Appl vol IA-20 no 1 pp 11ndash15 1984

[40] E I Amoiralis M A Tsili and A G Kladas ldquoEconomic evaluation of

transformer selection in electrical power systemsrdquo in 19th International

Conference on Electrical Machines 2010 pp 1ndash5

[41] B Suechoey J Ekburanawat N Kraisnachinda S Banjongjit C Chompoo

and M Kando ldquoAn analysis and selection of distribution transformer for

losses reductionrdquo in IEEE Power Engineering Society Winter Meeting 2000

pp 2290ndash2293

References

Page | 198

[42] B Suechoey S Bunjongjit and M Kando ldquoThe result analysis of economic

distribution transformer design in Thailandrdquo in Transmission and Distribution

Conference and Exhibition 2002 pp 1820ndash1823

[43] A Merlin and H Back ldquoSearch for a minimal-loss operating spanning tree

configuration in an urban power distribution systemrdquo in Proc 5th Power

System Computation Conf 1975 pp 1ndash18

[44] S Civanlar J J Grainger H Yin and S S H Lee ldquoDistribution feeder

reconfiguration for loss reductionrdquo IEEE Trans Power Deliv vol 3 no 3

pp 1217ndash1223 1988

[45] M-R Andervazh J Olamaei and M-R Haghifam ldquoAdaptive multi-

objective distribution network reconfiguration using multi-objective discrete

particles swarm optimisation algorithm and graph theoryrdquo IET Gener Transm

Distrib vol 7 no 12 pp 1367ndash1382 2013

[46] K Nara A Shiose M Kitagawa and T Ishihara ldquoImplementation of genetic

algorithm for distribution systems loss minimum re-configurationrdquo IEEE

Trans Power Syst vol 7 no 3 pp 1044ndash1051 1992

[47] J Z Zhu ldquoOptimal reconfiguration of electrical distribution network using

the refined genetic algorithmrdquo Electr Power Syst Res vol 62 no 1 pp 37ndash

42 2002

[48] B Enacheanu B Raison R Caire O Devaux W Bienia and N HadjSaid

ldquoRadial network reconfiguration using genetic algorithm based on the matroid

theoryrdquo IEEE Trans Power Syst vol 23 no 1 pp 186ndash195 2008

[49] J C Cebrian and N Kagan ldquoReconfiguration of distribution networks to

minimize loss and disruption costs using genetic algorithmsrdquo Electr Power

Syst Res vol 80 no 1 pp 53ndash62 2010

[50] H D Chiang and R Jean-Jumeau ldquoOptimal network reconfigurations in

distribution systems part 1 A new formulation and a solution methodologyrdquo


[51] Y J Jeon J C Kim and J O Kim ldquoAn efficient simulted annealing

algorithm for network reconfiguration in large-scale distribution systemsrdquo


[52] H Mori and Y Ogita ldquoA parallel tabu search based method for

reconfigurations of distribution systemsrdquo in Power Engineering Society

Summer Meeting 2000 pp 73ndash78

[53] D Zhang Z Fu and L Zhang ldquoAn improved TS algorithm for loss-

minimum reconfiguration in large-scale distribution systemsrdquo Electr Power

Syst Res vol 77 no 5ndash6 pp 685ndash694 2007

[54] A Y Abdelaziz F M Mohamed S F Mekhamer and M A L Badr

ldquoDistribution system reconfiguration using a modified Tabu Search algorithmrdquo

Electr Power Syst Res vol 80 no 8 pp 943ndash953 2010

[55] A Y Abdelaziz F M Mohammed S F Mekhamer and M A L Badr

References

Page | 199

ldquoDistribution systems reconfiguration using a modified particle swarm

optimization algorithmrdquo Electr Power Syst Res vol 79 no 11 pp 1521ndash

1530 2009

[56] A Skoonpong and S Sirisumrannukul ldquoNetwork reconfiguration for

reliability worth enhancement in distribution systems by simulated annealingrdquo

5th Int Conf Electr Eng Comput Telecommun Inf Technol ECTI-CON pp

937ndash940 2008

[57] S Elsaiah M Benidris and J Mitra ldquoReliability improvement of power

distribution system through feeder reconfigurationrdquo in 13th International

Conference on Probabilistic Methods Applied to Power Systems 2014

[58] A Kavousi-Fard and T Niknam ldquoOptimal distribution feeder reconfiguration

for reliability improvement considering uncertaintyrdquo IEEE Trans Power

Deliv vol 29 no 3 pp 1344ndash1353 2014

[59] S Ghasemi ldquoBalanced and unbalanced distribution networks reconfiguration

considering reliability indicesrdquo Ain Shams Eng J 2015

[60] A Saffar R Hooshmand and A Khodabakhshian ldquoA new fuzzy optimal

reconfiguration of distribution systems for loss reduction and load balancing

using ant colony search-based algorithmrdquo Appl Soft Comput J vol 11 no 5

pp 4021ndash4028 2011

[61] D Das ldquoA fuzzy multiobjective approach for network reconfiguration of

distribution systemsrdquo IEEE Trans Power Deliv vol 21 no 1 pp 202ndash209

2006

[62] J E Mendoza E A Loacutepez M E Loacutepez and C A Coello Coello

ldquoMicrogenetic multiobjective reconfiguration algorithm considering power

losses and reliability indices for medium voltage distribution networkrdquo IET

Gener Transm Distrib vol 3 no 9 pp 825ndash840 2009

[63] K M Muttaqi J Aghaei V Ganapathy and A E Nezhad ldquoTechnical

challenges for electric power industries with implementation of distribution

system automation in smart gridsrdquo Renew Sustain Energy Rev vol 46 pp

129ndash142 2015

[64] A Abiri-Jahromi M Fotuhi-Firuzabad M Parvania and M Mosleh

ldquoOptimized sectionalizing switch placement strategy in distribution systemsrdquo


[65] J Northcote-Green and R G Wilson Control and automation of electrical

power distribution systems vol 28 CRC Press 2006

[66] H Falaghi M R Haghifam and C Singh ldquoAnt colony optimization-based

method for placement of sectionalizing switches in distribution networks

using a fuzzy multiobjective approachrdquo IEEE Trans Power Deliv vol 24

no 1 pp 268ndash276 2009

[67] M Nematollahi and M Tadayon ldquoOptimal sectionalizing switches and DG

placement considering critical system conditionrdquo in 21st Iranian Conference

References

Page | 200

on Electrical Engineering 2013 pp 1ndash6

[68] J H Teng and C N Lu ldquoFeeder-switch relocation for customer interruption

cost minimizationrdquo IEEE Trans Power Deliv vol 17 no 1 pp 254ndash259

2002

[69] J H Teng and Y H Liu ldquoA novel ACS-based optimum switch relocation

methodrdquo IEEE Trans Power Syst vol 18 no 1 pp 113ndash120 2003

[70] V Miranda ldquoUsing fuzzy reliability in a decision aid environment for

establishing interconnection and switching location policiesrdquo in CIRED 1991

pp 1ndash6

[71] A Heidari V G Agelidis and M Kia ldquoConsiderations of sectionalizing

switches in distribution networks with distributed generationrdquo IEEE Trans

Power Deliv vol 30 no 3 pp 1401ndash1409 2015

[72] I v Zhezhelenko Y Papaika and others ldquoEstimating economic equivalent of

reactive power in the systems of enterprise electric power supplyrdquo Sci Bull

Natl Min Univ no 5 2016

[73] L Li and R Li ldquoStudy on the analysis software of economic operation of

transformerrdquo Adv Mater Res vol 1008ndash1009 pp 497ndash500 2014

[74] J Shang Z Tan C Zhang and L Ju ldquoThe transformer equipment selectionrsquos

update decision technical and economic analysis modelrdquo in Energy and

Power Engineering 2013 vol 5 no 4 pp 143ndash147

[75] B Amanulla S Chakrabarti and S N Singh ldquoReconfiguration of power

distribution systems considering reliability and power lossrdquo IEEE Trans


[76] R E Brown Electric power distribution reliability CRC press 2008

[77] P Zhou R Y Jin and L W Fan ldquoReliability and economic evaluation of

power system with renewables A reviewrdquo Renew Sustain Energy Rev vol

58 pp 537ndash547 2016

[78] R Billington and R N Allan Reliability evaluation of power systems

Plenum Publishing Corp New York NY 1996

[79] N G Paterakis et al ldquoMulti-objective reconfiguration of radial distribution

systems using reliability indicesrdquo IEEE Trans Power Syst vol 31 no 2 pp

1048ndash1062 2016

[80] B Sultana M W Mustafa U Sultana and A R Bhatti ldquoReview on

reliability improvement and power loss reduction in distribution system via

network reconfigurationrdquo Renew Sustain Energy Rev vol 66 pp 297ndash310

2016

[81] K Xie J Zhou and R Billinton ldquoReliability evaluation algorithm for

complex medium voltage electrical distribution networks based on the shortest

pathrdquo IEE Proceedings-Generation Transm Distrib vol 150 no 6 pp

686ndash690 2003

References

Page | 201

[82] Z Ghofrani-Jahromi M Kazemi and M Ehsan ldquoDistribution switches

upgrade for loss reduction and reliability improvementrdquo IEEE Trans Power


[83] P Ngatchou A Zarei and A El-Sharkawi ldquoPareto multi objective

optimizationrdquo in Proceedings of the 13th International Conference on

Intelligent Systems Application to Power Systems 2005 pp 84ndash91

[84] J S Savier and D Das ldquoImpact of network reconfiguration on loss allocation

of radial distribution systemsrdquo IEEE Trans Power Deliv vol 22 no 4 pp

2473ndash2480 2007

[85] T T Nguyen T T Nguyen A V Truong Q T Nguyen and T A Phung

ldquoMulti-objective electric distribution network reconfiguration solution using

runner-root algorithmrdquo Appl Soft Comput J vol 52 pp 93ndash108 2017

[86] N Gupta A Swarnkar R C Bansal and K R Niazi ldquoMulti-objective

reconfiguration of distribution systems using adaptive genetic algorithm in

fuzzy frameworkrdquo IET Gener Transm Distrib vol 4 no 12 pp 1288ndash1298

2010

[87] M R Narimani A Azizi Vahed R Azizipanah-Abarghooee and M

Javidsharifi ldquoEnhanced gravitational search algorithm for multi-objective

distribution feeder reconfiguration considering reliability loss and operational

costrdquo IET Gener Transm Distrib vol 8 no 1 pp 55ndash69 2014

[88] A Ahuja S Das and A Pahwa ldquoAn AIS-ACO hybrid approach for multi-

objective distribution system reconfigurationrdquo IEEE Trans Power Syst vol

22 no 3 pp 1101ndash1111 2007

[89] M Rostami A Kavousi-Fard and T Niknam ldquoExpected cost minimization

of smart grids with plug-in hybrid electric vehicles using optimal distribution

feeder reconfigurationrdquo Ind Informatics IEEE Trans vol 11 no 2 pp

388ndash397 2015

[90] S Oh J Kim S Kwon and S Chung ldquoMonte Carlo simulation of

phytosanitary irradiation treatment for mangosteen using MRI-based

geometryrdquo vol 39 no 3 pp 205ndash214 2014

[91] N HadjSaid and J C Sabonnadiere Electrical Distribution Networks

London ISTE Ltd 2011

[92] Y Li ldquoVoltage balancing on three-phase low voltage feederrdquo The Univerisity

of Manchester 2015

[93] K Bell and P R Allan ldquoComputation of the Value of Securityrdquo 1999

[94] M Dorigo V Maniezzo and A Colorni ldquoThe ant systems optimization by a

colony of cooperative agentsrdquo IEEE Trans Syst Man Cybern B vol 26 no

1 pp 1ndash13 1996

[95] M Dorigo and L M Gambardella ldquoAnt colony system a cooperative

learning approach to the traveling salesman problemrdquo IEEE Trans Evol

Comput vol 1 no 1 pp 53ndash66 1997

References

Page | 202

[96] M Lopez-Ibanez and T Stuetzle ldquoThe automatic design of multiobjective ant

colony optimization algorithmsrdquo IEEE Trans Evol Comput vol 16 no 6

pp 861ndash875 2012

[97] L Charles Daniel and S Ravichandran ldquoDistribution network reconfiguration

for loss reduction using ant colony system algorithmrdquo in IEEE Indicon 2005


[98] J F Goacutemez et al ldquoAnt colony system algorithm for the planning of primary

distribution circuitsrdquo IEEE Trans Power Syst vol 19 no 2 pp 996ndash1004

2004

[99] J Lu N Wang J Chen and F Su ldquoCooperative path planning for multiple

UCAVs using an AIS-ACO hybrid approachrdquo Proc 2011 Int Conf Electron

Mech Eng Inf Technol EMEIT 2011 vol 8 no 2 pp 4301ndash4305 2011

[100] J E Hunt and D E Cooke ldquoAn adaptive distributed learning system based

on the immune systemrdquo 1995 IEEE Int Conf Syst Man Cybern Intell Syst

21st Century vol 3 pp 2494ndash2499 1995

[101] C A C Coello and N C Cortes ldquoSolving multiobjective optimization

problems using an artificial immune systemrdquo Genet Program Evolvable

Mach vol 6 no 2 pp 163ndash190 2005

[102] L N De Castro and F J Von Zuben ldquoLearning and optimization using the

clonal selection principlerdquo IEEE Trans Evol Comput vol 6 no 3 pp 239ndash

251 2002

[103] Office for National Statistics Population and household estimates for the

United Kingdom UK 2011

[104] S Ingram S Probert and K Jackson ldquoThe impact of small scale embedded

generation on the operating parameters of distribution networksrdquo Department

of Trade and Industry (DTI) 2003 [Online] Available

httpwebarchivenationalarchivesgovuk20100919182407httpwwwensg

govukassets22_01_2004_phase1b_report_v10b_web_site_finalpdf

[105] 63 EDS 02-0027 Engineering design standard EDS 02-007 11 kV Triplex

Cable 2012

[106] TTH ldquo75 MVA-33-11 KV-GTP TTHrdquo 2014 [Online] Available

httpwwwtranstechtransformerscompdf75mva3311kvgtptth24012008pdf

[107] A M Tahboub V R Pandi and H H Zeineldin ldquoDistribution system

reconfiguration for annual energy loss reduction considering variable

distributed generation profilesrdquo IEEE Trans Power Deliv vol 30 no 4 pp

1677ndash1685 2015

[108] M E Baran and F F Wu ldquoNetwork reconfiguration in distribution systems

for loss reduction and load balancingrdquo Power Deliv IEEE Trans vol 4 no

2 pp 1401ndash1407 1989

[109] D Shirmohammadi and H W Hong ldquoReconfiguration of electric distribution

networks for resistive line losses reductionrdquo IEEE Trans Power Deliv vol 4

References

Page | 203

no 2 pp 1492ndash1498 1989

[110] R S Rao K Ravindra K Satish and S V L Narasimham ldquoPower loss

minimization in distribution system using network reconfiguration in the

presence of distributed generationrdquo IEEE Trans Power Syst vol 28 no 1

pp 1ndash9 2012

[111] D Sudha Rani N Subrahmanyam and M Sydulu ldquoMulti-objective invasive

weed optimization - an application to optimal network reconfiguration in

radial distribution systemsrdquo Int J Electr Power Energy Syst vol 73 pp

932ndash942 2015

[112] R L Haupt and S E Haupt Practical genetic algorithms John Wiley amp

Sons 2004

[113] X S Yang and S Deb ldquoCuckoo search via Levy flightsrdquo 2009 World Congr

Nat Biol Inspired Comput NABIC 2009 - Proc pp 210ndash214 2009

[114] R N Allan R Billinton I Sjarief L Goel and K S So ldquoA reliability test

system for educational purposes-basic distribution system data and resultsrdquo


[115] G Li and X-P Zhang ldquoModeling of plug-in hybrid electric vehicle charging

demand in probabilistic power flow calculationsrdquo Smart Grid IEEE Trans

vol 3 no 1 pp 492ndash499 2012

[116] UK Department for Transport ldquoNational Travel Survey England 2013 -

Statistical Releaserdquo no July p 26 2014

[117] A Mazza G Chicco and A Russo ldquoOptimal multi-objective distribution

system reconfiguration with multi criteria decision making-based solution

ranking and enhanced genetic operatorsrdquo Int J Electr Power Energy Syst

vol 54 pp 255ndash267 2014

[118] E Sortomme and M A El-Sharkawi ldquoOptimal charging strategies for

unidirectional vehicle-to-gridrdquo IEEE Trans Smart Grid vol 2 no 1 pp

119ndash126 2011

Page | 204

APPENDIX A Network Model Data

A1 UK generic distribution network

The line parameters given here is related to the single line diagram of the network

shown in Fig 45 which are used in the simulation study in Section 451 and 452


11 kV line type Cross

Sectional

Area

(CSA)

Positive sequence

Z

Zero-phase

sequence

Z

Approximate

Capacitance

C

Id Configuration Rph Xph R0 X0 C

(mm2) (Ωkm) (μFkm)

A Nexans

635011000

Volt Triplex

Cable

185 0415 0112 0988 0236 036

B 95 0220 0012 0530 0102 028

Appendix A Network Data

Page | 205

A2 33-bus system

Table A-2 Line and load data of 33-bus system

Branch

number

Sending end

node

Receiving end

node

R

(Ω)

X

(Ω)

P at receiving

end (kW)

Q at receiving

end (kVAr)

1 0 1 00922 0047 100 60

2 1 2 04930 02511 90 40

3 2 3 03660 01864 120 80

4 3 4 03811 01941 60 30

5 4 5 08190 07070 60 20

6 5 6 01872 06188 200 100

7 6 7 07114 02351 200 100

8 7 8 10300 07400 60 20

9 8 9 10440 07400 60 20

10 9 10 01966 00650 45 30

11 10 11 03744 01238 60 35

12 11 12 14680 11550 60 35

13 12 13 05416 07129 120 80

14 13 14 05910 05260 60 10

15 14 15 07463 05450 60 20

16 15 16 12890 17210 60 20

17 16 17 03720 05740 90 40

18 17 18 01640 01565 90 40

19 18 19 15042 13554 90 40

20 19 20 04095 04784 90 40

21 20 21 07089 09373 90 40

22 21 22 04512 03083 90 50

23 22 23 08980 07091 420 200

24 23 24 08960 07011 420 200

25 24 25 02030 01034 60 25

26 25 26 02842 01447 60 25

27 26 27 10590 09337 60 20

28 27 28 08042 07006 120 70

29 28 29 05075 02585 200 600

30 29 30 09744 09630 150 70

31 30 31 03105 03619 210 100

32 31 32 03410 05362 60 40

33 7 20 2 2 -- --

34 11 21 2 2 -- --

35 8 14 2 2 -- --

36 17 32 05 05 -- --

37 24 28 05 05 -- --


Page | 206

A3 69-bus system


Branch

number

Sending end

node

Receiving end

node

R

(Ω)

X

(Ω)

P at receiving

end (kW)

Q at receiving

end (kVAr)

1 0 1 00005 00012 0 0

2 1 2 00005 00012 0 0

3 2 3 00015 00036 0 0

4 3 4 00251 00294 0 0

5 4 5 0366 01864 26 22

6 5 6 0381 01941 404 30

7 6 7 00922 0047 75 54

8 7 8 00493 00251 30 22

9 8 9 0819 02707 28 19

10 9 10 01872 00619 145 104

11 10 11 07114 02351 145 104

12 11 12 103 034 8 5

13 12 13 1044 0345 8 55

14 13 14 1058 03496 0 0

15 14 15 01966 0065 455 30

16 15 16 03744 01238 60 35

17 16 17 00047 00016 60 35

18 17 18 03276 01083 0 0

19 18 19 02106 0069 1 06

20 19 20 03416 01129 114 81

21 20 21 0014 00046 5 35

22 21 22 01591 00526 0 0

23 22 23 03463 01145 28 20

24 23 24 07488 02475 0 0

25 24 25 03089 01021 14 10

26 25 26 01732 00572 14 10

27 26 27 00044 00108 26 186

28 27 28 0064 01565 26 186

29 28 29 03978 01315 0 0

30 29 30 00702 00232 0 0

31 30 31 0351 0116 0 0

32 31 32 0839 02816 14 10

33 32 33 1708 05646 195 14

34 33 34 1474 04873 6 4

35 34 35 00044 00108 26 1855

36 35 36 0064 01565 26 1855

37 36 37 01053 0123 0 0

38 37 38 00304 00355 24 17

39 38 39 00018 00021 24 17

40 39 40 07283 08509 12 1

41 40 41 031 03623 0 0


Page | 207

42 41 42 0041 00478 6 43

43 42 43 00092 00116 0 0

44 43 44 01089 01373 3922 263

45 44 45 00009 00012 3922 263

46 45 46 00034 00084 0 0

47 46 47 00851 02083 79 564

48 47 48 02898 07091 3847 2745

49 48 49 00822 02011 3847 2745

50 49 50 00928 00473 405 283

51 50 51 03319 01114 36 27

52 51 52 0174 00886 435 35

53 52 53 0203 01034 264 19

54 53 54 02842 01447 24 172

55 54 55 02813 01433 0 0

56 55 56 159 05337 0 0

57 56 57 07837 0263 0 0

58 57 58 03042 01006 100 72

59 58 59 03861 01172 0 0

60 59 60 05075 02585 1244 888

61 60 61 00974 00496 32 23

62 61 62 0145 00738 0 0

63 62 63 07105 03619 227 162

64 63 64 1041 05302 59 42

65 64 65 02012 00611 18 13

66 65 66 00047 00014 18 13

67 66 67 07394 02444 28 20

68 67 68 00047 00016 28 20

69 49 58 2 1 -- --

70 26 64 1 05 -- --

71 12 20 05 05 -- --

72 10 42 05 05 -- --

73 14 45 1 05 -- --

A4 RBTS Bus 4 system

Table A-4 Feeder data of RBTS Bus 4

Feeder

Type

Length

(km)

Feeder section number

1 060 2 6 10 14 17 21 25 28 30 34 38 41 43 46 49 51 55 58 61 64 67

68 69 70 71

2 075 1 4 7 9 12 16 19 22 24 27 29 32 3537 40 42 45 48 50 53 56 60

63 65

3 080 3 5 8 11 13 15 18 20 23 26 31 33 36 3944 47 52 54 57 59 62 66


Page | 208

Table A-5 Reliability Data for RBTS Bus 4

Equipment λA λP λM λt R RM

Lines 004 0 0 0 5 0

Buses 0001 0 1 001 2 8

Switches 0004 0002 1 006 4 72

Distribution Transformers 0015 0 1 0 200 120

λA Active failure rate in (fryrkm) for lines and (fryr) for other components

λP Passive failure rate in (fryrkm) for lines and (fryr) for other components

λM Maintenance outage rate in (fryrkm) for lines and (fryr) for other components

λP Transient failure rate in (fryrkm) for lines and (fryr) for other components

R Repair time of failures in (hr)

RM Maintenance outage time in (hr)

Page | 209

APPENDIX B Simulation Results

B1 Simulation results of Chapter 4

B11Tie-switch location

As discussed in Section 452 the location of tie-switch in Scenario 9 is changeable

and the relevant results are presented in Table B-1 It can be clearly seen that the

NOP is located in lsquoTW1rsquo between 0730 and 1000 1600 and 1630 while in lsquoTW5rsquo

for the rest of the day

Table B-1 The locations of tie-switch in Scenario 9

Time Loc Time Loc Time Loc Time Loc Time Loc Time Loc

0000 TW5 0400 TW5 0800 TW1 1200 TW5 1600 TW1 2000 TW5

0010 TW5 0410 TW5 0810 TW1 1210 TW5 1610 TW1 2010 TW5

0020 TW5 0420 TW5 0820 TW1 1220 TW5 1620 TW1 2020 TW5

0030 TW5 0430 TW5 0830 TW1 1230 TW5 1630 TW1 2030 TW5

0040 TW5 0440 TW5 0840 TW1 1240 TW5 1640 TW5 2040 TW5

0050 TW5 0450 TW5 0850 TW1 1250 TW5 1650 TW5 2050 TW5

0100 TW5 0500 TW5 0900 TW1 1300 TW5 1700 TW5 2100 TW5

0110 TW5 0510 TW5 0910 TW1 1310 TW5 1710 TW5 2110 TW5

0120 TW5 0520 TW5 0920 TW1 1320 TW5 1720 TW5 2120 TW5

0130 TW5 0530 TW5 0930 TW1 1330 TW5 1730 TW5 2130 TW5

0140 TW5 0540 TW5 0940 TW1 1340 TW5 1740 TW5 2140 TW5

0150 TW5 0550 TW5 0950 TW1 1350 TW5 1750 TW5 2150 TW5

0200 TW5 0600 TW5 1000 TW1 1400 TW5 1800 TW5 2200 TW5

0210 TW5 0610 TW5 1010 TW5 1410 TW5 1810 TW5 2210 TW5

0220 TW5 0620 TW5 1020 TW5 1420 TW5 1820 TW5 2220 TW5

0230 TW5 0630 TW5 1030 TW5 1430 TW5 1830 TW5 2230 TW5

0240 TW5 0640 TW5 1040 TW5 1440 TW5 1840 TW5 2240 TW5

0250 TW5 0650 TW5 1050 TW5 1450 TW5 1850 TW5 2250 TW5

0300 TW5 0700 TW5 1100 TW5 1500 TW5 1900 TW5 2300 TW5

0310 TW5 0710 TW5 1110 TW5 1510 TW5 1910 TW5 2310 TW5

0320 TW5 0720 TW5 1120 TW5 1520 TW5 1920 TW5 2320 TW5

0330 TW5 0730 TW1 1130 TW5 1530 TW5 1930 TW5 2330 TW5

0340 TW5 0740 TW1 1140 TW5 1540 TW5 1940 TW5 2340 TW5

0350 TW5 0750 TW1 1150 TW5 1550 TW5 1950 TW5 2350 TW5

Appendix B Simulation Results

Page | 210

B12 Voltage variations

For Test Case 2 in Section 452 the detailed voltage values of the mean and the

corresponding 95th

profiles at each node in the linked feeder are recorded in Table

B-2 and Table B-3

Table B-2 Mean voltage profiles at each node in the linked feeder

Node

No

Scenarios

S1 S2 S3 S4 S5 S6 S7 S8 S9

A4_1 09675 09787 09787 09766 09859 09859 09748 09825 09815

A4_2 09676 09784 09784 09766 09856 09856 09748 09822 09813

A4_3 09677 09782 09782 09767 09854 09854 09749 09819 09811

A4_4 09678 09780 09780 09768 09851 09851 09750 09817 09810

A4_5 09681 09777 09777 09771 09849 09849 09753 09814 09808

A4_6 09685 09775 09775 09775 09846 09846 09757 09812 09807

A4_7 09689 09773 09773 09779 09845 09845 09762 09811 09807

A4_8 09694 09772 09772 09784 09844 09844 09767 09810 09807

B4_8 09700 09772 09772 09790 09844 09844 09773 09810 09808

B4_7 09707 09773 09773 09797 09845 09845 09779 09811 09810

B4_6 09714 09775 09775 09804 09846 09846 09787 09812 09813

B4_5 09722 09777 09777 09813 09849 09849 09795 09814 09816

B4_4 09731 09780 09780 09821 09851 09851 09804 09817 09820

B4_3 09737 09782 09782 09827 09854 09854 09809 09819 09823

B4_2 09743 09784 09784 09833 09856 09856 09815 09822 09826

B4_1 09749 09787 09787 09839 09859 09859 09821 09825 09830

Table B-3 95th

voltage profiles at each node in the linked feeder

Node

No

Scenarios

S1 S2 S3 S4 S5 S6 S7 S8 S9

A4_1 09352 09573 09573 09537 09721 09721 09537 09721 09715

A4_2 09353 09567 09567 09537 09715 09715 09537 09715 09709

A4_3 09355 09562 09562 09539 09711 09711 09539 09711 09704

A4_4 09357 09558 09558 09541 09707 09707 09541 09707 09702

A4_5 09363 09553 09553 09547 09701 09701 09547 09701 09679

A4_6 09370 09548 09548 09555 09697 09697 09555 09697 09694

A4_7 09379 09545 09545 09563 09694 09694 09563 09794 09691

A4_8 09389 09544 09544 09573 09692 09692 09573 09792 09692

B4_8 09400 09544 09544 09585 09692 09692 09585 09792 09692

B4_7 09413 09545 09545 09598 09694 09694 09598 09794 09694

B4_6 09427 09548 09548 09613 09697 09697 09613 09697 09697

B4_5 09443 09553 09553 09628 09701 09701 09628 09701 09701

B4_4 09460 09558 09558 09646 09707 09707 09646 09707 09707


Page | 211

B4_3 09471 09562 09562 09656 09711 09711 09656 09711 09711

B4_2 09482 09567 09567 09668 09715 09715 09668 09715 09715

B4_1 09494 09573 09573 09680 09721 09721 09680 09721 09721


The network losses in each branch for all test cases of 33-bus system and 69-bus

system are listed in Table B-4 and Table B-5 respectively

Table B-4 Network losses in each branch of 33-bus system

Branch number Feeder loss (kW)

Case I Case II Case III Case IV

1 1227 1189 1010 1003

2 5192 2686 2051 2060

3 1995 756 112 490

4 1874 667 074 415

5 3833 1321 122 807

6 192 006 006 006

7 484 0 0 0

8 418 124 211 124

9 357 0 0 0

10 055 001 001 001

11 088 003 003 003

12 267 045 045 045

13 073 008 008 008

14 036 0 0 0

15 028 045 092 045

16 025 048 115 048

17 003 007 022 007

18 016 226 232 226

19 083 1809 1859 1808

20 01 424 436 423

21 004 118 071 118

22 319 316 914 315

23 516 512 1618 510

24 129 128 869 128

25 26 224 005 124

26 334 285 003 155

27 1133 962 003 510

28 786 664 0 345

29 391 326 199 159

30 160 110 018 003


Page | 212

31 021 012 0 000

32 001 0 013 0

33 0 563 809 563

34 0 215 215 215

35 0 174 320 174

36 0 002 033 002

37 0 0 263 0

Total 20314 13981 11753 10844




1 008 007 006 006

2 008 007 006 006

3 020 012 012 010

4 194 011 011 011

5 2829 159 155 159

6 2939 164 160 164

7 691 035 034 035

8 338 012 012 012

9 477 143 137 142

10 101 029 027 028

11 219 032 030 032

12 128 000 000 000

13 124 000 0 000

14 120 0 000 0

15 022 083 043 083

16 032 138 067 138

17 000 001 001 001

18 010 080 032 080

19 007 052 021 052

20 011 083 033 083

21 000 003 001 002

22 001 022 006 022

23 001 049 013 049

24 001 091 021 091

25 000 037 009 037

26 000 019 004 019

27 000 000 000 000

28 000 000 000 000

29 001 001 001 001

30 000 000 000 000

31 001 001 001 001


Page | 213

32 001 001 001 001

33 001 001 001 001

34 000 000 000 000

35 000 003 001 003

36 001 041 019 041

37 002 064 028 064

38 000 018 008 018

39 000 001 000 001

40 005 391 161 391

41 002 166 068 166

42 000 022 009 022

43 000 005 002 005

44 001 057 023 057

45 000 000 000 000

46 002 017 017 013

47 058 416 416 316

48 164 1321 1321 991

49 012 253 253 178

50 000 000 000 000

51 000 000 000 000

52 580 001 001 001

53 673 001 001 000

54 916 000 000 000

55 882 0 0 0

56 4986 000 000 000

57 2458 000 000 000

58 954 000 000 000

59 1071 627 626 379

60 1408 824 823 498

61 011 0 0 0

62 014 000 000 000

63 066 001 001 001

64 004 071 069 071

65 000 000 000 000

66 000 000 000 000

67 002 002 002 002

68 000 000 000 000

69 0 3783 3782 2384

70 0 102 052 102

71 0 0 0 0

72 0 0 0 0

73 0 423 252 423

Total 22562 9885 8758 7397


Page | 214


Table B-6 Pareto optimal solutions of multi-objective DNR (loss ECOST and SAIDI)

Tie-switches location Feeder loss (kW) ECOST ($yr) SAIDI

(hrscustomeryr)

70 68 71 69 321415 4640359 130895231648616

70 10 41 54 364131 431068083000 102819629963899

17 10 41 70 354092 411445783000000 105858799638989

17 26 10 70 383269 530285525000000 0968805806257521

7 26 54 69 435225 578907612000000 0825265794223827

7 54 41 69 406035 460067870000000 0915047984356197

7 26 54 70 442913 571756512000000 0836828971119134

17 10 71 70 345231 439663189000000 106361687725632

70 10 71 69 331470 443747189000000 110465057160048

70 10 41 69 340330 415529783000000 109962169073406

70 68 41 69 330274 435818516000000 130392343561974

7 54 71 69 397170 488285276000000 0920076865222623

41 10 54 69 356448 438219183000000 101663312274368

70 10 54 26 393311 549907825000000 0938414109506619

70 7 71 69 381047 465595876000000 100306543321300

70 7 41 17 403678 433294470000000 0957002858002407

70 10 54 71 355269 459285489000000 103322518050542

7 54 71 70 404856 481134176000000 0931640042117930

7 26 17 70 432867 552134212000000 0867220667870036

7 70 41 69 389911 437378470000000 0998036552346570

7 26 69 70 419096 556218212000000 0908254362214200

17 7 71 70 394813 461511876000000 0962031738868833

71 10 54 69 347586 466436589000000 102166200361011

10 26 54 69 385625 557058925000000 0926850932611312

70 26 10 69 369504 534369525000000 100983950060168

7 54 41 70 413721 452916770000000 0926611161251504


Page | 215


Table B-7 Pareto optimal solutions of multi-objective DNR (loss maximum node voltage deviation

feeder load balancing index) for 33-bus system in Case II

Tie-switches location Feeder loss

(kW)

Maximum node

Voltage deviation

Feeder load

balancing index

7 34 35 31 37 176962 0108696024464801 00228687361961248

7 11 35 32 28 143474 00613272038422790 00305387759787611

7 9 14 31 37 142477 00768537372742428 00252628392269486

6 8 12 36 37 151849 00696765908940439 00259144961258893

7 8 14 31 37 155399 00924077518455773 00239781364880477

6 8 12 31 37 169382 0104485611067200 00236077543160956

6 8 12 32 37 152876 00776641110366926 00250547432924683

33 8 14 30 37 171441 0108063061643879 00230652089068052

7 9 14 32 28 140261 00604355611623940 00310349101268755

7 11 35 32 37 143028 00639069227083702 00273727965037185

6 8 14 31 37 159752 00968913958755809 00236540473688646

6 33 35 32 37 170278 00826562726566354 00249194843739843

6 11 35 32 37 144683 00656445815841987 00261947314082027

6 8 14 32 37 146983 00705648561488426 00256096967694280

7 9 14 32 37 139815 00639015456844128 00280407351785895

6 9 14 32 37 143097 00625183468485540 00270001779728268

7 11 35 31 37 148829 00852978398065017 00245113845932977

7 34 35 30 37 202483 0130888991378581 00223050578905545

6 8 14 36 37 146991 00643933147100736 00266176555168500

6 11 35 31 37 154281 00897759906819439 00242838273201709

6 8 13 32 37 150430 00753226918458818 00253604605496161


feeder load balancing index) for 33-bus system in Case III


(kW)

Maximum node

Voltage deviation

Feeder load

balancing index

7 14 8 32 28 121696 00575193535569366 00264544805354717

7 11 35 31 37 123007 00712785797883380 00213250141648472

6 12 8 32 37 128324 00630309398395457 00223824361844486

6 14 8 30 37 145672 0101299721228755 00194921779245086

7 33 35 32 28 130184 00583420082867310 00261406698684195

7 14 8 30 37 140274 00967924815464314 00195001911353607

7 21 35 30 37 164190 0113945920950777 00189031534924873

6 13 8 32 37 126434 00607661484850486 00227035446761735

7 14 9 32 28 117726 00575130414815478 00271215548731366


Page | 216

6 14 8 32 28 125920 00566904604559002 00265195832133384

6 12 8 31 37 137974 00889877482038002 00200083704114662

7 11 35 30 37 133030 00891516445489180 00199682922816912

6 11 35 32 37 123013 00593840879899440 00235298833627789

7 14 9 32 37 121070 00631040005210335 00255168322432724

6 14 9 32 28 123916 00566872316455769 00273594084038335

7 14 9 30 37 126587 00812324184971598 00206873922472966

7 14 9 31 28 117529 00642736861104275 00240537048868074

6 14 9 32 37 122047 00593825021727904 00240927348267257

6 11 35 32 28 124883 00566888115014094 00269082055980326

6 11 35 31 37 126802 00756552348586014 00207586957663036

6 14 8 32 37 124050 00593857418451058 00230337877365745

7 13 8 32 28 124039 00575225874614865 00262247242500743

7 11 35 32 28 119522 00575159230231156 00267430211390231

7 14 9 31 37 118759 00642740886891275 00220228862077971

6 14 8 31 37 130316 00816654599427028 00201908840890301

33 14 8 30 37 140110 00923831702765571 00197570883486903

7 12 8 32 28 125895 00587758838819431 00259864524009700

6 13 8 31 37 134936 00865715938530326 00201790772057552


feeder load balancing index) for 33-bus system in Case IV

Tie-switches location DG location Feeder

loss

(kW)

Maximum node

Voltage deviation

Feeder load

balancing index

7 9 14 30 37 15 17 16 112506 00655990339384582 00207847799664288

6 8 14 31 37 14 11 15 120818 00728143829651942 00199639595336255

7 11 35 30 37 16 16 12 118637 00756705031931788 00198888055963062

6 8 14 31 37 11 29 14 125736 00822955381260978 00194988443664523

6 11 35 32 37 29 11 29 116999 00602917954784902 00213598898907595

7 9 14 31 37 15 14 16 110931 00518306996442978 00223689972435171

7 34 35 30 37 16 13 13 140652 00983575865184194 00182688360250883

7 8 14 30 37 14 11 15 128617 00876913785424229 00190954012999288

7 8 14 30 37 11 16 14 127141 00860397262006276 00191601352391895

7 9 14 36 37 30 30 29 109157 00520335391274761 00229564125698243

7 8 14 30 37 10 14 16 126706 00857230143750372 00192117850059117

7 11 35 30 37 13 16 12 121130 00786215737441328 00196617519208137

7 34 35 30 37 13 10 9 151352 0106960621828031 00178195736666725

7 34 35 30 37 10 12 9 152310 0107688512235453 00178046268710843

6 8 14 30 37 11 15 16 130550 00897068798318073 00189590122249633

6 8 14 30 37 16 14 10 130869 00901533044670202 00189271311922809

7 34 35 30 37 10 13 12 148089 0104837492639545 00178736074180585


Page | 217

7 34 35 30 37 13 11 16 143317 0100615335666250 00181553323058751

6 8 14 30 37 10 14 14 133299 00925968739633617 00188139999335965

7 34 35 30 37 13 9 12 148392 0105013682219175 00178453713901855

6 8 14 30 37 14 11 10 137593 00963962506644021 00186232592604301

6 8 14 30 37 11 8 14 136046 00951731865531927 00187106569470356

6 8 14 30 37 11 11 16 135639 00942616575802945 00187170876179048

7 8 14 30 37 15 16 14 122935 00815907052491111 00195198923102276

7 34 35 30 37 12 14 16 140640 00983915740315128 00182784576692257

6 33 35 31 37 11 11 13 146017 00888852225316270 00188548348595259

7 34 35 30 37 12 16 12 142144 00997534014352579 00181578155086060

6 8 14 30 37 14 11 15 132819 00921338781311946 00188143081376993

6 8 14 30 37 10 15 11 136651 00956093119043262 00186781475357014

7 9 14 31 37 14 14 16 111382 00525319705640723 00222591386298574

7 34 35 30 37 13 14 16 139957 00977014014811679 00183484070331887

7 34 35 30 37 12 15 16 139849 00976123852270839 00183745698300515

7 34 35 30 37 12 16 16 138589 00959671533698319 00184842191427931

7 34 35 30 37 16 13 16 137912 00952795751906571 00185525366651277

6 33 35 31 37 11 11 11 148785 00910856464605774 00187751047204272

7 34 35 30 37 12 16 13 141338 00990484927061306 00181980491991251

7 34 35 30 37 12 13 12 145536 0102926179499332 00179590185768212

6 8 14 30 37 14 10 15 132373 00918145642214576 00188660639598312

6 8 14 30 37 16 11 14 131312 00904718190224125 00188759872087077

7 34 35 30 37 13 15 16 139168 00969230570394858 00184436609617936

7 34 35 30 37 13 9 11 150730 0106620666560267 00178315514588942

6 8 14 30 37 14 11 14 133746 00929165522686308 00187615074100094

7 34 35 30 37 9 9 12 152656 0107867658396772 00178031242058681

6 8 14 30 37 10 11 16 135118 00939381882085281 00187414815201857

7 34 35 30 37 12 12 9 149341 0105739135263959 00178316539838164

7 9 14 36 28 32 32 32 110385 00489797931328652 00256323647901629

7 9 14 36 37 32 31 31 108599 00498935433820196 00235262740306846

7 9 14 32 37 31 30 31 108436 00537552050723257 00227898958267559

7 9 14 36 28 32 31 31 110203 00489682960875768 00259015702487973

7 34 35 30 37 8 12 9 154427 0108962750550623 00178021823053241


Page | 218




(kW)

Maximum node

Voltage deviation

Feeder load

balancing index

55 61 71 72 12 99036 00524391619987274 00196366946903149

69 61 71 9 14 145213 00664127006601768 00185315761508749

55 61 71 72 14 98845 00524393494628415 00194882148961848

69 70 71 10 14 145135 00666490251240782 00182871906896542

69 61 71 72 12 150267 00699556148777123 00161708619074924

55 61 71 10 14 104521 00524349487665904 00238104755589364

69 61 71 72 13 150383 00700225094171628 00161512783956020

55 61 71 72 13 98937 00524392488739880 00195710324132613

69 61 71 72 11 150792 00682108082577803 00171029450547815

55 61 71 9 14 105348 00524349082167884 00242117051986541

69 61 71 72 14 150513 00700911373758199 00161129748303495

55 61 71 72 11 105195 00524380932334678 00218572363716938




(kW)

Maximum node

Voltage deviation

Feeder load

balancing index

55 61 12 14 9 97461 00523081449765275 00226112450860475

69 61 71 14 9 130761 00662843002557533 00155527078006889

55 61 71 14 7 97263 00523080911134007 00226177446060770

55 61 12 71 72 87588 00523152959484715 00174558059214037

55 61 71 14 8 93176 00523082195004728 00211109499855264

55 61 71 13 72 87581 00523154440245970 00174392153380541

55 61 12 14 72 87755 00523153511186373 00174538759436512

55 61 12 71 7 97289 00523080869366065 00226232791264600

69 61 71 11 9 134009 00662855052002667 00154463391981039

69 61 12 14 9 130989 00662843776081034 00155381836375260

55 61 71 13 7 97273 00523080879708534 00227249951330579

55 61 71 14 9 90907 00523086904216601 00201865894567423

55 61 71 14 10 90291 00523088955157064 00199034032147027

69 61 71 14 10 130894 00665207578684145 00154263271797149

55 61 71 14 72 87582 00523156072908145 00174100597226583

69 61 71 11 10 134197 00665220013747228 00153401360203180

69 61 71 11 72 136858 00680828895070073 00147368269784675

69 61 12 14 10 131126 00665208386694061 00154135530565384

55 61 71 11 72 91274 00523126048676607 00184393848480773


Page | 219




loss

(kW)

Maximum node

Voltage deviation

Feeder load

balancing index

69 63 71 10 14 60 60 60 105879 00543213716422435 00153740505896722

69 63 12 72 71 60 62 62 109324 00575466375767690 00126779733811642

55 61 71 72 11 60 60 60 80324 00429183191505871 00183159151221229

69 63 12 72 71 61 61 62 109323 00575465740537586 00126842028893447

55 61 71 72 12 60 60 60 74165 00429193759769601 00159264876998350

69 63 14 10 71 62 62 62 106070 00543012249613587 00150279825984642

69 63 11 72 71 60 62 60 110547 00558290844078126 00139841427388105

69 63 14 9 71 62 62 62 106271 00540689205567605 00153025056850459

69 61 71 72 11 60 60 60 108838 00542584369620998 00141625735067141

55 61 71 72 14 60 56 60 75837 00436673338725839 00157367114339890

69 63 14 10 71 62 62 60 105960 00542966739560918 00151430448212008

69 61 71 10 14 60 60 60 104307 00527268149576859 00155323687715422

69 63 11 72 71 61 62 62 110652 00558333983851442 00137892112215884

69 63 13 72 71 62 62 62 109522 00576169823075075 00125440050970194

55 61 71 72 14 60 55 60 75975 00436701836501366 00156758120818947

69 63 71 10 14 60 60 62 105896 00542940500362948 00152768514567046

69 63 14 9 71 62 61 61 106159 00540643102892876 00154245882374843

55 61 71 72 13 60 60 60 74066 00429194617185072 00158554987038681

69 62 71 10 14 61 60 60 105886 00542959390978505 00153513700764165

69 63 14 72 71 62 62 62 109622 00576844280930477 00125002240983144

55 63 71 72 14 62 61 62 74382 00440379610790336 00155858821619573

69 63 71 72 11 60 60 60 110530 00558564471048234 00140822204796308

55 63 71 72 14 60 60 62 74285 00440350644694274 00157371695186626

55 63 14 72 71 62 62 62 74448 00440399072962552 00155438948075735

55 63 71 72 14 60 62 62 74344 00440368353288504 00156312863856681

69 63 71 9 14 60 61 60 105882 00542934725670071 00153515485666183

55 63 71 72 14 60 61 62 74305 00440356668532606 00156816031788752

55 61 20 72 13 60 60 60 80533 00429326269571468 00157463174391893

55 63 71 72 14 61 61 62 74343 00440367927398261 00156346520711234

69 61 71 72 14 60 60 60 107187 00561022028435777 00126909641069497

69 63 71 72 11 60 61 60 110533 00558285040786375 00140595150870697

69 63 12 72 71 62 62 62 109436 00575512407997617 00125707103016452

69 63 14 10 71 61 62 62 106000 00542983427485794 00150838099664421

69 63 11 72 71 60 61 62 110569 00558299818740340 00139149694834405

69 63 14 9 71 61 62 60 106118 00540626433897020 00154840963668230

69 61 71 72 12 60 60 60 107041 00559693311798567 00127785892138089

55 61 71 72 14 60 60 60 73974 00429195606297569 00157682511572302

69 63 14 10 71 61 61 62 105958 00542966109653011 00151492343922130

69 63 12 72 71 62 62 61 109365 00575483243249972 00126225992147273


Page | 220

69 63 11 72 71 62 62 60 110611 00558317226735644 00138490567525274

69 63 14 9 71 62 62 61 106201 00540660395254129 00153587525958041

69 63 14 10 71 61 60 62 105917 00542949434469265 00152083287358888

69 63 14 9 71 62 62 60 106160 00540643732226493 00154184014811756

69 63 11 72 71 61 61 62 110610 00558316590719640 00138552654427231

69 63 71 72 11 62 62 62 110723 00558362979744786 00137328015545176

69 61 71 72 13 60 60 60 107108 00560349171634668 00127435051911921

Page | 221

APPENDIX C Control Parameters of

Algorithms

C1 Control parameters of ACO algorithm in Chapter 5

Table C-1 ACO parameters for distribution network reconfiguration and DG allocation in Test Case

