strategies for reliability enhancement of electrical...

Strategies for Reliability Enhancement of Electrical

Distribution Systems

A Thesis submitted to Gujarat Technological University

for the Award of

Doctor of Philosophy

in

Electrical Engineering

By

Kela Kalpesh Bansidhar

Enrollment No. : 139997109005

under supervision of

Dr. Bhavik N. Suthar (Supervisor)

Dr. L D Arya (Co-supervisor)

GUJARAT TECHNOLOGICAL UNIVERSITY

AHMEDABAD

December 2018

iii

© Kela Kalpesh Bansidhar

iv

DECLARATION

I declare that the thesis entitled “Strategies for Reliability Enhancement of Electrical

Distribution Systems” submitted by me for the degree of Doctor of Philosophy, is the record

of research work carried out by me during the period from October 2013 to August 2018 under

the supervision of Dr. Bhavik N. Suthar, Professor & Head - Electrical Engineering

Department, Government Engineering College, Bhuj, and Dr. L D Arya , Sr. Professor-

Electrical Engineering Department, Medi-Caps University,Indore and this has not formed the

basis for the award of any degree, diploma, associateship , fellowship, titles in this or any other

University or other institution of higher learning.

I further declare that the material obtained from other sources has been duly acknowledged in

the thesis. I shall be solely responsible for any plagiarism or other irregularities, if noticed in the

thesis.

Signature of the Research Scholar: _____________________ Date:

Name of Research Scholar: Kela Kalpesh Bansidhar

Place: Ahmedabad.

v

CERTIFICATE

I certify that the work incorporated in the thesis titled as Strategies for Reliability

Enhancement of Electrical Distribution Systems submitted by Mr. Kela Kalpesh Bansidhar

was carried out by the candidate under our supervision/guidance. To the best of our knowledge:

(i) the candidate has not submitted the same research work to any other institution for any

degree/diploma, Associateship, Fellowship or other similar titles (ii) the thesis submitted is a

record of original research work done by the Research Scholar during the period of study under

our supervision, and (iii) the thesis represents independent research work on the part of the

Research Scholar.

Signature of Supervisor: Date:

Name of Supervisor: Dr. Bhavik N. Suthar

Place: Ahmedabad.

Name of Co-Supervisor: Dr. L D Arya Date:

Place: Indore

vi

Course-work Completion Certificate

This is to certify that Mr. Kela Kalpesh Bansidhar enrolment no 139997109005 is a PhD

scholar enrolled for PhD program in the branch Electrical of Gujarat Technological

University, Ahmedabad.

1 (Please tick the relevant option(s))

He/She has been exempted from the course-work (successfully completed during

M.Phil Course)

He/She has been exempted from Research Methodology Course only (successfully

completed during M.Phil Course)

He/She has successfully completed the PhD course work for the partial requirement

for the award of PhD Degree. His/ Her performance in the course work is as follows-

Grade Obtained in Research Methodology

(PH001)

Grade Obtained in Self Study Course (Core Subject)

(PH002)

BB AB

Supervisor’s Sign


Co- Supervisor’s Sign

Name of Co-Supervisor: Dr. L D Arya

vii

Originality Report Certificate

It is certified that PhD Thesis titled Strategies for Reliability Enhancement of Electrical

Distribution Systems submitted by Mr. Kela Kalpesh Bansidhar has been examined by me. I

undertake the following:

a. Thesis has significant new work / knowledge as compared already published or are under

consideration to be published elsewhere. No sentence, equation, diagram, table, paragraph or

section has been copied verbatim from previous work unless it is placed under quotation marks

and duly referenced.

b. The work presented is original and own work of the author (i.e. there is no plagiarism). No ideas,

processes, results or words of others have been presented as Author own work.

c. There is no fabrication of data or results which have been compiled / analyzed.

d. There is no falsification by manipulating research materials, equipment or processes, or changing

or omitting data or results such that the research is not accurately represented in the research

record.

e. The thesis has been checked using https://turnitin.com (copy of originality report attached) and

found within limits as per GTU Plagiarism Policy and instructions issued from time to time (i.e.

permitted similarity index <=25%).

Signature of Research Scholar: …………….. Date:


Place: Ahmedabad

Signature of Supervisor: …………….. Date:

Name of Supervisor: Dr. Bhavik N Suthar

Place: Ahmedabad

Signature of Supervisor: …………….. Date:

Name of Co-Supervisor: Dr. L D Arya

Place: Indore

ix

Ph. D. THESIS Non-Exclusive License to

GUJARAT TECHNOLOGICAL UNIVERSITY

In consideration of being a Ph. D. Research Scholar at GTU and in the interests of the facilitation

of research at GTU and elsewhere, I, Kela Kalpesh Bansidhar having Enrollment No.

139997109005 hereby grant a non-exclusive, royalty free and perpetual license to GTU on the

following terms:

a) GTU is permitted to archive, reproduce and distribute my thesis, in whole or in part, and/or my

abstract, in whole or in part ( referred to collectively as the “Work”) anywhere in the world, for

non-commercial purposes, in all forms of media;

b) GTU is permitted to authorize, sub-lease, sub-contract or procure any of the acts mentioned in

paragraph (a);

c) GTU is authorized to submit the Work at any National / International Library, under the authority

of their “Thesis Non-Exclusive License”;

d) The Universal Copyright Notice (©) shall appear on all copies made under the authority of this

license;

e) I undertake to submit my thesis, through my University, to any Library and Archives. Any

abstract submitted with the thesis will be considered to form part of the thesis.

f) I represent that my thesis is my original work, does not infringe any rights of others, including

privacy rights, and that I have the right to make the grant conferred by this non-exclusive license.

g) If third party copyrighted material was included in my thesis for which, under the terms of the

Copyright Act, written permission from the copyright owners is required, I have obtained such

permission from the copyright owners to do the acts mentioned in paragraph (a) above for the

full term of copyright protection.

x

h) I retain copyright ownership and moral rights in my thesis, and may deal with the copyright in

my thesis, in any way consistent with rights granted by me to my University in this non-exclusive

license.

i) I further promise to inform any person to whom I may hereafter assign or license my copyright

in my thesis of the rights granted by me to my University in this non- exclusive license.

j) I am aware of and agree to accept the conditions and regulations of PhD including all policy

matters related to authorship and plagiarism.

Signature of Research Scholar: Date:


Place: Ahmedabad

Signature of Supervisor: ………………... Date:


Place: Ahmedabad

Seal:

Signature of Co-Supervisor: ………………... Date:

Name of Supervisor: Dr. L D Arya

Place:

Seal:

xi

(The panel must give justifications for rejecting the research work)

Thesis Approval Form

The viva-voce of the Ph.D. Thesis submitted by Shri Kela Kalpesh Bansidhar (Enrollment No.

139997109005) entitled Strategies for Reliability Enhancement of Electrical Distribution

Systems was conducted on …………………….., (day and date) at Gujarat Technological

University.

(Please tick any one of the following option)

The performance of the candidate was satisfactory. We recommend that he be awarded the PhD

degree.

Any further modifications in research work recommended by the panel after 3 months from the

date of first viva-voce upon request of the Supervisor or request of Independent Research Scholar

after which viva-voce can be re-conducted by the same panel again.

The performance of the candidate was unsatisfactory. We recommend that he should not be

awarded the Ph.D. degree.

--------------------------------------------------

Name and Signature of Supervisor with Seal

---------------------------------------------------

Name and Signature of Co-Supervisor

---------------------------------------------------

External Examiner -1 Name and Signature

--------------------------------------------------


--------------------------------------------------


(briefly specify the modifications suggested by the panel)

xii

Abstract

Different strategies to enhance reliability of electrical distribution system have been

proposed in this thesis. Reliability of distribution system has been improved considering

specified budget allocation. The primary and customer and energy based reliability indices

have been optimized subject to constraint of budget allocation. A balance between the utility

cost and cost incurred to the customers due to interruptions have been found maintaining the

required targets of reliability of the system. The optimum value of reliability with least

combined costs have been evaluated. Further, distributed generators (DGs) have been added

at certain load points. Optimum values of customer interruption costs, system maintenance

costs and additional costs on DGs have been found achieving the required enhancement in

reliability of the system. Proper locations of DGs keep significance in the enhancement of

reliability. Proper placements of DGs have been found in this thesis and then reliability of

the system has been optimized considering the above mentioned cost values. A cost-benefit

analysis has been made to verify the possibility of its execution. In the process of optimizing

reliability the additional costs have to be spent by any utility which can be justified by

rendering reward to it by the regulating authority. Optimized values of rewards have been

obtained considering customer interruption costs and costs on maintenance of the system.

This has been done attaining required reliability targets.Voltage sag at different load points

due to occurrence of symmetrical and unsymmetrical faults in the system may lead to

momentary or sustained interruption affecting the reliability of the system. The study of

power quality confined to voltage sag has been incorporated in the enhancement of

reliability. The developed algorithms have been applied on sample radial distribution system,

sample meshed distribution system and Roy Billinton Test System-Bus 2.The solutions to

these different strategies for reliability enhancement have been done by applying soft

computing techniques like Flower pollination, Teaching learning based optimization and

Differential evolution. Comparison has been made between the optimized results obtained

by them.

xiii

Acknowledgment

With due respect, I would like to express my sincere gratitude towards Dr. Bhavik N Suthar,

Professor and Head , Electrical Department, Government Engineering College, Bhuj ,who

has been supervising me for my PhD thesis . It would not have been possible for me to opt

for this study had he not provided me the platform to embark upon. His continuous support,

motivation and positive approach has made my journey possible to reach to its destination. I

foresee the same cooperation in my future pursuit.

I have deep sense of respect and gratitude for a learned teacher Dr. L D Arya, Senior

Professor, Electrical Department, Medi-Caps University, Indore, who has been my co-

supervisor for my PhD work. He had been the ‘GURU’ of Professor Suthar as well as mine

during our respective tenure of post-graduation studies at S.G.S.I.T.S., Indore. He got me

introduced to a topic of reliability and its applications to power system during my post-

graduate studies and opened the doors for further studies by continuously inspiring me for

the same. I obsequiously owe to him, whatever meager I have achieved. Besides his

tremendous knowledge in his field, I have felt a human touch in him for the students. I expect

the same warmth and cooperation from him for the years to come.

I am highly thankful to my DPC members Dr. Sanjay R. Joshi, Principal, Government

Engineering College, Valsad and Dr. M C Chudasama , Professor and Head , Electrical

Department , L D College of Engineering ,Ahmedabad for their valuable suggestions and all

possible help.

I am very thankful to my institute and department for their kind support. I am thankful to

GTU V.C., Registrar, Controller of Examination and Ph.D. section for their kind support. I

extend my sincere gratitude to all those people who have helped me in achieving my

objective. I am also indebted to my colleagues who have helped me directly or indirectly

during my research work.

xiv

I am especially thankful to Dr. Rajesh Arya, a young researcher in the same area and son of

Dr. L D Arya, who has continuously helped me in abridging the gap due to physical distance

between me and my co-supervisor.

I would like to thank my whole family for their affection, prayer and continuous support

throughout my study.

I bow down to Almighty for giving me strength paving a right path for me.

Kalpesh B Kela

xv

Table of Contents

Abstract xii

Acknowledgement xiii

Table of contents xv

List of Abbreviations xviii

List of Symbols xix

List of Figures xxi

List of Tables xxiii

1 Introduction 1

1.1 General 1

1.1.2 Need of Reliability Evaluation of Distribution system 4

1.2 State of the Art 5

1.3 Motivation & Objectives 12

1.4 Outline of the thesis 14

2 Application of Metaheuristic Optimization Methods for Reliability

Enhancement of Electrical Distribution Systems based on AHP

16

2.1 Introduction 16

2.2 Indices Evaluation for Radial Distribution System 16

2.2.1 Basic Indices 16

2.3 Indices Evaluation for Meshed Distribution System 17

2.3.1 Approximate Relations for Evaluating Indices for Series and

Parallel configuration

18

2.4 Customer oriented and energy oriented indices 19

2.5 Problem Formulation 20

2.6 Analytic Hierarchical Process (AHP) 23

2.7 Solution Methodology using FP algorithm 24

2.8 Results and Discussions 27

2.8.1 Case-1 27

2.8.2 Case-2 27

2.8.3 Case-3 28

2.9 Conclusions 38

xvi

3 A Value Based Reliability Optimization of Electrical Distribution 39

Systems considering Expenditures on Maintenance and Customer

Interruptions

3.1 Introduction 39


3.3 Solution Methodology using FP algorithm 42


3.4.1 Distribution systems: Descriptions 45

3.5 Conclusions 60

4 Cost Benefit Analysis for Active Distribution Systems in Reliability 61

Enhancement

4.1 Introduction 61


4.2.1 Deciding locations of DGs 62

4.2.2 Connecting DGs as stand by units in the system 63

4.3 Cost-benefit analysis 66

4.4 Solution methodology 67

4.4.1 Finding the locations of DGs 67

4.4.2 Finding the optimized solution by FP 68

4.4.3 Doing cost-benefit analysis 69

4.5 Results and discussions 72

4.5.1 Distribution systems : Descriptions 72

4.6 Conclusions 86

5 Optimal Parameter Setting in Distribution System Reliability 87

Enhancement with Reward and Penalty

5.1 Introduction 87

5.2 Reward / Penalty Scheme (RPS) 88

5.2.1 Socio-economical perspectives of RPS 88

5.3 Problem formulation 89

5.4 Solution Methodology 94


5.5.1 Distribution systems: Descriptions 97

5.6 Conclusions 112

xvii

6 Reliability Performance Optimization of Radial Distribution System

Enhancing Power Quality Considering Voltage Sag

113

6.1 Introduction 113

6.2 Power Quality and Reliability Indices 115

6.3 Methodology for enhancing Reliability accounting Voltage Sag 115

6.3.1 Method to find out number of Voltage Sags and Interruptions 115

6.3.2 Problem Formulation for Optimization 116

6.4 Solution Methodology 119

6.5 Results and discussions 123

6.6 Conclusions 128

7 Conclusions and Guidelines for Future Work 129

7.1 General 129

7.2 Summary of important conclusions 130

7.3 Scope for further work 131

References 133

List of papers published/communicated 145

Appendix-A 146

Appendix-B 149

Appendix-C 153

Appendix-D 157

Appendix-E 159

Appendix-F 161

xviii

List of Abbreviations

AHP : Analytic hierarchical process

SAIFI : System average interruption frequency index

SAIDI : System average interruption duration index

CAIDI : Customer average interruption duration index

AENS : Average energy not supplied

EENS : Expected energy not supplied

CBUDGET : Cost of budget

CIC : Customer interruption cost

FP : Flower pollination

TLBO : Teaching learning based optimization

DE : Differential evolution

RBTS-2 : Roy Billinton Test System –Bus 2

DG : Distributed generation

CPV : Cumulative present value

RPS : Reward penalty scheme

PQ : Power quality

SARFI : System average RMS frequency index

xix

List of Symbols

λk, rk : failure rate and average repair time of kth distributor

segment respectively

Li : average load connected at ith load point

λsys,i : system failure rate at ith load point

Usys,i : system annual outage duration at ith load point

Ni : number of customers at load point i

Nc : total number of distributor segments

w1, w2, w3 and w4 : relative weightage given to the normalized values of

SAIFI, SAIDI , CAIDI and AENS

F : objective function

Cpk

: interruption cost of different distributor segments

(Rs./kW)

Rs. : Indian currency rupees

λk,min and rk,min : reachable minimum values of failure rate and repair time

of kth distributor segment

λk,max and rk,max : maximum allowable failure rate and repair time of kth

distributor segment

SAIFIt , SAIDIt ,

CAIDIt and AENSt

: target values of the respective indices

αK, βK : cost coefficients corresponding to failure rates and

repair time respectively

ADCOST : additional cost spent on DGs to purchase energy

EENSO : expected energy not supplied /year when DGs are not

connected

EENSD : expected energy not supplied/year when DGs are

connected

λdg : Failure rate of DG

rdg : average outage duration of DG

λsw : failure rate of the switch transferring load to the DG

s : switching time or service restoration time with DG

xx

X0 ij : jth parameter of Xi vector

Xj,min and Xj,max : lower and upper bounds on variable Xj

X(k) best

: the current best solution found among all solutions at the

current generation in FP

L : L´evy flight distribution step in FP

X(k) i

: solution vector at kth generation

X(k+1) i

: updated vector at kth generation

rand : random digit in the range [0,1]

R : reliability level of utility considering all customer and

energy based reliability indices

Ropt : socio-economical optimal reliability level

CRP : cost of reward/penalty to the utility

Cnetwork : total reliability cost of the network

Cutility total

: total reliability cost of utility

Csociety total

: total reliability cost of society

Nsag : total number of short duration of voltage deviation by all

possible fault events

NT : represents number of customers served from the section

of the system to be assessed

𝜆𝑘_𝑓𝑎𝑢𝑙𝑡 : fault rate of the 𝑘𝑡ℎ distributor segment

𝑁𝑖𝑛𝑡 : total number of annual interruptions per annum

SARFIt : target value of the index

𝛾𝑘 : cost coefficients corresponding to fault rates for re-

modified radial distribution system with DGs

λk_fault,max : Maximum allowable fault rate

λk_fault,min : reachable minimum values of fault rate

xxi

List of Figures

Fig. No. Title of the Figure Page No.

Fig.1.1 Hierarchical levels for reliability evaluation 2

Fig.2.1. Flow chart for solving the formulated problem in section 2.5 by

AHP & FP

26

Fig.3.1 Flow chart for solution of the problem formulated in section

3.2 by FP

44

Fig.3.2 Variation of Objective function (F) over number of generations

for sample radial system

54

Fig.3.3 Frequency distribution of the minimum values of objective

function (F) using FP for sample radial system

54


function (F) using TLBO for sample radial system

55


function (F) using DE for sample radial system

55


for sample meshed system

56


function (F) using FP for sample meshed system

56


function (F) using TLBO for sample meshed system

57


function (F) using DE for sample meshed system

57


for RBTS-2

58


function (F) using FP for RBTS-2

58


function (F) using TLBO for RBTS-2

59


function (F) using DE for RBTS-2

59

Fig.4.1 Flow chart for finding out the locations of DGs 70

Fig.4.2 Flow chart for enhancing reliability of distribution system

incorporating DGs by FP

71

Fig.5.1 The cost versus reliability depicting socio-economically

optimal reliability level

93

Fig.5.2 Different designs of RPS 93

Fig.5.3 Flow chart for the solution of the problem formulated in section

5.3 by FP

96

xxii

Fig.5.4 Impact of an optimal continuous RPS on different parameter

costs for sample radial distribution system

109


costs for sample meshed distribution system

110


costs for RBTS-2

111

Fig.6.1 Flow chart for the solution of the problem formulated in section

6.3.2 by FP

121

Fig.6.2 Re-modified Radial Distribution System with DG 122

Fig.A.1 Sample radial distribution system 146

Fig.A.2 Modified radial distribution system with DG 147

Fig.B.1 Sample Meshed Distribution System 149

Fig.B.2 Reliability logic diagram of the meshed distribution system 150

Fig.B.3 Modified Meshed Distribution System with DG 151

Fig.C.1 RBTS-2 153

Fig.C.2 Modified RBTS-2 with DG 154

xxiii

List of Tables

Table No. Title of the Table Page No.

Table 2.1 AHP Matrix 29

Table 2.2 Weightage Coefficients 29

Table 2.3 Control Parameters for FP, TLBO and DE for sample radial

network, meshed network and RBTS-2

29

Table 2.4 Optimized values of failure rates and repair times as obtained

by FP, TLBO and DE and corresponding cost incurred for

radial network

30

Table 2.5 Current and optimized reliability indices and corresponding

value of objective function for radial distribution system

30

Table 2.6 Statistical analysis of sample values of objective function for

radial network

31

Table 2.7 Sections involved in each block of Figure B.2 32



meshed network

33

Table 2.9 Current and optimized reliability indices and corresponding

value of objective function for meshed distribution system

34


meshed network

35

Table 2.11 Optimized values of failure rates and repair times for RBTS-2

as obtained by FP, TLBO and DE

36

Table 2.12 Current and optimized reliability indices for RBTS-2 36


RBTS-2

37

Table 3.1 Interruption costs at load points for sample radial distribution

system

48


network, meshed network and RBTS-2

48


by FP, TLBO and DE for sample radial distribution system

48

Table 3.4 Current and optimized values of Objective function (F)

obtained by FP, TLBO and DE for radial distribution system

49

Table 3.5 Current and optimized reliability indices for radial distribution

system

49

Table 3.6 Interruption cost at load points for sample meshed network 49

xxiv



meshed network

50


obtained by FP, TLBO and DE for meshed distribution system

51

Table 3.9 Current and optimized reliability indices for meshed

distribution system

51



52


obtained by FP, TLBO and DE for RBTS-2

53



system

75

Table 4.2 The parameter values without DG and with DG connected at

different load points of sample radial distribution system

75

Table 4.3 Ranking of the load points with reference to reliability

improvement from maximum to minimum for sample radial

distribution system

76

Table 4.4 Reliability with more than one generators connected

according to the load point ranking for sample radial

distribution system

76


distribution system, sample meshed distribution system and

RBTS-2

76

Table 4.6 Optimized values of failure rates and repair times for radial

system as obtained by FP, TLBO and DE

77


obtained by FP, TLBO and DE for sample radial distribution

system

77

Table 4.8 Current and optimized reliability indices for sample radial

distribution system

77

Table 4.9 Cost-Benefit Analysis for sample radial distribution system 78

Table 4.10 Interruption cost at load points for sample meshed network 78


different load points of meshed distribution system

78


improvement from maximum to minimum for sample meshed

distribution system

79

xxv


according to the load point ranking for sample meshed

distribution system

79

Table 4.14 Optimized values of failure rates and repair times for the

sample meshed distribution system as obtained by FP, TLBO

and DE

80


obtained by FP, TLBO and DE for sample meshed

distribution system

80

Table 4.16 Current and optimized reliability indices for sample meshed

distribution system

81

Table 4.17 Cost-Benefit Analysis for sample meshed distribution system 81


different load points of RBTS-2

82


improvement from maximum to minimum for RBTS-2

83


according to the load point ranking for RBTS-2

83



84


obtained by FP, TLBO and DE for RBTS-2

85


Table 4.24 Cost-Benefit Analysis for RBTS-2 85


system

100

Table 5.2 Optimized values of overall reliability R and other parameters

for sample radial distribution system

100


obtained by FP for sample radial distribution system

101

Table 5.4 Current and optimized reliability indices for sample radial

distribution system

101

Table 5.5 Optimal cost of network, utility and society considering the

impact of continuous RPS on utility for sample radial

distribution system

102

Table 5.6 Optimized values of failure rates and repair times for sample

radial distribution system as obtained by FP

102

Table 5.7 Interruption costs at load points for sample meshed

distribution system

103


for sample meshed distribution system

103

xxvi


obtained by FP for sample meshed distribution system

103

Table 5.10 Current and optimized reliability indices for sample meshed

distribution system

104


impact of continuous RPS on utility for sample meshed

distribution system

104

Table 5.12 Optimized values of failure rates and repair times for sample

meshed distribution system as obtained by FP

105


for RBTS-2

105


obtained by FP for RBTS-2

106



impact of continuous RPS on utility

107


as obtained by FP

108

Table 6.1 System data for Sample Radial Distribution System 124


system

124

Table 6.3 Weighting factors for different Voltage Sag Magnitude and

corresponding values of customer interruption cost (CIC)

124

Table 6.4 Cost coefficients αk, βk and 𝛾𝑘 for Radial Distribution System 124

Table 6.5 Control Parameters for FP, TLBO and DE 125

Table 6.6 Component reactance data 125

Table 6.7 Percentage of fault occurrence according to fault type 125

Table 6.8 Optimized values of failure rates for sample radial system as

obtained by DE, TLBO and FP

125

Table 6.9 Optimized values of fault rates for sample radial system as


126

Table 6.10 Optimized values of repair times for sample radial system as


126

Table 6.11 Current and optimized reliability and power quality indices

for sample radial system obtained by FP, TLBO and DE

126

Table 6.12 Current and optimized values of objective function (F) as

given by DE, TLBO and FP

127

Table A.1 Maximum allowable and minimum reachable values of failure

rates and repair times for sample radial distribution system

148

xxvii

Table A.2 Average load and number of customers at load points for

radial network

148

Table A.3 Cost coefficients 𝛼𝐾 and 𝛽𝐾 for radial network 148

Table B.1 Maximum allowable and minimum reachable values of failure

rates and repair times for sample meshed distribution system

152

Table B.2 Average load and number of customers at load points for

meshed network

152

Table B.3 Cost coefficients 𝛼𝐾 and 𝛽𝐾 for meshed network 152

Table C.1 Failure rates and average repair time of different components

of RBTS-2

154

Table C.2 Maximum allowable and minimum reachable values of failure

rates and repair times for RBTS-2

155

Table C.3 Cost coefficients 𝛼𝐾 and 𝛽𝐾 for RBTS-2 156

Table C.4 Customer data for RBTS-2 156

CHAPTER 1

Introduction

1.1 General:

Electric power systems are extremely complex due to physical size, widely dispersed

geography, national and international interconnections, and many other reasons. The

function of an electric power system is to satisfy the load requirement of the system with

proper maintenance of continuity and quality of service. The ability of the system to provide

electricity adequately is usually termed as reliability. The concept of power system reliability

is quite broad and contains various aspects of its ability to satisfy the requirements of

customers. Earlier prior to 1945, deterministic criteria were used for solving reliability

design problems [1, 2].

As the the primary emphasis has been on providing a reliable and economic supply of

electrical energy to customers, spare or redundant capacities in generation and network

facilities have been inbuilt in order to ensure adequate and acceptable continuity of supply

in the event of failures and forced outages of plant, and the removal of facilities for regular

scheduled maintenance. Along with redundancy, it has to be ensured that the supply should

be as economic as possible [3]. The probability of discontinuity of supply to consumers may

be reduced by increased investment during planning phase. Economic and reliability

constraints are competitive and may lead to difficult optimization problems at both the

planning and operating phases.

As system behavior is stochastic in nature, it is logical to consider the assessment of such

systems based on techniques that respond to this behavior (i.e., probabilistic techniques) [1,

2]. But, it is a fact that most of the present planning, design, and operational criteria are

based on deterministic techniques. However, use of probabilistic approach can be justified

in a way that more objective assessment in to the decision making process can be made by

it.

Power system reliability indices can be calculated using two main approaches which are

analytical and simulation. Analytical techniques represent the system by a mathematical

model and evaluate the reliability indices from this model using direct numerical solutions.

1

Introduction

As frequent assumptions are required to simplify the problem and to produce analytical

model, it sometimes loses some or much of its significance. When complex operating

systems are to be modeled it is utilized. In such situations, simulation techniques are

important. They estimate the reliability indices by simulating the actual process and random

behavior of the system therefore treating the problem as a series of real experiments,

theoretically taking into account virtually all aspects and contingencies inherent in the

planning, design, and operation of a power system.

Due to its large size and complexity, power system cannot be analyzed completely as a single

entity. But this problem can be solved by dividing it in to appropriate subsystems and then

analyzed them separately. Electric power system may be divided into functional zones of (i)

generation (ii) transmission and (iii) distribution. These zones have been combined to give

three hierarchical levels for reliability assignment as shown in Fig-1.1 [4]. The concept of

hierarchical levels (HL) has been developed in order to establish a consistent means of

identifying and grouping these functional zones.

The first level [HL I] relates to generation facility, the second level [HL II] involves

generation and transmission facilities and third level [HL III] refers to the complete system

including distribution network.

Generation

facilities

Transmission

facilities

Distribution

facilities

Hierarchical level I

HL I

Hierarchical level II

HL II

Fig-1.1 Hierarchical levels for reliability evaluation

Hierarchical level III

HL III

2

General

The first level [HL I] relates to generation facility, the second level [HL II] involves

generation and transmission facilities and third level [HL III] refers to the complete system

including distribution network.

The HL structure implies that all generation delivers energy through the transmission system.

Whereas now a days significant role is played by an increasingly amount of individually

small scale generation embedded or distributed within distribution system also. This affects

voltage profile and improves reliability and security of power system. The economical

operation of conventional generation may be affected by this. An optimum co-ordination are

required to be established between distributed generations (DG) and centrally located

conventional generators. Reliability of combined generation as well as transmission system

[HL II] in a single problem formulation have been evaluated by many researchers.

Evaluation of combined reliability of generation, transmission and distribution system using

in a single problem formulation [HLIII] is impractical. Reliability studies of distribution

systems are usually done separately since (i) distribution networks are connected to

transmission system through one supply point and load point indices evaluated may be used

to evaluate reliability indices if needed and (ii) 80% interruptions or unavailability of supply

are observed at distribution side[1,2].

The outages occurring in the system not only impact the revenue economy of the system but

also affects the customers in terms of interruption costs at their ends. In order to reduce the

frequency and duration of these events it becomes necessary to increase investment either in

the better design, operation or both of the system. In other words, reliability of the system is

required to be improved considering costs in mind as reliability and economics play a major

role in decision making. Thus, economics is an extremely important issue/constraint for

deciding threshold values of reliability indices. Acceptable reliability goals can be achieved

by enhanced investments. In order to perform cost-benefit analysis of any objective,

reliability and economics both must be considered together. Reliability improvement is an

important issue to be focussed upon not only while designing and planning phase but also

during operation phase also. During operational phase of a system reliability is improved by

preventive maintenance. It can be executed by trained personnel of the specific area. By

replacing components of the system at specific intervals, it can be improved further. Various

incentive schemes are provided by power companies to the field workers to reduce failure

rates and average repair times of the components. This in turn enhances the reliability

indices. Cost keeps a significant consideration in operational reliability optimization of

3

Introduction

power network. By associating cost values to the ‘reliabilities’ of the system components it

is possible to obtain optimum values of various parameters which provides desired values of

reliability with minimum cost functions. A relation between cost of improvement and

reliability may be obtained. From actual data cost function can be formulated. Past

experience is of great significance for having a reliability growth program wherein the cost

associated with each stage of improvement is quantified. Thus complete consideration of

reliability economics includes two aspects known as ‘reliability cost’ and ‘reliability worth’.

Reliability cost is the amount spent in achieving certain level of reliability. Reliability worth

is the monetary benefits or gain derived by the supplier and customers from that investment.

It is the cost associated with the outages at various levels. Reliability optimization can be

done keeping balance between the two at minimum value of cost function. Reliability worth

assessment is an important function of reliability studies at all levels [5,6,7].

1.1.2 Need of Reliability Evaluation of Distribution system:

Distribution systems are the final link between generation sides and end users. But over the

past few decades, they have been paid considerably less attention in terms of reliability

modeling and evaluation than the generation side since the later are individually very capital

intensive and inadequacy in supply may cause a widespread catastrophic impact both on

the society and environment. Consequently great emphasis have been given on them to

ensure adequacy in supply and meeting the requirements of this part of power system. As a

distribution system is relatively cheap and its outages have more or less localized impact, it

has been paid less attention in regards to the quantitative assessment of the adequacy of

various alternative designs and reinforcements. Contrarily, analysis from various utilities

regarding customer failure statistics shows that almost 80% of the interruptions are

contributed by distribution systems[2]. Most of such system are radial and the system is

exposed to adverse environmental conditions. Hence distribution systems are prone to have

higher frequency of failure and lengthy outage durations.

Distribution systems are currently exploring use of distributed generation (DG) that are

integrated within distribution network. DGs of various capacities may be installed at utility

locations throughout the distribution system to meet various needs e.g. loss reduction, power

quality improvement, transmission and distribution expansion deferral, transformer bank

relief etc. These may serve as standby power and thus useful for reliability improvement of

distribution systems [8]. Due to the presence of DGs, the distribution system has become a

mini composite system requiring analysis similar to [HL II]. The DGs are frequently

4

State of the Art

disconnected from the supply but still connected with the consumers. At that point, it is

important to make a decision that whether they must be continued supplying load from

reliability point of view or must be tripped from safety point of view. From reliability

consideration point of view, DGs are classified as (i) which can not operate without main

source of supply and (ii) which can be operated independently. Certain DGs like

photovoltaic produce real power only. Synchronous condenser type DGs provide only

reactive power. DGs like wind power provide real power but consumes reactive power from

the supply source [9]. Research efforts have been made to reduce unsupplied energy to the

consumers via distribution network. The methodologies used so far regarding reliability

enhancement of distribution systems are (i) reduction in section lengths by adding new

substations (ii) automatic reconfiguration of network to provide alternate paths (iii) using

insulated overhead lines or underground cables (iv) intensifying fault avoidance and

corrective repair methods [10,11,12,13,14].

The purpose of investigation is to develop computationally efficient algorithms for reliability

optimization of distribution systems. In the proposed work different strategies have been

adopted to enhance reliability of distribution systems. Enormous literature is available in this

area. The next section briefly discusses regarding literature survey concerned with this

thesis.

1.2 State of the Art

Considerable change is occurring in the structure and operation of electric power system

throughout the world. It is required to study these changes, the forces creating them and the

possible reliability issues associated with them. This thesis proposes the enhancement of

reliability of a radial and meshed distribution systems by different strategies and the

methodology to be adopted in optimizing it. In reliability evaluation, various methods have

been presented so far in the literature [15,16,17,18]. In its early stage, a methodology known

as gradient projection method was developed for evaluating optimal reliability indices for

distribution system [19]. Reliability issues in the prevailing electric power utility

environment considering the uncertainties associated with deregulation, wheeling and

transmission access and disintegration of the distribution systems have been discussed by

Billinton et al. [20] .

Pinheiro et al.[21] probed into the new IEEE Reliability Test System(RTS-96). A set of

investigations about the bulk reliability performance evaluation of (RTS-96) are presented in

the paper. Several bulk reliability system indices representing a hierarchical level two (HL-

5

Introduction

II) assessment of the new system are provided. This test system permits comparative and

benchmark studies to be performed on new and existing reliability evaluation techniques. It

was developed by modifying and updating the original IEEE RTS (referred to as RTS-79)

to reflect changes in evaluation methodologies and to overcome perceived deficiencies [22].

