Power System Repair and Restoration Optimisation - The ...

THE UNIVERSITY OF SYDNEY

Faculty of Engineering

School of Electrical and Information Engineering

Power System Repair and

Restoration Optimisation

by

Theyab R. Alsenani

(BSc, 2MSc, PE, CEM, CEA, PMP, PgMP, PMI-ACP)

Supervisors:

Dr. Jing Qiu and Prof. Zhao Yang Dong

A thesis submitted in partial fulfillment for the

degree of Doctor of Philosophy

May 2020

DECLARATION OF AUTHORSHIP

I, Theyab R. Alsenani, declare that this thesis entitled ”Power System Repair and

Restoration Optimisation” and the work presented in it are my own. I confirm

that: this work is original and was done wholly while in candidature for a research

degree at this University; this work has not been submitted in whole or in part for a

degree or any other qualification at this University or any other institution; where

I have consulted the published work of others, this is always clearly attributed;

all the assistance received in preparing this work and main sources have been

acknowledged; I designed the study and wrote the drafts of the papers of parts of

this work that have been published as:

Theyab R. Alsenani, Jing Qiu, “Mathematical Approach for Solving Power Sys-

tems Repair and Restoration Problem,” Saudi Arabia Smart Grid Conference

(SASG), Jeddah, November 2019.

Theyab R. Alsenani, Archie C. Chapman, Zhao Yang Dong, “Power System Re-

pair and Restoration — A Literature Review,” IET Journal of Engineering, 2020.

(Accepted).

Theyab R. Alsenani, Kui Zhang, Jing Qiu, “Studying Power Outages Trends and

the Smart Grid Technologies Investments.” IET Journal of Engineering, 2020.(Ac-

cepted).

Theyab R. Alsenani, Jing Qiu, “Reliability Assessment of Power Distribution Sys-

tem Considering Cold Load Pickups” IEEE Access, 2020. (Submitted).

Theyab R. Alsenani, Jing Qiu, “Advanced Approach for Solving Power Transmis-

sion System Repair and Restoration” IEEE Access, 2020. (Submitted).

Signature:

Date:

i

[REDACTION]

ABSTRACT

This thesis contributes to the power system restoration (PSR) field by studying (in

the aim of improving) the power system repair and restoration (PSRR) which is a

novel problem in PSR. The optimisation concept was our approach and mechanism

in tackling this topic. The thesis provides a basic contribution to the PSRR field

by studying some of its main subjects and presenting improvements to the best

practices in the field. This thesis is built on five research papers related to the

thesis title.

The thesis investigated a large number of high-quality published research papers,

and presented a novel, precise, and comprehensive overview of the topic that could

be considered a good introduction for anyone who would like to learn the topic.

This was presented in chapter two. We have presented a well developed and easy

to understand structure that starts from the basics of PSR and PSRR to their

details and relevant subjects.

Also, in this thesis we provided application-based studies using mathematical opti-

misation techniques, where we model a specific power system then solve the PSRR

problem aiming optimality. Different optimisation techniques were applied, anal-

ysed,and compared for both sides of the problem (i.e. the restoration problem,

and the repair problem) as well as different modelling for power systems. Our

findings in this chapter were interesting and align with other high-quality studies

in the literature. This was presented in details in chapter three.

This thesis also tackled a very important relevant subject which is the system

reliability under certain restoration scenarios. Where we studied the effects of

restoration actions under certain conditions such as cold load pickup events to the

reliability indices of the system. A novel Nature-inspired optimisation technique

was developed and compared to an old technique that was presented in a high-

quality study in the literature. This was presented in chapter four.

ii

iii

We concluded this thesis research by developing a statistical analysis for power

system outages for a decade period of time in the Australian industry as well as

investigating the potential benefits of smart grid technologies and their investments

to the power grid. Many statistical methods were applied and investigated using

state-of-the-art programming tools. This was presented in chapter five. We have

presented very interesting results and findings in this chapter.

KEYWORDS: Power System Restoration, Power System Repair and Restoration,

Mathematical Applications, Power-flow Models, Reliability Analysis, Cold Load

Pickup, Statistical Analysis, Smart Grid Technologies.

Contents

Abstract ii

Contents iv

List of Figures x

List of Tables xiii

Acronyms xv

List of Research Outcomes xvii

Acknowledgements 1

1 Introduction 1

1.1 Thesis Topic Overview . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Thesis Topic Motivation . . . . . . . . . . . . . . . . . . . . . . . . 3

1.3 Thesis Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . 6

1.4 Thesis Organisation . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2 Literature Review 8

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.1.1 Power System Repair and Restoration . . . . . . . . . . . . 9