2amp3

Parameter Value

Number of ants 50

Maximum number of iteration 200

Pheromone evaporation rate 120530 03

Higher bound of pheromone level 120533119846119834119857 1

Lower bound of pheromone level 120533119846119842119847 001

Constant accumulation number 120533119836 0002

Table C-2 ACO parameters for distribution network reconfiguration and DG allocation in Test Case 4

Parameter Value

Number of ants 100







Table C-3 ACO parameters for distribution network reconfiguration and transformer economic

operation

Parameter Value

Number of ants 150






Appendix C Control Parameters of Algorithms

Page | 222


Table C-4 ACO parameters for sectionalising switch placement in Test Case 1

Parameter Value

Number of ants 400







Parameter Value

Number of ants 500






C4 Control parameters of MOACO and AIS-ACO algorithm in

Chapter 8

Table C-6 MOACO parameters for multi-objective distribution network reconfiguration (loss

ECOST and SAIDI)

Parameter Value

Number of ants 100







Page | 223

Table C-7 AIS-ACO parameters for multi-objective distribution network reconfiguration (loss

ECOST and SAIDI)

Parameter Value






C5 Control parameters of ACO and AIS-ACO algorithm in

Chapter 9

Table C-8 ACO parameters for multi-objective DNR (loss maximum node voltage deviation feeder

load balancing index)

Parameter Value

Number of ants 200






Table C-9 AIS-ACO parameters for multi-objective DNR (loss maximum node voltage deviation

feeder load balancing index)

Parameter Value






Page | 224

APPENDIX D List of Publications

1 B Zhang and P A Crossley ldquoMinimum transformer losses based on transformer

economic operation and optimized tie-switches placementrdquo in Proceedings of the 6th

International Conference on Advanced Power System Automation and Protection

(APAP) pp 1-7 20-25 September 2015

2 B Zhang and P A Crossley ldquoReliability improvement using ant colony

optimization applied to placement of sectionalizing switchesrdquo in Proceedings of the

9th

International Conference on Applied Energy (ICAE) pp 1-7 21-24 August 2017

3 B Zhang and P A Crossley ldquoMinimization of distribution network loss using

ant colony optimization applied to transformer economic operation and relocation of

tie-switchesrdquo to be submitted to IEEE Transactions on Smart Grid

4 B Zhang and PA Crossley ldquoOptimized sectionalising switch placement for

reliability improvement in distribution systemsrdquo to be submitted to IEEE

Transactions on Power Delivery

5 B Zhang and P A Crossley ldquoAn ant colony optimization ndashbased method for

multi-objective distribution system reconfigurationrdquo in Proceedings of the 14th

International Conference on Developments in Power System Protection (DPSP) pp

1-6 12-15 March 2018

Page | 2

List of Contents

List of Contents 2

List of Figures 7

List of Tables 10

List of Abbreviations 14

Abstract 16

Declaration 17

Copyright Statement 18

Acknowledgements 19

CHAPTER 1 20

INTRODUCTION 20

11 Motivation 20

12 Objectives 22

13 Contribution of the work 23

14 Structure of the thesis 25

CHAPTER 2 28

DISTRIBUTION AUTOMATION 28

21 Introduction 28

22 Distribution Network Configurations 29

23 Switchgear for Distribution Network 30

231 Reclosers 30

232 Sectionalising Switches 31

233 Tie-switches 31



242 Literatures on Transformer Economic Operation 33



252 Literatures on Distribution Network Reconfiguration 36

26 Placement of Sectionalising Switches 38


262 Literatures on Sectionalising Switch Placement 41

Page | 3













211 Summary 58

CHAPTER 3 60


31 Introduction 60






35 Summary 68

CHAPTER 4 70



41 Introduction 70

42 Load Model 72


44 Methodology 73




451 Test Case 1 77

452 Test Case 2 85

Page | 4

46 Summary 90

CHAPTER 5 92



51 Introduction 92








55 Summary 109

CHAPTER 6 111



61 Introduction 111





651 Test Case 1 122

652 Test Case 2 123

653 Test Case 3 124

66 Summary 126

CHAPTER 7 128



71 Introduction 128





Page | 5







751 Test Case 1 138

752 Test Case 2 147

753 Test Case 3 147

76 Summary 148

CHAPTER 8 150



81 Introduction 150









86 Summary 164

CHAPTER 9 166



BALANCING 166

91 Introduction 166








Page | 6




95 Summary 187

CHAPTER 10 189


101 Conclusion 189

102 Future Work 193

References 195





Word count 51012

Page | 7

List of Figures





34


















comparison 74






Fig 4-8 11 kV 4th




Page | 8

Fig 4-11 11 kV 4th


























117









Page | 9





136




13 142





problem 157


problem 158



162
















Page | 10

List of Tables













102












13 143




2 147


3 148

Page | 11



163




Case II 173


174



Case III 176


III 176





IV 179



in Case II 181


II 181



in Case III 183


III 184


184



Page | 12


IV 186


187


204







Table B-3 95th





SAIDI) 214

















Page | 13













Page | 14
























EV Electric Vehicle





HC Hyper Cube


HV High Voltage

Page | 15


LV Low Voltage




MV Medium Voltage









TS Tabu Search





Page | 16

Abstract





December 2017






















for optimal DA

Page | 17

Declaration




Page | 18

Copyright Statement










copies made








andor Reproductions










Page | 19

Acknowledgements









encouragement





and support

Page | 20

CHAPTER 1

INTRODUCTION

11 Motivation
















increase profits




Page | 21




during one week






























Page | 22





12 Objectives







ACO) algorithm


















Page | 23
































Page | 24




































Page | 25

































Page | 26

































Page | 27














for all studies

Page | 28

CHAPTER 2


21 Introduction
















Page | 29

Tie-switch





















Page | 30





231 Reclosers














trip




Recloser locks

out on 2nd

reclose

as programmed

Recloser opens

Recloser recloses

fault still present

Recloser recloses

fault still present

Recloser re-opens

fault still present

Load current


Page | 31










233 Tie-switches










241 Basic Concepts









Page | 32

Tran

sfo

rme

r Lo

ss


1 Transformer

2 Transformers



















119878119871




Page | 33








improvement
























Page | 34





(Kw)







(Kw)














Page | 35








Transformer Size

(kVA)

No load loss

(kW)

Load loss

(kW)

Capital

price (euro)

Cost of loss

(euro)

Total cost

(euro)

A 1000 11 9 9074 34211 43285

B 1000 094 76 11362 28986 40348


251 Basic Concepts









and opened



Page | 36


































Page | 37



































Page | 38




operations








261 Basic Concepts


















Page | 39






















Page | 40


1 2 3 4 5 6 7


1 2 3 4 5 6 7


1 2 3 4 5 6 7


1 2 3 4 5 6 7


CB1 opened



CB1 CB2

CB1CB2

CB1 CB2

CB1 CB2





Interrupted

load



Page | 41


1 2 3 4 5 6 7


1 2 3 4 5 6 7


1 2 3 4 5 6 7


1 2 3 4 5 6 7


CB1 opened



CB1 CB2

CB1CB2

CB1 CB2

CB1 CB2





Interrupted

load









Page | 42





























Page | 43









network unit [72]

Open-circuit test






Page | 44

(a) Test circuit









119875119874119862 = 119875ℎ+119890 =119880119874119862

2

119877119888119871119881= 119880119874119862119868ℎ+119890 (2-1)


current

Short-circuit test




119880119900119888

119868ℎ+119890 119868120601

119868119900119888 119885119890119902 119871119881

119877119888 119871119881 119883119898 119871119881


Page | 45




(a) Test circuit






and expressed as

119875119878119862 = 1198681198781198622 119877119890119902119867119881 (2-2)




119880119904119888

119868119890119909

119868119904119888 119877119890119902 119867119881 119883119890119902 119867119881

(119899119890119892119897119890119888119905)


Page | 46

Active power loss



∆119875 = 119875119874119862 + 1205732119875119878119862 (2-3)

where 120573 =119878119871




Reactive power loss



as

∆119876 = 119876119874119862 + 1205732119876119878119862 (2-4)

119876119874119862 = 119878119874119862 =119868119874119862

119868119873∙ 119878119873 (2-5)

119876119878119862 = 119878119878119862 = 119880119878119862

119880119873∙ 119878119873 (2-6)








1198791198711 = 11988002119875119885119874119862 +

1205732

11988002 119875119885119878119862 (2-7)

119875119885119874119862 = 119875119874119862 + 119870119876119876119874119862 (2-8)


Page | 47

119875119885119878119862 = 119875119878119862 + 119870119876119876119878119862 (2-9)


120573 =119878119871















1198791198712 = 211988002119875119885119874119862 +

1

2

1205732

11988002 119875119885119878119862 (2-10)







Page | 48




119875119887119877 + 119895119876119887119877 = 119887119877 times 119868lowast (2-11)

119875119887 = 1198681198872 times 119877119887 (2-12)


119875119887 =119875119887119877

2 +1198761198871198772

1198811198871198772 times 119877119887 (2-13)







119864119871 = sum 119875119887119899119873119887119899 (2-14)











Page | 49



120582 = sum 120582119895119895 (2-15)

119880 = sum 120582119895119895 119903119895 (2-16)

119903 =119880

120582 (2-17)


point





119878119860119868119865119868 =sum 120582119894119873119894119894

sum 119873119894119894 (2-18)

119878119860119868119863119868 =sum 119880119894119873119894119894

sum 119873119894119894 (2-19)

119860119864119873119878 =sum 119880119894119871119894119894

sum 119873119894119894 (2-20)

119864119862119874119878119879 = sum 119888119898(119889119898)119891119898119871119898119872119898=1 (2-21)











Page | 50




Simulation method












memory

Analytical method






(FMEA)










Page | 51











Normal operation

Active

failure

Transient

failure

Passive

failure

Maintenance

120582119860 120582119879 120582119875 120582119872

120583119860 120583119879 120583119875

120583119872


Page | 52

Start











Next failure i=i+1


End

No

Yes












Page | 53















after failure











Page | 54

0

1


















120572 =

1 119883 le 119883119898119894119899119883119898119886119909minus119883

119883119898119886119909minus119883119898119894119899119883119898119894119899 lt 119883 lt 119883119898119886119909

0 119883 ge 119883119898119886119909

(2-22)





120572

119883119898119894119899 119883119898119886119909 119883


Page | 55










119872119886119909 119869 = 12059611205721 + 12059621205722 + ⋯ + 120596119899120572119899 (2-23)







selected objectives






Max-min method




119872119886119909 119869 = min 1205721 1205722 hellip 120572119899 (2-24)




Page | 56











reconfiguration





119872119886119909 119869 = (1205721 ∙ 1205722 ∙ hellip ∙ 120572119873)1 119899frasl (2-25)







Framework








Page | 57



forall 119894 = 12 hellip 119873119900119887119895 119865119894(119883) le 119865119894(119884) (2-26)

exist 119894 = 12 hellip 119873119900119887119895 119865119894(119883) lt 119865119894(119884) (2-27)














preferences











Page | 58

211 Summary
































Page | 59













Page | 60

CHAPTER 3


31 Introduction


















Page | 61









search space [13]




35













follows [93]

119862 = 119875(119883 minus 119871 le 120583 le 119883 + 119871) = int 119866(119883)119889119909119883+119871

119883minus119871 (3-1)

119871 = 119911lowast 120590

radic119899 (3-2)


Page | 62







095


119862 09 095 099 0999

119911lowast 1645 1960 2576 3291


119899 = (119911lowast120590

119871)2 (3-3)
















Page | 63
























Page | 64

the nest






















Page | 65

Start

Set Iteration n=1

Maximum iteration

reached

End

No

Yes









n=n+1












Page | 66


































Page | 67

Start

Cloning

Maximum iteration

reached

End

No

Yes


Hypermutation

Fitness evaluation


Pheromone updating

n=n+1












Page | 68










tables [88]

















35 Summary





Page | 69


























Page | 70

CHAPTER 4





41 Introduction














Page | 71



























Section 46



Page | 72

42 Load Model



modelled








Number of people

in household

1 2 3 4 ge5

Percentage () 3058 341 1557 1288 686






weekend


12


dwelling





Page | 73










follows

Minimise 119891 = 1198800

2119875119885119874119862 +1205732

11988002 119875119885119878119862 119905119903119886119899119904119891119900119903119898119890119903 119894119899 119904119894119899119892119897119890 119900119901119890119903119886119905119894119900119899

211988002119875119885119874119862 +

1

2

1205732

11988002 119875119885119878119862 119905119903119886119899119904119891119900119903119898119890119903119904 119894119899 119901119886119903119886119897119897119890119897 119900119901119890119903119886119905119894119900119899

(4-1)


120573 =119878119871




44 Methodology









Page | 74













obtained

Profile

generator of

domestic

electricity

demand profiles

Transformer

operation

modes

MATLAB

Distribution

network

model built

in OpenDSS

Analyse and

compare

simulation

results in

MATLAB




Page | 75

Start



modes considered

End

No

Yes


customer randomly


mode



Record results

Change

transformer

operation

mode

N=N+1




No

Yes







Page | 76














obtained


day is recorded


Profile

generator of

domestic

electricity

demand profiles

Tie-switch

status

MATLAB

Distribution

network

model built

in OpenDSS

Analyse and

compare

simulation

results in

MATLAB




Page | 77





451 Test Case 1








whilst the 4th
























Page | 78

A

A

A

A

B

B

B

B


Load4_2

Load4_3

Load4_4

Load4_5

Load4_6

Load4_7

Load4_8

75 MVA

33 kV

11 kV

33 kV

Voltage

Source

75 MVA



Sub-

sector

Transf

Rating

(kVA)

Conn Tapping

Range

Load

Losses

at

75

(kW)

No-

Load

Losses

(kW)

Impedance voltage


the principle

tapping

()

Reference

standard


6 steps of 25

Each

50

75

835 BS 171 amp

IEC 60076







Page | 79

0

10

20

30

40

50

60

70

80

90

100

0 2 4 6 8 10 12 14 16 18 20 22

Tran

sfo

rme

r Lo

ad F

acto

r

Time (h)

0

10

20

30

40

50

60

70

0 2 4 6 8 10 12 14 16 18 20 22

Tran

sfo

rme

r Lo

sse

s (k

W)

Time (h)

0

10

20

30

40

50

60

70

0 2 4 6 8 10 12 14 16 18 20 22

Tran

sfo

rme

r Lo

sse

s (k

W)

Time (h)




of Scenario 1


(a) Scenario 1

(b) Scenario 2



Page | 80

0

10

20

30

40

50

60

70

0 2 4 6 8 10 12 14 16 18 20 22

Tran

sfo

rme

r Lo

sse

s (k

W)

Time (h)

(c) Scenario 3














the 95th



The mean and 95th










Page | 81

0976

0978

098

0982

0984

0986

0988

099

0992


Vo

ltag

e (

pu

)

Scenario1

Scenario2

Scenario3

0974

0976

0978

098

0982

0984

0986

0988

099


Vo

ltag

e (

pu

)

Scenario1

Scenario2

Scenario3

(a) Mean value

(b) 95th

value

Fig 4-8 11 kV 4th



start of the 4th










Page | 82

088

09

092

094

096

098

1

0 2 4 6 8 10 12 14 16 18 20 22

Bu

s V

olt

age

(p

u)

Time (h)

088

09

092

094

096

098

1

0 2 4 6 8 10 12 14 16 18 20 22

Bu

s V

olt

age

(p

u)

Time (h)

088

09

092

094

096

098

1

0 2 4 6 8 10 12 14 16 18 20 22

Bu

s V

olt

age

(p

u)

Time (h)



(a) Scenario 1

(b) Scenario 2

(c) Scenario 3


Lower Limit

Lower Limit

Lower Limit



Page | 83

088

09

092

094

096

098

1

0 2 4 6 8 10 12 14 16 18 20 22

Bu

s V

olt

age

(p

u)

Time (h)

088

09

092

094

096

098

1

0 2 4 6 8 10 12 14 16 18 20 22

Bu

s V

olt

age

(p

u)

Time (h)

088

09

092

094

096

098

1

0 2 4 6 8 10 12 14 16 18 20 22

Bu

s V

olt

age

(p

u)

Time (h)

(a) Scenario 1

(b) Scenario 2

(c) Scenario 3


Lower Limit

Lower Limit

Lower Limit



Page | 84

0976

0978

098

0982

0984

0986

0988

099

0992


0 25

5244 75

100
















values 0 25 5244 75 and 100





Fig 4-11 11 kV 4th




Page | 85






TCLF () 0 25 5244 75 100

Transformer loss

(kWh)

55922 50783 47865 49414 53982




TCLF () 0 25 5244 75 100

Average number of


0 2 4 2 0

452 Test Case 2












Page | 86

0

02

04

06

08

1

12

14

16

0 2 4 6 8 10 12 14 16 18 20 22

Act

ive

Po

we

r (k

W)

Time (h)

TW1 TW2 TW3 TW4 TW5

A1

A2

A3


B1

B2

B3

EndA EndB

TW9TW8TW7TW6








B4_3 B4_4 B4_5 B4_6 B4_7 B4_8




(a) Group 1



Page | 87

0

002

004

006

008

01

012

014

016

018

02

0 2 4 6 8 10 12 14 16 18 20 22

Act

ive

Po

we

r (k

W)

Time (h)

(b) Group 2















at TW1


at TW5





Page | 88







operation












Loss

(kWhday)

11319 10848 10848 11399 11162 11162 9739 9572 9528













Page | 89

096

0962

0964

0966

0968

097

0972

0974

0976

0978

098


Vo

ltag

e (

pu

)

Scenario1

Scenario2

Scenario3

0955

096

0965

097

0975

098

0985

099


Vo

ltag

e (

pu

)

Scenario1

Scenario4

Scenario7













Page | 90


that in Scenario 4




46 Summary



























Page | 91





Page | 92

CHAPTER 5




51 Introduction











planning





Reduction

Page | 93



constraints


















conclusions




119872119894119899119894119898119894119904119890 119891 = sum 119896119894119877119894(119875119894

2+1198761198942

1198801198942 )

119873119887119894=1 (5-1)





Reduction

Page | 94



Subject to



119875119894 le 119875119894119898119886119909 (5-4)

det(119860) = 1 119900119903 minus 1 (5-5)












53 Solution Method







Reduction

Page | 95

Home

1 2 NP1NP1-1

1 2 NP1-1 NP1

1 2 NP1NP1-1

1 2 NP2-1 NP2

1 2 NP2NP2-1

1 2 NP2-1 NP2

1 2 NP2NP2-1

1 2 NP2-1 NP2

Food

Stage

1

2

NT-1

NT

NT+1

NT+2

NT+NDG-1

NT+NDG

Part 1 Number of


Part 2 Number

of DGs









Reduction

Page | 96
















five steps



constant value






stage y is

119875119895119910(119873) =

120591119895119910

(119873)

sum 120591119895119910

(119873)ℎisin∆119910

(5-6)

where 120591119895119910




Reduction

Page | 97










choose a new trail







120591119895119910

(119873) = (1 minus 120588)120591119895119910

(119873 minus 1) + 120591119888 (5-7)




this edge





120591119895119910(119873) = 120591119895

119910(119873) + 120588119891119887119890119904119905

119891119887119890119904119905(119873) (5-8)



120591119895119910(119873) = 120591119898119886119909 119894119891 120591119895

119910(119873) ge 120591119898119886119909 (5-9)

120591119895119910(119873) = 120591119898119894119899 119894119891 120591119895

119910(119873) le 120591119898119894119899 (5-10)


Reduction

Page | 98

Start

Set Iteration n=1

Maximum iteration

reached

Output best


No

Yes









n=n+1


all location lists


and load data







optimal solution



Reduction

Page | 99













method





simultaneously




Appendix C1

541 33-bus System








Reduction

Page | 100

10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

18 19 20 21

22 23 24

25 26 27 28 29 30 31 32


L18

L19 L20 L21

L22

L23 L24

L25

L26 L27 L28 L29 L30 L31 L32

L33

L34

L35

L36

L37





Case Active feeder

loss (kW)

Minimum voltage

(pu)

(Bus No)


on Fig 53

DG location

Case I 20314 09116 (B17) L33 L34 L35 L36 L37 NA

Case II 13981 09361 (B31) L7 L9 L14 L32 L37 NA



Case I base case



Bus 17








Reduction

Page | 101

10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

18 19 20 21

22 23 24

25 26 27 28 29 30 31 32


L18

L19 L20 L21

L22

L23 L24

L25

L26 L27 L28 L29 L30 L31 L32

L33

L34

L35

L36

L37










from it


Method Feeder loss

(kW)

Loss reduction

()


voltage (pu)


BEM [109] 14054 3082 L7 L10 L14 L32 L37 09361

HSA [110] 13981 3118 L7 L9 L14 L32 L37 09361

FWA [16] 14026 3095 L7 L9 L14 L28 L32 09396

PSO [55] 13981 3118 L7 L9 L14 L32 L37 09361

IWO [111] 13981 3118 L7 L9 L14 L32 L37 09361








Reduction

Page | 102

10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

18 19 20 21

22 23 24

25 26 27 28 29 30 31 32


L18

L19 L20 L21

L22

L23 L24

L25

L26 L27 L28 L29 L30 L31 L32

L33

L34

L35

L36

L37

DG2

DG1

DG3









CGA and CSA



computation

times

(second)


ACO 13981 13981 13981 0 228 821 1448

CGA [112] 14002 14619 13981 12121 5463 2986 3926

CSA [113] 13986 14028 13981 01328 8363 3425 7258










Reduction

Page | 103

10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

18 19 20 21

22 23 24

25 26 27 28 29 30 31 32


L18

L19 L20 L21

L22

L23 L24

L25

L26 L27 L28 L29 L30 L31 L32

L33

L34

L35

L36

L37

DG2DG1

DG3























Reduction

Page | 104

086

088

09

092

094

096

098

1

102

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32

Vo

ltag

e (

pu

)

Bus No

Case I

Case II

Case III

Case IV

0

20

40

60

80

100

120

140

160

180

200

100 400 700 1000

Fee

de

r lo

ss (

kW)

DG Capacity (kVA)












allocation



Reduction

Page | 105

10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

27

28

29

30

31 32 33 34

35

36

37

38 39 40 41 42 43 44 45

46 47 48 49

50

51

52

53 54 55 56 57 58 59 60 61 62 63 64

65 66

67 68


L27

L28

L29

L30

L31 L32 L33 L34

L35

L36

L37

L38 L39 L40 L41 L42 L43 L44 L45

L46

L47 L48 L49

L50

L51

L52

L53 L54 L55 L56 L57 L58 L59 L60 L61 L62 L63 L64

L65

L66

L67

L68

L69

L70

L71

L72L73

542 69-bus System










Case Active feeder

loss (kW)

Minimum voltage

(pu)

(Bus No)


Case I 22562 09072 (B64) L69 L70 L71 L72 L73 NA

Case II 9885 09476 (B60) L14 L55 L61 L71 L72 NA



Case I base case




Reduction

Page | 106

10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

27

28

29

30

31 32 33 34

35

36

37

38 39 40 41 42 43 44 45

46 47 48 49

50

51

52

53 54 55 56 57 58 59 60 61 62 63 64

65 66

67 68


L27

L28

L29

L30

L31 L32 L33 L34

L35

L36

L37

L38 L39 L40 L41 L42 L43 L44 L45

L46

L47 L48 L49

L50

L51

L52

L53 L54 L55 L56 L57 L58 L59 L60 L61 L62 L63 L64

L65

L66

L67

L68

L69

L70

L71

L72L73











Method Feeder loss

(kW)

Loss reduction

()


voltage (pu)


FWA [16] 9886 5618 L14 L56 L61 L71 L72 09476

HSA [110] 10546 5326 L13 L18 L56 L61 L72 09475

GA [110] 10242 5461 L14 L53 L61 L71 L72 09462





Reduction

Page | 107

10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

27

28

29

30

31 32 33 34

35

36

37

38 39 40 41 42 43 44 45

46 47 48 49

50

51

52

53 54 55 56 57 58 59 60 61 62 63 64

65 66

67 68


L27

L28

L29

L30

L31 L32 L33 L34

L35

L36

L37

L38 L39 L40 L41 L42 L43 L44 L45

L46

L47 L48 L49

L50

L51

L52

L53 L54 L55 L56 L57 L58 L59 L60 L61 L62 L63 L64

L65

L66

L67

L68

L69

L70

L71

L72L73

DG3

DG1

DG2

10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

27

28

29

30

31 32 33 34

35

36

37

38 39 40 41 42 43 44 45

46 47 48 49

50

51

52

53 54 55 56 57 58 59 60 61 62 63 64

65 66

67 68


L27

L28

L29

L30

L31 L32 L33 L34

L35

L36

L37

L38 L39 L40 L41 L42 L43 L44 L45

L46

L47 L48 L49

L50

L51

L52

L53 L54 L55 L56 L57 L58 L59 L60 L61 L62 L63 L64

L65

L66

L67

L68

L69

L70

L71

L72L73

DG3DG1

DG2









III respectively



Reduction

Page | 108

0

50

100

150

200

250

100 400 700 1000

Fee

de

r lo

ss (

kW)

DG Capacity (kVA)














configuration












Reduction

Page | 109

086

088

09

092

094

096

098

1

102

0 5 10 15 20 25 30 35 40 45 50 55 60 65

Vo

ltag

e (

pu

)

Bus No

Case I

Case II

Case III

Case IV


55 Summary



















Reduction

Page | 110








Page | 111

CHAPTER 6




LOSS REDUCTION

61 Introduction





system [82]









Page | 112












investigated




















Page | 113













load curve [82]









P1

P2

1199051 1199052 Time (h)



Page | 114

1198911 = sum (119864119871119905 + 119879119871119905)1199051minus1119905=1 + sum (119864119871119905 + 119879119871119905) 1199051

24119905=1199052 isin 1 2 hellip 24 (6-1)


Min 119891 = 1198911 + 1198912 (6-3)







and are disregarded


















Page | 115

Home

0 1

0 1

0 1

0 1

1 2 NPNP-1

1 2 NP-1 NP

1 2 NPNP-1

1 2 NP-1 NP

Food

Stage

1

2

Ns-1

Ns

Ns+1

Ns+2

Ns+Nt-1

Ns+Nt

Part 1

Number of

substations

Ns

Part 2 Number

of existing tie-

switches Nt








Page | 116

Tie-switch

Transformer





as a binary vector















Page | 117

Start


Maximum iteration

reached

Output best


No

Yes



Iteration N=1








N=N+1




and load data





T=T+1

Tgt2

Yes

t=t+1

No




Page | 118


LP8 LP9 LP10



LP29 LP30 LP31

LP26 LP27 LP28


19

20

21

22

23

24

26

25 27

28

29 30

71

13 15

14 16

17

18

69

1 3

2

5

4

7

6 8

10

9

68

11 12

56

57

58 60

59 61 62

65

64 66 67

50 52

51

54

53 55

44

45

46

47

48

49

70

31

32

33

34

36

35

39

37 38 40

41

42 43

63

F3

F2

F1

F7

F6

F5

F4


Subbus1

Subbus2

Subbus3

T1

T3

T5

Main

feeder

Main

feeder

Main

feeder

T2

T4

T6













Page | 119




Number

of load

points


(kW)

Q

(kVAr)

Number of

customers

4 1-2 9-10 residential 8869 8426 220

6 3-5 13-15 residential 8137 7731 200

12 6-7 16-17 23-25 28

30-31 37-38


6 8 11 18 26 32-33 industrial 2445 23228 1

10 12 19-22 27 29 34-

36












Page | 120






Page | 121




shown in Table 6-2



Spring

(Mar Apr May)

Weekdays 66 92

Weekends 26

Summer

(Jun Jul Aug)

Weekdays 66 92

Weekends 26

Autumn

(Sep Oct Nov)

Weekdays 65 91

Weekends 26

Winter

(Dec Jan Feb)

Weekdays 64 90

Weekends 26

Year 365 Days





buses









Page | 122

651 Test Case 1



network loss











Spring

weekday

Spring

weekend

Summer

weekday

Summer

weekend

Autumn

weekday

Autumn

weekend

Winter

weekday

Winter

weekend

Before

Reconfiguration


L70L71

L68L69

L70L71

L68L69

L70L71

L68L69

L70L71

L68L69

L70L71

L68L69

L70L71

L68L69

L70L71

L68L69

L70L71

Number of operated

transformers




Loss

(kWh)

Cable 9233 3498 8050 3151 9660 3665 11009 4080

Transformer 4301 3410 4109 3350 4372 3437 4597 3507

Total 13534 6908 12159 6501 14032 7102 15606 7587

After

Reconfiguration


23-24

0-6 0-7

23

0-7 0-7

22-23

0-6

0-7

22-23

0-6


L69L71

L68L69

L70L71

L17L68

L70L71

L17L68

L70L71

L17L68

L70L71

L68L69

L70L71

L17L68

L70L71

L68L69

L70L71

Number of operated

transformers






L65L70

L68L69

L70L71

L41L48

L65L69

L68L69

L70L71

L17L41

L65L70

L68L69

L70L71

L17L41

L65L70

L68L69

L70L71

Number of operated

transformers




Loss

(kWh)

Cable 9043 3516 7851 3169 9519 3685 10845 4103

Transformer 3955 2616 3759 2517 4036 2656 4264 2755

Total 12998 6132 11610 5686 13479 6341 15109 6858



Page | 123

0

05

1

15

2

25

3

35

4

45

05 1 15 2 25 3










652 Test Case 2











To

tal

loss

(G

Wh

)

DG Capacity (MW)



Page | 124

653 Test Case 3









120578times119875119862 (6-4)









the day



capability (mile)

Market share ()

Micro car 12 50 20









Page | 125

4

42

44

46

48

5

30 60 90



119878119874119862 = 0 119898 gt 119872119863119862

119872119863119862minus119898

119872119863119862 119898 le 119872119863119862 (6-5)


















To

tal

loss

(G

Wh

)




Page | 126

4

42

44

46

48

5

30 60 90











66 Summary













To

tal

loss

(G

Wh

)




Page | 127
















Page | 128

CHAPTER 7




71 Introduction
















Improvement

Page | 129






























weighted function


Improvement

Page | 130

119872119894119899 119869 = micro1 ∙ 119864119862119874119878119879 + micro2 ∙ 119878119862 (7-1)





Parameters






119872119886119909 119870 = 1205961 ∙ 120572119878119860 + 1205962 ∙ 120572119878119862 (7-2)

















Improvement

Page | 131

0

1

0

1

120572119878119860 =

1 119878119860119868119863119868 le 119878119860119868119863119868119898119894119899119878119860119868119863119868119900119903119894minus119878119860119868119863119868

119878119860119868119863119868119900119903119894minus119878119860119868119863119868119898119894119899119878119860119868119863119868119898119894119899 lt 119878119860119868119863119868 lt 119878119860119868119863119868119900119903119894

0 119878119860119868119863119868 ge 119878119860119868119863119868119900119903119894

(7-3)











120572119878119862 =

1 119878119862 le 119878119862119900119903119894119878119862119898119886119909minus119878119862

119878119862119898119886119909minus119878119862119900119903119894119878119862119900119903119894 lt 119878119862 lt 119878119862119898119886119909

0 119878119862 ge 119878119862119898119886119909

(7-4)





Parameters



120572119878119860

119878119860119868119863119868119898119894119899 119878119860119868119863119868119900119903119894 119878119860119868119863119868

120572119878119862

119878119862119900119903119894 119878119862119898119886119909 119878119862


Improvement

Page | 132

0

1





120572119864119862 =

1 119864119862119874119878119879 le 119864119862119874119878119879119898119894119899119864119862119874119878119879119900119903119894minus119864119862119874119878119879

119864119862119874119878119879119900119903119894minus119864119862119874119878119879119898119894119899119864119862119874119878119879119898119894119899 lt 119864119862119874119878119879 lt 119864119862119874119878119879119900119903119894

0 119864119862119874119878119879 ge 119864119862119874119878119879119900119903119894

(7-5)








Max 119871 = min (120572119878119860 120572119878119862 120572119864119862) (7-6)










120572119864119862

119864119862119874119878119879119898119894119899 119864119862119874119878119879119900119903119894 119864119862119874119878119879


Improvement

Page | 133



1 ( 1)

1 1 1 1 1 1


t t

b b k R k s

t b k j k j


(7-7)








rate




119878119860119868119863119868 = sum sum 120582119887∙119871119887[sum 119889119877

119873119862119877(119887)119899=1 +sum 119889119878

119873119862119878(119887)119899=1 ]

119873119887119887=1

119873119862119905119900119905119886119897119879

119905=1 (7-8)








119878119862 = 119862119868119878 ∙ 119873119899119890119908 + 119862119877119878 ∙ 119873119903119890119897 + sum 119872119862119879119905=1 ∙ (119873119899119890119908 + 119873119890119909119894119904) ∙ (1 + 119863119877)minus(119905minus1) (7-9)





Improvement

Page | 134

Home

0

1

0

1

0

1

0

1

Food





Problem
















Improvement

Page | 135









119887119890119899119890119891119894119905 = sum119864119862119874119878119879119887119886119904119890

119905 minus119864119862119874119878119879119900119901119905119905

(1+119863119877)119905119879119905=1 (7-10)

where 119864119862119874119878119879119887119886119904119890119905 and 119864119862119874119878119879119900119901119905





119861119862119877 =119887119890119899119890119891119894119905

119878119862 (7-11)






Improvement

Page | 136


LP8 LP9 LP10



LP29 LP30 LP31

LP26 LP27 LP28


9 10 11 12 13 33

6 7 8 31

1 2 3 4 5 30

25 26 27 29

22 23 24

19 20 21

32

14 15 16 17 18

28

F3

F2

F1

F7

F6

F5

F4


Subbus1

Subbus2

Subbus3

T1

T3

T5

Main

feeder

Main

feeder

Main

feeder

T2

T4

T6











Improvement

Page | 137







Number

of load

points


(kW)

Number of

customers

15 1-4 11-13 18-21 32-35 residential 545 220

7 5 14 15 22 23 36 37 residential 500 200

7 8 10 26-30 industrial 1000 1


7 6 7 16 17 24 25 38 commercial 415 10


















Improvement

Page | 138




Residential 006 11 16 26 316 5

Industrial 288 806 95 124 1387 276

Commercial 205 96 125 185 2151 6306




method






751 Test Case 1











Improvement

Page | 139


LP8 LP9 LP10



LP29 LP30 LP31

LP26 LP27 LP28


9 10 11 12 13 33

6 7 8 31

1 2 3 4 5 30

25 26 27 29

22 23 24

19 20 21

32

14 15 16 17 18

28

F3

F2

F1

F7

F6

F5

F4


Subbus1

Subbus2

Subbus3

T1

T3

T5

Main

feeder

Main

feeder

Main

feeder

T2

T4

T6










Improvement

Page | 140













Switch

No


Load (kW)


Type


2 2 7D 3500 LP9 1500 (industrial)



5 6 23D 3500 LP30 1000 (industrial)

6 7 28D 3595 LP36 500 (commercial)












Improvement

Page | 141


LP8 LP9 LP10



LP29 LP30 LP31

LP26 LP27 LP28


9 10 11 12 13 33

6 7 8 31

1 2 3 4 5 30

25 26 27 29

22 23 24

19 20 21

32

14 15 16 17 18

28

F3

F2

F1

F7

F6

F5

F4


Subbus1

Subbus2

Subbus3

T1

T3

T5

Main

feeder

Main

feeder

Main

feeder

T2

T4

T6



ECOST

($)

Number of

installed

switches

Capital and

installation cost

($)

Maintenance

and operation

cost ($)

Total system

cost ($)

Before switches

installation

472260 0 0 4830 477090

After switches

installation

221610 11 51700 13670 286980


Improvement

Page | 142


LP8 LP9 LP10



LP29 LP30 LP31

LP26 LP27 LP28


9 10 11 12 13 33

6 7 8 31

1 2 3 4 5 30

25 26 27 29

22 23 24

19 20 21

32

14 15 16 17 18

28

F3

F2

F1

F7

F6

F5

F4


Subbus1

Subbus2

Subbus3

T1

T3

T5

Main

feeder

Main

feeder

Main

feeder

T2

T4

T6


A Base case









Improvement

Page | 143

0

1

2

3

4

5

6

7

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

BC

R

Years








ECOST

($)

Number of

relocated

switches

Relocation

cost ($)

Number of

installed

switches

Capital and

installation

cost ($)

Maintenance

and operation

cost ($)

Total

system

cost ($)

Before switch

placement

472260 0 0 0 0 4830 477090

After switch

placement

221120 5 2500 8 37600 11260 272480











Improvement

Page | 144

0

20

40

60

80

100

120

140

160

05 1 15 2 25 3 35 4 45 5 55 6 65 7 75 8

Co

st (

th

ou

san

d $

)

CDF multiplier

ECOST

Switch costs

Total costs






















Improvement

Page | 145

0

5

10

15

20

25

30

35

40

05 1 15 2 25 3 35 4 45 5 55 6 65 7 75 8

Nu

mb

er

of

swit

che

s

CDF multiplier






















Improvement

Page | 146











01 273120 274810 272480 223

02 273400 275960 272480 175

03 273480 274810 272480 132

04 273100 274810 272480 110

05 273550 274810 272480 94

06 273440 274810 272480 81







400




100 273865 276120 272480 91

200 273100 274810 272480 110

300 273030 274370 272480 135

400 272820 274230 272480 168

500 273170 274230 272480 245


Improvement

Page | 147




752 Test Case 2














Function

SAIDI

(hrscustomer)

Switch costs ($)

Case 21 01 09 04909 09970 09464 1157 68275

Case 22 05 05 08456 09061 08758 556 67378

Case 23 09 01 09384 07761 09221 39936 153950



753 Test Case 3








Improvement

Page | 148


Objective

Function

120572119864119862 120572119878119860 120572119878119862 ECOST

($)

SAIDI

(hrscustomer)

Switch costs

($)

Before

switch

placement

0 0 0 1 472260 1989 4830

After switch

placement

08327 08327 08392 08384 188950 56723 112410

76 Summary

























Improvement

Page | 149




Page | 150

CHAPTER 8




IMPROVEMENT

81 Introduction














Improvement

Page | 151























set is obtained






conclusions


Improvement

Page | 152







119865(119866) = [1198911(119866)1198912(119866)1198913(119866)]119879 (8-3)


configuration G



1198911(119866) = sum 119896119894119877119894(119875119894

2+1198761198942

1198801198942 )

119873119887119894=1 (8-4)








1 ( 1)

1 1 1 1 1 1


t t

b b k R k s

t b k j k j


(8-5)





Improvement

Page | 153









119878119860119868119863119868 = sum sum 120582119887∙119871119887[sum 119889119877

119873119862119877(119887)119899=1 +sum 119889119878

119873119862119878(119887)119899=1 ]

119873119887119887=1

119873119862119905119900119905119886119897119879

119905=1 (8-6)




8214 Constraints








119891119901119904(119894) = sum 120596119895max(119900119891119895)minus119900119891119895(119875119878119894)

max(119900119891119895)minusmin (119900119891119895)

119873119900119887119895

119895=1 (8-7)








Improvement

Page | 154





tie-switches












number




weighted sum as

120591119894119909 = 1199011 ∙ 1205911198941199091 + |1199011 minus 1199012| ∙ 120591119894119909

2 + (1 minus 1199012) ∙ 1205911198941199093 (8-8)

where 1205911198941199091 120591119894119909





new matrix




Improvement

Page | 155



119875119894119909(119873) =120591119894119909(119873)

sum 120591119894119909(119873)ℎisin∆119909

(8-9)

















certain number [88]






follow

120591119894119909119899 (119873) = (1 minus 120588)120591119894119909

119899 (119873 minus 1) + 120591119888 (8-10)




Improvement

Page | 156



this edge





120591119894119909119899 (119873) = 120591119894119909

119899 (119873) + 120588119891119887119890119904119905

119899 (119873)

119891119887119890119904119905119899 (119873minus1)

(8-11)

where 119891119887119890119904119905119899 (119873 minus 1) and 119891119887119890119904119905





120591119894119909119899 (119873) = 120591119898119886119909 119894119891 120591119894119909

119899 (119873) ge 120591119898119886119909 (8-12)

120591119894119909119899 (119873) = 120591119898119894119899 119894119891 120591119894119909

119899 (119873) le 120591119898119894119899 (8-13)












Improvement

Page | 157

Start

Iteration N=1

Maximum ant number

reaches

Output Pareto

optimal set and end

No

Yes



Ant number m=1



matrices into one




for this ant

N=N+1


and load data


dominated solutions

Maximum iteration

reaches

Yes

m=m+1

No





Improvement

Page | 158

Start

Cloning

Maximum iteration

reached

Output Pareto

optimal set and end

No

Yes




dominated solutions



n=n+1











in Fig 8-2



Improvement

Page | 159
















119901119894119899 =

120591119894119899

sum 120591119895119899

119895 (8-14)











120591119894119899(119873) = 119898119886119909 (1 minus 120588)120591119894

119899(119873 minus 1) 120591119898119894119899 (8-15)




Improvement

Page | 160







updated as

120591119894119899(119873) = 119898119894119899120591119894

119899(119873) + 120588min (119891119899(119866))

119891119899(119866) 120591119898119886119909 (8-16)






next iteration





Improvement

Page | 161


LP8 LP9 LP10



LP29 LP30 LP31

LP26 LP27 LP28


19

20

21

22

23

24

26

25 27

28

29 30

71

13 15

14 16

17

18

69

1 3

2

5

4

7

6 8

10

9

68

11 12

56

57

58 60

59 61 62

65

64 66 67

50 52

51

54

53 55

44

45

46

47

48

49

70

31

32

33

34

36

35

39

37 38 40

41

42 43

63

F3

F2

F1

F7

F6

F5

F4


Subbus1

Subbus2

Subbus3

T1

T3

T5

Main

feeder

Main

feeder

Main

feeder

T2

T4

T6








downstream loads







Improvement

Page | 162

300

350

400

450

4

45

5

55

6

x 104

08

09

1

11

12

13

14

15


SA

IDI

(hrs

custo

mer

yr)


Number

of load

points


(kW)

Q

(kVAr)

Number of

customers

4 1-2 9-10 residential 545 51775 220

6 3-5 13-15 residential 500 475 200

12 6-7 16-17 23-25 28 30-

31 37-38


6 8 11 18 26 32-33 industrial 1500 1425 1

10 12 19-22 27 29 34-36 industrial 1000 950 1













Improvement

Page | 163




Mean

38074 48139 09975

Standard deviation

3431 5291 01165













(hrscustomeryr)


Minimum Loss

32142 46404 13090 68 69 70 71

Minimum ECOST

35409 41145 10586 10 17 41 70

Minimum SAIDI

43523 57891 08253 7 26 54 69






Improvement

Page | 164














compromise

solution

Feeder

loss

(kW)

ECOST

($yr)

SAIDI

(hrscustomeryr) 1205961 1205962 1205963

1 10 10 10 10 41 69 70 34033 41553 10996

2 10 1 1 68 69 70 71 32142 46404 13090

3 1 10 1 10 17 41 70 35409 41145 10586

4 1 1 10 7 26 54 69 43523 57891 08253

5 10 10 1 10 41 69 70 34033 41553 10996

6 10 1 10 10 54 69 71 34759 46644 10217

7 1 10 10 7 17 41 70 40368 43329 09570

86 Summary










Improvement

Page | 165














Page | 166

CHAPTER 9





BALANCING

91 Introduction













Page | 167















groups














Page | 168

0

1












respectively








9-1




120572119871

119871119874119878119878119898119894119899 119871119874119878119878119900119903119894 119871119874119878119878



Page | 169

0

1

120572119871 =

1 119871119874119878119878 le 119871119874119878119878119898119894119899119871119874119878119878119900119903119894minus119871119874119878119878

119871119874119878119878119900119903119894minus119871119874119878119878119898119894119899119871119874119878119878119898119894119899 lt 119871119874119878119878 lt 119871119874119878119878119900119903119894