In [23], an algorithm was developed by the researchers to obtain an optimal solution by

considering a nonlinear objective function with both linear and nonlinear constraints for a

large scale radial distribution system. In [13], an evolutionary algorithm was presented to

reliably design a distribution system using modified genetic algorithm for optimization.

Wang et al.[24] proposed an algorithm for assessing reliability indices of general

distribution system which presents a practical reliability assessment algorithm for

distribution systems of general network configurations. This algorithm is an extension of the

analytical simulation approach for radial distribution systems. Amjady et al.[25] published

paper on optimal reliable operation of hydrothermal power systems with random unit

outages in which, a new model for long term operation of hydrothermal power systems is

introduced and a method for obtaining an optimal solution is also developed. The objective

has been to minimize the total cost of the system as well as the expected interruption cost of

energy (EIC) during a given planning horizon. In [26], a composite reliability evaluation

model for different types of distribution systems was presented describing a set of composite

distribution system reliability evaluation models that can be applied to a non-radial type

system. The developed models reflect the effect of distribution substations, primary

distribution systems, and the interaction between them. Pedro et al. [27] presented a paper

in which a matured evolutionary –based application is used to search for the optimum trade

off between individual quality of service (QoS) and system reliability. Tradeoff results are

presented to compare the traditional with the modern regulation designs and also illustrated

that system optimum reliability must be decreased in order to improve individual quality at

constant investment. Reducing the overall cost and improving the reliability are two primary

but conflicting objectives for composite power system. Scheduling of appropriate preventive

maintenance requires optimization among multiple objectives. Yang and Chang [28]

developed an integrated methodology to achieve the mentioned objectives. A decomposed

approach for reliability design of a radial distribution system using PSO was presented in

[29]. A technique determining optimal interval for major maintenance activities in

distribution systems was given in [30]. In [31], authors proposed reliability enhancement of

distribution systems using sensitivity analysis. The paper describes a two stage methodology

for reliability enhancement using sensitivity analysis. The same authors developed a

6

State of the Art

technique for improving reliability indices of a radial distribution system in which a method

for optimum determination of failure rate and repair time for each component of a radial

distribution system is proposed. Here objective function is selected as to minimize the

increased cost which is a function of change in failure rate and repair time [32].Outages in

overhead distribution systems caused by different factors significantly impact their

reliability. A paper proposing a methodology for year-end analysis of animal-caused outages

in the past year has been presented by Gui et al. [33]. Vladimiro et al. [34] presented an

application of evolutionary particle swarm optimization (EPSO) based methods to evaluate

power system reliability. Here the results obtained with EPSO are compared to traditional

Monte Carlo simulation (MCS) and with other population based (PB) methods. Arya et al.

[35] proposed an algorithm for modifying failure rate and repair time of a distributor segment

considering the outage due to overloading and repair time omission, here termed as repair

tolerance time. This methodology has been implemented on a meshed distribution network.

The same authors have described a method for reliability optimization of radial distribution

systems by applying differential evolution. Penalty cost functions have been constructed.

They are functions of failure rates and repair times. Constraints on customer and energy

based indices have been considered. [36]. For overhead distribution systems, the reliability

of covered overhead line could considerably be improved using various alternative methods.

Li et al. [37] has applied the Monte Carlo simulation (MCS) to obtain reliability and safety

indices for a distribution system.

Arya et al. [38] have described a methodology for reliability assessment of electrical

distribution system accounting random repair time omission for each section. R. Arya et al.

[39] have described an algorithm for optimum modifications for failure rate and repair time

for a radial electrical distribution system. Coordinated aggregation based particle swarm

optimization (CAPSO) has been used for optimization. The same authors [40] have

described an analytical methodology for reliability evaluation and enhancement of

distribution system having distributed generation (DG). In this paper, standby mode of

operation of DG has been considered for this purpose. In [41], authors used Monte Carlo

simulation (MCS) along with PSO for reliability planning of power network in terms of

forced outage rate (FOR) allocation. In [42], authors used PSO for multi objective planning

and redundancy allocation. Distribution reliability indices neglecting random interruption

duration have been found in [43]. The algorithm is based on smooth boot strapping

technique along with Monte Carlo simulation (MCS). In [44], authors presented an efficient

Genetic Algorithms (GAs) based method to improve the reliability and power quality of

7

Introduction

distribution systems using network reconfiguration. Reliability centred maintenance

optimization for distribution systems has been presented in [45]. Bakkiyaraj et al. [46] have

given optimal reliability enhancement model by applying population based natural

computational optimization algorithms. Hashemi-Dezaki et al. [47] have proposed a novel

approach of internal loops (ILs) to optimize electrical distribution system reliability. Li Duan

et al. [48] have presented a method for the reconfiguration of distribution network for loss

reduction and reliability improvement by enhanced genetic algorithm. Yssaad et al. [49]

have presented a new rational reliability centred maintenance optimization method for power

distribution system.

As the electricity selling market has started becoming competitive, it is a challenging task

for any utility to provide qualitative service to the customers keeping the cost on its operation

and maintenance such as to provide low cost services to them. The optimum value of system

reliability with least combined cost thus found may lead towards value based reliability

planning of distribution systems [50]. Cossi et al. [51] gave a formulation regarding planning

of primary distribution networks considering the reliability costs obtained by calculating the

non-supplied energy due to the repairing and switching operations. Kahrobaee and

Asgarpoor [52] have determined the optimum standby electricity storage capacity in a smart

grid based on reliability indices such as Expected Interruption Cost (EIC) using particle

swarm optimization. Beni et al. [53] presented a practical method to estimate customer

damage function (CDF) which describes relationship between interruption duration and its

customer economic losses due to interruptions. Nelson and Lankutis [54] presented a method

to quantify the costs associated with interruptions of service to customers of electric utilities.

Schellenberg et al. [55] developed an Interruption Cost Estimate (ICE) calculator, a tool

designed for electric reliability planners at utilities, government organizations or other

entities that are interested in estimating interruption costs and/or the benefits associated with

reliability improvements. Tsao et al. [56] presented a value based reliability assessment

considering different topologies for planning a new distribution system based on comparison

of the distribution system reliability cost/worth analysis for different planning topologies.

Sonvane and Kushare [57] have increased reliability of distribution system by placing

capacitors in proper way. An optimized balance between the costs of reliability and capacitor

bank has been found in this paper. Narimani et al. [58] have presented an algorithm to

reconfigure distribution feeder considering reliability, loss and operational cost by applying

Enhanced Gravitational Search Algorithm (EGSA). Bakkiyaraj and Kumarappan [59] have

given optimal reliability enhancement model of electrical distribution system based on the

8

State of the Art

trade-off between the investments required for improving reliability and reduction in the

costs of power interruptions applying natural computational algorithms. The optimal

locations of distributed static series compensator (DSSC) to enhance the power system

reliability by reducing expected damage cost (EDC) have been found by Ghamsari et al.

[60]. An algorithm for reliability optimization of power distribution systems considering cost

minimization has been given by Banerjee et al.[61]. Ghosh and Kumar [62] have given a

methodology for feeder reconfiguration considering overall system cost and reliability

incorporating both primary and secondary power distribution systems. Küfeoğlu and

Lehtonen [63] have given a review summarizing the academic work done in the fields of

worth of electric power reliability and customer interruption costs assessment techniques

from the year 1990 to 2015. Lei Sun et al.[64] presented a smart substation allocation

model to determine the optimal number and allocation of smart substations in a given

distribution system with the upgrade costs of substations and the interruption costs of

customers taken into account considering reliability criterion.

Distributed generations (DGs) are becoming the best alternatives for power distribution

companies to increase reliability of distribution systems. DGs enhance performance of the

systems by improving reliability, voltage profile and reducing losses of the system. In recent

years, many researchers have worked to enhance reliability of distribution systems

employing DG. Yousefian and Monsef [65] have proposed a method to determine best

locations of DGs based on reliability indices using sequential Monte Carlo simulation. In

[66] authors have assessed the impact of conventional and renewable distributed generation

(DG) on the reliability of distribution system. An integrated Markov model which

incorporates the DG adequacy in terms of transition, DG mechanical failure and starting and

switching probability have been used for the DG reliability assessment. Awad et al.[67] have

proposed a methodology for allocating dispatchable distributed generation units in

distribution systems to improve system reliability economically. An optimized balance has

been obtained between the cost on installation and operation of DGs and the amount to be

paid worth of reliability by the customers in the research. Kumar et al.[68] have presented

optimal placement and sizing of multiple distributed generators to achieve higher system

reliability in large-scale primary distribution networks using a random search algorithm

known as cat swarm optimization. Abbasi and Hosseini [69] have studied the effect of

distribution network reconfiguration, size and allocation of DGs in the presence of storage

system on the reliability improvement of the system. Bagheri et al. [70] have proposed

9

Introduction

distribution network expansion planning incorporating DGs in an integrated way considering

reliability also as one of the aspects. Battu et al. [71] have given solution for optimal

locations of DGs in the distribution system for reliability improvement considering total cost

of of power consumed by the system. Arya [72] has presented a methodology for evaluating

customer and energy oriented reliability indices for distribution systems in the presence of

distributed generations, considering the effect of omission of random tolerable interruption

durations at load points. It has been done using Bootstrapping technique. In [73] authors

have found optimum value of primary reliability indices with and without DGs incorporated

in the distribution system. This has been done with differential search algorithm. Kansal et

al. [74] have found optimal allocations of DGs in distribution system considering

maximization of profit. In [75] authors have made DG scheduling maximizing reliability of

the system. A cost-benefit analysis is made here considering various costs involved in the

calculations.

Due to introduction of restructuring in power systems, service quality regulation has become

very important in distribution system. A reward and penalty scheme (RPS) regulates and

ensures the service reliability. It is a financial tool implemented by regulator to maintain

service reliability. A reward and penalty scheme (RPS) penalizes the distribution company

for poor reliability and rewards it for better one in performance based regulation (PBR). In

performance based regulations incentives are decided for strong efficiency (in terms of

profit) by the companies. In RPS financial incentives are created for distribution companies

to maintain or change their quality level. The regulator tries to maintain socioeconomically

optimum reliability level which minimizes the total reliability cost for society with RPS [76].

The concept of using reliability indices in RPS was discussed in [77].In [78] different

reward- penalty models using real system reliability data from Tehran Regional Electrical

Company had been applied presenting their applications and properties. An approach for

improving service reliability of distribution system with RPS integrated with clustering

analysis was presented in [79]. Here the utilities are categorized and the performance of

utilities in one cluster has been compared with the other members of same cluster. The effect

of system reliability improvement on the financial risk due to RPS has been mentioned in

[80]. In [81] main requirements for designing and implementing of an effective RPS have

been investigated. Here different types of RPS have been described comprehensively. In [82]

an algorithm is presented to obtain the parameters of RPS for each electric company by using

data envelopment analysis (DEA) and fuzzy c-means clustering (FCM) based on system

10

State of the Art

average interruption duration index. In [83] a method was proposed to not only motivate the

utilities to improve their service reliability but equalize the total rewards paid and total

penalties received by the regulators. In [84] a method for designing procedure for

reward/penalty scheme based on the concept of Yardstick theory has been proposed.

A modern electric power system must be designed such as to supply acceptable levels of

electrical energy to customers. Voltage sags are simple power quality disturbance events

which may cause considerable economic losses because industrial processes rely on

electronic power-control devices. Thus, the power supplied to utilities must be reliable

having good quality. In [85] authors have discussed impact of distributed generation on

reliability and power quality indices. Voltage sag mitigation and reliability improvement by

the network reconfiguration of utility power system has been discussed in [86]. An analytical

method for evaluating the voltage sag performance of a distribution network has been

discussed in [87]. The report [88] describes the relation between distributed generation and

power quality. The direct impact of increased wind power penetration on power quality and

reliability of distribution network has been focussed here. The authors in [89] have applied

an evolutionary-based approach for multi-objective reconfiguration in electrical power

distribution networks for improving power quality indicators like power system’s losses and

reliability indices. Here the micro genetic algorithm (mGA) is used to handle the

reconfiguration problem as a multi-objective optimization problem. In [90], a method for

improving bus voltage magnitude during voltage sag by applying network reconfiguration

to the exposed weak area in distribution systems is presented. In [91] authors have addressed

to enhance power quality issues such as harmonics and voltage sags while mitigating power

losses by applying network reconfiguration . It has been solved using a complicated

combinatorial optimization where best switching options are optimized. Based on the failure

modes and effects analysis framework (FMEA), the paper [92] has presented a non-

sequential Monte Carlo method (FMEA-NSMC) for distribution system reliability

assessment considering sustained interruptions, momentary interruptions and voltage sags.

In the paper [93], an optimization method is proposed to find the optimal and simultaneous

place and capacity of the DG units to reduce losses and to improve voltage profile of IEEE

30 bus test system calculated with and without DG placement. A Genetic Algorithms based

method has been presented in [94] to improve reliability and power quality of distribution

systems using network reconfiguration. Various power quality and reliability objectives such

as feeder power loss, system’s node voltage deviation, system’s average interruption

11

Introduction

frequency index, average interruption unavailability index and energy not supplied are

considered in a single objective function. Reliability and power quality have been improved

in [95] by minimizing the number of voltage sags (Nsag) propagated and other reliability

indices such as the average system interruption frequency index, sustained average

interruption frequency index, and momentary average interruption frequency index

employing optimum network reconfiguration. In [93] a new method using particle swarm

optimization has been proposed to considerably reduce the total power loss in the system

and improved voltage profiles of the buses and reliability indices. It has been done by

employing optimum location, size and number of distributed generations. The paper [96] has

presented a review of the main power quality (PQ) problems with their associated causes

and solutions with codes and standards. D-STATCOM has been used in [97] for voltage sag

and swell mitigation in renewable energy based distributed generation systems. In [98] it has

been shown to identify the power quality issues and the impact of DG or other non-linear

loads on LV distribution networks aiming to develop an equipment able to remove or

mitigate all electromagnetic disturbances considering the characteristics and sensitivity of

end use equipment within customer facilities.

1.3 Motivation & Objectives

It has been observed from literature survey that limited work has been done on the

development of quantitative technique for distribution system reliability evaluation and

enhancement. As distribution system being final link between transmission network and

ultimate customers, it is one of the most important parts of the power system. Due to less

cost and localized effect of outages on it compared to transmission network, it has been given

less importance. But the statistical data in technical reports show that more than 80% of all

customer interruptions occur due to failure/outage in distribution systems only. This requires

the distribution system to be adequately reliable and the need to evaluate its reliability.

Several other aspects are also considered which show the need to evaluate the reliability of

distribution systems. A given reinforcements scheme may be relatively inexpensive but large

sums of money are expanded collectively on such system. It is also necessary to ensure

balance in the reliability of generation, transmission and distribution. Another important

point of consideration is to select an option for reliability improvement among the number

of alternatives available. To achieve this, various methodologies have been developed by

researchers for reliability evaluation of distribution system.

12

Motivation & Objectives

In view of the above mentioned work done by various researchers in the evaluation and

enhancement of distribution system reliability so far, this thesis too covers the work in the

same line. In this thesis, reliability enhancement is done on a sample radial [31] and mesh

distribution [13] network and Roy Billinton Test System (RBTS-2) [99]. The motivation in

the present work is to develop computationally efficient algorithm for reliability

optimization using soft computing techniques [100,101,102]. Literature survey reveals

deficiency in the following aspect of reliability studies of distribution systems.

(i) Limited research efforts have been made in the area of distribution system

reliability enhancement.

(ii) Inclusion of DG for reliability enhancement. Location of DGs from reliability

point of view. The effects of DG need to be incorporated in optimization

algorithm.

(iii) Inclusion of reward/penalty studies in an optimization algorithm.

(iv) Effect of voltage sag on reliability studies and its inclusion in an optimization

algorithm.

The objectives of the proposed research work in this thesis are as follows.

I. Defining different methodologies by which reliability of electrical distribution

systems can be enhanced.

II. Improvement in reliability indices below their target values considering the budget

allocated to achieve the same by developing an algorithm embedding metaheuristic

optimization techniques.

III. Developing an algorithm to enhance reliability of the distribution system by

achieving proper balance between the cost incurred on customers due to interruptions

and the utility cost to achieve the desired reliability targets.

IV. Enhancing reliability by placing DGs at various locations. Deciding locations of DGs

from the point of view of enhancing reliability optimally by developing

methodologies for both the tasks.

V. Incorporating reward/penalty imposed to the utility for achieving reliability targets

below/above certain target values. Deciding the optimum value of reward/penalty

corresponding to achieving the desired reliability targets.

13

Introduction

VI. Assessment and enhancement of reliability of distribution system considering power

quality (PQ) disturbance events, such as voltage sags for different kind of faults in

the system.

In all the objectives mentioned above, optimized values of primary as well as customer and

energy oriented reliability indices [103] are to be found so as to set targets for distribution

companies for achieving them.

1.4. Outline of the thesis

The thesis includes the work done organised in the following way.

Chapter - 1 presents a critical survey of the past works concerning power system reliability

and clearly spells out the motivations and objectives of the research work carried out in this

thesis.

Chapter – 2 describes a computationally efficient algorithm for reliability optimization of

sample radial distribution system, meshed distribution system and RBTS-2 modifying the

values of the two decision variables (failure rate and repair time) of different section of the

distribution systems. Here optimization has been done considering the constraint of allocated

budget to enhance reliability. As customer and energy based reliability indices are in terms

of primary indices, they too are optimized. The optimization has been done by flower

pollination (FP) [101], teaching learning based optimization (TLBO) [102] and differential

evolution (DE) [103]. The developed algorithm has been implemented on a sample radial

distribution network, sample mesh distribution network and Roy Billinton Test System-Bus-

2 (RBTS_2) and the results thus obtained by the three methods have been compared.

Chapter – 3 presents a proposed methodology which shows enhancement of reliability by

optimizing total reliability cost of electrical distribution systems. The total reliability cost

consists of cost incurred by utility and customers both. An objective function in terms of

failure rates and repair times i.e. primary reliability indices has been formulated which

depicts both these costs . Hence, optimization of the objective function will give a balance

between these costs with optimized values of primary reliability indices. This optimization

has been done considering the constraints of achieving customer and energy based reliability

indices below threshold/target values. The methodology has been applied on a sample radial

network, sample mesh network and Roy Billinton Test System- Bus 2 (RBTS-2).

14

Outline of the thesis

Chapter – 4 provides the development of an algorithm for reliability optimization of

electrical distribution system accounting the effect of distributed generation (DG) connected

at load points. Here, an algorithm finding out proper locations for connecting DGs from

reliability point of view has been presented. A cost function which accounts cost of failure

rate and repair time modification and customer interruption cost along with additional cost

of expected energy supplied by DG has been constructed. The effect of DG on reliability

and parameter modifications have been obtained by implementing the developed algorithm

on the three sample systems as before and results have been obtained using FP,TLBO and

DE strategies.

Chapter – 5 represents the development of algorithm for reliability optimization of electrical

distribution system incorporating reward/penalty scheme (RPS). Here the cost function

formulated includes cost of reward/penalty. Optimized values of reward/penalty have been

found for the set value of target reliability indices. Optimized values of maintenance cost,

customer interruption cost and additional cost required to be spent by DGs to achieve the

reliability targets have been found by the computational methods in consideration and this

algorithm has been applied on all the systems as considered so far.

Chapter – 6 depicts the algorithm for reliability enhancement considering effect of power

quality disturbance such as voltage sag . For different kinds of fault, the voltage sag

occurring at different load points and substantially its effect on reliability of system has been

considered and optimized values of reliability indices and power quality index have been

found considering the constraints imposed. It has been implemented on the distribution

systems under consideration.

Chapter – 7 highlights the main conclusions and significant contributions of this thesis and

presents scope for future work in the area of distribution system reliability evaluation and

optimization. The methodologies developed in the contributory chapters 2-6 have been

implemented on sample radial and meshed distribution networks and Roy Billinton Test

System -Bus-2 (RBTS-2). The vital findings, contribution of the thesis and future scope are

described in this chapter.

15

CHAPTER 2

Application of Metaheuristic Optimization

Methods for Reliability Enhancement of Electrical

Distribution Systems based on AHP

2.1. Introduction

As the distribution systems proves to be final link between transmission network and end

customers, they are supposed to render continuous and quality electric service to their

customers at a reasonable rate with economical use of available facilities and options. It is

required to intensify fault prevention and corrective maintenance measures for maintaining

reliable services to the customers. Additional budget is required for the same. In fact by

doing so, failure rate and repair time of the sections are modified. Generally fault tolerant

measures should be included during planning stage only. Later on such additional measures

may not be always justified as they require extra expenditures to fulfil them. In this chapter,

the objective has been to achieve desired reliability goals after having modified the failure

rates and repair times of the distributor sections. Here, this modification has been done by

providing rational weightage to the customer and energy oriented reliability indices.

Regarding the evaluation and enhancement of distribution reliability, various aspects have

been presented so far by researchers [103].

This chapter deals with developing an algorithm to enhance the reliability indices of

distribution system using an analytic hierarchical process (AHP) [104]. The AHP method

has proven to be effective in solving multi-criteria problems, involving many kinds of

aspects. In view of this a multi-objective function has been proposed to achieve the motives

of this chapter giving proper weightage to all the terms in the function.

2.2 Indices Evaluation for Radial Distribution System [103]

2.2.1 Basic Indices: A radial distribution system consists of a set of series components,

including lines, cables, disconnects (or isolators), busbars, etc. A customer connected to any

load point of such a

16

Indices Evaluation for Meshed Distribution System

system requires all components between itself and the supply point to be operating.

Consequently the principle of series systems can be applied directly to these systems. The

three basic reliability indices i.e. average failure rate, 𝜆𝑠𝑦𝑠 , average outage time, 𝑟𝑠𝑦𝑠 , and

average annual outage time, U𝑠𝑦𝑠 are given by

𝜆𝑠𝑦𝑠,𝑖 = ∑ 𝜆𝑘 (2.1)

U𝑠𝑦𝑠,𝑖 = ∑ 𝜆𝑘𝑟𝑘 (2.2)

𝑟𝑠𝑦𝑠 =𝑈𝑠𝑦𝑠

𝜆𝑠𝑦𝑠=

∑ 𝜆𝑘𝑟𝑘

∑ 𝜆𝑘 (2.3)

Where,

𝜆𝑠𝑦𝑠 System failure rate.

𝜆𝑘 Failure rate of 𝑘𝑡ℎ section.

𝑟𝑘 Average repair time of 𝑘𝑡ℎ section.

U𝑠𝑦𝑠 Unavailability of series system (hrs/year).

𝑟𝑠𝑦𝑠 Average interruption duration of the series system.

𝜆𝑠𝑦𝑠 , 𝑟𝑠𝑦𝑠 and U𝑠𝑦𝑠 are the basic indices required to evaluate for a distribution system

reliability.

2.3 Indices Evaluation for Meshed Distribution System [103]

The basic techniques used to evaluate the reliability of distribution systems (sec 2.2) have

been applied to simple radial networks for long. Though these basic techniques have been

used in practice for some considerable time, they are restricted in their application because

they cannot directly be used for systems containing parallel circuits or meshed networks. In

recent years distribution reliability evaluation techniques have been enhanced and developed

rapidly [103] and now comprehensive evaluation is also possible. These techniques are very

useful in complete analysis of parallel and meshed networks and can be used for all failure

as well as repair modes known to the system planner or operator. The network being analysed

17

Application of Metaheuristic Optimization Methods for Reliability Enhancement of Electrical


is divided into groups, and the indices evaluated for a group is used as an input to the next

level and so on until the customer load points have been reached. The basic indices

commonly used to represent distribution system reliability are system failure rate and

interruption duration at the load point.

2.3.1 Approximate Relations for Evaluation of Indices for Series and Parallel

configuration

A distribution system being radial or mesh, can be solved as explained here. A radial network

can be solved by applying series law of reliability (sec. 2.2). For a meshed system, the

network is sequentially reduced by combining gradually series and parallel components.

Approximate relations used to evaluate three reliability indices are as follows.

System failure rate (𝜆ser)

𝜆ser = ∑ 𝜆𝑘 / year (2.4)

Average interruption duration per year (𝑈ser)

𝑈𝑠𝑒𝑟 = ∑ 𝜆𝑘𝑟𝑘 h/year (2.5)

Average interruption duration (𝑟ser)

𝑟𝑠𝑒𝑟 = 𝑈ser 𝜆ser ⁄ h (2.6)

𝜆𝑘, 𝑟𝑘 are failure rate and average repair time of 𝑘𝑡ℎ distributor segment respectively, where

𝑘 ∈ 𝑠, 𝑠 being the set of distributor segments connected in series.

If two components are in parallel having 𝜆𝑖 and 𝜆𝑗 as failure rates and 𝑟𝑖 and 𝑟𝑗 are repair

times, then the three basic reliability indices are given as follows

𝜆𝑝𝑎𝑟𝑎 =𝜆𝑖𝜆𝑗(𝑟𝑖+𝑟𝑗)

8760 /year (2.7)

𝑟𝑝𝑎𝑟𝑎 =𝑟𝑖𝑟𝑗

𝑟𝑖+𝑟𝑗 h (2.8)

𝑈𝑝𝑎𝑟𝑎 = 𝜆𝑝𝑎𝑟𝑎𝑟𝑝𝑎𝑟𝑎 h/year (2.9)

In evaluating these relations, it is assumed that repair rate is much greater than failure rate.

18

Customer oriented and energy oriented indices

2.4 Customer oriented and energy oriented indices:

The three primary indices are fundamentally important but they do not always give a

complete representation of the system behaviour and response as they do not consider

number of customers and average load at load points. In order to exhibit the severity or

significance of an outage, additional reliability indices are frequently evaluated. The

additional indices that are most commonly used are defined as [103]:

(a) Customer-orientated indices:

(i) System average interruption frequency index, SAIFI

SAIFI =total number of customer interruptions

total number of customers served=

∑ 𝜆𝑠𝑦𝑠,𝑖 𝑁𝑖

∑ 𝑁𝑖 (2.10)

(ii) System average interruption duration index, SAIDI

SAIDI =sum of customer interruption durations

total number of customers =

∑ 𝑈𝑠𝑦𝑠,𝑖𝑁𝑖

∑ 𝑁𝑖 (2.11)

(iii) Customer average interruption duration index, CAIDI

CAIDI =sum of customer interruption durations

total number of customer interruptions=

∑ 𝑈𝑠𝑦𝑠,𝑖𝑁𝑖

∑ 𝜆𝑠𝑦𝑠,𝑖 𝑁𝑖 (2.12)

(b) Energy –oriented indices:

(i) Expected energy not supplied index, (EENS)

EENS = ∑ Li Usys,i (2.13)

(ii) Average energy not supplied, AENS or average system curtailment index,

(ASCI)

AENS =total energy not supplied

total number of customers served=

∑ 𝐿𝑖𝑈𝑠𝑦𝑠,𝑖

∑ 𝑁𝑖 (2.14)

19



Where,

𝑖 Load point,

𝜆𝑠𝑦𝑠,𝑖 Average failure rate of load point 𝑖 ,

U𝑠𝑦𝑠,𝑖 Average annual interruption duration,

N𝑖 Number of customers connected to load point ,

L𝑖 Average load connected to load point ,

Where,

𝜆𝑝𝑎𝑟𝑎 Failure rate of parallel combinations

𝑟𝑝𝑎𝑟𝑎 Average interruption duration of parallel combination

𝑈𝑝𝑎𝑟𝑎 Average interruption duration per year of the parallel combination

2.5 Problem Formulation

This sections depicts a method for enhancing reliability of radial distribution system. Here,

to achieve this, optimal values of failure rates and repair times of the distributor segments

are found. These are the primary reliability indices and they measure the adequacy of the

system undoubtedly. Though these indices are of fundamental importance, they may not

always give the total performance of the system. As severity of the outages are given by

customer and energy based indices mentioned in section 2.4, they are frequently used to

depict the characterization of distribution system.

Various associated cost are represented implicitly by these indices and they may be reduced

by proper selection of the desired values of these indices. Cost associated to system failure

is represented by SAIFI considering relative weightage of customers also connected to the

load points. In the same way, SAIDI shows the system interruption duration which is the

product of system failure rate and average annual outage (𝜆𝑠𝑦𝑠𝑟𝑠𝑦𝑠) of the system. CAIDI

represents satisfaction of the customers for the overall system. Cost of energy not supplied

to consumer is depicted implicitly by AENS and hence is an indicator of not only customer

satisfaction but also represents loss of revenue to the utility. Hence, these indices are very

20

Problem Formulation

important and their desired threshold/target values are required to be selected. As these

indices mainly depend on failure rates and repair times of the distributor sections,

modification of them will require additional budget to achieve the desired targets. Hence

lesser the target values of these indices are, higher is the cost associated with preventive

maintenance and corrective repair.

Though all these indices keep significance from the performance point of view of the system,

AENS may be given little more significance sometimes as it is related to energy not supplied

during the interruptions. Considering this, weightage to this indices has been decided. This

has been done by Analytic Hierarchy Process (AHP) which is used to solve multi objective

problems effectively.

In view of this, reliability optimization problem is formulated as follows. The objective

function to be optimized is selected as,

F = (𝑤1SAIFI

SAIFIt) + (𝑤2

SAIDI

SAIDIt) + (𝑤2

CAIDI

CAIDIt) + (𝑤3

AENS

AENSt) (2.15)

Objective function (2.15) is optimized subject to following inequality constraints.

(i) Constraints on the decision variables

λk,min ≤ λk ≤ λk,max (2.16)

rk,min ≤ rk ≤ rk,max (2.17)

k = 1, … … … … … , Nc

(ii) The total cost of modification of failure rates and repair times of all the sections should

be less than the fixed allocated budget

∑ (αK λK2⁄ + βK rK⁄ )NC

K=1 ≤ CBUDGET (2.18)

Where,

λk ,rk are average failure rate and repair time of kth section. λk,min and rk,min are

reachable minimum values of failure rate and repair time of kth section. λk,max and rk,max

are maximum allowable failure rate and repair time respectively.

SAIFIt, , SAIDIt, CAIDIt and AENSt are target/threshold values of the respective indices.

CBUDGET is the total specific budget available for preventive maintenance and corrective

21



repair. αK, βK are cost coefficients. w1, w2, w3 and w4 are the relative weightage given to

the normalized values of SAIFI, SAIDI , CAIDI and AENS in the objective function (2.15).

The objective function of equation (2.15) is minimized subject to constraints (2.16), (2.17)

and (2.18) obtaining optimal values of failure rate and repair time for each section of the

distribution systems. The overall failure rate is contributed by various failure modes. Some

may have constant failure rates while some modes of failure contribute to increasing failure

rate. Such types require preventive maintenance and repairing or replacement of

subcomponent in time so as to have overall failure rate practically constant. In this chapter,

optimization has been carried out considering overall failure rate which is combination of

failure rates due to various modes of failure.

By failure rate optimization, targets can be assigned to the crew involved in maintenance

activities: preventive maintenance and repair and persons involved in managerial work.

Thus, by doing so ultimately failure rates can be reduced reaching to their root causes. The

modes responsible for higher failure rates should be given more weightage in regards to

preventive maintenance efforts. In the same way, targets may be set to reduce corrective

repair time. The objective function is the sum of the normalized weighted values of SAIFI,

SAIDI , CAIDI and AENS. The weightage are decided by AHP which is explained in the

later section. Constraints (2.16) and (2.17) impose bounds on the decision variables. Lower

bounds represent minimum reachable value of the decision variables decided with respect to

reliability growth testing model [105]. Similarly reliability monitoring mode give upper

bounds on these decision variables. With the change in the values of decision variables, cost

varies. Cost required to achieve lesser values of decision variables will be higher and vice

versa. A cost curve can be plotted and a cost function can be decided based on past data.

Based on Duane’s growth model [105], the typical cost functions have been selected for each

component in this chapter. Inequality constraints on total cost of repair time and failure rate

has been considered and given as relation (2.18).

The formulated problem is proposed to be solved using flower pollination (FP) [100]

,teaching learning based optimization (TLBO)[101] and differential evolution optimization

algorithms[102] for the sample radial and meshed networks and Roy Billinton Test

System,Bus-2 (RBTS-2). Thus for each section of the distribution systems under

consideration, optimal values of repair time and failure rates are obtained considering budget

allocated for them.

22

Analytic Hierarchical Process (AHP)

2.6 Analytic Hierarchical Process (AHP)

The AHP method has proved to be effective in solving multi-objective problem [104]. It is

used as the decision making technique because of its efficiency in handling quantitative and

qualitative criteria for solution of a problem.

The AHP divides a complex decision problem in to a hierarchical structure. A pairwise

comparison is made to decide relative weightage for different individual options/alternatives

/objectives. Pairwise comparisons are usually quantified by the linear scale or the nine-point

intensity scale proposed by Saaty [104]. By doing pairwise comparison, each linguistic term

is transformed in to numerical intensity values like {9,8,7,6,5,4,3,2,1,1/2,1/3,1/4,1/5,

1/6,1/7,1/8,1/9}. A judgement matrix is formed based on this as follows.

𝑀 = [

𝑎11 𝑎12 ⋯ 𝑎1𝑛

𝑎21 𝑎22 ⋯ 𝑎2𝑛

⋮ ⋮ ⋱ ⋮𝑎𝑛1 𝑎𝑛2 ⋯ 𝑎𝑛𝑛

] (2.19)

Where, 𝑎𝑖𝑗 ∈ {9,8,7,6,5,4,3,2,1, 1 2⁄ , 1 3⁄ , 1 4⁄ , 1 5⁄ , 1 6⁄ , 1 7⁄ , 1 8⁄ , 1 9⁄ } and 𝑎𝑖𝑖 =

1,

where 1 ≤ 𝑖, 𝑗 ≤ 𝑛 . 𝑎𝑖𝑗 shows pairwise judgement representation. Here, 𝑎𝑖𝑗 =1

𝑎𝑖𝑗 .