iv

CONTENTS v

2.1.2 The Decomposition Technique . . . . . . . . . . . . . . . . . 10

2.1.3 AC Load Pickup Problem AC-LPP . . . . . . . . . . . . . . 10

2.1.4 The Restoration Order problem . . . . . . . . . . . . . . . . 11

2.1.5 The Restoration Problem . . . . . . . . . . . . . . . . . . . 11

2.1.6 Routing Repair Crews Problem . . . . . . . . . . . . . . . . 12

2.2 Power System Modeling for Restoration Study . . . . . . . . . . . . 13

2.2.1 Power Flow Tool in Restoration Study . . . . . . . . . . . . 14

2.3 The Restoration Problem . . . . . . . . . . . . . . . . . . . . . . . . 15

2.3.1 Goals and Steps in Power System Restoration . . . . . . . . 16

2.3.2 Bulk Power System Restoration Issues . . . . . . . . . . . . 17

2.3.3 Restoration Problem in Transmission Systems . . . . . . . . 19

2.3.4 Restoration Problem in Distribution Systems . . . . . . . . . 21

2.3.5 Restoration Optimisation Problem Formulation . . . . . . . 22

2.3.6 Methodologies and Analysis in Restoration . . . . . . . . . . 24

2.3.7 Technical Issues in Restoration Problem . . . . . . . . . . . 25

2.3.7.1 Generators Start-up Sequence Problem . . . . . . 25

2.3.7.2 Cold Load Pickup . . . . . . . . . . . . . . . . . . 26

2.3.7.3 Parallel Restoration . . . . . . . . . . . . . . . . . 26

2.4 The Routing Repair Crews Problem . . . . . . . . . . . . . . . . . . 27

2.4.1 The Routing Repair Crews Problem Formulation . . . . . . 27

2.4.2 RRCP Computational Considerations . . . . . . . . . . . . . 29

2.4.3 Technical Issues in Routing Repair Crews Problem . . . . . 29

2.4.3.1 Stockpile of Resources . . . . . . . . . . . . . . . . 30

2.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

CONTENTS vi

3 Mathematical Applications on Power System Repair and Restora-

tion 32

3.1 Mathematical Approach for Solving Power Transmission System

Repair and Restoration Problem . . . . . . . . . . . . . . . . . . . . 32

3.1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

3.1.2 Proposed Approach . . . . . . . . . . . . . . . . . . . . . . . 33

3.1.3 Mathematical Formulation . . . . . . . . . . . . . . . . . . . 34

3.1.3.1 Power System Operation . . . . . . . . . . . . . . . 36

3.1.3.2 Routing Repair Crews . . . . . . . . . . . . . . . . 36

3.1.3.3 Availability of Resources . . . . . . . . . . . . . . . 37

3.1.3.4 Evaluating Damages . . . . . . . . . . . . . . . . . 37

3.1.3.5 Decoupling Approach . . . . . . . . . . . . . . . . 37

3.1.4 Results and discussion . . . . . . . . . . . . . . . . . . . . . 38

3.1.4.1 Depots Distributing . . . . . . . . . . . . . . . . . 39

3.1.4.2 Results using TSRRP Approach . . . . . . . . . . . 39

3.1.4.3 Results using Decoupling Approach . . . . . . . . . 42

3.1.5 Conclusion and future work . . . . . . . . . . . . . . . . . . 43

3.2 Advanced Approach for Solving Power Transmission System Repair

and Restoration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

3.2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

3.2.2 Proposed Method . . . . . . . . . . . . . . . . . . . . . . . . 45

3.2.3 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . 46

3.2.3.1 Operation of Power Transmission System . . . . . . 48

3.2.3.2 Repair Crews Routing . . . . . . . . . . . . . . . . 48

3.2.3.3 Resources Availability . . . . . . . . . . . . . . . . 49

3.2.3.4 Damages Evaluation . . . . . . . . . . . . . . . . . 49

CONTENTS vii

3.2.3.5 Decoupling Methodology . . . . . . . . . . . . . . . 50

3.2.4 Results and discussion . . . . . . . . . . . . . . . . . . . . . 51

3.2.4.1 Depots Allocation . . . . . . . . . . . . . . . . . . 52

3.2.4.2 TSRR Methodology Results . . . . . . . . . . . . . 52

3.2.4.3 Decoupling (Route First) Methodology Results . . 55

3.2.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

4 Reliability Analysis in Power System Restoration 57

4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

4.2 Load Modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

4.3 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . 61

4.3.1 Mathematical Formulation . . . . . . . . . . . . . . . . . . . 61

4.3.2 Selected Test System . . . . . . . . . . . . . . . . . . . . . . 63

4.4 Proposed Methodology . . . . . . . . . . . . . . . . . . . . . . . . . 64

4.4.1 Monte Carlo Platform . . . . . . . . . . . . . . . . . . . . . 64

4.4.2 LSA and A-LSA Optimisation Platform . . . . . . . . . . . 64

4.5 Results and Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 67

4.5.1 Load Model Results . . . . . . . . . . . . . . . . . . . . . . . 67

4.5.2 Optimal Restoration of One Outage Resulting in CLPU . . . 68

4.5.3 Reliability Assessment Results . . . . . . . . . . . . . . . . . 70

4.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

4.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

5 Statistical Analysis for Power System Outages 75

5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

5.2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

CONTENTS viii

5.2.1 Smart Grid . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

5.2.2 Smart Grid Investments in Australia . . . . . . . . . . . . . 79

5.2.3 Environmental Reasons . . . . . . . . . . . . . . . . . . . . . 80

5.2.4 Weather Trends in Australia . . . . . . . . . . . . . . . . . . 81

5.2.5 The Australian Electricity Infrastructure . . . . . . . . . . . 82

5.2.5.1 National Power Generation Data: . . . . . . . . . . 83

5.2.6 Australian Electric Infrastructure Security: . . . . . . . . . 84

5.2.7 Cascading Outages . . . . . . . . . . . . . . . . . . . . . . . 86

5.3 Study Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

5.3.1 Power Disturbances Hypotheses: . . . . . . . . . . . . . . . . 87

5.3.2 Reliability Hypotheses: . . . . . . . . . . . . . . . . . . . . . 87

5.3.3 Used Statistical Methods: . . . . . . . . . . . . . . . . . . . 88

5.4 Research Hypotheses Analysis . . . . . . . . . . . . . . . . . . . . . 88

5.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

5.5.1 Power Disturbances Hypotheses: . . . . . . . . . . . . . . . . 109

5.5.2 Reliability Hypotheses: . . . . . . . . . . . . . . . . . . . . . 110

5.6 Conclusion and Recommendations . . . . . . . . . . . . . . . . . . . 111

6 Conclusions and Future Work 114

6.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114

6.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

Bibliography 117

7 Appendix 135

7.1 Tools used in this Thesis . . . . . . . . . . . . . . . . . . . . . . . . 135

7.2 Awards and Achievements . . . . . . . . . . . . . . . . . . . . . . . 136

List of Figures

1.1 Illustration of a Restoration Process [21] . . . . . . . . . . . . . . . 5

2.1 A sequence of restoration order problem. . . . . . . . . . . . . . . . 11

2.2 A general framework for the PSRRP. . . . . . . . . . . . . . . . . . 13

2.3 Power system operating states. . . . . . . . . . . . . . . . . . . . . 16

2.4 Power system restoration steps and areas. . . . . . . . . . . . . . . 16

2.5 An example of power system restoration strategy. . . . . . . . . . . 17

2.6 Example of cold load pick-up transient over time. . . . . . . . . . . 19

2.7 A general framework for routing repair crews problem. . . . . . . . 28

2.8 A representation for the impact of routing repair crews performance

on power system. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

3.1 K-Means Clustering Algorithm Procedure. . . . . . . . . . . . . . . 34

3.2 Example of repair crews routing and service restoration. . . . . . . 34

3.3 IEEE 30-bus transmission system. . . . . . . . . . . . . . . . . . . . 39

3.4 Cluster assignments and depots. . . . . . . . . . . . . . . . . . . . . 40

3.5 Total restored loads for TSRRP and Decoupling Approach. . . . . . 43

3.6 K-Means Clustering Algorithm Procedure. . . . . . . . . . . . . . . 45

3.7 Example of TSRR operation. . . . . . . . . . . . . . . . . . . . . . 46

3.8 IEEE 30-bus transmission system. . . . . . . . . . . . . . . . . . . . 51

ix

LIST OF FIGURES x

3.9 Cluster assignments and depots. . . . . . . . . . . . . . . . . . . . . 52

3.10 Total restored loads for TSRR and Decoupling Methodologies. . . . 56

4.1 A general figure for delayed exponential model with CLPU. . . . . . 60

4.2 Radial power distribution system. . . . . . . . . . . . . . . . . . . . 63

4.3 General flowchart represents the fundamental mechanisms for the

Advanced LSA Algorithm. . . . . . . . . . . . . . . . . . . . . . . . 66

4.4 Time to Use (TOU) curves of different customers. . . . . . . . . . . 67

4.5 Model for Summer day and Winter day. . . . . . . . . . . . . . . . 68

4.6 CLPU curves of the distribution system. . . . . . . . . . . . . . . . 68

4.7 Low TCL demand and restoration after extended outage. . . . . . . 69

4.8 Low bus voltage restoration without planning. . . . . . . . . . . . . 69

4.9 Optimal load restoration with A-LSA algorithm. . . . . . . . . . . . 70

4.10 Comparison of converging between the Advanced LSA and previous

LSA algorithm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

4.11 For sample duration, status of sections 9 and 10, and LP10. . . . . 72

5.1 Figure showing the increase of customers number in millions by year. 77

5.2 The Australian total electricity generation by year in GWh. . . . . 77

5.3 The relationship between the number of costumers and the electric-

ity generation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

5.4 The average household electricity bills annually and the average

commercial and industrial prices from 2007-17 by ACCC. . . . . . . 78

5.5 Annual average temperature change in the world over 167 years

period. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

5.6 Annual sea surface temperature change in Australia over 118 years

period . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

5.7 A map of electricity transmission lines in Australia. . . . . . . . . . 82

LIST OF FIGURES xi

5.8 Australia total generation by source, 27 July to16 August, 2017. . . 83

5.9 Worldwide Cyber-Attacks events on critical infrastructure and in-

dustrial control systems (ICS). . . . . . . . . . . . . . . . . . . . . . 84

5.10 The administrative principles for the development of the AESCSF. . 85

5.11 Criticality scale and bands by energy market sub-sectors [160]. . . . 85

5.12 SAIFI index for each utility in NEM region . . . . . . . . . . . . . . 102

5.13 Q-Q Plot for SAIFI index in each state. . . . . . . . . . . . . . . . . 103

5.14 CAIDI index for each utility in NEM region. . . . . . . . . . . . . . 104

5.15 Q-Q Plot for CAIDI index in each state. . . . . . . . . . . . . . . . 104

List of Tables

2.1 Power system models and evaluation algorithms for operation stud-

ies including Restoration [119]. . . . . . . . . . . . . . . . . . . . . . 13

2.2 Power system operations planning timeframe [8]. . . . . . . . . . . . 13

3.1 Locations and capacity of the generators. . . . . . . . . . . . . . . . 40

3.2 Summary of damaged components. . . . . . . . . . . . . . . . . . . 40

3.3 Repair crews path for TSRRP. . . . . . . . . . . . . . . . . . . . . . 41

3.4 Times when each component is available for TSRRP (variable zi,t). 41

3.5 Repair crews path for decoupling approach. . . . . . . . . . . . . . 42

3.6 Times when each component is available for decoupling approach

(variable zi,t). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

3.7 Location and capacity of system generators. . . . . . . . . . . . . . 52

3.8 Damages numbers and damaged elements. . . . . . . . . . . . . . . 53

3.9 Repair crews paths for TSRR. . . . . . . . . . . . . . . . . . . . . . 54