0 119871119874119878119878 ge 119871119874119878119878119900119903119894

(9-2)














120572119881 =

1 119881119863 le 119881119863119898119894119899119881119863119900119903119894minus119881119863

119881119863119900119903119894minus119881119863119898119894119899119881119863119898119894119899 lt 119881119863 lt 119881119863119900119903119894

0 119881119863 ge 119881119863119900119903119894

(9-3)



120572119881

119881119863119898119894119899 119881119863119900119903119894 119881119863



Page | 170

0

1



119871119861119868 = 119881119886119903[1198681

1198681119898119886119909

1198682

1198682119898119886119909 hellip

119868119894

119868119894119898119886119909 hellip

119868119899

119868119899119898119886119909] (9-4)




120572119861 =

1 119871119861119868 le 119871119861119868119898119894119899119871119861119868119900119903119894minus119871119861119868

119871119861119868119900119903119894minus119871119861119868119898119894119899119871119861119868119898119894119899 lt 119871119861119868 lt 119871119861119868119900119903119894

0 119871119861119868 ge 119871119861119868119900119903119894

(9-5)





Optimality


of the vector

119865(119866) = [1198911(119866)1198912(119866)1198913(119866)]119879 (9-6)




120572119861

119871119861119868119898119894119899 119871119861119868119900119903119894 119871119861119868



Page | 171



Domain



























Page | 172








simultaneously





B4 in detail

941 33-bus System







Case I base case






Page | 173

10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

18 19 20 21

22 23 24

25 26 27 28 29 30 31 32


L18

L19 L20 L21

L22

L23 L24

L25

L26 L27 L28 L29 L30 L31 L32

L33

L34

L35

L36

L37









Fig 9-4



(kW)

Maximum node

voltage deviation

(pu)

Feeder Load

balancing index

Tie-switches

location

08734 14310 00625 00270 6 9 14 32 37







Page | 174

120140

160180

200220

006

008

01

012

014

016

0022

0024

0026

0028

003

0032

0034

0036


Feeder

load b

ala

ncin

g index




deviation (pu)


Mean

15499 00815 00256

Standard deviation

1549 00194 00023











Page | 175

10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

18 19 20 21

22 23 24

25 26 27 28 29 30 31 32


L18

L19 L20 L21

L22

L23 L24

L25

L26 L27 L28 L29 L30 L31 L32

L33

L34

L35

L36

L37

DG2

DG1

DG3







index


Minimum Loss

13981 00639 00280 7 9 14 32 37


14026 00604 00310 7 9 14 28 32


20248 01309 00223 7 30 34 35 37














Page | 176

110120

130140

150160

170

004

006

008

01

0120018

002

0022

0024

0026

0028

003


Feeder

load b

ala

ncin

g index



(kW)

Maximum node

voltage deviation

(pu)

Feeder Load

balancing index

Tie-switches

location

08590 12405 00594 00230 6 8 14 32 37







deviation (pu)


Mean

12850 00711 00231

Standard deviation

1003 00166 00029



Page | 177

















index


Minimum Loss

11753 00643 00241 7 9 14 28 31


12592 00567 00265 6 8 14 28 32


16419 01139 00189 7 21 30 35 37









locations



Page | 178

10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

18 19 20 21

22 23 24

25 26 27 28 29 30 31 32


L18

L19 L20 L21

L22

L23 L24

L25

L26 L27 L28 L29 L30 L31 L32

L33

L34

L35

L36

L37

DG1

DG3

DG2

100110

120130

140150

160

004

006

008

01

012

0016

0018

002

0022

0024

0026

0028


Feeder

load b

ala

ncin

g index


in Case IV

Objective

function

Feeder loss

(kW)

Maximum node

voltage

deviation (pu)

Feeder Load

balancing

index

Tie-switches

location

DGs location

08961 10878 00499 00232 7 9 14 36 37 B32 B32 B32









Page | 179




deviation (pu)


Mean

13295 00873 00194

Standard deviation

1354 00179 00019
















voltage deviation

(pu)

Feeder Load

balancing index

Tie-switches

location

DGs location

Minimum Loss

10844 00538 00228 7 9 14 32 37 B30 B31 B31


11020 00490 00259 7 9 14 28 36 B31 B31 B32


15443 01090 00178 7 30 34 35 37 B8 B9 B12



Page | 180

10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

27

28

29

30

31 32 33 34

35

36

37

38 39 40 41 42 43 44 45

46 47 48 49

50

51

52

53 54 55 56 57 58 59 60 61 62 63 64

65 66

67 68


L27

L28

L29

L30

L31 L32 L33 L34

L35

L36

L37

L38 L39 L40 L41 L42 L43 L44 L45

L46

L47 L48 L49

L50

L51

L52

L53 L54 L55 L56 L57 L58 L59 L60 L61 L62 L63 L64

L65

L66

L67

L68

L69

L70

L71

L72L73

942 69-bus System







respectively

Case I base case















Page | 181

80

100

120

140

160

005

006

007

0080016

0018

002

0022

0024

0026

0028


Feeder

load b

ala

ncin

g index



(kW)

Maximum node

voltage deviation

(pu)

Feeder Load

balancing index

Tie-switches

location

09676 9885 00524 00195 14 55 61 71 72








deviation (pu)


Mean

12535 00605 00192

Standard deviation

2458 00085 00028



Page | 182











initial case





index


Minimum Loss

9885 00524 00195 14 55 61 71 72


10535 00523 00242 9 14 55 61 71


15051 00701 00161 14 61 69 71 72













Page | 183

10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

27

28

29

30

31 32 33 34

35

36

37

38 39 40 41 42 43 44 45

46 47 48 49

50

51

52

53 54 55 56 57 58 59 60 61 62 63 64

65 66

67 68


L27

L28

L29

L30

L31 L32 L33 L34

L35

L36

L37

L38 L39 L40 L41 L42 L43 L44 L45

L46

L47 L48 L49

L50

L51

L52

L53 L54 L55 L56 L57 L58 L59 L60 L61 L62 L63 L64

L65

L66

L67

L68

L69

L70

L71

L72L73

DG3

DG1

DG2

8090

100110

120130

140

005

006

007

008

0014

0016

0018

002

0022

0024


Feeder

load b

ala

ncin

g index



(kW)

Maximum node

voltage deviation

(pu)

Feeder Load

balancing index

Tie-switches

location

08829 8758 00523 00174 14 55 61 71 72







Page | 184





deviation (pu)


Mean

10707 00576 00183

Standard deviation

2042 00071 00029

















index


Minimum Loss

8758 00523 00174 13 55 61 71 72


9729 00522 00226 7 12 55 61 71


13686 00681 00147 11 61 69 71 72



Page | 185

10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

27

28

29

30

31 32 33 34

35

36

37

38 39 40 41 42 43 44 45

46 47 48 49

50

51

52

53 54 55 56 57 58 59 60 61 62 63 64

65 66

67 68


L27

L28

L29

L30

L31 L32 L33 L34

L35

L36

L37

L38 L39 L40 L41 L42 L43 L44 L45

L46

L47 L48 L49

L50

L51

L52

L53 L54 L55 L56 L57 L58 L59 L60 L61 L62 L63 L64

L65

L66

L67

L68

L69

L70

L71

L72L73

DG3DG1

DG2









ACO algorithm


system in Case IV

Objective

function

Feeder loss

(kW)

Maximum

node voltage

deviation (pu)

Feeder Load

balancing

index

Tie-switches

location

DGs location

08882 7397 00429 00158 14 55 61 71 72 B60 B60 B60





9-17



Page | 186

70

80

90

100

110

120

004

0045

005

0055

006

0012

0013

0014

0015

0016

0017

0018

0019


Feeder

load b

ala

ncin

g index




deviation (pu)


Mean

9872 00520 00147

Standard deviation

1491 00055 00013













Page | 187






voltage deviation

(pu)

Feeder Load

balancing index

Tie-switches

location

DGs location

Minimum Loss

7397 00429 00158 14 55 61 71 72 B60 B60 B60


8032 00428 00183 11 55 61 71 72 B60 B60 B60


10962 00577 00125 14 63 69 71 72 B62 B62 B62

95 Summary


















Page | 188





Page | 189

CHAPTER 10


101 Conclusion








results





cost







Page | 190


































Page | 191




























demand times







Page | 192














SAIDI




















Page | 193



102 Future Work












supply each feeder














load on feeders


Page | 194





























Page | 195

References




2001



2015




2 pp 15ndash22 2015








2010

















References

Page | 196

2012






vol 63 pp 461ndash472 2014






652ndash660 2009



pp 1878ndash1887 2010



6 no 2 pp 182ndash197 2002














York 1986



pp 2157ndash2165 2015


1994



References

Page | 197


2016










62ndash66




Wiley 1990




170ndash180 2013






2006 pp 4ndash6















pp 2290ndash2293

References

Page | 198









pp 1217ndash1223 1988










42 2002























References

Page | 199



1530 2009




937ndash940 2008












pp 4021ndash4028 2011



2006








129ndash142 2015









no 1 pp 268ndash276 2009



References

Page | 200




2002





pp 1ndash6


















58 pp 537ndash547 2016





1048ndash1062 2016




2016




686ndash690 2003

References

Page | 201









2473ndash2480 2007







2010







22 no 3 pp 1101ndash1111 2007




388ndash397 2015







of Manchester 2015




1 pp 1ndash13 1996




References

Page | 202



pp 861ndash875 2012






2004












251 2002









Cable 2012






1677ndash1685 2015



2 pp 1401ndash1407 1989



References

Page | 203

no 2 pp 1492ndash1498 1989




pp 1ndash9 2012




932ndash942 2015


Sons 2004














vol 54 pp 255ndash267 2014



119ndash126 2011

Page | 204







Sectional

Area

(CSA)

Positive sequence

Z

Zero-phase

sequence

Z

Approximate

Capacitance

C



A Nexans

635011000

Volt Triplex

Cable

185 0415 0112 0988 0236 036

B 95 0220 0012 0530 0102 028


Page | 205

A2 33-bus system


Branch

number

Sending end

node

Receiving end

node

R

(Ω)

X

(Ω)

P at receiving

end (kW)

Q at receiving

end (kVAr)

1 0 1 00922 0047 100 60

2 1 2 04930 02511 90 40

3 2 3 03660 01864 120 80

4 3 4 03811 01941 60 30

5 4 5 08190 07070 60 20

6 5 6 01872 06188 200 100

7 6 7 07114 02351 200 100

8 7 8 10300 07400 60 20

9 8 9 10440 07400 60 20

10 9 10 01966 00650 45 30

11 10 11 03744 01238 60 35

12 11 12 14680 11550 60 35

13 12 13 05416 07129 120 80

14 13 14 05910 05260 60 10

15 14 15 07463 05450 60 20

16 15 16 12890 17210 60 20

17 16 17 03720 05740 90 40

18 17 18 01640 01565 90 40

19 18 19 15042 13554 90 40

20 19 20 04095 04784 90 40

21 20 21 07089 09373 90 40

22 21 22 04512 03083 90 50

23 22 23 08980 07091 420 200

24 23 24 08960 07011 420 200

25 24 25 02030 01034 60 25

26 25 26 02842 01447 60 25

27 26 27 10590 09337 60 20

28 27 28 08042 07006 120 70

29 28 29 05075 02585 200 600

30 29 30 09744 09630 150 70

31 30 31 03105 03619 210 100

32 31 32 03410 05362 60 40

33 7 20 2 2 -- --

34 11 21 2 2 -- --

35 8 14 2 2 -- --

36 17 32 05 05 -- --

37 24 28 05 05 -- --


Page | 206

A3 69-bus system


Branch

number

Sending end

node

Receiving end

node

R

(Ω)

X

(Ω)

P at receiving

end (kW)

Q at receiving

end (kVAr)

1 0 1 00005 00012 0 0

2 1 2 00005 00012 0 0

3 2 3 00015 00036 0 0

4 3 4 00251 00294 0 0

5 4 5 0366 01864 26 22

6 5 6 0381 01941 404 30

7 6 7 00922 0047 75 54

8 7 8 00493 00251 30 22

9 8 9 0819 02707 28 19

10 9 10 01872 00619 145 104

11 10 11 07114 02351 145 104

12 11 12 103 034 8 5

13 12 13 1044 0345 8 55

14 13 14 1058 03496 0 0

15 14 15 01966 0065 455 30

16 15 16 03744 01238 60 35

17 16 17 00047 00016 60 35

18 17 18 03276 01083 0 0

19 18 19 02106 0069 1 06

20 19 20 03416 01129 114 81

21 20 21 0014 00046 5 35

22 21 22 01591 00526 0 0

23 22 23 03463 01145 28 20

24 23 24 07488 02475 0 0

25 24 25 03089 01021 14 10

26 25 26 01732 00572 14 10

27 26 27 00044 00108 26 186

28 27 28 0064 01565 26 186

29 28 29 03978 01315 0 0

30 29 30 00702 00232 0 0

31 30 31 0351 0116 0 0

32 31 32 0839 02816 14 10

33 32 33 1708 05646 195 14

34 33 34 1474 04873 6 4

35 34 35 00044 00108 26 1855

36 35 36 0064 01565 26 1855

37 36 37 01053 0123 0 0

38 37 38 00304 00355 24 17

39 38 39 00018 00021 24 17

40 39 40 07283 08509 12 1

41 40 41 031 03623 0 0


Page | 207

42 41 42 0041 00478 6 43

43 42 43 00092 00116 0 0

44 43 44 01089 01373 3922 263

45 44 45 00009 00012 3922 263

46 45 46 00034 00084 0 0

47 46 47 00851 02083 79 564

48 47 48 02898 07091 3847 2745

49 48 49 00822 02011 3847 2745

50 49 50 00928 00473 405 283

51 50 51 03319 01114 36 27

52 51 52 0174 00886 435 35

53 52 53 0203 01034 264 19

54 53 54 02842 01447 24 172

55 54 55 02813 01433 0 0

56 55 56 159 05337 0 0

57 56 57 07837 0263 0 0

58 57 58 03042 01006 100 72

59 58 59 03861 01172 0 0

60 59 60 05075 02585 1244 888

61 60 61 00974 00496 32 23

62 61 62 0145 00738 0 0

63 62 63 07105 03619 227 162

64 63 64 1041 05302 59 42

65 64 65 02012 00611 18 13

66 65 66 00047 00014 18 13

67 66 67 07394 02444 28 20

68 67 68 00047 00016 28 20

69 49 58 2 1 -- --

70 26 64 1 05 -- --

71 12 20 05 05 -- --

72 10 42 05 05 -- --

73 14 45 1 05 -- --



Feeder

Type

Length

(km)


1 060 2 6 10 14 17 21 25 28 30 34 38 41 43 46 49 51 55 58 61 64 67

68 69 70 71

2 075 1 4 7 9 12 16 19 22 24 27 29 32 3537 40 42 45 48 50 53 56 60

63 65

3 080 3 5 8 11 13 15 18 20 23 26 31 33 36 3944 47 52 54 57 59 62 66


Page | 208



Lines 004 0 0 0 5 0

Buses 0001 0 1 001 2 8

Switches 0004 0002 1 006 4 72








Page | 209










0000 TW5 0400 TW5 0800 TW1 1200 TW5 1600 TW1 2000 TW5

0010 TW5 0410 TW5 0810 TW1 1210 TW5 1610 TW1 2010 TW5

0020 TW5 0420 TW5 0820 TW1 1220 TW5 1620 TW1 2020 TW5

0030 TW5 0430 TW5 0830 TW1 1230 TW5 1630 TW1 2030 TW5

0040 TW5 0440 TW5 0840 TW1 1240 TW5 1640 TW5 2040 TW5

0050 TW5 0450 TW5 0850 TW1 1250 TW5 1650 TW5 2050 TW5

0100 TW5 0500 TW5 0900 TW1 1300 TW5 1700 TW5 2100 TW5

0110 TW5 0510 TW5 0910 TW1 1310 TW5 1710 TW5 2110 TW5

0120 TW5 0520 TW5 0920 TW1 1320 TW5 1720 TW5 2120 TW5

0130 TW5 0530 TW5 0930 TW1 1330 TW5 1730 TW5 2130 TW5

0140 TW5 0540 TW5 0940 TW1 1340 TW5 1740 TW5 2140 TW5

0150 TW5 0550 TW5 0950 TW1 1350 TW5 1750 TW5 2150 TW5

0200 TW5 0600 TW5 1000 TW1 1400 TW5 1800 TW5 2200 TW5

0210 TW5 0610 TW5 1010 TW5 1410 TW5 1810 TW5 2210 TW5

0220 TW5 0620 TW5 1020 TW5 1420 TW5 1820 TW5 2220 TW5

0230 TW5 0630 TW5 1030 TW5 1430 TW5 1830 TW5 2230 TW5

0240 TW5 0640 TW5 1040 TW5 1440 TW5 1840 TW5 2240 TW5

0250 TW5 0650 TW5 1050 TW5 1450 TW5 1850 TW5 2250 TW5

0300 TW5 0700 TW5 1100 TW5 1500 TW5 1900 TW5 2300 TW5

0310 TW5 0710 TW5 1110 TW5 1510 TW5 1910 TW5 2310 TW5

0320 TW5 0720 TW5 1120 TW5 1520 TW5 1920 TW5 2320 TW5

0330 TW5 0730 TW1 1130 TW5 1530 TW5 1930 TW5 2330 TW5

0340 TW5 0740 TW1 1140 TW5 1540 TW5 1940 TW5 2340 TW5

0350 TW5 0750 TW1 1150 TW5 1550 TW5 1950 TW5 2350 TW5


Page | 210



corresponding 95th


B-2 and Table B-3


Node

No

Scenarios

S1 S2 S3 S4 S5 S6 S7 S8 S9

A4_1 09675 09787 09787 09766 09859 09859 09748 09825 09815

A4_2 09676 09784 09784 09766 09856 09856 09748 09822 09813

A4_3 09677 09782 09782 09767 09854 09854 09749 09819 09811

A4_4 09678 09780 09780 09768 09851 09851 09750 09817 09810

A4_5 09681 09777 09777 09771 09849 09849 09753 09814 09808

A4_6 09685 09775 09775 09775 09846 09846 09757 09812 09807

A4_7 09689 09773 09773 09779 09845 09845 09762 09811 09807

A4_8 09694 09772 09772 09784 09844 09844 09767 09810 09807

B4_8 09700 09772 09772 09790 09844 09844 09773 09810 09808

B4_7 09707 09773 09773 09797 09845 09845 09779 09811 09810

B4_6 09714 09775 09775 09804 09846 09846 09787 09812 09813

B4_5 09722 09777 09777 09813 09849 09849 09795 09814 09816

B4_4 09731 09780 09780 09821 09851 09851 09804 09817 09820

B4_3 09737 09782 09782 09827 09854 09854 09809 09819 09823

B4_2 09743 09784 09784 09833 09856 09856 09815 09822 09826

B4_1 09749 09787 09787 09839 09859 09859 09821 09825 09830

Table B-3 95th


Node

No

Scenarios

S1 S2 S3 S4 S5 S6 S7 S8 S9

A4_1 09352 09573 09573 09537 09721 09721 09537 09721 09715

A4_2 09353 09567 09567 09537 09715 09715 09537 09715 09709

A4_3 09355 09562 09562 09539 09711 09711 09539 09711 09704

A4_4 09357 09558 09558 09541 09707 09707 09541 09707 09702

A4_5 09363 09553 09553 09547 09701 09701 09547 09701 09679

A4_6 09370 09548 09548 09555 09697 09697 09555 09697 09694

A4_7 09379 09545 09545 09563 09694 09694 09563 09794 09691

A4_8 09389 09544 09544 09573 09692 09692 09573 09792 09692

B4_8 09400 09544 09544 09585 09692 09692 09585 09792 09692

B4_7 09413 09545 09545 09598 09694 09694 09598 09794 09694

B4_6 09427 09548 09548 09613 09697 09697 09613 09697 09697

B4_5 09443 09553 09553 09628 09701 09701 09628 09701 09701

B4_4 09460 09558 09558 09646 09707 09707 09646 09707 09707


Page | 211

B4_3 09471 09562 09562 09656 09711 09711 09656 09711 09711

B4_2 09482 09567 09567 09668 09715 09715 09668 09715 09715

B4_1 09494 09573 09573 09680 09721 09721 09680 09721 09721







1 1227 1189 1010 1003

2 5192 2686 2051 2060

3 1995 756 112 490

4 1874 667 074 415

5 3833 1321 122 807

6 192 006 006 006

7 484 0 0 0

8 418 124 211 124

9 357 0 0 0

10 055 001 001 001

11 088 003 003 003

12 267 045 045 045

13 073 008 008 008

14 036 0 0 0

15 028 045 092 045

16 025 048 115 048

17 003 007 022 007

18 016 226 232 226

19 083 1809 1859 1808

20 01 424 436 423

21 004 118 071 118

22 319 316 914 315

23 516 512 1618 510

24 129 128 869 128

25 26 224 005 124

26 334 285 003 155

27 1133 962 003 510

28 786 664 0 345

29 391 326 199 159

30 160 110 018 003


Page | 212

31 021 012 0 000

32 001 0 013 0

33 0 563 809 563

34 0 215 215 215

35 0 174 320 174

36 0 002 033 002

37 0 0 263 0

Total 20314 13981 11753 10844




1 008 007 006 006

2 008 007 006 006

3 020 012 012 010

4 194 011 011 011

5 2829 159 155 159

6 2939 164 160 164

7 691 035 034 035

8 338 012 012 012

9 477 143 137 142

10 101 029 027 028

11 219 032 030 032

12 128 000 000 000

13 124 000 0 000

14 120 0 000 0

15 022 083 043 083

16 032 138 067 138

17 000 001 001 001

18 010 080 032 080

19 007 052 021 052

20 011 083 033 083

21 000 003 001 002

22 001 022 006 022

23 001 049 013 049

24 001 091 021 091

25 000 037 009 037

26 000 019 004 019

27 000 000 000 000

28 000 000 000 000

29 001 001 001 001

30 000 000 000 000

31 001 001 001 001


Page | 213

32 001 001 001 001

33 001 001 001 001

34 000 000 000 000

35 000 003 001 003

36 001 041 019 041

37 002 064 028 064

38 000 018 008 018

39 000 001 000 001

40 005 391 161 391

41 002 166 068 166

42 000 022 009 022

43 000 005 002 005

44 001 057 023 057

45 000 000 000 000

46 002 017 017 013

47 058 416 416 316

48 164 1321 1321 991

49 012 253 253 178

50 000 000 000 000

51 000 000 000 000

52 580 001 001 001

53 673 001 001 000

54 916 000 000 000

55 882 0 0 0

56 4986 000 000 000

57 2458 000 000 000

58 954 000 000 000

59 1071 627 626 379

60 1408 824 823 498

61 011 0 0 0

62 014 000 000 000

63 066 001 001 001

64 004 071 069 071

65 000 000 000 000

66 000 000 000 000

67 002 002 002 002

68 000 000 000 000

69 0 3783 3782 2384

70 0 102 052 102

71 0 0 0 0

72 0 0 0 0

73 0 423 252 423

Total 22562 9885 8758 7397


Page | 214




(hrscustomeryr)

70 68 71 69 321415 4640359 130895231648616

70 10 41 54 364131 431068083000 102819629963899

17 10 41 70 354092 411445783000000 105858799638989

17 26 10 70 383269 530285525000000 0968805806257521

7 26 54 69 435225 578907612000000 0825265794223827

7 54 41 69 406035 460067870000000 0915047984356197

7 26 54 70 442913 571756512000000 0836828971119134

17 10 71 70 345231 439663189000000 106361687725632

70 10 71 69 331470 443747189000000 110465057160048

70 10 41 69 340330 415529783000000 109962169073406

70 68 41 69 330274 435818516000000 130392343561974

7 54 71 69 397170 488285276000000 0920076865222623

41 10 54 69 356448 438219183000000 101663312274368

70 10 54 26 393311 549907825000000 0938414109506619

70 7 71 69 381047 465595876000000 100306543321300

70 7 41 17 403678 433294470000000 0957002858002407

70 10 54 71 355269 459285489000000 103322518050542

7 54 71 70 404856 481134176000000 0931640042117930

7 26 17 70 432867 552134212000000 0867220667870036

7 70 41 69 389911 437378470000000 0998036552346570

7 26 69 70 419096 556218212000000 0908254362214200

17 7 71 70 394813 461511876000000 0962031738868833

71 10 54 69 347586 466436589000000 102166200361011

10 26 54 69 385625 557058925000000 0926850932611312

70 26 10 69 369504 534369525000000 100983950060168

7 54 41 70 413721 452916770000000 0926611161251504


Page | 215





(kW)

Maximum node

Voltage deviation

Feeder load

balancing index

7 34 35 31 37 176962 0108696024464801 00228687361961248

7 11 35 32 28 143474 00613272038422790 00305387759787611

7 9 14 31 37 142477 00768537372742428 00252628392269486

6 8 12 36 37 151849 00696765908940439 00259144961258893

7 8 14 31 37 155399 00924077518455773 00239781364880477

6 8 12 31 37 169382 0104485611067200 00236077543160956

6 8 12 32 37 152876 00776641110366926 00250547432924683

33 8 14 30 37 171441 0108063061643879 00230652089068052

7 9 14 32 28 140261 00604355611623940 00310349101268755

7 11 35 32 37 143028 00639069227083702 00273727965037185

6 8 14 31 37 159752 00968913958755809 00236540473688646

6 33 35 32 37 170278 00826562726566354 00249194843739843

6 11 35 32 37 144683 00656445815841987 00261947314082027

6 8 14 32 37 146983 00705648561488426 00256096967694280

7 9 14 32 37 139815 00639015456844128 00280407351785895

6 9 14 32 37 143097 00625183468485540 00270001779728268

7 11 35 31 37 148829 00852978398065017 00245113845932977

7 34 35 30 37 202483 0130888991378581 00223050578905545

6 8 14 36 37 146991 00643933147100736 00266176555168500

6 11 35 31 37 154281 00897759906819439 00242838273201709

6 8 13 32 37 150430 00753226918458818 00253604605496161




(kW)

Maximum node

Voltage deviation

Feeder load

balancing index

7 14 8 32 28 121696 00575193535569366 00264544805354717

7 11 35 31 37 123007 00712785797883380 00213250141648472

6 12 8 32 37 128324 00630309398395457 00223824361844486

6 14 8 30 37 145672 0101299721228755 00194921779245086

7 33 35 32 28 130184 00583420082867310 00261406698684195

7 14 8 30 37 140274 00967924815464314 00195001911353607

7 21 35 30 37 164190 0113945920950777 00189031534924873

6 13 8 32 37 126434 00607661484850486 00227035446761735

7 14 9 32 28 117726 00575130414815478 00271215548731366


Page | 216

6 14 8 32 28 125920 00566904604559002 00265195832133384

6 12 8 31 37 137974 00889877482038002 00200083704114662

7 11 35 30 37 133030 00891516445489180 00199682922816912

6 11 35 32 37 123013 00593840879899440 00235298833627789

7 14 9 32 37 121070 00631040005210335 00255168322432724

6 14 9 32 28 123916 00566872316455769 00273594084038335

7 14 9 30 37 126587 00812324184971598 00206873922472966

7 14 9 31 28 117529 00642736861104275 00240537048868074

6 14 9 32 37 122047 00593825021727904 00240927348267257

6 11 35 32 28 124883 00566888115014094 00269082055980326

6 11 35 31 37 126802 00756552348586014 00207586957663036

6 14 8 32 37 124050 00593857418451058 00230337877365745

7 13 8 32 28 124039 00575225874614865 00262247242500743

7 11 35 32 28 119522 00575159230231156 00267430211390231

7 14 9 31 37 118759 00642740886891275 00220228862077971

6 14 8 31 37 130316 00816654599427028 00201908840890301

33 14 8 30 37 140110 00923831702765571 00197570883486903

7 12 8 32 28 125895 00587758838819431 00259864524009700

6 13 8 31 37 134936 00865715938530326 00201790772057552




loss

(kW)

Maximum node

Voltage deviation

Feeder load

balancing index

7 9 14 30 37 15 17 16 112506 00655990339384582 00207847799664288

6 8 14 31 37 14 11 15 120818 00728143829651942 00199639595336255

7 11 35 30 37 16 16 12 118637 00756705031931788 00198888055963062

6 8 14 31 37 11 29 14 125736 00822955381260978 00194988443664523

6 11 35 32 37 29 11 29 116999 00602917954784902 00213598898907595

7 9 14 31 37 15 14 16 110931 00518306996442978 00223689972435171

7 34 35 30 37 16 13 13 140652 00983575865184194 00182688360250883

7 8 14 30 37 14 11 15 128617 00876913785424229 00190954012999288

7 8 14 30 37 11 16 14 127141 00860397262006276 00191601352391895

7 9 14 36 37 30 30 29 109157 00520335391274761 00229564125698243

7 8 14 30 37 10 14 16 126706 00857230143750372 00192117850059117

7 11 35 30 37 13 16 12 121130 00786215737441328 00196617519208137

7 34 35 30 37 13 10 9 151352 0106960621828031 00178195736666725

7 34 35 30 37 10 12 9 152310 0107688512235453 00178046268710843

6 8 14 30 37 11 15 16 130550 00897068798318073 00189590122249633

6 8 14 30 37 16 14 10 130869 00901533044670202 00189271311922809

7 34 35 30 37 10 13 12 148089 0104837492639545 00178736074180585


Page | 217

7 34 35 30 37 13 11 16 143317 0100615335666250 00181553323058751

6 8 14 30 37 10 14 14 133299 00925968739633617 00188139999335965

7 34 35 30 37 13 9 12 148392 0105013682219175 00178453713901855

6 8 14 30 37 14 11 10 137593 00963962506644021 00186232592604301

6 8 14 30 37 11 8 14 136046 00951731865531927 00187106569470356

6 8 14 30 37 11 11 16 135639 00942616575802945 00187170876179048

7 8 14 30 37 15 16 14 122935 00815907052491111 00195198923102276

7 34 35 30 37 12 14 16 140640 00983915740315128 00182784576692257

6 33 35 31 37 11 11 13 146017 00888852225316270 00188548348595259

7 34 35 30 37 12 16 12 142144 00997534014352579 00181578155086060

6 8 14 30 37 14 11 15 132819 00921338781311946 00188143081376993

6 8 14 30 37 10 15 11 136651 00956093119043262 00186781475357014

7 9 14 31 37 14 14 16 111382 00525319705640723 00222591386298574

7 34 35 30 37 13 14 16 139957 00977014014811679 00183484070331887

7 34 35 30 37 12 15 16 139849 00976123852270839 00183745698300515

7 34 35 30 37 12 16 16 138589 00959671533698319 00184842191427931

7 34 35 30 37 16 13 16 137912 00952795751906571 00185525366651277

6 33 35 31 37 11 11 11 148785 00910856464605774 00187751047204272

7 34 35 30 37 12 16 13 141338 00990484927061306 00181980491991251

7 34 35 30 37 12 13 12 145536 0102926179499332 00179590185768212

6 8 14 30 37 14 10 15 132373 00918145642214576 00188660639598312

6 8 14 30 37 16 11 14 131312 00904718190224125 00188759872087077

7 34 35 30 37 13 15 16 139168 00969230570394858 00184436609617936

7 34 35 30 37 13 9 11 150730 0106620666560267 00178315514588942

6 8 14 30 37 14 11 14 133746 00929165522686308 00187615074100094

7 34 35 30 37 9 9 12 152656 0107867658396772 00178031242058681

6 8 14 30 37 10 11 16 135118 00939381882085281 00187414815201857

7 34 35 30 37 12 12 9 149341 0105739135263959 00178316539838164

7 9 14 36 28 32 32 32 110385 00489797931328652 00256323647901629

7 9 14 36 37 32 31 31 108599 00498935433820196 00235262740306846

7 9 14 32 37 31 30 31 108436 00537552050723257 00227898958267559

7 9 14 36 28 32 31 31 110203 00489682960875768 00259015702487973

7 34 35 30 37 8 12 9 154427 0108962750550623 00178021823053241


Page | 218




(kW)

Maximum node

Voltage deviation

Feeder load

balancing index

55 61 71 72 12 99036 00524391619987274 00196366946903149

69 61 71 9 14 145213 00664127006601768 00185315761508749

55 61 71 72 14 98845 00524393494628415 00194882148961848

69 70 71 10 14 145135 00666490251240782 00182871906896542

69 61 71 72 12 150267 00699556148777123 00161708619074924

55 61 71 10 14 104521 00524349487665904 00238104755589364

69 61 71 72 13 150383 00700225094171628 00161512783956020

55 61 71 72 13 98937 00524392488739880 00195710324132613

69 61 71 72 11 150792 00682108082577803 00171029450547815

55 61 71 9 14 105348 00524349082167884 00242117051986541

69 61 71 72 14 150513 00700911373758199 00161129748303495

55 61 71 72 11 105195 00524380932334678 00218572363716938




(kW)

Maximum node

Voltage deviation

Feeder load

balancing index

55 61 12 14 9 97461 00523081449765275 00226112450860475

69 61 71 14 9 130761 00662843002557533 00155527078006889

55 61 71 14 7 97263 00523080911134007 00226177446060770

55 61 12 71 72 87588 00523152959484715 00174558059214037

55 61 71 14 8 93176 00523082195004728 00211109499855264

55 61 71 13 72 87581 00523154440245970 00174392153380541

55 61 12 14 72 87755 00523153511186373 00174538759436512

55 61 12 71 7 97289 00523080869366065 00226232791264600

69 61 71 11 9 134009 00662855052002667 00154463391981039

69 61 12 14 9 130989 00662843776081034 00155381836375260

55 61 71 13 7 97273 00523080879708534 00227249951330579

55 61 71 14 9 90907 00523086904216601 00201865894567423

55 61 71 14 10 90291 00523088955157064 00199034032147027

69 61 71 14 10 130894 00665207578684145 00154263271797149

55 61 71 14 72 87582 00523156072908145 00174100597226583

69 61 71 11 10 134197 00665220013747228 00153401360203180

69 61 71 11 72 136858 00680828895070073 00147368269784675

69 61 12 14 10 131126 00665208386694061 00154135530565384

55 61 71 11 72 91274 00523126048676607 00184393848480773


Page | 219




loss

(kW)

Maximum node

Voltage deviation

Feeder load

balancing index

69 63 71 10 14 60 60 60 105879 00543213716422435 00153740505896722

69 63 12 72 71 60 62 62 109324 00575466375767690 00126779733811642

55 61 71 72 11 60 60 60 80324 00429183191505871 00183159151221229

69 63 12 72 71 61 61 62 109323 00575465740537586 00126842028893447

55 61 71 72 12 60 60 60 74165 00429193759769601 00159264876998350

69 63 14 10 71 62 62 62 106070 00543012249613587 00150279825984642

69 63 11 72 71 60 62 60 110547 00558290844078126 00139841427388105

69 63 14 9 71 62 62 62 106271 00540689205567605 00153025056850459

69 61 71 72 11 60 60 60 108838 00542584369620998 00141625735067141

55 61 71 72 14 60 56 60 75837 00436673338725839 00157367114339890

69 63 14 10 71 62 62 60 105960 00542966739560918 00151430448212008

69 61 71 10 14 60 60 60 104307 00527268149576859 00155323687715422

69 63 11 72 71 61 62 62 110652 00558333983851442 00137892112215884

69 63 13 72 71 62 62 62 109522 00576169823075075 00125440050970194

55 61 71 72 14 60 55 60 75975 00436701836501366 00156758120818947

69 63 71 10 14 60 60 62 105896 00542940500362948 00152768514567046

69 63 14 9 71 62 61 61 106159 00540643102892876 00154245882374843

55 61 71 72 13 60 60 60 74066 00429194617185072 00158554987038681

69 62 71 10 14 61 60 60 105886 00542959390978505 00153513700764165

69 63 14 72 71 62 62 62 109622 00576844280930477 00125002240983144

55 63 71 72 14 62 61 62 74382 00440379610790336 00155858821619573

69 63 71 72 11 60 60 60 110530 00558564471048234 00140822204796308

55 63 71 72 14 60 60 62 74285 00440350644694274 00157371695186626

55 63 14 72 71 62 62 62 74448 00440399072962552 00155438948075735

55 63 71 72 14 60 62 62 74344 00440368353288504 00156312863856681

69 63 71 9 14 60 61 60 105882 00542934725670071 00153515485666183

55 63 71 72 14 60 61 62 74305 00440356668532606 00156816031788752

55 61 20 72 13 60 60 60 80533 00429326269571468 00157463174391893

55 63 71 72 14 61 61 62 74343 00440367927398261 00156346520711234

69 61 71 72 14 60 60 60 107187 00561022028435777 00126909641069497

69 63 71 72 11 60 61 60 110533 00558285040786375 00140595150870697

69 63 12 72 71 62 62 62 109436 00575512407997617 00125707103016452

69 63 14 10 71 61 62 62 106000 00542983427485794 00150838099664421

69 63 11 72 71 60 61 62 110569 00558299818740340 00139149694834405

69 63 14 9 71 61 62 60 106118 00540626433897020 00154840963668230

69 61 71 72 12 60 60 60 107041 00559693311798567 00127785892138089

55 61 71 72 14 60 60 60 73974 00429195606297569 00157682511572302

69 63 14 10 71 61 61 62 105958 00542966109653011 00151492343922130

69 63 12 72 71 62 62 61 109365 00575483243249972 00126225992147273


Page | 220

69 63 11 72 71 62 62 60 110611 00558317226735644 00138490567525274

69 63 14 9 71 62 62 61 106201 00540660395254129 00153587525958041

69 63 14 10 71 61 60 62 105917 00542949434469265 00152083287358888

69 63 14 9 71 62 62 60 106160 00540643732226493 00154184014811756

69 63 11 72 71 61 61 62 110610 00558316590719640 00138552654427231

69 63 71 72 11 62 62 62 110723 00558362979744786 00137328015545176

69 61 71 72 13 60 60 60 107108 00560349171634668 00127435051911921

Page | 221


Algorithms



2amp3

Parameter Value

Number of ants 50







Parameter Value

Number of ants 100








operation

Parameter Value

Number of ants 150







Page | 222



Parameter Value

Number of ants 400







Parameter Value

Number of ants 500







Chapter 8


ECOST and SAIDI)

Parameter Value

Number of ants 100







Page | 223


ECOST and SAIDI)

Parameter Value







Chapter 9



Parameter Value

Number of ants 200








Parameter Value






Page | 224








9th











1-6 12-15 March 2018

Page | 3













211 Summary 58

CHAPTER 3 60


31 Introduction 60






35 Summary 68

CHAPTER 4 70



41 Introduction 70

42 Load Model 72


44 Methodology 73




451 Test Case 1 77

452 Test Case 2 85

Page | 4

46 Summary 90

CHAPTER 5 92



51 Introduction 92








55 Summary 109

CHAPTER 6 111



61 Introduction 111





651 Test Case 1 122

652 Test Case 2 123

653 Test Case 3 124

66 Summary 126

CHAPTER 7 128



71 Introduction 128





Page | 5







751 Test Case 1 138

752 Test Case 2 147

753 Test Case 3 147

76 Summary 148

CHAPTER 8 150



81 Introduction 150









86 Summary 164

CHAPTER 9 166



BALANCING 166

91 Introduction 166








Page | 6




95 Summary 187

CHAPTER 10 189


101 Conclusion 189

102 Future Work 193

References 195





Word count 51012

Page | 7

List of Figures





34


















comparison 74






Fig 4-8 11 kV 4th




Page | 8

Fig 4-11 11 kV 4th


























117









Page | 9





136




13 142





problem 157


problem 158



162
















Page | 10

List of Tables













102












13 143




2 147


3 148

Page | 11



163




Case II 173


174



Case III 176


III 176





IV 179



in Case II 181


II 181



in Case III 183


III 184


184



Page | 12


IV 186


187


204







Table B-3 95th





SAIDI) 214

















Page | 13













Page | 14
























EV Electric Vehicle





HC Hyper Cube


HV High Voltage

Page | 15


LV Low Voltage




MV Medium Voltage









TS Tabu Search





Page | 16

Abstract





December 2017






















for optimal DA

Page | 17

Declaration




Page | 18

Copyright Statement










copies made








andor Reproductions










Page | 19

Acknowledgements









encouragement





and support

Page | 20

CHAPTER 1

INTRODUCTION

11 Motivation
















increase profits




Page | 21




during one week






























Page | 22





12 Objectives







ACO) algorithm


















Page | 23
































Page | 24




































Page | 25

































Page | 26

































Page | 27














for all studies

Page | 28

CHAPTER 2


21 Introduction
















Page | 29

Tie-switch





















Page | 30





231 Reclosers














trip




Recloser locks

out on 2nd

reclose

as programmed

Recloser opens

Recloser recloses

fault still present

Recloser recloses

fault still present

Recloser re-opens

fault still present

Load current


Page | 31










233 Tie-switches










241 Basic Concepts









Page | 32

Tran

sfo

rme

r Lo

ss


1 Transformer

2 Transformers



















119878119871




Page | 33








improvement
























Page | 34





(Kw)







(Kw)














Page | 35








Transformer Size

(kVA)

No load loss

(kW)

Load loss

(kW)

Capital

price (euro)

Cost of loss

(euro)

Total cost

(euro)

A 1000 11 9 9074 34211 43285

B 1000 094 76 11362 28986 40348


251 Basic Concepts









and opened



Page | 36


































Page | 37



































Page | 38




operations








261 Basic Concepts


















Page | 39






















Page | 40


1 2 3 4 5 6 7


1 2 3 4 5 6 7


1 2 3 4 5 6 7


1 2 3 4 5 6 7


CB1 opened



CB1 CB2

CB1CB2

CB1 CB2

CB1 CB2





Interrupted

load



Page | 41


1 2 3 4 5 6 7


1 2 3 4 5 6 7


1 2 3 4 5 6 7


1 2 3 4 5 6 7


CB1 opened



CB1 CB2

CB1CB2

CB1 CB2

CB1 CB2





Interrupted

load









Page | 42





























Page | 43









network unit [72]

Open-circuit test






Page | 44

(a) Test circuit









119875119874119862 = 119875ℎ+119890 =119880119874119862

2

119877119888119871119881= 119880119874119862119868ℎ+119890 (2-1)


current

Short-circuit test




119880119900119888

119868ℎ+119890 119868120601

119868119900119888 119885119890119902 119871119881

119877119888 119871119881 119883119898 119871119881


Page | 45




(a) Test circuit






and expressed as

119875119878119862 = 1198681198781198622 119877119890119902119867119881 (2-2)




119880119904119888

119868119890119909

119868119904119888 119877119890119902 119867119881 119883119890119902 119867119881

(119899119890119892119897119890119888119905)


Page | 46

Active power loss



∆119875 = 119875119874119862 + 1205732119875119878119862 (2-3)

where 120573 =119878119871




Reactive power loss



as

∆119876 = 119876119874119862 + 1205732119876119878119862 (2-4)

119876119874119862 = 119878119874119862 =119868119874119862

119868119873∙ 119878119873 (2-5)

119876119878119862 = 119878119878119862 = 119880119878119862

119880119873∙ 119878119873 (2-6)








1198791198711 = 11988002119875119885119874119862 +

1205732

11988002 119875119885119878119862 (2-7)

119875119885119874119862 = 119875119874119862 + 119870119876119876119874119862 (2-8)


Page | 47

119875119885119878119862 = 119875119878119862 + 119870119876119876119878119862 (2-9)


120573 =119878119871















1198791198712 = 211988002119875119885119874119862 +

1

2

1205732

11988002 119875119885119878119862 (2-10)







Page | 48




119875119887119877 + 119895119876119887119877 = 119887119877 times 119868lowast (2-11)

119875119887 = 1198681198872 times 119877119887 (2-12)


119875119887 =119875119887119877

2 +1198761198871198772

1198811198871198772 times 119877119887 (2-13)







119864119871 = sum 119875119887119899119873119887119899 (2-14)











Page | 49



120582 = sum 120582119895119895 (2-15)

119880 = sum 120582119895119895 119903119895 (2-16)

119903 =119880

120582 (2-17)


point





119878119860119868119865119868 =sum 120582119894119873119894119894

sum 119873119894119894 (2-18)

119878119860119868119863119868 =sum 119880119894119873119894119894

sum 119873119894119894 (2-19)

119860119864119873119878 =sum 119880119894119871119894119894

sum 119873119894119894 (2-20)

119864119862119874119878119879 = sum 119888119898(119889119898)119891119898119871119898119872119898=1 (2-21)











Page | 50




Simulation method












memory

Analytical method






(FMEA)










Page | 51











Normal operation

Active

failure

Transient

failure

Passive

failure

Maintenance

120582119860 120582119879 120582119875 120582119872

120583119860 120583119879 120583119875

120583119872


Page | 52

Start











Next failure i=i+1


End

No

Yes












Page | 53















after failure











Page | 54

0

1


















120572 =

1 119883 le 119883119898119894119899119883119898119886119909minus119883

119883119898119886119909minus119883119898119894119899119883119898119894119899 lt 119883 lt 119883119898119886119909

0 119883 ge 119883119898119886119909

(2-22)





120572

119883119898119894119899 119883119898119886119909 119883


Page | 55










119872119886119909 119869 = 12059611205721 + 12059621205722 + ⋯ + 120596119899120572119899 (2-23)







selected objectives






Max-min method




119872119886119909 119869 = min 1205721 1205722 hellip 120572119899 (2-24)




Page | 56











reconfiguration





119872119886119909 119869 = (1205721 ∙ 1205722 ∙ hellip ∙ 120572119873)1 119899frasl (2-25)







Framework








Page | 57



forall 119894 = 12 hellip 119873119900119887119895 119865119894(119883) le 119865119894(119884) (2-26)

exist 119894 = 12 hellip 119873119900119887119895 119865119894(119883) lt 119865119894(119884) (2-27)














preferences











Page | 58

211 Summary
































Page | 59













Page | 60

CHAPTER 3


31 Introduction


















Page | 61









search space [13]