If M is perfectly consistent, then the principal eigenvalue 𝐷𝑚𝑎𝑥 is equal to number of

comparisons n.

That is 𝑀𝑤 = 𝑛𝑤.

Where, 𝑤 = (𝑤1, 𝑤2, … . , 𝑤𝑛)𝑇 is the principal eigenvector corresponding to 𝐷𝑚𝑎𝑥.

The effectiveness of the judgement matrix M and consistency of the results are checked by

an index called consistency ratio (CR) as follows [106].

𝐶𝑅 =(

𝐷𝑚𝑎𝑥−𝑛

𝑛−1)

𝑅𝐼 (2.20)

Where, 𝐷𝑚𝑎𝑥 is the largest eigenvalue of matrix M and RI is the random index. Here RI=0.58

for n=3 [104].

The AHP algorithm:

The steps of the AHP algorithm are as follows.

23



1. Set up the hierarchical model by comparing the different objectives to be evaluated.

2. Construct a judgement matrix M. It reflects the user’s knowledge about the relative

importance of each objective. For the objective function used in this chapter, the

matrix formed is as shown in Table 2.1

3. Calculate the maximum eigenvalue and corresponding eigenvector for the

judgement matrix M. By normalizing the eigenvector the vector containing the

weightage of different objectives is found as shown in Table 2.2.

4. Find consistency ratio CR by relation (2.20).

5. A consistency ratio of 0.10 or less is considered acceptable.

The nominal weightage coefficients have been obtained using AHP and are as shown in

Table 2.2. However, if satisfactory adequate indices in terms of the threshold values are not

obtained, these have to be judiciously varied so as to get all indices within threshold limit.

Due to normalization, these additional variation in weighting factor has not been required as

all the indices found are within threshold limit.

2.7 Solution Methodology using FP algorithm

The overview of Flower pollination algorithm has been presented in Appendix D. The

method of solving the formulated problem mentioned in section 2.5 by FP is as follows.

Step 1. Data input 𝜆𝑘,𝑚𝑎𝑥,𝑟𝑘,𝑚𝑎𝑥 , 𝜆𝑘,𝑚𝑖𝑛, 𝑟𝑘,𝑚𝑖𝑛 and SAIFIt, SAIDIt, CAIDIt and AENSt .

Step 2. Initialization: Generate a population of size ‘M’ (flowers) for failure rate λ and repair

time r each by relation (D.3), where each vector of respective population consists of failure

rate and repair time of each component respectively. These values are obtained by sampling

uniformly between lower and upper limits as given by relation (2.16) and (2.17).

Step 3. Evaluate 𝜆𝑠𝑦𝑠,𝑖 , 𝑟𝑠𝑦𝑠,𝑖 and 𝑈𝑠𝑦𝑠,𝑖 at each load point.

Step 4. Evaluate SAIFI, SAIDI, CAIDI and AENS as mentioned in the relations (2.10),

(2.11), (2.12) and (2.14) respectively for vectors of the population.

Step 5. Calculate value of objective function 𝐹 for all vectors in the population i.e.𝐹(𝑋𝑖(𝑘)

),

𝑖 = 1, … … … … … , ′𝑀′ as given by relation (2.15).

Step 6. Evaluate inequality constraints from the relations (2.16), (2.17) and (2.18] for each

vector of the population. Vectors satisfying these constraints will be feasible otherwise not

24

Solution Methodology using FP algorithm

feasible vectors. From among the feasible vectors, based on the value of objective function,

identify the best solution vector 𝑋𝑏𝑒𝑠𝑡(𝑘)

.

Step 7. Set generation counter 𝑘 = 1 .

Step 8. Select target vector, 𝑖 = 1 .

Step 9. Find the updated value of the vector by relation (D.4).

Step 10. Compare the fitness of the updated vectors with that of the initial vectors and retain

the best ones using relation (D.9).

Step 11.Repeat from Step 3.to Step 6. for the updated vector.

Step 12. Increase target vector 𝑖 = 𝑖 + 1. If 𝑖 ≤ 𝑀, repeat from Step 9 otherwise increase

generation count 𝑘 = 𝑘 + 1 .

Step 13. Repeat from step 8 if the desired optimum value is not found or 𝑘 ≤ 𝑘𝑚𝑎𝑥 .

In the same way, the same problem can be solved by TLBO and DE. The overview of both

the optimization methods have been presented in the Appendix E and Appendix F

respectively. Fig. 2.1 shows the flow chart for solving the formulated problem by FP.

25



END

START

Evaluate SAIFI, SAIDI, CAIDI and AENS

Set generation counter k=1

Evaluate the constraints for each updated solution

Print solution

generation = k+1

NO YESIs solution

converged?

Calculate value of objective function F for all vectors in

the population and Identify the ( ) &best bestkX F

If any updated solution violates the

inequality constraints , then set the values

of the vectors to ( )kiX

Select target vector, i=1 and find updated value of

each vector by D.4

Compare the fitness of the updated vectors with that of

the initial vectors and retain the best ones by D.9

( 1)kiX

( )kiX

Calculate value of objective function F for all vectors in the

population and identify ( )best

kX

Generate a population of size ‘M’ for failure rate λ and

repair time r each between lower and upper limits . , 0 00 0 0 0 0 0, , , X , , .,

1 2 1 2i

TS X X X X X X

M iDi i

Data input,

SAIFIt, SAIDIt, CAIDIt and AENSt

,max ,min ,max ,mink k k kr r

Decide values of w1, w2, w3, & w4 by AHP

Fig. 2.1 Flow chart for solving the formulated problem in section 2.5 by AHP & FP

26

Results and Discussions

2.8 Results and Discussions

The developed methodology has been implemented on the sample radial, mesh and Roy

Billinton test systems and results are described as and results are described as case-1, case-

2 case-3.

2.8.1. Case-1

In this case the developed algorithm has been implemented on a sample radial distribution

system [29] as shown in Fig.A.1. The system consists of seven load points LP-2 to LP-8

labelled in the diagram. Table-A.1 gives maximum allowable values (𝜆𝑘,𝑚𝑎𝑥 , 𝑟𝑘,𝑚𝑎𝑥) and

minimum reachable values (𝜆𝑘,𝑚𝑖𝑛, 𝑟𝑘,𝑚𝑖𝑛) of failure rates and repair times respectively.

Table- A.2 depicts average load and number of customers at load points. Table A.3 gives

cost coefficients for each segment of the distributor. The total budget CBUDGET has been

given Rs. 95000 as required in relation (2.18). Table 2.4 depicts optimized values of failure

rates and repair times as obtained by all the techniques. Table 2.5 shows the current and

optimized values of all reliability indices and objective function obtained by all methods.

Table 2.6 gives statistical analysis of samples of objective function. For the analysis, thirty

random sample values of the objective function were taken for all the methods with various

values of self-generated different initial populations. Student-t distribution has been used to

evaluate confidence interval of mean value of minimized objective function with confidence

coefficient γ=0.95

2.8.2 Case-2

The developed algorithm in this case has been implemented on a sample meshed distribution

system [13] as shown in Fig.B.1 for reliability optimization. The system consists of four load

points LP-T1 to LP-T4 labelled in the diagram. Table B.1 shows maximum allowable values

(𝜆𝑘,𝑚𝑎𝑥, 𝑟𝑘,𝑚𝑎𝑥) and minimum reachable values (𝜆𝑘,𝑚𝑖𝑛 , 𝑟𝑘,𝑚𝑖𝑛) of failure rates and repair

times of each section of Fig.B.1 respectively. Table B.2 depicts average load and number of

customers at load points. Table B.3 gives cost coefficients for each segment of the

distributor. The total budget CBUDGET is Rs. 4x106 as required in relation (2.18). Fig. B.2

is a reliability logic diagram of the meshed distribution system of Fig.B.1 to evaluate

reliability indices at load points LP-T1 to LP-T4. In Fig. B.2, there are three different paths

(A, C, D), (A, B, D) and (A, E) to reach LP-T from the source. The sections included in

blocks A, B, C, D and E to reach each load point from the source is shown in Table 2.7. In

27



each block sections are in series. The network is solved sequentially up to load point by

applying series and parallel laws of reliability as mentioned in section 2.3 and hence average

failure rate, 𝜆𝑠𝑦𝑠 , average outage time, 𝑟𝑠𝑦𝑠, and average annual outage time, 𝑈𝑠𝑦𝑠 for all

load points are found. The customer and energy oriented reliability indices for the load points

are calculated from relations 2.10-2.14. Optimized values of failure rates and repair times

as obtained by all the techniques are given in Table 2.8. The current and optimized values of

all reliability indices and objective function obtained by all the methods are given in Table

2.9. Statistical analysis done by taking thirty random sample values of minimized objective

function F is shown in Table 2.10. It has been done with the same procedure as mentioned

in section 2.8.1.

2.8.3 Case-3

The developed algorithm in this case has been implemented on RBTS-2 [99] as shown in

Fig.C.1 for reliability optimization. The total budget CBUDGET has been given Rs. 5.6

x106 as required in relation (2.18). Table-C.1 gives failure rates and average repair time of

different components of RBTS-2. Table C.2 shows maximum allowable values

(𝜆𝑘,𝑚𝑎𝑥, 𝑟𝑘,𝑚𝑎𝑥) and minimum reachable values (𝜆𝑘,𝑚𝑖𝑛 , 𝑟𝑘,𝑚𝑖𝑛) of failure rates and repair

times of each section of Fig.C.1 respectively. Table C.3 gives cost coefficients for each

segment of RBTS-2. The customer data of RBTS-2 is shown in Table C.4. All these data of

RBTS-2 have been taken from [99, 72]. Table 2.11 gives optimized values of failure rates

and repair times as obtained by all the techniques. Table 2.12 shows the current and

optimized values of all reliability indices and objective function obtained by all the methods.

Table 2.13 depicts statistical analysis for this system as done in the previous two cases.

Table 2.3 gives control parameters for FP, TLBO and DE techniques for all the sample

distribution systems in consideration.

28


Table 2.1 AHP Matrix

SAIFI SAIDI CAIDI AENS

SAIFI 1 1/5 1/5 1/5

SAIDI 5 1 1 1

CAIDI 5 5 1 1

AENS 5 1 1 1

Table 2.2 Weightage Coefficients

𝒘𝟏 𝒘𝟐 𝒘𝟑 𝒘𝟒

0.0625

0.313

0.313

0.313

Table 2.3 Control Parameters for FP, TLBO and DE for sample radial network, meshed network and

RBTS-2

Sr No. Parameters Values of parameters

1 Population size(FP,TLBO,DE) 20

2 Max generation specified(kmax) (FP,TLBO,DE) 1000

3 Updated step size (∝) (FP) 0.01

4 Distribution factor (𝛽) (FP) 1.5

5 Switch probability (FP) 0.8

6 Step size (F) (DE) 0.8

7 Cross over rate (Cr) (DE) 0.7

29



Table 2.4 Optimized values of failure rates and repair times as obtained by FP, TLBO and DE and

corresponding cost incurred for radial network

Variables Magnitudes as obtained

by FP

Magnitudes as obtained by

TLBO

Magnitudes as obtained

by DE

𝜆1 /year 0.200000 0.200000 0.223634

𝜆2 /year 0.050000 0.050000 0.067726

𝜆3 /year 0.100001 0.100216 0.123634

𝜆4 /year 0.100000 0.100000 0.147268

𝜆5 /year 0.150000 0.150001 0.155909

𝜆6 /year 0.056906 0.057048 0.055909

𝜆7 /year 0.100000 0.100000 0.055909

r 1(h) 6.000000 6.000000 6.032479

r 2(h) 6.001086 6.000000 6.024359

r 3(h) 4.000000 4.000008 4.064958

r 4(h) 8.000000 8.000001 8.097437

r 5(h) 7.000000 7.000003 7.064958

r 6(h) 8.000000 6.000000 6.01624

r 7(h) 6.001575 6.000005 6.048719

Cost

incurred(Rs.)

94970.51732

94801.278113

94927.3867

Table 2.5 Current and optimized reliability indices and corresponding value of objective function for

radial distribution system

Sr.

No.

Index Current

Values

Optimized values Threshold

values

FP TLBO DE

1 SAIFI(interruptions/customer) 0.7200 0.299572

0.299636

0.345223

0.5000

2 SAIDI(h/customer) 8.4500 1.876613

1.842774

2.149817

4.0000

3 CAIDI(h/customer

interruption)

11.7361 6.604517

7.047034

6.430872

8.0000

4 AENS(kW/customer) 26.4100 5.699442

5.660151

6.630001

10.000

Objective function (F) 7.6597 2.463806

2.506860

2.694759

30


Table 2.6 Statistical analysis of sample values of objective function for radial network

Optimization

method

Sample

Mean (

F)

Sample

Variance

(σF2)

Sample

Standard

deviation

(σ)

Sample

Median(F)

Min(F) Max(F) Coefficient

of

variation(cv)

Frequency of

convergence(f)

CONFγ(γ=0.95) Length of

confidence

interval of

(F)

FP 2.532549

0.001082

0.006005

2.533971

2.463806

2.587286

0.002371

0.566667

(2.520267, 2.544830)

0.024563

TLBO 2.563355

0.001547

0.007183

2.567007

2.506860

2.627623

0.002802

0.631353

(2.548665,2.578045)

0.029379

DE 2.800179

0.0057612

0.0138579

2.7773987

2.694759

2.985234

0.0049489

0.533333

(2.7718399,2.8285188)

0.0566788

31



Table 2.7 Sections involved in each block of Figure B.2

Load point Blocks Sections involved

For LP-T1 A 1,18

B 9,10,11

C 2,3,4,5,6,7,8

D 17

E 12,13,14,15,16

For LP-T2 A 1,15

B 9,10,11

C 2,3,4,5,6,7,8

D 16,17,18

E 12,13,14

For LP-T3 A 1,5

B 9,10,11

C 12,13,14,15,16,17,18

D 6,7,8

E 2,3,4

For LP-T4 A 1,7

B 9,10,11

C 12,13,14,15,16,17,18

D 8

E 2,3,4,5,6

32


Table 2.8 Optimized values of failure rates and repair times as obtained by FP, TLBO and DE and

corresponding cost incurred for meshed network


by FP


by TLBO


by DE

𝜆1 /year 0.254201 0.294427 0.328754

𝜆2 /year 0.12957058 0.097152 0.115491

𝜆3 /year 0.10514493 0.057423 0.071714

𝜆4 /year 0.10870638 0.071586 0.073280

𝜆5 /year 0.08330304 0.093439 0.112782

𝜆6 /year 0.01588112 0.011389 0.011394

𝜆7 /year 0.09485342 0.111542 0.119163

𝜆8 /year 0.17224346 0.098350 0.115610

𝜆9 /year 0.00542577 0.006182 0.006170

𝜆10 /year 0.06710431 0.042832 0.038513

𝜆11 /year 0.18062197 0.113593 0.132740

𝜆12 /year 0.12280254 0.128550 0.132740

𝜆13 /year 0.10964525 0.061832 0.071714

𝜆14 /year 0.06829886 0.062165 0.073280

𝜆15 /year 0.08172781 0.075800 0.094018

𝜆16 /year 0.0173002 0.011878 0.011394

𝜆17 /year 0.09122349 0.101662 0.115610

𝜆18 /year 0.13022653 0.090152 0.112782

r 1(h) 3.5449659 3.355670 3.358106

r 2(h) 3.2074669 3.137684 3.070081

r 3(h) 17.368277 10.815550 10.765800

r 4(h) 2.8455409 2.149450 2.133019

r 5(h) 3.9297324 3.614628 3.409275

r 6(h) 13.378692 9.331444 9.263219

r 7(h) 3.9665742 3.569844 3.409275

r 8(h) 3.7539499 3.901679 3.770399

r 9(h) 6.4000603 8.516112 6.428649

r 10(h) 24.350023 20.227300 18.587450

r 11(h) 2.0124065 2.562779 2.022167

r 12(h) 5.124369 2.113666 2.022167

r 13(h) 20.427964 15.600660 10.765750

r 14(h) 2.2620942 2.172341 2.133019

r 15(h) 6.403899 6.612923 6.365820

r 16(h) 13.28581 11.048240 9.263219

r 17(h) 4.6775905 4.968170 4.370771

r 18(h) 4.9195583 3.423207 3.409275

Cost

incurred(Rs.)

3976795

3956863

3989327.645

33



Table 2.9 Current and optimized reliability indices and corresponding value of objective function for

meshed distribution system

Sr.

No.

Index Current

Values

Optimized values Threshold

values

FP TLBO DE

1 SAIFI(interruptions/customer) 0.689895

0.355732

0.389773

0.440188

0.5000

2 SAIDI(h/customer) 4.854797

1.379787

1.369254

1.537291

3.0000

3 CAIDI(h/customer

interruption)

7.037003

3.878721

3.512954

3.492352

5.0000

4 AENS(kW/customer) 20.533869

5.786142

5.794515

6.496036

9.000

Objective function (F) 5.526503

2.119866

2.14043

2.350846

34


Table 2.10 Statistical analysis of sample values of objective function for meshed network

Optimization

method

Sample

Mean

( F)

Sample

Variance

(σF2)

Sample

Standard

deviation

(σ)

Sample

Median(F)

Min(F) Max(F) Coefficient

of

variation(cv)

Frequency of

convergence(f)


confidence

interval of

(F)

FP 2.199801

0.002880

0.009798432

2.218620

2.123239

2.309730

0.004454

0.6

(2.179764 ,2.219839)

0.040075

TLBO 2.160977

0.001688

0.007502166

2.140666

2.140430

2.287644

0.003471

0.7

(2.145634,2.176318)

0.0306838

DE 2.451934

0.0172337

0.0239678

2.403646

2.350846

2.962969

0.009775

0.733333

(2.402920,2.500948) 0.0980285

35



Table 2.11 Optimized values of failure rates and repair times for RBTS-2 as obtained by FP, TLBO

and DE

Failure rates (/Year) Repair times (in hrs)

Distributor

segment

By FP

By TLBO

By DE

By FP

By TLBO

By DE

1 0.036650 0.036650 0.036650 2.252263 2.252347 2.252313

2 0.011270 0.011319 0.012878 4.504504 4.504504 4.504516

3 0.039090 0.039090 0.039094 4.504504 4.504694 4.504504

4 0.036090 0.036090 0.036094 2.252252 2.252252 2.252252

5 0.011270 0.011270 0.012122 4.504504 4.504892 4.508222

6 0.013873 0.015279 0.011953 4.504504 4.504504 4.504504

7 0.036650 0.036650 0.036697 2.252314 2.252252 2.254525

8 0.011278 0.011279 0.011281 4.504509 4.518765 4.504509

9 0.013770 0.011278 0.012859 4.504504 4.514888 4.504504

10 0.029323 0.029323 0.029429 2.252252 2.252326 2.252252

11 0.011278 0.011278 0.011279 4.504505 4.511500 4.504504

12 0.036650 0.036650 0.037005 2.252250 2.252300 2.252250

13 0.039097 0.039097 0.039136 2.252250 2.252250 2.252250

14 0.029324 0.029323 0.029371 2.252250 2.252250 2.252360

15 0.039097 0.039434 0.039119 2.252251 2.252250 2.252250

16 0.036650 0.036650 0.036650 2.252250 2.252250 2.252250

17 0.011278 0.011278 0.011361 4.504500 4.513518 4.504500

18 0.039099 0.039097 0.039216 2.252250 2.252250 2.252253

19 0.011278 0.011278 0.011371 4.504500 4.504500 4.504757

20 0.011278 0.011278 0.011340 4.504502 4.504501 4.504500

21 0.029323 0.029323 0.029530 2.252251 2.252250 2.252255

22 0.011278 0.011608 0.021116 4.504651 4.504540 4.504585

23 0.014813 0.016704 0.011423 4.504500 4.504500 4.523343

24 0.036650 0.036650 0.036650 2.252250 2.252250 2.252250

25 0.011278 0.011282 0.011278 4.504530 4.504500 4.524141

26 0.039097 0.039097 0.039099 2.252250 2.252263 2.252250

27 0.015025 0.011278 0.011285 4.504500 4.504504 4.504500

28 0.011278 0.011278 0.012235 4.504500 4.504500 4.504549

29 0.036650 0.036650 0.036650 2.252250 2.252609 2.252250

30 0.011282 0.011278 0.011474 4.504511 4.504500 4.504923

31 0.011278 0.011296 0.011279 4.504500 4.505667 4.504500

32 0.036650 0.036650 0.036682 2.252250 2.252250 2.252250

33 0.011279 0.014680 0.011279 4.504516 4.504500 4.504500

34 0.029323 0.029323 0.029332 2.252250 2.252250 2.252250

35 0.011414 0.012563 0.012546 4.504540 4.504500 4.504500

36 0.011279 0.012101 0.011316 4.504500 4.504500 4.504500

Table 2.12 Current and optimized reliability indices for RBTS-2

Sr.

No. Index

Current

Values

Optimized Values Threshold

Values

FP TLBO DE

1 SAIFI(interruptions/customer) 0.0986 0.074149

0.074132

0.074576

0.085

2 SAIDI(h/customer) 0.5882 0.199349

0.19929

0.201212

0.35

3 CAIDI(h/customer

interruption)

5.9666 2.688509

2.688172

2.697489

3.50 4 AENS(kW/customer) 4.6641 1.594604

1.60041

1.604065

2.5

Objective function (F) 6.3108 2.772857

2.774727

2.789118

Cost incurred (Rupees) 5597472

5594369

5588765

36


Table 2.13 Statistical analysis of sample values of objective function for RBTS-2

Optimization

method

Sample

Mean

( F)

Sample

Variance

(σF2)

Sample

Standard

deviation

(σ)

Sample

Median(F)

Min(F) Max(F) Coefficient of

variation(cv)

Frequency of

convergence(f)


confidence

interval of

(F)

FP 2.791576

0.001342

0.006688

2.777867

2.772857

2.917537

0.002396 0.833333

(2.777899 ,

2.805254)

0.027356

TLBO 2.801056

0.001435

0.006916

2.787007

2.796860

2.927623

0.002469

0.8000

(2.786912

,2.815200)

0.028287

DE 2.81255

0.001797

0.007740

2.797121

2.799660

2.939223

0.002752

0.8000

(2.796722,2.828378)

0.031656

37



2.9 Conclusions

The algorithm in this chapter is used to find out optimum values of customer oriented and

energy based reliability indices while specified budget is allocated to achieve the same. Here,

in the objective function different weightage has been given to all the indices. The weighting

factors are found by AHP. As all the indices are normalized with respect their respective

threshold values, the optimized values found have been within the threshold limit. This

algorithm is applied to sample radial distribution system, sample meshed distribution system

and RBTS-2 in this chapter. The optimum values are found by FP, TLBO and DE

optimization algorithms. It has been authenticated by making comparison of the values found

by all the optimization methods.

38

CHAPTER 3

A Value Based Reliability Optimization of

Electrical Distribution Systems considering

Expenditures on Maintenance and Customer

Interruptions

3.1 Introduction

It has been observed that the customers look for value-added service from their utilities.

Failures in identifying customer needs may lead to drastic fall in the business of utilities as

the electricity selling market has started becoming competitive. It is a challenging task for

any utility to provide qualitative service to the customers keeping the cost on its operation

and maintenance such as to provide low cost services to them. In this chapter a balance

between the utility cost and cost incurred to the customers due to interruptions have been

found maintaining the required targets of reliability of the system. The optimum value of

system reliability with least combined cost thus found may lead towards value based

reliability planning of distribution systems [50].

In this chapter, a methodology is proposed which shows enhancement of reliability by

optimizing total reliability cost of electrical distribution systems. The total reliability cost

consists of cost incurred by utility and customers both.

In this chapter, interruptions costs at the customer end have been focused and also tried for

their reduction. This chapter aims at reducing the total reliability cost of system by reducing

customer interruptions and hence consequently enhancing the reliability of distribution

systems.

This chapter has been organized as follows. In section 3.2, the problem to be solved has been

formulated. Section 3.3 gives solution methodology for the problem by FP. Section 3.4 is

regarding discussion of the results obtained in this chapter. Section 3.5 leads to the

conclusions evaluated.

39

A Value Based Reliability Optimization of Electrical Distribution Systems considering

Expenditures on Maintenance and Customer Interruptions


Distribution system reliability should be based on proper balance between cost to the utility

and benefits received by the customers. If the customer interruptions are less, the benefits in

terms of profit to the customers and customer satisfaction are more. Thus to design a

reliability planning rationally so as to maintain proper service continuity requires

incorporating the utility costs and the costs incurred by the customers associated with service

interruptions in the analysis.

In view of this, the objective function is designed as follows.

𝐹 = ∑ 𝛼𝑘 𝜆𝑘2⁄𝑁𝑐

𝑘=1 + ∑ 𝛽𝑘 𝑟𝑘⁄𝑁𝑐𝑘=1 + ∑ 𝐶𝐼𝐶

𝑁𝑐𝑘=1 (3.1)

where, 𝐶𝐼𝐶 = 𝜆𝑘 × 𝑟𝑘 × 𝐿𝑖 × 𝐶𝑝𝑘 (3.2)

In the relation (3.1), 𝜆𝑘 is the failure rate of 𝑘𝑡ℎ section ; 𝑟𝑘 is the average repair time of

𝑘𝑡ℎ section ; 𝛼𝑘 and 𝛽𝑘 are the cost coefficients ; 𝐶𝐼𝐶 is customer interruption cost at

various load points ; 𝐿𝑖 is the average connected load at load point 𝑖 ; 𝐶𝑝𝑘 is the cost of

interruption in rupees per kilowatt for an outage duration of 𝑟𝑘 associated with 𝑘𝑡ℎ section

; 𝑁𝑐 is the total number sections of the distribution system.

The objective function consists of three terms. The first two terms are related to modification

costs related to maintenance activities. The first term shows cost of modification of failure

rates of each section. The failure rates can be reduced by investing in maintenance activities

on regular basis. The second term is related to cost of modifications in average repair time.

Lesser the values of these terms are; more are the costs or investments associated with

preventive maintenance and corrective repair required by utility to achieve them [111]. Both

these terms are based on Duane’s reliability growth model [105]. The third part of the

relation (3.1); i.e. cost of interruption depicts the costs incurred at the customers end in terms

of loss at the time of power fail. When a utility is engaged in supplying power to industrial

and commercial facilities, the high costs associated with power outages of course keep more

significance. The total cost of interruptions for any load point 𝑖 can be determined by adding

the cost of all section outages. The total cost of customer interruptions for all customers can

then be evaluated. The value of service which is equivalent to the cost of reliability, depicted

40

Problem Formulation

in terms of cost of customer interruptions can be derived by doing actual surveys of

customers regarding their expectations in regard to the level of reliability of supply. By

defining specific values in rupees for specific level of service reliability a balance in

distribution reliability can be established. The customer cost at a single customer load point

depends entirely on the cost characteristics of the customers at that load point. The customer

cost associated to any load point due to any interruption is the combination of the costs of

all type of customers affected due to that distribution outage [50]. Objective function (3.1)

is minimized based on the following customer and energy based constraints [103].


𝜆𝑘,𝑚𝑖𝑛 ≤ 𝜆𝑘 ≤ 𝜆𝑘,𝑚𝑎𝑥 (3.3)

𝑟𝑘,𝑚𝑖𝑛 ≤ 𝑟𝑘 ≤ 𝑟𝑘,𝑚𝑎𝑥 (3.4)

𝑘 = 1, … … … … … , 𝑁𝑐

where,

λk,min and rk,min are minimum reachable values of failure rate and repair time of 𝑘𝑡ℎ

section. λk,max and rk,max are maximum allowable failure rate and repair time

respectively.

(ii) Inequality constraints on the system average interruption frequency index SAIFI

SAIFI ≤ SAIFIt (3.5)

(iii) Inequality constraints on the system average interruption duration index (SAIDI)

SAIDI ≤ SAIDIt (3.6)

(iv) Inequality constraints on the customer average interruption duration index (CAIDI)

CAIDI ≤ CAIDIt (3.7)

(v) Inequality constraints on the average energy not supplied index (AENS)

AENS ≤ AENSt (3.8)

41



SAIFI , SAIDI , CAIDI and AENS have already been defined in section 2.4. SAIFIt , SAIDIt

, CAIDIt and AENSt are target/threshold values of the respective indices. They depend on

the managerial/administrative decisions.

Li is average load connected at ith load point. This may be obtained from load duration

curve. Ni is number of customers at load point i , λsys,i is the system failure rate at ith load

point and Usys,i is system annual outage duration at ith load point. λsys,i, Usys,i and rsys,i at

a specific load point are derived by gradually solving the network with series and parallel

laws of reliability [112].

In this formulation, an attempt has been made to apply value based reliability planning in

which minimum cost solution is ensured. The cost to be minimized is the total reliability

cost of the distribution system which combines cost of maintenance incurred on utility plus

the customer outage cost keeping in mind the constraints mentioned in the relations (3.3),

(3.4), (3.5), (3.6),(3.7) and (3.8). When the combined utility and customer interruption costs

are minimized, the utility customers will receive the least cost service. As both these costs

incorporated in the objective function are in terms of failure rate and repair time, constrained

minimization of the function will give minimized values of these primary indices enhancing

the reliability of the system. The cost of reliability enhancement is the benefit, which is the

expected reduction in customer damage cost.

In this chapter, recently developed metaheuristic, called Flower pollination (FP)

optimization[100] is used for the first time to solve the formulated problem for the radial

sample network, meshed sample network and RBTS-2 and a comparison is made with the

results obtained by Teaching learning based optimization (TLBO)[101] and Differential

evolution (DE)[102] methods. Thus by minimizing the function achieving the required target

values of the reliability indices will give the optimized values of the maintenance and

customer expenditure costs with reliability enhancement.

3.3. Solution Methodology using FP algorithm



Step 1. Data input 𝜆𝑘,𝑚𝑎𝑥, 𝑟𝑘,𝑚𝑎𝑥 , 𝜆𝑘,𝑚𝑖𝑛, 𝑟𝑘,𝑚𝑖𝑛 and cost of interruption (𝐶𝑝𝑘). SAIFIt,

SAIDIt, CAIDIt and AENSt .

42

Solution Methodology using FP algorithm




uniformly between lower and upper limits as given by relation (3.3) and (3.4).

Step 3. Evaluate 𝜆𝑠𝑦𝑠,𝑖 , 𝑟𝑠𝑦𝑠,𝑖 and 𝑈𝑠𝑦𝑠,𝑖 at each load point.



Step 5. Calculate value of objective function 𝐹 for all vectors in the population i.e.𝐹(𝑋𝑖(𝑘)

),

𝑖 = 1, … … … … … , ′𝑀′ as given by relation (3.1) and (3.2).

Step 6. Evaluate inequality constraints from the relations (3.5), (3.6), (3.7) and (3.8) for each

vector of the population. Vectors satisfying these constraints will be feasible otherwise not

feasible vectors. From among the feasible vectors, based on the value of objective function,

identify the best solution vector 𝑋𝑏𝑒𝑠𝑡(𝑘)

.

Step 7. Set generation counter 𝑘 = 1 .

Step 8. Select target vector, 𝑖 = 1 .





Step 12. Increase target vector 𝑖 = 𝑖 + 1. If 𝑖 ≤ 𝑀, repeat from Step 9 otherwise increase

generation count 𝑘 = 𝑘 + 1 .

Step 13. Repeat from step 8 if the desired optimum value is not found or 𝑘 ≤ 𝑘𝑚𝑎𝑥 .



respectively. Fig. 3.1 shows the flow chart for solving the formulated problem by FP.

43



Fig. 3.1 Flow chart for solution of the problem formulated in section 3.2 by FP

44


3.4. Results and Discussions

The developed algorithm in this chapter has been implemented on three distribution systems

as follows. The problem has been solved by FP algorithm and comparison has been made

with the results obtained by TLBO and DE. The algorithms used have been coded in

MATLAB-13.

3.4.1 Distribution systems: Descriptions

(A) Sample radial distribution system [29]:

The radial system consists of seven load points LP-2 to LP-8 labelled in Fig. A.1. The data

regarding the maximum allowable and minimum reachable values of failure rates and repair

times, average load and number of customers at load points and cost coefficients for each

segment of radial distributor have been taken from [111] .They are shown as Table A.1

,Table A.2 and Table A.3 in Appendix. Table 3.1 gives interruption cost (𝐶𝑝𝑘) at different

load points for the sample radial distribution system. The customer and energy based

reliability indices for the load points are calculated from relations (2.10), (2.11), (2.12) and

(2.14) using laws of reliability [103]. Table 3.3 gives optimized values of failure rates and

repair times of different sections of radial distribution system. Table 3.4 gives the optimized

values of objective function (F) which shows the total expenditure costs of the sample radial

distribution system due to maintenance activity and customer interruptions. Table 3.5 shows

the current and optimized values of customer and energy based reliability indices obtained

by all the methods. Fig.3.2 shows convergence plots of objective function (F) for all the

methods for specified number of generations for the sample radial distribution

system.Fig.3.3 , Fig. 3.4 and Fig.3.5 show frequency distribution plots for minimum values

of (F) obtained by FP ,TLBO and DE respectively for sample radial distribution system.

These histograms have been plotted from the 40 random values of minimum (F) obtained by

the respective optimization method.

(B) Sample meshed distribution system [13]

The developed algorithm in this case has been implemented on a sample meshed distribution

system [13] as shown in Fig.B.1. The system consists of four load points LP-T1 to LP-T4

labelled in the diagram. Table B.1 shows maximum allowable values (𝜆𝑘,𝑚𝑎𝑥 , 𝑟𝑘,𝑚𝑎𝑥) and

minimum reachable values (𝜆𝑘,𝑚𝑖𝑛 , 𝑟𝑘,𝑚𝑖𝑛) of failure rates and repair times of each section

of Fig.2.2 respectively. Table B.2 depicts average load and number of customers at load

45



points. Table B.3 gives cost coefficients for each segment of the distributor. Table 3.6 gives

interruption cost (𝐶𝑝𝑘) at different load points for the sample meshed distribution system.