3.10 The time when each element is available for TSRR (variable zi,t). . 54

3.11 Repair crews paths for Decoupling Methodology. . . . . . . . . . . 55

3.12 The time when each component is available for Decoupling Method-

ology (variable zi,t). . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

4.1 Results for A-LSA and LSA optimisation algorithms. . . . . . . . . 70

4.2 Results for A-LSA and LSA optimisation algorithms. . . . . . . . . 71

xii

LIST OF TABLES xiii

4.3 Reliability indices values for A-LSA and LSA optimisation algorithms. 71

4.4 Reliability indices values for A-LSA and LSA optimisation algo-

rithms for different procedures. . . . . . . . . . . . . . . . . . . . . 73

5.1 Smart grid applications deployed in the SGSC project [1]. . . . . . . 80

5.2 Australia electricity generation data for the period of 27 July to 16

August 2017. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

5.3 Descriptive Analysis Table For the USA Department of Energy out-

ages data from 2002 to 2019. . . . . . . . . . . . . . . . . . . . . . . 92

5.4 Descriptive Analysis Table for SAIFI and CAIDI indices statistics

for Australian power system data from 2006-2017. . . . . . . . . . . 102

Acronyms

AC Alternative Current

AMPL Algebric Modeling Programming Language

BSGU Black Start Generating Units

CLPU Cold load Pickup

CP Constrained Programming

DC Direct Current

DER Distributed Energy Resources

DSRRP Distribution System Repair and Restoration Problem

EHV Extra High Voltage

ES Expert System

HV High Voltage

KB Knowledge-Based

LNS Large Neighborhood Search

LP Linear Programming

LPAC Linear Aproximation of Alternative Current

LPP Load Pickup Problem

MIP Mixed Integer Programming

MIQCP Mixed-integer Quadratically-constrained Program

xiv

Acronyms xv

NBSGU None-Black Start Generation Units

NISAC The National Infrastructure Simulation and Analysis Center

PSRP Power System Restoration Problem

PSRRP Power System Repair and Restoration Problem

PSSSP Power System Stochastic Storage Problem

RAD Randomized Adaptive Decomposition

ROP Restoration Ordering Problem

RRCP Rputing Repair Crews Problem

SDP Semidefinite Programming

SOCP Second-order Cone Programming

TSRRP Transmission System Repair and Restoration Problem

UCP Unit Commitement Problem

List of Research Outcomes

The research outcomes during my research candidature are listed as follows:

1. Theyab R. Alsenani, Jing Qiu, “Mathematical Approach for Solving Power

Systems Repair and Restoration Problem,” Saudi Arabia Smart Grid Conference

(SASG), Jeddah, November 2019.

2. Theyab R. Alsenani, Archie C. Chapman, Zhao Yang Dong, “Power System

Repair and Restoration — A Literature Review,” IET Journal of Engineering,

2020. (Accepted).

3. Theyab R. Alsenani, Kui Zhang, Jing Qiu, “Studying Power Outages Trends

and the Smart Grid Technologies Investments.” IET Journal of Engineering, 2020.

(Accepted).

4. Theyab R. Alsenani, Jing Qiu, “Reliability Assessment of Power Distribution

System Considering Cold Load Pickups” IEEE Access, 2020. (Submitted).

5. Theyab R. Alsenani, Jing Qiu, “Advanced Approach for Solving Power Trans-

mission System Repair and Restoration” IEEE Access, 2020. (Submitted).

xvi

Acknowledgements

First of all I would like to thank Allah for his guidance through life storms, for

easing the hard days, and giving me the strength to deal with the ups and downs.

Secondly, I must thank myself to make it to this point despite the unbearable

obstacles that I have faced during this journey. Also, I would like to express

my deepest and heartfelt gratitude and appreciation to my supervisors, Dr. Jing

Qiu, and Prof. Zhao Yang Dong, for all the kindness, guidance, encouragement,

inspiration, assistance, direction, and advice they have given me. Special thanks

and appreciation to Prof. Zhao Yang Dong for his sincere and constant support

and kindness from the beginning of my journey. He was a wise man with a great

character and professional skills, I was lucky meeting him and starting with him in

my journey. You all have been exceptional for me and provided what I needed most

and what I see is the main criteria for students when choosing their supervisors,

kindness and mutual respect. Thank you immensely for your efforts and support.

I also own a special gratitude and appreciation to my previous and first super-

visor in my postgraduate studies Dr. Sumit Paudyal (at Florida International

University, USA) and Prof. Kui Zhang (at Michigan Technological University,

USA), for their immense support in my work. You have all taught and inspired

me in different ways. I gratefully acknowledge the financial support provided by

Prince Sattam Bin Abdulaziz University (PSAU) − Saudi Arabia, and the Saudi

Arabian Cultural Mission in Australia (SACM), for my PhD studies. Thank you

immensely for your support.

Furthermore, I would like to thank all members of the Centre for Future Energy

Networks at the school of Electrical and Information Engineering, the University of

Sydney, for being such a dynamic team and for being supportive and encouraging.

To my friends and colleagues, thank you immensely for your kind support and

efforts.

xvii

Acknowledgements xviii

Finally, to my supportive grandmother, my dear mother, my father, my sisters, my

brother, my uncles, my aunties, thank you sincerely and wholeheartedly for your

relentless support, efforts, prayers, and sacrifices − I could not have completed

this without you.

To . . .my Mom, my fututre wife and children

xix

Chapter 1

Introduction

In this chapter, an introduction for the thesis topic, its motivation and the contri-

butions made to the topic by this thesis will be presented.

1.1 Thesis Topic Overview

The bulk power system currently provides a highly reliable supply of electric power.

Nevertheless, due to growing demand, increasing in size and complexity, deregula-

tion, and economic competition the power system tends to work to its maximum

design limits. In combination with this and due to unpredictable circumstances,

such as natural disasters (e.g. hurricanes, heavy ice, or floods), there is always a

possibility of a system-wide outage. Therefore, it is wise to be ready for such situ-

ation by having an up-to-date, simply understood, and readily accessible restora-

tion plan that allows a fast and arranged recovery from the outage, with resulting

minimum impact on human and economic welfare.

Although blackouts are rare events, they can happen. And when they happen, the

impacts on the industry, commerce, and daily life of people could be quite severe.

The subject of critical importance after a blackout is how to restore the power

system as fast as possible in order to minimise the cost of the outage economically

and socially. As mentioned in the previous paragraph, the electric utilities have

pre-established restoration plans to restore the power system to its normal condi-

tions. However, it must be mentioned that these restoration plans and procedures

are made under specific assumptions of system conditions after the blackout, this

together with the highly stressed conditions encountered after the blackout could

1

Chapter 1. Introduction 2

make these pre-established restoration plans and procedures not valid. In other

words, it reduces the success rate of this practice. The main reason behind the low

success level is that the assumed situations of the power system when the restora-

tion plan was established might vary completely from the system conditions after

the blackout.

As an effort to improve the power system restoration process, too much effort has

been put on computational tools and other methods of system automation. Re-

cently, many power restoration approaches are proposed to provide new techniques

to tackle the problem as a substitute for the older commonly used techniques and

procedures.

The restoration process involves many generation, transmission and distribution,

and load constraints [2],[3]. The Power System Repair and Restoration Problem

PSRRP after a brownout/partial or a blackout/complete is as old as the electric

industry itself. Most electric utilities have developed restoration plans that meet

the requirement of their specific systems. These plans and schemes give a good

deal of awareness into how the restoration procedures are seen by the operators and

planners and what constraints and conditions any scheme should operate under.

Power system repair and restoration after a blackout or brownout is one of the

most important missions for power system operators in a control centre [4]. The

task arises after a system disturbance or a disaster and it is an essential part of

disaster recovery. Specifically, the power system repair and restoration problem

PSRRP is a complex process that aims to (i) repair damaged power system com-

ponents or reactivate disconnected ones in order to (ii) restore the system back to

normal operating conditions after a wide outage. It has been observed that most

power system restoration studies assume that all power system components are op-

erational and only need to be reactivated [5] and this is what differs the restoration

problem from the repair and restoration problem. The PSRRP is tremendously

difficult from a computational angle. It comprises of two challenging subproblems:

(i) the restoration problem and (ii) the routing repair crews problem.

As mentioned in previously, power system operators rely on pre-established restora-

tion schemes to restore a power system to its steady-state operation. This involves

the following steps: (i) evaluate system conditions, (ii) restart the black start

generators, (iii) create transmission path to power other non-black-start NBSGU

generating units, (iv) pick up the critical loads to soothe the power system and (v)

coordinate the islands created by the outage. A typical method to simplify this job

is to split the power system restoration process into steps (e.g. assessment, system


restoration and load restoration steps) [6]. However, one common measurement

connecting each of these steps is the generation capability at each restoration step

for soothing the system, creating the transmission skeleton/path and restoring the

load. Succeeding a system blackout, other conventional units might need a crank-

ing power from an external source to be able to start. While other generation units

might have time-constraints so it can be restarted successfully or else they have to

be off-line for a long time, so-called minimum down times previously, they could

be resumed and re-synchronized to the power grid. Consequently, it is vital that,

through power system restoration, to maximise the capability of the generation

units available in the system.

Assuming that there are a limited number of black-start generating units BSGU

and many system constraints on different units, by finding the optimal start-up

sequence of all generating units available in the system, we can reach the maximum

accessible generation.

The power system repair and restoration problem PSRRP consists of dispatch-

ing crews to repair damaged electrical components in order to minimise the size

of the blackout [4]. The PSRRP can be modeled as a multi-objective, multi-

stage large-scale combinatorial mixed nonconvex, nonlinear constrained optimisa-

tion problem, including both routing components and the nonlinear steady-state

power flow equations [4].