35













follows [93]

119862 = 119875(119883 minus 119871 le 120583 le 119883 + 119871) = int 119866(119883)119889119909119883+119871

119883minus119871 (3-1)

119871 = 119911lowast 120590

radic119899 (3-2)


Page | 62







095


119862 09 095 099 0999

119911lowast 1645 1960 2576 3291


119899 = (119911lowast120590

119871)2 (3-3)
















Page | 63
























Page | 64

the nest






















Page | 65

Start

Set Iteration n=1

Maximum iteration

reached

End

No

Yes









n=n+1












Page | 66


































Page | 67

Start

Cloning

Maximum iteration

reached

End

No

Yes


Hypermutation

Fitness evaluation


Pheromone updating

n=n+1












Page | 68










tables [88]

















35 Summary





Page | 69


























Page | 70

CHAPTER 4





41 Introduction














Page | 71



























Section 46



Page | 72

42 Load Model



modelled








Number of people

in household

1 2 3 4 ge5

Percentage () 3058 341 1557 1288 686






weekend


12


dwelling





Page | 73










follows

Minimise 119891 = 1198800

2119875119885119874119862 +1205732

11988002 119875119885119878119862 119905119903119886119899119904119891119900119903119898119890119903 119894119899 119904119894119899119892119897119890 119900119901119890119903119886119905119894119900119899

211988002119875119885119874119862 +

1

2

1205732

11988002 119875119885119878119862 119905119903119886119899119904119891119900119903119898119890119903119904 119894119899 119901119886119903119886119897119897119890119897 119900119901119890119903119886119905119894119900119899

(4-1)


120573 =119878119871




44 Methodology









Page | 74













obtained

Profile

generator of

domestic

electricity

demand profiles

Transformer

operation

modes

MATLAB

Distribution

network

model built

in OpenDSS

Analyse and

compare

simulation

results in

MATLAB




Page | 75

Start



modes considered

End

No

Yes


customer randomly


mode



Record results

Change

transformer

operation

mode

N=N+1




No

Yes







Page | 76














obtained


day is recorded


Profile

generator of

domestic

electricity

demand profiles

Tie-switch

status

MATLAB

Distribution

network

model built

in OpenDSS

Analyse and

compare

simulation

results in

MATLAB




Page | 77





451 Test Case 1








whilst the 4th
























Page | 78

A

A

A

A

B

B

B

B


Load4_2

Load4_3

Load4_4

Load4_5

Load4_6

Load4_7

Load4_8

75 MVA

33 kV

11 kV

33 kV

Voltage

Source

75 MVA



Sub-

sector

Transf

Rating

(kVA)

Conn Tapping

Range

Load

Losses

at

75

(kW)

No-

Load

Losses

(kW)

Impedance voltage


the principle

tapping

()

Reference

standard


6 steps of 25

Each

50

75

835 BS 171 amp

IEC 60076







Page | 79

0

10

20

30

40

50

60

70

80

90

100

0 2 4 6 8 10 12 14 16 18 20 22

Tran

sfo

rme

r Lo

ad F

acto

r

Time (h)

0

10

20

30

40

50

60

70

0 2 4 6 8 10 12 14 16 18 20 22

Tran

sfo

rme

r Lo

sse

s (k

W)

Time (h)

0

10

20

30

40

50

60

70

0 2 4 6 8 10 12 14 16 18 20 22

Tran

sfo

rme

r Lo

sse

s (k

W)

Time (h)




of Scenario 1


(a) Scenario 1

(b) Scenario 2



Page | 80

0

10

20

30

40

50

60

70

0 2 4 6 8 10 12 14 16 18 20 22

Tran

sfo

rme

r Lo

sse

s (k

W)

Time (h)

(c) Scenario 3














the 95th



The mean and 95th










Page | 81

0976

0978

098

0982

0984

0986

0988

099

0992


Vo

ltag

e (

pu

)

Scenario1

Scenario2

Scenario3

0974

0976

0978

098

0982

0984

0986

0988

099


Vo

ltag

e (

pu

)

Scenario1

Scenario2

Scenario3

(a) Mean value

(b) 95th

value

Fig 4-8 11 kV 4th



start of the 4th










Page | 82

088

09

092

094

096

098

1

0 2 4 6 8 10 12 14 16 18 20 22

Bu

s V

olt

age

(p

u)

Time (h)

088

09

092

094

096

098

1

0 2 4 6 8 10 12 14 16 18 20 22

Bu

s V

olt

age

(p

u)

Time (h)

088

09

092

094

096

098

1

0 2 4 6 8 10 12 14 16 18 20 22

Bu

s V

olt

age

(p

u)

Time (h)



(a) Scenario 1

(b) Scenario 2

(c) Scenario 3


Lower Limit

Lower Limit

Lower Limit



Page | 83

088

09

092

094

096

098

1

0 2 4 6 8 10 12 14 16 18 20 22

Bu

s V

olt

age

(p

u)

Time (h)

088

09

092

094

096

098

1

0 2 4 6 8 10 12 14 16 18 20 22

Bu

s V

olt

age

(p

u)

Time (h)

088

09

092

094

096

098

1

0 2 4 6 8 10 12 14 16 18 20 22

Bu

s V

olt

age

(p

u)

Time (h)

(a) Scenario 1

(b) Scenario 2

(c) Scenario 3


Lower Limit

Lower Limit

Lower Limit



Page | 84

0976

0978

098

0982

0984

0986

0988

099

0992


0 25

5244 75

100
















values 0 25 5244 75 and 100





Fig 4-11 11 kV 4th




Page | 85






TCLF () 0 25 5244 75 100

Transformer loss

(kWh)

55922 50783 47865 49414 53982




TCLF () 0 25 5244 75 100

Average number of


0 2 4 2 0

452 Test Case 2












Page | 86

0

02

04

06

08

1

12

14

16

0 2 4 6 8 10 12 14 16 18 20 22

Act

ive

Po

we

r (k

W)

Time (h)

TW1 TW2 TW3 TW4 TW5

A1

A2

A3


B1

B2

B3

EndA EndB

TW9TW8TW7TW6








B4_3 B4_4 B4_5 B4_6 B4_7 B4_8




(a) Group 1



Page | 87

0

002

004

006

008

01

012

014

016

018

02

0 2 4 6 8 10 12 14 16 18 20 22

Act

ive

Po

we

r (k

W)

Time (h)

(b) Group 2















at TW1


at TW5





Page | 88







operation












Loss

(kWhday)

11319 10848 10848 11399 11162 11162 9739 9572 9528













Page | 89

096

0962

0964

0966

0968

097

0972

0974

0976

0978

098


Vo

ltag

e (

pu

)

Scenario1

Scenario2

Scenario3

0955

096

0965

097

0975

098

0985

099


Vo

ltag

e (

pu

)

Scenario1

Scenario4

Scenario7













Page | 90


that in Scenario 4




46 Summary



























Page | 91





Page | 92

CHAPTER 5




51 Introduction











planning





Reduction

Page | 93



constraints


















conclusions




119872119894119899119894119898119894119904119890 119891 = sum 119896119894119877119894(119875119894

2+1198761198942

1198801198942 )

119873119887119894=1 (5-1)





Reduction

Page | 94



Subject to



119875119894 le 119875119894119898119886119909 (5-4)

det(119860) = 1 119900119903 minus 1 (5-5)












53 Solution Method







Reduction

Page | 95

Home

1 2 NP1NP1-1

1 2 NP1-1 NP1

1 2 NP1NP1-1

1 2 NP2-1 NP2

1 2 NP2NP2-1

1 2 NP2-1 NP2

1 2 NP2NP2-1

1 2 NP2-1 NP2

Food

Stage

1

2

NT-1

NT

NT+1

NT+2

NT+NDG-1

NT+NDG

Part 1 Number of


Part 2 Number

of DGs









Reduction

Page | 96
















five steps



constant value






stage y is

119875119895119910(119873) =

120591119895119910

(119873)

sum 120591119895119910

(119873)ℎisin∆119910

(5-6)

where 120591119895119910




Reduction

Page | 97










choose a new trail







120591119895119910

(119873) = (1 minus 120588)120591119895119910

(119873 minus 1) + 120591119888 (5-7)




this edge





120591119895119910(119873) = 120591119895

119910(119873) + 120588119891119887119890119904119905

119891119887119890119904119905(119873) (5-8)



120591119895119910(119873) = 120591119898119886119909 119894119891 120591119895

119910(119873) ge 120591119898119886119909 (5-9)

120591119895119910(119873) = 120591119898119894119899 119894119891 120591119895

119910(119873) le 120591119898119894119899 (5-10)


Reduction

Page | 98

Start

Set Iteration n=1

Maximum iteration

reached

Output best


No

Yes









n=n+1


all location lists


and load data







optimal solution



Reduction

Page | 99













method





simultaneously




Appendix C1

541 33-bus System








Reduction

Page | 100

10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

18 19 20 21

22 23 24

25 26 27 28 29 30 31 32


L18

L19 L20 L21

L22

L23 L24

L25

L26 L27 L28 L29 L30 L31 L32

L33

L34

L35

L36

L37





Case Active feeder

loss (kW)

Minimum voltage

(pu)

(Bus No)


on Fig 53

DG location

Case I 20314 09116 (B17) L33 L34 L35 L36 L37 NA

Case II 13981 09361 (B31) L7 L9 L14 L32 L37 NA



Case I base case



Bus 17








Reduction

Page | 101

10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

18 19 20 21

22 23 24

25 26 27 28 29 30 31 32


L18

L19 L20 L21

L22

L23 L24

L25

L26 L27 L28 L29 L30 L31 L32

L33

L34

L35

L36

L37










from it


Method Feeder loss

(kW)

Loss reduction

()


voltage (pu)


BEM [109] 14054 3082 L7 L10 L14 L32 L37 09361

HSA [110] 13981 3118 L7 L9 L14 L32 L37 09361

FWA [16] 14026 3095 L7 L9 L14 L28 L32 09396

PSO [55] 13981 3118 L7 L9 L14 L32 L37 09361

IWO [111] 13981 3118 L7 L9 L14 L32 L37 09361








Reduction

Page | 102

10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

18 19 20 21

22 23 24

25 26 27 28 29 30 31 32


L18

L19 L20 L21

L22

L23 L24

L25

L26 L27 L28 L29 L30 L31 L32

L33

L34

L35

L36

L37

DG2

DG1

DG3









CGA and CSA



computation

times

(second)


ACO 13981 13981 13981 0 228 821 1448

CGA [112] 14002 14619 13981 12121 5463 2986 3926

CSA [113] 13986 14028 13981 01328 8363 3425 7258










Reduction

Page | 103

10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

18 19 20 21

22 23 24

25 26 27 28 29 30 31 32


L18

L19 L20 L21

L22

L23 L24

L25

L26 L27 L28 L29 L30 L31 L32

L33

L34

L35

L36

L37

DG2DG1

DG3























Reduction

Page | 104

086

088

09

092

094

096

098

1

102

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32

Vo

ltag

e (

pu

)

Bus No

Case I

Case II

Case III

Case IV

0

20

40

60

80

100

120

140

160

180

200

100 400 700 1000

Fee

de

r lo

ss (

kW)

DG Capacity (kVA)












allocation



Reduction

Page | 105

10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

27

28

29

30

31 32 33 34

35

36

37

38 39 40 41 42 43 44 45

46 47 48 49

50

51

52

53 54 55 56 57 58 59 60 61 62 63 64

65 66

67 68


L27

L28

L29

L30

L31 L32 L33 L34

L35

L36

L37

L38 L39 L40 L41 L42 L43 L44 L45

L46

L47 L48 L49

L50

L51

L52

L53 L54 L55 L56 L57 L58 L59 L60 L61 L62 L63 L64

L65

L66

L67

L68

L69

L70

L71

L72L73

542 69-bus System










Case Active feeder

loss (kW)

Minimum voltage

(pu)

(Bus No)


Case I 22562 09072 (B64) L69 L70 L71 L72 L73 NA

Case II 9885 09476 (B60) L14 L55 L61 L71 L72 NA



Case I base case




Reduction

Page | 106

10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

27

28

29

30

31 32 33 34

35

36

37

38 39 40 41 42 43 44 45

46 47 48 49

50

51

52

53 54 55 56 57 58 59 60 61 62 63 64

65 66

67 68


L27

L28

L29

L30

L31 L32 L33 L34

L35

L36

L37

L38 L39 L40 L41 L42 L43 L44 L45

L46

L47 L48 L49

L50

L51

L52

L53 L54 L55 L56 L57 L58 L59 L60 L61 L62 L63 L64

L65

L66

L67

L68

L69

L70

L71

L72L73











Method Feeder loss

(kW)

Loss reduction

()


voltage (pu)


FWA [16] 9886 5618 L14 L56 L61 L71 L72 09476

HSA [110] 10546 5326 L13 L18 L56 L61 L72 09475

GA [110] 10242 5461 L14 L53 L61 L71 L72 09462





Reduction

Page | 107

10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

27

28

29

30

31 32 33 34

35

36

37

38 39 40 41 42 43 44 45

46 47 48 49

50

51

52

53 54 55 56 57 58 59 60 61 62 63 64

65 66

67 68


L27

L28

L29

L30

L31 L32 L33 L34

L35

L36

L37

L38 L39 L40 L41 L42 L43 L44 L45

L46

L47 L48 L49

L50

L51

L52

L53 L54 L55 L56 L57 L58 L59 L60 L61 L62 L63 L64

L65

L66

L67

L68

L69

L70

L71

L72L73

DG3

DG1

DG2

10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

27

28

29

30

31 32 33 34

35

36

37

38 39 40 41 42 43 44 45

46 47 48 49

50

51

52

53 54 55 56 57 58 59 60 61 62 63 64

65 66

67 68


L27

L28

L29

L30

L31 L32 L33 L34

L35

L36

L37

L38 L39 L40 L41 L42 L43 L44 L45

L46

L47 L48 L49

L50

L51

L52

L53 L54 L55 L56 L57 L58 L59 L60 L61 L62 L63 L64

L65

L66

L67

L68

L69

L70

L71

L72L73

DG3DG1

DG2









III respectively



Reduction

Page | 108

0

50

100

150

200

250

100 400 700 1000

Fee

de

r lo

ss (

kW)

DG Capacity (kVA)














configuration












Reduction

Page | 109

086

088

09

092

094

096

098

1

102

0 5 10 15 20 25 30 35 40 45 50 55 60 65

Vo

ltag

e (

pu

)

Bus No

Case I

Case II

Case III

Case IV


55 Summary



















Reduction

Page | 110








Page | 111

CHAPTER 6




LOSS REDUCTION

61 Introduction





system [82]









Page | 112












investigated




















Page | 113













load curve [82]









P1

P2

1199051 1199052 Time (h)



Page | 114

1198911 = sum (119864119871119905 + 119879119871119905)1199051minus1119905=1 + sum (119864119871119905 + 119879119871119905) 1199051

24119905=1199052 isin 1 2 hellip 24 (6-1)


Min 119891 = 1198911 + 1198912 (6-3)







and are disregarded


















Page | 115

Home

0 1

0 1

0 1

0 1

1 2 NPNP-1

1 2 NP-1 NP

1 2 NPNP-1

1 2 NP-1 NP

Food

Stage

1

2

Ns-1

Ns

Ns+1

Ns+2

Ns+Nt-1

Ns+Nt

Part 1

Number of

substations

Ns

Part 2 Number

of existing tie-

switches Nt








Page | 116

Tie-switch

Transformer





as a binary vector















Page | 117

Start


Maximum iteration

reached

Output best


No

Yes



Iteration N=1








N=N+1




and load data





T=T+1

Tgt2

Yes

t=t+1

No




Page | 118


LP8 LP9 LP10



LP29 LP30 LP31

LP26 LP27 LP28


19

20

21

22

23

24

26

25 27

28

29 30

71

13 15

14 16

17

18

69

1 3

2

5

4

7

6 8

10

9

68

11 12

56

57

58 60

59 61 62

65

64 66 67

50 52

51

54

53 55

44

45

46

47

48

49

70

31

32

33

34

36

35

39

37 38 40

41

42 43

63

F3

F2

F1

F7

F6

F5

F4


Subbus1

Subbus2

Subbus3

T1

T3

T5

Main

feeder

Main

feeder

Main

feeder

T2

T4

T6













Page | 119




Number

of load

points


(kW)

Q

(kVAr)

Number of

customers

4 1-2 9-10 residential 8869 8426 220

6 3-5 13-15 residential 8137 7731 200

12 6-7 16-17 23-25 28

30-31 37-38


6 8 11 18 26 32-33 industrial 2445 23228 1

10 12 19-22 27 29 34-

36












Page | 120






Page | 121




shown in Table 6-2



Spring

(Mar Apr May)

Weekdays 66 92

Weekends 26

Summer

(Jun Jul Aug)

Weekdays 66 92

Weekends 26

Autumn

(Sep Oct Nov)

Weekdays 65 91

Weekends 26

Winter

(Dec Jan Feb)

Weekdays 64 90

Weekends 26

Year 365 Days





buses









Page | 122

651 Test Case 1



network loss











Spring

weekday

Spring

weekend

Summer

weekday

Summer

weekend

Autumn

weekday

Autumn

weekend

Winter

weekday

Winter

weekend

Before

Reconfiguration


L70L71

L68L69

L70L71

L68L69

L70L71

L68L69

L70L71

L68L69

L70L71

L68L69

L70L71

L68L69

L70L71

L68L69

L70L71

Number of operated

transformers




Loss

(kWh)

Cable 9233 3498 8050 3151 9660 3665 11009 4080

Transformer 4301 3410 4109 3350 4372 3437 4597 3507

Total 13534 6908 12159 6501 14032 7102 15606 7587

After

Reconfiguration


23-24

0-6 0-7

23

0-7 0-7

22-23

0-6

0-7

22-23

0-6


L69L71

L68L69

L70L71

L17L68

L70L71

L17L68

L70L71

L17L68

L70L71

L68L69

L70L71

L17L68

L70L71

L68L69

L70L71

Number of operated

transformers






L65L70

L68L69

L70L71

L41L48

L65L69

L68L69

L70L71

L17L41

L65L70

L68L69

L70L71

L17L41

L65L70

L68L69

L70L71

Number of operated

transformers




Loss

(kWh)

Cable 9043 3516 7851 3169 9519 3685 10845 4103

Transformer 3955 2616 3759 2517 4036 2656 4264 2755

Total 12998 6132 11610 5686 13479 6341 15109 6858



Page | 123

0

05

1

15

2

25

3

35

4

45

05 1 15 2 25 3










652 Test Case 2











To

tal

loss

(G

Wh

)

DG Capacity (MW)



Page | 124

653 Test Case 3









120578times119875119862 (6-4)









the day



capability (mile)

Market share ()

Micro car 12 50 20









Page | 125

4

42

44

46

48

5

30 60 90



119878119874119862 = 0 119898 gt 119872119863119862

119872119863119862minus119898

119872119863119862 119898 le 119872119863119862 (6-5)


















To

tal

loss

(G

Wh

)




Page | 126

4

42

44

46

48

5

30 60 90











66 Summary













To

tal

loss

(G

Wh

)




Page | 127
















Page | 128

CHAPTER 7




71 Introduction
















Improvement

Page | 129






























weighted function


Improvement

Page | 130

119872119894119899 119869 = micro1 ∙ 119864119862119874119878119879 + micro2 ∙ 119878119862 (7-1)





Parameters






119872119886119909 119870 = 1205961 ∙ 120572119878119860 + 1205962 ∙ 120572119878119862 (7-2)

















Improvement

Page | 131

0

1

0

1

120572119878119860 =

1 119878119860119868119863119868 le 119878119860119868119863119868119898119894119899119878119860119868119863119868119900119903119894minus119878119860119868119863119868

119878119860119868119863119868119900119903119894minus119878119860119868119863119868119898119894119899119878119860119868119863119868119898119894119899 lt 119878119860119868119863119868 lt 119878119860119868119863119868119900119903119894

0 119878119860119868119863119868 ge 119878119860119868119863119868119900119903119894

(7-3)











120572119878119862 =

1 119878119862 le 119878119862119900119903119894119878119862119898119886119909minus119878119862

119878119862119898119886119909minus119878119862119900119903119894119878119862119900119903119894 lt 119878119862 lt 119878119862119898119886119909

0 119878119862 ge 119878119862119898119886119909

(7-4)





Parameters



120572119878119860

119878119860119868119863119868119898119894119899 119878119860119868119863119868119900119903119894 119878119860119868119863119868

120572119878119862

119878119862119900119903119894 119878119862119898119886119909 119878119862


Improvement

Page | 132

0

1





120572119864119862 =

1 119864119862119874119878119879 le 119864119862119874119878119879119898119894119899119864119862119874119878119879119900119903119894minus119864119862119874119878119879

119864119862119874119878119879119900119903119894minus119864119862119874119878119879119898119894119899119864119862119874119878119879119898119894119899 lt 119864119862119874119878119879 lt 119864119862119874119878119879119900119903119894

0 119864119862119874119878119879 ge 119864119862119874119878119879119900119903119894

(7-5)








Max 119871 = min (120572119878119860 120572119878119862 120572119864119862) (7-6)










120572119864119862

119864119862119874119878119879119898119894119899 119864119862119874119878119879119900119903119894 119864119862119874119878119879


Improvement

Page | 133



1 ( 1)

1 1 1 1 1 1


t t

b b k R k s

t b k j k j


(7-7)








rate




119878119860119868119863119868 = sum sum 120582119887∙119871119887[sum 119889119877

119873119862119877(119887)119899=1 +sum 119889119878

119873119862119878(119887)119899=1 ]

119873119887119887=1

119873119862119905119900119905119886119897119879

119905=1 (7-8)








119878119862 = 119862119868119878 ∙ 119873119899119890119908 + 119862119877119878 ∙ 119873119903119890119897 + sum 119872119862119879119905=1 ∙ (119873119899119890119908 + 119873119890119909119894119904) ∙ (1 + 119863119877)minus(119905minus1) (7-9)





Improvement

Page | 134

Home

0

1

0

1

0

1

0

1

Food





Problem
















Improvement

Page | 135









119887119890119899119890119891119894119905 = sum119864119862119874119878119879119887119886119904119890

119905 minus119864119862119874119878119879119900119901119905119905

(1+119863119877)119905119879119905=1 (7-10)

where 119864119862119874119878119879119887119886119904119890119905 and 119864119862119874119878119879119900119901119905





119861119862119877 =119887119890119899119890119891119894119905

119878119862 (7-11)






Improvement

Page | 136


LP8 LP9 LP10



LP29 LP30 LP31

LP26 LP27 LP28


9 10 11 12 13 33

6 7 8 31

1 2 3 4 5 30

25 26 27 29

22 23 24

19 20 21

32

14 15 16 17 18

28

F3

F2

F1

F7

F6

F5

F4


Subbus1

Subbus2

Subbus3

T1

T3

T5

Main

feeder

Main

feeder

Main

feeder

T2

T4

T6











Improvement

Page | 137







Number

of load

points


(kW)

Number of

customers

15 1-4 11-13 18-21 32-35 residential 545 220

7 5 14 15 22 23 36 37 residential 500 200

7 8 10 26-30 industrial 1000 1


7 6 7 16 17 24 25 38 commercial 415 10


















Improvement

Page | 138




Residential 006 11 16 26 316 5

Industrial 288 806 95 124 1387 276

Commercial 205 96 125 185 2151 6306




method






751 Test Case 1











Improvement

Page | 139


LP8 LP9 LP10



LP29 LP30 LP31

LP26 LP27 LP28


9 10 11 12 13 33

6 7 8 31

1 2 3 4 5 30

25 26 27 29

22 23 24

19 20 21

32

14 15 16 17 18

28

F3

F2

F1

F7

F6

F5

F4


Subbus1

Subbus2

Subbus3

T1

T3

T5

Main

feeder

Main

feeder

Main

feeder

T2

T4

T6










Improvement

Page | 140













Switch

No


Load (kW)


Type


2 2 7D 3500 LP9 1500 (industrial)



5 6 23D 3500 LP30 1000 (industrial)

6 7 28D 3595 LP36 500 (commercial)












Improvement

Page | 141


LP8 LP9 LP10



LP29 LP30 LP31

LP26 LP27 LP28


9 10 11 12 13 33

6 7 8 31

1 2 3 4 5 30

25 26 27 29

22 23 24

19 20 21

32

14 15 16 17 18

28

F3

F2

F1

F7

F6

F5

F4


Subbus1

Subbus2

Subbus3

T1

T3

T5

Main

feeder

Main

feeder

Main

feeder

T2

T4

T6



ECOST

($)

Number of

installed

switches

Capital and

installation cost

($)

Maintenance

and operation

cost ($)

Total system

cost ($)

Before switches

installation

472260 0 0 4830 477090

After switches

installation

221610 11 51700 13670 286980


Improvement

Page | 142


LP8 LP9 LP10



LP29 LP30 LP31

LP26 LP27 LP28


9 10 11 12 13 33

6 7 8 31

1 2 3 4 5 30

25 26 27 29

22 23 24

19 20 21

32

14 15 16 17 18

28

F3

F2

F1

F7

F6

F5

F4


Subbus1

Subbus2

Subbus3

T1

T3

T5

Main

feeder

Main

feeder

Main

feeder

T2

T4

T6


A Base case









Improvement

Page | 143

0

1

2

3

4

5

6

7

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

BC

R

Years








ECOST

($)

Number of

relocated

switches

Relocation

cost ($)

Number of

installed

switches

Capital and

installation

cost ($)

Maintenance

and operation

cost ($)

Total

system

cost ($)

Before switch

placement

472260 0 0 0 0 4830 477090

After switch

placement

221120 5 2500 8 37600 11260 272480











Improvement

Page | 144

0

20

40

60

80

100

120

140

160

05 1 15 2 25 3 35 4 45 5 55 6 65 7 75 8

Co

st (

th

ou

san

d $

)

CDF multiplier

ECOST

Switch costs

Total costs






















Improvement

Page | 145

0

5

10

15

20

25

30

35

40

05 1 15 2 25 3 35 4 45 5 55 6 65 7 75 8

Nu

mb

er

of

swit

che

s

CDF multiplier






















Improvement

Page | 146











01 273120 274810 272480 223

02 273400 275960 272480 175

03 273480 274810 272480 132

04 273100 274810 272480 110

05 273550 274810 272480 94

06 273440 274810 272480 81







400




100 273865 276120 272480 91

200 273100 274810 272480 110

300 273030 274370 272480 135

400 272820 274230 272480 168

500 273170 274230 272480 245


Improvement

Page | 147




752 Test Case 2














Function

SAIDI

(hrscustomer)

Switch costs ($)

Case 21 01 09 04909 09970 09464 1157 68275

Case 22 05 05 08456 09061 08758 556 67378

Case 23 09 01 09384 07761 09221 39936 153950



753 Test Case 3








Improvement

Page | 148


Objective

Function

120572119864119862 120572119878119860 120572119878119862 ECOST

($)

SAIDI

(hrscustomer)

Switch costs

($)

Before

switch

placement

0 0 0 1 472260 1989 4830

After switch

placement

08327 08327 08392 08384 188950 56723 112410

76 Summary

























Improvement

Page | 149




Page | 150

CHAPTER 8




IMPROVEMENT

81 Introduction














Improvement

Page | 151























set is obtained






conclusions


Improvement

Page | 152







119865(119866) = [1198911(119866)1198912(119866)1198913(119866)]119879 (8-3)


configuration G



1198911(119866) = sum 119896119894119877119894(119875119894

2+1198761198942

1198801198942 )

119873119887119894=1 (8-4)








1 ( 1)

1 1 1 1 1 1


t t

b b k R k s

t b k j k j


(8-5)





Improvement

Page | 153









119878119860119868119863119868 = sum sum 120582119887∙119871119887[sum 119889119877

119873119862119877(119887)119899=1 +sum 119889119878

119873119862119878(119887)119899=1 ]

119873119887119887=1

119873119862119905119900119905119886119897119879

119905=1 (8-6)




8214 Constraints








119891119901119904(119894) = sum 120596119895max(119900119891119895)minus119900119891119895(119875119878119894)

max(119900119891119895)minusmin (119900119891119895)

119873119900119887119895

119895=1 (8-7)








Improvement

Page | 154





tie-switches












number




weighted sum as

120591119894119909 = 1199011 ∙ 1205911198941199091 + |1199011 minus 1199012| ∙ 120591119894119909

2 + (1 minus 1199012) ∙ 1205911198941199093 (8-8)

where 1205911198941199091 120591119894119909





new matrix




Improvement

Page | 155



119875119894119909(119873) =120591119894119909(119873)

sum 120591119894119909(119873)ℎisin∆119909

(8-9)

















certain number [88]






follow

120591119894119909119899 (119873) = (1 minus 120588)120591119894119909

119899 (119873 minus 1) + 120591119888 (8-10)




Improvement

Page | 156



this edge





120591119894119909119899 (119873) = 120591119894119909

119899 (119873) + 120588119891119887119890119904119905

119899 (119873)

119891119887119890119904119905119899 (119873minus1)

(8-11)

where 119891119887119890119904119905119899 (119873 minus 1) and 119891119887119890119904119905





120591119894119909119899 (119873) = 120591119898119886119909 119894119891 120591119894119909

119899 (119873) ge 120591119898119886119909 (8-12)

120591119894119909119899 (119873) = 120591119898119894119899 119894119891 120591119894119909

119899 (119873) le 120591119898119894119899 (8-13)












Improvement

Page | 157

Start

Iteration N=1

Maximum ant number

reaches

Output Pareto

optimal set and end

No

Yes



Ant number m=1



matrices into one




for this ant

N=N+1


and load data


dominated solutions

Maximum iteration

reaches

Yes

m=m+1

No





Improvement

Page | 158

Start

Cloning

Maximum iteration

reached

Output Pareto

optimal set and end

No

Yes




dominated solutions



n=n+1











in Fig 8-2



Improvement

Page | 159
















119901119894119899 =

120591119894119899

sum 120591119895119899

119895 (8-14)











120591119894119899(119873) = 119898119886119909 (1 minus 120588)120591119894

119899(119873 minus 1) 120591119898119894119899 (8-15)




Improvement

Page | 160







updated as

120591119894119899(119873) = 119898119894119899120591119894

119899(119873) + 120588min (119891119899(119866))

119891119899(119866) 120591119898119886119909 (8-16)






next iteration





Improvement

Page | 161


LP8 LP9 LP10



LP29 LP30 LP31

LP26 LP27 LP28


19

20

21

22

23

24

26

25 27

28

29 30

71

13 15

14 16

17

18

69

1 3

2

5

4

7

6 8

10

9

68

11 12

56

57

58 60

59 61 62

65

64 66 67

50 52

51

54

53 55

44

45

46

47

48

49

70

31

32

33

34

36

35

39

37 38 40

41

42 43

63

F3

F2

F1

F7

F6

F5

F4


Subbus1

Subbus2

Subbus3

T1

T3

T5

Main

feeder

Main

feeder

Main

feeder

T2

T4

T6








downstream loads







Improvement

Page | 162

300

350

400

450

4

45

5

55

6

x 104

08

09

1

11

12

13

14

15


SA

IDI

(hrs

custo

mer

yr)


Number

of load

points


(kW)

Q

(kVAr)

Number of

customers

4 1-2 9-10 residential 545 51775 220

6 3-5 13-15 residential 500 475 200

12 6-7 16-17 23-25 28 30-

31 37-38


6 8 11 18 26 32-33 industrial 1500 1425 1

10 12 19-22 27 29 34-36 industrial 1000 950 1













Improvement

Page | 163




Mean

38074 48139 09975

Standard deviation

3431 5291 01165













(hrscustomeryr)


Minimum Loss

32142 46404 13090 68 69 70 71

Minimum ECOST

35409 41145 10586 10 17 41 70

Minimum SAIDI

43523 57891 08253 7 26 54 69






Improvement

Page | 164














compromise

solution

Feeder

loss

(kW)

ECOST

($yr)

SAIDI

(hrscustomeryr) 1205961 1205962 1205963

1 10 10 10 10 41 69 70 34033 41553 10996

2 10 1 1 68 69 70 71 32142 46404 13090

3 1 10 1 10 17 41 70 35409 41145 10586

4 1 1 10 7 26 54 69 43523 57891 08253

5 10 10 1 10 41 69 70 34033 41553 10996

6 10 1 10 10 54 69 71 34759 46644 10217

7 1 10 10 7 17 41 70 40368 43329 09570

86 Summary










Improvement

Page | 165














Page | 166

CHAPTER 9





BALANCING

91 Introduction













Page | 167















groups














Page | 168

0

1












respectively








9-1




120572119871

119871119874119878119878119898119894119899 119871119874119878119878119900119903119894 119871119874119878119878



Page | 169

0

1

120572119871 =

1 119871119874119878119878 le 119871119874119878119878119898119894119899119871119874119878119878119900119903119894minus119871119874119878119878

119871119874119878119878119900119903119894minus119871119874119878119878119898119894119899119871119874119878119878119898119894119899 lt 119871119874119878119878 lt 119871119874119878119878119900119903119894

0 119871119874119878119878 ge 119871119874119878119878119900119903119894

(9-2)














120572119881 =

1 119881119863 le 119881119863119898119894119899119881119863119900119903119894minus119881119863

119881119863119900119903119894minus119881119863119898119894119899119881119863119898119894119899 lt 119881119863 lt 119881119863119900119903119894

0 119881119863 ge 119881119863119900119903119894

(9-3)



120572119881

119881119863119898119894119899 119881119863119900119903119894 119881119863



Page | 170

0

1



119871119861119868 = 119881119886119903[1198681

1198681119898119886119909

1198682

1198682119898119886119909 hellip

119868119894

119868119894119898119886119909 hellip

119868119899

119868119899119898119886119909] (9-4)




120572119861 =

1 119871119861119868 le 119871119861119868119898119894119899119871119861119868119900119903119894minus119871119861119868

119871119861119868119900119903119894minus119871119861119868119898119894119899119871119861119868119898119894119899 lt 119871119861119868 lt 119871119861119868119900119903119894

0 119871119861119868 ge 119871119861119868119900119903119894

(9-5)





Optimality


of the vector

119865(119866) = [1198911(119866)1198912(119866)1198913(119866)]119879 (9-6)




120572119861

119871119861119868119898119894119899 119871119861119868119900119903119894 119871119861119868



Page | 171



Domain



























Page | 172








simultaneously





B4 in detail

941 33-bus System







Case I base case






Page | 173

10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

18 19 20 21

22 23 24

25 26 27 28 29 30 31 32


L18

L19 L20 L21

L22

L23 L24

L25

L26 L27 L28 L29 L30 L31 L32

L33

L34

L35

L36

L37









Fig 9-4



(kW)

Maximum node

voltage deviation

(pu)

Feeder Load

balancing index

Tie-switches

location

08734 14310 00625 00270 6 9 14 32 37







Page | 174

120140

160180

200220

006

008

01

012

014

016

0022

0024

0026

0028

003

0032

0034

0036


Feeder

load b

ala

ncin

g index




deviation (pu)


Mean

15499 00815 00256

Standard deviation

1549 00194 00023











Page | 175

10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

18 19 20 21

22 23 24

25 26 27 28 29 30 31 32


L18

L19 L20 L21

L22

L23 L24

L25

L26 L27 L28 L29 L30 L31 L32

L33

L34

L35

L36

L37

DG2

DG1

DG3







index


Minimum Loss

13981 00639 00280 7 9 14 32 37


14026 00604 00310 7 9 14 28 32


20248 01309 00223 7 30 34 35 37














Page | 176

110120

130140

150160

170

004

006

008

01

0120018

002

0022

0024

0026

0028

003


Feeder

load b

ala

ncin

g index



(kW)

Maximum node

voltage deviation

(pu)

Feeder Load

balancing index

Tie-switches

location

08590 12405 00594 00230 6 8 14 32 37







deviation (pu)


Mean

12850 00711 00231

Standard deviation

1003 00166 00029



Page | 177

















index


Minimum Loss

11753 00643 00241 7 9 14 28 31


12592 00567 00265 6 8 14 28 32


16419 01139 00189 7 21 30 35 37









locations



Page | 178

10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

18 19 20 21

22 23 24

25 26 27 28 29 30 31 32


L18

L19 L20 L21

L22

L23 L24

L25

L26 L27 L28 L29 L30 L31 L32

L33

L34

L35

L36

L37

DG1

DG3

DG2

100110

120130

140150

160

004

006

008

01

012

0016

0018

002

0022

0024

0026

0028


Feeder

load b

ala

ncin

g index


in Case IV

Objective

function

Feeder loss

(kW)

Maximum node

voltage

deviation (pu)

Feeder Load

balancing

index

Tie-switches

location

DGs location

08961 10878 00499 00232 7 9 14 36 37 B32 B32 B32









Page | 179




deviation (pu)


Mean

13295 00873 00194

Standard deviation

1354 00179 00019
















voltage deviation

(pu)

Feeder Load

balancing index

Tie-switches

location

DGs location

Minimum Loss

10844 00538 00228 7 9 14 32 37 B30 B31 B31


11020 00490 00259 7 9 14 28 36 B31 B31 B32


15443 01090 00178 7 30 34 35 37 B8 B9 B12



Page | 180

10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

27

28

29

30

31 32 33 34

35

36

37

38 39 40 41 42 43 44 45

46 47 48 49

50

51

52

53 54 55 56 57 58 59 60 61 62 63 64

65 66

67 68


L27

L28

L29

L30

L31 L32 L33 L34

L35

L36

L37

L38 L39 L40 L41 L42 L43 L44 L45

L46

L47 L48 L49

L50

L51

L52

L53 L54 L55 L56 L57 L58 L59 L60 L61 L62 L63 L64

L65

L66

L67

L68

L69

L70

L71

L72L73

942 69-bus System







respectively

Case I base case















Page | 181

80

100

120

140

160

005

006

007

0080016

0018

002

0022

0024

0026

0028


Feeder

load b

ala

ncin

g index



(kW)

Maximum node

voltage deviation

(pu)

Feeder Load

balancing index

Tie-switches

location

09676 9885 00524 00195 14 55 61 71 72








deviation (pu)


Mean

12535 00605 00192

Standard deviation

2458 00085 00028



Page | 182











initial case





index


Minimum Loss

9885 00524 00195 14 55 61 71 72


10535 00523 00242 9 14 55 61 71


15051 00701 00161 14 61 69 71 72













Page | 183

10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

27

28

29

30

31 32 33 34

35

36

37

38 39 40 41 42 43 44 45

46 47 48 49

50

51

52

53 54 55 56 57 58 59 60 61 62 63 64

65 66

67 68


L27

L28

L29

L30

L31 L32 L33 L34

L35

L36

L37

L38 L39 L40 L41 L42 L43 L44 L45

L46

L47 L48 L49

L50

L51

L52

L53 L54 L55 L56 L57 L58 L59 L60 L61 L62 L63 L64

L65

L66

L67

L68

L69

L70

L71

L72L73

DG3

DG1

DG2

8090

100110

120130

140

005

006

007

008

0014

0016

0018

002

0022

0024


Feeder

load b

ala

ncin

g index



(kW)

Maximum node

voltage deviation

(pu)

Feeder Load

balancing index

Tie-switches

location

08829 8758 00523 00174 14 55 61 71 72







Page | 184





deviation (pu)


Mean

10707 00576 00183

Standard deviation

2042 00071 00029

















index


Minimum Loss

8758 00523 00174 13 55 61 71 72


9729 00522 00226 7 12 55 61 71


13686 00681 00147 11 61 69 71 72



Page | 185

10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

27

28

29

30

31 32 33 34

35

36

37

38 39 40 41 42 43 44 45

46 47 48 49

50

51

52

53 54 55 56 57 58 59 60 61 62 63 64

65 66

67 68


L27

L28

L29

L30

L31 L32 L33 L34

L35

L36

L37

L38 L39 L40 L41 L42 L43 L44 L45

L46

L47 L48 L49

L50

L51

L52

L53 L54 L55 L56 L57 L58 L59 L60 L61 L62 L63 L64

L65

L66

L67

L68

L69

L70

L71

L72L73

DG3DG1

DG2









ACO algorithm


system in Case IV

Objective

function

Feeder loss

(kW)

Maximum

node voltage

deviation (pu)

Feeder Load

balancing

index

Tie-switches

location

DGs location

08882 7397 00429 00158 14 55 61 71 72 B60 B60 B60





9-17



Page | 186

70

80

90

100

110

120

004

0045

005

0055

006

0012

0013

0014

0015

0016

0017

0018

0019


Feeder

load b

ala

ncin

g index




deviation (pu)


Mean

9872 00520 00147

Standard deviation

1491 00055 00013













Page | 187






voltage deviation

(pu)

Feeder Load

balancing index

Tie-switches

location

DGs location

Minimum Loss

7397 00429 00158 14 55 61 71 72 B60 B60 B60


8032 00428 00183 11 55 61 71 72 B60 B60 B60


10962 00577 00125 14 63 69 71 72 B62 B62 B62

95 Summary


















Page | 188





Page | 189

CHAPTER 10


101 Conclusion








results





cost







Page | 190


































Page | 191




























demand times







Page | 192














SAIDI




















Page | 193



102 Future Work












supply each feeder














load on feeders


Page | 194





























Page | 195

References




2001



2015




2 pp 15ndash22 2015








2010

















References

Page | 196

2012






vol 63 pp 461ndash472 2014






652ndash660 2009



pp 1878ndash1887 2010



6 no 2 pp 182ndash197 2002














York 1986



pp 2157ndash2165 2015


1994



References

Page | 197


2016










62ndash66




Wiley 1990




170ndash180 2013






2006 pp 4ndash6















pp 2290ndash2293

References

Page | 198









pp 1217ndash1223 1988










42 2002























References

Page | 199



1530 2009




937ndash940 2008












pp 4021ndash4028 2011



2006








129ndash142 2015









no 1 pp 268ndash276 2009



References

Page | 200




2002





pp 1ndash6


















58 pp 537ndash547 2016





1048ndash1062 2016




2016




686ndash690 2003

References

Page | 201









2473ndash2480 2007







2010







22 no 3 pp 1101ndash1111 2007




388ndash397 2015







of Manchester 2015




1 pp 1ndash13 1996




References

Page | 202



pp 861ndash875 2012






2004












251 2002









Cable 2012






1677ndash1685 2015



2 pp 1401ndash1407 1989



References

Page | 203

no 2 pp 1492ndash1498 1989




pp 1ndash9 2012




932ndash942 2015


Sons 2004














vol 54 pp 255ndash267 2014



119ndash126 2011

Page | 204







Sectional

Area

(CSA)

Positive sequence

Z

Zero-phase

sequence

Z

Approximate

Capacitance

C



A Nexans

635011000

Volt Triplex

Cable

185 0415 0112 0988 0236 036

B 95 0220 0012 0530 0102 028


Page | 205

A2 33-bus system


Branch

number

Sending end

node

Receiving end

node

R

(Ω)

X

(Ω)

P at receiving

end (kW)

Q at receiving

end (kVAr)

1 0 1 00922 0047 100 60

2 1 2 04930 02511 90 40

3 2 3 03660 01864 120 80

4 3 4 03811 01941 60 30

5 4 5 08190 07070 60 20

6 5 6 01872 06188 200 100

7 6 7 07114 02351 200 100

8 7 8 10300 07400 60 20

9 8 9 10440 07400 60 20

10 9 10 01966 00650 45 30

11 10 11 03744 01238 60 35

12 11 12 14680 11550 60 35

13 12 13 05416 07129 120 80

14 13 14 05910 05260 60 10

15 14 15 07463 05450 60 20

16 15 16 12890 17210 60 20

17 16 17 03720 05740 90 40

18 17 18 01640 01565 90 40

19 18 19 15042 13554 90 40

20 19 20 04095 04784 90 40

21 20 21 07089 09373 90 40

22 21 22 04512 03083 90 50

23 22 23 08980 07091 420 200

24 23 24 08960 07011 420 200

25 24 25 02030 01034 60 25

26 25 26 02842 01447 60 25

27 26 27 10590 09337 60 20

28 27 28 08042 07006 120 70

29 28 29 05075 02585 200 600

30 29 30 09744 09630 150 70

31 30 31 03105 03619 210 100

32 31 32 03410 05362 60 40

33 7 20 2 2 -- --

34 11 21 2 2 -- --

35 8 14 2 2 -- --

36 17 32 05 05 -- --

37 24 28 05 05 -- --


Page | 206

A3 69-bus system


Branch

number

Sending end

node

Receiving end

node

R

(Ω)

X

(Ω)

P at receiving

end (kW)

Q at receiving

end (kVAr)