Table 3.7 gives optimized values of failure rates and repair times of different sections of

meshed distribution system. Fig. B.2 is a reliability logic diagram of the meshed distribution

system of Fig.B.1 to evaluate reliability indices at load points LP-T1 to LP-T4. The

procedure for the same has already been explained in section 2.8.2. Table 3.8 gives the

optimized values of objective function (F) which shows the total expenditure costs of the

sample meshed distribution system due to maintenance activity and customer interruptions.

Table 3.9 shows the current and optimized values of customer and energy based reliability

indices obtained by all the methods. Fig.3.10 shows convergence plots of objective function

(F) for all the methods for specified number of generations for the sample meshed

distribution system. Fig. 3.11 , Fig. 3.12 and Fig.3.13 show frequency distribution plots for

minimum values of (F) obtained by FP ,TLBO and DE respectively for sample meshed

distribution system. These histograms have been plotted from the 40 random values of

minimum (F) obtained by the respective optimization method.

(B) Roy Billinton Test System-Bus 2 (RBTS-2) [99]:

Another test system which has been used in this chapter is Roy Billinton Test System-Bus 2

as shown in Fig.C.1. Table C.1 represents failure rates and average repair times of different

components of RBTS-2. Table C.2 gives maximum allowable (𝜆𝑘,𝑚𝑎𝑥 /year) and minimum

reachable (λk,min/year) failure rates, maximum allowable (𝑟𝑘,𝑚𝑎𝑥 (h)) and minimum

reachable (rk,min (h)) average repair times. Table C.3 gives cost coefficients 𝛼𝐾 and 𝛽𝐾

for failure rates and repair times respectively of the different sections of RBTS-2. Table C.4

represents sector wise customer data. Table-(C.1-C.4) are shown in the Appendix. Table

3.10 gives optimized values of failure rates and repair times for different sections of RBTS-

2 by the three optimization methods in consideration. Table 3.11 gives the optimized values

of maintenance cost, customer interruption cost and objective function (F) for RBTS-2.

Table 3.12 shows the current and optimized values of customer and energy based reliability

indices. The convergence of minimum value of objective function (F) over the number of

generations for all the optimization methods are shown in Fig. 3.10. The frequency

distribution plots of minimum values of (F) due to FP, TLBO and DE are shown in Fig. 3.11,

Fig.3.12 and Fig. 3.13 respectively.

46


Table 3.2 gives control parameters for all the three optimization methods; FP, TLBO and

DE applied in this chapter for all the distribution test systems in consideration.

47



Table 3.1 Interruption costs at load points for sample radial distribution system

Distributor Load points(LP) #2 #3 #4 #5 #6 #7 #8

Interruption Cost(𝑪𝒑𝒌)(Rs./kW) 15 13 17 20 20 12 14

Table 3.2 Control Parameters for FP, TLBO and DE for sample radial network, meshed network and

RBTS-2









Table 3.3 Optimized values of failure rates and repair times as obtained by FP, TLBO and DE for

sample radial distribution system


by FP


TLBO


DE

𝜆1 /year 0.200001 0.200000 0.200005

𝜆2 /year 0.099307 0.099573 0.130767

𝜆3 /year 0.121371 0.120466 0.163934

𝜆4 /year 0.100000 0.100012 0.100068

𝜆5 /year 0.150000 0.150000 0.151810

𝜆6 /year 0.100000 0.100000 0.100000

𝜆7 /year 0.100000 0.099999 0.100000

r 1(h) 7.053993 6.023147 6.000011

r 2(h) 7.468035 6.000003 6.029284

r 3(h) 6.979073 11.981230 4.000000

r 4(h) 8.099595 19.999997 8.000005

r 5(h) 15.000000 14.999999 7.002543

r 6(h) 7.999764 6.000118 6.000013

r 7(h) 6.000052 12.000000 8.125879

48


Table 3.4 Current and optimized values of Objective function (F) obtained by FP, TLBO and DE for

radial distribution system

Sr.

No.

Current Values (Rs.)

(In Rupees)

Optimized Values(Rs.) (In Rupees)

FP TLBO DE

1 Maintenance cost

(∑ 𝛼𝑘 𝜆𝑘2⁄𝑁𝑐

𝑘=1 + ∑ 𝛽𝑘 𝑟𝑘⁄𝑁𝑐𝑘=1 )

133640 38650.264 38271.185 37124.837

2 Customer interruption cost

(∑ 𝐶𝐼𝐶𝑁𝑐𝑘=1 )

450920 103543.623 103905.846 105818.215

3 Objective function (F) 584560 142193.888

142177.032

142943.053

Table 3.5 Current and optimized reliability indices for radial distribution system

Table 3.6 Interruption cost at load points for sample meshed network

Load point(LP) LP-T1 LP-T2 LP-T3 LP-T4

Interruption Cost(𝐶𝑝𝑘)(Rs./kW) 45 39 51 68

Sr.

No.

Index Current

Values


Values

FP TLBO DE

1 SAIFI(interruptions/customer) 0.7200 0.355884 0.356937 0.363519 0.5000

2 SAIDI(h/customer) 8.4500 2.167820 2.174372 2.226317 4.0000

3 CAIDI(h/customer

interruption)

11.7361 6.096659 6.095436 6.124353 8.0000

4 AENS(kW/customer) 26.4100 6.437391 6.457199 6.596871 10.000

49



Table 3.7 Optimized values of failure rates and repair times as obtained by FP, TLBO and DE for

meshed network


by FP


TLBO


DE

𝜆1 /year 0.2553 0.2546 0.2542

𝜆2 /year 0.1770 0.1774 0.1776

𝜆3 /year 0.1100 0.1102 0.1100

𝜆4 /year 0.1135 0.1104 0.0823

𝜆5 /year 0.1409 0.1846 0.1847

𝜆6 /year 0.0188 0.0216 0.0270

𝜆7 /year 0.0977 0.0939 0.1845

𝜆8 /year 0.1780 0.1780 0.1760

𝜆9 /year 0.0130 0.0105 0.0099

𝜆10 /year 0.0690 0.0690 0.0690

𝜆11 /year 0.2052 0.2139 0.2054

𝜆12 /year 0.2052 0.2053 0.2053

𝜆13 /year 0.1100 0.1100 0.1105

𝜆14 /year 0.1135 0.1135 0.1137

𝜆15 /year 0.0779 0.0916 0.1065

𝜆16 /year 0.0183 0.0225 0.0248

𝜆17 /year 0.1780 0.1780 0.1844

𝜆18 /year 0.1846 0.1846 0.0894

r 1(h) 3.3497 3.3551 3.3967

r 2(h) 3.0703 3.0966 3.9018

r 3(h) 13.0590 10.7526 22.7541

r 4(h) 3.4867 2.2564 2.6154

r 5(h) 3.3992 3.4063 3.4441

r 6(h) 13.0687 9.2661 13.4836

r 7(h) 3.3962 3.8256 3.3967

r 8(h) 3.7523 5.1322 4.5333

r 9(h) 9.8108 11.8247 7.3207

r 10(h) 18.5600 23.9913 19.0307

r 11(h) 5.2414 5.2366 2.0130

r 12(h) 2.0328 2.0825 2.1480

r 13(h) 10.7323 11.1655 11.3504

r 14(h) 2.2283 2.1229 5.6074

r 15(h) 10.7150 6.7947 6.3526

r 16(h) 10.0676 10.5634 9.3792

r 17(h) 9.7627 4.4298 4.3556

r 18(h) 3.3940 3.4074 3.4348

50




Sr.

No.

Current Values (Rs.)

(In Rupees)

Optimized Values(Rs.) (In

Rupees)

FP TLBO DE

1 Maintenance cost


𝑘=1 + ∑ 𝛽𝑘 𝑟𝑘⁄𝑁𝑐𝑘=1 )

5990100 1140410

1288345 1293725



1345365 376491.4 379059.6

394511.2

3 Objective function (F) 7335465 1516901 1667404 1688237

Table 3.9 Current and optimized reliability indices for meshed distribution system

Sr.

No.

Index Current

Values


Values

FP TLBO DE

1 SAIFI(interruptions/customer) 0.689895499

0.382709

0.390077

0.394655

0.5000

2 SAIDI(h/customer) 4.85479713 1.397391 1.388927 1.403352 3.0000

3 CAIDI(h/customer

interruption)

7.03700363 3.651317 3.560645 3.555901 5.0000

4 AENS(kW/customer) 20.53386959 5.863466 5.856543 5.983471 9.000

51



Table 3.10 Optimized values of failure rates and repair times for RBTS-2 as obtained by FP, TLBO

and DE

Failure rates (/year) Repair times (in hours)

Distributor

segment

By FP

By TLBO

By DE By FP

By TLBO By DE

1 0.04067 0.03980 0.04180 2.34895 2.40811 2.41678

2 0.01423 0.01404 0.01372 4.56710 4.61473 4.61094

3 0.04768 0.04806 0.04774 4.50648 4.50465 4.50655

4 0.04068 0.04077 0.04077 2.32691 2.33253 2.33265

5 0.01312 0.01312 0.01300 5.05549 4.74732 4.99724

6 0.01491 0.01494 0.01493 5.20528 5.10142 5.16181

7 0.03883 0.03902 0.03903 2.26240 2.26318 2.26357

8 0.01401 0.01307 0.01308 4.64416 4.71025 4.74558

9 0.01490 0.01487 0.01489 4.55736 4.56210 4.55732

10 0.03533 0.03467 0.03492 2.25480 2.25600 2.25568

11 0.01296 0.01305 0.01305 4.54916 4.54507 4.54465

12 0.03894 0.03876 0.03928 2.25404 2.25462 2.25448

13 0.04250 0.04555 0.04533 2.34997 2.31891 2.32369

14 0.03458 0.03420 0.03487 2.35791 2.36782 2.35036

15 0.04488 0.04565 0.04571 2.34296 2.38577 2.38756

16 0.04311 0.04312 0.04316 2.39287 2.26125 2.39336

17 0.01361 0.01427 0.01353 4.68361 4.63416 4.71301

18 0.04621 0.04628 0.04595 2.38859 2.36988 2.40849

19 0.01373 0.01435 0.01386 4.59464 4.53633 4.59258

20 0.01496 0.01496 0.01495 6.18585 6.30544 6.31555

21 0.03000 0.02998 0.03001 2.35188 2.34865 2.34762

22 0.01499 0.01491 0.01488 4.93747 4.56683 4.57449

23 0.01436 0.01411 0.01409 4.50663 4.51735 4.51706

24 0.04383 0.04531 0.04522 2.41031 2.42249 2.42519

25 0.01258 0.01268 0.01281 4.66017 4.60806 4.77149

26 0.04531 0.04487 0.04502 2.29775 2.30302 2.30232

27 0.01355 0.01354 0.01352 4.59393 4.57949 4.56971

28 0.01406 0.01433 0.01381 4.60544 4.67907 4.73198

29 0.04202 0.04234 0.04223 2.25610 2.25654 2.25627

30 0.01329 0.01347 0.01322 4.66126 4.63142 4.64577

31 0.01497 0.01497 0.01497 4.51927 4.52424 4.51887

32 0.04344 0.04259 0.04257 2.32004 2.32091 2.32403

33 0.01386 0.01366 0.01374 4.65211 4.72676 4.70384

34 0.03364 0.03388 0.03381 2.25934 2.25996 2.25982

35 0.01371 0.01359 0.01353 4.61507 4.64740 4.62705

36 0.01331 0.01347 0.01340 4.52793 4.52579 4.52585

52



RBTS-2

Sr.

No.

Current Values

(Rs.) (In

Rupees)

Optimized Values(Rs.) (In Rupees)

FP TLBO DE

1 Maintenance cost


𝑘=1 ∑ 𝛽𝑘 𝑟𝑘⁄𝑁𝑐𝑘=1 )

232680 277346.7 277639.6 281772.4



828680 327034.3 328533.5 331767.3

3 Objective function (F) 1061360 604381 606173.1 613539.8


Sr.

No.

Index Current

Values


Values

FP TLBO DE


2 SAIDI(h/customer) 0.58817 0.244802 0.243527 0.246796 0.510

3 CAIDI(h/customer

interruption)

5.9665 2.838637 2.829866 2.847023 5.700

4 AENS(kW/customer) 4.6640 1.889124 1.882015 1.904028 3.750

53



Fig. 3.2 Variation of Objective function (F) over number of generations for sample radial system

Fig. 3.3 Frequency distribution of the minimum values of objective function (F) using FP for sample

radial system

54


Fig.3.4 Frequency distribution of the minimum values of objective function (F) using TLBO for sample

radial system

Fig. 3.5 Frequency distribution of the minimum values of objective function (F) using DE for sample

radial system

55



Fig. 3.6 Variation of Objective function (F) over number of generations for sample meshed system

Fig.3.7. Frequency distribution of the minimum values of objective function (F) using FP for sample meshed

system

56


Fig.3.8 Frequency distribution of the minimum values of objective function (F) using TLBO for sample

meshed system

Fig.3.9 Frequency distribution of the minimum values of objective function (F) using DE for sample

meshed system

57



Fig. 3.10 Variation of Objective function (F) over number of generations for RBTS-2

Fig.3.11 Frequency distribution of the minimum values of objective function (F) using FP for RBTS-2

58


Fig.3.12 Frequency distribution of the minimum values of objective function (F) using TLBO for

RBTS-2

Fig.3.13 Frequency distribution of the minimum values of objective function (F) using DE for RBTS-2

59



3.5 Conclusions

The aim of this chapter has been to improve reliability of a distribution system by finding

out a balance between costs of maintenance and customer interruptions. When these

combined costs become minimum, customers will get service with least costs leading to

enhanced customer satisfaction level. In this chapter, this has been achieved by optimizing

the objective function formulated subject to achieving the desired reliability level with

reduction in the customer interruption costs. It has been applied on a sample radial network,

sample meshed distribution network and RBTS-2 finding the results by FP, TLBO and DE.

60

CHAPTER 4

Cost Benefit Analysis for Active Distribution

Systems in Reliability Enhancement

4.1 Introduction

Active distribution system consists of infrastructure of power delivery and active resources

say combining passive infrastructure with active. The active distribution system is developed

to create an energy efficient, high power quality and reliable network. Distributed

generations (DGs) are becoming the best alternatives for power distribution companies to

increase reliability of distribution systems. DGs enhance performance of the systems by

improving reliability, voltage profile and reducing losses of the system. The use of small

capacity DGs at customer ends is also increasing due to many reasons like reducing

resources of fossil fuels, growing demands, pollution problems etc.

By modifying failure rates and repair times of different sections of distribution system

reliability of the system may be improved. By incorporating DGs at customer ends the

additional cost to achieve this can be reduced. On the other end, cost of energy purchased

from DGs may be high. The interruption time in the reliability indices can be reduced to

momentary interruption if the switch over time of DGs are less.

The impact of DGs in distribution system on reliability and other parameters highly depends

on proper locations and size of DGs. Reliability of the distribution system has been improved

by DGs at predefined locations [40]. In many literatures the locations of DGs have been

found minimizing the loss. But for certain loads reliability may keep more worth than the

loss and voltage profile. Various costs related to investment, maintenance, operations etc.

are also involved with the incorporation of DGs in the distribution system. Hence costs and

benefits to the customers and the utilities due to installation of DGs must be calculated.

In line to the above discussions, this chapter aims at improving reliability of distribution

system by modifying the failure rates and repair times of different sections thereof while

61

Cost Benefit Analysis for Active Distribution Systems in Reliability Enhancement

DGs are incorporated in it. This has been done by optimizing an objective function

formulated here. But this optimization has been done after having found proper locations of

DGs from the reliability improvement aspects and not with any presumed locations. Of

course, cost-benefit analysis has been performed for justification.

The rest of the chapter has been arranged this way. Section 4.2 describes the mathematical

formulation of the problem. Section 4.3 gives briefs about cost-benefit analysis. Section 4.4

represents steps to solve the problem. Section 4.5 is regarding results and its interpretation.

Conclusion is drawn in section 4.6.


The aim of this article is to improve reliability of distribution system by reducing failure

rates and repair times of different sections of the system defining proper locations of DGs.

In this regard, two objective functions have been considered as follows.

4.2.1 Deciding locations of DGs

As the main criterion for deciding location of DGs is improvement in reliability, the

objective function considered is as below.

J =SAIFI

SAIFIt+

SAIDI

SAIDIt+

CAIDI

CAIDIt+

AENS

AENSt (4.1)

Here, the objective function in (4.1) is the sum of the normalized values of customer and

energy based reliability indices i.e. SAIFI, SAIDI, CAIDI and AENS. The normalization is

with respect to respective target/threshold values of the indices. Hence all the indices will be

given equal weightage in the procedure.

First the value of J is found connecting DG at load point 1. The value of J here represents

overall reliability of the system. Gradually DGs are connected individually at all the

remaining load points one by one and value of J is found. Improvement in reliability of the

system is found at all the load points as DG is connected at those load points. The

improvement in reliability at all load points in terms of J is arranged in descending order and

ranked accordingly. Now, first two numbers from the ranking are taken, DGs are connected

at those load points and value of J is found. Then first three numbers of ranking are taken

and the same procedure is followed. This procedure may be continued till the desired value

of reliability is achieved. It is explained in detail in section 4.4.1.

62

Problem Formulation

After having found the locations of DGs, optimized values of reliability indices are found as

follows.

4.2.2 Connecting DGs as stand by units in the system

The DGs may be owned by the distribution company itself or it may encourage large

customers to own their DGs. The DGs owned and controlled by customer/or any other

agency may prove to be highly significant in improving reliability of the system. Due to

incorporation of DGs, the outage time reduces and the expense spent in the improvement of

failure rates and repair time is reduced. The interruption cost at the customer ends can also

be reduced. On the other hand, the cost of energy borrowed through DG may be high due to

its higher per unit rates [40]. In view of this, the objective function is formulated as follows.

F = ∑ αk λk2⁄Nc

k=1 + ∑ βk rk⁄Nck=1 + ∑ CIC

Nck=1 + ADCOST(EENSO − EENSD) (4.2)

where, CIC = λk × rk × Li × Cpk (4.3)

In the relations (4.2) and (4.3), λk is the failure rate of kth section;rk is the average repair

time of kth section; αk and βk are the cost coefficients; CIC is customer interruption cost

at various load points; Li is the average connected load at load point i ; Cpk is the cost of

interruption in rupees per kilowatt for an outage duration of rk associated with kth section

; Nc is the total number sections of the distribution system. EENSO is the expected energy

not supplied without DG and EENSD is the expected energy not supplied when DGs are

connected. ADCOST is the additional cost per kWH to be paid to the DG owner. It is assumed

to be Rs.2/kWH.

The objective function consists of four terms. The first two terms are related to modification

costs related to maintenance activities, i.e. cost for modifying failure rates and average repair

times of each section of the distribution system respectively. Lesser are the values of these

terms; more are the costs or investments associated with preventive maintenance and

corrective repair required by utility to achieve them [111]. Both these terms are based on

Duane’s reliability growth model [105]. The third part of the relation (4.2); i.e. cost of

interruption depicts the costs incurred at the customers end in terms of loss at the time of

power fail. When a utility is engaged in supplying power to industrial and commercial

facilities, the high costs associated with power outages of course keep more significance.

The total cost of interruptions for any load point i can be determined by adding the cost of

63


all section outages. The total cost of customer interruptions for all customers can then be

evaluated. The customer cost at a single customer load point depends entirely on the cost

characteristics of the customers at that load point. The customer cost associated to any load

point due to any interruption is the combination of the costs of all type of customers affected

due to that distribution outage [50]. For modified radial distribution system (Fig.A.2), for

modified meshed distribution system (Fig.B.3) and modified RBTS-2 (Fig.C.2) it is as

shown in the Table 4.1, Table 4.10 and Table C.4 respectively. The fourth part depicts the

additional cost to be given to the DG owners for the energy purchased from them. It is

multiplication of energy provided by DGs and additional charge (ADCOST) in Rs. /kWH.

Thus the objective function provides balance between the cost spent on DGs and the cost of

maintenance plus customer interruptions. As the expense on DGs increases, the other two

costs are supposed to decrease. This is achieved by minimizing the objective function as

formulated in relation (4.2).

Expected energy not supplied (EENS) is calculated as below.

EENS = ∑ LiUsys,i (4.4)

Where Li average load is connected at ith load point and Usys,i is system annual outage

duration at ith load point. Without DG in the system Usys,i can be calculated as shown in

relation (2.2).

With DG present in the system as a standby unit, load may be transferred to DG in case of

any disruption of supply to the load points from the source. In this case failure rate and

switching time of the switch transferring the load to DG should be considered. The reliability

model of this can be represented by considering the transfer switch in series with the parallel

combination of the system and DG. The equivalent failure rate and repair time when DG is

connected as a stand by unit at a load point is given by following approximate formulas [40].

λeq = λsλdg(rs + rdg) + λsw (4.5)

req =λs.λdg.rs.rdg+λsw.s

λs.λdg(rs+rdg)+λsw (4.6)

Ueq = λeqreq (4.7)

Where λeq is the equivalent failure rate , req the equivalent interruption duration , λs

represents total failure rate up to load point from the source , rs represents average

64

Problem Formulation

interruption duration from the source up to the load point , λdg the failure rate of DG , rdg

the average outage duration of DG ,λsw the failure rate of the switch transferring load to the

DG and s is the switching time or service restoration time with DG. Ueq is the equivalent

annual outage duration of load points when DGs are connected in the system.

The objective function (4.2) is optimized subject to fulfilling the following constraints.


λk,min ≤ λk ≤ λk,max and rk,min ≤ rk ≤ rk,max , k = 1, … … … … … , Nc (4.8)

Inequality constraints on the customer oriented and energy based indices





where,

λk,max and rk,max are maximum allowable failure rate and repair time respectively. λk,min

and rk,minare minimum reachable values of failure rate and repair time of 𝑘𝑡ℎ section which

are achieved in optimization process. These lower bound values are obtained by failure and

repair data analysis along with the associated costs and it is done through reliability growth

model [105].

SAIFIt ,SAIDIt , CAIDIt and AENSt are target/threshold values of the respective indices. They

depend on the managerial/administrative decisions.

The formulated problem is solved by flower pollination (FP) optimization method [100].

The same has been verified by other two optimization methods named teaching learning

optimization (TLBO) [101] and differential evolution (DE) [102]. The method in this paper

has been applied on a sample radial distribution network, sample meshed distribution

network and Roy Billinton Test System Bus-2 (RBTS-2). The optimized values obtained

after having solved the problem may be given as target values to the crew to enhance the

reliability of the system.

65


4.3 Cost-benefit analysis

Over a long run, whether the fixed and variable amount spent on DGs embedded in the

distribution system would yield in benefit or not, can be found by doing cost benefit analysis.

It justifies the installation of specific numbers of DGs at the locations found in this paper.

The cumulative present value (CPV) method [113, 114] has been applied to evaluate the

total costs and benefits when specific number of DGs is connected at specific locations for

the economic life cycle considered. The method of the time value of money or the CPV

method is based on the premise that an investor prefers to receive a payment of a fixed

amount of money today rather than an equal amount in the future. This method converts all

costs and benefits of the plan during the lifecycle to the first year of operation. The following

equations depict the concept.

Benefit = CICDGO − CICDG − ADCOSTDG − CostMDG − DGI − DGM (4.13)

where,

CICDGO = CICDGO × CPV1

CICDGO= Customer interruption cost when DGs are not connected (4.14)

CICDG = CIC × CPV1

CICDG= Customer interruption cost when DGs are connected (4.15)

ADCOSTDG = ADCOST × CPV1

ADCOSTDG = Additional cost required on the operation of DGs in Rs./kWh (4.16)

CostMDG = CostMDG × CPV2

CostMDG = cost of maintenance required to achieve the desired reliability in the system.

(4.17)

DGI = ∑ DGIi × CPV2

n

i=1

DGI = Installation cost of all the DGs connected (4.18)

DGM = ∑ DGMi × CPV2

n

i=1

66

Solution Methodology

DGM = Maintenance cost of all the DGs connected in the system (4.19)

CPV1 =(1−PV1

EL)

(1−PV1) (4.20)

PV1 =(1+Iinf)×(1+LG)

(1+Iint) (4.21)

CPV2 =(1−PV2

EL)

(1−PV2) (4.22)

PV2 =(1+Iinf)

(1+Iint) (4.23)

EL is the economic lifecycle of equipments . LG is load growth rate. Iinf and Iint stand for

inflation rate and interest rate respectively.

4.4 Solution Methodology

The steps to solve the whole problem are described as follows.

4.4.1 Finding the locations of DGs

Step 1. Data input λk , rk, , λdg , rdg , λsw , s , Cpk , N , La , SAIFIt , SAIDIt , CAIDIt

and AENSt .

Step 2. Evaluate load point indices (failure rate and repair time).

Step 3. Evaluate SAIFI, SAIDI, CAIDI, AENS, EENS, ADCOST and CIC for the system.

Step 4. Calculate value of objective function given by relation (4.1) for the system.

Step 5. Connect DG at load point 1 only and calculate the values of all the indices and

objective function given by relation (4.1).

Step 6. Now connect DG at next load point only and calculate all the indices and J as in

(4.1).In the same way , connect DG at all load points one by one and calculate the values of

all indices and J as in (4.1).

Step 7. Find out the improvement in reliability at all the load points due to DG from the

values of J in (4.1).

67


Step 8. Arrange the improvement in reliability at load points (in terms of J as in (4.1)) in

descending order and rank them accordingly.

Step 9.Take first two numbers from ranking and connect DGs at those load points. Calculate

all the indices and value of J for DGs connected at these load points.

Step 10. Take first three numbers from ranking. Connect DGs at these load points and

calculate all the indices and J for the system.

Step 11. Increase the number from the ranking in this way and connect DGs at the respective

load points finding out all the indices and J .

Step 12. Continue till the desired value of reliability is achieved.

4.4.2 Finding the optimized solution by FP



Step 1. Data input λk,max, rk,max , λk,min, rk,min and cost of interruption (Cpk ). SAIFIt ,

SAIDIt , CAIDIt and AENSt .




uniformly between lower and upper limits as given by relation (4.8).

Step 3. Evaluate λsys,i , rsys,i and Usys,i at each load point.



Step 5. Calculate value of objective function F for all vectors in the population i.e.F (Xi(k)

),

i = 1, … … … … … , ′M′ as given by relation (4.2) and (4.3).

Step 6. Evaluate inequality constraints from the relations (4.9), (4.10), (4.11) and (4.12) for

each vector of the population. Vectors satisfying these constraints will be feasible otherwise

not feasible vectors. From among the feasible vectors, based on the value of objective

function, identify the best solution vector Xbest(k)

.

Step 7. Set generation counter k = 1 .

68


Step 8. Select target vector, i = 1 .




Step 11.Repeat from Step 3.to Step 6.for the updated vector.

Step 12. Increase target vector i = i + 1. If i ≤ M, repeat from Step 9 otherwise increase

generation count k = k + 1 .

Step 13. Repeat from step 8 if the desired optimum value is not found or k ≤ kmax .



respectively. Fig. 4.1 shows the flow chart to find out locations of DGs from reliability point

of view. Fig 4.2 shows the flow chart for solving the formulated problem by FP.

4.4.3 Doing cost-benefit analysis

Step 1.Do cost- benefit analysis with the relations (4.13)-(4.23) for certain planning

periods i.e. 5 years, 10 years and 15 years and make decisions accordingly.

69


START

Evaluate SAIFI, SAIDI, CAIDI,AENS, EENS, ADCOST, CIC for the system

Connect DG at Load point 1 only and calculate the values of all the indices and objective function J

Take first two number from raking and connect DGs at those load points.

Calculate all the indicies and value of J for DGs connected at these load points

,

,, , ,Data input ,

, , , , , &,k t t t ti i

swk k dg dg

SAIFI SAIDI AIDIS Cp N L C AENS

r r

Evaluate load point indices (Failure rate and Repair time)

Increase the number from the ranking in this way and connect DGs at the respective load points

finidng out all the indices and J

Continue till the desired value of reliability is achieved

Take first three number from raking and connect DGs at these load points. Calculate all the indicies and

value of J for DGs connected at these load points

Now Connect DG at next load point only and calculate the values of all the indices and

objective function J, In the same way, connect DG at all load points one by one and

calculate the values of all indices and objective function J

Find out the improvement in reliability at all the load points due to DG from the values of J

Arrange the improvement in reliability at load points (in terms of J) in descending order and

rank them accordingly

Calculate value of objective function

t t t t

SAIFI SAIDI CAIDI AENSfor the system

SAIFI SAIDI CAIDI AENSJ

END

Fig. 4.1 Flow chart for finding out the locations of DGs

70


Fig. 4.2 Flow chart for enhancing reliability of distribution system incorporating DGs by FP

71


4.5 Results and discussions

The developed methodology in this paper has been implemented on a sample radial

distribution system, sample meshed distribution system and RBTS-2. The problem has been

solved by FP algorithm and comparison has been made with the results obtained by TLBO

and DE. The algorithms used have been coded in MATLAB-13.



The radial system is shown in Fig. A.2. It has been modified with DGs being connected at

its different load points. The data regarding the current and minimum reachable values of

failure rates and repair times, average load and number of customers at load points and cost

coefficients for each segment of radial distributor have been taken from [111]. They have

been represented in Table A.1-Table A.3 in Appendix. Table 4.1 gives interruption cost

(𝐶𝑝𝑘) at different load points for the sample radial distribution system. Table 4.2 gives the

values of customer and energy based reliability indices, customer interruption cost,

additional cost expended on DG and the value of J as given by relation (4.1) when single

DG is connected to different load points of the distribution system one by one. The values

of J found in Table 4.2 are ranked according to improvement in reliability of the distribution

system in descending order as shown in Table 4.3. Reliability with more than one DGs

connected at different load points is found as per ranking as shown in Table 4.4. From Table

4.4 the locations of DGs are found. In this chapter, DGs are connected at load points 5, 6

and 7 and the objective function F in relation (4.2) has been optimized by FP, TLBO and

DE. Table 4.6 gives the optimized values of failure rates and repair times obtained by the

three methods. Table 4.7 gives the optimized values of maintenance cost, customer

interruption cost, additional expense made in purchasing energy from the generators

connected and objective function (F) for sample radial distribution system obtained by all

the three methods. Table 4.8 shows the optimized values of customer and energy based

reliability indices obtained by all the three methods. The cost benefit analysis has been made

according to the section 4.3 in Table 4.9.

(B) Sample meshed distribution system [13,107]

This test system used in this chapter is as shown in Fig.B3. It is a modified system with DGs

being connected at its different load points to solve the problem formulated in this chapter.

72

Results and discussions

The data regarding failure rates and average repair times of different components of meshed

system have been taken from [13,107]. Table B.1 gives maximum allowable (λk,max/year)

and minimum reachable (λk,min/year) failure rates, and maximum allowable (rk,max (h))

and minimum reachable (rk,min (h)) average repair times. Table B.3 gives cost coefficients

for different distributor segments corresponding to failure rate and repair time. Table 4.10

gives interruption cost (𝐶𝑝𝑘) at different load points for the sample meshed distribution

system. Table 4.11 gives the values of customer and energy based reliability indices,

customer interruption cost, additional cost expended on DG and the value of J as given by

relation (4.1) when single DG is connected to different load points of the distribution system

one by one. The values of J found in Table 4.11 are ranked according to improvement in

reliability of the distribution system in descending order as shown in Table 4.12. Reliability

with more than one DGs connected at different load points is found as per ranking as shown

in Table 4.13. From Table 4.13, the locations of DGs are found. In this chapter, DGs are

connected at load points 1 and 4 for the meshed system and the objective function F in

relation (4.2) has been optimized by FP, TLBO and DE. Table 4.14 gives the optimized

values of failure rates and repair times obtained by the three methods. Table 4.15 gives the

optimized values of maintenance cost, customer interruption cost, and additional expense

made in purchasing energy from the generators connected and objective function (F) for

sample meshed distribution system obtained by all the three methods. Table 4.16 shows the

optimized values of customer and energy based reliability indices obtained by all the three

methods. The cost benefit analysis has been made according to the section 4.3 in Table 4.17.

(C) Roy Billinton Test System-Bus 2 (RBTS-2) [99]:


as shown in Fig.C.2. It is a modified system with DGs being connected at its different load

points as per the requirement of the problem formulated in this chapter. The data regarding

failure rates and average repair times of different components of RBTS-2 have been taken

from [99, 72]. Table C.2 gives maximum allowable (λk,max/year) and minimum reachable

(λk,min/year) failure rates, maximum allowable (rk,max (h)) and minimum reachable

(rk,min (h)) average repair times. Cost coefficients 𝛼𝐾 and 𝛽𝐾 for failure rates and repair

times respectively of the different sections of RBTS-2 are shown in Table C.3. Table C.4

represents sector wise customer data. The results which have been found for the sample

radial and meshed distribution system, have also been found for RBTS-2 in the same way.

73


They have been shown in from Table 4.18 to Table 4.24. The locations of DGs found for

RBTS-2 are 2, 3, 11, 12 and 18. The optimized values of the objective function (F) has been

found at these locations for RBTS-2.

Table 4.5 gives control parameters for the three optimization methods; FP, TLBO and DE

applied in this chapter for all the distribution test systems. Here, the DGs to be connected

are taken as standby units. The failure rate and average down time of DG taken in this chapter

are 0.5 failures/year and 13.25 hrs. respectively for all the three systems. Failure rate and

service restoration time of the changeover switch of DG are 0.1 failures/year and 0.25 hrs.

respectively for all the systems. Installation and maintenance cost of the DGs connected in

the system have been taken as Rs. 25/kW and Rs. 5.94/kW respectively for all systems. The

inflation rate, interest rate and load growth rate have been taken as 5%, 10% and 5 %

respectively. The calculations have been made for economical life cycle plans of 5 years, 10

years and 15 years by all the three optimization methods and comparison has been made in

all the case studies.