The main aim of this thesis research is to optimise/improve the process of PSRRP.

This goal was the main goal tackled in this thesis and covers the main idea behind

the thesis topic. However, there were side studies tied to this topic as well and they

were presented and covered in this thesis chapters. The main relevant subjects

studied were system reliability in restoration process and statistical analysis for

power system outages in the Australian power industry.

The optimisation concept is widely used in scientific research recently. It aims

to enhance the current practices in any scientific field. Thus, the optimisation

component in the thesis topic was our mechanism in dealing with the thesis topic

and its chosen relevant subjects presented in this thesis.

1.2 Thesis Topic Motivation

The restoration of power system after a large disturbance like a natural disaster

is an important process with large consequences on human and economic welfare.


Especially with the noticeable climate change in the world and the increase in bad

weather induced disasters. An example for the economic side, the economic loss

from San Diego 24-hour blackout in 2011 that was estimated by 100 million dollars

[4]. Also, large natural disasters such as the hurricane Sandy and Irene usually

cause a blackout that lasts up to a week leaving a huge portion of the population

without heating, air conditioning, lighting, refrigeration, telecommunication use,

etc. Hence, it is sensible that power system restoration is a main mission in

natural disaster recovery. The common used method in power system restoration

is called the “best practice’ in the field, which uses simple optimisation methods by

applying a power system restoration order devoted by governmental related sector

that is based on network utilization heuristic and then uses a greedy agent-based

routing algorithm that implement the restoration order [4].

Thus, the main motivation of this study is to tackle the probable benefits of math-

ematical programming for the repair and restoration of power system after a large

disruption. The objective of the mathematical applications on power system re-

pair and restoration studies represented in this thesis is to dispatch crews to repair

the power system affected elements in the system as quickly as possible objecting

minimising the size of the outage over time. It is known now that the large outages

last many days as the case of hurricane Irene in 2011. The power system repair

and restoration problem PSRRP is a very complex problem even when ignoring

all transient aspects and considering the steady-state behaviour of the power grid.

The problem is a large scale mixed nonlinear, nonconvex optimisation problem

when modeled globally. Additionally, the two subproblems of the PSRRP which

are the sequence of restoration and the repairs job scheduling are complex from

a computational point of view. Where the repair work scheduling is equivalent

to a pickup and delivery vehicle-routing problem minimising the sum of delivery

completing time periods [4].

In this thesis research we focus on how to use mathematical programming methods

to improve the “best practice” in the this field. This paper [4] which inspired

the thesis topic idea, proposes a scalable algorithm to the TSRRP based on two

stages approach that decouples the restoration order and the routing aspects of

the problem. The first stage is a restoration order problem ROP that finds the

restoration sequence that minimises the power outage size, ignoring the logistics

of scheduling repairs works. The second stage is a large-scale pickup and repair

routing problem that applies the restoration orders computed in the first stage.

Both stages are found to be computationally complex as mentioned in [4].


Figure 1.1: Illustration of a Restoration Process [21]

The restoration order problem ROP is a mixed nonlinear, nonconvex optimisation

problem as it considers the power flow equations for active and reactive powers.

Additionally, the power restoration process is applied when the power system is

damaged and when the objective is to restore and serve as much load as possible,

which is different from the traditional optimal power flow problems [4]. Thus,

solving the power flow equations is challenging in such conditions [7].

The second stage is the routing problem which is modeled mathematically in this

thesis. Our main reference [4] findings shows that a constrained program in ad-

dition to a large neighborhood search and a randomised adaptive decomposition

provide a scalable approach to scheduling the repairs. Their approach was not

investigated in this thesis, however, a similar mathematical approaches was devel-

oped and studied on specific benchmarks.

Additional motivation for studying this topic is the importance and criticality

of power system reliability especially in outages management. Costumers need

a reliable power supply and consider the power supply reliability an important

criteria when choosing their power provider.

Another motivation is that the high importance of having statistical analysis stud-

ies that rank the power utilities and represent the performance of these utilities to

the public, as well as providing a detailed answers to the utilities for where their

vulnerabilities are in order to enhance their services.


1.3 Thesis Contributions

The contributions of this thesis research are performed on many aspects of its topic.

We tried to cover the thesis topic fully. At first, we did an extensive literature

review for the topic. The literature review was done on hundreds of high quality

peer-reviewed references that tackle all possible sides of the problem and present

them to the readers in a clear an systematic way.

As recent research in power system repair and restoration is pushed toward a more

efficient restoration strategies, to save costs for both utilities and costumers. We

have developed mathematical programming methods for the problem to rise the

efficiency of power restoration process (i.e minimising the time of outage duration),

thus minimising the duration time of outage by improving the techniques of tack-

ling the whole restoration problem; then we applied them on different standard

IEEE systems. The mathematical representation used a common model (DCOPF)

for one of the studies, then we extended and enhanced the mathematical represen-

tation of the power system with an advance and more accurate model that takes

voltages magnitudes, line losses and reactive power (which are critical for contin-

gencies studies) into account called (LPAC-OPF) [8] in another study. We have

shown in these studies that used model that represents the operational/physical

aspects of the power system is a major variable in the results accuracy and relia-

bility. A major contribution of these two studies is showing that the restoration

problem can be approximated by a mixed integer program MIP which linearises

the power flow equations and represent the operational/physical aspects of the

power system in two different linear models.

Another important contribution of this thesis research was developing and imple-

menting an advanced heuristic method to assess the reliability of power distribu-

tion system under abnormal power restoration conditions such as cold load pickup

events (CLPU).

An additional contribution of this thesis research was studying the power system

outages using statistical methods which provides guidance to the power utilities in

Australia in terms of decision-making regarding the optimality of their networks

operations. Final contribution was assessing the probable benefits of smart grid

technologies in power outages prevention.


1.4 Thesis Organisation

The thesis content is systematically organised and presented as follows. Chap-

ter 2 presents the related works, Literature review of the thesis topic which gives

a comprehensive information about this thesis topic and all its related subjects.

Chapter 3 presents the related works, Mathematical Applications on Power Sys-

tem Repair and Restoration. In this chapter we present two application-based

studies on the problem, where one is a basic study and the next one is an im-

proved application of the same study. Chapter 4 presents the related works,

Reliability Analysis on Power System Restoration. In this chapter we present a

detailed reliability analysis for the system in restorative state under special con-

dition (CLPU). Chapter 5 presents the Statistical Analysis for Power System

Outages. In this chapter we investigate the Australian gird outages data and

present useful recommendations for the industry. Chapter 6 summarises our

findings and gives directions for future work.

In the next chapter, the related literature will be reviewed.

Chapter 2

Literature Review

With the rapid pace developments and improvements in the power industry tech-

nologies, new technical articles and research efforts addressing the raising power

system repair and restoration issues is brought out to the industry. Given the

recent focus of research activity on the Power System Restoration Problem PSRP

and the Power System Repair and Restoration Problem PSRRP, and the prolif-

eration of approaches adopted by them, a comprehensive review of methods and

techniques is needed. This chapter systematically and comprehensively reviews

work on the power system restoration problem and the power system repair and

restoration problem. The chapter covers almost all aspects of these two subjects.

The goal of this chapter is to clarify the problem nature and considerations, formu-

lation, and technical issues. The hope of the is chapter is to give new researchers

on the restoration and repair field a good understanding of the problem in order

to improve the current practice in the field.

2.1 Introduction

As stated in the first chapter, power system operators rely on pre-established

restoration schemes to restore/recover the network to its steady-state operation.

This involves the following steps: (i) evaluate system conditions, (ii) restart the

black start generators BSGU, (iii) create transmission path to power different non-

black-start generation units NBSGU, (iv) pick up the critical loads to soothe the

power network and (v) coordinate the islands formed by the outage. A typical

method to make this job simple is to split the power system restoration course

into steps (e.g. groundwork, system restoration and load restoration steps) [6].

8

Chapter 2. Literature Review 9

However, one mutual measurement connecting every one of these steps is the gen-

eration capability at every restoration step for soothing the network, creating the

transmission skeleton/path and recovering the load. Following a network black-

out, some conventional units will need a cranking/starting power from an external

source in order to be able to start. Other generation units might have time-

constraints so it can be restarted successfully or else they have to be off-line for

a long time, so-called minimum down times before they can be restarted and re-

synchronized to the power network. Consequently, it is vital that, through power

network restoration, to maximize the capability of the generation units available

in the system. Assuming that there are a limited number of black-start generating

units BSGU and many system constraints on different units, by finding the best

start-up sequence of all generating units available in the network, we can reach

the maximum accessible generation.