1 0 1 00005 00012 0 0

2 1 2 00005 00012 0 0

3 2 3 00015 00036 0 0

4 3 4 00251 00294 0 0

5 4 5 0366 01864 26 22

6 5 6 0381 01941 404 30

7 6 7 00922 0047 75 54

8 7 8 00493 00251 30 22

9 8 9 0819 02707 28 19

10 9 10 01872 00619 145 104

11 10 11 07114 02351 145 104

12 11 12 103 034 8 5

13 12 13 1044 0345 8 55

14 13 14 1058 03496 0 0

15 14 15 01966 0065 455 30

16 15 16 03744 01238 60 35

17 16 17 00047 00016 60 35

18 17 18 03276 01083 0 0

19 18 19 02106 0069 1 06

20 19 20 03416 01129 114 81

21 20 21 0014 00046 5 35

22 21 22 01591 00526 0 0

23 22 23 03463 01145 28 20

24 23 24 07488 02475 0 0

25 24 25 03089 01021 14 10

26 25 26 01732 00572 14 10

27 26 27 00044 00108 26 186

28 27 28 0064 01565 26 186

29 28 29 03978 01315 0 0

30 29 30 00702 00232 0 0

31 30 31 0351 0116 0 0

32 31 32 0839 02816 14 10

33 32 33 1708 05646 195 14

34 33 34 1474 04873 6 4

35 34 35 00044 00108 26 1855

36 35 36 0064 01565 26 1855

37 36 37 01053 0123 0 0

38 37 38 00304 00355 24 17

39 38 39 00018 00021 24 17

40 39 40 07283 08509 12 1

41 40 41 031 03623 0 0


Page | 207

42 41 42 0041 00478 6 43

43 42 43 00092 00116 0 0

44 43 44 01089 01373 3922 263

45 44 45 00009 00012 3922 263

46 45 46 00034 00084 0 0

47 46 47 00851 02083 79 564

48 47 48 02898 07091 3847 2745

49 48 49 00822 02011 3847 2745

50 49 50 00928 00473 405 283

51 50 51 03319 01114 36 27

52 51 52 0174 00886 435 35

53 52 53 0203 01034 264 19

54 53 54 02842 01447 24 172

55 54 55 02813 01433 0 0

56 55 56 159 05337 0 0

57 56 57 07837 0263 0 0

58 57 58 03042 01006 100 72

59 58 59 03861 01172 0 0

60 59 60 05075 02585 1244 888

61 60 61 00974 00496 32 23

62 61 62 0145 00738 0 0

63 62 63 07105 03619 227 162

64 63 64 1041 05302 59 42

65 64 65 02012 00611 18 13

66 65 66 00047 00014 18 13

67 66 67 07394 02444 28 20

68 67 68 00047 00016 28 20

69 49 58 2 1 -- --

70 26 64 1 05 -- --

71 12 20 05 05 -- --

72 10 42 05 05 -- --

73 14 45 1 05 -- --



Feeder

Type

Length

(km)


1 060 2 6 10 14 17 21 25 28 30 34 38 41 43 46 49 51 55 58 61 64 67

68 69 70 71

2 075 1 4 7 9 12 16 19 22 24 27 29 32 3537 40 42 45 48 50 53 56 60

63 65

3 080 3 5 8 11 13 15 18 20 23 26 31 33 36 3944 47 52 54 57 59 62 66


Page | 208



Lines 004 0 0 0 5 0

Buses 0001 0 1 001 2 8

Switches 0004 0002 1 006 4 72








Page | 209










0000 TW5 0400 TW5 0800 TW1 1200 TW5 1600 TW1 2000 TW5

0010 TW5 0410 TW5 0810 TW1 1210 TW5 1610 TW1 2010 TW5

0020 TW5 0420 TW5 0820 TW1 1220 TW5 1620 TW1 2020 TW5

0030 TW5 0430 TW5 0830 TW1 1230 TW5 1630 TW1 2030 TW5

0040 TW5 0440 TW5 0840 TW1 1240 TW5 1640 TW5 2040 TW5

0050 TW5 0450 TW5 0850 TW1 1250 TW5 1650 TW5 2050 TW5

0100 TW5 0500 TW5 0900 TW1 1300 TW5 1700 TW5 2100 TW5

0110 TW5 0510 TW5 0910 TW1 1310 TW5 1710 TW5 2110 TW5

0120 TW5 0520 TW5 0920 TW1 1320 TW5 1720 TW5 2120 TW5

0130 TW5 0530 TW5 0930 TW1 1330 TW5 1730 TW5 2130 TW5

0140 TW5 0540 TW5 0940 TW1 1340 TW5 1740 TW5 2140 TW5

0150 TW5 0550 TW5 0950 TW1 1350 TW5 1750 TW5 2150 TW5

0200 TW5 0600 TW5 1000 TW1 1400 TW5 1800 TW5 2200 TW5

0210 TW5 0610 TW5 1010 TW5 1410 TW5 1810 TW5 2210 TW5

0220 TW5 0620 TW5 1020 TW5 1420 TW5 1820 TW5 2220 TW5

0230 TW5 0630 TW5 1030 TW5 1430 TW5 1830 TW5 2230 TW5

0240 TW5 0640 TW5 1040 TW5 1440 TW5 1840 TW5 2240 TW5

0250 TW5 0650 TW5 1050 TW5 1450 TW5 1850 TW5 2250 TW5

0300 TW5 0700 TW5 1100 TW5 1500 TW5 1900 TW5 2300 TW5

0310 TW5 0710 TW5 1110 TW5 1510 TW5 1910 TW5 2310 TW5

0320 TW5 0720 TW5 1120 TW5 1520 TW5 1920 TW5 2320 TW5

0330 TW5 0730 TW1 1130 TW5 1530 TW5 1930 TW5 2330 TW5

0340 TW5 0740 TW1 1140 TW5 1540 TW5 1940 TW5 2340 TW5

0350 TW5 0750 TW1 1150 TW5 1550 TW5 1950 TW5 2350 TW5


Page | 210



corresponding 95th


B-2 and Table B-3


Node

No

Scenarios

S1 S2 S3 S4 S5 S6 S7 S8 S9

A4_1 09675 09787 09787 09766 09859 09859 09748 09825 09815

A4_2 09676 09784 09784 09766 09856 09856 09748 09822 09813

A4_3 09677 09782 09782 09767 09854 09854 09749 09819 09811

A4_4 09678 09780 09780 09768 09851 09851 09750 09817 09810

A4_5 09681 09777 09777 09771 09849 09849 09753 09814 09808

A4_6 09685 09775 09775 09775 09846 09846 09757 09812 09807

A4_7 09689 09773 09773 09779 09845 09845 09762 09811 09807

A4_8 09694 09772 09772 09784 09844 09844 09767 09810 09807

B4_8 09700 09772 09772 09790 09844 09844 09773 09810 09808

B4_7 09707 09773 09773 09797 09845 09845 09779 09811 09810

B4_6 09714 09775 09775 09804 09846 09846 09787 09812 09813

B4_5 09722 09777 09777 09813 09849 09849 09795 09814 09816

B4_4 09731 09780 09780 09821 09851 09851 09804 09817 09820

B4_3 09737 09782 09782 09827 09854 09854 09809 09819 09823

B4_2 09743 09784 09784 09833 09856 09856 09815 09822 09826

B4_1 09749 09787 09787 09839 09859 09859 09821 09825 09830

Table B-3 95th


Node

No

Scenarios

S1 S2 S3 S4 S5 S6 S7 S8 S9

A4_1 09352 09573 09573 09537 09721 09721 09537 09721 09715

A4_2 09353 09567 09567 09537 09715 09715 09537 09715 09709

A4_3 09355 09562 09562 09539 09711 09711 09539 09711 09704

A4_4 09357 09558 09558 09541 09707 09707 09541 09707 09702

A4_5 09363 09553 09553 09547 09701 09701 09547 09701 09679

A4_6 09370 09548 09548 09555 09697 09697 09555 09697 09694

A4_7 09379 09545 09545 09563 09694 09694 09563 09794 09691

A4_8 09389 09544 09544 09573 09692 09692 09573 09792 09692

B4_8 09400 09544 09544 09585 09692 09692 09585 09792 09692

B4_7 09413 09545 09545 09598 09694 09694 09598 09794 09694

B4_6 09427 09548 09548 09613 09697 09697 09613 09697 09697

B4_5 09443 09553 09553 09628 09701 09701 09628 09701 09701

B4_4 09460 09558 09558 09646 09707 09707 09646 09707 09707


Page | 211

B4_3 09471 09562 09562 09656 09711 09711 09656 09711 09711

B4_2 09482 09567 09567 09668 09715 09715 09668 09715 09715

B4_1 09494 09573 09573 09680 09721 09721 09680 09721 09721







1 1227 1189 1010 1003

2 5192 2686 2051 2060

3 1995 756 112 490

4 1874 667 074 415

5 3833 1321 122 807

6 192 006 006 006

7 484 0 0 0

8 418 124 211 124

9 357 0 0 0

10 055 001 001 001

11 088 003 003 003

12 267 045 045 045

13 073 008 008 008

14 036 0 0 0

15 028 045 092 045

16 025 048 115 048

17 003 007 022 007

18 016 226 232 226

19 083 1809 1859 1808

20 01 424 436 423

21 004 118 071 118

22 319 316 914 315

23 516 512 1618 510

24 129 128 869 128

25 26 224 005 124

26 334 285 003 155

27 1133 962 003 510

28 786 664 0 345

29 391 326 199 159

30 160 110 018 003


Page | 212

31 021 012 0 000

32 001 0 013 0

33 0 563 809 563

34 0 215 215 215

35 0 174 320 174

36 0 002 033 002

37 0 0 263 0

Total 20314 13981 11753 10844




1 008 007 006 006

2 008 007 006 006

3 020 012 012 010

4 194 011 011 011

5 2829 159 155 159

6 2939 164 160 164

7 691 035 034 035

8 338 012 012 012

9 477 143 137 142

10 101 029 027 028

11 219 032 030 032

12 128 000 000 000

13 124 000 0 000

14 120 0 000 0

15 022 083 043 083

16 032 138 067 138

17 000 001 001 001

18 010 080 032 080

19 007 052 021 052

20 011 083 033 083

21 000 003 001 002

22 001 022 006 022

23 001 049 013 049

24 001 091 021 091

25 000 037 009 037

26 000 019 004 019

27 000 000 000 000

28 000 000 000 000

29 001 001 001 001

30 000 000 000 000

31 001 001 001 001


Page | 213

32 001 001 001 001

33 001 001 001 001

34 000 000 000 000

35 000 003 001 003

36 001 041 019 041

37 002 064 028 064

38 000 018 008 018

39 000 001 000 001

40 005 391 161 391

41 002 166 068 166

42 000 022 009 022

43 000 005 002 005

44 001 057 023 057

45 000 000 000 000

46 002 017 017 013

47 058 416 416 316

48 164 1321 1321 991

49 012 253 253 178

50 000 000 000 000

51 000 000 000 000

52 580 001 001 001

53 673 001 001 000

54 916 000 000 000

55 882 0 0 0

56 4986 000 000 000

57 2458 000 000 000

58 954 000 000 000

59 1071 627 626 379

60 1408 824 823 498

61 011 0 0 0

62 014 000 000 000

63 066 001 001 001

64 004 071 069 071

65 000 000 000 000

66 000 000 000 000

67 002 002 002 002

68 000 000 000 000

69 0 3783 3782 2384

70 0 102 052 102

71 0 0 0 0

72 0 0 0 0

73 0 423 252 423

Total 22562 9885 8758 7397


Page | 214




(hrscustomeryr)

70 68 71 69 321415 4640359 130895231648616

70 10 41 54 364131 431068083000 102819629963899

17 10 41 70 354092 411445783000000 105858799638989

17 26 10 70 383269 530285525000000 0968805806257521

7 26 54 69 435225 578907612000000 0825265794223827

7 54 41 69 406035 460067870000000 0915047984356197

7 26 54 70 442913 571756512000000 0836828971119134

17 10 71 70 345231 439663189000000 106361687725632

70 10 71 69 331470 443747189000000 110465057160048

70 10 41 69 340330 415529783000000 109962169073406

70 68 41 69 330274 435818516000000 130392343561974

7 54 71 69 397170 488285276000000 0920076865222623

41 10 54 69 356448 438219183000000 101663312274368

70 10 54 26 393311 549907825000000 0938414109506619

70 7 71 69 381047 465595876000000 100306543321300

70 7 41 17 403678 433294470000000 0957002858002407

70 10 54 71 355269 459285489000000 103322518050542

7 54 71 70 404856 481134176000000 0931640042117930

7 26 17 70 432867 552134212000000 0867220667870036

7 70 41 69 389911 437378470000000 0998036552346570

7 26 69 70 419096 556218212000000 0908254362214200

17 7 71 70 394813 461511876000000 0962031738868833

71 10 54 69 347586 466436589000000 102166200361011

10 26 54 69 385625 557058925000000 0926850932611312

70 26 10 69 369504 534369525000000 100983950060168

7 54 41 70 413721 452916770000000 0926611161251504


Page | 215





(kW)

Maximum node

Voltage deviation

Feeder load

balancing index

7 34 35 31 37 176962 0108696024464801 00228687361961248

7 11 35 32 28 143474 00613272038422790 00305387759787611

7 9 14 31 37 142477 00768537372742428 00252628392269486

6 8 12 36 37 151849 00696765908940439 00259144961258893

7 8 14 31 37 155399 00924077518455773 00239781364880477

6 8 12 31 37 169382 0104485611067200 00236077543160956

6 8 12 32 37 152876 00776641110366926 00250547432924683

33 8 14 30 37 171441 0108063061643879 00230652089068052

7 9 14 32 28 140261 00604355611623940 00310349101268755

7 11 35 32 37 143028 00639069227083702 00273727965037185

6 8 14 31 37 159752 00968913958755809 00236540473688646

6 33 35 32 37 170278 00826562726566354 00249194843739843

6 11 35 32 37 144683 00656445815841987 00261947314082027

6 8 14 32 37 146983 00705648561488426 00256096967694280

7 9 14 32 37 139815 00639015456844128 00280407351785895

6 9 14 32 37 143097 00625183468485540 00270001779728268

7 11 35 31 37 148829 00852978398065017 00245113845932977

7 34 35 30 37 202483 0130888991378581 00223050578905545

6 8 14 36 37 146991 00643933147100736 00266176555168500

6 11 35 31 37 154281 00897759906819439 00242838273201709

6 8 13 32 37 150430 00753226918458818 00253604605496161




(kW)

Maximum node

Voltage deviation

Feeder load

balancing index

7 14 8 32 28 121696 00575193535569366 00264544805354717

7 11 35 31 37 123007 00712785797883380 00213250141648472

6 12 8 32 37 128324 00630309398395457 00223824361844486

6 14 8 30 37 145672 0101299721228755 00194921779245086

7 33 35 32 28 130184 00583420082867310 00261406698684195

7 14 8 30 37 140274 00967924815464314 00195001911353607

7 21 35 30 37 164190 0113945920950777 00189031534924873

6 13 8 32 37 126434 00607661484850486 00227035446761735

7 14 9 32 28 117726 00575130414815478 00271215548731366


Page | 216

6 14 8 32 28 125920 00566904604559002 00265195832133384

6 12 8 31 37 137974 00889877482038002 00200083704114662

7 11 35 30 37 133030 00891516445489180 00199682922816912

6 11 35 32 37 123013 00593840879899440 00235298833627789

7 14 9 32 37 121070 00631040005210335 00255168322432724

6 14 9 32 28 123916 00566872316455769 00273594084038335

7 14 9 30 37 126587 00812324184971598 00206873922472966

7 14 9 31 28 117529 00642736861104275 00240537048868074

6 14 9 32 37 122047 00593825021727904 00240927348267257

6 11 35 32 28 124883 00566888115014094 00269082055980326

6 11 35 31 37 126802 00756552348586014 00207586957663036

6 14 8 32 37 124050 00593857418451058 00230337877365745

7 13 8 32 28 124039 00575225874614865 00262247242500743

7 11 35 32 28 119522 00575159230231156 00267430211390231

7 14 9 31 37 118759 00642740886891275 00220228862077971

6 14 8 31 37 130316 00816654599427028 00201908840890301

33 14 8 30 37 140110 00923831702765571 00197570883486903

7 12 8 32 28 125895 00587758838819431 00259864524009700

6 13 8 31 37 134936 00865715938530326 00201790772057552




loss

(kW)

Maximum node

Voltage deviation

Feeder load

balancing index

7 9 14 30 37 15 17 16 112506 00655990339384582 00207847799664288

6 8 14 31 37 14 11 15 120818 00728143829651942 00199639595336255

7 11 35 30 37 16 16 12 118637 00756705031931788 00198888055963062

6 8 14 31 37 11 29 14 125736 00822955381260978 00194988443664523

6 11 35 32 37 29 11 29 116999 00602917954784902 00213598898907595

7 9 14 31 37 15 14 16 110931 00518306996442978 00223689972435171

7 34 35 30 37 16 13 13 140652 00983575865184194 00182688360250883

7 8 14 30 37 14 11 15 128617 00876913785424229 00190954012999288

7 8 14 30 37 11 16 14 127141 00860397262006276 00191601352391895

7 9 14 36 37 30 30 29 109157 00520335391274761 00229564125698243

7 8 14 30 37 10 14 16 126706 00857230143750372 00192117850059117

7 11 35 30 37 13 16 12 121130 00786215737441328 00196617519208137

7 34 35 30 37 13 10 9 151352 0106960621828031 00178195736666725

7 34 35 30 37 10 12 9 152310 0107688512235453 00178046268710843

6 8 14 30 37 11 15 16 130550 00897068798318073 00189590122249633

6 8 14 30 37 16 14 10 130869 00901533044670202 00189271311922809

7 34 35 30 37 10 13 12 148089 0104837492639545 00178736074180585


Page | 217

7 34 35 30 37 13 11 16 143317 0100615335666250 00181553323058751

6 8 14 30 37 10 14 14 133299 00925968739633617 00188139999335965

7 34 35 30 37 13 9 12 148392 0105013682219175 00178453713901855

6 8 14 30 37 14 11 10 137593 00963962506644021 00186232592604301

6 8 14 30 37 11 8 14 136046 00951731865531927 00187106569470356

6 8 14 30 37 11 11 16 135639 00942616575802945 00187170876179048

7 8 14 30 37 15 16 14 122935 00815907052491111 00195198923102276

7 34 35 30 37 12 14 16 140640 00983915740315128 00182784576692257

6 33 35 31 37 11 11 13 146017 00888852225316270 00188548348595259

7 34 35 30 37 12 16 12 142144 00997534014352579 00181578155086060

6 8 14 30 37 14 11 15 132819 00921338781311946 00188143081376993

6 8 14 30 37 10 15 11 136651 00956093119043262 00186781475357014

7 9 14 31 37 14 14 16 111382 00525319705640723 00222591386298574

7 34 35 30 37 13 14 16 139957 00977014014811679 00183484070331887

7 34 35 30 37 12 15 16 139849 00976123852270839 00183745698300515

7 34 35 30 37 12 16 16 138589 00959671533698319 00184842191427931

7 34 35 30 37 16 13 16 137912 00952795751906571 00185525366651277

6 33 35 31 37 11 11 11 148785 00910856464605774 00187751047204272

7 34 35 30 37 12 16 13 141338 00990484927061306 00181980491991251

7 34 35 30 37 12 13 12 145536 0102926179499332 00179590185768212

6 8 14 30 37 14 10 15 132373 00918145642214576 00188660639598312

6 8 14 30 37 16 11 14 131312 00904718190224125 00188759872087077

7 34 35 30 37 13 15 16 139168 00969230570394858 00184436609617936

7 34 35 30 37 13 9 11 150730 0106620666560267 00178315514588942

6 8 14 30 37 14 11 14 133746 00929165522686308 00187615074100094

7 34 35 30 37 9 9 12 152656 0107867658396772 00178031242058681

6 8 14 30 37 10 11 16 135118 00939381882085281 00187414815201857

7 34 35 30 37 12 12 9 149341 0105739135263959 00178316539838164

7 9 14 36 28 32 32 32 110385 00489797931328652 00256323647901629

7 9 14 36 37 32 31 31 108599 00498935433820196 00235262740306846

7 9 14 32 37 31 30 31 108436 00537552050723257 00227898958267559

7 9 14 36 28 32 31 31 110203 00489682960875768 00259015702487973

7 34 35 30 37 8 12 9 154427 0108962750550623 00178021823053241


Page | 218




(kW)

Maximum node

Voltage deviation

Feeder load

balancing index

55 61 71 72 12 99036 00524391619987274 00196366946903149

69 61 71 9 14 145213 00664127006601768 00185315761508749

55 61 71 72 14 98845 00524393494628415 00194882148961848

69 70 71 10 14 145135 00666490251240782 00182871906896542

69 61 71 72 12 150267 00699556148777123 00161708619074924

55 61 71 10 14 104521 00524349487665904 00238104755589364

69 61 71 72 13 150383 00700225094171628 00161512783956020

55 61 71 72 13 98937 00524392488739880 00195710324132613

69 61 71 72 11 150792 00682108082577803 00171029450547815

55 61 71 9 14 105348 00524349082167884 00242117051986541

69 61 71 72 14 150513 00700911373758199 00161129748303495

55 61 71 72 11 105195 00524380932334678 00218572363716938




(kW)

Maximum node

Voltage deviation

Feeder load

balancing index

55 61 12 14 9 97461 00523081449765275 00226112450860475

69 61 71 14 9 130761 00662843002557533 00155527078006889

55 61 71 14 7 97263 00523080911134007 00226177446060770

55 61 12 71 72 87588 00523152959484715 00174558059214037

55 61 71 14 8 93176 00523082195004728 00211109499855264

55 61 71 13 72 87581 00523154440245970 00174392153380541

55 61 12 14 72 87755 00523153511186373 00174538759436512

55 61 12 71 7 97289 00523080869366065 00226232791264600

69 61 71 11 9 134009 00662855052002667 00154463391981039

69 61 12 14 9 130989 00662843776081034 00155381836375260

55 61 71 13 7 97273 00523080879708534 00227249951330579

55 61 71 14 9 90907 00523086904216601 00201865894567423

55 61 71 14 10 90291 00523088955157064 00199034032147027

69 61 71 14 10 130894 00665207578684145 00154263271797149

55 61 71 14 72 87582 00523156072908145 00174100597226583

69 61 71 11 10 134197 00665220013747228 00153401360203180

69 61 71 11 72 136858 00680828895070073 00147368269784675

69 61 12 14 10 131126 00665208386694061 00154135530565384

55 61 71 11 72 91274 00523126048676607 00184393848480773


Page | 219




loss

(kW)

Maximum node

Voltage deviation

Feeder load

balancing index

69 63 71 10 14 60 60 60 105879 00543213716422435 00153740505896722

69 63 12 72 71 60 62 62 109324 00575466375767690 00126779733811642

55 61 71 72 11 60 60 60 80324 00429183191505871 00183159151221229

69 63 12 72 71 61 61 62 109323 00575465740537586 00126842028893447

55 61 71 72 12 60 60 60 74165 00429193759769601 00159264876998350

69 63 14 10 71 62 62 62 106070 00543012249613587 00150279825984642

69 63 11 72 71 60 62 60 110547 00558290844078126 00139841427388105

69 63 14 9 71 62 62 62 106271 00540689205567605 00153025056850459

69 61 71 72 11 60 60 60 108838 00542584369620998 00141625735067141

55 61 71 72 14 60 56 60 75837 00436673338725839 00157367114339890

69 63 14 10 71 62 62 60 105960 00542966739560918 00151430448212008

69 61 71 10 14 60 60 60 104307 00527268149576859 00155323687715422

69 63 11 72 71 61 62 62 110652 00558333983851442 00137892112215884

69 63 13 72 71 62 62 62 109522 00576169823075075 00125440050970194

55 61 71 72 14 60 55 60 75975 00436701836501366 00156758120818947

69 63 71 10 14 60 60 62 105896 00542940500362948 00152768514567046

69 63 14 9 71 62 61 61 106159 00540643102892876 00154245882374843

55 61 71 72 13 60 60 60 74066 00429194617185072 00158554987038681

69 62 71 10 14 61 60 60 105886 00542959390978505 00153513700764165

69 63 14 72 71 62 62 62 109622 00576844280930477 00125002240983144

55 63 71 72 14 62 61 62 74382 00440379610790336 00155858821619573

69 63 71 72 11 60 60 60 110530 00558564471048234 00140822204796308

55 63 71 72 14 60 60 62 74285 00440350644694274 00157371695186626

55 63 14 72 71 62 62 62 74448 00440399072962552 00155438948075735

55 63 71 72 14 60 62 62 74344 00440368353288504 00156312863856681

69 63 71 9 14 60 61 60 105882 00542934725670071 00153515485666183

55 63 71 72 14 60 61 62 74305 00440356668532606 00156816031788752

55 61 20 72 13 60 60 60 80533 00429326269571468 00157463174391893

55 63 71 72 14 61 61 62 74343 00440367927398261 00156346520711234

69 61 71 72 14 60 60 60 107187 00561022028435777 00126909641069497

69 63 71 72 11 60 61 60 110533 00558285040786375 00140595150870697

69 63 12 72 71 62 62 62 109436 00575512407997617 00125707103016452

69 63 14 10 71 61 62 62 106000 00542983427485794 00150838099664421

69 63 11 72 71 60 61 62 110569 00558299818740340 00139149694834405

69 63 14 9 71 61 62 60 106118 00540626433897020 00154840963668230

69 61 71 72 12 60 60 60 107041 00559693311798567 00127785892138089

55 61 71 72 14 60 60 60 73974 00429195606297569 00157682511572302

69 63 14 10 71 61 61 62 105958 00542966109653011 00151492343922130

69 63 12 72 71 62 62 61 109365 00575483243249972 00126225992147273


Page | 220

69 63 11 72 71 62 62 60 110611 00558317226735644 00138490567525274

69 63 14 9 71 62 62 61 106201 00540660395254129 00153587525958041

69 63 14 10 71 61 60 62 105917 00542949434469265 00152083287358888

69 63 14 9 71 62 62 60 106160 00540643732226493 00154184014811756

69 63 11 72 71 61 61 62 110610 00558316590719640 00138552654427231

69 63 71 72 11 62 62 62 110723 00558362979744786 00137328015545176

69 61 71 72 13 60 60 60 107108 00560349171634668 00127435051911921

Page | 221


Algorithms



2amp3

Parameter Value

Number of ants 50







Parameter Value

Number of ants 100








operation

Parameter Value

Number of ants 150







Page | 222



Parameter Value

Number of ants 400







Parameter Value

Number of ants 500







Chapter 8


ECOST and SAIDI)

Parameter Value

Number of ants 100







Page | 223


ECOST and SAIDI)

Parameter Value







Chapter 9



Parameter Value

Number of ants 200








Parameter Value






Page | 224








9th











1-6 12-15 March 2018

Page | 4

46 Summary 90

CHAPTER 5 92



51 Introduction 92








55 Summary 109

CHAPTER 6 111



61 Introduction 111





651 Test Case 1 122

652 Test Case 2 123

653 Test Case 3 124

66 Summary 126

CHAPTER 7 128



71 Introduction 128





Page | 5







751 Test Case 1 138

752 Test Case 2 147

753 Test Case 3 147

76 Summary 148

CHAPTER 8 150



81 Introduction 150









86 Summary 164

CHAPTER 9 166



BALANCING 166

91 Introduction 166








Page | 6




95 Summary 187

CHAPTER 10 189


101 Conclusion 189

102 Future Work 193

References 195





Word count 51012

Page | 7

List of Figures





34


















comparison 74






Fig 4-8 11 kV 4th




Page | 8

Fig 4-11 11 kV 4th


























117









Page | 9





136




13 142





problem 157


problem 158



162
















Page | 10

List of Tables













102












13 143




2 147


3 148

Page | 11



163




Case II 173


174



Case III 176


III 176





IV 179



in Case II 181


II 181



in Case III 183


III 184


184



Page | 12


IV 186


187


204







Table B-3 95th





SAIDI) 214

















Page | 13













Page | 14
























EV Electric Vehicle





HC Hyper Cube


HV High Voltage

Page | 15


LV Low Voltage




MV Medium Voltage









TS Tabu Search





Page | 16

Abstract





December 2017






















for optimal DA

Page | 17

Declaration




Page | 18

Copyright Statement










copies made








andor Reproductions










Page | 19

Acknowledgements









encouragement





and support

Page | 20

CHAPTER 1

INTRODUCTION

11 Motivation
















increase profits




Page | 21




during one week






























Page | 22





12 Objectives







ACO) algorithm


















Page | 23
































Page | 24




































Page | 25

































Page | 26

































Page | 27














for all studies

Page | 28

CHAPTER 2


21 Introduction
















Page | 29

Tie-switch





















Page | 30





231 Reclosers














trip




Recloser locks

out on 2nd

reclose

as programmed

Recloser opens

Recloser recloses

fault still present

Recloser recloses

fault still present

Recloser re-opens

fault still present

Load current


Page | 31










233 Tie-switches










241 Basic Concepts









Page | 32

Tran

sfo

rme

r Lo

ss


1 Transformer

2 Transformers



















119878119871




Page | 33








improvement
























Page | 34





(Kw)







(Kw)














Page | 35








Transformer Size

(kVA)

No load loss

(kW)

Load loss

(kW)

Capital

price (euro)

Cost of loss

(euro)

Total cost

(euro)

A 1000 11 9 9074 34211 43285

B 1000 094 76 11362 28986 40348


251 Basic Concepts









and opened



Page | 36


































Page | 37



































Page | 38




operations








261 Basic Concepts


















Page | 39






















Page | 40


1 2 3 4 5 6 7


1 2 3 4 5 6 7


1 2 3 4 5 6 7


1 2 3 4 5 6 7


CB1 opened



CB1 CB2

CB1CB2

CB1 CB2

CB1 CB2





Interrupted

load



Page | 41


1 2 3 4 5 6 7


1 2 3 4 5 6 7


1 2 3 4 5 6 7


1 2 3 4 5 6 7


CB1 opened



CB1 CB2

CB1CB2

CB1 CB2

CB1 CB2





Interrupted

load









Page | 42





























Page | 43









network unit [72]

Open-circuit test






Page | 44

(a) Test circuit









119875119874119862 = 119875ℎ+119890 =119880119874119862

2

119877119888119871119881= 119880119874119862119868ℎ+119890 (2-1)


current

Short-circuit test




119880119900119888

119868ℎ+119890 119868120601

119868119900119888 119885119890119902 119871119881

119877119888 119871119881 119883119898 119871119881


Page | 45




(a) Test circuit






and expressed as

119875119878119862 = 1198681198781198622 119877119890119902119867119881 (2-2)




119880119904119888

119868119890119909

119868119904119888 119877119890119902 119867119881 119883119890119902 119867119881

(119899119890119892119897119890119888119905)


Page | 46

Active power loss



∆119875 = 119875119874119862 + 1205732119875119878119862 (2-3)

where 120573 =119878119871




Reactive power loss



as

∆119876 = 119876119874119862 + 1205732119876119878119862 (2-4)

119876119874119862 = 119878119874119862 =119868119874119862

119868119873∙ 119878119873 (2-5)

119876119878119862 = 119878119878119862 = 119880119878119862

119880119873∙ 119878119873 (2-6)








1198791198711 = 11988002119875119885119874119862 +

1205732

11988002 119875119885119878119862 (2-7)

119875119885119874119862 = 119875119874119862 + 119870119876119876119874119862 (2-8)


Page | 47

119875119885119878119862 = 119875119878119862 + 119870119876119876119878119862 (2-9)


120573 =119878119871















1198791198712 = 211988002119875119885119874119862 +

1

2

1205732

11988002 119875119885119878119862 (2-10)







Page | 48




119875119887119877 + 119895119876119887119877 = 119887119877 times 119868lowast (2-11)

119875119887 = 1198681198872 times 119877119887 (2-12)


119875119887 =119875119887119877

2 +1198761198871198772

1198811198871198772 times 119877119887 (2-13)







119864119871 = sum 119875119887119899119873119887119899 (2-14)











Page | 49



120582 = sum 120582119895119895 (2-15)

119880 = sum 120582119895119895 119903119895 (2-16)

119903 =119880

120582 (2-17)


point





119878119860119868119865119868 =sum 120582119894119873119894119894

sum 119873119894119894 (2-18)

119878119860119868119863119868 =sum 119880119894119873119894119894

sum 119873119894119894 (2-19)

119860119864119873119878 =sum 119880119894119871119894119894

sum 119873119894119894 (2-20)

119864119862119874119878119879 = sum 119888119898(119889119898)119891119898119871119898119872119898=1 (2-21)











Page | 50




Simulation method












memory

Analytical method






(FMEA)










Page | 51











Normal operation

Active

failure

Transient

failure

Passive

failure

Maintenance

120582119860 120582119879 120582119875 120582119872

120583119860 120583119879 120583119875

120583119872


Page | 52

Start











Next failure i=i+1


End

No

Yes












Page | 53















after failure











Page | 54

0

1


















120572 =

1 119883 le 119883119898119894119899119883119898119886119909minus119883

119883119898119886119909minus119883119898119894119899119883119898119894119899 lt 119883 lt 119883119898119886119909

0 119883 ge 119883119898119886119909

(2-22)





120572

119883119898119894119899 119883119898119886119909 119883


Page | 55










119872119886119909 119869 = 12059611205721 + 12059621205722 + ⋯ + 120596119899120572119899 (2-23)







selected objectives






Max-min method




119872119886119909 119869 = min 1205721 1205722 hellip 120572119899 (2-24)




Page | 56











reconfiguration





119872119886119909 119869 = (1205721 ∙ 1205722 ∙ hellip ∙ 120572119873)1 119899frasl (2-25)







Framework








Page | 57



forall 119894 = 12 hellip 119873119900119887119895 119865119894(119883) le 119865119894(119884) (2-26)

exist 119894 = 12 hellip 119873119900119887119895 119865119894(119883) lt 119865119894(119884) (2-27)














preferences











Page | 58

211 Summary
































Page | 59













Page | 60

CHAPTER 3


31 Introduction


















Page | 61









search space [13]




35













follows [93]

119862 = 119875(119883 minus 119871 le 120583 le 119883 + 119871) = int 119866(119883)119889119909119883+119871

119883minus119871 (3-1)

119871 = 119911lowast 120590

radic119899 (3-2)


Page | 62







095


119862 09 095 099 0999

119911lowast 1645 1960 2576 3291


119899 = (119911lowast120590

119871)2 (3-3)
















Page | 63
























Page | 64

the nest






















Page | 65

Start

Set Iteration n=1

Maximum iteration

reached

End

No

Yes









n=n+1












Page | 66


































Page | 67

Start

Cloning

Maximum iteration

reached

End

No

Yes


Hypermutation

Fitness evaluation


Pheromone updating

n=n+1












Page | 68










tables [88]

















35 Summary





Page | 69


























Page | 70

CHAPTER 4





41 Introduction














Page | 71



























Section 46



Page | 72

42 Load Model



modelled








Number of people

in household

1 2 3 4 ge5

Percentage () 3058 341 1557 1288 686






weekend


12


dwelling





Page | 73










follows

Minimise 119891 = 1198800

2119875119885119874119862 +1205732

11988002 119875119885119878119862 119905119903119886119899119904119891119900119903119898119890119903 119894119899 119904119894119899119892119897119890 119900119901119890119903119886119905119894119900119899

211988002119875119885119874119862 +

1

2

1205732

11988002 119875119885119878119862 119905119903119886119899119904119891119900119903119898119890119903119904 119894119899 119901119886119903119886119897119897119890119897 119900119901119890119903119886119905119894119900119899

(4-1)


120573 =119878119871




44 Methodology









Page | 74













obtained

Profile

generator of

domestic

electricity

demand profiles

Transformer

operation

modes

MATLAB

Distribution

network

model built

in OpenDSS

Analyse and

compare

simulation

results in

MATLAB




Page | 75

Start



modes considered

End

No

Yes


customer randomly


mode



Record results

Change

transformer

operation

mode

N=N+1




No

Yes







Page | 76














obtained


day is recorded


Profile

generator of

domestic

electricity

demand profiles

Tie-switch

status

MATLAB

Distribution

network

model built

in OpenDSS

Analyse and

compare

simulation

results in

MATLAB




Page | 77





451 Test Case 1








whilst the 4th
























Page | 78

A

A

A

A

B

B

B

B


Load4_2

Load4_3

Load4_4

Load4_5

Load4_6

Load4_7

Load4_8

75 MVA

33 kV

11 kV

33 kV

Voltage

Source

75 MVA



Sub-

sector

Transf

Rating

(kVA)

Conn Tapping

Range

Load

Losses

at

75

(kW)

No-

Load

Losses

(kW)

Impedance voltage


the principle

tapping

()

Reference

standard


6 steps of 25

Each

50

75

835 BS 171 amp

IEC 60076







Page | 79

0

10

20

30

40

50

60

70

80

90

100

0 2 4 6 8 10 12 14 16 18 20 22

Tran

sfo

rme

r Lo

ad F

acto

r

Time (h)

0

10

20

30

40

50

60

70

0 2 4 6 8 10 12 14 16 18 20 22

Tran

sfo

rme

r Lo

sse

s (k

W)

Time (h)

0

10

20

30

40

50

60

70

0 2 4 6 8 10 12 14 16 18 20 22

Tran

sfo

rme

r Lo

sse

s (k

W)

Time (h)




of Scenario 1


(a) Scenario 1

(b) Scenario 2



Page | 80

0

10

20

30

40

50

60

70

0 2 4 6 8 10 12 14 16 18 20 22

Tran

sfo

rme

r Lo

sse

s (k

W)

Time (h)

(c) Scenario 3














the 95th



The mean and 95th










Page | 81

0976

0978

098

0982

0984

0986

0988

099

0992


Vo

ltag

e (

pu

)

Scenario1

Scenario2

Scenario3

0974

0976

0978

098

0982

0984

0986

0988

099


Vo

ltag

e (

pu

)

Scenario1

Scenario2

Scenario3

(a) Mean value

(b) 95th

value

Fig 4-8 11 kV 4th



start of the 4th










Page | 82

088

09

092

094

096

098

1

0 2 4 6 8 10 12 14 16 18 20 22

Bu

s V

olt

age

(p

u)

Time (h)

088

09

092

094

096

098

1

0 2 4 6 8 10 12 14 16 18 20 22

Bu

s V

olt

age

(p

u)

Time (h)

088

09

092

094

096

098

1

0 2 4 6 8 10 12 14 16 18 20 22

Bu

s V

olt

age

(p

u)

Time (h)



(a) Scenario 1

(b) Scenario 2

(c) Scenario 3


Lower Limit

Lower Limit

Lower Limit



Page | 83

088

09

092

094

096

098

1

0 2 4 6 8 10 12 14 16 18 20 22

Bu

s V

olt

age

(p

u)

Time (h)

088

09

092

094

096

098

1

0 2 4 6 8 10 12 14 16 18 20 22

Bu

s V

olt

age

(p

u)

Time (h)

088

09

092

094

096

098

1

0 2 4 6 8 10 12 14 16 18 20 22

Bu

s V

olt

age

(p

u)

Time (h)

(a) Scenario 1

(b) Scenario 2

(c) Scenario 3


Lower Limit

Lower Limit

Lower Limit



Page | 84

0976

0978

098

0982

0984

0986

0988

099

0992


0 25

5244 75

100
















values 0 25 5244 75 and 100





Fig 4-11 11 kV 4th




Page | 85






TCLF () 0 25 5244 75 100

Transformer loss

(kWh)

55922 50783 47865 49414 53982




TCLF () 0 25 5244 75 100

Average number of


0 2 4 2 0

452 Test Case 2












Page | 86

0

02

04

06

08

1

12

14

16

0 2 4 6 8 10 12 14 16 18 20 22

Act

ive

Po

we

r (k

W)

Time (h)

TW1 TW2 TW3 TW4 TW5

A1

A2

A3


B1

B2

B3

EndA EndB

TW9TW8TW7TW6








B4_3 B4_4 B4_5 B4_6 B4_7 B4_8




(a) Group 1



Page | 87

0

002

004

006

008

01

012

014

016

018

02

0 2 4 6 8 10 12 14 16 18 20 22

Act

ive

Po

we

r (k

W)

Time (h)

(b) Group 2















at TW1


at TW5





Page | 88







operation












Loss

(kWhday)

11319 10848 10848 11399 11162 11162 9739 9572 9528













Page | 89

096

0962

0964

0966

0968

097

0972

0974

0976

0978

098


Vo

ltag

e (

pu

)

Scenario1

Scenario2

Scenario3

0955

096

0965

097

0975

098

0985

099


Vo

ltag

e (

pu

)

Scenario1

Scenario4

Scenario7













Page | 90


that in Scenario 4




46 Summary



























Page | 91





Page | 92

CHAPTER 5




51 Introduction











planning





Reduction

Page | 93



constraints


















conclusions




119872119894119899119894119898119894119904119890 119891 = sum 119896119894119877119894(119875119894

2+1198761198942

1198801198942 )

119873119887119894=1 (5-1)





Reduction

Page | 94



Subject to



119875119894 le 119875119894119898119886119909 (5-4)

det(119860) = 1 119900119903 minus 1 (5-5)












53 Solution Method







Reduction

Page | 95

Home

1 2 NP1NP1-1

1 2 NP1-1 NP1

1 2 NP1NP1-1

1 2 NP2-1 NP2

1 2 NP2NP2-1

1 2 NP2-1 NP2

1 2 NP2NP2-1

1 2 NP2-1 NP2

Food

Stage

1

2

NT-1

NT

NT+1

NT+2

NT+NDG-1

NT+NDG

Part 1 Number of


Part 2 Number

of DGs









Reduction

Page | 96
















five steps



constant value






stage y is

119875119895119910(119873) =

120591119895119910

(119873)

sum 120591119895119910

(119873)ℎisin∆119910

(5-6)

where 120591119895119910




Reduction

Page | 97










choose a new trail







120591119895119910

(119873) = (1 minus 120588)120591119895119910

(119873 minus 1) + 120591119888 (5-7)




this edge





120591119895119910(119873) = 120591119895

119910(119873) + 120588119891119887119890119904119905

119891119887119890119904119905(119873) (5-8)



120591119895119910(119873) = 120591119898119886119909 119894119891 120591119895

119910(119873) ge 120591119898119886119909 (5-9)

120591119895119910(119873) = 120591119898119894119899 119894119891 120591119895

119910(119873) le 120591119898119894119899 (5-10)


Reduction

Page | 98

Start

Set Iteration n=1

Maximum iteration

reached

Output best


No

Yes









n=n+1


all location lists


and load data







optimal solution



Reduction

Page | 99













method





simultaneously




Appendix C1

541 33-bus System








Reduction

Page | 100

10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

18 19 20 21

22 23 24

25 26 27 28 29 30 31 32


L18

L19 L20 L21

L22

L23 L24

L25

L26 L27 L28 L29 L30 L31 L32

L33

L34

L35

L36

L37





Case Active feeder

loss (kW)

Minimum voltage

(pu)

(Bus No)


on Fig 53

DG location

Case I 20314 09116 (B17) L33 L34 L35 L36 L37 NA

Case II 13981 09361 (B31) L7 L9 L14 L32 L37 NA



Case I base case



Bus 17








Reduction

Page | 101

10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

18 19 20 21

22 23 24

25 26 27 28 29 30 31 32


L18

L19 L20 L21

L22

L23 L24

L25

L26 L27 L28 L29 L30 L31 L32

L33

L34

L35

L36

L37










from it


Method Feeder loss

(kW)

Loss reduction

()


voltage (pu)


BEM [109] 14054 3082 L7 L10 L14 L32 L37 09361

HSA [110] 13981 3118 L7 L9 L14 L32 L37 09361

FWA [16] 14026 3095 L7 L9 L14 L28 L32 09396

PSO [55] 13981 3118 L7 L9 L14 L32 L37 09361

IWO [111] 13981 3118 L7 L9 L14 L32 L37 09361








Reduction

Page | 102

10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

18 19 20 21

22 23 24

25 26 27 28 29 30 31 32


L18

L19 L20 L21

L22

L23 L24

L25

L26 L27 L28 L29 L30 L31 L32

L33

L34

L35

L36

L37

DG2

DG1

DG3









CGA and CSA



computation

times

(second)


ACO 13981 13981 13981 0 228 821 1448

CGA [112] 14002 14619 13981 12121 5463 2986 3926

CSA [113] 13986 14028 13981 01328 8363 3425 7258










Reduction

Page | 103

10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

18 19 20 21

22 23 24

25 26 27 28 29 30 31 32


L18

L19 L20 L21

L22

L23 L24

L25

L26 L27 L28 L29 L30 L31 L32

L33

L34

L35

L36

L37

DG2DG1

DG3























Reduction

Page | 104

086

088

09

092

094

096

098

1

102

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32

Vo

ltag

e (

pu

)

Bus No

Case I

Case II

Case III

Case IV

0

20

40

60

80

100

120

140

160

180

200

100 400 700 1000

Fee

de

r lo

ss (

kW)

DG Capacity (kVA)












allocation



Reduction

Page | 105

10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

27

28

29

30

31 32 33 34

35

36

37

38 39 40 41 42 43 44 45

46 47 48 49

50

51

52

53 54 55 56 57 58 59 60 61 62 63 64

65 66

67 68


L27

L28

L29

L30

L31 L32 L33 L34

L35

L36

L37

L38 L39 L40 L41 L42 L43 L44 L45

L46

L47 L48 L49

L50

L51

L52

L53 L54 L55 L56 L57 L58 L59 L60 L61 L62 L63 L64

L65

L66

L67

L68

L69

L70

L71

L72L73

542 69-bus System










Case Active feeder

loss (kW)

Minimum voltage

(pu)

(Bus No)


Case I 22562 09072 (B64) L69 L70 L71 L72 L73 NA

Case II 9885 09476 (B60) L14 L55 L61 L71 L72 NA



Case I base case




Reduction

Page | 106

10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

27

28

29

30

31 32 33 34

35

36

37

38 39 40 41 42 43 44 45

46 47 48 49

50

51

52

53 54 55 56 57 58 59 60 61 62 63 64

65 66

67 68


L27

L28

L29

L30

L31 L32 L33 L34

L35

L36

L37

L38 L39 L40 L41 L42 L43 L44 L45

L46

L47 L48 L49

L50

L51

L52

L53 L54 L55 L56 L57 L58 L59 L60 L61 L62 L63 L64

L65

L66

L67

L68

L69

L70

L71

L72L73











Method Feeder loss

(kW)

Loss reduction

()


voltage (pu)