74





Table 4.2 The parameter values without DG and with DG connected at different load points of sample radial distribution system

Parameters Without DG With DG (Load point locations)

LP2 LP3 LP4 LP5 LP6 LP7 LP8

1 SAIFI(interruptions/customer) 0.72 0.7403 0.7054 0.6805 0.6607 0.6608 0.6710 0.7053

2 SAIDI(h/customer) 8.45 7.8015 7.6949 7.5885 6.4682 6.8313 6.9937 8.0993

3 CAIDI(h/customer interruption) 11.7361 10.5388 10.9086 11.1510 9.7895 10.3388 10.4230 11.4839

4 AENS(kWh/customer) 26.4100 23.1676 22.8860 22.9640 19.8039 21.5540 25.2449 25.3580

5 EENS (kWh) 26410 23168 22886 22964 19803 21554 25245 25358

6 Additional cost incurred on DG ( Rs.) ------- 6484.9 7048.1 6891.9 13212 9711.9 2330.1 2104

7 CIC (Rs) 450920 402280 405110 392340 318800 353800 436940 436190

8 J (Objective function) 7.6605 7.0650 6.9867 6.9485 6.1426 6.4771 6.9177 7.4067

75


Table 4.3 Ranking of the load points with reference to reliability improvement from maximum to

minimum for sample radial distribution system

Sr.

No.

Ranking of the load

points according to

reliability

improvement when

connected with DG

Increase in

reliability in

(%)

(In terms of

J)

1 LP5 28.8483

2 LP6 20.1377

3 LP7 12.1372

4 LP4 11.9957

5 LP3 11.6366

6 LP2 9.1929

7 LP8 3.6577

Table 4.4 Reliability with more than one generators connected according to the load point ranking for


Table 4.5 Control Parameters for FP, TLBO and DE for sample radial distribution system, sample

meshed distribution system and RBTS-2.









Parameters Without DG With DG

LP(5,6) LP(5,6,7)

1 SAIFI(interruptions/customer) 0.72 0.601474 0.552457

2 SAIDI(h/customer) 8.45 4.849518 3.393176

3 CAIDI(h/customer interruption) 11.7361 8.062717 6.141971

4 AENS(kWh/customer) 26.4100 14.94795 13.78287

5 EENS (kWh) 26410 14947.95 13782.87

6 Additional cost incurred on DG ( Rs.) -------- 22924.11 25254.26

7 CIC (Rs.) 450920 221678.9 207698

8 J (Objective function) 7.6605 4.917963 4.099242

76


Table 4.6 Optimized values of failure rates and repair times for radial system as obtained by FP,

TLBO and DE

failure rates ( /year) repair times (in hrs.)

Distributor

segment

By FP

By TLBO

By DE

By FP

By TLBO By DE

1 0.2000 0.2928 0.2963 6.0000 6.0390 6.1524

2 0.1285 0.1273 0.1559 6.0001 6.0529 6.1516

3 0.1703 0.1733 0.2113 4.0002 4.0060 4.2394

4 0.4995 0.5000 0.4159 8.0000 8.0000 15.8651

5 0.2000 0.1993 0.1840 12.1000 8.8418 9.9972

6 0.1000 0.1000 0.0955 6.0001 6.1225 7.0922

7 0.1000 0.1000 0.0958 6.0132 6.5993 6.1514



Sr.

No.

Current

Values

(Rs.)

Optimized Values(Rs.)

FP TLBO DE

1 Maintenance cost (∑ 𝛼𝑘 𝜆𝑘2⁄𝑁𝑐

𝑘=1 + ∑ 𝛽𝑘 𝑟𝑘⁄𝑁𝑐𝑘=1 ) 133640 31864.70 30855.39 30338.75

2 Customer interruption cost (∑ 𝐶𝐼𝐶𝑁𝑐𝑘=1 ) 450920 61168.52 80151.95 86759.55

Addditional cost to be paid while generators are

connected (ADCOST) --------

44529.4021 41941.55 41058.82

3 Objective function (F) 584560 137562.63 152948.91 158157.13

Table 4.8 Current and optimized reliability indices for sample radial distribution system

Sr.

No. Index

Current

Values Optimized Values

Threshold

Values

FP TLBO DE


2 SAIDI(h/customer) 8.4500 0.97358 1.26255 1.36716 2.0

3 CAIDI(h/customer

interruption)

11.7361 4.50893 4.81322 4.95223 5.25

4 AENS(kW/customer) 26.4100 4.14529 5.43922 5.88058 7.0

77


Table 4.9 Cost-Benefit Analysis for sample radial distribution system

Sr. No Economic

lifecycle

planning

( In Years)

Benefit in Rs.

Optimization Methods

FP TLBO DE

1 5 1496660 1481797 1392532

2 10 3062288 3047702 2960448

3 15 4687144 4448412 4366869

Table 4.10 Interruption cost at load points for sample meshed network


Interruption Cost(𝐶𝑝𝑖)(Rs./kW) 45 39 51 68

Table 4.11 The parameter values without DG and with DG connected at different load points of


SAIFI SAIDI CAIDI AENS EENS Additional

cost

incurred

on DG

(Rs.)

CIC

(Rs.)

J ((

Without

DG

0.689895 4.854797 7.037003 20.533869 26694 ________ 1345365 8.614597

With

DG

( At

Load

points)

LP1 0.506889 3.376967 6.662140 14.992007 19489 14408 1021166 6.665947

LP2 0.580880 3.906521 6.725177 16.740767 21762 9862 1153055 7.345548

LP3 0.598379 4.115833 6.878297 16.839053 21890 9606 1100399 7.545763

LP4 0.484016 3.192271 6.595373 13.144866 17088 19211 769023 6.288435

78



minimum for sample meshed distribution system

Sr.

No.

Ranking of

the load

points

according to

reliability

improvement

when

connected

with DG

Increase

in

reliability

in (%)

(In terms

of J)

1 LP4 36.991095

2 LP1 29.232890

3 LP2 16.818020

4 LP3 14.164684


sample meshed distribution system

DGs

connected

atLoad points


cost

incurred

on DG

(Rs.)

CIC

(Rs.)

J

4,1 0.301010 1.714441 5.695621 7.603005 9883 33620 444824 4.189817

4,1,2 0.191995 0.766166 3.990551 3.809902 4952 43482 252514 2.522699

79


Table 4.14 Optimized values of failure rates and repair times for the sample meshed distribution

system as obtained by FP, TLBO and DE


Distributor

segment

By FP

By TLBO

By DE

By FP

By TLBO By DE

1 0.2543 0.2586 0.5108 3.3638 6.4239 3.3488

2 0.1777 0.1732 0.1789 3.0692 4.0616 3.1863

3 0.1100 0.1102 0.1102 13.6459 14.1663 15.2239

4 0.1136 0.1135 0.1135 5.2832 5.5838 5.5767

5 0.0845 0.1836 0.0936 3.8810 3.3947 3.6861

6 0.0271 0.0284 0.0216 12.8049 11.4817 9.8042

7 0.1847 0.1846 0.1895 8.3979 8.8077 5.0402

8 0.1720 0.1784 0.1782 7.6295 5.7566 4.3617

9 0.0125 0.0124 0.0107 15.2188 6.5967 6.6022

10 0.0691 0.0693 0.0690 20.5688 20.0002 23.2368

11 0.2052 0.2091 0.2056 2.7692 5.2598 4.5500

12 0.2562 0.2008 0.2060 2.0162 4.8160 4.5732

13 0.1075 0.1100 0.1163 18.0929 24.5014 12.8537

14 0.1136 0.1135 0.1135 6.1741 2.1240 5.1153

15 0.0683 0.0903 0.1569 10.7236 6.8451 6.4803

16 0.0269 0.0275 0.0215 13.5553 9.3975 11.3589

17 0.1779 0.1780 0.1331 9.7524 13.8321 6.8392

18 0.1853 0.1846 0.1847 4.2503 8.5663 3.7627



Sr.

No.

Current

Values (Rs.) Optimized Values(Rs.)

FP TLBO DE

1

Maintenance cost


𝑘=1 + ∑ 𝛽𝑘 𝑟𝑘⁄𝑁𝑐𝑘=1 ) 5990100 924368.54 907796.36 1267214.73

2 Customer interruption cost (∑ 𝐶𝐼𝐶𝑁𝑐𝑘=1 ) 1345365 127239.70 210511.40 216164.70

Addditional cost to be paid while

generators are connected (ADCOST) --------

47659.68

44068.38 43636.45184

3 Objective function (F) 7335465 1099267.92 1162376.15 1527016.89

80


Table 4.16 Current and optimized reliability indices for sample meshed distribution system

Sr.

No. Index

Current


Threshold

Values

FP TLBO DE


2 SAIDI(h/customer) 4.854797 0.504747 0.807696 0.858059 2.00

3 CAIDI(h/customer

interruption) 7.037003 2.807004 4.021537 2.988605 3.5

4 AENS(kW/customer) 20.533869 2.203200 3.584467 3.750595 6.00

Table 4.17 Cost-Benefit Analysis for sample meshed distribution system

Sr. No Economic

lifecycle

planning

( In Years)

Benefit in Rs.


FP TLBO DE

1 5 1164232 839678 -827526

2 10 3374027 2704648 -289509

3 15 6427093 5395824 1344290

81


Table 4.18 The parameter values without DG and with DG connected at different load points of RBTS-2


cost

incurred

on DG

(Rs.)

CIC

(Rs.)

J

Without

DG

0.0986 0.5882 5.9666 4.6641 8899 ________ 828680 5.663

With

DG

( At

Load

points)

LP1 0.102576 0.550374 5.365523 4.567758 8715.282 367.4939 824578.4 5.432647

LP2 0.098509 0.509682 5.173954 4.464089 8517.482 763.0945 820168.4 5.201177

LP3 0.097299 0.523979 5.385271 4.500513 8586.979 624.0997 821717.9 5.287815

LP4 0.098572 0.58787 5.963838 4.491036 8568.898 660.2624 820756.8 5.603837

LP5 0.098547 0.587742 5.964087 4.418784 8431.039 935.9788 817450.3 5.579199

LP6 0.098262 0.583842 5.941668 4.467319 8523.645 750.7674 756231.6 5.576713

LP7 0.098058 0.582821 5.943626 4.420955 8435.182 927.6935 739159.6 5.55682

LP8 0.098578 0.587938 5.96418 4.426446 8445.66 906.738 714689 5.582629

LP9 0.098558 0.587836 5.96438 4.273329 8153.512 1491.034 641237.1 5.531147

LP10 0.102575 0.550371 5.365532 4.567749 8715.265 367.5265 827564.2 5.432628

LP11 0.096857 0.521774 5.387035 4.494895 8576.26 645.5377 826723.9 5.27574

LP12 0.096939 0.524936 5.415099 4.521772 8627.541 542.9756 827033.9 5.300572

LP13 0.09855 0.587757 5.964058 4.427286 8447.262 903.5328 817839.4 5.582098

LP14 0.09855 0.587757 5.964058 4.427286 8447.262 903.5328 817839.4 5.582098

LP15 0.098037 0.582715 5.943829 4.416179 8426.07 945.9166 863237.8 5.554772

LP16 0.098752 0.58629 5.937007 4.578467 8735.715 326.6273 795406.9 5.624409

LP17 0.102045 0.550469 5.394395 4.579221 8737.154 323.7495 825945.5 5.437743

LP18 0.096939 0.524936 5.415099 4.521772 8627.541 542.9756 825282.9 5.300572

LP19 0.096939 0.524936 5.415099 4.521772 8627.541 542.9756 826898.8 5.300572

LP20 0.098545 0.587732 5.964108 4.412835 8419.689 958.6804 815427.1 5.57717

LP21 0.098524 0.587629 5.964307 4.355028 8309.393 1179.271 812781.6 5.557458

LP22 0.098037 0.582715 5.943829 4.416179 8426.07 945.9166 735650.2 5.554772

82



minimum for RBTS-2


RBTS-2

DGs

connected

atLoad points


cost

incurred

on DG

(Rs.)

CIC (Rs.) J

2,11 0.09678 0.44328 4.579908 4.294923 8194.713 1408.63 818217.3 4.810259

2,3,11 0.09550 0.379084 3.969128 4.131375 7882.663 2032.73 811260.1 4.427674

2,3,11,12 0.093869 0.315844 3.364737 3.989085 7611.175 2575.70 809619 4.051987

2,3,11,12,18 0.09223 0.252604 2.738863 3.846796 7339.687 3118.68 807977.9 3.670929

2,3,11,12,18,19 0.09059 0.18936 2.09033 3.70450 7068.1994 3661.658 806336.717 3.28420

Sr.

No.

Ranking of

the load

points

according to

reliability

improvement

when

connected

with DG

Increase

in

reliability

in (%)

(In terms

of J)

Sr.

No.

Ranking of

the load

points

according to

reliability

improvement

when

connected

with DG

Increase

in

reliability

in (%)

(In terms

of J)

1 LP2 8.879202 12 LP22 1.948386

2 LP11 7.340399 13 LP7 1.9108

3 LP3 7.095283 14 LP21 1.899099

4 LP12 6.837517 15 LP6 1.547274

5 LP18 6.837517 16 LP20 1.53895

6 LP19 6.837517 17 LP5 1.502031

7 LP10 4.24052 18 LP13 1.449311

8 LP1 4.24017 19 LP14 1.449311

9 LP17 4.14248 20 LP8 1.439657

10 LP9 2.383825 21 LP4 1.055767

11 LP15 1.948386 22 LP16 0.686126

83


Table 4.21 Optimized values of failure rates and repair times for RBTS-2 as obtained by FP,

TLBO and DE


Distributor

segment

By FP

By TLBO

By DE

By FP

By TLBO

By DE

1 0.0367 0.0367 0.0398 2.2523 2.2523 2.2523

2 0.0150 0.0150 0.0149 4.5045 4.5045 4.5045

3 0.0391 0.0520 0.0474 4.5088 4.5045 4.5045

4 0.0361 0.0361 0.0361 2.2526 2.2523 2.2523

5 0.0150 0.0150 0.0148 9.9978 10.0000 10.0000

6 0.0150 0.0150 0.0149 4.5136 4.5045 4.5045

7 0.0367 0.0367 0.0372 2.2528 2.2523 2.2523

8 0.0150 0.0150 0.0147 4.5160 4.5045 4.5045

9 0.0150 0.0150 0.0148 4.5053 4.5045 4.5045

10 0.0390 0.0293 0.0297 2.2524 2.2523 2.2523

11 0.0150 0.0150 0.0150 4.5050 4.5045 4.5045

12 0.0367 0.0367 0.0367 2.2525 2.2523 2.2523

13 0.0391 0.0391 0.0391 2.2579 2.2523 2.2523

14 0.0390 0.0293 0.0293 2.2553 2.2523 2.2523

15 0.0391 0.0391 0.0397 2.2530 2.2523 2.2523

16 0.0367 0.0367 0.0371 2.2681 2.2523 2.2523

17 0.0150 0.0150 0.0150 9.9870 4.5045 4.5045

18 0.0391 0.0391 0.0394 2.2625 2.2523 2.2523

19 0.0150 0.0150 0.0142 4.5100 4.5045 4.5045

20 0.0150 0.0150 0.0150 4.5050 4.5045 4.5045

22 0.0293 0.0293 0.0316 2.2525 2.2523 2.2523

23 0.0150 0.0150 0.0145 4.5083 4.5045 4.5045

24 0.0150 0.0150 0.0144 4.5049 4.5045 4.5045

25 0.0487 0.0367 0.0374 2.2561 2.2523 2.2523

26 0.0150 0.0150 0.0149 4.5068 4.5045 4.5045

27 0.0392 0.0391 0.0400 2.2529 2.2523 2.2523

28 0.0150 0.0150 0.0146 4.5058 4.5045 4.5045

29 0.0150 0.0150 0.0141 9.9824 4.5045 4.5045

30 0.0487 0.0367 0.0368 2.2534 2.2523 2.2523

31 0.0150 0.0150 0.0150 4.5054 4.5045 4.5045

32 0.0150 0.0150 0.0149 4.5383 4.5045 4.5045

33 0.0367 0.0367 0.0417 2.2529 2.2523 2.2523

34 0.0150 0.0150 0.0150 9.9800 4.5045 4.5045

35 0.0293 0.0306 0.0295 2.2529 2.2523 2.2523

36 0.0150 0.0150 0.0149 9.9384 4.5045 4.5045

84


Table 4.22 Current and optimized values of Objective function (F) obtained by FP, TLBO

and DE for RBTS-2

Sr.

No.

Current


FP TLBO DE

1

Maintenance cost


𝑘=1 + ∑ 𝛽𝑘 𝑟𝑘⁄𝑁𝑐𝑘=1 )

232680

254692.6 254620.043 253861.34

2 Customer interruption cost (∑ 𝐶𝐼𝐶

𝑁𝑐𝑘=1 ) 828680 284052.8 284985.027 285949.06

Addditional cost to be paid while generators

are connected(ADCOST) --------

12398.98 12262.9861 12237.510

3 Objective function (F) 1061360 551144.3 551868.056

552047.91


Sr.

No. Index

Current


Threshold

Values

FP TLBO DE


2 SAIDI(h/customer) 0.5882 0.111135 0.132302 0.174741 0.4

3 CAIDI(h/customer interruption) 5.9666 1.301081 1.586033 2.163416 4.0

4 AENS(kW/customer) 4.6641 1.414852 1.560067 1.688404 2.2

Table 4.24 Cost-Benefit Analysis for RBTS-2

Sr. No Economic

lifecycle

planning

( In Years)

Benefit in Rs.


FP TLBO DE

1 5 1128600 1173100 972060

2 10 2658400 2540400 2280500

3 15 4438500 4137300 3895700

85


4.6 Conclusions

In this chapter, reliability of distribution systems (a sample radial distribution system, a

sample meshed system and RBTS-2) have been enhanced with DGs connected at different

load points of the systems. The locations of DGs have been found with a methodology

considering improvement in reliability as the chief motive. With these locations thus found,

the objective function formulated in this paper has been optimized by three optimization

methods say FP, TLBO and DE. To justify the installation of DGs in a long run, the cost-

benefit analysis has been made. It has been shown that for specific locations of DGs in the

distribution system, reliability enhancement is better. Of course, additional amount has to be

spent on the energy purchased from DGs but that too has been justified for specific period

of life cycle of DGs by doing cost-benefit analysis.

86

CHAPTER 5

Optimal Parameter Setting in Distribution System

Reliability Enhancement with Reward and Penalty

5.1 Introduction

The distribution companies are transiting gradually from the conventional cost based (cost

of service or rate of return) regulation to performance based regulation (PBR) in many

countries of the world for efficiency improvement. In performance based regulations

incentives are decided for strong efficiency (in terms of profit) by the companies. This may

lead to deterioration of quality services to customers [115].

In order to reach out such conditions, many performance based regulations are embedded

with quality regulations adopting direct or indirect quality controls [116]. In indirect quality

control, customers are provided information regarding quality of performance of distribution

companies while in direct control, the performance is evaluated in terms of financial

incentives provided by the regulators for maintaining adequate service quality [117]. The

quality of services rendered by distribution companies are defined in three ways; reliability

of services /continuity of supply, voltage quality and commercial quality [115].This paper

focuses on service reliability regulations. Service reliability has been regulated by different

mechanisms introduced by regulators. The reward and penalty scheme (RPS), which is a

direct quality control, is an effective and highly accepted mechanism for regulatory purpose

in distribution systems. The regulator uses this tool to regulate service reliability index like

SAIFI, SAIDI and AENS. Reward or penalty to the distribution company is decided

depending on the achievement of these indices below their target levels.

In RPS financial incentives are created for distribution companies to maintain or change

their quality level. The regulator tries to maintain socioeconomically optimum reliability

level which minimizes the total reliability cost for society with RPS [117].

This chapter focuses on enhancing the reliability of distribution system incorporating

reward/penalty imposed on distribution systems by the regulator. Here the optimized values

of reward /penalty have been found achieving the target values of reliability indices. By

87

Optimal Parameter Setting in Distribution System Reliability Enhancement with Reward and Penalty

finding optimum values of reward/penalty it is possible to limit financial risk of distribution

companies and unnecessary tariff changes for the customers.

The chapter is arranged as follows. The RPS theory is depicted in section 5.2. In Section 5.3

the problem formulated in this chapter has been described. Section 5.4 is regarding the

solution methodology of the problem by FP. In section 5.5 results obtained for the three

distribution systems i.e. sample radial, sample mesh and RBTS-2 are discussed. Conclusions

are drawn in section 5.6.

5.2. Reward / Penalty Scheme (RPS)

In RPS regulator uses system quality indicators to measure the reliability of the system.

Target levels of these indicators are imposed on the utilities by the regulators. Success or

failure in achieving them decides the reward or penalty for the utility. The higher the

reliability level, higher will be the profit of utility. Thus the market-like conditions are tried

to be replicated by regulator. The quality indicators commonly used are system average

interruption frequency index (SAIFI) and system average interruption duration index

(SAIDI) from reliability point of view. Both are customer based indices. Energy based

reliability index (EENS) can also be integrated with these indices.

5.2.1 Socio-economical perspectives of RPS

With RPS the regulator tries to achieve socio-economically optimum reliability level [115].

The socio-economical reliability relates to the customer interruption costs and network costs.

For poor reliability customer interruption costs are high. Higher reliability of the system

reduces interruption costs to the customers but it requires higher expenditures on capital and

maintenance activities which is ultimately paid by the customers in terms of tariffs.

Somewhere in between is the socioeconomic optimal reliability level which is the sum of

customer interruption costs and network costs, minimizing the total reliability cost for

society [118]. The cost versus reliability depicting socio-economically optimal reliability

level is shown in Fig.5.1.The optimal reliability Ropt is achieved when the rate of increase

of network costs equals the rate of decrease of customer interruption costs.

∂Cnetwork

∂R|

R=Ropt

= − ∂CIC

∂R|

R=Ropt

(5.1)

The utility’s optimum may or may not be the socio-economical optimum as the utility tries

to set the optimum at its minimum cost. In optimum RPS incentives are given to achieve the

88

Reward / Penalty Scheme (RPS)

socio-economical reliability by including the customer interruption costs in their own cost

functions [119]. In actual the socio-economical reliability level is not known to the regulator,

instead a target value is set for the quality indicator which measures reliability. The increase

or decrease in customer interruption costs due to deviation of reliability from this target value

is adjusted by the utility in terms of either reward or penalty. It is the financial risk CRP(cost

of reward/penalty) borne by the utility when it succeeds or fails in achieving the target

reliability level, which is reflected in either profit or loss of the utility. Here CRP < 0 stands

for reward to the utility and CRP > 0 as penalty to the utility. Thus the ultimate aim here

is to bring the minimum of total reliability cost curve of the utility, which includes the impact

of RPS, to the socio-economical reliability level Ropt .

The various RPS schemes are as shown in Fig. 5.2 [120]. This paper focuses on continuous

scheme where rewards/penalties increase with the deviation from the set target level.

5.3 Problem formulation

In context to the discussions made in the previous sections, the problem is formulated as

follows.

The adjustment of utility’s cost curve such that its minimum occurs at the same reliability

level Ropt as society, leads to defining the optimum values of reward and penalty CRP .

With impact of RPS, at the socio-economically optimal reliability level Ropt, the total

reliability cost for society is minimized.

∂Ctotalsociety

∂R|

R=Ropt

= ∂(Cnetwork+CIC)

∂R|

R=Ropt

= 0 (5.2)

For an optimal RPS following must also be satisfied.

∂Ctotalsociety

∂R|

R=Ropt

= ∂(Cnetwork+CRP)

∂R|

R=Ropt

= 0 (5.3)

From (8) and (9), an optimal RPS must fulfill

∂CRP

∂R|

R=Ropt

= ∂CIC

∂R|

R=Ropt

(5.4)

89


In [120] it is shown that for an optimal RPS (5.4) can be written as below.

∂CRP

∂R=

∂CIC

∂R , ∀ R (5.5)

CRP = CIC − K , ∀ R (5.6)

K is an arbitrary constant.

The derivative ∂CRP ∂R⁄ is the monetary value per unit system quality indicator for

reliability and is known as incentive rate. For this paper it is a slope for continuous type RPS.

As per (5.6), optimal reward/penalty at specific reliability level is a function of customer

interruption costs CIC at that reliability level. Thus it depends on the ability of regulator to

measure and reconstruct CIC to get optimal reward/penalty [120].

For the continuous RPS scheme in Fig.5.2 the slope (incentive rate) is constant. Hence, the

relation between system reliability and customer interruption costs is liner for (5.5) to be

satisfied. As long as (5.5) is satisfied, socio-economically optimal reliability level is

achieved at any value of K in (5.6). The value of K is responsible for the transaction between

the utility and customers. If value of K is set to zero, all the customer interruption costs will

be transferred to the utility. Hence, the utility will operate on society’s total reliability cost.

In this case, a profit maximizing utility may likely to incur loss as the allowed revenue only

covers the utility’s total reliability cost for the target value set. Hence, setting the value of K

in continuous RPS corresponds to setting of target level for system quality indicator for

reliability.

K = CIC (R = Rtarget ) (5.7)

Relation (5.6) must be zero for (5.7). From this it can be depicted that irrespective of the

target level set, optimum reliability level is achieved by the profit maximizing utility if

incentive rate is set on the basis of customer interruption costs.

With the objective of enhancing reliability with finding out optimum values of

reward/penalty, the objective function is defined as follows.

F = ∑ αk λk2⁄Nc

k=1 + ∑ βk rk⁄Nck=1 + ∑ CIC

Nck=1 + ADCOST(EENSO − EENSD) + ∑ CRP

Nck=1

(5.8)

90

Problem formulation

where, CIC = λk × rk × Li × Cpk (5.9)

The objective function consists of five terms. The first two terms are related to modification

costs related to maintenance activities, i.e. cost for modifying failure rates and average repair

times of each section of the distribution system respectively. Lesser are the values of these

terms; more are the costs or investments associated with preventive maintenance and

corrective repair required by utility to achieve them [111]. Both these terms are based on

Duane’s reliability growth model [105]. The third part of the relation (5.8); i.e. cost of

interruption depicts the costs incurred at the customers end in terms of loss at the time of

power fail. When a utility is engaged in supplying power to industrial and commercial

facilities, the high costs associated with power outages of course keep more significance.

The total cost of interruptions for any load point i can be determined by adding the cost of

all section outages. The total cost of customer interruptions for all customers can then be

evaluated. The fourth part depicts the additional cost to be given to the DG owners for the

energy purchased from them. It is multiplication of energy provided by DGs and additional

charge (ADCOST) in Rs. /kWH. In this chapter, the DGs considered are working as standby

units. The reliability model followed here is as per [40]. The fifth part is related to cost of

reward/penalty which has already been depicted in detail. Thus the objective function

provides balance between the cost spent on DGs, the cost of maintenance, customer

interruption costs and cost of reward/penalty. This is achieved by minimizing the objective

function as formulated in relation (5.8).



λk,min ≤ λk ≤ λk,max and rk,min ≤ rk ≤ rk,max , k = 1, … … … … … , Nc (5.10)

(ii) Inequality constraints on the customer and energy based indices





91


As all these indices are interdependent, in this chapter, the reliability level(R)

has been defined considering the impact of all the customer and energy based reliability

indices as shown below.

R =SAIFI

SAIFIt+

SAIDI

SAIDIt+

CAIDI

CAIDIt+

AENS

AENSt . (5.15)

Here R is the sum of the normalized values of customer and energy oriented reliability

indices i.e. SAIFI, SAIDI, CAIDI and AENS. The normalization is with respect to respective

threshold/target values of the indices. Hence all the indices will be given equal weightage in

the procedure. The customer and energy oriented indices have already been represented in

section 2.4.

λk,max and rk,max are maximum allowable failure rate and repair time of kth section

respectively. λk,min and rk,min are minimum reachable values of failure rate and repair

time of kth section which are achieved in optimization process. These lower bound values

are obtained by failure and repair data analysis along with the associated costs and it is done

through reliability growth model [105]. Nc stands for total number of sections in the


SAIFIt , SAIDIt , CAIDIt and AENSt are target/threshold values of the respective indices.

They depend on the managerial/administrative decisions.

The formulated problem is solved by flower pollination optimization method (FP) [100].

The method in this chapter has been applied on a sample radial distribution system, sample

meshed distribution system and RBTS-2. The optimized values obtained after having solved

the problem may be given as target values to the crew with setting up optimum

reward/penalty values to the utilities and their reliability being enhanced.

92

Problem formulation

Fig. 5.1 The cost versus reliability depicting socio-economically optimal reliability level

Fig. 5.2 Different designs of RPS

93


5.4 Solution Methodology



Step 1. Data input λk,max, rk,max , λk,min, rk,min , λdg , rdg , λsw , cost of interruption ( Cpk

) , Ni, Li, SAIFIt , SAIDIt , CAIDIt and AENSt .

Step 2. Find value K at target values of indices.




uniformly between lower and upper limits as given by relation (5.10).

Step 4. Evaluate λsys,i , rsys,i and Usys,i at each load point.




),

i = 1, … … … … … , ′M′ as given by relation (5.8) and (5.9).

Step 7. Calculate value of overall reliability R for all vectors in the population by relation

(5.15).

Step 8. Evaluate inequality constraints from the relations (5.1), (5.12), (5.13) and (5.14) for

each vector of the population. Vectors satisfying these constraints will be feasible otherwise

not feasible vectors. From among the feasible vectors, based on the value of objective

function, identify the best solution vector Xbest(k)

.







94







respectively. Fig 5.3 shows the flow chart for solving the formulated problem by FP.

95


END

START

Evaluate SAIFI, SAIDI, CAIDI, AENS, EENS, ADCOST,CIC



Print solution

generation = k+1

NO

YES

Is solution

converged?

Find value of K at the target values of indices

Generate a population of size ‘M’ for failure rate λ and repair time r each between lower and upper limits

0 00 0 0 0 0 0, , , X , , .,

1 2 1 2i

TS X X X X X XM i i iD

Calculate the optimum values of SAIFI, SAIDI, CAIDI, AENS, overall reliability R & CRP


population and Identify the( )

&best best

kX F

Select target vector, i=1 and find updated value of each vector by D.4

Calculate value of objective function F for all vectors in the population and identify ( )best

kX

If any updated solution violates the inequality constraints , then set the values of the vectors to ( )kiX

Compare the fitness of the updated vectors with that of the initial vectors and retain the best ones by D.9 ( 1)k

iX

( )kiX

,

,,max ,min ,max ,minData input , , , , ,

, , , , , ,,k t t t ti i

swk k k k dg

dgSAIFI SAIDI AIDIS Cp N L C AENS

r r

r

Fig.5.3 Flow chart for the solution of the problem formulated in section 5.3 by FP

96


5.5. Results and Discussions

The developed methodology in this paper has been implemented on a sample radial

distribution system, sample meshed system and RBTS-2. The problem has been solved by

FP algorithm. The algorithms used have been coded in MATLAB-13.



The radial system is as shown in Fig. A.2. It is a modified system with DGs.The data

regarding the maximum allowable and minimum reachable values of failure rates and repair

times, average load and number of customers at load points and cost coefficients for each

segment of radial distributor have been taken from [111]. The basic data have been shown

in Table (A.1-A.2). Table A.3 gives cost coefficients corresponding to failure rates and

repair times for all the sections of the system. Table 5.1 shows interruption cost (Cpk) at

different load points for the sample radial distribution system. Optimized values of

maintenance cost and additional cost spent on DGs corresponding to different level of

reliability achieved around a target reliability level are shown in Table 5.2. In this chapter,

DGs are connected at load points 5, 6 and 7 for sample radial system. Table 5.3 represents

optimized values of maintenance cost, additional cost spent on DGs for purchasing energy,

customer interruption cost, cost of reward/penalty and objective function (F) for specific

values of reliability indices (SAIFI= 0.202724, SAIDI=0.90335, CAIDI=4.456051 and

AENS= 3.855498). Table 5.4 shows the extent of enhancement of these reliability indices

compared to their respective threshold values. Table 5.5 shows optimal costs of network,

utility and society considering the impact of continuous RPS on utility (considering SAIFIt =

0.254709 , SAIDIt = 1.220574, CAIDIt = 4.792019, AENSt = 5.273897 ) . Optimized

values of reward/penalties and customer interruption costs for different reliability level are

shown here. Table 5.6 represents the optimized values of failure rates and repair times

different sections of the sample radial distribution system.

(B) Sample meshed distribution system [13,107]:

This test system used in this chapter is as shown in Fig.B.3. It is a modified system with

DGs.The data regarding failure rates and average repair times of different components of

meshed system have been taken from [13,107]. Table B.1 gives maximum allowable

(λk,max/year) and minimum reachable (λk,min/year) failure rates, and maximum allowable

97


(rk,max (h)) and minimum reachable (rk,min (h)) average repair times. Table B.3 gives cost

coefficients for different distributor segments corresponding to failure rate and repair time.

Table 5.7 gives interruption cost (𝐶𝑝𝑘) at different load points for the sample meshed

distribution system. Optimized values of maintenance cost and additional cost spent on DGs

corresponding to different level of reliability achieved around a target reliability level are

shown in Table 5.8. In this chapter, DGs are connected at load points 1 and 4 for sample

meshed system. Table 5.9 represents optimized values of maintenance cost, additional cost

spent on DGs for purchasing energy, customer interruption cost, cost of reward/penalty and

objective function (F) for specific values of reliability indices (SAIFI= 0.19547226,

SAIDI=0.494002204, CAIDI=2.527223971 and AENS= 2.205591604). Table 5.10 shows

the extent of enhancement of these reliability indices compared to their respective threshold

values. Table 5.11 shows optimal costs of network, utility and society considering the impact

of continuous RPS on utility (considering SAIFIt = 0.249358965 , SAIDIt =

0.889319751, CAIDIt = 3.566423809, AENSt = 3.916585348) . Optimized values of

reward/penalties and customer interruption costs for different reliability level are shown

here. Table 5.12 represents the optimized values of failure rates and repair times different

sections of the sample meshed distribution system.