The power system repair and restoration problem PSRRP consist of sending off

crews/teams to fix damaged network elements to minimize the magnitude of the

blackout [4]. The PSRRP can be expressed as a multi-objective, multi-stage large-

scale combinatorial mixed nonconvex, nonlinear constrained optimisation problem,

which includes the routing elements and the nonlinear steady-state power flow

equations [4].

2.1.1 Power System Repair and Restoration

The first step in solving the PSRRP is to define the power system. In general, let

P be the power system comprising a set of B buses and L lines, P = (B,L), and

a graph G = (S,W ) where S are the locations of interest for restoration, and W

are the set of switches among these locations [4]. Each bus is categorized by its

real and reactive power desired. The line between every two buses is characterized

by its electrical admittance and line thermal capacity. A detailed, concrete model

is instantiated by defining the constraints that apply for a particular setting or

network. Specifically, all or some of the operational and engineering constraints

stated in Section 2.3.5 are applied to this optimisation problem based on the

system’s nature (transmission or distribution).


2.1.2 The Decomposition Technique

The PSRRP is best to be approached as a multi-stage problem for scalability

benefits, decomposing the power system restoration/operation and the routing

repair crews problem RRCP. The first stage comprises a set of load pickup problems

LPP named restoration order problem ROP which is independent of the second

problem the routing repair crews problem RRCP [9]. The second stage of the

PSRRP is an RRCP which receives a group of precedence constraints that deliver

a partial order from the ROP resultant repairs. The computational benefits of

decomposing the PSRRP in this way arises because the LPP/ROP can be treated

independently of the routing repair crews problem RRCP [4].

2.1.3 AC Load Pickup Problem AC-LPP

The optimisation problem could be formulated as follows:

max∑n∈N

plnln (2.1)

s.t. pgn − plnln =∑

(n,m)∈L

pnm ∀(n ∈ N) (2.2)

qgn − qlnln =∑

(n,m)∈L

qnm ∀(n ∈ N) (2.3)

pnm = v2ngnm − vnvmgnm cos(θn − θm)

− vnvmbnm sin(θn − θm) ∀(n,m ∈ L) (2.4)

qnm = v2nbnm − vnvmbnm cos(θn − θm)

− vnvmgnm sin(θn − θm) ∀(n,m ∈ L) (2.5)

p2nm + q2

nm ≤ S2nm ∀(n,m ∈ L) (2.6)

The optimisation objective fucnction (2.1) maximizes the active load served.

Constraints (2.2–2.3) represent Kirchhoff’s Current Law, the flow conservation.

Constraints (2.4–2.5) capture the active and reactive power flow on lines and

constraint (2.6) applies lines thermal limits.

The optimisation inputs are as follows: The power network P = (N,L), the

admittance between buses n and m, gnm and bnm, the required active and reactive

loads at bus n, pln qln, and the loading limit on line (n,m) Snm.


The optimisation variables are as follows: The phase angle of bus n, θn ∈(−∞,∞), the voltage magnitude of bus n, vn ∈ (vminn , vmaxn ), active power gen-

erated at bus n, pgn ∈ (pg(min)n , p

g(max)n ), and the reactive power generated at bus

n, qgn ∈ (qg(min)n , q

g(max)n ), percentage of active load served at bus n, ln ∈ [0, 100],

active and reactive power on line (n,m) , pnm qnm ∈(-Snm,Snm).

2.1.4 The Restoration Order problem

The first phase of the PSRRP is comprised of modeling an LPP as power system

restoration/operation problem. Where the objective is to obtain a steady state

solution for the system that pushes the system to accept as much load as feasible.

This operation is repeated R times where R is the set of damaged components

in the system. A precedence constraint M is injected from each previous LPP

solution to the follows LPP problem after repairing one system’s component each

time. This process is repeated until reaching the final steady state of the system

that comes after repairing the R set of damaged components. This process is also

called a restoration order problem ROP [4].

Figure 2.1: A sequence of restoration order problem.

2.1.5 The Restoration Problem

The power system main troubles are mainly triggered by transient faults and

natural disasters such as Hurricanes and primary happen in power transmission

systems. Many of these sources of supply interruption are because of temporary

faults like lightening, which is cleared instantly by the system protective relays.

However, in other cases, these short-term sources lead to cascading effects which

could be lasting and that may include the loss of generation units, loads and

interconnections. These following impacts may result in partial or complete failure

of the unfaulted sides of the power system. Consequently, assessing the system

status after fault may help to enhance restoration.

At the early phases of the restoration course, the system operator’s main objective

is to steady the network’s constraints and recover the key transmission system.

When the goal moves from sustaining proper situations for load recovering to


minimising the blackout effect, then the planned restoration technique might be

implemented. The main part in initial efforts to restoring power system is in

restart and rebuilding plans for generating units and transmission corridors in

conjunction to load pickup in these initial phases. Because that could help in

getting generators to their steady generation points and upholding the voltage

profile. To minimise the probability and period of major failures in bulk power

systems, initial preparation, remedial and restorative arrangements are essential.

In the past decades, the industry has commenced considerable efforts in these

areas. However, there is still need for additional efforts in the path of decreasing

the period of an outage.

2.1.6 Routing Repair Crews Problem

The second phase of the PSRRP decomposition approach is the routing repair

crews problem RRCP, which is approached as a vehicle routing problem (VRP).

The RRCP is also known as the pickup and delivery vehicle-routing optimisation

problem. This problem was studied for long-term in operations research [4]. Al-

though, for practical system sizes, it is hard to obtain an optimal solution for it,

especially when the objective function is to minimise the nominal transport time,

which is linked to the PSRRP objective function [4]. It was shown in [9] that mixed

integer programming MIP methods face major scalability issues. In addition, the

restoration objective, which is maximising the served load or minimising the black-

out size generalizes the optimal transmission switching problem, which was shown

to be difficult for MIP solvers [10]. Moreover, it was shown to be difficult even

with the use of linear approximations for the power-flow equations [4].

The RRCP receives two inputs from the ROP. The restoration sites graph rep-

resentation G and the group of precedence constraints obtained M . The RRCP

calculates a routing scheme for the repair crews that satisfies the stated problem

constraints and the precedence constraints received from the ROP. The objective

of the RRCP is to minimise the overall time of repair visits. Fig. 2.2 gives an

illustration for the PSRRP general framework.


Figure 2.2: A general framework for the PSRRP.

2.2 Power System Modeling for Restoration Study

Fundamentally, restoring or restarting a power system relies heavily on tools and

methods for modelling network transients and power-flows. These tools are essen-

tial to forming any restoration plan. Modeling the power system is the process

of forming an approximation of a real-world system. Modeling the power system

infrastructure is the first part of doing any study on the system such as planning,

operation, restoration etc. An accurate model results in more accurate results, al-

though it may lead to the need for more computational time. Consequently, there

is a trade-off between the results accuracy and the computational time required

[11]. These trade-offs are summarised in Tables 2.1 and 2.2. Thus, the power

system restoration results are only as accurate as the physical assumptions that

are made.

Table 2.1: Power system models and evaluation algorithms for operation stud-ies including Restoration [119].

Table 2.2: Power system operations planning timeframe [8].


2.2.1 Power Flow Tool in Restoration Study

The AC power flow equations of real and reactive power provide the main op-

erational constraints in restoration studies, as they are nonlinear and nonconvex

(see, for example, [Mhanna, PSCC, 2016]). Which even when given to a nonlinear

solver like IPOPT [12], it is not assured that it will converge to feasible results

or it may produce low-voltage results that are not practical in reality [13]. Thus,

linear approximations to the AC Power-flow equations have been introduced.

The AC power flow equations:

pnm = v2ngnm − vnvmgnmcos(θn − θm)

−vnvmbnmsin(θn − θm) ∀(n,m ∈ L) (AC1)

qnm = v2nbnm − vnvmbnmcos(θn − θm)

−vnvmgnmsin(θn − θm) ∀(n,m ∈ L) (AC2)

The most common approximation used in power system applications is the DC

Power flow model [14]. This model was derived through assumptions and simpli-

fications such as assuming the voltage magnitudes of two connected buses is 1.0

per unit, the conductance of the physical network is very small comparing to the

susceptance, and the reactive power is small and could be neglected comparing

to the real power. Additionally, the phase angle difference is assumed to be very

small. Consequently, The DC model can not measure reactive power, voltage mag-

nitudes, and system losses, which are very important aspects of the restoration

study.

That led the research community to try to introduce better linear approximations

such as the approximation called LPAC [9]. The LPAC model is derived through a

set of mathematical approximations and relaxation steps. This model successfully

considers the reactive power, line losses, and voltage magnitudes. Thus, it is

obviously performing better than the DC model in the case where the system is

weak and stressed as the situation in the restoration study. For more details on

the LPAC model refer to [9].