FWA [16] 9886 5618 L14 L56 L61 L71 L72 09476

HSA [110] 10546 5326 L13 L18 L56 L61 L72 09475

GA [110] 10242 5461 L14 L53 L61 L71 L72 09462





Reduction

Page | 107

10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

27

28

29

30

31 32 33 34

35

36

37

38 39 40 41 42 43 44 45

46 47 48 49

50

51

52

53 54 55 56 57 58 59 60 61 62 63 64

65 66

67 68


L27

L28

L29

L30

L31 L32 L33 L34

L35

L36

L37

L38 L39 L40 L41 L42 L43 L44 L45

L46

L47 L48 L49

L50

L51

L52

L53 L54 L55 L56 L57 L58 L59 L60 L61 L62 L63 L64

L65

L66

L67

L68

L69

L70

L71

L72L73

DG3

DG1

DG2

10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

27

28

29

30

31 32 33 34

35

36

37

38 39 40 41 42 43 44 45

46 47 48 49

50

51

52

53 54 55 56 57 58 59 60 61 62 63 64

65 66

67 68


L27

L28

L29

L30

L31 L32 L33 L34

L35

L36

L37

L38 L39 L40 L41 L42 L43 L44 L45

L46

L47 L48 L49

L50

L51

L52

L53 L54 L55 L56 L57 L58 L59 L60 L61 L62 L63 L64

L65

L66

L67

L68

L69

L70

L71

L72L73

DG3DG1

DG2









III respectively



Reduction

Page | 108

0

50

100

150

200

250

100 400 700 1000

Fee

de

r lo

ss (

kW)

DG Capacity (kVA)














configuration












Reduction

Page | 109

086

088

09

092

094

096

098

1

102

0 5 10 15 20 25 30 35 40 45 50 55 60 65

Vo

ltag

e (

pu

)

Bus No

Case I

Case II

Case III

Case IV


55 Summary



















Reduction

Page | 110








Page | 111

CHAPTER 6




LOSS REDUCTION

61 Introduction





system [82]









Page | 112












investigated




















Page | 113













load curve [82]









P1

P2

1199051 1199052 Time (h)



Page | 114

1198911 = sum (119864119871119905 + 119879119871119905)1199051minus1119905=1 + sum (119864119871119905 + 119879119871119905) 1199051

24119905=1199052 isin 1 2 hellip 24 (6-1)


Min 119891 = 1198911 + 1198912 (6-3)







and are disregarded


















Page | 115

Home

0 1

0 1

0 1

0 1

1 2 NPNP-1

1 2 NP-1 NP

1 2 NPNP-1

1 2 NP-1 NP

Food

Stage

1

2

Ns-1

Ns

Ns+1

Ns+2

Ns+Nt-1

Ns+Nt

Part 1

Number of

substations

Ns

Part 2 Number

of existing tie-

switches Nt








Page | 116

Tie-switch

Transformer





as a binary vector















Page | 117

Start


Maximum iteration

reached

Output best


No

Yes



Iteration N=1








N=N+1




and load data





T=T+1

Tgt2

Yes

t=t+1

No




Page | 118


LP8 LP9 LP10



LP29 LP30 LP31

LP26 LP27 LP28


19

20

21

22

23

24

26

25 27

28

29 30

71

13 15

14 16

17

18

69

1 3

2

5

4

7

6 8

10

9

68

11 12

56

57

58 60

59 61 62

65

64 66 67

50 52

51

54

53 55

44

45

46

47

48

49

70

31

32

33

34

36

35

39

37 38 40

41

42 43

63

F3

F2

F1

F7

F6

F5

F4


Subbus1

Subbus2

Subbus3

T1

T3

T5

Main

feeder

Main

feeder

Main

feeder

T2

T4

T6













Page | 119




Number

of load

points


(kW)

Q

(kVAr)

Number of

customers

4 1-2 9-10 residential 8869 8426 220

6 3-5 13-15 residential 8137 7731 200

12 6-7 16-17 23-25 28

30-31 37-38


6 8 11 18 26 32-33 industrial 2445 23228 1

10 12 19-22 27 29 34-

36












Page | 120






Page | 121




shown in Table 6-2



Spring

(Mar Apr May)

Weekdays 66 92

Weekends 26

Summer

(Jun Jul Aug)

Weekdays 66 92

Weekends 26

Autumn

(Sep Oct Nov)

Weekdays 65 91

Weekends 26

Winter

(Dec Jan Feb)

Weekdays 64 90

Weekends 26

Year 365 Days





buses









Page | 122

651 Test Case 1



network loss











Spring

weekday

Spring

weekend

Summer

weekday

Summer

weekend

Autumn

weekday

Autumn

weekend

Winter

weekday

Winter

weekend

Before

Reconfiguration


L70L71

L68L69

L70L71

L68L69

L70L71

L68L69

L70L71

L68L69

L70L71

L68L69

L70L71

L68L69

L70L71

L68L69

L70L71

Number of operated

transformers




Loss

(kWh)

Cable 9233 3498 8050 3151 9660 3665 11009 4080

Transformer 4301 3410 4109 3350 4372 3437 4597 3507

Total 13534 6908 12159 6501 14032 7102 15606 7587

After

Reconfiguration


23-24

0-6 0-7

23

0-7 0-7

22-23

0-6

0-7

22-23

0-6


L69L71

L68L69

L70L71

L17L68

L70L71

L17L68

L70L71

L17L68

L70L71

L68L69

L70L71

L17L68

L70L71

L68L69

L70L71

Number of operated

transformers






L65L70

L68L69

L70L71

L41L48

L65L69

L68L69

L70L71

L17L41

L65L70

L68L69

L70L71

L17L41

L65L70

L68L69

L70L71

Number of operated

transformers




Loss

(kWh)

Cable 9043 3516 7851 3169 9519 3685 10845 4103

Transformer 3955 2616 3759 2517 4036 2656 4264 2755

Total 12998 6132 11610 5686 13479 6341 15109 6858



Page | 123

0

05

1

15

2

25

3

35

4

45

05 1 15 2 25 3










652 Test Case 2











To

tal

loss

(G

Wh

)

DG Capacity (MW)



Page | 124

653 Test Case 3









120578times119875119862 (6-4)









the day



capability (mile)

Market share ()

Micro car 12 50 20









Page | 125

4

42

44

46

48

5

30 60 90



119878119874119862 = 0 119898 gt 119872119863119862

119872119863119862minus119898

119872119863119862 119898 le 119872119863119862 (6-5)


















To

tal

loss

(G

Wh

)




Page | 126

4

42

44

46

48

5

30 60 90











66 Summary













To

tal

loss

(G

Wh

)




Page | 127
















Page | 128

CHAPTER 7




71 Introduction
















Improvement

Page | 129






























weighted function


Improvement

Page | 130

119872119894119899 119869 = micro1 ∙ 119864119862119874119878119879 + micro2 ∙ 119878119862 (7-1)





Parameters






119872119886119909 119870 = 1205961 ∙ 120572119878119860 + 1205962 ∙ 120572119878119862 (7-2)

















Improvement

Page | 131

0

1

0

1

120572119878119860 =

1 119878119860119868119863119868 le 119878119860119868119863119868119898119894119899119878119860119868119863119868119900119903119894minus119878119860119868119863119868

119878119860119868119863119868119900119903119894minus119878119860119868119863119868119898119894119899119878119860119868119863119868119898119894119899 lt 119878119860119868119863119868 lt 119878119860119868119863119868119900119903119894

0 119878119860119868119863119868 ge 119878119860119868119863119868119900119903119894

(7-3)











120572119878119862 =

1 119878119862 le 119878119862119900119903119894119878119862119898119886119909minus119878119862

119878119862119898119886119909minus119878119862119900119903119894119878119862119900119903119894 lt 119878119862 lt 119878119862119898119886119909

0 119878119862 ge 119878119862119898119886119909

(7-4)





Parameters



120572119878119860

119878119860119868119863119868119898119894119899 119878119860119868119863119868119900119903119894 119878119860119868119863119868

120572119878119862

119878119862119900119903119894 119878119862119898119886119909 119878119862


Improvement

Page | 132

0

1





120572119864119862 =

1 119864119862119874119878119879 le 119864119862119874119878119879119898119894119899119864119862119874119878119879119900119903119894minus119864119862119874119878119879

119864119862119874119878119879119900119903119894minus119864119862119874119878119879119898119894119899119864119862119874119878119879119898119894119899 lt 119864119862119874119878119879 lt 119864119862119874119878119879119900119903119894

0 119864119862119874119878119879 ge 119864119862119874119878119879119900119903119894

(7-5)








Max 119871 = min (120572119878119860 120572119878119862 120572119864119862) (7-6)










120572119864119862

119864119862119874119878119879119898119894119899 119864119862119874119878119879119900119903119894 119864119862119874119878119879


Improvement

Page | 133



1 ( 1)

1 1 1 1 1 1


t t

b b k R k s

t b k j k j


(7-7)








rate




119878119860119868119863119868 = sum sum 120582119887∙119871119887[sum 119889119877

119873119862119877(119887)119899=1 +sum 119889119878

119873119862119878(119887)119899=1 ]

119873119887119887=1

119873119862119905119900119905119886119897119879

119905=1 (7-8)








119878119862 = 119862119868119878 ∙ 119873119899119890119908 + 119862119877119878 ∙ 119873119903119890119897 + sum 119872119862119879119905=1 ∙ (119873119899119890119908 + 119873119890119909119894119904) ∙ (1 + 119863119877)minus(119905minus1) (7-9)





Improvement

Page | 134

Home

0

1

0

1

0

1

0

1

Food





Problem
















Improvement

Page | 135









119887119890119899119890119891119894119905 = sum119864119862119874119878119879119887119886119904119890

119905 minus119864119862119874119878119879119900119901119905119905

(1+119863119877)119905119879119905=1 (7-10)

where 119864119862119874119878119879119887119886119904119890119905 and 119864119862119874119878119879119900119901119905





119861119862119877 =119887119890119899119890119891119894119905

119878119862 (7-11)






Improvement

Page | 136


LP8 LP9 LP10



LP29 LP30 LP31

LP26 LP27 LP28


9 10 11 12 13 33

6 7 8 31

1 2 3 4 5 30

25 26 27 29

22 23 24

19 20 21

32

14 15 16 17 18

28

F3

F2

F1

F7

F6

F5

F4


Subbus1

Subbus2

Subbus3

T1

T3

T5

Main

feeder

Main

feeder

Main

feeder

T2

T4

T6











Improvement

Page | 137







Number

of load

points


(kW)

Number of

customers

15 1-4 11-13 18-21 32-35 residential 545 220

7 5 14 15 22 23 36 37 residential 500 200

7 8 10 26-30 industrial 1000 1


7 6 7 16 17 24 25 38 commercial 415 10


















Improvement

Page | 138




Residential 006 11 16 26 316 5

Industrial 288 806 95 124 1387 276

Commercial 205 96 125 185 2151 6306




method






751 Test Case 1











Improvement

Page | 139


LP8 LP9 LP10



LP29 LP30 LP31

LP26 LP27 LP28


9 10 11 12 13 33

6 7 8 31

1 2 3 4 5 30

25 26 27 29

22 23 24

19 20 21

32

14 15 16 17 18

28

F3

F2

F1

F7

F6

F5

F4


Subbus1

Subbus2

Subbus3

T1

T3

T5

Main

feeder

Main

feeder

Main

feeder

T2

T4

T6










Improvement

Page | 140













Switch

No


Load (kW)


Type


2 2 7D 3500 LP9 1500 (industrial)



5 6 23D 3500 LP30 1000 (industrial)

6 7 28D 3595 LP36 500 (commercial)












Improvement

Page | 141


LP8 LP9 LP10



LP29 LP30 LP31

LP26 LP27 LP28


9 10 11 12 13 33

6 7 8 31

1 2 3 4 5 30

25 26 27 29

22 23 24

19 20 21

32

14 15 16 17 18

28

F3

F2

F1

F7

F6

F5

F4


Subbus1

Subbus2

Subbus3

T1

T3

T5

Main

feeder

Main

feeder

Main

feeder

T2

T4

T6



ECOST

($)

Number of

installed

switches

Capital and

installation cost

($)

Maintenance

and operation

cost ($)

Total system

cost ($)

Before switches

installation

472260 0 0 4830 477090

After switches

installation

221610 11 51700 13670 286980


Improvement

Page | 142


LP8 LP9 LP10



LP29 LP30 LP31

LP26 LP27 LP28


9 10 11 12 13 33

6 7 8 31

1 2 3 4 5 30

25 26 27 29

22 23 24

19 20 21

32

14 15 16 17 18

28

F3

F2

F1

F7

F6

F5

F4


Subbus1

Subbus2

Subbus3

T1

T3

T5

Main

feeder

Main

feeder

Main

feeder

T2

T4

T6


A Base case









Improvement

Page | 143

0

1

2

3

4

5

6

7

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

BC

R

Years








ECOST

($)

Number of

relocated

switches

Relocation

cost ($)

Number of

installed

switches

Capital and

installation

cost ($)

Maintenance

and operation

cost ($)

Total

system

cost ($)

Before switch

placement

472260 0 0 0 0 4830 477090

After switch

placement

221120 5 2500 8 37600 11260 272480











Improvement

Page | 144

0

20

40

60

80

100

120

140

160

05 1 15 2 25 3 35 4 45 5 55 6 65 7 75 8

Co

st (

th

ou

san

d $

)

CDF multiplier

ECOST

Switch costs

Total costs






















Improvement

Page | 145

0

5

10

15

20

25

30

35

40

05 1 15 2 25 3 35 4 45 5 55 6 65 7 75 8

Nu

mb

er

of

swit

che

s

CDF multiplier






















Improvement

Page | 146











01 273120 274810 272480 223

02 273400 275960 272480 175

03 273480 274810 272480 132

04 273100 274810 272480 110

05 273550 274810 272480 94

06 273440 274810 272480 81







400




100 273865 276120 272480 91

200 273100 274810 272480 110

300 273030 274370 272480 135

400 272820 274230 272480 168

500 273170 274230 272480 245


Improvement

Page | 147




752 Test Case 2














Function

SAIDI

(hrscustomer)

Switch costs ($)

Case 21 01 09 04909 09970 09464 1157 68275

Case 22 05 05 08456 09061 08758 556 67378

Case 23 09 01 09384 07761 09221 39936 153950



753 Test Case 3








Improvement

Page | 148


Objective

Function

120572119864119862 120572119878119860 120572119878119862 ECOST

($)

SAIDI

(hrscustomer)

Switch costs

($)

Before

switch

placement

0 0 0 1 472260 1989 4830

After switch

placement

08327 08327 08392 08384 188950 56723 112410

76 Summary

























Improvement

Page | 149




Page | 150

CHAPTER 8




IMPROVEMENT

81 Introduction














Improvement

Page | 151























set is obtained






conclusions


Improvement

Page | 152







119865(119866) = [1198911(119866)1198912(119866)1198913(119866)]119879 (8-3)


configuration G



1198911(119866) = sum 119896119894119877119894(119875119894

2+1198761198942

1198801198942 )

119873119887119894=1 (8-4)








1 ( 1)

1 1 1 1 1 1


t t

b b k R k s

t b k j k j


(8-5)





Improvement

Page | 153









119878119860119868119863119868 = sum sum 120582119887∙119871119887[sum 119889119877

119873119862119877(119887)119899=1 +sum 119889119878

119873119862119878(119887)119899=1 ]

119873119887119887=1

119873119862119905119900119905119886119897119879

119905=1 (8-6)




8214 Constraints








119891119901119904(119894) = sum 120596119895max(119900119891119895)minus119900119891119895(119875119878119894)

max(119900119891119895)minusmin (119900119891119895)

119873119900119887119895

119895=1 (8-7)








Improvement

Page | 154





tie-switches












number




weighted sum as

120591119894119909 = 1199011 ∙ 1205911198941199091 + |1199011 minus 1199012| ∙ 120591119894119909

2 + (1 minus 1199012) ∙ 1205911198941199093 (8-8)

where 1205911198941199091 120591119894119909





new matrix




Improvement

Page | 155



119875119894119909(119873) =120591119894119909(119873)

sum 120591119894119909(119873)ℎisin∆119909

(8-9)

















certain number [88]






follow

120591119894119909119899 (119873) = (1 minus 120588)120591119894119909

119899 (119873 minus 1) + 120591119888 (8-10)




Improvement

Page | 156



this edge





120591119894119909119899 (119873) = 120591119894119909

119899 (119873) + 120588119891119887119890119904119905

119899 (119873)

119891119887119890119904119905119899 (119873minus1)

(8-11)

where 119891119887119890119904119905119899 (119873 minus 1) and 119891119887119890119904119905





120591119894119909119899 (119873) = 120591119898119886119909 119894119891 120591119894119909

119899 (119873) ge 120591119898119886119909 (8-12)

120591119894119909119899 (119873) = 120591119898119894119899 119894119891 120591119894119909

119899 (119873) le 120591119898119894119899 (8-13)












Improvement

Page | 157

Start

Iteration N=1

Maximum ant number

reaches

Output Pareto

optimal set and end

No

Yes



Ant number m=1



matrices into one




for this ant

N=N+1


and load data


dominated solutions

Maximum iteration

reaches

Yes

m=m+1

No





Improvement

Page | 158

Start

Cloning

Maximum iteration

reached

Output Pareto

optimal set and end

No

Yes




dominated solutions



n=n+1











in Fig 8-2



Improvement

Page | 159
















119901119894119899 =

120591119894119899

sum 120591119895119899

119895 (8-14)











120591119894119899(119873) = 119898119886119909 (1 minus 120588)120591119894

119899(119873 minus 1) 120591119898119894119899 (8-15)




Improvement

Page | 160







updated as

120591119894119899(119873) = 119898119894119899120591119894

119899(119873) + 120588min (119891119899(119866))

119891119899(119866) 120591119898119886119909 (8-16)






next iteration





Improvement

Page | 161


LP8 LP9 LP10



LP29 LP30 LP31

LP26 LP27 LP28


19

20

21

22

23

24

26

25 27

28

29 30

71

13 15

14 16

17

18

69

1 3

2

5

4

7

6 8

10

9

68

11 12

56

57

58 60

59 61 62

65

64 66 67

50 52

51

54

53 55

44

45

46

47

48

49

70

31

32

33

34

36

35

39

37 38 40

41

42 43

63

F3

F2

F1

F7

F6

F5

F4


Subbus1

Subbus2

Subbus3

T1

T3

T5

Main

feeder

Main

feeder

Main

feeder

T2

T4

T6








downstream loads







Improvement

Page | 162

300

350

400

450

4

45

5

55

6

x 104

08

09

1

11

12

13

14

15


SA

IDI

(hrs

custo

mer

yr)


Number

of load

points


(kW)

Q

(kVAr)

Number of

customers

4 1-2 9-10 residential 545 51775 220

6 3-5 13-15 residential 500 475 200

12 6-7 16-17 23-25 28 30-

31 37-38


6 8 11 18 26 32-33 industrial 1500 1425 1

10 12 19-22 27 29 34-36 industrial 1000 950 1













Improvement

Page | 163




Mean

38074 48139 09975

Standard deviation

3431 5291 01165













(hrscustomeryr)


Minimum Loss

32142 46404 13090 68 69 70 71

Minimum ECOST

35409 41145 10586 10 17 41 70

Minimum SAIDI

43523 57891 08253 7 26 54 69






Improvement

Page | 164














compromise

solution

Feeder

loss

(kW)

ECOST

($yr)

SAIDI

(hrscustomeryr) 1205961 1205962 1205963

1 10 10 10 10 41 69 70 34033 41553 10996

2 10 1 1 68 69 70 71 32142 46404 13090

3 1 10 1 10 17 41 70 35409 41145 10586

4 1 1 10 7 26 54 69 43523 57891 08253

5 10 10 1 10 41 69 70 34033 41553 10996

6 10 1 10 10 54 69 71 34759 46644 10217

7 1 10 10 7 17 41 70 40368 43329 09570

86 Summary










Improvement

Page | 165














Page | 166

CHAPTER 9





BALANCING

91 Introduction













Page | 167















groups














Page | 168

0

1












respectively








9-1




120572119871

119871119874119878119878119898119894119899 119871119874119878119878119900119903119894 119871119874119878119878



Page | 169

0

1

120572119871 =

1 119871119874119878119878 le 119871119874119878119878119898119894119899119871119874119878119878119900119903119894minus119871119874119878119878

119871119874119878119878119900119903119894minus119871119874119878119878119898119894119899119871119874119878119878119898119894119899 lt 119871119874119878119878 lt 119871119874119878119878119900119903119894

0 119871119874119878119878 ge 119871119874119878119878119900119903119894

(9-2)














120572119881 =

1 119881119863 le 119881119863119898119894119899119881119863119900119903119894minus119881119863

119881119863119900119903119894minus119881119863119898119894119899119881119863119898119894119899 lt 119881119863 lt 119881119863119900119903119894

0 119881119863 ge 119881119863119900119903119894

(9-3)



120572119881

119881119863119898119894119899 119881119863119900119903119894 119881119863



Page | 170

0

1



119871119861119868 = 119881119886119903[1198681

1198681119898119886119909

1198682

1198682119898119886119909 hellip

119868119894

119868119894119898119886119909 hellip

119868119899

119868119899119898119886119909] (9-4)




120572119861 =

1 119871119861119868 le 119871119861119868119898119894119899119871119861119868119900119903119894minus119871119861119868

119871119861119868119900119903119894minus119871119861119868119898119894119899119871119861119868119898119894119899 lt 119871119861119868 lt 119871119861119868119900119903119894

0 119871119861119868 ge 119871119861119868119900119903119894

(9-5)





Optimality


of the vector

119865(119866) = [1198911(119866)1198912(119866)1198913(119866)]119879 (9-6)




120572119861

119871119861119868119898119894119899 119871119861119868119900119903119894 119871119861119868



Page | 171



Domain



























Page | 172








simultaneously





B4 in detail

941 33-bus System







Case I base case






Page | 173

10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

18 19 20 21

22 23 24

25 26 27 28 29 30 31 32


L18

L19 L20 L21

L22

L23 L24

L25

L26 L27 L28 L29 L30 L31 L32

L33

L34

L35

L36

L37









Fig 9-4



(kW)

Maximum node

voltage deviation

(pu)

Feeder Load

balancing index

Tie-switches

location

08734 14310 00625 00270 6 9 14 32 37







Page | 174

120140

160180

200220

006

008

01

012

014

016

0022

0024

0026

0028

003

0032

0034

0036


Feeder

load b

ala

ncin

g index




deviation (pu)


Mean

15499 00815 00256

Standard deviation

1549 00194 00023











Page | 175

10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

18 19 20 21

22 23 24

25 26 27 28 29 30 31 32


L18

L19 L20 L21

L22

L23 L24

L25

L26 L27 L28 L29 L30 L31 L32

L33

L34

L35

L36

L37

DG2

DG1

DG3







index


Minimum Loss

13981 00639 00280 7 9 14 32 37


14026 00604 00310 7 9 14 28 32


20248 01309 00223 7 30 34 35 37














Page | 176

110120

130140

150160

170

004

006

008

01

0120018

002

0022

0024

0026

0028

003


Feeder

load b

ala

ncin

g index



(kW)

Maximum node

voltage deviation

(pu)

Feeder Load

balancing index

Tie-switches

location

08590 12405 00594 00230 6 8 14 32 37







deviation (pu)


Mean

12850 00711 00231

Standard deviation

1003 00166 00029



Page | 177

















index


Minimum Loss

11753 00643 00241 7 9 14 28 31


12592 00567 00265 6 8 14 28 32


16419 01139 00189 7 21 30 35 37









locations



Page | 178

10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

18 19 20 21

22 23 24

25 26 27 28 29 30 31 32


L18

L19 L20 L21

L22

L23 L24

L25

L26 L27 L28 L29 L30 L31 L32

L33

L34

L35

L36

L37

DG1

DG3

DG2

100110

120130

140150

160

004

006

008

01

012

0016

0018

002

0022

0024

0026

0028


Feeder

load b

ala

ncin

g index


in Case IV

Objective

function

Feeder loss

(kW)

Maximum node

voltage

deviation (pu)

Feeder Load

balancing

index

Tie-switches

location

DGs location

08961 10878 00499 00232 7 9 14 36 37 B32 B32 B32









Page | 179




deviation (pu)


Mean

13295 00873 00194

Standard deviation

1354 00179 00019
















voltage deviation

(pu)

Feeder Load

balancing index

Tie-switches

location

DGs location

Minimum Loss

10844 00538 00228 7 9 14 32 37 B30 B31 B31


11020 00490 00259 7 9 14 28 36 B31 B31 B32


15443 01090 00178 7 30 34 35 37 B8 B9 B12



Page | 180

10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

27

28

29

30

31 32 33 34

35

36

37

38 39 40 41 42 43 44 45

46 47 48 49

50

51

52

53 54 55 56 57 58 59 60 61 62 63 64

65 66

67 68


L27

L28

L29

L30

L31 L32 L33 L34

L35

L36

L37

L38 L39 L40 L41 L42 L43 L44 L45

L46

L47 L48 L49

L50

L51

L52

L53 L54 L55 L56 L57 L58 L59 L60 L61 L62 L63 L64

L65

L66

L67

L68

L69

L70

L71

L72L73

942 69-bus System







respectively

Case I base case















Page | 181

80

100

120

140

160

005

006

007

0080016

0018

002

0022

0024

0026

0028


Feeder

load b

ala

ncin

g index



(kW)

Maximum node

voltage deviation

(pu)

Feeder Load

balancing index

Tie-switches

location

09676 9885 00524 00195 14 55 61 71 72








deviation (pu)


Mean

12535 00605 00192

Standard deviation

2458 00085 00028



Page | 182











initial case





index


Minimum Loss

9885 00524 00195 14 55 61 71 72


10535 00523 00242 9 14 55 61 71


15051 00701 00161 14 61 69 71 72













Page | 183

10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

27

28

29

30

31 32 33 34

35

36

37

38 39 40 41 42 43 44 45

46 47 48 49

50

51

52

53 54 55 56 57 58 59 60 61 62 63 64

65 66

67 68


L27

L28

L29

L30

L31 L32 L33 L34

L35

L36

L37

L38 L39 L40 L41 L42 L43 L44 L45

L46

L47 L48 L49

L50

L51

L52

L53 L54 L55 L56 L57 L58 L59 L60 L61 L62 L63 L64

L65

L66

L67

L68

L69

L70

L71

L72L73

DG3

DG1

DG2

8090

100110

120130

140

005

006

007

008

0014

0016

0018

002

0022

0024


Feeder

load b

ala

ncin

g index



(kW)

Maximum node

voltage deviation

(pu)

Feeder Load

balancing index

Tie-switches

location

08829 8758 00523 00174 14 55 61 71 72







Page | 184





deviation (pu)


Mean

10707 00576 00183

Standard deviation

2042 00071 00029

















index


Minimum Loss

8758 00523 00174 13 55 61 71 72


9729 00522 00226 7 12 55 61 71


13686 00681 00147 11 61 69 71 72



Page | 185

10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

27

28

29

30

31 32 33 34

35

36

37

38 39 40 41 42 43 44 45

46 47 48 49

50

51

52

53 54 55 56 57 58 59 60 61 62 63 64

65 66

67 68


L27

L28

L29

L30

L31 L32 L33 L34

L35

L36

L37

L38 L39 L40 L41 L42 L43 L44 L45

L46

L47 L48 L49

L50

L51

L52

L53 L54 L55 L56 L57 L58 L59 L60 L61 L62 L63 L64

L65

L66

L67

L68

L69

L70

L71

L72L73

DG3DG1

DG2









ACO algorithm


system in Case IV

Objective

function

Feeder loss

(kW)

Maximum

node voltage

deviation (pu)

Feeder Load

balancing

index

Tie-switches

location

DGs location

08882 7397 00429 00158 14 55 61 71 72 B60 B60 B60





9-17



Page | 186

70

80

90

100

110

120

004

0045

005

0055

006

0012

0013

0014

0015

0016

0017

0018

0019


Feeder

load b

ala

ncin

g index




deviation (pu)


Mean

9872 00520 00147

Standard deviation

1491 00055 00013













Page | 187






voltage deviation

(pu)

Feeder Load

balancing index

Tie-switches

location

DGs location

Minimum Loss

7397 00429 00158 14 55 61 71 72 B60 B60 B60


8032 00428 00183 11 55 61 71 72 B60 B60 B60


10962 00577 00125 14 63 69 71 72 B62 B62 B62

95 Summary


















Page | 188





Page | 189

CHAPTER 10


101 Conclusion








results





cost







Page | 190


































Page | 191




























demand times







Page | 192














SAIDI




















Page | 193



102 Future Work












supply each feeder














load on feeders


Page | 194





























Page | 195

References




2001



2015




2 pp 15ndash22 2015








2010

















References

Page | 196

2012






vol 63 pp 461ndash472 2014






652ndash660 2009



pp 1878ndash1887 2010



6 no 2 pp 182ndash197 2002














York 1986



pp 2157ndash2165 2015


1994



References

Page | 197


2016










62ndash66




Wiley 1990




170ndash180 2013






2006 pp 4ndash6















pp 2290ndash2293

References

Page | 198









pp 1217ndash1223 1988










42 2002























References

Page | 199



1530 2009




937ndash940 2008












pp 4021ndash4028 2011



2006








129ndash142 2015









no 1 pp 268ndash276 2009



References

Page | 200




2002





pp 1ndash6


















58 pp 537ndash547 2016





1048ndash1062 2016




2016




686ndash690 2003

References

Page | 201









2473ndash2480 2007







2010







22 no 3 pp 1101ndash1111 2007




388ndash397 2015







of Manchester 2015




1 pp 1ndash13 1996




References

Page | 202



pp 861ndash875 2012






2004












251 2002









Cable 2012






1677ndash1685 2015



2 pp 1401ndash1407 1989



References

Page | 203

no 2 pp 1492ndash1498 1989




pp 1ndash9 2012




932ndash942 2015


Sons 2004














vol 54 pp 255ndash267 2014



119ndash126 2011

Page | 204







Sectional

Area

(CSA)

Positive sequence

Z

Zero-phase

sequence

Z

Approximate

Capacitance

C



A Nexans

635011000

Volt Triplex

Cable

185 0415 0112 0988 0236 036

B 95 0220 0012 0530 0102 028


Page | 205

A2 33-bus system


Branch

number

Sending end

node

Receiving end

node

R

(Ω)

X

(Ω)

P at receiving

end (kW)

Q at receiving

end (kVAr)

1 0 1 00922 0047 100 60

2 1 2 04930 02511 90 40

3 2 3 03660 01864 120 80

4 3 4 03811 01941 60 30

5 4 5 08190 07070 60 20

6 5 6 01872 06188 200 100

7 6 7 07114 02351 200 100

8 7 8 10300 07400 60 20

9 8 9 10440 07400 60 20

10 9 10 01966 00650 45 30

11 10 11 03744 01238 60 35

12 11 12 14680 11550 60 35

13 12 13 05416 07129 120 80

14 13 14 05910 05260 60 10

15 14 15 07463 05450 60 20

16 15 16 12890 17210 60 20

17 16 17 03720 05740 90 40

18 17 18 01640 01565 90 40

19 18 19 15042 13554 90 40

20 19 20 04095 04784 90 40

21 20 21 07089 09373 90 40

22 21 22 04512 03083 90 50

23 22 23 08980 07091 420 200

24 23 24 08960 07011 420 200

25 24 25 02030 01034 60 25

26 25 26 02842 01447 60 25

27 26 27 10590 09337 60 20

28 27 28 08042 07006 120 70

29 28 29 05075 02585 200 600

30 29 30 09744 09630 150 70

31 30 31 03105 03619 210 100

32 31 32 03410 05362 60 40

33 7 20 2 2 -- --

34 11 21 2 2 -- --

35 8 14 2 2 -- --

36 17 32 05 05 -- --

37 24 28 05 05 -- --


Page | 206

A3 69-bus system


Branch

number

Sending end

node

Receiving end

node

R

(Ω)

X

(Ω)

P at receiving

end (kW)

Q at receiving

end (kVAr)

1 0 1 00005 00012 0 0

2 1 2 00005 00012 0 0

3 2 3 00015 00036 0 0

4 3 4 00251 00294 0 0

5 4 5 0366 01864 26 22

6 5 6 0381 01941 404 30

7 6 7 00922 0047 75 54

8 7 8 00493 00251 30 22

9 8 9 0819 02707 28 19

10 9 10 01872 00619 145 104

11 10 11 07114 02351 145 104

12 11 12 103 034 8 5

13 12 13 1044 0345 8 55

14 13 14 1058 03496 0 0

15 14 15 01966 0065 455 30

16 15 16 03744 01238 60 35

17 16 17 00047 00016 60 35

18 17 18 03276 01083 0 0

19 18 19 02106 0069 1 06

20 19 20 03416 01129 114 81

21 20 21 0014 00046 5 35

22 21 22 01591 00526 0 0

23 22 23 03463 01145 28 20

24 23 24 07488 02475 0 0

25 24 25 03089 01021 14 10

26 25 26 01732 00572 14 10

27 26 27 00044 00108 26 186

28 27 28 0064 01565 26 186

29 28 29 03978 01315 0 0

30 29 30 00702 00232 0 0

31 30 31 0351 0116 0 0

32 31 32 0839 02816 14 10

33 32 33 1708 05646 195 14

34 33 34 1474 04873 6 4

35 34 35 00044 00108 26 1855

36 35 36 0064 01565 26 1855

37 36 37 01053 0123 0 0

38 37 38 00304 00355 24 17

39 38 39 00018 00021 24 17

40 39 40 07283 08509 12 1

41 40 41 031 03623 0 0


Page | 207

42 41 42 0041 00478 6 43

43 42 43 00092 00116 0 0

44 43 44 01089 01373 3922 263

45 44 45 00009 00012 3922 263

46 45 46 00034 00084 0 0

47 46 47 00851 02083 79 564

48 47 48 02898 07091 3847 2745

49 48 49 00822 02011 3847 2745

50 49 50 00928 00473 405 283

51 50 51 03319 01114 36 27

52 51 52 0174 00886 435 35

53 52 53 0203 01034 264 19

54 53 54 02842 01447 24 172

55 54 55 02813 01433 0 0

56 55 56 159 05337 0 0

57 56 57 07837 0263 0 0

58 57 58 03042 01006 100 72

59 58 59 03861 01172 0 0

60 59 60 05075 02585 1244 888

61 60 61 00974 00496 32 23

62 61 62 0145 00738 0 0

63 62 63 07105 03619 227 162

64 63 64 1041 05302 59 42

65 64 65 02012 00611 18 13

66 65 66 00047 00014 18 13

67 66 67 07394 02444 28 20

68 67 68 00047 00016 28 20

69 49 58 2 1 -- --

70 26 64 1 05 -- --

71 12 20 05 05 -- --

72 10 42 05 05 -- --

73 14 45 1 05 -- --



Feeder

Type

Length

(km)


1 060 2 6 10 14 17 21 25 28 30 34 38 41 43 46 49 51 55 58 61 64 67

68 69 70 71

2 075 1 4 7 9 12 16 19 22 24 27 29 32 3537 40 42 45 48 50 53 56 60

63 65

3 080 3 5 8 11 13 15 18 20 23 26 31 33 36 3944 47 52 54 57 59 62 66


Page | 208



Lines 004 0 0 0 5 0

Buses 0001 0 1 001 2 8

Switches 0004 0002 1 006 4 72








Page | 209










0000 TW5 0400 TW5 0800 TW1 1200 TW5 1600 TW1 2000 TW5

0010 TW5 0410 TW5 0810 TW1 1210 TW5 1610 TW1 2010 TW5

0020 TW5 0420 TW5 0820 TW1 1220 TW5 1620 TW1 2020 TW5

0030 TW5 0430 TW5 0830 TW1 1230 TW5 1630 TW1 2030 TW5

0040 TW5 0440 TW5 0840 TW1 1240 TW5 1640 TW5 2040 TW5

0050 TW5 0450 TW5 0850 TW1 1250 TW5 1650 TW5 2050 TW5

0100 TW5 0500 TW5 0900 TW1 1300 TW5 1700 TW5 2100 TW5

0110 TW5 0510 TW5 0910 TW1 1310 TW5 1710 TW5 2110 TW5

0120 TW5 0520 TW5 0920 TW1 1320 TW5 1720 TW5 2120 TW5

0130 TW5 0530 TW5 0930 TW1 1330 TW5 1730 TW5 2130 TW5

0140 TW5 0540 TW5 0940 TW1 1340 TW5 1740 TW5 2140 TW5

0150 TW5 0550 TW5 0950 TW1 1350 TW5 1750 TW5 2150 TW5

0200 TW5 0600 TW5 1000 TW1 1400 TW5 1800 TW5 2200 TW5

0210 TW5 0610 TW5 1010 TW5 1410 TW5 1810 TW5 2210 TW5

0220 TW5 0620 TW5 1020 TW5 1420 TW5 1820 TW5 2220 TW5

0230 TW5 0630 TW5 1030 TW5 1430 TW5 1830 TW5 2230 TW5

0240 TW5 0640 TW5 1040 TW5 1440 TW5 1840 TW5 2240 TW5

0250 TW5 0650 TW5 1050 TW5 1450 TW5 1850 TW5 2250 TW5

0300 TW5 0700 TW5 1100 TW5 1500 TW5 1900 TW5 2300 TW5

0310 TW5 0710 TW5 1110 TW5 1510 TW5 1910 TW5 2310 TW5

0320 TW5 0720 TW5 1120 TW5 1520 TW5 1920 TW5 2320 TW5

0330 TW5 0730 TW1 1130 TW5 1530 TW5 1930 TW5 2330 TW5

0340 TW5 0740 TW1 1140 TW5 1540 TW5 1940 TW5 2340 TW5

0350 TW5 0750 TW1 1150 TW5 1550 TW5 1950 TW5 2350 TW5


Page | 210



corresponding 95th


B-2 and Table B-3


Node

No

Scenarios

S1 S2 S3 S4 S5 S6 S7 S8 S9

A4_1 09675 09787 09787 09766 09859 09859 09748 09825 09815

A4_2 09676 09784 09784 09766 09856 09856 09748 09822 09813

A4_3 09677 09782 09782 09767 09854 09854 09749 09819 09811

A4_4 09678 09780 09780 09768 09851 09851 09750 09817 09810

A4_5 09681 09777 09777 09771 09849 09849 09753 09814 09808

A4_6 09685 09775 09775 09775 09846 09846 09757 09812 09807

A4_7 09689 09773 09773 09779 09845 09845 09762 09811 09807

A4_8 09694 09772 09772 09784 09844 09844 09767 09810 09807

B4_8 09700 09772 09772 09790 09844 09844 09773 09810 09808

B4_7 09707 09773 09773 09797 09845 09845 09779 09811 09810

B4_6 09714 09775 09775 09804 09846 09846 09787 09812 09813

B4_5 09722 09777 09777 09813 09849 09849 09795 09814 09816

B4_4 09731 09780 09780 09821 09851 09851 09804 09817 09820

B4_3 09737 09782 09782 09827 09854 09854 09809 09819 09823

B4_2 09743 09784 09784 09833 09856 09856 09815 09822 09826

B4_1 09749 09787 09787 09839 09859 09859 09821 09825 09830

Table B-3 95th


Node

No

Scenarios

S1 S2 S3 S4 S5 S6 S7 S8 S9

A4_1 09352 09573 09573 09537 09721 09721 09537 09721 09715

A4_2 09353 09567 09567 09537 09715 09715 09537 09715 09709

A4_3 09355 09562 09562 09539 09711 09711 09539 09711 09704

A4_4 09357 09558 09558 09541 09707 09707 09541 09707 09702

A4_5 09363 09553 09553 09547 09701 09701 09547 09701 09679

A4_6 09370 09548 09548 09555 09697 09697 09555 09697 09694

A4_7 09379 09545 09545 09563 09694 09694 09563 09794 09691

A4_8 09389 09544 09544 09573 09692 09692 09573 09792 09692

B4_8 09400 09544 09544 09585 09692 09692 09585 09792 09692

B4_7 09413 09545 09545 09598 09694 09694 09598 09794 09694

B4_6 09427 09548 09548 09613 09697 09697 09613 09697 09697

B4_5 09443 09553 09553 09628 09701 09701 09628 09701 09701

B4_4 09460 09558 09558 09646 09707 09707 09646 09707 09707


Page | 211

B4_3 09471 09562 09562 09656 09711 09711 09656 09711 09711

B4_2 09482 09567 09567 09668 09715 09715 09668 09715 09715

B4_1 09494 09573 09573 09680 09721 09721 09680 09721 09721







1 1227 1189 1010 1003

2 5192 2686 2051 2060

3 1995 756 112 490

4 1874 667 074 415

5 3833 1321 122 807

6 192 006 006 006

7 484 0 0 0

8 418 124 211 124

9 357 0 0 0

10 055 001 001 001

11 088 003 003 003

12 267 045 045 045

13 073 008 008 008

14 036 0 0 0

15 028 045 092 045

16 025 048 115 048

17 003 007 022 007

18 016 226 232 226

19 083 1809 1859 1808

20 01 424 436 423

21 004 118 071 118

22 319 316 914 315

23 516 512 1618 510

24 129 128 869 128

25 26 224 005 124

26 334 285 003 155

27 1133 962 003 510

28 786 664 0 345

29 391 326 199 159

30 160 110 018 003


Page | 212

31 021 012 0 000

32 001 0 013 0

33 0 563 809 563

34 0 215 215 215

35 0 174 320 174

36 0 002 033 002

37 0 0 263 0

Total 20314 13981 11753 10844




1 008 007 006 006

2 008 007 006 006

3 020 012 012 010

4 194 011 011 011

5 2829 159 155 159

6 2939 164 160 164

7 691 035 034 035

8 338 012 012 012

9 477 143 137 142

10 101 029 027 028

11 219 032 030 032

12 128 000 000 000

13 124 000 0 000

14 120 0 000 0

15 022 083 043 083

16 032 138 067 138

17 000 001 001 001

18 010 080 032 080

19 007 052 021 052

20 011 083 033 083

21 000 003 001 002

22 001 022 006 022

23 001 049 013 049

24 001 091 021 091

25 000 037 009 037

26 000 019 004 019

27 000 000 000 000

28 000 000 000 000

29 001 001 001 001

30 000 000 000 000

31 001 001 001 001


Page | 213

32 001 001 001 001

33 001 001 001 001

34 000 000 000 000

35 000 003 001 003

36 001 041 019 041

37 002 064 028 064

38 000 018 008 018

39 000 001 000 001

40 005 391 161 391

41 002 166 068 166

42 000 022 009 022

43 000 005 002 005

44 001 057 023 057

45 000 000 000 000

46 002 017 017 013

47 058 416 416 316

48 164 1321 1321 991

49 012 253 253 178

50 000 000 000 000

51 000 000 000 000

52 580 001 001 001

53 673 001 001 000

54 916 000 000 000

55 882 0 0 0

56 4986 000 000 000

57 2458 000 000 000

58 954 000 000 000

59 1071 627 626 379

60 1408 824 823 498

61 011 0 0 0

62 014 000 000 000

63 066 001 001 001

64 004 071 069 071

65 000 000 000 000

66 000 000 000 000

67 002 002 002 002

68 000 000 000 000

69 0 3783 3782 2384

70 0 102 052 102

71 0 0 0 0

72 0 0 0 0

73 0 423 252 423

Total 22562 9885 8758 7397


Page | 214




(hrscustomeryr)

70 68 71 69 321415 4640359 130895231648616

70 10 41 54 364131 431068083000 102819629963899

17 10 41 70 354092 411445783000000 105858799638989

17 26 10 70 383269 530285525000000 0968805806257521

7 26 54 69 435225 578907612000000 0825265794223827

7 54 41 69 406035 460067870000000 0915047984356197

7 26 54 70 442913 571756512000000 0836828971119134

17 10 71 70 345231 439663189000000 106361687725632

70 10 71 69 331470 443747189000000 110465057160048

70 10 41 69 340330 415529783000000 109962169073406

70 68 41 69 330274 435818516000000 130392343561974

7 54 71 69 397170 488285276000000 0920076865222623

41 10 54 69 356448 438219183000000 101663312274368

70 10 54 26 393311 549907825000000 0938414109506619

70 7 71 69 381047 465595876000000 100306543321300

70 7 41 17 403678 433294470000000 0957002858002407

70 10 54 71 355269 459285489000000 103322518050542

7 54 71 70 404856 481134176000000 0931640042117930

7 26 17 70 432867 552134212000000 0867220667870036

7 70 41 69 389911 437378470000000 0998036552346570

7 26 69 70 419096 556218212000000 0908254362214200

17 7 71 70 394813 461511876000000 0962031738868833

71 10 54 69 347586 466436589000000 102166200361011

10 26 54 69 385625 557058925000000 0926850932611312

70 26 10 69 369504 534369525000000 100983950060168

7 54 41 70 413721 452916770000000 0926611161251504


Page | 215





(kW)

Maximum node

Voltage deviation

Feeder load

balancing index

7 34 35 31 37 176962 0108696024464801 00228687361961248

7 11 35 32 28 143474 00613272038422790 00305387759787611

7 9 14 31 37 142477 00768537372742428 00252628392269486

6 8 12 36 37 151849 00696765908940439 00259144961258893

7 8 14 31 37 155399 00924077518455773 00239781364880477

6 8 12 31 37 169382 0104485611067200 00236077543160956

6 8 12 32 37 152876 00776641110366926 00250547432924683

33 8 14 30 37 171441 0108063061643879 00230652089068052

7 9 14 32 28 140261 00604355611623940 00310349101268755

7 11 35 32 37 143028 00639069227083702 00273727965037185

6 8 14 31 37 159752 00968913958755809 00236540473688646

6 33 35 32 37 170278 00826562726566354 00249194843739843

6 11 35 32 37 144683 00656445815841987 00261947314082027

6 8 14 32 37 146983 00705648561488426 00256096967694280

7 9 14 32 37 139815 00639015456844128 00280407351785895

6 9 14 32 37 143097 00625183468485540 00270001779728268

7 11 35 31 37 148829 00852978398065017 00245113845932977

7 34 35 30 37 202483 0130888991378581 00223050578905545

6 8 14 36 37 146991 00643933147100736 00266176555168500

6 11 35 31 37 154281 00897759906819439 00242838273201709

6 8 13 32 37 150430 00753226918458818 00253604605496161




(kW)