(C) Roy Billinton Test System-Bus 2 (RBTS-2) [99]:


as shown in Fig.C.2.It is a modified system as per the requirement of the problem formulated

in this chapter. The data regarding failure rates and average repair times of different

components of RBTS-2 have been taken from [99,72]. Table C.2 gives maximum allowable

(λk,max/year) and minimum reachable (λk,min/year) failure rates, maximum allowable

(rk,max (h)) and minimum reachable (rk,min (h)) average repair times. Table C.3 gives cost

coefficients 𝛼𝐾 and 𝛽𝐾 for failure rates and repair times respectively of the different sections

of RBTS-2. Table C.4 represents sector wise customer data. Table 5.13 represents optimized

values of maintenance cost and additional cost spent on DGs corresponding to different

levels of reliability achieved around a target reliability level. The locations of DGs for

RBTS-2 are 2, 3, 11, 12 and 18 in this chapter. Table 5.14 represents optimized values of

maintenance cost, additional cost spent on DGs for purchasing energy, customer interruption

cost, cost of reward/penalty and objective function (F) for specific values of reliability

indices (For SAIFI= 0.080462, SAIDI=0.177953, CAIDI=2.2301 and AENS= 1.667670).

98


Table 5.15 shows the extent of enhancement of these reliability indices compared to their

respective threshold values. Table 5.16 shows optimal costs of network, utility and society

considering the impact of continuous RPS on the utility (consideringSAIFIt =

0.084746 , SAIDIt = 0.198559, CAIDIt = 2.435000, AENSt = 1.806670 ). Optimized

values of reward/penalties and customer interruption costs for different reliability level are

shown here. Table 5.17 represents the optimized values of failure rates and repair times

different sections of RBTS-2.

In Table 5.5, Table 5.11 and Table 5.16, the Cnetwork has been taken considering the cost of

maintenance and ADCOST.

The optimization method applied to solve the problem to all the three systems is FP. The

control parameters taken for both system are as follows. Population size is 30, max

generation specified (kmax) is 1000, updated step size (∝) is 0.01, distribution factor (β) is

1.5 and switch probability is 0.8.

Here, the DGs to be connected are taken as standby units. The failure rate and average down

time of DG taken in this chapter are 0.5 failures/year and 13.25 hrs. respectively for all the

systems. Failure rate and service restoration time of the changeover switch of DG are 0.1

failures/year and 0.25 hrs. respectively for all the systems.

Fig.5.4, Fig. 5.5 and Fig.5.6 represent impact of an optimal continuous RPS on the different

parameter costs for sample radial distribution system, sample meshed distribution system

and RBTS-2 respectively. Here, the optimal costs of network, utility, society, and

reward/penalty and customer interruptions for different optimal reliability levels are shown

graphically.

99





Table 5.2 Optimized values of overall reliability R and other parameters (considering SAIFIt =

0.254709 , SAIDIt = 1.220574, CAIDIt = 4.792019, AENSt = 5.273897 ) for sample radial distribution

system

Sr

No.

Maintenance

cost

ADCOST SAIFI SAIDI CAIDI AENS F R

1 30798.39 38806.75 0.320538 1.619708 5.048653 7.006626 199316.9 4.967553

2 31088.81 39388.04 0.3047 1.559464 5.291998 6.71598 191991.9 4.851686

3 34642.64 39807.21 0.269647 1.514092 5.617732 6.506395 189364.8 4.705128

4 39700.64 40692.63 0.242534 1.412223 5.867464 6.063685 182582.8 4.483391

5 32354.31 40831.04 0.274817 1.392263 5.027384 5.994482 173244.2 4.405355

6 37848.65 41100.75 0.218936 1.356924 6.046232 5.859623 174261.9 4.34405

7 37186.95 41578.9 0.269569 1.304547 4.842746 5.620551 167572.9 4.203453

8 30215.71 42034.58 0.257399 1.263473 4.9094 5.392708 154712.9 4.092729

9 46374.53 42020.28 0.242871 1.249995 5.212499 5.399858 170648.4 4.089254

10 39862.73 42238.59 0.219782 1.232748 5.588844 5.290704 161503.6 4.042314

11 41401.91 42367.68 0.24085 1.211027 5.025977 5.226161 160760.2 3.977537

12 39646.99 42580.06 0.251573 1.188188 4.724997 5.119969 155999.1 3.917981

13 38078.5 42874.51 0.238869 1.15296 4.829063 4.972743 150194.6 3.833043

14 32888.81 43207.45 0.223323 1.123043 5.044864 4.806275 140974.1 3.760967

15 39575.15 44440.8 0.212177 0.990427 4.667917 4.189601 130539.7 3.412966

16 53422.76 44498.82 0.19987 0.973452 4.871609 4.160588 143375.1 3.387744

17 36498.06 44911.49 0.204953 0.929797 4.536846 3.954257 120890.9 3.262954

18 38130.06 45109 0.202724 0.90335 4.456051 3.855498 119720.4 3.196949

19 52484.85 45352.6 0.195331 0.872065 4.471005 3.7337 130673.9 3.122317

100


Table 5.3 Current and optimized values of Objective function (F) obtained by FP for sample radial

distribution system (For SAIFI= 0.202724, SAIDI=0.90335, CAIDI=4.456051 and AENS= 3.855498)

Sr.

No. Current Values (Rs.) Optimized Values(Rs.)

FP

1 Maintenance cost (∑ 𝛼𝑘 𝜆𝑘

2⁄𝑁𝑐𝑘=1 + ∑ 𝛽𝑘 𝑟𝑘⁄𝑁𝑐

𝑘=1 ) 133640 38130.06


𝑁𝑐𝑘=1 ) 138860 56826.49

3 Additional cost to be paid while generators are

connected (ADCOST) 35115

45109

4 Reward/Penalty (∑ 𝐶𝑅𝑃

𝑁𝑐𝑘=1 )

61688 -20345.2


Table 5.4 Current and optimized reliability indices for sample radial distribution system

(For SAIFI= 0.202724, SAIDI=0.90335, CAIDI=4.456051 and AENS= 3.855498)

Sr. No. Index Current Values Optimized

Values

Threshold

Values FP


2 SAIDI(h/customer) 8.4500 0.90335 1.220574


4 AENS(kW/customer) 26.4100 3.855498 5.273897

101


Table 5.5 Optimal cost of network, utility and society considering the impact of continuous RPS on

utility (considering SAIFIt = 0.254709 , SAIDIt = 1.220574, CAIDIt = 4.792019, AENSt = 5.273897 )

for sample radial distribution system

Sr No. 𝐂𝐈𝐂 𝐂𝐑𝐏 𝐂𝐧𝐞𝐭𝐰𝐨𝐫𝐤 𝐂𝐭𝐨𝐭𝐚𝐥𝐮𝐭𝐢𝐥𝐢𝐭𝐲

= 𝐂𝐧𝐞𝐭𝐰𝐨𝐫𝐤 + 𝐂𝐑𝐏 𝐂𝐭𝐨𝐭𝐚𝐥𝐬𝐨𝐜𝐢𝐞𝐭𝐲

= 𝐂𝐧𝐞𝐭𝐰𝐨𝐫𝐤 + 𝐂𝐈𝐂 𝐑

1 103441.8 26270.06 69605.13335 95875.18925 173046.8856 4.967553

2 99343.39 22171.69 70476.84515 92648.53864 169820.235 4.851686

3 96043.32 18871.63 74449.85414 93321.4801 170493.1764 4.705128

4 89680.61 12508.91 80393.27286 92902.18687 170073.8832 4.483391

5 88615.27 11443.57 73185.34189 84628.91224 161800.6086 4.405355

6 86242.08 9070.388 78949.40583 88019.7936 165191.4899 4.34405

7 82989.39 5817.695 78765.84991 84583.54517 161755.2415 4.203453

8 79817.16 2645.463 72250.29019 74895.75305 152067.4494 4.092729

9 79712.62 2540.923 88394.81422 90935.73745 168107.4338 4.089254

10 78287.01 1115.312 82101.32533 83216.63688 160388.3332 4.042314

11 77081.16 -90.5391 83769.59327 83679.0542 160850.7505 3.977537

12 75471.86 -1699.83 82227.05043 80527.21763 157698.914 3.917981

13 73206.65 -3965.04 80953.01612 76987.97267 154159.669 3.833043

14 71024.76 -6146.94 76096.26314 69949.32787 147121.0242 3.760967

15 61847.71 -15324 84015.94759 68691.95883 145863.6552 3.412966

16 61312.61 -15859.1 97921.58514 82062.50064 159234.197 3.387744

17 58326.53 -18845.2 81409.5417 62564.37401 139736.0703 3.262954

18 56826.49 -20345.2 83239.0693 62893.86578 140065.5621 3.196949

19 55004.06 -22167.6 97837.4538 75669.81549 152841.5118 3.122317

Table 5.6 Optimized values of failure rates and repair times for sample radial distribution system as

obtained by FP (For SAIFI= 0.202724, SAIDI=0.90335, CAIDI=4.456051 and AENS= 3.855498)

failure rates

( /year)

repair

times

(in hrs.)

Distributor

segment

By FP

By FP

1 0.20000 6.00003

2 0.09858 6.00000

3 0.12815 4.03472

4 0.46368 10.18818

5 0.18284 10.30196

6 0.10000 6.00032

7 0.09985 6.00679

102


Table 5.7 Interruption costs at load points for sample meshed distribution system

Distributor Load points(LP) #1 #2 #3 #4

Interruption Cost(𝐶𝑝𝑘)(Rs./kW) 45 39 51 60


0.249358965 , SAIDIt = 0.889319751, CAIDIt = 3.566423809, AENSt = 3.916585348 ) for sample


Sr No. Maintenance cost ADCOST SAIFI SAIDI CAIDI AENS F R

1 1772970 37320.29124 0.282981 1.397184 4.937379 6.179888 2303808 5.668187

2 1924724 40923.01712 0.270251 1.086869 4.021705 4.794224 2296061 4.657657

3 1870741 41722.00093 0.300166 1.015511 3.383167 4.486923 2208300 4.439884

4 1924738 42201.83822 0.210338 0.975149 4.636094 4.30237 2240457 4.338456

5 1935662 42854.25257 0.300693 0.919314 3.057319 4.051441 2222278 4.131274

6 1659570 42857.35179 0.29623 0.921081 3.10934 4.050249 1944790 4.129647

7 1084723 43101.72096 0.299282 0.897566 2.999068 3.956261 1360670 4.060523

8 1887726 44695.43922 0.229252 0.761488 3.321624 3.343293 2092366 3.560608

9 1602372 45247.38113 0.208406 0.715315 3.432316 3.131007 1781738 3.401927

10 1505257 45783.45383 0.220983 0.665849 3.013124 2.924825 1662949 3.226559

11 1498295 46496.78823 0.206862 0.607311 2.93582 2.650466 1622590 3.012382

12 1477021 47014.27825 0.199655 0.566487 2.837325 2.451431 1576096 2.859139

13 1329648 47449.09315 0.197876 0.513538 2.59526 2.284195 1419132 2.681891

14 1444479 47653.46183 0.195472 0.494002 2.527224 2.205592 1526139 2.61114

15 1369748 48248.09819 0.179971 0.448075 2.489708 1.976885 1421817 2.428417

16 1734180 48295.00614 0.180722 0.445403 2.464572 1.958844 1783284 2.416772

17 1572818 48345.19558 0.17999 0.44048 2.44725 1.93954 1620084 2.398512

18 1074699 48349.229 0.179806 0.440314 2.448832 1.937989 1121699 2.397637

19 1094404 48360.21741 0.179664 0.439299 2.445114 1.933763 1140925 2.393804

Table 5.9 Current and optimized values of Objective function (F) obtained by FP for sample meshed

distribution system (For SAIFI= 0.19547226, SAIDI=0.494002204, CAIDI=2.527223971 and AENS=

2.205591604)

Sr.


FP



𝑘=1 ) 5990100 1444479.383


𝑁𝑐𝑘=1 ) 1345365 130892.7156


connected(ADCOST) 33620

47653.46183


𝑁𝑐𝑘=1 )

217044 -96886.4521


103


Table 5.10 Current and optimized reliability indices for sample meshed distribution system



Values

Threshold

Values FP


2 SAIDI(h/customer) 4.854797 0.494002204 0.88931975


4 AENS(kW/customer) 20.533869 2.205591604 3.9165853

Table 5.11 Optimal cost of network, utility and society considering the impact of continuous RPS on

utility (considering SAIFIt = 0.249358965 , SAIDIt = 0.889319751, CAIDIt = 3.566423809, AENSt =

3.916585348 ) for sample meshed distribution system

Sr No. 𝐂𝐈𝐂 𝐂𝐑𝐏 𝐂𝐧𝐞𝐭𝐰𝐨𝐫𝐤

𝐂𝐭𝐨𝐭𝐚𝐥𝐮𝐭𝐢𝐥𝐢𝐭𝐲

= 𝐂𝐧𝐞𝐭𝐰𝐨𝐫𝐤 +

𝐂𝐑𝐏 𝐂𝐭𝐨𝐭𝐚𝐥

𝐬𝐨𝐜𝐢𝐞𝐭𝐲= 𝐂𝐧𝐞𝐭𝐰𝐨𝐫𝐤 + 𝐂𝐈𝐂

𝐑

1 360648.3967 132869.22 1810290 1943159.299 2170938.467 5.668187

2 279096.5508 51317.383 1965647 2016964.664 2244743.832 4.657657

3 261808.1469 34028.979 1912463 1946491.996 2174271.164 4.439884

4 250648.3983 22869.23 1966940 1989808.898 2217588.066 4.338456

5 235770.7489 7991.5811 1978516 1986507.742 2214286.91 4.131274

6 235070.5675 7291.3997 1702428 1709719.103 1937498.271 4.129647

7 230311.9049 2532.7371 1127825 1130357.894 1358137.062 4.060523

8 193861.7708 -33917.396 1932421 1898503.919 2126283.087 3.560608

9 180948.9067 -46830.261 1647619 1600789.14 1828568.308 3.401927

10 169843.8596 -57935.30 1551041 1493105.584 1720884.752 3.226559

11 152788.4079 -74990.759 1544792 1469801.421 1697580.588 3.012382

12 139919.9301 -87859.237 1524035 1436175.635 1663954.802 2.859139

13 134907.07 -92872.097 1377097 1284225.256 1512004.424 2.681891

14 130892.7156 -96886.45 1492133 1395246.393 1623025.56 2.61114

15 115799.9339 -111979.23 1417997 1306017.356 1533796.524 2.428417

16 114293.8314 -113485.33 1782475 1668989.726 1896768.894 2.416772

17 113349.8037 -114429.36 1621164 1506734.197 1734513.365 2.398512

18 113215.3972 -114563.77 1123048 1008484.012 1236263.18 2.397637

19 112969.6452 -114809.52 1142765 1027955.191 1255734.359 2.393804

104


Table 5.12 Optimized values of failure rates and repair times for sample meshed distribution system as

obtained by FP (For SAIFI= 0.19547226, SAIDI=0.494002204, CAIDI=2.527223971 and

AENS= 2.205591604)

failure rates

( /year)

repair

times

(in hrs.)

Distributor

segment

By FP

By FP

1 0.2542 3.3531

2 0.1776 3.0817

3 0.1100 21.7324

4 0.1146 3.8403

5 0.1846 3.3945

6 0.0190 10.1910

7 0.1846 3.5109

8 0.1780 4.5522

9 0.0105 7.1412

10 0.0802 27.5656

11 0.2053 5.2349

12 0.2052 2.1985

13 0.1140 12.7190

14 0.1176 3.3301

15 0.0699 6.3538

16 0.0176 13.5615

17 0.1781 9.6232

18 0.1849 8.3621


0.084746 , SAIDIt = 0.198559, CAIDIt = 2.435000, AENSt = 1.806670) for RBTS-2

Sr. No. Maintenance

cost

ADCOST SAIFI SAIDI CAIDI AENS F R

1 292425.5 10128 0.086 0.225 2.623 2.01 667137.2 3.132

2 290868.1 10385 0.085 0.223 2.66 1.943 656514 3.094 3 295194.8 10630 0.082 0.226 2.757 1.878 658002 3.06

4 264349.6 10650 0.086 0.204 2.417 1.873 617472.5 2.964 5 275661.7 10687 0.086 0.198 2.286 1.864 623918.5 2.916

6 281435.6 10933.7 0.0829 0.203 2.322 1.798 620153.9 2.871

7 266436.7 11206 0.081 0.19 2.383 1.728 574835.8 2.8 8 266249.7 11252 0.083 0.187 2.253 1.715 574703.2 2.775

9 270691.6 11340 0.083 0.176 2.156 1.692 576717.2 2.712 10 283167 11400 0.083 0.178 2.14 1.677 585878.1 2.707

11 295181.6 11375 0.082 0.175 2.156 1.683 597618.4 2.698

12 306348.7 11434 0.08 0.178 2.23 1.668 604785.9 2.696

13 268835.9 11471 0.084 0.172 2.115 1.658 560790.9 2.691

14 287743.7 11574 0.083 0.17 2.056 1.631 585959.7 2.645 15 275668.9 11618 0.082 0.166 2.074 1.62 571269.7 2.623

16 271853.2 11595 0.08 0.166 2.121 1.626 562966.3 2.619 17 275059.6 11605 0.081 0.166 2.091 1.623 568568 2.616

18 287907.5 11526 0.08 0.166 2.063 1.644 578949.5 2.614

105


Table 5.14 Current and optimized values of Objective function (F) obtained by FP for RBTS-2


Sr.


FP



𝑘=1 ) 232680 306348.71


𝑁𝑐𝑘=1 ) 807980 302267.59



11434.22


𝑁𝑐𝑘=1 )

490450 -15264.67





Values

Threshold

Values

FP


2 SAIDI(h/customer) 0.5882 0.177953 0.198559


4 AENS(kW/customer) 4.6641 1.667670 1.806670

106


Table 5.16 Optimal cost of network, utility and society considering the impact of continuous RPS on utility

(considering SAIFIt = 0.084746 , SAIDIt = 0.198559, CAIDIt = 2.435000, AENSt = 1.806670) for RBTS-2

Sr

No. 𝐂𝐈𝐂 𝐂𝐑𝐏 𝐂𝐧𝐞𝐭𝐰𝐨𝐫𝐤 𝐂𝐭𝐨𝐭𝐚𝐥

𝐮𝐭𝐢𝐥𝐢𝐭𝐲= 𝐂𝐧𝐞𝐭𝐰𝐨𝐫𝐤 +

𝐂𝐑𝐏 𝐂𝐭𝐨𝐭𝐚𝐥

𝐬𝐨𝐜𝐢𝐞𝐭𝐲= 𝐂𝐧𝐞𝐭𝐰𝐨𝐫𝐤 + 𝐂𝐈𝐂

𝐑

1 341057.99 23525.732 302553.5096 326079.2416 643611.5094 3.132077

2 336396.39 18864.131 301253.4363 320117.5669 637649.8347 3.0939145

3 334854.53 17322.268 305825.2102 323147.4785 640679.7463 3.0603485

4 330002.67 12470.406 274999.4572 287469.8636 605002.1314 2.963884

5 327551.30 10019.036 286348.1753 296367.2114 613899.4791 2.9163098

6 322658.38 5126.11 292369.40 297495.5196 615027.7874 2.8714413

7 307362.90 -10169.36 277642.2999 267472.9406 585005.2084 2.8000841

8 307366.70 -10165.56 277502.0912 267336.532 584868.7998 2.7751445

9 306108.78 -11423.48 282031.8602 270608.3757 588140.6435 2.7116754

10 304421.57 -13110.69 294567.1973 281456.5055 598988.7733 2.7073760

11 304297.26 -13235 306556.1356 293321.1365 610853.4043 2.6984982

12 302267.59 -15264.68 317782.9447 302518.268 620050.5358 2.6960579

13 299008.20 -18524.07 280306.7189 261782.6536 579314.9213 2.6909185

14 302086.95 -15445.31 299318.1045 283872.7911 601405.0588 2.6446134

15 300757.62 -16774.65 287286.6803 270512.0334 588044.3011 2.6231037

16 298525.19 -19007.07 283448.1982 264441.1262 581973.394 2.6188200

17 299718.06 -17814.21 286664.1614 268849.9537 586382.2215 2.6159990

18 298523.97 -19008.3 299433.8125 280425.5158 597957.7836 2.6138074

107


Table 5.17 Optimized values of failure rates and repair times for RBTS-2 as obtained by FP


failure rates

( /year)

repair

times

(in hrs.)

Distributor

segment

By FP

By FP

1 0.03679 2.25225

2 0.01497 4.50497

3 0.03910 4.60288

4 0.03609 2.25237

5 0.01127 4.96719

6 0.01500 9.34639

7 0.03665 2.25229

8 0.01237 9.43417

9 0.01500 4.50613

10 0.03899 2.25525

11 0.01128 4.50491

12 0.03665 2.27395

13 0.03943 2.44635

14 0.03102 2.25353

15 0.03911 2.25225

16 0.04238 2.25229

17 0.01499 9.97048

18 0.03910 2.27024

19 0.01500 9.97133

20 0.01485 9.98236

21 0.02934 2.75800

22 0.01260 5.03652

23 0.01136 5.11156

24 0.04780 2.25635

25 0.01500 4.50450

26 0.03910 2.31682

27 0.01481 4.52148

28 0.01128 9.85532

29 0.03665 2.25238

30 0.01500 9.53818

31 0.01500 9.99991

32 0.04875 2.25870

33 0.01283 4.50450

34 0.02996 2.25408

35 0.01153 5.59178

36 0.01128 4.50450

108


Fig. 5.4 Impact of an optimal continuous RPS on different parameter costs for sample radial distribution system

-50000

0

50000

100000

150000

200000

4.9

68

4.8

52

4.7

05

4.4

83

4.4

05

4.3

44

4.2

03

4.0

93

4.0

89

4.0

42

3.9

78

3.9

18

3.8

33

3.7

61

3.4

13

3.3

88

3.2

63

3.1

97

3.1

22

Op

tim

um

An

nu

al C

ost

Optimum Reliability

CRP

CIC

Cnetwork

Ctotal_utility= Cnetwork + CRP

Ctotal_society= Cnetwork + CIC

R

109


Fig. 5.5 Impact of an optimal continuous RPS on different parameter costs for sample meshed distribution system

-500000

0

500000

1000000

1500000

2000000

2500000

Op

tim

um

An

nu

al C

ost

Optimum Reliability

CRP

CIC

Cnetwork


Ctotal_society= Cnetwork +CIC

110


Fig. 5.6 Impact of an optimal continuous RPS on different parameter costs for RBTS-2

-100000

0

100000

200000

300000

400000

500000

600000

700000

3.1

32

3.0

94

3.0

60

2.9

64

2.9

16

2.8

71

2.8

00

2.7

75

2.7

12

2.7

07

2.6

98

2.6

96

2.6

91

2.6

45

2.6

23

2.6

19

2.6

16

2.6

14

Op

tim

um

An

nu

al C

ost

Optimum Reliability

CRP

CIC

Cnetwork


Ctotal_society= Cnetwork + CIC

R

111


5.6 Conclusions

In this chapter, reliability of distribution system has been enhanced incorporating

reward/penalty to the utilities by the regulator. The optimum values of reward/penalties have

been found considering the target values of customer and energy based reliability indices. It

is clear from the results obtained that when all these indices are below their target values,

utility is rewarded otherwise penalized. The objective function formulated has been

optimized by FP. Along with optimized values of all reliability indices, optimized values of

other terms in the objective function like maintenance cost, customer interruptions and

additional cost required to achieve this reliability level have also been obtained. The

algorithm developed has been implemented on the three test distribution systems in

consideration.

112

CHAPTER 6

Reliability Performance Optimization of Radial

Distribution System Enhancing Power Quality

Considering Voltage Sag

6.1 Introduction

For long time the main concern of consumers of electricity was the continuity of the supply,

i.e. the reliability. Nowadays consumers want not only reliability, but quality too. Any

distribution system is supposed to supply ideally an uninterrupted flow of power with smooth

sinusoidal voltage at its rated magnitude level and frequency to its customers [121]. As the

distribution company practically consists of numerous nonlinear loads, the quality and purity

of power supply is considerably affected. Besides these loads, some systems events like

capacitor switching, motor starting and various faults which do occur frequently, too affect

the power quality problems [122]. The three most significant power quality problems

concerned to most of the customers are voltage sags, momentary interruptions and sustained

interruptions. Different customers are affected differently. Residential customers generally

suffer sustained interruptions and momentary interruptions whereas for commercial and

industrial customers sag and momentary interruptions are main problems. These three power

quality problems are caused due to faults in the utility power system and mostly in the

distribution system. Of course, faults can never be eliminated but their impact on the

customers can be minimized. Among many problems related to power quality, these three

are the most common [123]. Generally industrial processes rely on electronic power control

devices so, simple power quality problems like voltage sag may affect economically in a

considerable way. Thus power supplied must be reliable and of good quality. Power quality

can be defined in a simple and concise way as: “It is a set of electrical boundaries that allows

a piece of equipment to function in its intended manner without significant loss of

performance or life expectancy” [124].

During one or more outages customers are no more supplied with electricity, are known as

interruptions. Interruptions may be long or short and are both power quality events. During

113

Reliability Performance Optimization of Radial Distribution System Enhancing Power Quality Considering Voltage Sag

long interruptions, voltage at the customer connections or at the equipment terminals drops

to zero and does not come back automatically. It has to be terminated manually. The

interruptions which are terminated automatically through automatic reclosures or switching

are short interruptions [122]. According to official IEC definitions, long interruptions are for

minimum three minutes. To evaluate power system reliability number and duration of long

interruptions are stochastically predicted. The performance of the utilities are tracked by

reliability indices by many utilities. Regulators require the utilities to report their reliability

performance. The regulatory trend is moving towards performance base rates where better

performance is rewarded otherwise penalized. Reliability assessment indices are customer

and energy oriented indices mostly used for distribution systems.

In this chapter, the reliability of distribution system has been tried to enhance incorporating

simple power quality problem like voltage sag. In this chapter, voltage sags due to faults

only have been considered. Voltage sags often cause load outages. So, the reliability indices

of the distribution systems are adversely affected by voltage sag propagation.

The interests in the voltage sags are increasing because they cause the detrimental effects on

the several equipments used in modern process control as they are sensitive to voltage sags.

Malfunctioning or failure of this equipment may be caused by voltage sags leading to work

or production stops with significant associated cost. Thus the disruption affect the reliability

level. According to IEEE standard 1159-1995, a voltage sag is defined as a decrease in rms

voltage down to 90% to 10% of nominal voltage (between 0.1 and 0.9 p.u. ) for a time

greater than 0.5 cycles of the power frequency but less than or equal to one minute[125].

The literature regarding this has been discussed rigorously in Chapter 1 however, in all the

work mentioned, voltage sag propagation and voltage sag related reliability index like

system average RMS variation frequency index (SARFI) have been meagrely focussed.

Voltage sags and interruptions are related power quality problems as both are usually caused

by faults in the power system and switching actions in isolating the faulty sections.

Reliability level is adversely affected due to voltage sags at different load points. In this

chapter, number of voltage sags are reduced by employing DGs at different load points of

the distribution system.

In line to the above discussion, this chapter aims at improving reliability of distribution

system by modifying the failure rates and repair times of different sections of the system

114

Power Quality and Reliability Indices

considering reduction in power quality index related to voltage sag i.e. SARFI with the help

of DGs connected at different load points. This has been done by optimizing an objective

function formulated here.

6.2 Power Quality and Reliability Indices

Several power quality indices have been introduced which are similar to the reliability

indices. They are used by the utilities for some of the same purposes as reliability indices:

targeting areas for maintenance, circuit up- gradation, observing the performance of regions

and accordingly documenting the performance to the regulators etc. The most widely used

index is SARFI [126, 127] (System Average RMS (Variation) Frequency Index) represents

the average number of specified rms variation measurement events that occurred over the

assessment period per customer served. SARFI-90 calculates all voltage sags with remaining

voltages of less than 90% regardless of sag duration. Therefore, the total expected number

of sags (𝑁𝑠𝑎𝑔) caused by different faults in the system are used to calculate SARFI of the

whole system [138]. The customers served in the assessment area are considered the

customers supplied by all system buses Nbus .

SARFI =∑ Nsag

NT (6.1)

Nsag represents the number of customers experiencing short duration of voltage deviation

by all possible fault events during the assessment period. NT represents number of customers

served from the section of the system to be assessed . The number of sags in SARFI can be

calculated from the different ranges of voltage sag falling between 0 to 1 p.u.

The customer and energy based reliability indices are SAIFI, SAIDI CAIDI and AENS

[103]. They have been defined in section 2.4.

6.3 Methodology for enhancing Reliability accounting Voltage Sag

This section describes the required components to improve power quality and reliability of

distribution systems optimally employing DGs at different load points. It includes system

sag calculation, problem formulation for optimization, proposed optimization method and

solution methodology using the same.

6.3.1 Method to find out number of Voltage Sags and Interruptions

Voltage sag propagation depends on the type of fault and location of fault in the system.

Buses which are far from the fault experience less severity [129]. The main cause of voltage

115


sags are line faults. All the symmetrical and unsymmetrical faults can be calculated by fault

analysis. The system branches inducing great sag exposure can be determined by fault

analysis

Total number of estimated line faults per year can be determined as follows.

𝑓𝑡𝑜𝑡𝑎𝑙 = ∑ ∑ 𝐿𝑘𝜆𝑘_𝑓𝑎𝑢𝑙𝑡𝑁𝐿𝑘=1

4𝑝=1 (6.2)

Where, 𝑝 is the types of faults like line to ground (LG), line-to-line-to-ground (LLG), line-

to-line (LL) and three phase (LLL) faults. 𝐿𝑘 is the length of the 𝑘𝑡ℎ distributor segment .

𝑁𝐿 represents total number of distributor segments up to the fault point. 𝜆𝑘_𝑓𝑎𝑢𝑙𝑡 is the fault

rate of the 𝑘𝑡ℎ distributor segment. In this work, different kinds of faults are considered at

a specific load points and the values of sag are found. 𝑁𝑠𝑎𝑔 per year can be found from the

magnitudes of voltage sags as below.

𝑁𝑠𝑎𝑔 = ∑ ∑ { 1 𝑖𝑓 0.1 𝑝. 𝑢. < 𝑉𝑖 < 0.9 𝑝. 𝑢.

0 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒 𝑡𝑜𝑡𝑎𝑙𝑓=1

𝑁𝑏𝑢𝑠𝑖=1 (6.3)

When the value of voltage sag due to any fault at any load point is less than 0.1 p.u., it will

lead to sustained interruption. The total number of annual interruptions per annum (𝑁𝑖𝑛𝑡)

can be obtained as below.

𝑁𝑖𝑛𝑡 = ∑ ∑ { 1 𝑖𝑓 𝑉𝑖 < 0.1 𝑝. 𝑢.

0 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒 𝑡𝑜𝑡𝑎𝑙𝑓=1

𝑁𝑏𝑢𝑠𝑖=1 (6.4)

From relation (6.3), power quality index SARFI can be determined using relation (6.1). The

interruptions obtained from relation (6.4) are used along with the interruptions due to failures

of different distributor segments due to ageing, environmental reasons, accidents etc. to find

out customer and energy based reliability indices.

As different magnitudes of voltage sags have different impact from the viewpoint of

customer interruption costs, they have been given weighting factors for the purpose of

economic analysis. Table 6.3 depicts the same.

6.3.2 Problem Formulation for Optimization

With the objective of enhancing reliability of radial distribution system considering voltage

sags, the objective function is defined as follows.

116

Methodology for enhancing Reliability accounting Voltage Sag

F = ∑ (αk λk_failure2⁄Nc

k=1 + (γk λk_fault2⁄ ) + ∑ βk rk⁄Nc

k=1 + ∑ CICNck=1 + ADCOST(EENSO −

EENSD) + ∑ 𝐶𝑅𝑃Nck=1 (6.5)

where,

CIC = λk × rk × Li × Cpk (6.6)

CIC = CIC1 + CIC2 + CIC3 + CIC4 (6.7)

λk = λk_failure + λk_fault (Sustained interruptions) (6.8)

λk_fault = fault rate of kthdistributor segment (6.9)

In the objective function (6.5), first three terms depict the cost related to maintenance. First

two terms are amount spent to reduce failure rates and fault rates of each section of the

distribution system. The third term relates to the cost required to modify repair time for the

distributor segment. Lesser are the values of these terms; more are the costs or investments

associated with preventive maintenance and corrective repair required by utility to achieve

them [111]. These terms are related to Duane’s reliability growth model [105]. The fourth

part is related to interruption cost at the customers end. The momentary and sustained

interruptions affect economically if load is sensitive for the interruptions. On this basis, the

segmental interruption costs to the customers are as shown in Table 6.3. The total cost of

interruptions for any load point i can be determined by adding the cost of all section outages.

The total cost of customer interruptions for all customers can then be evaluated. The fifth

term is related to the additional cost of energy provided by the DGs connected at different

load points. It is multiplication of energy provided by DGs and additional charge (ADCOST)

in Rs. /kWH. In this chapter, the DGs considered are working as standby units. The reliability

model followed here is as per [40]. Here , the standby DGs are connected in combination

with uninterrupted emergency power supplies (UPS) which supply power in case of

occurrence of failure or fault for a very short period of time until DGs at those load points

are connected to supply power. The sixth term is related to the cost of reward/penalty to the

utility. If reliability of the utility is below the set target value, it is rewarded otherwise

penalized. Thus the objective function provides balance between the cost spent on DGs, the

cost of maintenance, customer interruption costs and cost of reward/penalty. This objective

function not only tries to improve reliability of the system by reducing failure rates and repair

times of the distribution system but also tries to reduce fault rates of various sections of the

117


distribution system leading to improvement in the power quality index related to voltage sag.