Another approximation approach is to develop efficient convex relaxations, with

the second-order cone programming (SOCP) and the semidefinite programming

(SDP) relaxations recieving much attention. The SDP relaxation is proven to be

exact or tight on a variety of case studies [15], [16]. However, in many practical


OPF instances, the SDP relaxation yields inexact solutions [17], [18], and more-

over, an AC feasible solution cannot be recovered from the SDP relaxed solution.

The main drawback of the SDP relaxation is that it cannot be readily embedded

in MIP models as easily as LP models. Similarly, much attention has recently been

given to the SOCP relaxation [19], [20], [21], [22]. One advantage of the SOCP

relaxation of the AC optimal power flow problem is that it is straightforward to

extend it to a mixed-integer quadratically-constrained program (MIQCP), to suit

applications with discrete variables, such as the PSRRP. More efforts have been

made to linearise the power-flow equations such as in [23].

All power-flow models such as DC model and LPAC model and other richer models

exhibit Braess’s paradox in RRCP.

Braess’s Paradox definition: Adding additional capacity to a system when the

moving objects selfishly [least resistance] choose their own route, can in some

cases reduce the over-all performance [24].

2.3 The Restoration Problem

Generally, many problems in power system restoration contain several actions

such as reactive power balance, load-generation balance, control, monitoring, pro-

tective system structures, energy storage systems, distributed energy resources,

planning, and training. To analyse the power system restoration problem, it is

good to mention the four different states of the power system as illustrated in Fig.

2.3 [25]. In the normal state, system reconfiguration could be done to minimise

losses, balance loads and advance operation efficiency. When the system operating

constraints are placed in jeopardy, the system will enter the pre-outage state, for

example, when an element is being overloaded such that protection devices may

disconnect it. Preventive actions in this state could take the network back to its

normal operational conditions. Some activities in the pre-outage state have the

same features of restorative state action. The power system will enter the outage

state when a component in the system is out of service, either because of a failure

or overloading. In this case, the component cannot go back to normal operation

conditions before the source of its outage is cleared. If the outage cause is cleared

it is likely for the network to go back to its normal operational condition. Other-

wise, the system will enter the restorative state which will deliver the best possible

service with the left system components. In case another outage occurs during the

restorative state that will move the system to the outage state again.


Figure 2.3: Power system operating states.

2.3.1 Goals and Steps in Power System Restoration

An illustration for the power system restoration steps and aimed goals are given in

Fig. 2.4 below [26]. Before going into details, we give an overview of the objectives

and strategies employed in the restoration problem.

Figure 2.4: Power system restoration steps and areas.

The restoration objective is to recover as much load as conceivable as fast as

possible starting from critical loads at the early stage of restoration in order to

steady the power network and coordinate the formed islands if there is any, which

is very different from the routing repair crews objective which is the minimum

travel distance between sites, that will be discussed in the routing repair crews

problem RRCP in later sections.

An applied strategy to simplify automatic power system restoration is to create

separate modules for generation, transmission, and distribution systems. These

parts are connected and synchronised over the strategy module for the recovering

of power networks [25]; see Fig. 2.5.

After a major disturbance in a power system, the generation capability must be

maximised in order to rapidly restore the whole power system. Though, it is a

complex combinatorial problem to optimise the utilization of available BSGU [25]

as we describe in later sections.


Figure 2.5: An example of power system restoration strategy.

2.3.2 Bulk Power System Restoration Issues

The distributed nature of the current electric industry is far different than the

original centralised and integrated industry. The formal combined electric system

construction (generation, transmission, and distribution) has changed, and these

components no longer belong to the same utility [27]. Nowadays, generation, trans-

mission, and distribution companies perform their operation independently. This

environment leads to a competitive electricity market which leads to more electric

power transactions along the transmission system. All these factors combined may

cause the bulk power system to work near to their design bounds, which leads the

system to be exposed to more possible blackouts. All these new policies intro-

duce new challenges to the power system restoration problem, which is already a

complex problem.

One of the leading efforts that addressed the bulk power system restoration prob-

lem was the power system restoration task force that was introduced by M. M.

Adibi et al [3] in 1987. Soon after that, a second task force report followed [28]

which was focusing on discussing the main problems in power system restoration

and different ways to enhance the process. Restoration schemes and strategies

differ based on the system characteristics, the system generating unit mix (steam,


hydro, gas turbines and combined cycles units), and the extent of the system’s

interconnection.

When designing a practical restoration plan, the initial settings of the network as

well as the issues that arise during the restoration process are of big importance.

One of the main measures of system stability is the network’s frequency. The

network’s frequency indicates the balancing state between the power supplied and

the loads.

The acceptable operation for the system is found by maintaining the frequency

nominal value during operation and make it limited to specific limits. Nevertheless,

because of the abnormal nature of the system during system restoration, it is

difficult to maintain a perfect balance between the supplied and the consumed

real power at all time stages. Also, due to the present network configuration and

the turbine-governor characteristics of the power plants, the load pickup amount

at any time point is limited.

From practice, it is being noted that when a load raise of 5 percent from the

synchronised system’s generation that leads to a 0.5 Hz decrease in the system’s

current frequency [3]. More discussion on the frequency-real power response is

introduced in [25].

Another major issue that arises during restoration is the voltage-reactive power

relationship. The voltage profile during restoration is of an important considera-

tion. In order to keep the system within normal operating conditions, the voltages

must be maintained between certain minimum and maximum values. Generally, a

good voltage profile is obtained by having enough reactive power sources that are

able to satisfy the systems requirements. The reactive power is usually provided

and/or adjusted by generating units, synchronous condensers, shunt capacitors

and other power system electronics. However, due to the nonlinear behaviour

of reactive power and the need to be sent on long distances, fulfilling the reac-

tive power balance is not easy. Furthermore, other phenomena’s in power system

restoration such as energising high voltage transmission lines results in charging

currents which cause an unexpected change in the system’s reactive power. The

mentioned unexpected changes are recognised as switching operations transient

voltages, which rise the voltage magnitudes to unsafe points subject to the trans-

mission line features. These issues along with others arise the importance of proper

allocation of reactive power sources and their control capabilities in order to ap-

ply a good restoration plan. More discussion on transmission corridors energising

could be found in [29].


An additional important issue in the restoration process is load pickup. When

some loads experience a failure and being de-energised for a while they usually ex-

perience some transients when reenergised. These transients are caused by inrush

currents and the loss of diversity. They commonly called cold load pickup CLPU.

The CLPU transients are affected by several parameters such as the weather and

the outage duration [30]. On a residential feeder, a representative performance for

the cold load pickup transients could be expressed as an exponentially decaying

function as can be seen in Fig. 2.6 [31].

Figure 2.6: Example of cold load pick-up transient over time.

Additionally, when reenergising a distribution feeder, close attention need to be

paid to the integral transients of loads. For example, reenergising a certain feeder

that has a large number of induction elements may lead to a voltage drop in the

feeder as a result of the reactive power requirements.

2.3.3 Restoration Problem in Transmission Systems

The problem of transmission system restoration is a major side of the power sys-

tem restoration procedure. Its importance initiate from the need of building the

restoration skeleton/path to enable the restoration of generation and distribution

network. The transmission skeleton is the main path that generation units follow

to pickup the proper amount of lost loads to maintain the balance among power

supplied and power consumed throughout the restoration course. The transmis-

sion system restoration problem is of a combinatorial nature. It contains mul-

tiple time-consuming switching functions to reenergise the stumbled high-voltage


transmission corridors. In general, the transmission network restoration is a mixed

variable problem, the transmission line status (i.e. connected or disconnected) is

binary and the other constraints are real numbers. Thus, the restoration problem

of the transmission network is formed as an optimisation problem that has multi-

ple objectives and subjected to operational and engineering constraints. Problems

faced in transmission system restoration include:

Energising high or extra-high voltage EHV transmission corridors lead to

over-voltages transients [32].

Energising unloaded or softly loaded EHV transmission corridors, or under-

ground cables will lead to constant frequency over-voltages [25].

Constant over-voltages could overexcite transformers, which may lead to

overheating or harmonic distortions, and may lead to generator self-excitation,

and instability [25].

Reenergising transmission lines can lead to a harmonic-resonance. The har-

monic resonance on long softly loaded transmission lines can lead to an

extremely high-voltage which could also be enlarged by transformer over-

excitation [33].

The switching operation of circuit breakers will lead to high transients.

Switching operation transients on lengthy HV transmission corridors, even

of a small period of time, can incur arrestor failures, especially if joined with

sustained over-voltages situations [25].

For the duration of the transmission system restoration, at any time, the

reactive absorption or the under-excitation capability of the generation units

in the power system is important to keep a good and steady transmission

line re-energisation [25].