Maximum node

Voltage deviation

Feeder load

balancing index

7 14 8 32 28 121696 00575193535569366 00264544805354717

7 11 35 31 37 123007 00712785797883380 00213250141648472

6 12 8 32 37 128324 00630309398395457 00223824361844486

6 14 8 30 37 145672 0101299721228755 00194921779245086

7 33 35 32 28 130184 00583420082867310 00261406698684195

7 14 8 30 37 140274 00967924815464314 00195001911353607

7 21 35 30 37 164190 0113945920950777 00189031534924873

6 13 8 32 37 126434 00607661484850486 00227035446761735

7 14 9 32 28 117726 00575130414815478 00271215548731366


Page | 216

6 14 8 32 28 125920 00566904604559002 00265195832133384

6 12 8 31 37 137974 00889877482038002 00200083704114662

7 11 35 30 37 133030 00891516445489180 00199682922816912

6 11 35 32 37 123013 00593840879899440 00235298833627789

7 14 9 32 37 121070 00631040005210335 00255168322432724

6 14 9 32 28 123916 00566872316455769 00273594084038335

7 14 9 30 37 126587 00812324184971598 00206873922472966

7 14 9 31 28 117529 00642736861104275 00240537048868074

6 14 9 32 37 122047 00593825021727904 00240927348267257

6 11 35 32 28 124883 00566888115014094 00269082055980326

6 11 35 31 37 126802 00756552348586014 00207586957663036

6 14 8 32 37 124050 00593857418451058 00230337877365745

7 13 8 32 28 124039 00575225874614865 00262247242500743

7 11 35 32 28 119522 00575159230231156 00267430211390231

7 14 9 31 37 118759 00642740886891275 00220228862077971

6 14 8 31 37 130316 00816654599427028 00201908840890301

33 14 8 30 37 140110 00923831702765571 00197570883486903

7 12 8 32 28 125895 00587758838819431 00259864524009700

6 13 8 31 37 134936 00865715938530326 00201790772057552




loss

(kW)

Maximum node

Voltage deviation

Feeder load

balancing index

7 9 14 30 37 15 17 16 112506 00655990339384582 00207847799664288

6 8 14 31 37 14 11 15 120818 00728143829651942 00199639595336255

7 11 35 30 37 16 16 12 118637 00756705031931788 00198888055963062

6 8 14 31 37 11 29 14 125736 00822955381260978 00194988443664523

6 11 35 32 37 29 11 29 116999 00602917954784902 00213598898907595

7 9 14 31 37 15 14 16 110931 00518306996442978 00223689972435171

7 34 35 30 37 16 13 13 140652 00983575865184194 00182688360250883

7 8 14 30 37 14 11 15 128617 00876913785424229 00190954012999288

7 8 14 30 37 11 16 14 127141 00860397262006276 00191601352391895

7 9 14 36 37 30 30 29 109157 00520335391274761 00229564125698243

7 8 14 30 37 10 14 16 126706 00857230143750372 00192117850059117

7 11 35 30 37 13 16 12 121130 00786215737441328 00196617519208137

7 34 35 30 37 13 10 9 151352 0106960621828031 00178195736666725

7 34 35 30 37 10 12 9 152310 0107688512235453 00178046268710843

6 8 14 30 37 11 15 16 130550 00897068798318073 00189590122249633

6 8 14 30 37 16 14 10 130869 00901533044670202 00189271311922809

7 34 35 30 37 10 13 12 148089 0104837492639545 00178736074180585


Page | 217

7 34 35 30 37 13 11 16 143317 0100615335666250 00181553323058751

6 8 14 30 37 10 14 14 133299 00925968739633617 00188139999335965

7 34 35 30 37 13 9 12 148392 0105013682219175 00178453713901855

6 8 14 30 37 14 11 10 137593 00963962506644021 00186232592604301

6 8 14 30 37 11 8 14 136046 00951731865531927 00187106569470356

6 8 14 30 37 11 11 16 135639 00942616575802945 00187170876179048

7 8 14 30 37 15 16 14 122935 00815907052491111 00195198923102276

7 34 35 30 37 12 14 16 140640 00983915740315128 00182784576692257

6 33 35 31 37 11 11 13 146017 00888852225316270 00188548348595259

7 34 35 30 37 12 16 12 142144 00997534014352579 00181578155086060

6 8 14 30 37 14 11 15 132819 00921338781311946 00188143081376993

6 8 14 30 37 10 15 11 136651 00956093119043262 00186781475357014

7 9 14 31 37 14 14 16 111382 00525319705640723 00222591386298574

7 34 35 30 37 13 14 16 139957 00977014014811679 00183484070331887

7 34 35 30 37 12 15 16 139849 00976123852270839 00183745698300515

7 34 35 30 37 12 16 16 138589 00959671533698319 00184842191427931

7 34 35 30 37 16 13 16 137912 00952795751906571 00185525366651277

6 33 35 31 37 11 11 11 148785 00910856464605774 00187751047204272

7 34 35 30 37 12 16 13 141338 00990484927061306 00181980491991251

7 34 35 30 37 12 13 12 145536 0102926179499332 00179590185768212

6 8 14 30 37 14 10 15 132373 00918145642214576 00188660639598312

6 8 14 30 37 16 11 14 131312 00904718190224125 00188759872087077

7 34 35 30 37 13 15 16 139168 00969230570394858 00184436609617936

7 34 35 30 37 13 9 11 150730 0106620666560267 00178315514588942

6 8 14 30 37 14 11 14 133746 00929165522686308 00187615074100094

7 34 35 30 37 9 9 12 152656 0107867658396772 00178031242058681

6 8 14 30 37 10 11 16 135118 00939381882085281 00187414815201857

7 34 35 30 37 12 12 9 149341 0105739135263959 00178316539838164

7 9 14 36 28 32 32 32 110385 00489797931328652 00256323647901629

7 9 14 36 37 32 31 31 108599 00498935433820196 00235262740306846

7 9 14 32 37 31 30 31 108436 00537552050723257 00227898958267559

7 9 14 36 28 32 31 31 110203 00489682960875768 00259015702487973

7 34 35 30 37 8 12 9 154427 0108962750550623 00178021823053241


Page | 218




(kW)

Maximum node

Voltage deviation

Feeder load

balancing index

55 61 71 72 12 99036 00524391619987274 00196366946903149

69 61 71 9 14 145213 00664127006601768 00185315761508749

55 61 71 72 14 98845 00524393494628415 00194882148961848

69 70 71 10 14 145135 00666490251240782 00182871906896542

69 61 71 72 12 150267 00699556148777123 00161708619074924

55 61 71 10 14 104521 00524349487665904 00238104755589364

69 61 71 72 13 150383 00700225094171628 00161512783956020

55 61 71 72 13 98937 00524392488739880 00195710324132613

69 61 71 72 11 150792 00682108082577803 00171029450547815

55 61 71 9 14 105348 00524349082167884 00242117051986541

69 61 71 72 14 150513 00700911373758199 00161129748303495

55 61 71 72 11 105195 00524380932334678 00218572363716938




(kW)

Maximum node

Voltage deviation

Feeder load

balancing index

55 61 12 14 9 97461 00523081449765275 00226112450860475

69 61 71 14 9 130761 00662843002557533 00155527078006889

55 61 71 14 7 97263 00523080911134007 00226177446060770

55 61 12 71 72 87588 00523152959484715 00174558059214037

55 61 71 14 8 93176 00523082195004728 00211109499855264

55 61 71 13 72 87581 00523154440245970 00174392153380541

55 61 12 14 72 87755 00523153511186373 00174538759436512

55 61 12 71 7 97289 00523080869366065 00226232791264600

69 61 71 11 9 134009 00662855052002667 00154463391981039

69 61 12 14 9 130989 00662843776081034 00155381836375260

55 61 71 13 7 97273 00523080879708534 00227249951330579

55 61 71 14 9 90907 00523086904216601 00201865894567423

55 61 71 14 10 90291 00523088955157064 00199034032147027

69 61 71 14 10 130894 00665207578684145 00154263271797149

55 61 71 14 72 87582 00523156072908145 00174100597226583

69 61 71 11 10 134197 00665220013747228 00153401360203180

69 61 71 11 72 136858 00680828895070073 00147368269784675

69 61 12 14 10 131126 00665208386694061 00154135530565384

55 61 71 11 72 91274 00523126048676607 00184393848480773


Page | 219




loss

(kW)

Maximum node

Voltage deviation

Feeder load

balancing index

69 63 71 10 14 60 60 60 105879 00543213716422435 00153740505896722

69 63 12 72 71 60 62 62 109324 00575466375767690 00126779733811642

55 61 71 72 11 60 60 60 80324 00429183191505871 00183159151221229

69 63 12 72 71 61 61 62 109323 00575465740537586 00126842028893447

55 61 71 72 12 60 60 60 74165 00429193759769601 00159264876998350

69 63 14 10 71 62 62 62 106070 00543012249613587 00150279825984642

69 63 11 72 71 60 62 60 110547 00558290844078126 00139841427388105

69 63 14 9 71 62 62 62 106271 00540689205567605 00153025056850459

69 61 71 72 11 60 60 60 108838 00542584369620998 00141625735067141

55 61 71 72 14 60 56 60 75837 00436673338725839 00157367114339890

69 63 14 10 71 62 62 60 105960 00542966739560918 00151430448212008

69 61 71 10 14 60 60 60 104307 00527268149576859 00155323687715422

69 63 11 72 71 61 62 62 110652 00558333983851442 00137892112215884

69 63 13 72 71 62 62 62 109522 00576169823075075 00125440050970194

55 61 71 72 14 60 55 60 75975 00436701836501366 00156758120818947

69 63 71 10 14 60 60 62 105896 00542940500362948 00152768514567046

69 63 14 9 71 62 61 61 106159 00540643102892876 00154245882374843

55 61 71 72 13 60 60 60 74066 00429194617185072 00158554987038681

69 62 71 10 14 61 60 60 105886 00542959390978505 00153513700764165

69 63 14 72 71 62 62 62 109622 00576844280930477 00125002240983144

55 63 71 72 14 62 61 62 74382 00440379610790336 00155858821619573

69 63 71 72 11 60 60 60 110530 00558564471048234 00140822204796308

55 63 71 72 14 60 60 62 74285 00440350644694274 00157371695186626

55 63 14 72 71 62 62 62 74448 00440399072962552 00155438948075735

55 63 71 72 14 60 62 62 74344 00440368353288504 00156312863856681

69 63 71 9 14 60 61 60 105882 00542934725670071 00153515485666183

55 63 71 72 14 60 61 62 74305 00440356668532606 00156816031788752

55 61 20 72 13 60 60 60 80533 00429326269571468 00157463174391893

55 63 71 72 14 61 61 62 74343 00440367927398261 00156346520711234

69 61 71 72 14 60 60 60 107187 00561022028435777 00126909641069497

69 63 71 72 11 60 61 60 110533 00558285040786375 00140595150870697

69 63 12 72 71 62 62 62 109436 00575512407997617 00125707103016452

69 63 14 10 71 61 62 62 106000 00542983427485794 00150838099664421

69 63 11 72 71 60 61 62 110569 00558299818740340 00139149694834405

69 63 14 9 71 61 62 60 106118 00540626433897020 00154840963668230

69 61 71 72 12 60 60 60 107041 00559693311798567 00127785892138089

55 61 71 72 14 60 60 60 73974 00429195606297569 00157682511572302

69 63 14 10 71 61 61 62 105958 00542966109653011 00151492343922130

69 63 12 72 71 62 62 61 109365 00575483243249972 00126225992147273


Page | 220

69 63 11 72 71 62 62 60 110611 00558317226735644 00138490567525274

69 63 14 9 71 62 62 61 106201 00540660395254129 00153587525958041

69 63 14 10 71 61 60 62 105917 00542949434469265 00152083287358888

69 63 14 9 71 62 62 60 106160 00540643732226493 00154184014811756

69 63 11 72 71 61 61 62 110610 00558316590719640 00138552654427231

69 63 71 72 11 62 62 62 110723 00558362979744786 00137328015545176

69 61 71 72 13 60 60 60 107108 00560349171634668 00127435051911921

Page | 221


Algorithms



2amp3

Parameter Value

Number of ants 50







Parameter Value

Number of ants 100








operation

Parameter Value

Number of ants 150







Page | 222



Parameter Value

Number of ants 400







Parameter Value

Number of ants 500







Chapter 8


ECOST and SAIDI)

Parameter Value

Number of ants 100







Page | 223


ECOST and SAIDI)

Parameter Value







Chapter 9



Parameter Value

Number of ants 200








Parameter Value






Page | 224








9th











1-6 12-15 March 2018

Page | 5







751 Test Case 1 138

752 Test Case 2 147

753 Test Case 3 147

76 Summary 148

CHAPTER 8 150



81 Introduction 150









86 Summary 164

CHAPTER 9 166



BALANCING 166

91 Introduction 166








Page | 6




95 Summary 187

CHAPTER 10 189


101 Conclusion 189

102 Future Work 193

References 195





Word count 51012

Page | 7

List of Figures





34


















comparison 74






Fig 4-8 11 kV 4th




Page | 8

Fig 4-11 11 kV 4th


























117









Page | 9





136




13 142





problem 157


problem 158



162
















Page | 10

List of Tables













102












13 143




2 147


3 148

Page | 11



163




Case II 173


174



Case III 176


III 176





IV 179



in Case II 181


II 181



in Case III 183


III 184


184



Page | 12


IV 186


187


204







Table B-3 95th





SAIDI) 214

















Page | 13













Page | 14
























EV Electric Vehicle





HC Hyper Cube


HV High Voltage

Page | 15


LV Low Voltage




MV Medium Voltage









TS Tabu Search





Page | 16

Abstract





December 2017






















for optimal DA

Page | 17

Declaration




Page | 18

Copyright Statement










copies made








andor Reproductions










Page | 19

Acknowledgements









encouragement





and support

Page | 20

CHAPTER 1

INTRODUCTION

11 Motivation
















increase profits




Page | 21




during one week






























Page | 22





12 Objectives







ACO) algorithm


















Page | 23
































Page | 24




































Page | 25

































Page | 26

































Page | 27














for all studies

Page | 28

CHAPTER 2


21 Introduction
















Page | 29

Tie-switch





















Page | 30





231 Reclosers














trip




Recloser locks

out on 2nd

reclose

as programmed

Recloser opens

Recloser recloses

fault still present

Recloser recloses

fault still present

Recloser re-opens

fault still present

Load current


Page | 31










233 Tie-switches










241 Basic Concepts









Page | 32

Tran

sfo

rme

r Lo

ss


1 Transformer

2 Transformers



















119878119871




Page | 33








improvement
























Page | 34





(Kw)







(Kw)














Page | 35








Transformer Size

(kVA)

No load loss

(kW)

Load loss

(kW)

Capital

price (euro)

Cost of loss

(euro)

Total cost

(euro)

A 1000 11 9 9074 34211 43285

B 1000 094 76 11362 28986 40348


251 Basic Concepts









and opened



Page | 36


































Page | 37



































Page | 38




operations








261 Basic Concepts


















Page | 39






















Page | 40


1 2 3 4 5 6 7


1 2 3 4 5 6 7


1 2 3 4 5 6 7


1 2 3 4 5 6 7


CB1 opened



CB1 CB2

CB1CB2

CB1 CB2

CB1 CB2





Interrupted

load



Page | 41


1 2 3 4 5 6 7


1 2 3 4 5 6 7


1 2 3 4 5 6 7


1 2 3 4 5 6 7


CB1 opened



CB1 CB2

CB1CB2

CB1 CB2

CB1 CB2





Interrupted

load









Page | 42





























Page | 43









network unit [72]

Open-circuit test






Page | 44

(a) Test circuit









119875119874119862 = 119875ℎ+119890 =119880119874119862

2

119877119888119871119881= 119880119874119862119868ℎ+119890 (2-1)


current

Short-circuit test




119880119900119888

119868ℎ+119890 119868120601

119868119900119888 119885119890119902 119871119881

119877119888 119871119881 119883119898 119871119881


Page | 45




(a) Test circuit






and expressed as

119875119878119862 = 1198681198781198622 119877119890119902119867119881 (2-2)




119880119904119888

119868119890119909

119868119904119888 119877119890119902 119867119881 119883119890119902 119867119881

(119899119890119892119897119890119888119905)


Page | 46

Active power loss



∆119875 = 119875119874119862 + 1205732119875119878119862 (2-3)

where 120573 =119878119871




Reactive power loss



as

∆119876 = 119876119874119862 + 1205732119876119878119862 (2-4)

119876119874119862 = 119878119874119862 =119868119874119862

119868119873∙ 119878119873 (2-5)

119876119878119862 = 119878119878119862 = 119880119878119862

119880119873∙ 119878119873 (2-6)








1198791198711 = 11988002119875119885119874119862 +

1205732

11988002 119875119885119878119862 (2-7)

119875119885119874119862 = 119875119874119862 + 119870119876119876119874119862 (2-8)


Page | 47

119875119885119878119862 = 119875119878119862 + 119870119876119876119878119862 (2-9)


120573 =119878119871















1198791198712 = 211988002119875119885119874119862 +

1

2

1205732

11988002 119875119885119878119862 (2-10)







Page | 48




119875119887119877 + 119895119876119887119877 = 119887119877 times 119868lowast (2-11)

119875119887 = 1198681198872 times 119877119887 (2-12)


119875119887 =119875119887119877

2 +1198761198871198772

1198811198871198772 times 119877119887 (2-13)







119864119871 = sum 119875119887119899119873119887119899 (2-14)











Page | 49



120582 = sum 120582119895119895 (2-15)

119880 = sum 120582119895119895 119903119895 (2-16)

119903 =119880

120582 (2-17)


point





119878119860119868119865119868 =sum 120582119894119873119894119894

sum 119873119894119894 (2-18)

119878119860119868119863119868 =sum 119880119894119873119894119894

sum 119873119894119894 (2-19)

119860119864119873119878 =sum 119880119894119871119894119894

sum 119873119894119894 (2-20)

119864119862119874119878119879 = sum 119888119898(119889119898)119891119898119871119898119872119898=1 (2-21)











Page | 50




Simulation method












memory

Analytical method






(FMEA)










Page | 51











Normal operation

Active

failure

Transient

failure

Passive

failure

Maintenance

120582119860 120582119879 120582119875 120582119872

120583119860 120583119879 120583119875

120583119872


Page | 52

Start











Next failure i=i+1


End

No

Yes












Page | 53















after failure











Page | 54

0

1


















120572 =

1 119883 le 119883119898119894119899119883119898119886119909minus119883

119883119898119886119909minus119883119898119894119899119883119898119894119899 lt 119883 lt 119883119898119886119909

0 119883 ge 119883119898119886119909

(2-22)





120572

119883119898119894119899 119883119898119886119909 119883


Page | 55










119872119886119909 119869 = 12059611205721 + 12059621205722 + ⋯ + 120596119899120572119899 (2-23)







selected objectives






Max-min method




119872119886119909 119869 = min 1205721 1205722 hellip 120572119899 (2-24)




Page | 56











reconfiguration





119872119886119909 119869 = (1205721 ∙ 1205722 ∙ hellip ∙ 120572119873)1 119899frasl (2-25)







Framework








Page | 57



forall 119894 = 12 hellip 119873119900119887119895 119865119894(119883) le 119865119894(119884) (2-26)

exist 119894 = 12 hellip 119873119900119887119895 119865119894(119883) lt 119865119894(119884) (2-27)














preferences











Page | 58

211 Summary
































Page | 59













Page | 60

CHAPTER 3


31 Introduction


















Page | 61









search space [13]




35













follows [93]

119862 = 119875(119883 minus 119871 le 120583 le 119883 + 119871) = int 119866(119883)119889119909119883+119871

119883minus119871 (3-1)

119871 = 119911lowast 120590

radic119899 (3-2)


Page | 62







095


119862 09 095 099 0999

119911lowast 1645 1960 2576 3291


119899 = (119911lowast120590

119871)2 (3-3)
















Page | 63
























Page | 64

the nest






















Page | 65

Start

Set Iteration n=1

Maximum iteration

reached

End

No

Yes









n=n+1












Page | 66


































Page | 67

Start

Cloning

Maximum iteration

reached

End

No

Yes


Hypermutation

Fitness evaluation


Pheromone updating

n=n+1












Page | 68










tables [88]

















35 Summary





Page | 69


























Page | 70

CHAPTER 4





41 Introduction














Page | 71



























Section 46



Page | 72

42 Load Model



modelled








Number of people

in household

1 2 3 4 ge5

Percentage () 3058 341 1557 1288 686






weekend


12


dwelling





Page | 73










follows

Minimise 119891 = 1198800

2119875119885119874119862 +1205732

11988002 119875119885119878119862 119905119903119886119899119904119891119900119903119898119890119903 119894119899 119904119894119899119892119897119890 119900119901119890119903119886119905119894119900119899

211988002119875119885119874119862 +

1

2

1205732

11988002 119875119885119878119862 119905119903119886119899119904119891119900119903119898119890119903119904 119894119899 119901119886119903119886119897119897119890119897 119900119901119890119903119886119905119894119900119899

(4-1)


120573 =119878119871




44 Methodology









Page | 74













obtained

Profile

generator of

domestic

electricity

demand profiles

Transformer

operation

modes

MATLAB

Distribution

network

model built

in OpenDSS

Analyse and

compare

simulation

results in

MATLAB




Page | 75

Start



modes considered

End

No

Yes


customer randomly


mode



Record results

Change

transformer

operation

mode

N=N+1




No

Yes







Page | 76














obtained


day is recorded


Profile

generator of

domestic

electricity

demand profiles

Tie-switch

status

MATLAB

Distribution

network

model built

in OpenDSS

Analyse and

compare

simulation

results in

MATLAB




Page | 77





451 Test Case 1








whilst the 4th
























Page | 78

A

A

A

A

B

B

B

B


Load4_2

Load4_3

Load4_4

Load4_5

Load4_6

Load4_7

Load4_8

75 MVA

33 kV

11 kV

33 kV

Voltage

Source

75 MVA



Sub-

sector

Transf

Rating

(kVA)

Conn Tapping

Range

Load

Losses

at

75

(kW)

No-

Load

Losses

(kW)

Impedance voltage


the principle

tapping

()

Reference

standard


6 steps of 25

Each

50

75

835 BS 171 amp

IEC 60076







Page | 79

0

10

20

30

40

50

60

70

80

90

100

0 2 4 6 8 10 12 14 16 18 20 22

Tran

sfo

rme

r Lo

ad F

acto

r

Time (h)

0

10

20

30

40

50

60

70

0 2 4 6 8 10 12 14 16 18 20 22

Tran

sfo

rme

r Lo

sse

s (k

W)

Time (h)

0

10

20

30

40

50

60

70

0 2 4 6 8 10 12 14 16 18 20 22

Tran

sfo

rme

r Lo

sse

s (k

W)

Time (h)




of Scenario 1


(a) Scenario 1

(b) Scenario 2



Page | 80

0

10

20

30

40

50

60

70

0 2 4 6 8 10 12 14 16 18 20 22

Tran

sfo

rme

r Lo

sse

s (k

W)

Time (h)

(c) Scenario 3














the 95th



The mean and 95th










Page | 81

0976

0978

098

0982

0984

0986

0988

099

0992


Vo

ltag

e (

pu

)

Scenario1

Scenario2

Scenario3

0974

0976

0978

098

0982

0984

0986

0988

099


Vo

ltag

e (

pu

)

Scenario1

Scenario2

Scenario3

(a) Mean value

(b) 95th

value

Fig 4-8 11 kV 4th



start of the 4th










Page | 82

088

09

092

094

096

098

1

0 2 4 6 8 10 12 14 16 18 20 22

Bu

s V

olt

age

(p

u)

Time (h)

088

09

092

094

096

098

1

0 2 4 6 8 10 12 14 16 18 20 22

Bu

s V

olt

age

(p

u)

Time (h)

088

09

092

094

096

098

1

0 2 4 6 8 10 12 14 16 18 20 22

Bu

s V

olt

age

(p

u)

Time (h)



(a) Scenario 1

(b) Scenario 2

(c) Scenario 3


Lower Limit

Lower Limit

Lower Limit



Page | 83

088

09

092

094

096

098

1

0 2 4 6 8 10 12 14 16 18 20 22

Bu

s V

olt

age

(p

u)

Time (h)

088

09

092

094

096

098

1

0 2 4 6 8 10 12 14 16 18 20 22

Bu

s V

olt

age

(p

u)

Time (h)

088

09

092

094

096

098

1

0 2 4 6 8 10 12 14 16 18 20 22

Bu

s V

olt

age

(p

u)

Time (h)

(a) Scenario 1

(b) Scenario 2

(c) Scenario 3


Lower Limit

Lower Limit

Lower Limit



Page | 84

0976

0978

098

0982

0984

0986

0988

099

0992


0 25

5244 75

100
















values 0 25 5244 75 and 100





Fig 4-11 11 kV 4th




Page | 85






TCLF () 0 25 5244 75 100

Transformer loss

(kWh)

55922 50783 47865 49414 53982




TCLF () 0 25 5244 75 100

Average number of


0 2 4 2 0

452 Test Case 2












Page | 86

0

02

04

06

08

1

12

14

16

0 2 4 6 8 10 12 14 16 18 20 22

Act

ive

Po

we

r (k

W)

Time (h)

TW1 TW2 TW3 TW4 TW5

A1

A2

A3


B1

B2

B3

EndA EndB

TW9TW8TW7TW6








B4_3 B4_4 B4_5 B4_6 B4_7 B4_8




(a) Group 1



Page | 87

0

002

004

006

008

01

012

014

016

018

02

0 2 4 6 8 10 12 14 16 18 20 22

Act

ive

Po

we

r (k

W)

Time (h)

(b) Group 2















at TW1


at TW5





Page | 88







operation












Loss

(kWhday)

11319 10848 10848 11399 11162 11162 9739 9572 9528













Page | 89

096

0962

0964

0966

0968

097

0972

0974

0976

0978

098


Vo

ltag

e (

pu

)

Scenario1

Scenario2

Scenario3

0955

096

0965

097

0975

098

0985

099


Vo

ltag

e (

pu

)

Scenario1

Scenario4

Scenario7













Page | 90


that in Scenario 4




46 Summary



























Page | 91





Page | 92

CHAPTER 5




51 Introduction











planning





Reduction

Page | 93



constraints


















conclusions




119872119894119899119894119898119894119904119890 119891 = sum 119896119894119877119894(119875119894

2+1198761198942

1198801198942 )

119873119887119894=1 (5-1)





Reduction

Page | 94



Subject to



119875119894 le 119875119894119898119886119909 (5-4)

det(119860) = 1 119900119903 minus 1 (5-5)












53 Solution Method







Reduction

Page | 95

Home

1 2 NP1NP1-1

1 2 NP1-1 NP1

1 2 NP1NP1-1

1 2 NP2-1 NP2

1 2 NP2NP2-1

1 2 NP2-1 NP2

1 2 NP2NP2-1

1 2 NP2-1 NP2

Food

Stage

1

2

NT-1

NT

NT+1

NT+2

NT+NDG-1

NT+NDG

Part 1 Number of


Part 2 Number

of DGs









Reduction

Page | 96
















five steps



constant value






stage y is

119875119895119910(119873) =

120591119895119910

(119873)

sum 120591119895119910

(119873)ℎisin∆119910

(5-6)

where 120591119895119910




Reduction

Page | 97










choose a new trail







120591119895119910

(119873) = (1 minus 120588)120591119895119910

(119873 minus 1) + 120591119888 (5-7)




this edge





120591119895119910(119873) = 120591119895

119910(119873) + 120588119891119887119890119904119905

119891119887119890119904119905(119873) (5-8)



120591119895119910(119873) = 120591119898119886119909 119894119891 120591119895

119910(119873) ge 120591119898119886119909 (5-9)

120591119895119910(119873) = 120591119898119894119899 119894119891 120591119895

119910(119873) le 120591119898119894119899 (5-10)


Reduction

Page | 98

Start

Set Iteration n=1

Maximum iteration

reached

Output best


No

Yes









n=n+1


all location lists


and load data







optimal solution



Reduction

Page | 99













method





simultaneously




Appendix C1

541 33-bus System








Reduction

Page | 100

10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

18 19 20 21

22 23 24

25 26 27 28 29 30 31 32


L18

L19 L20 L21

L22

L23 L24

L25

L26 L27 L28 L29 L30 L31 L32

L33

L34

L35

L36

L37





Case Active feeder

loss (kW)

Minimum voltage

(pu)

(Bus No)


on Fig 53

DG location

Case I 20314 09116 (B17) L33 L34 L35 L36 L37 NA

Case II 13981 09361 (B31) L7 L9 L14 L32 L37 NA



Case I base case



Bus 17








Reduction

Page | 101

10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

18 19 20 21

22 23 24

25 26 27 28 29 30 31 32


L18

L19 L20 L21

L22

L23 L24

L25

L26 L27 L28 L29 L30 L31 L32

L33

L34

L35

L36

L37










from it


Method Feeder loss

(kW)

Loss reduction

()


voltage (pu)


BEM [109] 14054 3082 L7 L10 L14 L32 L37 09361

HSA [110] 13981 3118 L7 L9 L14 L32 L37 09361

FWA [16] 14026 3095 L7 L9 L14 L28 L32 09396

PSO [55] 13981 3118 L7 L9 L14 L32 L37 09361

IWO [111] 13981 3118 L7 L9 L14 L32 L37 09361








Reduction

Page | 102

10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

18 19 20 21

22 23 24

25 26 27 28 29 30 31 32


L18

L19 L20 L21

L22

L23 L24

L25

L26 L27 L28 L29 L30 L31 L32

L33

L34

L35

L36

L37

DG2

DG1

DG3









CGA and CSA



computation

times

(second)


ACO 13981 13981 13981 0 228 821 1448

CGA [112] 14002 14619 13981 12121 5463 2986 3926

CSA [113] 13986 14028 13981 01328 8363 3425 7258










Reduction

Page | 103

10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

18 19 20 21

22 23 24

25 26 27 28 29 30 31 32


L18

L19 L20 L21

L22

L23 L24

L25

L26 L27 L28 L29 L30 L31 L32

L33

L34

L35

L36

L37

DG2DG1

DG3























Reduction

Page | 104

086

088

09

092

094

096

098

1

102

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32

Vo

ltag

e (

pu

)

Bus No

Case I

Case II

Case III

Case IV

0

20

40

60

80

100

120

140

160

180

200

100 400 700 1000

Fee

de

r lo

ss (

kW)

DG Capacity (kVA)












allocation



Reduction

Page | 105

10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

27

28

29

30

31 32 33 34

35

36

37

38 39 40 41 42 43 44 45

46 47 48 49

50

51

52

53 54 55 56 57 58 59 60 61 62 63 64

65 66

67 68


L27

L28

L29

L30

L31 L32 L33 L34

L35

L36

L37

L38 L39 L40 L41 L42 L43 L44 L45

L46

L47 L48 L49

L50

L51

L52

L53 L54 L55 L56 L57 L58 L59 L60 L61 L62 L63 L64

L65

L66

L67

L68

L69

L70

L71

L72L73

542 69-bus System










Case Active feeder

loss (kW)

Minimum voltage

(pu)

(Bus No)


Case I 22562 09072 (B64) L69 L70 L71 L72 L73 NA

Case II 9885 09476 (B60) L14 L55 L61 L71 L72 NA



Case I base case




Reduction

Page | 106

10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

27

28

29

30

31 32 33 34

35

36

37

38 39 40 41 42 43 44 45

46 47 48 49

50

51

52

53 54 55 56 57 58 59 60 61 62 63 64

65 66

67 68


L27

L28

L29

L30

L31 L32 L33 L34

L35

L36

L37

L38 L39 L40 L41 L42 L43 L44 L45

L46

L47 L48 L49

L50

L51

L52

L53 L54 L55 L56 L57 L58 L59 L60 L61 L62 L63 L64

L65

L66

L67

L68

L69

L70

L71

L72L73











Method Feeder loss

(kW)

Loss reduction

()


voltage (pu)


FWA [16] 9886 5618 L14 L56 L61 L71 L72 09476

HSA [110] 10546 5326 L13 L18 L56 L61 L72 09475

GA [110] 10242 5461 L14 L53 L61 L71 L72 09462





Reduction

Page | 107

10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

27

28

29

30

31 32 33 34

35

36

37

38 39 40 41 42 43 44 45

46 47 48 49

50

51

52

53 54 55 56 57 58 59 60 61 62 63 64

65 66

67 68


L27

L28

L29

L30

L31 L32 L33 L34

L35

L36

L37

L38 L39 L40 L41 L42 L43 L44 L45

L46

L47 L48 L49

L50

L51

L52

L53 L54 L55 L56 L57 L58 L59 L60 L61 L62 L63 L64

L65

L66

L67

L68

L69

L70

L71

L72L73

DG3

DG1

DG2

10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

27

28

29

30

31 32 33 34

35

36

37

38 39 40 41 42 43 44 45

46 47 48 49

50

51

52

53 54 55 56 57 58 59 60 61 62 63 64

65 66

67 68


L27

L28

L29

L30

L31 L32 L33 L34

L35

L36

L37

L38 L39 L40 L41 L42 L43 L44 L45

L46

L47 L48 L49

L50

L51

L52

L53 L54 L55 L56 L57 L58 L59 L60 L61 L62 L63 L64

L65

L66

L67

L68

L69

L70

L71

L72L73

DG3DG1

DG2









III respectively



Reduction

Page | 108

0

50

100

150

200

250

100 400 700 1000

Fee

de

r lo

ss (

kW)

DG Capacity (kVA)














configuration












Reduction

Page | 109

086

088

09

092

094

096

098

1

102

0 5 10 15 20 25 30 35 40 45 50 55 60 65

Vo

ltag

e (

pu

)

Bus No

Case I

Case II

Case III

Case IV


55 Summary



















Reduction

Page | 110








Page | 111

CHAPTER 6




LOSS REDUCTION

61 Introduction





system [82]









Page | 112












investigated




















Page | 113













load curve [82]









P1

P2

1199051 1199052 Time (h)



Page | 114

1198911 = sum (119864119871119905 + 119879119871119905)1199051minus1119905=1 + sum (119864119871119905 + 119879119871119905) 1199051

24119905=1199052 isin 1 2 hellip 24 (6-1)


Min 119891 = 1198911 + 1198912 (6-3)







and are disregarded


















Page | 115

Home

0 1

0 1

0 1

0 1

1 2 NPNP-1

1 2 NP-1 NP

1 2 NPNP-1

1 2 NP-1 NP

Food

Stage

1

2

Ns-1

Ns

Ns+1

Ns+2

Ns+Nt-1

Ns+Nt

Part 1

Number of

substations

Ns

Part 2 Number

of existing tie-

switches Nt








Page | 116

Tie-switch

Transformer





as a binary vector















Page | 117

Start


Maximum iteration

reached

Output best


No

Yes



Iteration N=1








N=N+1




and load data





T=T+1

Tgt2

Yes

t=t+1

No




Page | 118


LP8 LP9 LP10



LP29 LP30 LP31

LP26 LP27 LP28


19

20

21

22

23

24

26

25 27

28

29 30

71

13 15

14 16

17

18

69

1 3

2

5

4

7

6 8

10

9

68

11 12

56

57

58 60

59 61 62

65

64 66 67

50 52

51

54

53 55

44

45

46

47

48

49

70

31

32

33

34

36

35

39

37 38 40

41

42 43

63

F3

F2

F1

F7

F6

F5

F4


Subbus1

Subbus2

Subbus3

T1

T3

T5

Main

feeder

Main

feeder

Main

feeder

T2

T4

T6













Page | 119




Number

of load

points


(kW)

Q

(kVAr)

Number of

customers

4 1-2 9-10 residential 8869 8426 220

6 3-5 13-15 residential 8137 7731 200

12 6-7 16-17 23-25 28

30-31 37-38


6 8 11 18 26 32-33 industrial 2445 23228 1

10 12 19-22 27 29 34-

36












Page | 120






Page | 121




shown in Table 6-2



Spring

(Mar Apr May)

Weekdays 66 92

Weekends 26

Summer

(Jun Jul Aug)

Weekdays 66 92

Weekends 26

Autumn

(Sep Oct Nov)

Weekdays 65 91

Weekends 26

Winter

(Dec Jan Feb)

Weekdays 64 90

Weekends 26

Year 365 Days





buses









Page | 122

651 Test Case 1



network loss











Spring

weekday

Spring

weekend

Summer

weekday

Summer

weekend

Autumn

weekday

Autumn

weekend

Winter

weekday

Winter

weekend

Before

Reconfiguration


L70L71

L68L69

L70L71

L68L69

L70L71

L68L69

L70L71

L68L69

L70L71

L68L69

L70L71

L68L69

L70L71

L68L69

L70L71

Number of operated

transformers




Loss

(kWh)

Cable 9233 3498 8050 3151 9660 3665 11009 4080

Transformer 4301 3410 4109 3350 4372 3437 4597 3507

Total 13534 6908 12159 6501 14032 7102 15606 7587

After

Reconfiguration


23-24

0-6 0-7

23

0-7 0-7

22-23

0-6

0-7

22-23

0-6


L69L71

L68L69

L70L71

L17L68

L70L71

L17L68

L70L71

L17L68

L70L71

L68L69

L70L71

L17L68

L70L71

L68L69

L70L71

Number of operated

transformers






L65L70

L68L69

L70L71

L41L48

L65L69

L68L69

L70L71

L17L41

L65L70

L68L69

L70L71

L17L41

L65L70

L68L69

L70L71

Number of operated

transformers




Loss

(kWh)

Cable 9043 3516 7851 3169 9519 3685 10845 4103

Transformer 3955 2616 3759 2517 4036 2656 4264 2755

Total 12998 6132 11610 5686 13479 6341 15109 6858



Page | 123

0

05

1

15

2

25

3

35

4

45

05 1 15 2 25 3










652 Test Case 2











To

tal

loss

(G

Wh

)

DG Capacity (MW)



Page | 124

653 Test Case 3









120578times119875119862 (6-4)









the day



capability (mile)

Market share ()

Micro car 12 50 20









Page | 125

4

42

44

46

48

5

30 60 90



119878119874119862 = 0 119898 gt 119872119863119862

119872119863119862minus119898

119872119863119862 119898 le 119872119863119862 (6-5)


















To

tal

loss

(G

Wh

)




Page | 126

4

42

44

46

48

5

30 60 90











66 Summary













To

tal

loss

(G

Wh

)




Page | 127
















Page | 128

CHAPTER 7




71 Introduction
















Improvement

Page | 129






























weighted function


Improvement

Page | 130

119872119894119899 119869 = micro1 ∙ 119864119862119874119878119879 + micro2 ∙ 119878119862 (7-1)





Parameters






119872119886119909 119870 = 1205961 ∙ 120572119878119860 + 1205962 ∙ 120572119878119862 (7-2)

















Improvement

Page | 131

0

1

0

1

120572119878119860 =

1 119878119860119868119863119868 le 119878119860119868119863119868119898119894119899119878119860119868119863119868119900119903119894minus119878119860119868119863119868

119878119860119868119863119868119900119903119894minus119878119860119868119863119868119898119894119899119878119860119868119863119868119898119894119899 lt 119878119860119868119863119868 lt 119878119860119868119863119868119900119903119894

0 119878119860119868119863119868 ge 119878119860119868119863119868119900119903119894

(7-3)











120572119878119862 =

1 119878119862 le 119878119862119900119903119894119878119862119898119886119909minus119878119862

119878119862119898119886119909minus119878119862119900119903119894119878119862119900119903119894 lt 119878119862 lt 119878119862119898119886119909

0 119878119862 ge 119878119862119898119886119909

(7-4)





Parameters



120572119878119860

119878119860119868119863119868119898119894119899 119878119860119868119863119868119900119903119894 119878119860119868119863119868

120572119878119862

119878119862119900119903119894 119878119862119898119886119909 119878119862


Improvement

Page | 132

0

1





120572119864119862 =

1 119864119862119874119878119879 le 119864119862119874119878119879119898119894119899119864119862119874119878119879119900119903119894minus119864119862119874119878119879

119864119862119874119878119879119900119903119894minus119864119862119874119878119879119898119894119899119864119862119874119878119879119898119894119899 lt 119864119862119874119878119879 lt 119864119862119874119878119879119900119903119894

0 119864119862119874119878119879 ge 119864119862119874119878119879119900119903119894

(7-5)








Max 119871 = min (120572119878119860 120572119878119862 120572119864119862) (7-6)










120572119864119862

119864119862119874119878119879119898119894119899 119864119862119874119878119879119900119903119894 119864119862119874119878119879


Improvement

Page | 133



1 ( 1)

1 1 1 1 1 1


t t

b b k R k s

t b k j k j


(7-7)








rate




119878119860119868119863119868 = sum sum 120582119887∙119871119887[sum 119889119877

119873119862119877(119887)119899=1 +sum 119889119878

119873119862119878(119887)119899=1 ]

119873119887119887=1

119873119862119905119900119905119886119897119879

119905=1 (7-8)








119878119862 = 119862119868119878 ∙ 119873119899119890119908 + 119862119877119878 ∙ 119873119903119890119897 + sum 119872119862119879119905=1 ∙ (119873119899119890119908 + 119873119890119909119894119904) ∙ (1 + 119863119877)minus(119905minus1) (7-9)





Improvement

Page | 134

Home

0

1

0

1

0

1

0

1

Food





Problem
















Improvement

Page | 135









119887119890119899119890119891119894119905 = sum119864119862119874119878119879119887119886119904119890

119905 minus119864119862119874119878119879119900119901119905119905

(1+119863119877)119905119879119905=1 (7-10)

where 119864119862119874119878119879119887119886119904119890119905 and 119864119862119874119878119879119900119901119905





119861119862119877 =119887119890119899119890119891119894119905

119878119862 (7-11)






Improvement

Page | 136


LP8 LP9 LP10



LP29 LP30 LP31

LP26 LP27 LP28


9 10 11 12 13 33

6 7 8 31

1 2 3 4 5 30

25 26 27 29

22 23 24

19 20 21

32

14 15 16 17 18

28

F3

F2

F1

F7

F6

F5

F4


Subbus1

Subbus2

Subbus3

T1

T3

T5

Main

feeder

Main

feeder

Main

feeder

T2

T4

T6











Improvement

Page | 137







Number

of load

points


(kW)

Number of

customers

15 1-4 11-13 18-21 32-35 residential 545 220

7 5 14 15 22 23 36 37 residential 500 200

7 8 10 26-30 industrial 1000 1


7 6 7 16 17 24 25 38 commercial 415 10


















Improvement

Page | 138




Residential 006 11 16 26 316 5

Industrial 288 806 95 124 1387 276

Commercial 205 96 125 185 2151 6306




method






751 Test Case 1











Improvement

Page | 139


LP8 LP9 LP10



LP29 LP30 LP31

LP26 LP27 LP28


9 10 11 12 13 33

6 7 8 31

1 2 3 4 5 30

25 26 27 29

22 23 24

19 20 21

32

14 15 16 17 18

28

F3

F2

F1

F7

F6

F5

F4


Subbus1

Subbus2

Subbus3

T1

T3

T5

Main

feeder

Main

feeder

Main

feeder

T2

T4

T6










Improvement

Page | 140













Switch

No


Load (kW)


Type


2 2 7D 3500 LP9 1500 (industrial)



5 6 23D 3500 LP30 1000 (industrial)

6 7 28D 3595 LP36 500 (commercial)












Improvement

Page | 141


LP8 LP9 LP10



LP29 LP30 LP31

LP26 LP27 LP28


9 10 11 12 13 33

6 7 8 31

1 2 3 4 5 30

25 26 27 29

22 23 24

19 20 21

32

14 15 16 17 18

28

F3

F2

F1

F7

F6

F5

F4


Subbus1

Subbus2

Subbus3

T1

T3

T5

Main

feeder

Main

feeder

Main

feeder

T2

T4

T6



ECOST

($)

Number of

installed

switches

Capital and

installation cost

($)

Maintenance

and operation

cost ($)

Total system

cost ($)

Before switches

installation

472260 0 0 4830 477090

After switches

installation

221610 11 51700 13670 286980


Improvement

Page | 142


LP8 LP9 LP10



LP29 LP30 LP31

LP26 LP27 LP28


9 10 11 12 13 33

6 7 8 31

1 2 3 4 5 30

25 26 27 29

22 23 24

19 20 21

32

14 15 16 17 18

28

F3

F2

F1

F7

F6

F5

F4


Subbus1

Subbus2

Subbus3

T1

T3

T5

Main

feeder

Main

feeder

Main

feeder

T2

T4

T6


A Base case









Improvement

Page | 143

0

1

2

3

4

5

6

7

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

BC

R

Years








ECOST

($)

Number of

relocated

switches

Relocation

cost ($)

Number of

installed

switches

Capital and

installation

cost ($)

Maintenance

and operation

cost ($)

Total

system

cost ($)

Before switch

placement

472260 0 0 0 0 4830 477090

After switch

placement

221120 5 2500 8 37600 11260 272480











Improvement

Page | 144

0

20

40

60

80

100

120

140

160

05 1 15 2 25 3 35 4 45 5 55 6 65 7 75 8

Co

st (

th

ou

san

d $

)