DGs combined with emergency UPS help to achieve this. The optimal solution is achieved

by minimizing the objective function as formulated in relation (6.5).



λk_failure,min ≤ λk_failure ≤ λk_failure,max , λk_fault,min ≤ λk_fault ≤ λk_fault,max and

rk,min ≤ rk ≤ rk,max , k = 1, … … … … … , Nc (6.10)

(ii) Inequality constraints on the customer and energy based indices





SARFI ≤ SARFIt (6.15)

As all the reliability indices mentioned from (6.11) to (6.14) are interdependent, in this

chapter, the reliability level(R) has been defined considering the impact of all the customer

and energy based reliability indices as shown below.

R =SAIFI

SAIFIt+

SAIDI

SAIDIt+

CAIDI

CAIDIt+

AENS

AENSt . (6.16)

Here R is the sum of the normalized values of customer and energy oriented reliability

indices i.e. SAIFI, SAIDI, CAIDI and AENS. The normalization is with respect to respective

target values of the indices. Hence all the indices will be given equal weightage in the

procedure.

λk,max and rk,max are maximum allowable failure rate and repair time of kth section

respectively. λk,min and rk,min are minimum reachable values of failure rate and repair

time of kth section which are achieved in optimization process. These lower bound values

are obtained by failure and repair data analysis along with the associated costs and it is done

through reliability growth model [105]. Nc stands for total number of sections in the


118


SAIFIt , SAIDIt , CAIDIt , AENSt and SARFIt are target/threshold values of the respective

indices. They depend on the managerial/administrative decisions.

The formulated problem is solved by flower pollination optimization method (FP) [100].

The method in this chapter has been applied on a sample radial distribution system. The

optimized values obtained after having solved the problem may be given as target values to

the crew for the enhancement of reliability and power quality of the distribution system.

6.4. Solution Methodology


method of solving the formulated problem mentioned in section 6.3.2 by FP is as follows.

Step 1. Data input λk_failure,max , λk_failure,min , λk_fault,max , λk_fault,min , rk,max , rk,min ,

λdg , rdg , λsw , cost of interruption ( Cpk ) , Ni, Li, SAIFIt , SAIDIt , CAIDIt , AENSt and

SARFIt .

Step 2. Find value K at target values of indices.

Step 3. Initialization: Generate a population of size ‘M’ (flowers) for failure rate (λ_failure)

and fault rate (λ_fault) and repair time r each by relation (D.3), where each vector of

respective population consists of failure rate and repair time of each component respectively.

These values are obtained by sampling uniformly between lower and upper limits as given

by relation (6.10).

Step 4. Evaluate λsys,i , rsys,i and Usys,i and 𝑁𝑠𝑎𝑔 at each load point.

Step 5. Evaluate SARFI, SAIFI, SAIDI, CAIDI and AENS as mentioned in the relations

(6.1), (2.10), (2.11), (2.12) and (2.14) respectively for vectors of the population.


),

i = 1, … … … … … , ′M′ as given by relation (6.5) - (6.9).

Step 7. Calculate value of overall reliability R for all vectors in the population by relation

(6.16).

Step 8. Evaluate inequality constraints from the relations (6.11)-(6.15) for each vector of the

population. Vectors satisfying these constraints will be feasible otherwise not feasible

119


vectors. From among the feasible vectors, based on the value of objective function, identify

the best solution vector Xbest(k)

.












respectively. Fig 6.1 shows the flow chart for solving the formulated problem by FP.

120


END

START

Evaluate SAIFI, SAIDI, CAIDI, AENS, EENS, SARFI, ADCOST, CIC



Print solution

generation = k+1

NO

YES

Is solution

converged?

Find value of K at the target values of indices

Generate a population of size ‘M’ for failure rate λ and repair time r each between lower and upper limits

0 00 0 0 0 0 0, , , X , , .,

1 2 1 2i

TS X X X X X XM i i iD

Calculate the optimum values of SAIFI, SAIDI, CAIDI, AENS, SARFI, overall reliability R & CRP


population and Identify the( )

&best best

kX F

Select target vector, i=1 and find updated value of each vector by D.4

Calculate value of objective function F for all vectors in the population and identify ( )best

kX

If any updated solution violates the inequality constraints , then set the values of the vectors to ( )kiX

Compare the fitness of the updated vectors with that of the initial vectors and retain the best ones by D.9 ( 1)k

iX

( )kiX

,

,max ,min ,max ,min _ ,max

_ ,min

Data input , , , , , , ,

, , , , , , , ,,k t t t t ti i

swk k k k dg k fault

k fault dgSAIFI SAIDI AIDI SARFIS Cp N L C AENS

r r

r

Fig. 6.1 Flow chart for the solution of the problem formulated in section 6.3.2 by FP

121


Fig. 6.2 Re-modified Radial Distribution System with DG

122


6.5 Results and discussions

The developed methodology in this chapter has been implemented on a sample radial

distribution system. The problem has been solved by FP algorithm and comparison has been

made with the results obtained by TLBO and DE. The algorithms used have been coded in

MATLAB-13.

Sample radial distribution system [29]:

The radial system is as shown in Fig. 6.2. The system has been re-modified in terms of

locations of DGs for the problem formulated in this chapter to show the effectiveness of the

methodology. The data regarding the current and minimum reachable values of failure rates

and repair times, average load and number of customers at load points and cost coefficients

for each segment of radial distributor have been taken from [111]. Table 6.1 shows the

failure rates, fault rates and repair times related data for the different sections of the sample

radial distribution system. Table 6.2 depicts the interruption cost at various load points of

the system. On the basis of sustained and momentary interruptions, the total contribution to

the cost of customer interruptions is decided according to the weightage considered as shown

in Table 6.3 for the different ranges of the voltage sag values. Table A.2. gives average load

and number of customers at different load points. Table 6.4 represents cost coefficients for

failure rates, fault rates and repair times of different segments. Table 6.5 gives control

parameters for the three optimization methods, FP, TLBO and DE used in this work. Table

6.6 gives component reactance related data. Percentage of occurrence of different kind of

faults are according to Table 6.7. Optimized values of failure rates, fault rates and repair

times of different distributor segments are given in (Table 6.8-Table 6.10) respectively.

Optimized values of reliability and power quality indices as given by FP.TLBO and DE are

given in Table 6.11. Table 6.12 gives optimized value of objective function and all the cost

components thereof as obtained by FP, TLBO and DE. In this work, DGs are connected at

load points 3, 6 and 7 in the sample radial distribution system so as to show the effectiveness

of the methodology.

Here, the DGs to be connected are taken as standby units. The failure rate and average down

time of DG taken in this chapter are 0.5 failures/year and 13.25 hrs. respectively. Failure rate

and service restoration time of the changeover switch of DG are 0.1 failures/year and 0.25

hrs. respectively.

123


Table 6.1 System data for Sample Radial Distribution System

Distributor segment #1 #2 #3 #4 #5 #6 #7

𝜆𝑘_𝑓𝑎𝑖𝑙𝑢𝑟𝑒0 /𝑦𝑒𝑎𝑟 0.4 0.2 0.3 0.5 0.2 0.1 0.1

𝜆𝑘_𝑓𝑎𝑢𝑙𝑡0 /𝑦𝑒𝑎𝑟 4.5 2.25 3.3 5.6 2.25 1.1 1.1

Average repair time 𝑟𝑘0 (ℎ) 10 9 12 20 15 8 12

λk_failure,min/year 0.2 0.05 0.1 0.1 0.15 0.05 0.05

λk_fault,min/year 2.25 0.56 1.1 1.12 1.68 0.55 0.55

𝑟𝑘,𝑚𝑖𝑛(ℎ) 6 6 4 8 7 6 6

Length (km) 0.83 2.08 3.03 1.73 2.98 2.78 3.63


Distributor Load points (LP) #2 #3 #4 #5 #6 #7 #8

Interruption Cost (Rs./kW) 15 13 17 20 20 12 14

Table 6.3 Weighting factors for different Voltage Sag Magnitude and corresponding values of

customer interruption cost (CIC)

Category of event Weighting for economic

analysis

Corresponding CIC

Interruption 1.0 CIC1

Sag with minimum voltage below 50 % 0.8 CIC2

Sag with minimum voltage between 50% and

70%

0.4 CIC3

Sag with minimum voltage between 70% and

90%

0.1 CIC4

Table 6.4 Cost coefficients αk, βk and 𝜸𝒌 for Radial Distribution System


αk Rs. 240 300 180 120 240 285 300

βk

Rs. 400 360 200 200 320 240 220

𝛾𝑘 Rs. 1500 2000 1250 900 1500 1850 2000

124


Table 6.5 Control Parameters for FP, TLBO and DE









Table 6.6 Component reactance data

Feeder Source/generator

Positive sequence 0.23 pu/km 0.60

Negative sequence 0.23 pu/km 0.60

Zero sequence 0.276 0

Table 6.7 Percentage of fault occurrence according to fault type

Fault type L-G fault LL-G fault LL fault LLL fault

Occurrence percentage 73% 17% 6% 4%

Table 6.8 Optimized values of failure rates for sample radial system as obtained by DE, TLBO and FP

Distributor

segment

Current values

( /year) Optimized values ( /year)

By DE By TLBO By FP

1 0.4 0.2000 0.2000 0.2000

2 0.2 0.2000 0.1772 0.1767

3 0.3 0.1940 0.1931 0.1922

4 0.5 0.1466 0.1322 0.1315

5 0.2 0.1798 0.1786 0.1783

6 0.1 0.1000 0.1000 0.1000

7 0.1 0.1000 0.1000 0.1000

125


Table 6.9 Optimized values of fault rates for sample radial system as obtained by DE, TLBO and FP

Distributor

segment

Current values

( /year) Optimized values ( /year)

By DE By TLBO By FP

1 4.5 2.2500 2.2500 2.2500

2 2.25 0.7607 0.7524 0.7523

3 3.3 1.1000 1.1000 1.1000

4 5.6 3.5579 1.1200 1.1200

5 2.25 1.6875 1.6875 1.6875

6 1.1 1.1000 1.1000 1.1000

7 1.1 1.0999 1.1000 1.1000

Table 6.10 Optimized values of repair times for sample radial system as obtained by DE, TLBO and FP

Distributor

segment

Current values

(in hrs) Optimized values (in hrs)

By DE By TLBO By FP

1 10 6.0000 6.0000 6.0000

2 9 6.0040 6.0000 6.0000

3 12 4.0000 4.0000 4.0000

4 20 8.0000 8.0000 8.0000

5 15 7.0025 7.0000 7.0000

6 8 6.0000 6.0000 6.0000

7 12 6.0000 6.0000 6.0000

Table 6.11 Current and optimized reliability and power quality indices for sample radial system

obtained by FP, TLBO and DE

Sr. No. Index Current


FP TLBO DE

1 SAIFI(interruptions/customer) 0.3205 0.176946 0.177221 0.182307

2 SAIDI(h/customer) 3.2030 1.066906 1.068554 1.102044

3 CAIDI(h/customer interruption) 9.9929 6.029546 6.029495 6.044994

4 AENS(kW/customer) 12.1076 3.982938 3.988557 4.103098

5 SARFI 0.0156 0.007096 0.007096 0.007962

6 Overall Reliability (R) 6.6095 2.871777 2.874789 2.936356

126


Table 6.12 Current and optimized values of objective function (F) as given by DE, TLBO and FP

Sr.

No.

Current


FP TLBO DE



𝑘=1 ) 422610 103091.7 102884.8 98675.96


𝑁𝑐𝑘=1 ) 1893550 384043.5 384150.3 406212.3

Addditional cost to be paid while generators are


44854.12 44842.89 44613.8

Reward /Penalty (∑ 𝐶𝑅𝑃Nck=1 ) 113360

-24398.5 -24297.1 -22299.8

3 Objective function (F) 2035500 507590.8 507580.9

527202.3

127


6.6 Conclusions

In this chapter, reliability of a sample radial distribution system has been enhanced

incorporating power quality problem like voltage sag. Voltage sags often cause load outages.

So, the reliability indices of the distribution systems are adversely affected by voltage sag

propagation. The objective function which has been optimized is in terms of failure rate,

fault rate and repair time. As the customer and energy based indices and power quality index

based on voltage sag depend on these primary indices, optimized values of these indices

have been found for radial distribution system. It has been found that with the specific

locations of DGs as shown in the sample radial distribution system (Fig. 6.1), the reliability

indices as well as power quality index for voltage sag have been enhanced optimally.

Optimized values of maintenance cost, customer interruption cost, additional energy spent

on DGs and value of reward have also been found.

128

CHAPTER 7

Conclusions and Guidelines for Future Work

7.1 General

Power system reliability evaluation and its optimization are of significant importance for

planning, operation and control. For the solution of this, there has been a continuous interest

and subsequent efforts to develop more sophisticated, robust and computationally efficient

models and methodologies. Reliability evaluation is the performance of the system whereas

optimization results help in giving targets to the field crew members and planners to reduce

failure rates and repair times to further enhance reliability

Following aspects were observed from the state of art in the domain of power system

reliability;

(i) As compared to distribution system reliability studies, large number of

methodologies have been developed for the reliability evaluation of generation

system and composite power system.

(ii) In distribution system reliability optimization mostly classical and evolutionary

algorithms e.g. GA have been used. Latest and computationally efficient

metaheuristic optimization methods have not been focused much

(iii) In most of the work related to distribution reliability, work is based on primary

reliability indices i.e. failure rate, average repair time and average

interruption/outage duration per year. In practice these indices may not

represent the actual performance of the system in terms of reliability. Reliability

indices based on customer and energy must be considered to have a realistic

picture of the performance of distribution system.

(iv) Effects of distributed generation (DG) is very important from reliability point

of view. The locations of DGs too keep importance in enhancing reliability of

distribution system. These have not been considered effectively so far.

(v) Reward /Penalty scheme affects reliability of distribution system. The optimized

values of reward/penalties with reference to specific target values of customer

and energy based reliability indices have not been focused yet.

129


(vi) Optimizing reliability of distribution system incorporating optimization of

power quality index representing voltage sag has not been focused much.

In view of the above, work carried out in this thesis was to focus on distribution system

reliability evaluation and optimization accounting the above mentioned uncovered areas.

The aim of this chapter is to highlight the important contribution made in this thesis and to

mention the further scope in the very significant area of reliability assessment and

enhancement of distribution system.

7.2 Summary of important conclusions

In chapter 2, a computationally efficient algorithm is developed to enhance the reliability of

distribution system. The objective function to be optimized consists of all the customer and

energy based reliability indices. Here each index has been given weightage by Analytical

Hierarchical Process (AHP). Further, each index is normalized with reference to their

respective target/threshold value. Every index has been given weightage in regards to its

contributory importance in the overall reliability of the system. Optimum values of customer

oriented and energy based reliability indices are found while specified budget is allocated to

achieve the same. Here optimized values of reliability indices for the allocated budget have

been found. More is the budget better is reliability and vice versa. This algorithm is applied

to sample radial distribution network, sample meshed system and RBTS-2 in this thesis. The

optimum values are found by flower Pollination (FP) optimization algorithm, teaching

learning based optimization (TLBO) and differential evolution (DE). It has been

authenticated by making comparison of the values found.

In chapter 3, the aim has been to improve reliability of a distribution system by finding out

a balance between costs of maintenance and customer interruptions. When these combined

costs become minimum, customers will get service with least costs leading to enhanced

customer satisfaction level. In this chapter, this has been achieved by optimizing the

objective function formulated subject to achieving the desired reliability level with reduction

in the customer interruption costs. It has been applied on a sample radial network, sample

meshed network and RBTS-2 finding the results by FP, TLBO and DE.

130

Scope for further work

In chapter 4, reliability of distribution systems (a sample radial distribution system, sample

meshed system and RBTS-2) have been enhanced with DGs connected at different load

points. The locations of DGs have been found with a methodology considering improvement

in reliability as the chief motive. With these locations thus found, the objective function

formulated in this chapter has been optimized by three optimization methods say FP, TLBO

and DE. To justify the installation of DGs in a long run, the cost-benefit analysis has been

made. Here, DGs are operating on standby mode. Enhanced values of reliability indices and

reduced customer interruption cost than those obtained in the previous chapter have been

achieved by spending additional amounts on a generator.

In chapter 5, reliability of distribution system has been enhanced incorporating

reward/penalty to the utilities by the regulator. The optimum values of reward/penalties have

been found considering the target values of customer and energy based reliability indices. It

is clear from the results obtained that when all these indices are below their target values,

utility is rewarded otherwise penalized. The objective function formulated has been

optimized by FP. Along with optimized values of all reliability indices, optimized values of

other terms in the objective function like maintenance cost, customer interruptions and

additional cost required to achieve this reliability level have also been obtained. The

algorithm has been applied on all the three test systems considered here.

In chapter 6, reliability of a sample radial distribution system has been enhanced

incorporating simple power quality problem like voltage sag. Voltage sags often cause load

outages. So, the reliability indices of the distribution systems are adversely affected by

voltage sag propagation. The objective function to be optimized is in terms of failure rate,

fault rate and repair time. As the customer and energy based indices and power quality index

based on voltage sag depend on these, optimized values of these indices have been found for

radial distribution system. Optimized values of maintenance cost, customer interruption cost,

additional energy spent on DGs and value of reward have also been found.

7.3 Scope for further work

As a consequences of investigation made in reliability assessment and optimal reliability

performance evaluation of distribution systems, following suggestions are made for future

research.

(i) In reliability performance optimization of distribution system, decision variables

taken are for all the sections of distribution system. They may be reduced. In view

131


of this a line outage ranking algorithm may be developed and selected sections

which are more valuable for reliable supply view point may be considered in

reliability optimization. For meshed distribution system, this may prove to be an

important study.

(ii) In this thesis, reliability optimization of distribution system has been done.

Reliability optimization algorithm of a distribution network accounting network

reconfiguration can be developed along with network limitations resulting in loss

minimization.

(iii) Reliability enhancement of distribution system incorporating DGs have been

done in the thesis. Here, the location of DGs are found by ranking algorithm

considering reliability enhancement as a chief motive. Locations of DGs may be

found by any binary optimization including capacity of them.

(iv) Reliability improvement may be obtained using fault tolerant measures. An

algorithm may be developed to this extent.

(v) Algorithm may be developed for reliability assessment of electrical distribution

systems accounting voltage stability constraints.

(vi) Algorithm may be developed including load and capacity models. In fact basic

reliability indices may be evaluated using Monte Carlo simulation.

132

References

1. W. J. Lyman, 'Fundamental consideration in preparing master system plan’,

Electrical World, 101(24) (1933): 788-92.

2. Dean, S. M. "Considerations involved in making system investments for improved

service reliability." EEI Bulletin 6.1 (1938): 491-596.

3. Billinton, Roy, and Ronald N. Allan. "Power-system reliability in

perspective." Electronics and Power 30.3 (1984) : 231-236.

4. Allan, Ronald, and Roy Billinton. "Probabilistic assessment of power

systems." Proceedings of the IEEE 88.2 (2000): 140-162.

5. Shipley, R. Bruce, Alton D. Patton, and J. S. Denison. "Power reliability cost vs

worth." IEEE transactions on Power Apparatus and Systems 5 (1972): 2204-2212.

6. Billinton, Roy. "Evaluation of reliability worth in an electric power

system." Reliability Engineering & System Safety 46.1 (1994): 15-23.

7. Goel, L., X. Liang, and Y. Ou. "Monte Carlo simulation-based customer service

reliability assessment." Electric power systems research 49.3 (1999): 185-194.

8. Hegazy, Y. G., M. M. A. Salama, and A. Y. Chikhani. "Adequacy assessment of

distributed generation systems using Monte Carlo simulation." IEEE Transactions

on Power Systems 18.1 (2003): 48-52.

9. Ermiş, M., et al. "Various induction generator schemes for wind-electricity

generation." Electric Power Systems Research 23.1 (1992): 71-83.

10. Levitin, Gregory, Shmuel Mazal-Tov, and David Elmakis. "Optimal sectionalizer

allocation in electric distribution systems by genetic algorithm." Electric Power

Systems Research 31.2 (1994): 97-102.

11. Levitin, Gregory, Shmuel Mazal-Tov, and David Elmakis. "Genetic algorithm for

optimal sectionalizing in radial distribution systems with alternative

supply." Electric Power Systems Research 35.3 (1995): 149-155.

12. Levitin, Gregory, Shmuel Mazal-Tov, and David Elmakis. "Optimal insulation in

radial distribution networks." Electric Power Systems Research 37.2 (1996): 97-103.

13. Su, Ching-Tzong, and Guor-Rurng Lii. "Reliability design of distribution systems

using modified genetic algorithms." Electric Power Systems Research 60.3 (2002):

201-206.

133

References

14. Chang, Wei-Fu, and Yu-Chi Wu. "Optimal reliability design in an electrical

distribution system via a polynomial-time algorithm." International journal of

electrical power & energy systems 25.8 (2003): 659-666.

15. Billinton, R., T. K. P. Medicherla, and M. S. Sachdev. "Common-cause outages in

multiple circuit transmission lines." IEEE Transactions on Reliability 27.2 (1978):

128-131.

16. Allan, R. N., E. N. Dialynas, and I. R. Homer. "Modelling and evaluating the

reliability of distribution systems." IEEE Transactions on Power Apparatus and

systems 6 (1979): 2181-2189.

17. Allan, R. N., E. N. Dialynas, and I. R. Homer. "Modeling Common -Mode Failures

In The Reliability Evaluation Of Power-System Networks." IEEE Transactions On

Power Apparatus And Systems. Vol. 98. No. 4. 345 E 47th ST, New York, NY 10017-

2394: IEEE-Inst Electrical Electronics Engineers Inc, 1979.

18. Billinton, R., and Y. Kumar. "Transmission line reliability models including

common mode and adverse weather effects." IEEE Transactions on Power

Apparatus and Systems8 (1981): 3899-3910.

19. Sallam, Abdelhay A., Mohamed Desouky, and Hussien Desouky. "Evaluation of

optimal-reliability indices for electrical distribution systems." IEEE transactions on

reliability 39.3 (1990): 259-264.

20. Billinton, R., et al. "Reliability issues in today's electric power utility

environment." IEEE Transactions on Power Systems 12.4 (1997): 1708-1714.

21. Pinheiro, J. M. S., et al. "Probing the new IEEE reliability test system (RTS-96): HL-

II assessment." IEEE Transactions on Power Systems 13.1 (1998): 171-176.

22. Force, RTS Task. "The IEEE reliability test system-1996." IEEE Trans. Power

Syst 14.3 (1999): 1010-1020.

23. Bhowmik, S., S. K. Goswami, and P. K. Bhattacherjee. "A new power distribution

system planning through reliability evaluation technique." Electric Power Systems

Research 54.3 (2000): 169-179.

24. Wang, Zhuding, Farrokh Shokooh, and Jun Qiu. "An efficient algorithm for

assessing reliability indexes of general distribution systems." IEEE Transactions on

Power Systems17.3 (2002): 608-614.

134

References

25 Amjady, Nima, Davood Farrokhzad, and Mohammad Modarres. "Optimal reliable

operation of hydrothermal power systems with random unit outages." IEEE

Transactions on Power Systems 18.1 (2003): 279-287.

26. Tsao, Teng-Fa, and Hong-Chan Chang. "Composite reliability evaluation model for

different types of distribution systems." IEEE Transactions on power systems 18.2

(2003): 924-930.

27. Carvalho, Pedro MS, and Luìs AFM Ferreira. "Distribution quality of service and

reliability optimal design: individual standards and regulation effectiveness." IEEE


28. Yang, F., and C. S. Chang. "Multiobjective evolutionary optimization of

maintenance schedules and extents for composite power systems." IEEE


29. Arya, R., S. C. Choube, and L. D. Arya. "A decomposed approach for optimum

failure rate and repair time allocation for radial distribution systems." Journal of The

Institution of Engineers (India) 89.June (2008): 3-7.

30. Louit, Darko, Rodrigo Pascual, and Dragan Banjevic. "Optimal interval for major

maintenance actions in electricity distribution networks." International Journal of

Electrical Power & Energy Systems 31.7-8 (2009): 396-401.

31. Arya, R., S. C. Choube, and L. D. Arya. "Reliability enhancement of distribution

system using sensitivity analysis." J. Inst. Eng 90 (2009): 46-50.

32. Arya, R., S. C. Choube, and L. D. Arya. "A technique for improving Reliability

indices of a radial distribution system." J. Inst. Eng.(India), pt. EL 90 (2009): 12-17.

33. Gui, Min, Anil Pahwa, and Sanjoy Das. "Analysis of animal-related outages in

overhead distribution systems with wavelet decomposition and immune systems-

based neural networks." IEEE transactions on power systems 24.4 (2009): 1765-

1771.

34. Miranda, Vladimiro, et al. "Improving power system reliability calculation

efficiency with EPSO variants." IEEE Transactions on Power Systems 24.4 (2009):

1772-1779.

35. Arya, L. D., S. C. Choube, and Rajesh Arya. "Probabilistic reliability indices

evaluation of electrical distribution system accounting outage due to overloading and

repair time omission." International Journal of Electrical Power & Energy

Systems 33.2 (2011): 296-302.

135

References

36. Arya, L. D., S. C. Choube, and Rajesh Arya. "Differential evolution applied for

reliability optimization of radial distribution systems." International Journal of

Electrical Power & Energy Systems 33.2 (2011): 271-277.

37. Li, Ming-Bin, Ching-Tzong Su, and Chih-Lung Shen. "The impact of covered

overhead conductors on distribution reliability and safety." International journal of

electrical power & energy systems 32.4 (2010): 281-289.

38. Arya, L. D., et al. "Evaluation of reliability indices accounting omission of random

repair time for distribution systems using Monte Carlo simulation." International

Journal of Electrical Power & Energy Systems 42.1 (2012): 533-541.

39. Arya, Rajesh, et al. "Reliability enhancement of a radial distribution system using

coordinated aggregation based particle swarm optimization considering customer

and energy based indices." Applied soft computing 12.11 (2012): 3325-3331.

39. Arya, Rajesh, S. C. Choube, and L. D. Arya. "Reliability evaluation and

enhancement of distribution systems in the presence of distributed generation based

on standby mode." International Journal of Electrical Power & Energy Systems43.1

(2012): 607-616.

40. Bakkiyaraj, R. Ashok, and N. Kumarappan. "Optimal reliability planning for a

composite electric power system based on Monte Carlo simulation using particle

swarm optimization." International Journal of Electrical Power & Energy

Systems 47 (2013): 109-116.

41. Khalili-Damghani, Kaveh, Amir-Reza Abtahi, and Madjid Tavana. "A new multi-

objective particle swarm optimization method for solving reliability redundancy

allocation problems." Reliability Engineering & System Safety 111 (2013): 58-75.

42. Arya, Rajesh, et al. "A smooth bootstrapping based technique for evaluating

distribution system reliability indices neglecting random interruption

duration." International Journal of Electrical Power & Energy Systems 51 (2013):

307-310.

43. Gupta, Nikhil, Anil Swarnkar, and K. R. Niazi. "Distribution network

reconfiguration for power quality and reliability improvement using Genetic

Algorithms." International Journal of Electrical Power & Energy Systems 54

(2014): 664-671.

136

References

44. Yssaad, B., M. Khiat, and A. Chaker. "Reliability centered maintenance optimization

for power distribution systems." International Journal of Electrical Power & Energy

Systems 55 (2014): 108-115.

45. Bakkiyaraj, R. Ashok, and N. Kumarappan. "Application of natural computational

algorithms in optimal enhancement of reliability parameters for electrical

distribution system." Advances in Engineering and Technology (ICAET), 2014

International Conference on. IEEE, 2014.:1-6

46. Hashemi-Dezaki, H., H. Askarian-Abyaneh, and H. Haeri-Khiavi. "Reliability

optimization of electrical distribution systems using internal loops to minimize

energy not-supplied (ENS)." Journal of applied research and technology 13.3

(2015): 416-424.

47. Hashemi-Dezaki, H., H. Askarian-Abyaneh, and H. Haeri-Khiavi. "Reliability

optimization of electrical distribution systems using internal loops to minimize

energy not-supplied (ENS)." Journal of applied research and technology 13.3

(2015): 416-424.

48. Duan, Dong-Li, et al. "Reconfiguration of distribution network for loss reduction

and reliability improvement based on an enhanced genetic algorithm." International

Journal of Electrical Power & Energy Systems 64 (2015): 88-95.

49. Yssaad, B., and A. Abene. "Rational reliability centered maintenance optimization

for power distribution systems." International Journal of Electrical Power & Energy

Systems 73 (2015): 350-360.

50. Chowdhury, Ali, and Don Koval. Power distribution system reliability: practical

methods and applications. Vol. 48. John Wiley & Sons, 2011.

51. Cossi, A. M., et al. "Primary power distribution systems planning taking into account

reliability, operation and expansion costs." IET generation, transmission &

distribution6.3 (2012): 274-284.

52. Kahrobaee, Salman, and Sohrab Asgarpoor. "Reliability-driven optimum standby

electric storage allocation for power distribution systems." Technologies for

Sustainability (SusTech), 2013 1st IEEE Conference on. IEEE, 2013.:44-48

53. Beni, Sadegh Amani, M-R. Haghifam, and Rahmatullah Hammamian. "Estimation

of customers damage function by questionnaire method." 22nd International

Conference and Exhibition on Electricity Distribution (CIRED 2013), Stockholm,

2013, pp. 1-4.doi: 10.1049/cp.2013.1078

137

References

54. Nelson, John P., and J. David Lankutis. "Accurate evaluation of cost for power

reliability issues for electric utility customers." Rural Electric Power Conference

(REPC), 2014 IEEE. IEEE, 2014.: C2-1 - C2-11

55. Schellenberg, Josh A., Michael J. Sullivan, and Joe H. Eto. "Incorporating customer

interruption costs into reliability planning." Rural Electric Power Conference

(REPC), 2014 iEEE. IEEE, 2014.: C1-1-C1-5. doi: 10.1109/REPCon.2014.6842206

56. Tsao, Teng-Fa, and Hsiang-Bin Cheng. "Value-based distribution systems reliability

assessment considering different topologies." Machine Learning and Cybernetics

(ICMLC), 2014 International Conference on. Vol. 2. IEEE, 2014.:621:626

57. Sonwane, Pravin Machhindra, and Bansidhar Eknath Kushare. "Optimal capacitor

placement and sizing for enhancement of distribution system reliability and power

quality using PSO." Convergence of Technology (I2CT), 2014 International

Conference for. IEEE, 2014.:1-7

58. Narimani, Mohammad Rasoul, et al. "Enhanced gravitational search algorithm for

multi-objective distribution feeder reconfiguration considering reliability, loss and

operational cost." IET Generation, Transmission & Distribution 8.1 (2014): 55-69.

59. Bakkiyaraj, R. Ashok, and N. Kumarappan. "Application of natural computational

algorithms in optimal enhancement of reliability parameters for electrical

distribution system." Advances in Engineering and Technology (ICAET), 2014

International Conference on. IEEE, 2014.:1-6

60. Dorostkar-Ghamsari, Mohammadreza, et al. "Optimal distributed static series

compensator placement for enhancing power system loadability and reliability." IET

Generation, Transmission & Distribution 9.11 (2015): 1043-1050.

61. Banerjee, Avishek, et al. "A fuzzy hybrid approach for reliability optimization

problem in power distribution systems." Electrical and Power Engineering (EPE),

2016 International Conference and Exposition on. IEEE, 2016.:809-814

62. Ghosh, Ayan, and Deepak Kumar. "Optimal merging of primary and secondary

power distribution systems considering overall system cost and reliability." Power

Electronics, Intelligent Control and Energy Systems (ICPEICES), IEEE

International Conference on. IEEE, 2016.: 1-6

63. Küfeoğlu, Sinan, and Matti Lehtonen. "A review on the theory of electric power

reliability worth and customer interruption costs assessment techniques." European

138

References

Energy Market (EEM), 2016 13th International Conference on the. IEEE, 2016.: 1-

6

64. Sun, Lei, et al. "Optimal Allocation of Smart Substations in a Distribution System

Considering Interruption Costs of Customers." IEEE Transactions on Smart Grid 99

(2016).: 1-1

65. Yousefian, R., and H. Monsef. "DG-allocation based on reliability indices by means

of Monte Carlo simulation and AHP." Environment and Electrical Engineering

(EEEIC), 2011 10th International Conference on. IEEE, 2011.: 1-4

66. Al-Muhaini, Mohammad, and Gerald T. Heydt. "Evaluating future power

distribution system reliability including distributed generation." IEEE transactions

on power delivery 28.4 (2013): 2264-2272.

67. Awad, Ahmed SA, Tarek HM El-Fouly, and Magdy MA Salama. "Optimal

distributed generation allocation and load shedding for improving distribution

system reliability." Electric Power Components and Systems 42.6 (2014): 576-584.

68. Kumar, Deepak, et al. "Reliability-constrained based optimal placement and sizing

of multiple distributed generators in power distribution network using cat swarm

optimization." Electric Power Components and Systems 42.2 (2014): 149-164.

69. Abbasi, Fazel, and Seyed Mehdi Hosseini. "Optimal DG allocation and sizing in

presence of storage systems considering network configuration effects in distribution

systems." IET Generation, Transmission & Distribution 10.3 (2016): 617-624.

70. Bagheri, A., H. Monsef, and H. Lesani. "Integrated distribution network expansion

planning incorporating distributed generation considering uncertainties, reliability,

and operational conditions." International Journal of Electrical Power & Energy

Systems 73 (2015): 56-70.

71. Battu, Neelakanteshwar Rao, A. R. Abhyankar, and Nilanjan Senroy. "DG planning

with amalgamation of economic and reliability considerations." International

Journal of Electrical Power & Energy Systems 73 (2015): 273-282.

72. Arya, Rajesh. "Determination of customer perceived reliability indices for active

distribution systems including omission of tolerable interruption durations

employing bootstrapping." IET Generation, Transmission & Distribution 10.15

(2016): 3795-3802.