For the period of the transmission restoration course, the issue of lag and

lead reactive power ability bounds of synchronous machineries in the re-

established network needs appropriate consideration. The mentioned limits

are significant to keep voltages under the acceptable limits for high charging-

current necessities of unloaded and softly loaded transmission lines, or for

the large reactive-currents drained by the start-up of the power system plant

ancillary engines [25], [34], [35], [36].


Most of these transient issues are addressed by manipulating the following control

variables:

Assuring adequate under-excitation capability on the generators.

Adjusting transformer taps.

Switching on shunt-reactors.

Considering loads with low power-factor.

Controlled islanding.

Since modifications to these control variables are influenced by the constraints

forced by plants and system operational requirements, the entire outcome of the

control variables would govern the decision if the transmission line could be reen-

ergised effectively or not [37], It is this coupling between the control elements that

makes the RP such a difficult problem to solve. Nevertheless, the transmission

lines considered for recovering might not be energised instantaneously, and for

every transmission switching process we must consider it solely based on many

factors such as Braess’s Paradox [24] and other network effects.

Many procedures that are dealing with the transmission system restoration differ-

ent issues discussed above can be found in the following references [38],[39],[40],[41],

[42], [43],[44],[45],[46], [5], [32],[47],[30],[48],[49],[50].

2.3.4 Restoration Problem in Distribution Systems

Distribution network restoration or typically named load restoration is the field

of interest in recent years. This increased interest is a normal outcome of new

practices related to deregulation, marketing and the technical advances used in

the distribution network. The restoration problem in general aims to minimise

the impact and duration of the outage by discovering the best sequence of healthy

distribution feeders that should be recovered. This problem is similar to the unit

commitment problem UCP [51]. The distribution network restoration problem

with the UCP exhibit similarities in nature and structure which might advise that

the two problems are duals of each other [25].

Some issues in distribution system restoration problem might be because of these

parameters [25]:


Combinatorial nature of the problem.

Bulky network dimensions and a large number of integrated devices.

Distributed generation units.

Several operational objectives that might be opposite to each other.

The need for fast network restoration.

The likability of suboptimal solutions.

The problem of distribution network restoration aims to re-establish the service

after the outage and minimise its impacts on economic and human welfare. This

mission is started once a significant portion of the transmission system has been

recovered to a sable state. In this process, the fluctuations in the system’s fre-

quency and voltage control are not the main concern for the system’s operator

since some generation and loads have been connected. However, there are several

challenges facing the operator due to the different decision variables in the opti-

misation formulation, the large dimension of the network and the combinatorial

nature of the problem. More discussion on issues in distribution system restora-

tion could be found in the following references, load estimation [52], loss reduction

[53], distribution network reconfiguration [54], among others.

2.3.5 Restoration Optimisation Problem Formulation

The main goal of service restoration/recovering is to restore/recover as much dis-

tribution network loads as we can considering the critical loads first by minimising

the out-of-service load zones. This could be done by shifting the de-energised loads

through system reconfiguration to different healthy feeders in the system with no

violations to the operational and physical constraints of the system.

As mentioned in previous sections, the power system restoration optimisation

problem could be expressed as a mixed nonlinear, nonconvex, combinatorial, con-

strained problem with the following possible objectives [55]:

Maximising the summation of power transfer capability.

Maximising the restored power to the unfaulted areas.

Minimising the switching operations.


Minimising the losses in the created network.

Minimising the total time of the restoration process.

These possible objective functions are subjected to a whole or a partial set of the

following constraints based on the restoration system:

Voltage limits.

Frequency limits.

Power balance constraints for both real and reactive power.

Power-flow equations.

line thermal limits.

Current limits.

Load constraints.

Switching time.

Loads priority.

Time of finding restoration solution.

Reliability.

Feasibility.

Man-machine interface.

Radiality (specific for distribution networks restoration problems).

Transient Stability.

Generators ramp rates.

Feasibility of islanding.

A major task in finding a restoration plan is formulating these constraints in

a tractable mathematical representation. This consideration was touched on in

Section 2.2, with respect to power-flow tools. More generally, in the past, the

more common methods used were knowledge-based (KB) and expert system (ES),


and they were deployed and used for specific systems. After 1993 power system

restoration studies started using and applying other non-traditional techniques

[55] including heuristic, optimisation-based and automated restoration planning

methods, as discussed next. After this, we discuss some of the many technical

issues that arise in restoration problems.

2.3.6 Methodologies and Analysis in Restoration

Given to the operational problems identified in power system restoration, studying

the problem for off-line planning or on-line/near on-line operations is significant.

Studying the power system restoration problem needs an accurate model for the

system as mentioned in previous sections, and the use of many analytical tech-

niques. These techniques must consider the static, transient and dynamics of the

network to be able to yield a suitable restoration plan. Thus, to provide restora-

tion plans that can support the operator in decision-making through power system

restoration, many methods and techniques were applied in the bulk power system,

transmission system, and distribution system as follows:

KB System [56],[57],[58],[53],[59],[60],[61],[62],[56] methods usually need un-

usual software implements where their repair and upkeep are unfeasible for

the electric power business.

ES [63],[64],[65],[53],[61],[66],[67],[68],[69],[70],[37],[71],[72],[73],[74],[75] is a

smart software that use human-knowledge and interpretation actions to

tackle problems that are very hard to the point they necessitate substan-

tial human knowledge to obtain an answer to the problem. However, this

method is dependent on human expertise in the field but unlike human be-

ing software and programs will not learn from their experiences thus, the

human-knowledge must be collected and coded in a proper coding language.

Heuristic Methods [76],[77],[78],[79],[80],[81],[54],[82],[77] were applied exten-

sively to resolve this problem, however, the computations need extra time

than available in practice through the restoration process.

Soft Computing Methods such as Petri net [83],[63],[84],[85],[86], artificial

neural networks [87],[88],[89],[87, 90], fuzzy logic [63],[91],[52],[92],[93],[94],

genetic algorithm [95],[96],[97], [98],[99], Tabu search [100], Artificial Intel-

ligence [101],[102],[103],[104], ANT colony search algorithm [105],[106],[107]


are original methods that impersonate the system operator movements. Nev-

ertheless, the lack of accuracy may not lead to an accurate solution at a

critical time such as in the restoration study.

Some common optimisation techniques have been used to deliver more pre-

cise solutions. Most of them rely on: mathematical programming [108],

dynamic programming [109], mixed-integer programming method [110],a

restoration index [111], Benders decomposition [112], and Lagrangian re-

laxation [113]. These optimisation methods need a suitable and accurate

model to reach global optimality.

Hybrid Models [114],[115],[116],[117],[118], [119],[120],[121] it was observed

from the literature that there is a necessity for development to the current

restoration methods. As some algorithms are simple but provide a subopti-

mal solution other give accurate solutions but they are complex. To reach an

improvement in the current techniques, one algorithm should complement

the other. Thus, many algorithms have been merged together in order to

reach an improved performance and meet the industry needs.

2.3.7 Technical Issues in Restoration Problem

There are many issues arise during the system restoration. They include all

restoration areas; generation, transmission, distribution, operations, and compu-

tation. In this section, we will cover some of the main problems and issues during

system restoration.

2.3.7.1 Generators Start-up Sequence Problem

Generation units are categorised into two types, the Black Start Units BSGU and

the Non-Black Start Units NBSGU. The BSGU has the ability to start by itself,

examples for this type are combustion turbine units and Hydro units. On the other

hand, the NBSGU does not have this ability and needs a starting power to be pro-

vided from an external source to be able to start, an example of this type is steam

turbine units. As mentioned in previous sections, a main objective of the restora-

tion problem is to maximise the network’s generation capability so that it could

be utilised to crank the NBSGU in the system during the restoration/recovering

process.


The network’s total generation capacity is the sum of the MW capacity left after

subtracting the total start-up needs. The NBSGU have many physical require-

ments and characteristics such as the critical maximum and minimum time inter-

vals constraints. An NBSGU with critical minimum time interval constraint will

not be able to restart till the time interval finishes. Also, if it cannot start in the

critical maximum time interval constraint, it may not be accessible till after some

time delay. In addition, all NBSGU have a start-up power prerequisite constraint,

that means they could be restarted only when the system has enough cranking/s-

tarting power. The generators start-up sequence problem could be expressed as

an optimisation problem with an objective function of maximising the total gen-

eration capability which is subjected to the previously mentioned constraints. For

more see reference [25].