CDF multiplier

ECOST

Switch costs

Total costs






















Improvement

Page | 145

0

5

10

15

20

25

30

35

40

05 1 15 2 25 3 35 4 45 5 55 6 65 7 75 8

Nu

mb

er

of

swit

che

s

CDF multiplier






















Improvement

Page | 146











01 273120 274810 272480 223

02 273400 275960 272480 175

03 273480 274810 272480 132

04 273100 274810 272480 110

05 273550 274810 272480 94

06 273440 274810 272480 81







400




100 273865 276120 272480 91

200 273100 274810 272480 110

300 273030 274370 272480 135

400 272820 274230 272480 168

500 273170 274230 272480 245


Improvement

Page | 147




752 Test Case 2














Function

SAIDI

(hrscustomer)

Switch costs ($)

Case 21 01 09 04909 09970 09464 1157 68275

Case 22 05 05 08456 09061 08758 556 67378

Case 23 09 01 09384 07761 09221 39936 153950



753 Test Case 3








Improvement

Page | 148


Objective

Function

120572119864119862 120572119878119860 120572119878119862 ECOST

($)

SAIDI

(hrscustomer)

Switch costs

($)

Before

switch

placement

0 0 0 1 472260 1989 4830

After switch

placement

08327 08327 08392 08384 188950 56723 112410

76 Summary

























Improvement

Page | 149




Page | 150

CHAPTER 8




IMPROVEMENT

81 Introduction














Improvement

Page | 151























set is obtained






conclusions


Improvement

Page | 152







119865(119866) = [1198911(119866)1198912(119866)1198913(119866)]119879 (8-3)


configuration G



1198911(119866) = sum 119896119894119877119894(119875119894

2+1198761198942

1198801198942 )

119873119887119894=1 (8-4)








1 ( 1)

1 1 1 1 1 1


t t

b b k R k s

t b k j k j


(8-5)





Improvement

Page | 153









119878119860119868119863119868 = sum sum 120582119887∙119871119887[sum 119889119877

119873119862119877(119887)119899=1 +sum 119889119878

119873119862119878(119887)119899=1 ]

119873119887119887=1

119873119862119905119900119905119886119897119879

119905=1 (8-6)




8214 Constraints








119891119901119904(119894) = sum 120596119895max(119900119891119895)minus119900119891119895(119875119878119894)

max(119900119891119895)minusmin (119900119891119895)

119873119900119887119895

119895=1 (8-7)








Improvement

Page | 154





tie-switches












number




weighted sum as

120591119894119909 = 1199011 ∙ 1205911198941199091 + |1199011 minus 1199012| ∙ 120591119894119909

2 + (1 minus 1199012) ∙ 1205911198941199093 (8-8)

where 1205911198941199091 120591119894119909





new matrix




Improvement

Page | 155



119875119894119909(119873) =120591119894119909(119873)

sum 120591119894119909(119873)ℎisin∆119909

(8-9)

















certain number [88]






follow

120591119894119909119899 (119873) = (1 minus 120588)120591119894119909

119899 (119873 minus 1) + 120591119888 (8-10)




Improvement

Page | 156



this edge





120591119894119909119899 (119873) = 120591119894119909

119899 (119873) + 120588119891119887119890119904119905

119899 (119873)

119891119887119890119904119905119899 (119873minus1)

(8-11)

where 119891119887119890119904119905119899 (119873 minus 1) and 119891119887119890119904119905





120591119894119909119899 (119873) = 120591119898119886119909 119894119891 120591119894119909

119899 (119873) ge 120591119898119886119909 (8-12)

120591119894119909119899 (119873) = 120591119898119894119899 119894119891 120591119894119909

119899 (119873) le 120591119898119894119899 (8-13)












Improvement

Page | 157

Start

Iteration N=1

Maximum ant number

reaches

Output Pareto

optimal set and end

No

Yes



Ant number m=1



matrices into one




for this ant

N=N+1


and load data


dominated solutions

Maximum iteration

reaches

Yes

m=m+1

No





Improvement

Page | 158

Start

Cloning

Maximum iteration

reached

Output Pareto

optimal set and end

No

Yes




dominated solutions



n=n+1











in Fig 8-2



Improvement

Page | 159
















119901119894119899 =

120591119894119899

sum 120591119895119899

119895 (8-14)











120591119894119899(119873) = 119898119886119909 (1 minus 120588)120591119894

119899(119873 minus 1) 120591119898119894119899 (8-15)




Improvement

Page | 160







updated as

120591119894119899(119873) = 119898119894119899120591119894

119899(119873) + 120588min (119891119899(119866))

119891119899(119866) 120591119898119886119909 (8-16)






next iteration





Improvement

Page | 161


LP8 LP9 LP10



LP29 LP30 LP31

LP26 LP27 LP28


19

20

21

22

23

24

26

25 27

28

29 30

71

13 15

14 16

17

18

69

1 3

2

5

4

7

6 8

10

9

68

11 12

56

57

58 60

59 61 62

65

64 66 67

50 52

51

54

53 55

44

45

46

47

48

49

70

31

32

33

34

36

35

39

37 38 40

41

42 43

63

F3

F2

F1

F7

F6

F5

F4


Subbus1

Subbus2

Subbus3

T1

T3

T5

Main

feeder

Main

feeder

Main

feeder

T2

T4

T6








downstream loads







Improvement

Page | 162

300

350

400

450

4

45

5

55

6

x 104

08

09

1

11

12

13

14

15


SA

IDI

(hrs

custo

mer

yr)


Number

of load

points


(kW)

Q

(kVAr)

Number of

customers

4 1-2 9-10 residential 545 51775 220

6 3-5 13-15 residential 500 475 200

12 6-7 16-17 23-25 28 30-

31 37-38


6 8 11 18 26 32-33 industrial 1500 1425 1

10 12 19-22 27 29 34-36 industrial 1000 950 1













Improvement

Page | 163




Mean

38074 48139 09975

Standard deviation

3431 5291 01165













(hrscustomeryr)


Minimum Loss

32142 46404 13090 68 69 70 71

Minimum ECOST

35409 41145 10586 10 17 41 70

Minimum SAIDI

43523 57891 08253 7 26 54 69






Improvement

Page | 164














compromise

solution

Feeder

loss

(kW)

ECOST

($yr)

SAIDI

(hrscustomeryr) 1205961 1205962 1205963

1 10 10 10 10 41 69 70 34033 41553 10996

2 10 1 1 68 69 70 71 32142 46404 13090

3 1 10 1 10 17 41 70 35409 41145 10586

4 1 1 10 7 26 54 69 43523 57891 08253

5 10 10 1 10 41 69 70 34033 41553 10996

6 10 1 10 10 54 69 71 34759 46644 10217

7 1 10 10 7 17 41 70 40368 43329 09570

86 Summary










Improvement

Page | 165














Page | 166

CHAPTER 9





BALANCING

91 Introduction













Page | 167















groups














Page | 168

0

1












respectively








9-1




120572119871

119871119874119878119878119898119894119899 119871119874119878119878119900119903119894 119871119874119878119878



Page | 169

0

1

120572119871 =

1 119871119874119878119878 le 119871119874119878119878119898119894119899119871119874119878119878119900119903119894minus119871119874119878119878

119871119874119878119878119900119903119894minus119871119874119878119878119898119894119899119871119874119878119878119898119894119899 lt 119871119874119878119878 lt 119871119874119878119878119900119903119894

0 119871119874119878119878 ge 119871119874119878119878119900119903119894

(9-2)














120572119881 =

1 119881119863 le 119881119863119898119894119899119881119863119900119903119894minus119881119863

119881119863119900119903119894minus119881119863119898119894119899119881119863119898119894119899 lt 119881119863 lt 119881119863119900119903119894

0 119881119863 ge 119881119863119900119903119894

(9-3)



120572119881

119881119863119898119894119899 119881119863119900119903119894 119881119863



Page | 170

0

1



119871119861119868 = 119881119886119903[1198681

1198681119898119886119909

1198682

1198682119898119886119909 hellip

119868119894

119868119894119898119886119909 hellip

119868119899

119868119899119898119886119909] (9-4)




120572119861 =

1 119871119861119868 le 119871119861119868119898119894119899119871119861119868119900119903119894minus119871119861119868

119871119861119868119900119903119894minus119871119861119868119898119894119899119871119861119868119898119894119899 lt 119871119861119868 lt 119871119861119868119900119903119894

0 119871119861119868 ge 119871119861119868119900119903119894

(9-5)





Optimality


of the vector

119865(119866) = [1198911(119866)1198912(119866)1198913(119866)]119879 (9-6)




120572119861

119871119861119868119898119894119899 119871119861119868119900119903119894 119871119861119868



Page | 171



Domain



























Page | 172








simultaneously





B4 in detail

941 33-bus System







Case I base case






Page | 173

10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

18 19 20 21

22 23 24

25 26 27 28 29 30 31 32


L18

L19 L20 L21

L22

L23 L24

L25

L26 L27 L28 L29 L30 L31 L32

L33

L34

L35

L36

L37









Fig 9-4



(kW)

Maximum node

voltage deviation

(pu)

Feeder Load

balancing index

Tie-switches

location

08734 14310 00625 00270 6 9 14 32 37







Page | 174

120140

160180

200220

006

008

01

012

014

016

0022

0024

0026

0028

003

0032

0034

0036


Feeder

load b

ala

ncin

g index




deviation (pu)


Mean

15499 00815 00256

Standard deviation

1549 00194 00023











Page | 175

10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

18 19 20 21

22 23 24

25 26 27 28 29 30 31 32


L18

L19 L20 L21

L22

L23 L24

L25

L26 L27 L28 L29 L30 L31 L32

L33

L34

L35

L36

L37

DG2

DG1

DG3







index


Minimum Loss

13981 00639 00280 7 9 14 32 37


14026 00604 00310 7 9 14 28 32


20248 01309 00223 7 30 34 35 37














Page | 176

110120

130140

150160

170

004

006

008

01

0120018

002

0022

0024

0026

0028

003


Feeder

load b

ala

ncin

g index



(kW)

Maximum node

voltage deviation

(pu)

Feeder Load

balancing index

Tie-switches

location

08590 12405 00594 00230 6 8 14 32 37







deviation (pu)


Mean

12850 00711 00231

Standard deviation

1003 00166 00029



Page | 177

















index


Minimum Loss

11753 00643 00241 7 9 14 28 31


12592 00567 00265 6 8 14 28 32


16419 01139 00189 7 21 30 35 37









locations



Page | 178

10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

18 19 20 21

22 23 24

25 26 27 28 29 30 31 32


L18

L19 L20 L21

L22

L23 L24

L25

L26 L27 L28 L29 L30 L31 L32

L33

L34

L35

L36

L37

DG1

DG3

DG2

100110

120130

140150

160

004

006

008

01

012

0016

0018

002

0022

0024

0026

0028


Feeder

load b

ala

ncin

g index


in Case IV

Objective

function

Feeder loss

(kW)

Maximum node

voltage

deviation (pu)

Feeder Load

balancing

index

Tie-switches

location

DGs location

08961 10878 00499 00232 7 9 14 36 37 B32 B32 B32









Page | 179




deviation (pu)


Mean

13295 00873 00194

Standard deviation

1354 00179 00019
















voltage deviation

(pu)

Feeder Load

balancing index

Tie-switches

location

DGs location

Minimum Loss

10844 00538 00228 7 9 14 32 37 B30 B31 B31


11020 00490 00259 7 9 14 28 36 B31 B31 B32


15443 01090 00178 7 30 34 35 37 B8 B9 B12



Page | 180

10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

27

28

29

30

31 32 33 34

35

36

37

38 39 40 41 42 43 44 45

46 47 48 49

50

51

52

53 54 55 56 57 58 59 60 61 62 63 64

65 66

67 68


L27

L28

L29

L30

L31 L32 L33 L34

L35

L36

L37

L38 L39 L40 L41 L42 L43 L44 L45

L46

L47 L48 L49

L50

L51

L52

L53 L54 L55 L56 L57 L58 L59 L60 L61 L62 L63 L64

L65

L66

L67

L68

L69

L70

L71

L72L73

942 69-bus System







respectively

Case I base case















Page | 181

80

100

120

140

160

005

006

007

0080016

0018

002

0022

0024

0026

0028


Feeder

load b

ala

ncin

g index



(kW)

Maximum node

voltage deviation

(pu)

Feeder Load

balancing index

Tie-switches

location

09676 9885 00524 00195 14 55 61 71 72








deviation (pu)


Mean

12535 00605 00192

Standard deviation

2458 00085 00028



Page | 182











initial case





index


Minimum Loss

9885 00524 00195 14 55 61 71 72


10535 00523 00242 9 14 55 61 71


15051 00701 00161 14 61 69 71 72













Page | 183

10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

27

28

29

30

31 32 33 34

35

36

37

38 39 40 41 42 43 44 45

46 47 48 49

50

51

52

53 54 55 56 57 58 59 60 61 62 63 64

65 66

67 68


L27

L28

L29

L30

L31 L32 L33 L34

L35

L36

L37

L38 L39 L40 L41 L42 L43 L44 L45

L46

L47 L48 L49

L50

L51

L52

L53 L54 L55 L56 L57 L58 L59 L60 L61 L62 L63 L64

L65

L66

L67

L68

L69

L70

L71

L72L73

DG3

DG1

DG2

8090

100110

120130

140

005

006

007

008

0014

0016

0018

002

0022

0024


Feeder

load b

ala

ncin

g index



(kW)

Maximum node

voltage deviation

(pu)

Feeder Load

balancing index

Tie-switches

location

08829 8758 00523 00174 14 55 61 71 72







Page | 184





deviation (pu)


Mean

10707 00576 00183

Standard deviation

2042 00071 00029

















index


Minimum Loss

8758 00523 00174 13 55 61 71 72


9729 00522 00226 7 12 55 61 71


13686 00681 00147 11 61 69 71 72



Page | 185

10 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

27

28

29

30

31 32 33 34

35

36

37

38 39 40 41 42 43 44 45

46 47 48 49

50

51

52

53 54 55 56 57 58 59 60 61 62 63 64

65 66

67 68


L27

L28

L29

L30

L31 L32 L33 L34

L35

L36

L37

L38 L39 L40 L41 L42 L43 L44 L45

L46

L47 L48 L49

L50

L51

L52

L53 L54 L55 L56 L57 L58 L59 L60 L61 L62 L63 L64

L65

L66

L67

L68

L69

L70

L71

L72L73

DG3DG1

DG2









ACO algorithm


system in Case IV

Objective

function

Feeder loss

(kW)

Maximum

node voltage

deviation (pu)

Feeder Load

balancing

index

Tie-switches

location

DGs location

08882 7397 00429 00158 14 55 61 71 72 B60 B60 B60





9-17



Page | 186

70

80

90

100

110

120

004

0045

005

0055

006

0012

0013

0014

0015

0016

0017

0018

0019


Feeder

load b

ala

ncin

g index




deviation (pu)


Mean

9872 00520 00147

Standard deviation

1491 00055 00013













Page | 187






voltage deviation

(pu)

Feeder Load

balancing index

Tie-switches

location

DGs location

Minimum Loss

7397 00429 00158 14 55 61 71 72 B60 B60 B60


8032 00428 00183 11 55 61 71 72 B60 B60 B60


10962 00577 00125 14 63 69 71 72 B62 B62 B62

95 Summary


















Page | 188





Page | 189

CHAPTER 10


101 Conclusion








results





cost







Page | 190


































Page | 191




























demand times







Page | 192














SAIDI




















Page | 193



102 Future Work












supply each feeder














load on feeders


Page | 194





























Page | 195

References




2001



2015




2 pp 15ndash22 2015








2010

















References

Page | 196

2012






vol 63 pp 461ndash472 2014






652ndash660 2009



pp 1878ndash1887 2010



6 no 2 pp 182ndash197 2002














York 1986



pp 2157ndash2165 2015


1994



References

Page | 197


2016










62ndash66




Wiley 1990




170ndash180 2013






2006 pp 4ndash6















pp 2290ndash2293

References

Page | 198









pp 1217ndash1223 1988










42 2002























References

Page | 199



1530 2009




937ndash940 2008












pp 4021ndash4028 2011



2006








129ndash142 2015









no 1 pp 268ndash276 2009



References

Page | 200




2002





pp 1ndash6


















58 pp 537ndash547 2016





1048ndash1062 2016




2016




686ndash690 2003

References

Page | 201









2473ndash2480 2007







2010







22 no 3 pp 1101ndash1111 2007




388ndash397 2015







of Manchester 2015




1 pp 1ndash13 1996




References

Page | 202



pp 861ndash875 2012






2004












251 2002









Cable 2012






1677ndash1685 2015



2 pp 1401ndash1407 1989



References

Page | 203

no 2 pp 1492ndash1498 1989




pp 1ndash9 2012




932ndash942 2015


Sons 2004














vol 54 pp 255ndash267 2014



119ndash126 2011

Page | 204







Sectional

Area

(CSA)

Positive sequence

Z

Zero-phase

sequence

Z

Approximate

Capacitance

C



A Nexans

635011000

Volt Triplex

Cable

185 0415 0112 0988 0236 036

B 95 0220 0012 0530 0102 028


Page | 205

A2 33-bus system


Branch

number

Sending end

node

Receiving end

node

R

(Ω)

X

(Ω)

P at receiving

end (kW)

Q at receiving

end (kVAr)

1 0 1 00922 0047 100 60

2 1 2 04930 02511 90 40

3 2 3 03660 01864 120 80

4 3 4 03811 01941 60 30

5 4 5 08190 07070 60 20

6 5 6 01872 06188 200 100

7 6 7 07114 02351 200 100

8 7 8 10300 07400 60 20

9 8 9 10440 07400 60 20

10 9 10 01966 00650 45 30

11 10 11 03744 01238 60 35

12 11 12 14680 11550 60 35

13 12 13 05416 07129 120 80

14 13 14 05910 05260 60 10

15 14 15 07463 05450 60 20

16 15 16 12890 17210 60 20

17 16 17 03720 05740 90 40

18 17 18 01640 01565 90 40

19 18 19 15042 13554 90 40

20 19 20 04095 04784 90 40

21 20 21 07089 09373 90 40

22 21 22 04512 03083 90 50

23 22 23 08980 07091 420 200

24 23 24 08960 07011 420 200

25 24 25 02030 01034 60 25

26 25 26 02842 01447 60 25

27 26 27 10590 09337 60 20

28 27 28 08042 07006 120 70

29 28 29 05075 02585 200 600

30 29 30 09744 09630 150 70

31 30 31 03105 03619 210 100

32 31 32 03410 05362 60 40

33 7 20 2 2 -- --

34 11 21 2 2 -- --

35 8 14 2 2 -- --

36 17 32 05 05 -- --

37 24 28 05 05 -- --


Page | 206

A3 69-bus system


Branch

number

Sending end

node

Receiving end

node

R

(Ω)

X

(Ω)

P at receiving

end (kW)

Q at receiving

end (kVAr)

1 0 1 00005 00012 0 0

2 1 2 00005 00012 0 0

3 2 3 00015 00036 0 0

4 3 4 00251 00294 0 0

5 4 5 0366 01864 26 22

6 5 6 0381 01941 404 30

7 6 7 00922 0047 75 54

8 7 8 00493 00251 30 22

9 8 9 0819 02707 28 19

10 9 10 01872 00619 145 104

11 10 11 07114 02351 145 104

12 11 12 103 034 8 5

13 12 13 1044 0345 8 55

14 13 14 1058 03496 0 0

15 14 15 01966 0065 455 30

16 15 16 03744 01238 60 35

17 16 17 00047 00016 60 35

18 17 18 03276 01083 0 0

19 18 19 02106 0069 1 06

20 19 20 03416 01129 114 81

21 20 21 0014 00046 5 35

22 21 22 01591 00526 0 0

23 22 23 03463 01145 28 20

24 23 24 07488 02475 0 0

25 24 25 03089 01021 14 10

26 25 26 01732 00572 14 10

27 26 27 00044 00108 26 186

28 27 28 0064 01565 26 186

29 28 29 03978 01315 0 0

30 29 30 00702 00232 0 0

31 30 31 0351 0116 0 0

32 31 32 0839 02816 14 10

33 32 33 1708 05646 195 14

34 33 34 1474 04873 6 4

35 34 35 00044 00108 26 1855

36 35 36 0064 01565 26 1855

37 36 37 01053 0123 0 0

38 37 38 00304 00355 24 17

39 38 39 00018 00021 24 17

40 39 40 07283 08509 12 1

41 40 41 031 03623 0 0


Page | 207

42 41 42 0041 00478 6 43

43 42 43 00092 00116 0 0

44 43 44 01089 01373 3922 263

45 44 45 00009 00012 3922 263

46 45 46 00034 00084 0 0

47 46 47 00851 02083 79 564

48 47 48 02898 07091 3847 2745

49 48 49 00822 02011 3847 2745

50 49 50 00928 00473 405 283

51 50 51 03319 01114 36 27

52 51 52 0174 00886 435 35

53 52 53 0203 01034 264 19

54 53 54 02842 01447 24 172

55 54 55 02813 01433 0 0

56 55 56 159 05337 0 0

57 56 57 07837 0263 0 0

58 57 58 03042 01006 100 72

59 58 59 03861 01172 0 0

60 59 60 05075 02585 1244 888

61 60 61 00974 00496 32 23

62 61 62 0145 00738 0 0

63 62 63 07105 03619 227 162

64 63 64 1041 05302 59 42

65 64 65 02012 00611 18 13

66 65 66 00047 00014 18 13

67 66 67 07394 02444 28 20

68 67 68 00047 00016 28 20

69 49 58 2 1 -- --

70 26 64 1 05 -- --

71 12 20 05 05 -- --

72 10 42 05 05 -- --

73 14 45 1 05 -- --



Feeder

Type

Length

(km)


1 060 2 6 10 14 17 21 25 28 30 34 38 41 43 46 49 51 55 58 61 64 67

68 69 70 71

2 075 1 4 7 9 12 16 19 22 24 27 29 32 3537 40 42 45 48 50 53 56 60

63 65

3 080 3 5 8 11 13 15 18 20 23 26 31 33 36 3944 47 52 54 57 59 62 66


Page | 208



Lines 004 0 0 0 5 0

Buses 0001 0 1 001 2 8

Switches 0004 0002 1 006 4 72








Page | 209










0000 TW5 0400 TW5 0800 TW1 1200 TW5 1600 TW1 2000 TW5

0010 TW5 0410 TW5 0810 TW1 1210 TW5 1610 TW1 2010 TW5

0020 TW5 0420 TW5 0820 TW1 1220 TW5 1620 TW1 2020 TW5

0030 TW5 0430 TW5 0830 TW1 1230 TW5 1630 TW1 2030 TW5

0040 TW5 0440 TW5 0840 TW1 1240 TW5 1640 TW5 2040 TW5

0050 TW5 0450 TW5 0850 TW1 1250 TW5 1650 TW5 2050 TW5

0100 TW5 0500 TW5 0900 TW1 1300 TW5 1700 TW5 2100 TW5

0110 TW5 0510 TW5 0910 TW1 1310 TW5 1710 TW5 2110 TW5

0120 TW5 0520 TW5 0920 TW1 1320 TW5 1720 TW5 2120 TW5

0130 TW5 0530 TW5 0930 TW1 1330 TW5 1730 TW5 2130 TW5

0140 TW5 0540 TW5 0940 TW1 1340 TW5 1740 TW5 2140 TW5

0150 TW5 0550 TW5 0950 TW1 1350 TW5 1750 TW5 2150 TW5

0200 TW5 0600 TW5 1000 TW1 1400 TW5 1800 TW5 2200 TW5

0210 TW5 0610 TW5 1010 TW5 1410 TW5 1810 TW5 2210 TW5

0220 TW5 0620 TW5 1020 TW5 1420 TW5 1820 TW5 2220 TW5

0230 TW5 0630 TW5 1030 TW5 1430 TW5 1830 TW5 2230 TW5

0240 TW5 0640 TW5 1040 TW5 1440 TW5 1840 TW5 2240 TW5

0250 TW5 0650 TW5 1050 TW5 1450 TW5 1850 TW5 2250 TW5

0300 TW5 0700 TW5 1100 TW5 1500 TW5 1900 TW5 2300 TW5

0310 TW5 0710 TW5 1110 TW5 1510 TW5 1910 TW5 2310 TW5

0320 TW5 0720 TW5 1120 TW5 1520 TW5 1920 TW5 2320 TW5

0330 TW5 0730 TW1 1130 TW5 1530 TW5 1930 TW5 2330 TW5

0340 TW5 0740 TW1 1140 TW5 1540 TW5 1940 TW5 2340 TW5

0350 TW5 0750 TW1 1150 TW5 1550 TW5 1950 TW5 2350 TW5


Page | 210



corresponding 95th


B-2 and Table B-3


Node

No

Scenarios

S1 S2 S3 S4 S5 S6 S7 S8 S9

A4_1 09675 09787 09787 09766 09859 09859 09748 09825 09815

A4_2 09676 09784 09784 09766 09856 09856 09748 09822 09813

A4_3 09677 09782 09782 09767 09854 09854 09749 09819 09811

A4_4 09678 09780 09780 09768 09851 09851 09750 09817 09810

A4_5 09681 09777 09777 09771 09849 09849 09753 09814 09808

A4_6 09685 09775 09775 09775 09846 09846 09757 09812 09807

A4_7 09689 09773 09773 09779 09845 09845 09762 09811 09807

A4_8 09694 09772 09772 09784 09844 09844 09767 09810 09807

B4_8 09700 09772 09772 09790 09844 09844 09773 09810 09808

B4_7 09707 09773 09773 09797 09845 09845 09779 09811 09810

B4_6 09714 09775 09775 09804 09846 09846 09787 09812 09813

B4_5 09722 09777 09777 09813 09849 09849 09795 09814 09816

B4_4 09731 09780 09780 09821 09851 09851 09804 09817 09820

B4_3 09737 09782 09782 09827 09854 09854 09809 09819 09823

B4_2 09743 09784 09784 09833 09856 09856 09815 09822 09826

B4_1 09749 09787 09787 09839 09859 09859 09821 09825 09830

Table B-3 95th


Node

No

Scenarios

S1 S2 S3 S4 S5 S6 S7 S8 S9

A4_1 09352 09573 09573 09537 09721 09721 09537 09721 09715

A4_2 09353 09567 09567 09537 09715 09715 09537 09715 09709

A4_3 09355 09562 09562 09539 09711 09711 09539 09711 09704

A4_4 09357 09558 09558 09541 09707 09707 09541 09707 09702

A4_5 09363 09553 09553 09547 09701 09701 09547 09701 09679

A4_6 09370 09548 09548 09555 09697 09697 09555 09697 09694

A4_7 09379 09545 09545 09563 09694 09694 09563 09794 09691

A4_8 09389 09544 09544 09573 09692 09692 09573 09792 09692

B4_8 09400 09544 09544 09585 09692 09692 09585 09792 09692

B4_7 09413 09545 09545 09598 09694 09694 09598 09794 09694

B4_6 09427 09548 09548 09613 09697 09697 09613 09697 09697

B4_5 09443 09553 09553 09628 09701 09701 09628 09701 09701

B4_4 09460 09558 09558 09646 09707 09707 09646 09707 09707


Page | 211

B4_3 09471 09562 09562 09656 09711 09711 09656 09711 09711

B4_2 09482 09567 09567 09668 09715 09715 09668 09715 09715

B4_1 09494 09573 09573 09680 09721 09721 09680 09721 09721







1 1227 1189 1010 1003

2 5192 2686 2051 2060

3 1995 756 112 490

4 1874 667 074 415

5 3833 1321 122 807

6 192 006 006 006

7 484 0 0 0

8 418 124 211 124

9 357 0 0 0

10 055 001 001 001

11 088 003 003 003

12 267 045 045 045

13 073 008 008 008

14 036 0 0 0

15 028 045 092 045

16 025 048 115 048

17 003 007 022 007

18 016 226 232 226

19 083 1809 1859 1808

20 01 424 436 423

21 004 118 071 118

22 319 316 914 315

23 516 512 1618 510

24 129 128 869 128

25 26 224 005 124

26 334 285 003 155

27 1133 962 003 510

28 786 664 0 345

29 391 326 199 159

30 160 110 018 003


Page | 212

31 021 012 0 000

32 001 0 013 0

33 0 563 809 563

34 0 215 215 215

35 0 174 320 174

36 0 002 033 002

37 0 0 263 0

Total 20314 13981 11753 10844




1 008 007 006 006

2 008 007 006 006

3 020 012 012 010

4 194 011 011 011

5 2829 159 155 159

6 2939 164 160 164

7 691 035 034 035

8 338 012 012 012

9 477 143 137 142

10 101 029 027 028

11 219 032 030 032

12 128 000 000 000

13 124 000 0 000

14 120 0 000 0

15 022 083 043 083

16 032 138 067 138

17 000 001 001 001

18 010 080 032 080

19 007 052 021 052

20 011 083 033 083

21 000 003 001 002

22 001 022 006 022

23 001 049 013 049

24 001 091 021 091

25 000 037 009 037

26 000 019 004 019

27 000 000 000 000

28 000 000 000 000

29 001 001 001 001

30 000 000 000 000

31 001 001 001 001


Page | 213

32 001 001 001 001

33 001 001 001 001

34 000 000 000 000

35 000 003 001 003

36 001 041 019 041

37 002 064 028 064

38 000 018 008 018

39 000 001 000 001

40 005 391 161 391

41 002 166 068 166

42 000 022 009 022

43 000 005 002 005

44 001 057 023 057

45 000 000 000 000

46 002 017 017 013

47 058 416 416 316

48 164 1321 1321 991

49 012 253 253 178

50 000 000 000 000

51 000 000 000 000

52 580 001 001 001

53 673 001 001 000

54 916 000 000 000

55 882 0 0 0

56 4986 000 000 000

57 2458 000 000 000

58 954 000 000 000

59 1071 627 626 379

60 1408 824 823 498

61 011 0 0 0

62 014 000 000 000

63 066 001 001 001

64 004 071 069 071

65 000 000 000 000

66 000 000 000 000

67 002 002 002 002

68 000 000 000 000

69 0 3783 3782 2384

70 0 102 052 102

71 0 0 0 0

72 0 0 0 0

73 0 423 252 423

Total 22562 9885 8758 7397


Page | 214




(hrscustomeryr)

70 68 71 69 321415 4640359 130895231648616

70 10 41 54 364131 431068083000 102819629963899

17 10 41 70 354092 411445783000000 105858799638989

17 26 10 70 383269 530285525000000 0968805806257521

7 26 54 69 435225 578907612000000 0825265794223827

7 54 41 69 406035 460067870000000 0915047984356197

7 26 54 70 442913 571756512000000 0836828971119134

17 10 71 70 345231 439663189000000 106361687725632

70 10 71 69 331470 443747189000000 110465057160048

70 10 41 69 340330 415529783000000 109962169073406

70 68 41 69 330274 435818516000000 130392343561974

7 54 71 69 397170 488285276000000 0920076865222623

41 10 54 69 356448 438219183000000 101663312274368

70 10 54 26 393311 549907825000000 0938414109506619

70 7 71 69 381047 465595876000000 100306543321300

70 7 41 17 403678 433294470000000 0957002858002407

70 10 54 71 355269 459285489000000 103322518050542

7 54 71 70 404856 481134176000000 0931640042117930

7 26 17 70 432867 552134212000000 0867220667870036

7 70 41 69 389911 437378470000000 0998036552346570

7 26 69 70 419096 556218212000000 0908254362214200

17 7 71 70 394813 461511876000000 0962031738868833

71 10 54 69 347586 466436589000000 102166200361011

10 26 54 69 385625 557058925000000 0926850932611312

70 26 10 69 369504 534369525000000 100983950060168

7 54 41 70 413721 452916770000000 0926611161251504


Page | 215





(kW)

Maximum node

Voltage deviation

Feeder load

balancing index

7 34 35 31 37 176962 0108696024464801 00228687361961248

7 11 35 32 28 143474 00613272038422790 00305387759787611

7 9 14 31 37 142477 00768537372742428 00252628392269486

6 8 12 36 37 151849 00696765908940439 00259144961258893

7 8 14 31 37 155399 00924077518455773 00239781364880477

6 8 12 31 37 169382 0104485611067200 00236077543160956

6 8 12 32 37 152876 00776641110366926 00250547432924683

33 8 14 30 37 171441 0108063061643879 00230652089068052

7 9 14 32 28 140261 00604355611623940 00310349101268755

7 11 35 32 37 143028 00639069227083702 00273727965037185

6 8 14 31 37 159752 00968913958755809 00236540473688646

6 33 35 32 37 170278 00826562726566354 00249194843739843

6 11 35 32 37 144683 00656445815841987 00261947314082027

6 8 14 32 37 146983 00705648561488426 00256096967694280

7 9 14 32 37 139815 00639015456844128 00280407351785895

6 9 14 32 37 143097 00625183468485540 00270001779728268

7 11 35 31 37 148829 00852978398065017 00245113845932977

7 34 35 30 37 202483 0130888991378581 00223050578905545

6 8 14 36 37 146991 00643933147100736 00266176555168500

6 11 35 31 37 154281 00897759906819439 00242838273201709

6 8 13 32 37 150430 00753226918458818 00253604605496161




(kW)

Maximum node

Voltage deviation

Feeder load

balancing index

7 14 8 32 28 121696 00575193535569366 00264544805354717

7 11 35 31 37 123007 00712785797883380 00213250141648472

6 12 8 32 37 128324 00630309398395457 00223824361844486

6 14 8 30 37 145672 0101299721228755 00194921779245086

7 33 35 32 28 130184 00583420082867310 00261406698684195

7 14 8 30 37 140274 00967924815464314 00195001911353607

7 21 35 30 37 164190 0113945920950777 00189031534924873

6 13 8 32 37 126434 00607661484850486 00227035446761735

7 14 9 32 28 117726 00575130414815478 00271215548731366


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6 14 8 32 28 125920 00566904604559002 00265195832133384

6 12 8 31 37 137974 00889877482038002 00200083704114662

7 11 35 30 37 133030 00891516445489180 00199682922816912

6 11 35 32 37 123013 00593840879899440 00235298833627789

7 14 9 32 37 121070 00631040005210335 00255168322432724

6 14 9 32 28 123916 00566872316455769 00273594084038335

7 14 9 30 37 126587 00812324184971598 00206873922472966

7 14 9 31 28 117529 00642736861104275 00240537048868074

6 14 9 32 37 122047 00593825021727904 00240927348267257

6 11 35 32 28 124883 00566888115014094 00269082055980326

6 11 35 31 37 126802 00756552348586014 00207586957663036

6 14 8 32 37 124050 00593857418451058 00230337877365745

7 13 8 32 28 124039 00575225874614865 00262247242500743

7 11 35 32 28 119522 00575159230231156 00267430211390231

7 14 9 31 37 118759 00642740886891275 00220228862077971

6 14 8 31 37 130316 00816654599427028 00201908840890301

33 14 8 30 37 140110 00923831702765571 00197570883486903

7 12 8 32 28 125895 00587758838819431 00259864524009700

6 13 8 31 37 134936 00865715938530326 00201790772057552




loss

(kW)

Maximum node

Voltage deviation

Feeder load

balancing index

7 9 14 30 37 15 17 16 112506 00655990339384582 00207847799664288

6 8 14 31 37 14 11 15 120818 00728143829651942 00199639595336255

7 11 35 30 37 16 16 12 118637 00756705031931788 00198888055963062

6 8 14 31 37 11 29 14 125736 00822955381260978 00194988443664523

6 11 35 32 37 29 11 29 116999 00602917954784902 00213598898907595

7 9 14 31 37 15 14 16 110931 00518306996442978 00223689972435171

7 34 35 30 37 16 13 13 140652 00983575865184194 00182688360250883

7 8 14 30 37 14 11 15 128617 00876913785424229 00190954012999288

7 8 14 30 37 11 16 14 127141 00860397262006276 00191601352391895

7 9 14 36 37 30 30 29 109157 00520335391274761 00229564125698243

7 8 14 30 37 10 14 16 126706 00857230143750372 00192117850059117

7 11 35 30 37 13 16 12 121130 00786215737441328 00196617519208137

7 34 35 30 37 13 10 9 151352 0106960621828031 00178195736666725

7 34 35 30 37 10 12 9 152310 0107688512235453 00178046268710843

6 8 14 30 37 11 15 16 130550 00897068798318073 00189590122249633

6 8 14 30 37 16 14 10 130869 00901533044670202 00189271311922809

7 34 35 30 37 10 13 12 148089 0104837492639545 00178736074180585


Page | 217

7 34 35 30 37 13 11 16 143317 0100615335666250 00181553323058751

6 8 14 30 37 10 14 14 133299 00925968739633617 00188139999335965

7 34 35 30 37 13 9 12 148392 0105013682219175 00178453713901855

6 8 14 30 37 14 11 10 137593 00963962506644021 00186232592604301

6 8 14 30 37 11 8 14 136046 00951731865531927 00187106569470356

6 8 14 30 37 11 11 16 135639 00942616575802945 00187170876179048

7 8 14 30 37 15 16 14 122935 00815907052491111 00195198923102276

7 34 35 30 37 12 14 16 140640 00983915740315128 00182784576692257

6 33 35 31 37 11 11 13 146017 00888852225316270 00188548348595259

7 34 35 30 37 12 16 12 142144 00997534014352579 00181578155086060

6 8 14 30 37 14 11 15 132819 00921338781311946 00188143081376993

6 8 14 30 37 10 15 11 136651 00956093119043262 00186781475357014

7 9 14 31 37 14 14 16 111382 00525319705640723 00222591386298574

7 34 35 30 37 13 14 16 139957 00977014014811679 00183484070331887

7 34 35 30 37 12 15 16 139849 00976123852270839 00183745698300515

7 34 35 30 37 12 16 16 138589 00959671533698319 00184842191427931

7 34 35 30 37 16 13 16 137912 00952795751906571 00185525366651277

6 33 35 31 37 11 11 11 148785 00910856464605774 00187751047204272

7 34 35 30 37 12 16 13 141338 00990484927061306 00181980491991251

7 34 35 30 37 12 13 12 145536 0102926179499332 00179590185768212

6 8 14 30 37 14 10 15 132373 00918145642214576 00188660639598312

6 8 14 30 37 16 11 14 131312 00904718190224125 00188759872087077

7 34 35 30 37 13 15 16 139168 00969230570394858 00184436609617936

7 34 35 30 37 13 9 11 150730 0106620666560267 00178315514588942

6 8 14 30 37 14 11 14 133746 00929165522686308 00187615074100094

7 34 35 30 37 9 9 12 152656 0107867658396772 00178031242058681

6 8 14 30 37 10 11 16 135118 00939381882085281 00187414815201857

7 34 35 30 37 12 12 9 149341 0105739135263959 00178316539838164

7 9 14 36 28 32 32 32 110385 00489797931328652 00256323647901629

7 9 14 36 37 32 31 31 108599 00498935433820196 00235262740306846

7 9 14 32 37 31 30 31 108436 00537552050723257 00227898958267559

7 9 14 36 28 32 31 31 110203 00489682960875768 00259015702487973

7 34 35 30 37 8 12 9 154427 0108962750550623 00178021823053241


Page | 218




(kW)

Maximum node

Voltage deviation

Feeder load

balancing index

55 61 71 72 12 99036 00524391619987274 00196366946903149

69 61 71 9 14 145213 00664127006601768 00185315761508749

55 61 71 72 14 98845 00524393494628415 00194882148961848

69 70 71 10 14 145135 00666490251240782 00182871906896542

69 61 71 72 12 150267 00699556148777123 00161708619074924

55 61 71 10 14 104521 00524349487665904 00238104755589364

69 61 71 72 13 150383 00700225094171628 00161512783956020

55 61 71 72 13 98937 00524392488739880 00195710324132613

69 61 71 72 11 150792 00682108082577803 00171029450547815

55 61 71 9 14 105348 00524349082167884 00242117051986541

69 61 71 72 14 150513 00700911373758199 00161129748303495

55 61 71 72 11 105195 00524380932334678 00218572363716938




(kW)

Maximum node

Voltage deviation

Feeder load

balancing index

55 61 12 14 9 97461 00523081449765275 00226112450860475

69 61 71 14 9 130761 00662843002557533 00155527078006889

55 61 71 14 7 97263 00523080911134007 00226177446060770

55 61 12 71 72 87588 00523152959484715 00174558059214037

55 61 71 14 8 93176 00523082195004728 00211109499855264

55 61 71 13 72 87581 00523154440245970 00174392153380541

55 61 12 14 72 87755 00523153511186373 00174538759436512

55 61 12 71 7 97289 00523080869366065 00226232791264600

69 61 71 11 9 134009 00662855052002667 00154463391981039

69 61 12 14 9 130989 00662843776081034 00155381836375260

55 61 71 13 7 97273 00523080879708534 00227249951330579

55 61 71 14 9 90907 00523086904216601 00201865894567423

55 61 71 14 10 90291 00523088955157064 00199034032147027

69 61 71 14 10 130894 00665207578684145 00154263271797149

55 61 71 14 72 87582 00523156072908145 00174100597226583

69 61 71 11 10 134197 00665220013747228 00153401360203180

69 61 71 11 72 136858 00680828895070073 00147368269784675

69 61 12 14 10 131126 00665208386694061 00154135530565384

55 61 71 11 72 91274 00523126048676607 00184393848480773


Page | 219




loss

(kW)

Maximum node

Voltage deviation

Feeder load

balancing index

69 63 71 10 14 60 60 60 105879 00543213716422435 00153740505896722

69 63 12 72 71 60 62 62 109324 00575466375767690 00126779733811642

55 61 71 72 11 60 60 60 80324 00429183191505871 00183159151221229

69 63 12 72 71 61 61 62 109323 00575465740537586 00126842028893447

55 61 71 72 12 60 60 60 74165 00429193759769601 00159264876998350

69 63 14 10 71 62 62 62 106070 00543012249613587 00150279825984642

69 63 11 72 71 60 62 60 110547 00558290844078126 00139841427388105

69 63 14 9 71 62 62 62 106271 00540689205567605 00153025056850459

69 61 71 72 11 60 60 60 108838 00542584369620998 00141625735067141

55 61 71 72 14 60 56 60 75837 00436673338725839 00157367114339890

69 63 14 10 71 62 62 60 105960 00542966739560918 00151430448212008

69 61 71 10 14 60 60 60 104307 00527268149576859 00155323687715422

69 63 11 72 71 61 62 62 110652 00558333983851442 00137892112215884

69 63 13 72 71 62 62 62 109522 00576169823075075 00125440050970194

55 61 71 72 14 60 55 60 75975 00436701836501366 00156758120818947

69 63 71 10 14 60 60 62 105896 00542940500362948 00152768514567046

69 63 14 9 71 62 61 61 106159 00540643102892876 00154245882374843

55 61 71 72 13 60 60 60 74066 00429194617185072 00158554987038681

69 62 71 10 14 61 60 60 105886 00542959390978505 00153513700764165

69 63 14 72 71 62 62 62 109622 00576844280930477 00125002240983144

55 63 71 72 14 62 61 62 74382 00440379610790336 00155858821619573

69 63 71 72 11 60 60 60 110530 00558564471048234 00140822204796308

55 63 71 72 14 60 60 62 74285 00440350644694274 00157371695186626

55 63 14 72 71 62 62 62 74448 00440399072962552 00155438948075735

55 63 71 72 14 60 62 62 74344 00440368353288504 00156312863856681

69 63 71 9 14 60 61 60 105882 00542934725670071 00153515485666183

55 63 71 72 14 60 61 62 74305 00440356668532606 00156816031788752

55 61 20 72 13 60 60 60 80533 00429326269571468 00157463174391893

55 63 71 72 14 61 61 62 74343 00440367927398261 00156346520711234

69 61 71 72 14 60 60 60 107187 00561022028435777 00126909641069497

69 63 71 72 11 60 61 60 110533 00558285040786375 00140595150870697

69 63 12 72 71 62 62 62 109436 00575512407997617 00125707103016452

69 63 14 10 71 61 62 62 106000 00542983427485794 00150838099664421

69 63 11 72 71 60 61 62 110569 00558299818740340 00139149694834405

69 63 14 9 71 61 62 60 106118 00540626433897020 00154840963668230

69 61 71 72 12 60 60 60 107041 00559693311798567 00127785892138089

55 61 71 72 14 60 60 60 73974 00429195606297569 00157682511572302

69 63 14 10 71 61 61 62 105958 00542966109653011 00151492343922130

69 63 12 72 71 62 62 61 109365 00575483243249972 00126225992147273


Page | 220

69 63 11 72 71 62 62 60 110611 00558317226735644 00138490567525274

69 63 14 9 71 62 62 61 106201 00540660395254129 00153587525958041

69 63 14 10 71 61 60 62 105917 00542949434469265 00152083287358888

69 63 14 9 71 62 62 60 106160 00540643732226493 00154184014811756

69 63 11 72 71 61 61 62 110610 00558316590719640 00138552654427231

69 63 71 72 11 62 62 62 110723 00558362979744786 00137328015545176

69 61 71 72 13 60 60 60 107108 00560349171634668 00127435051911921

Page | 221


Algorithms



2amp3

Parameter Value

Number of ants 50







Parameter Value

Number of ants 100








operation

Parameter Value

Number of ants 150







Page | 222



Parameter Value

Number of ants 400







Parameter Value

Number of ants 500







Chapter 8


ECOST and SAIDI)

Parameter Value

Number of ants 100







Page | 223


ECOST and SAIDI)

Parameter Value







Chapter 9



Parameter Value

Number of ants 200








Parameter Value






Page | 224








9th











1-6 12-15 March 2018

DISTRIBUTION NETWORK AUTOMATION FOR MULTI- …

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