139

References

73. Ray, Saheli, Aniruddha Bhattacharya, and Subhadeep Bhattacharjee. "Differential

search algorithm for reliability enhancement of radial distribution system." Electric

Power Components and Systems 44.1 (2016): 29-42.

74. Kansal, Satish, Barjeev Tyagi, and Vishal Kumar. "Cost–benefit analysis for optimal

distributed generation placement in distribution systems." International Journal of

Ambient Energy38.1 (2017): 45-54.

75. Rahiminejad, Abolfazl, et al. "Simultaneous distributed generation placement,

capacitor placement, and reconfiguration using a modified teaching-learning-based

optimization algorithm." Electric Power Components and Systems 44.14 (2016):

1631-1644.

76. Alvehag, Karin, and Kehinde Awodele. "Impact of reward and penalty scheme on

the incentives for distribution system reliability." IEEE Transactions on Power

Systems 29.1 (2014): 386-394.

77. Billinton, Roy, and Zhaoming Pan. "Historic performance-based distribution system

risk assessment." IEEE transactions on power delivery 19.4 (2004): 1759-1765.

78. Fotuhi, M., et al. "Reliability assessment of utilities using an enhanced reward-

penalty model in performance based regulation system." Power System Technology,

. PowerCon 2006. International Conference on. IEEE, 2006.: 1-6

79. Mohammadnezhad-Shourkaei, H., M. Fotuhi-Firuzabad, and R. Billinton.

"Integration of clustering analysis and reward/penalty mechanisms for regulating

service reliability in distribution systems." IET generation, transmission &

distribution 5.11 (2011): 1192-1200.

80. Billinton, Roy, and Zhaoming Pan. "Incorporating reliability index probability

distributions in performance based regulation." Electrical and Computer

Engineering, 2002. IEEE CCECE 2002. Canadian Conference on. Vol. 1. IEEE.:

12-17

81. Mohammadnezhad-Shourkaei, H., and M. Fotuhi-Firuzabad. "Principal

requirements of designing the reward-penalty schemes for reliability improvement

in distribution systems." Proc. 21st Int. Conf. Electricity Distribution (CIRED2011).

2011.

82. Simab, Mohsen, et al. "Designing reward and penalty scheme in performance-based

regulation for electric distribution companies." IET generation, transmission &

distribution 6.9 (2012): 893-901.

140

References

83. Mohammadnezhad-Shourkaei, H., and M. Fotuhi-Firuzabad. "Impact of penalty–

reward mechanism on the performance of electric distribution systems and regulator

budget." IET generation, transmission & distribution 4.7 (2010): 770-779.

84. Jooshaki, M., et al. "A new reward-penalty mechanism for distribution companies

based on concept of competition." Innovative Smart Grid Technologies Conference

Europe (ISGT-Europe), 2014 IEEE PES. IEEE, 2014.:1-5

85. McDermott, Thomas E., and Roger C. Dugan. "Distributed generation impact on

reliability and power quality indices." Rural Electric Power Conference, 2002. 2002

IEEE. IEEE, 2002.: D3-1

86. Chen, S. L., et al. "Mitigation of voltage sags by network reconfiguration of a utility

power system." Transmission and Distribution Conference and Exhibition 2002:

Asia Pacific. IEEE/PES. Vol. 3. IEEE, 2002.:2067-2072

87. Wang, J., S. Chen, and T. T. Lie. "System voltage sag performance

estimation." IEEE transactions on power delivery 20.2 (2005): 1738-1747.

88. Yang, Yongtao, and Math HJ Bollen. Power quality and reliability in distribution

networks with increased levels of distributed generation. Elforsk, 2008.

89. Mendoza, J. E., et al. "Microgenetic multiobjective reconfiguration algorithm

considering power losses and reliability indices for medium voltage distribution

network." IET Generation, Transmission & Distribution 3.9 (2009): 825-840.

90. Salman, Nesrallh, Azah Mohamed, and Hussain Shareef. "Voltage sag mitigation in

distribution systems by using genetically optimized switching actions." Power

Engineering and Optimization Conference (PEOCO), 2011 5th International. IEEE,

2011.:329-334

91. Jazebi, Saeed, and Behrooz Vahidi. "Reconfiguration of distribution networks to

mitigate utilities power quality disturbances." Electric Power Systems Research 91

(2012): 9-17.

92. Tao, Shun, et al. "Power quality & reliability assessment of distribution system

considering voltage interruptions and sags." Harmonics and Quality of Power

(ICHQP), 2012 IEEE 15th International Conference on. IEEE, 2012.:751-757

93. Mishra, Ankita, and Arti Bhandakkar. "Power quality improvement of distribution

system by optimal location and size of DGs using particle swarm optimization." Int.

J. Sci. Res. Eng. Technol 3 (2014): 72-78.

141

References

94. Gupta, Nikhil, Anil Swarnkar, and K. R. Niazi. "Distribution network

reconfiguration for power quality and reliability improvement using Genetic

Algorithms." International Journal of Electrical Power & Energy Systems 54

(2014): 664-671.

95. Shareef, H., et al. "Power quality and reliability enhancement in distribution systems

via optimum network reconfiguration by using quantum firefly

algorithm." International Journal of Electrical Power & Energy Systems 58 (2014):

160-169.

96. Balasubramaniam, P. M., and S. U. Prabha. "Power quality issues, solutions and

standards: A technology review." J. Appl. Sci. Eng. 18.4 (2015): 371-380.

97. Hamoud, Faris, Mamadou Lamine Doumbia, and Ahmed Chériti. "Voltage sag and

swell mitigation using D-STATCOM in renewable energy based distributed

generation systems." Ecological Vehicles and Renewable Energies (EVER), 2017

Twelfth International Conference on. IEEE, 2017.:1-6

98. Chindris, M., A. Cziker, and Anca Miron. "UPQC—The best solution to improve

power quality in low voltage weak distribution networks." Modern Power Systems

(MPS), 2017 International Conference on. IEEE, 2017.:1-8

99. Allan, Ronald N., et al. "A reliability test system for educational purposes-basic

distribution system data and results." IEEE Transactions on Power systems 6.2

(1991): 813-820.

100. Yang, Xin-She. "Flower pollination algorithm for global

optimization." International conference on unconventional computing and natural

computation. Springer, Berlin, Heidelberg, 2012.:240:249

101. Rao, R. Venkata, Vimal J. Savsani, and D. P. Vakharia. "Teaching–learning-based

optimization: an optimization method for continuous non-linear large scale

problems." Information sciences 183.1 (2012): 1-15.

102. Price, Kenneth, Rainer M. Storn, and Jouni A. Lampinen. Differential evolution: a

practical approach to global optimization. Springer Science & Business Media,

2006.

103. R. Billinton and R.N. Allan, ‘Reliability evaluation of power system’ Springer

International Edition, 1996.

142

References

104. Saaty, T. "The Analytic Hierarchy Process: Planning, Priority Setting, Resource

Allocation. The Analytic Hierarchy Process Series, vol. I.", New York: McGraw-

Hill (1990).

105. Ebeling, Charles E. An introduction to reliability and maintainability engineering.

Tata McGraw-Hill Education, 2004.

106. Saaty, Thomas L., and Liem T. Tran. "On the invalidity of fuzzifying numerical

judgments in the Analytic Hierarchy Process." Mathematical and Computer

Modelling 46.7-8 (2007): 962-975.

107. Arya, L. D., and Kela K. B.. "Reliability performance optimization of meshed

electrical distribution system considering customer and energy based reliability

indices." Journal of The Institution of Engineers (India): Series B 94.4 (2013): 237-

246.

108. Pavlyukevich, Ilya. "Lévy flights, non-local search and simulated

annealing." Journal of Computational Physics 226.2 (2007): 1830-1844.

109. Yang, Xin-She. Nature-inspired metaheuristic algorithms. Luniver press, 2010.

110. Tvrdík, Josef. "Adaptation in differential evolution: A numerical

comparison." Applied Soft Computing 9.3 (2009): 1149-1155.

111. Kela, K. B., and Arya L.D. "Reliability optimization of radial distribution systems

employing differential evolution and bare bones particle swarm

optimization." Journal of The Institution of Engineers (India): Series B 95.3 (2014):

231-239.

112. Billinton, Roy, and Ronald Norman Allan. Reliability evaluation of engineering

systems. New York: Plenum press, 1992.

113. Kellison, Stephen G. "The theory of interest." New York: McGraw-Hill/Irwin, 3rd

ed., Chap. 1, 2008.:4-12

114. Raoofat, Mahdi, and Ahmad Reza Malekpour. "Optimal allocation of distributed

generations and remote controllable switches to improve the network performance

considering operation strategy of distributed generations." Electric Power

Components and Systems 39.16 (2011): 1809-1827.

115. Fumagalli, Elena, Luca Schiavo, and Florence Delestre. Service quality regulation

in electricity distribution and retail. Springer Science & Business Media, 2007.

116. CEER, 5th CEER benchmarking report on the quality of electricity supply, Council

of European Energy Regulators, Tech. Rep, Brussels, Belgium, 2011.

143

References

117. Alvehag, Karin, and Kehinde Awodele. "Impact of reward and penalty scheme on

the incentives for distribution system reliability." IEEE Transactions on Power

Systems 29.1 (2014): 386-394.

118. Billinton, R., and Li, W. Reliability Assessment of Electrical Power Systems using

Monte Carlo Methods. New York, NY, USA: Plenum, 1994.

119. Sappington, David EM. "Regulating service quality: A survey." Journal of

regulatory economics 27.2 (2005): 123-154.

120. Ajodhia, Virendra Shailesh. "Regulating beyond price." Integrated Price-Quality

Regulation for Electricity Distribution Networks (2005). Ph.D. dissertation, Delft

Univ., Delft, The Netherlands, 2005. [Online]. Available: http://www. leonardo-

energy.org/regulating-beyond price.

121. De Almeida, A., L. Moreira, and J. Delgado. "Power quality problems and new

solutions." International conference on renewable energies and power quality. Vol.

3. 2003.

122. Bollen, Math HJ, and Math HJ Bollen. Understanding power quality problems:

voltage sags and interruptions. Vol. 445. New York: IEEE press, 2000.

123. Short, Thomas Allen. Distribution reliability and power quality. Crc Press, 2005.

124. Sankaran, C. Power quality. CRC press, 2001.

125. Smith, J. Charles, G. Hensley, and L. Ray. "IEEE recommended practice for

monitoring electric power quality." IEEE Std (1995): 1159-1995.

126. McGranaghan, M., D. Brooks, and D. Mueller. "EPRI reliability benchmarking

application guide for Utility/Customer PQ indices: Guide for utilizing the EPRI

reliability benchmarking, methodology power quality indices and customer specific

indices as service quality benchmarks." EPRI. USA (1999).

127. Sabin, D. Daniel, Thomas E. Grebe, and A. Sundaram. "RMS voltage variation

statistical analysis for a survey of distribution system power quality

performance." Power Engineering Society 1999 Winter Meeting, IEEE. Vol. 2.

IEEE, 1999.:1235-1240

128. Brooks, Daniel L., et al. "Indices for assessing utility distribution system RMS

variation performance." IEEE transactions on power delivery 13.1 (1998): 254-259.

129. Heising, C. "IEEE recommended practice for the design of reliable industrial and

commercial power systems." IEEE Inc., New York (2007).

144

List of papers published/communicated

(1) K. B. Kela, B. N. Suthar, and L. D. Arya, ‘Application of Metaheuristic Optimization

Methods for Reliability Enhancement of Meshed Distribution System based on

AHP,” International Journal of Advance Engineering and Research Development.,

vol.5, no. 1, pp 309-316, ISSN : 2348-4470.

(2) K. B. Kela, B. N. Suthar, and L. D. Arya, “Reliability Enhancement of RBTS-2 by

Jaya Optimization Algorithm,”International Journal of Emerging Technology and

Advanced Engineering, vol. 8, no. 2, pp. 71–76, 2018., ISSN : 2250-2459

(3) K. B. Kela, B. N. Suthar, and L. D. Arya, “Cost Benefit Analysis for Active

Distribution Systems in Reliability Enhancement” communicated to Electric Power

Components and Systems.

(4) K. B. Kela, B. N. Suthar, and L. D. Arya, “A Value Based Reliability Optimization

of Electrical Distribution Systems considering Expenditures on Maintenance and

Customer Interruptions” communicated to Indonesian Journal of Electrical

Engineering and Computer Science.

(5) K. B. Kela, B. N. Suthar, and L. D. Arya, “Optimal Parameter Setting in Distribution

System Reliability Enhancement with Reward and Penalty” communicated to Journal

of Electrical Systems and Information Technology, Elsevier.

145

http://www.ijaerd.com/PastIssues.php?ao




http://www.ijetae.com/Volume8Issue2.html



APPENDIX-A

A.1 Radial Distribution System [29]

Fig.-A.1 Sample radial distribution system

146

Radial Distribution System

Fig. A.2 Modified radial distribution system with DG

147

APPENDIX-A

Table A.1 Maximum allowable and minimum reachable values of failure rates and repair times for



𝜆𝑘,𝑚𝑎𝑥 /year (failure rate) 0.4 0.2 0.3 0.5 0.2 0.1 0.1

𝑟𝑘,𝑚𝑎𝑥 (h) (repair time) 10 9 12 20 15 8 12

𝜆𝑘,𝑚𝑖𝑛/year (failure rate) 0.2 0.05 0.1 0.1 0.15 0.05 0.05

𝑟𝑘,𝑚𝑖𝑛 (h) (repair time) 6 6 4 8 7 6 6

Table A.2 Average load and number of customers at load points for radial network

Load

point(LP)

2 3 4 5 6 7 8

Average load

Li(kW)

1000 700 400 500 300 200 150

Number of

customers,Ni

200 150 100 150 100 250 50

Table A.3 Cost coefficients 𝜶𝑲 and 𝜷𝑲 for radial network


𝛼𝐾 Rs. 80 100 60 40 80 95 100

𝛽𝐾 Rs. 100 90 50 50 80 60 55

148

APPENDIX-B

B.1 Meshed Distribution System [13]

Fig. B.1 Sample Meshed Distribution System

149

APPENDIX-B

Fig B.2 Reliability logic diagram of the meshed distribution system

150

Meshed Distribution System

Fig. B.3 Modified Meshed Distribution System with DG

151

APPENDIX-B

Table B.1 Maximum allowable and minimum reachable values of failure rates and repair times for


Distributor

segment

𝜆𝑘,𝑚𝑎𝑥 /year

(failure rate)

𝑟𝑘,𝑚𝑎𝑥(h)

(repair time)

𝜆𝑘,𝑚𝑖𝑛/year

(failure rate)

𝑟𝑘,𝑚𝑖𝑛 (h)

repair time

1 0.510402 6.423706 0.254201 3.348734

2 0.177600 4.061540 0.090000 3.067050

3 0.110000 21.732271 0.056000 10.732271

4 0.113525 5.565712 0.056762 2.122525

5 0.184607 8.397691 0.083303 3.394025

6 0.017640 13.555102 0.008830 9.250098

7 0.184607 8.397691 0.092304 3.394025

8 0.178010 9.752112 0.090000 3.752112

9 0.008460 15.800000 0.005230 6.400000

10 0.069000 27.565217 0.026000 18.560000

11 0.205200 5.234919 0.103000 2.012345

12 0.205200 5.234919 0.103000 2.012345

13 0.110000 21.732210 0.056000 10.732221

14 0.113525 5.565712 0.056762 2.122525

15 0.156600 10.714943 0.068333 6.352524

16 0.017640 13.555102 0.008830 9.250098

17 0.178010 9.752120 0.090000 4.354320

18 0.184607 8.397691 0.083303 3.394025

Table B.2 Average load and number of customers at load points for meshed network


Average load Li(kW) 1500 1000 1000 2000

Number of customers, Ni 400 250 200 450

Table B.3 Cost coefficients 𝜶𝑲 and 𝜷𝑲 for meshed network

Distributor

segment

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

𝛼𝐾 Rs 80 100 60 40 80 95 100 80 95 75 85 65 45 50 75 80 80 90

𝛽𝐾 Rs 100 90 50 50 80 60 55 100 50 55 70 80 75 90 40 60 85 100

152

APPENDIX-C

C.1 Roy Billinton Test System Bus-2 (RBTS-2) [99]

Fig. C.1 RBTS-2

153

APPENDIX-C

Fig. C.2 Modified RBTS-2 with DG

Table C.1 Failure rates and average repair time of different components of RBTS-2

Sr.

No.

Transformers / Feeder sections Failure

rate(failures/year) λ

Repair/

replacement time

(hr) r

1 Transformer 1-22 (except 8,9 ) 0.01500 10

2 Feeder sections (0.6 km)

2,6,10,14,17,21,25,28,30,34

0.06500 5


1,4,7,9,12,16,19,22,24,27,29,32,35

0.06500 5


3,5,8,11,13,15,18,20,23,26,31,33,36

0.06500 5

154

Roy Billinton Test System Bus-2

Table C.2 Maximum allowable and minimum reachable values of failure rates and repair times for

RBTS-2

Distributor

segment

𝜆𝑘,𝑚𝑎𝑥/

year (failure

rate)

λk,min/year

(failure rate)

rk,max (h)

(repair time)

rk,min (h)

(repair

time)

#1 0.048750 0.036650 5.000 2.252252

#2 0.015000 0.011270 10.000 4.504504

#3 0.052000 0.039090 10.000 4.504504

#4 0.048000 0.036090 5.000 2.252252

#5 0.015000 0.011270 10.000 4.504504

#6 0.015000 0.011270 10.000 4.504504

#7 0.048750 0.036650 5.000 2.252252

#8 0.015000 0.011278 10.000 4.504504

#9 0.015000 0.011278 10.000 4.504504

#10 0.039000 0.029323 5.000 2.252252

#11 0.015000 0.011278 10.000 4.504504

#12 0.048750 0.036650 5.000 2.252250

#13 0.052000 0.039097 5.000 2.252250

#14 0.039000 0.029323 5.000 2.252250

#15 0.052000 0.039097 5.000 2.252250

#16 0.048750 0.036650 5.000 2.252250

#17 0.015000 0.011278 10.000 4.504500

#18 0.052000 0.039097 5.000 2.252250

#19 0.015000 0.011278 10.000 4.504500

#20 0.015000 0.011278 10.000 4.504500

#21 0.039000 0.029323 5.000 2.252250

#22 0.015000 0.011278 10.000 4.504500

#23 0.015000 0.011278 10.000 4.504500

#24 0.048750 0.036650 5.000 2.252250

#25 0.015000 0.011278 10.000 4.504500

#26 0.052000 0.039097 5.000 2.252250

#27 0.015000 0.011278 10.000 4.504500

#28 0.015000 0.011278 10.000 4.504500

#29 0.048750 0.036650 5.000 2.252250

#30 0.015000 0.011278 10.000 4.504500

#31 0.015000 0.011278 10.000 4.504500

#32 0.048750 0.036650 5.000 2.252250

#33 0.015000 0.011278 10.000 4.504500

#34 0.039000 0.029323 5.000 2.252250

#35 0.015000 0.011278 10.000 4.504500

#36 0.015000 0.011278 10.000 4.504500

155

APPENDIX-C

Table C.3 Cost coefficients 𝜶𝑲 and 𝜷𝑲 for RBTS-2

Distributor

segment 𝛼𝐾 (Rs.) 𝛽𝐾 (Rs.× 102)

#1 2.564 22.649

#2 3.205 17.589

#3 1.923 4.291

#4 1.282 4.291

#5 2.564 13.258

#6 3.045 6.647

#7 3.205 5.394

#8 2.564 22.649

#9 3.205 17.589

#10 1.923 4.291

#11 1.282 4.291

#12 2.564 22.649

#13 3.205 17.589

#14 2.564 22.649

#15 3.205 17.589

#16 2.564 22.649

#17 3.205 17.589

#18 1.923 4.291

#19 1.282 4.291

#20 2.564 13.258

#21 3.045 6.647

#22 2.564 22.649

#23 3.205 17.589

#24 1.923 4.291

#25 1.282 4.291

#26 2.564 22.649

#27 3.205 17.589

#28 1.923 4.291

#29 1.282 4.291

#30 2.564 13.258

#31 3.045 6.647

#32 3.205 5.394

#33 2.564 22.649

#34 3.205 17.589

#35 1.923 4.291

#36 1.282 4.291

Table C.4 Customer data for RBTS-2

Sr.

No

Load point Customer

type

Average load

at each load

point (MW)

Number of

customers

Interruption

Cost (𝐶𝑝𝑘)

(Rs./kW)

1 1-3,10,11 residential 0.535 210 22.29

2 12,17-19 residential 0.450 200 6.045

3 8 small user 1.000 1 251.42

4 9 small user 1.150 1 251.42

5 4,5,13,14,20,21 govt./ inst. 0.566 1 23.98

6 6,7,15,16,22 commercial 0.454 10 192.98

156

APPENDIX-D

An Overview of Flower Pollination Algorithm (FP):

The Flower Pollination (FP) algorithm was developed by Xin-She Yang [100] in 2012 and

is inspired by the flow pollination process of flowering plants. The certain rules defining the

process in brief are: (a) Biotic and cross-pollination are global pollination process and

pollen-carrying pollinators travel in a way which obeys Levy flights. (b) A-biotic and self-

pollination are local pollination. (c) Pollinators such as insects can develop flower reliability,

which is equivalent to a reproduction probability and it is proportional to the similarity of

two flowers implicated. (d) A switch probability 𝑝 ∈ [0,1] controls local pollination and

global pollination.

Local pollination do have a significant fraction 𝑝 in the overall pollination activities due to

the physical proximity and other factors such as wind.

Following are the notations used for describing the FP.

𝑀 : population of flowers /pollen gametes

𝐷 : number of variables

𝑘𝑚𝑎𝑥 : maximum number of allowable generations

𝑝 : switch probability ∈ [0,1]

Step-(a) Initialization: An initial population of size ‘𝑀’ is generated as follows.

S0 = [𝑋1

0, 𝑋20, … … , 𝑋𝑀

0 ] (D.1)

Xi0 = [𝑋𝑖1

0 , 𝑋𝑖20 , … . , 𝑋𝑖𝐷

0 ]T (D.2)

𝑋𝑖𝑗0

i.e. 𝑗𝑡ℎ parameter of 𝑋𝑖 vector is obtained from uniform distribution as follows.

𝑋𝑖𝑗0 = 𝑋𝑗,𝑚𝑖𝑛 + (𝑋𝑗,𝑚𝑎𝑥 − 𝑋𝑗,𝑚𝑖𝑛)𝑟𝑎𝑛𝑑𝑗 (D.3)

𝑋𝑗,𝑚𝑖𝑛 and 𝑋𝑗,𝑚𝑎𝑥 are lower and upper bounds on variable 𝑋𝑗. 𝑟𝑎𝑛𝑑𝑗 is a random digit in the

range [0,1].

157

APPENDIX-D

Step-(b) Updating vectors by global and local pollination

𝑋𝑖(𝑘+1)

= {𝑋𝑖

𝑘+ ∝ × 𝐿 (𝑋𝑏𝑒𝑠𝑡(𝑘)

− 𝑋𝑖𝑘), 𝑖𝑓 𝑟𝑎𝑛𝑑 < 𝑝

𝑋𝑖(𝑘)

+∈ (𝑋𝑗(𝑘)

− 𝑋𝑘(𝑘)

) 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒. 𝑤ℎ𝑒𝑟𝑒, 𝑋𝑗(𝑘)

≠ 𝑋𝑘(𝑘)

(D.4)

𝑋𝑏𝑒𝑠𝑡(𝑘)

is the current best solution found among all solutions at the current

generation/iteration. ∈ is drawn from uniform distribution [0,1] .

∝ > 0 is a scaling factor to control the step size. The parameter 𝐿 is the strength of the

pollination, which essentially is a step size. Since insects may move over a long distance

with various distance steps, a L´evy flight can be used to represent this characteristic

efficiently [108,109].

Lévy distribution:

𝐿 = 𝑣 ×𝜎𝑥(𝛽)

𝜎𝑦(𝛽) (D.5)

𝑣 =𝑟𝑎𝑛𝑑𝑥

|𝑟𝑎𝑛𝑑𝑦|1

𝛽⁄ (D.6)

Where 𝑟𝑎𝑛𝑑𝑥 and 𝑟𝑎𝑛𝑑𝑦 are two normally distributed stochastic variables with standard

deviation 𝜎𝑥(𝛽) and 𝜎𝑦(𝛽) given by:

𝜎𝑥(𝛽) = [⎾(1+𝛽)× (

𝜋𝛽

2)

⎾ (1+𝛽

2)× 2

(𝛽−1

2)]

1𝛽⁄

(D.7)

𝜎𝑦(𝛽) = 1 (D.8)

Where 𝛽 is the distribution factor (0.3 ≤ 𝛽 ≤ 1.99) and Γ (.) is the gamma distribution

function.

Step-(c) Comparing the fitness of the updated vectors with the initial vectors

𝑋𝑖(𝑘+1)

= {𝑋𝑖

𝑘+1, 𝑖𝑓 𝑓(𝑋𝑖𝑘+1) < 𝑓(𝑋𝑖

(𝑘))

𝑋𝑖(𝑘)

𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒 (D.9)

The current best solution 𝑋𝑏𝑒𝑠𝑡(𝑘)

and its fitness is then found.This process is executed for all

target vector index 𝑖 and a new population is created till the optimal solution is obtained or

the pre-specified generations (𝑘𝑚𝑎𝑥) have been executed.

158

APPENDIX-E

Teaching Learning Based Optimization (TLBO): An Overview

Teaching-learning-based- optimization (TLBO) algorithm is also one of the most recently

developed metaheuristicalgorithms [101]. Similar to most other evolutionary optimization

methods, TLBO is a population-based algorithm inspired by learning process in a classroom.

A group of learners constitute the population in TLBO. In any optimization algorithms there

are D numbers of different design variables. The different design variables in TLBO are

analogous to different subjects offered to learners and the learners’ result is analogous to the

‘fitness’, as in other population-based optimization techniques. The searching process

consists of two phases, i.e. Teacher Phase and Learner Phase. In teacher phase, learners first

get knowledge from a teacher and then from classmates in learner phase through interaction

between them. In the entire population, the best solution is considered as the teacher

(𝑋𝑇𝑒𝑎𝑐ℎ𝑒𝑟).

The fundamental steps are explained below.

Following are the notations used for describing the TLBO.

𝑀 : number of learners in class i.e. “ class size ”

𝐷 : number of courses offered to the learners

𝑘𝑚𝑎𝑥 : maximum number of allowable generations

Step-(a) Initialization: an initial population of size ‘𝑀’ is generated as follows

S0 = [𝑋1

0, 𝑋20, … … , 𝑋𝑀

0 ] (E.1)

Xi0 = [𝑋𝑖1

0 , 𝑋𝑖20 , … . , 𝑋𝑖𝐷

0 ]T (E.2)

𝑋𝑖𝑗0 i.e. 𝑗𝑡ℎ parameter of 𝑋𝑖 vector is obtained from uniform distribution as follows.

𝑋𝑖𝑗0 = 𝑋𝑗,𝑚𝑖𝑛 + (𝑋𝑗,𝑚𝑎𝑥 − 𝑋𝑗,𝑚𝑖𝑛)𝑟𝑎𝑛𝑑𝑗 (E.3)

𝑋𝑗,𝑚𝑖𝑛and𝑋𝑗,𝑚𝑎𝑥 are lower and upper bounds on variable 𝑋𝑗. 𝑟𝑎𝑛𝑑𝑗 is a random digit in the

range [0,1].

159

APPENDIX-E

Step-(b) Teacher phase:

The mean parameter 𝑋𝑀𝑒𝑎𝑛𝑘 of each subject of the learners in the class at generation 𝑘 is

given as 𝑋𝑀𝑒𝑎𝑛𝑘 = [𝑋1

𝑘, 𝑋2𝑘 , … . , 𝑋𝐷

𝑘]T.

The learner with the minimum objective function value is considered as the teacher

𝑋𝑇𝑒𝑎𝑐ℎ𝑒𝑟(𝑘)

for respective generation. In order to maintain stochastic features of the search,

two randomly-generated parameters 𝑟𝑎𝑛𝑑and 𝑇𝐹 are applied in update formula for the

solution 𝑋𝑖 as:

𝑋𝑁𝑒𝑤𝑘 = 𝑋𝑖

𝑘 + 𝑟𝑎𝑛𝑑 × (𝑋𝑇𝑒𝑎𝑐ℎ𝑒𝑟(𝑘)

− 𝑇𝐹 𝑋𝑀𝑒𝑎𝑛𝑘 ) (E.4)

𝑇𝐹is the teaching factor which decides the value of mean to be changed. Value of 𝑇𝐹 can

be either 1 or 2. The value of 𝑇𝐹 is decided randomly with equal probability as,

𝑇𝐹 = 𝑟𝑜𝑢𝑛𝑑 [1 + 𝑟𝑎𝑛𝑑(0,1){2 − 1}] (E.5)

If 𝑋𝑁𝑒𝑤𝑘 is found to be a superior learner than 𝑋𝑖

𝑘 in generation 𝑘 , than it replaces inferior

learner 𝑋𝑖𝑘 in the matrix.

Step-(c) Learner phase:

In this phase the interaction of learners with one another takes place. The process of mutual

interaction tends to increase the knowledge of the learner. The random interaction among

learners improves his or her knowledge. For a given learner 𝑋𝑖𝑘 , another learner 𝑋𝑟

𝑘is

randomly selected 𝑖 ≠ 𝑟 . The 𝑖𝑡ℎ parameter of the matrix 𝑋𝑁𝑒𝑤,𝑖𝑘 in the learner phase is

given as

𝑋𝑁𝑒𝑤,𝑖𝑘 = {

𝑋𝑖𝑘 + 𝑟𝑎𝑛𝑑 × (𝑋𝑖

𝑘 − 𝑋𝑟𝑘), 𝑖𝑓 𝑓(𝑋𝑖

𝑘) < 𝑓(𝑋𝑟𝑘)

𝑋𝑖𝑘 + 𝑟𝑎𝑛𝑑 × (𝑋𝑟

𝑘 − 𝑋𝑖𝑘) 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒

(E.6)

This process is executed for all target vector index 𝑖 and a new population is created till the

optimal solution is obtained. The procedure is terminated if a maximum number of

generations (𝑘𝑚𝑎𝑥) have been executed or no improvement in objective function is noticed

in a pre-specified generations.

160

APPENDIX-F

Differential Evolution (DE): An overview

Differential evolution (DE) developed by Storn and Price is a very simple population based,

stochastic function minimizer and has been found very powerful to solve various nature of

engineering problems[102,110]. DE attacks the optimization problem by sampling the

objective function at multiple randomly chosen initial points. Pre-set parameter bounds

define the region from which ‘M’ vectors in this initial population are chosen. DE generates

new solution points in ‘D’ dimensional space that are perturbations of existing points. It

perturbs vectors with the scaled difference of two randomly selected population vectors. To

produce a mutated vector, DE adds the scaled, random vector difference to a third selected

population vector (called as based vector). Further DE also employs a uniform cross over to

produce trial vector from target vector and mutated vector.

The three fundamental steps are explained below.

Step-(a) Initialization: An initial population of size ‘M’ is generated as follows

S0 = [X1

0, X20, … … , XM

0 ] (F.1)

Xi0 = [Xi1

0 , Xi20 , … . , XiD

0 ]T (F.2)

X0 ij i.e. jth parameter of Xi vector is obtained from uniform distribution as follows.

Xij0 = Xj,min + (Xj,max − Xj,min)randj (F.3)

Xj,min and Xj,max are lower and upper bounds on variable Xj. randj is a random digit in the

range [0,1].

Step-(b) Mutation: DE mutates and recombines the population to produce a population of

‘M’ trial vectors. Differential mutation adds a scaled, randomly sampled, vector difference

to a third vector as follows.

V__𝑖(k)

= Xbase(k)

+ σ(Xp(k)

− Xq(k)

) (F.4)

σ is known as scale factor usually lies in the range [0,1]. Xp(k)

and Xq(k)

are two randomly

selected vectors (p≠ q). Xbase(k)

is known as base vector. V__𝑖(k)

is a mutant vector. The base

161

APPENDIX-F

vector index ‘base’ may be determined in variety of ways. This may be a randomly chosen

vector (base≠ p≠ q).

Step (c) Crossover: DE employs a uniform cross over strategy. Crossover generates trial

vectors tij(k)

as follows

tij(k)

= {vij

(k), if (randj ≤ Cr or j = jrand

Xij(k)

otherwise (F.5)

Cr is crossover probability lies in the range [0, 1]. Cr is user defined value which controls the

number of parameter values which are copied from the mutant. If the random number randj

is less than or equal to Cr, the trial parameter is adopted from the mutant V__𝑖(k)

. Further, the

trial parameter with randomly chosen index, jrand is taken from the mutant to ensure that trial

vector does not duplicate target vector Xi(k)

. Otherwise the parameter is adopted from the

target vector Xi(k)

.

Step-(d) Selection: Objective function is evaluated for target vector and trial vector, trial

vector is selected if it provides better value of the function than target vector as follows.

Xi(k+1)

= {ti

(k), if f(ti

(k)) < f(Xi

(k))

Xi(k)

otherwise (F.6)

The process of mutation, crossover and selection is executed for all target vector index i and

a new population is created till the optimal solution is obtained. The procedure is terminated

if a maximum number of generations (kmax) have been executed or no improvement in

objective function is noticed in a pre-specified generations. Various benchmark versions of

DE that differ in the new generation methods largely are available [102]. In this paper

DE/best/1/bin has been selected. The first term after DE i.e. ‘best’ specifies the way base

vector is chosen. In this selected scheme, the base vector is the current best so far vector. ‘1’

after the best denotes that one vector difference contributes to the differential. Last term ‘bin’

denotes binomial distribution that results because of uniform crossover. Number of

parameters denoted by mutant vector closely follows binomial distribution. It is to be noted

that best, target and difference vector indices are all different.

162

strategies for reliability enhancement of electrical...

Documents