2.3.7.2 Cold Load Pickup

The cold load pickup has a main concern, which is the uncertainty of the load fore-

casting because of the unidentified configuration of loads at the time of restora-

tion. Reference by Adibi in [30] gives a general framework for modeling and

classifying the loads during restoration. Many studies were done to explain the

cold load pickup problem in system recovering/restoration [122], [123]. There are

many other issues that require the attention of the system operator during sys-

tem restoration, in addition to the main issues, voltage, frequency, load pickup

coordination. Some of these issues are, standing phase angle reduction [124],

protection schemes [125], overvoltage control [33], reactive power limitation in

synchronous machines [35], intentional islanding, local load shedding, switching,

generating units sequencing, remote cranking power, and excessive alarms during

system restoration [30], [126]. Many of these problems are due to the system’s

characteristics, whereas others are due to the interface between different variables

during system restoration.

2.3.7.3 Parallel Restoration

It was shown that parallel restoration method is a good way of speeding the system

restoration process. Parallel restoration consists of the following three steps:

Sectionalising the power system to subsystems (Microgrids).

Restoring the formed islands separately.


Synchronisation of the formed islands throw tie-lines.

The parallel restoration method is commonly used in power system utilities. And

it faces the same issues mentioned in previous sections. The main criteria to decide

whether the parallel restoration method can be implemented and feasible is that

the availability of BSGU and their geographical locations in the system. When

the feasibility criteria of parallel restoration are found then it is time to define the

boundaries of the created islands in a systematic way, which can efficiently speed

up the restoration process [25]. When a decision has been made to use the parallel

restoration method, splitting the system needs to satisfy the following conditions:

Each island must have at least one BSGU, where they must be coordinated

based on each unit sequence and the starting power capability.

In every formed island, the generation-load balance should be maintained as

much as possible.

No transmission capacity limits should be violated [25].

2.4 The Routing Repair Crews Problem

As stated in Section 2.1, the RRCP is the second stage of the PSRRP decomposi-

tion approach, which is approached as a vehicle routing problem. In this part we

will illustrate the RRCP formulation and its computational considerations.

2.4.1 The Routing Repair Crews Problem Formulation

The main goal in the routing repair crews process is to rout the repair teams

efficiently in order to repair the damaged components as fast as possible. The

routing repair crews problem could be expressed as a combinatorial optimisation

problem with an objective function of minimising the nominal delivery time.

These objective function is subjected to a whole or a partial set of the following

constraints based on the system needs:

available resources;


travelling time;

repair time;

damage type;

routing crew skills; and

vehicle capacity.

Figure 2.7: A general framework for routing repair crews problem.

Figure 2.8: A representation for the impact of routing repair crews perfor-mance on power system.

Fig. 2.7 shows a general framework for the routing repair crews problem. This

figure illustrates an instance of the problem with two repair crews. Where each

crew is assigned to visit specific resources pickup sites and repair sites with specific

time frame. For example, crew 1 starts at the start point in the depot and visits


the resources pickup sites A+ and B+ and carry a specified resource based on the

vehicle’s capacity, then reaches site C− at Time = 25 and repair it, then reaches

the next site D− at Time = 35 and repair it. The same process happens for crew

2.

It can be seen from Fig. 2.8 that the power restored to the system is 50 percent

at Time = 25 (where C− site is repaired). Also, it can be noted that repairing

site F− does not contribute positively to the power restored to the system, that

can highlight the Braess Paradox phenomenon. This phenomenon is addressed

well in the model presented in reference [4]. We can observe that the full power

restoration could not be reached before repairing site D− at Time = 35.

2.4.2 RRCP Computational Considerations

The RRCP is computationally difficult as mentioned in previous sections. Mixed

liner Programming MIP with the Constrained Programming CP approaches have

difficulty in finding optimal solutions, even for small systems. However, it was

shown in [4] that a combination of CP along with Large Neighborhood Search

LNS are proved to be effective and scalable in finding optimal solution even for

complex large-scale routing problems [127], [128]. There are four types of the LNS:

Random, Spatial, Temporal and Vehicle neighborhood. The random neighborhood

search was proved to be the best strategy in selecting the routing sites [129].

However, it was shown that a combination of LNS with the Randomized Adaptive

Decomposition RAD can improve the RRCP solution significantly [130].

The key difference between LNS and RAD is that the routing problem using RAD

is compeletly broke down, consequently the search space is smaller [4]. More

advanced spatial and temporal decouplings were investigated in [130]. As a result,

RAD was recommended to solve the RRCP in [4].

2.4.3 Technical Issues in Routing Repair Crews Problem

There are problems and issues realted to the routing repair crews problem, in this

section we will cover the main one.


2.4.3.1 Stockpile of Resources

The National Infrastructure Simulation and Analysis Center NISAC in Los Alamos

national laboratory in the USA has delivered a procedure in dealing with natural

disasters impacts on electric infrastructure. They use Hurricane Katrina as a

general example. The procedure has two steps:

Pre-Disaster: NISAC aim is to focus on providing situational awareness.

Post-Disaster: Highlights the need for a decision support tool that helps

in mitigating negative impacts and guides to use the available resources

efficiently.

Thus, NISAC was required to provide a ”fast response” analysis and decision

support tool when a disaster has occurred or is pending. In the fast response

procedure on how to stockpile power network elements through a state to minimise

the restoration time following a natural disaster [131], many issues have risen:

The stochasticity of the disasters.

The optimum locating of the capacitated warehouse.

The routing repair crews problem.

The modeling of the nonlinear power system.

The fast solution requirement (minutes/hours, not days) [131].

The main task is how to stockpile power system elements through a state to

minimise the restoration time after a natural disaster. Because of the problem

difficulty, stochasticity, and runtime constraints, obtaining an optimal solution

is very hard. The key goals of their effort are to overcome the quality of the

current best practices and bound the quality of the solution using mathematical

relaxations [131].

Given the disaster recovery equipment such as warehouses with fixed storage ca-

pacity, a fixed-size vehicle fleet, and a stochastic set of disaster scenarios, each with,

destroyed power system elements (which need repair times), location-to-location

travel times. The disaster recovery objectives are: preparation costs (money),

minimising the blackout size (welfare), the restoration time (distance) [131].

Therefore, the disaster recovery main questions are:


Where to optimally locate the recovery supplies?

How much of each elements to stockpile?

In a specific disaster, how to deliver a fast recovery plan? [131]

A research effort has been made to address these questions. Carleton Coffrin et

al [131] have made a good job on that. They named the problem, Power System

Stochastic Storage Problem PSSSP. Their paper introduced an original application

in determining how to store power system elements through an occupied area

where the objective is to maximise the total power restored following an outage.

Their applied approaches reached a better solution comparing to the common best

practice in the field.

2.5 Conclusion

This chapter provides an in-depth review and investigations for a large number of

published articles in the field of PSRRP. An overview of the concepts of the PSRRP

has been provided. This chapter studies the power system repair and restoration

problem PSRRP, which is a generalisation of the transmission system repair and

restoration problem TSRRP and the distribution system repair and restoration

problem DSRRP. It covers almost all aspects of the system restoration problem

and system repair problem. All issues in the PSRRP have been investigated.

PSRRP historical development, formulation, objectives, and main concerns.

In addition, it addresses the literature developed over the years in dealing with

the problem issues and aspects. All operational characteristics and computational

tools have been analysed and categorised based on the recent advancements and

achievements in the field. A major application of this chapter is to illustrate the

problem for new power engineers and researchers, as they will lead the future work

in the industry.

Chapter 3

Mathematical Applications on

Power System Repair and

Restoration

In this chapter, the application-based studies of this thesis research will be pre-

sented and discussed fully.

3.1 Mathematical Approach for Solving Power

Transmission System Repair and Restora-

tion Problem

3.1.1 Introduction

Severe weather conditions and natural disasters increase highlights the need of im-

proved restoration methods of power systems. The literature has several research

efforts that tackles the power system restoration [132], however, more high-level

research on new restoration schemes is needed.

The focus of this study is optimising the power-flow in transmission system, and

routing repair crews (RRC) optimally. The problem was first examined in [133],

the study suggested a multi-stage style that decouples the power-flow and RRC

problems. The paper proposed two sub-problems to find a minimised set of ele-

ments that could lead in recovering the system to its full capacity, and discover an

32

Chapter 3. Mathematical Applications on Power System Repair andRestoration 33

optimised restoration order that could help to minimise the outage duration. Ref-

erence [134] has provided an extension for this study, by proposing a randomised

adjustable vehicle decomposition method in order to solve large-scale problems.

In this study, we present a mathematical approach for solving the transmission

system repair and restoration problem (TSRRP) with no decomposition. A mixed

integer linear program (MILP) is modelled to pickup as much loads as possible.

In this study we have modelled the operational constraints of the system using

the linearised (DCOPF). The RRC to damages problem was modelled as a vehicle

routing problem (VRP). Where the VRP is modelled as a combinatorial optimi-

sation and integer programming approach that seeks finding the a fleet of vehicles

best route [135], [136], [137].

Repair teams start their jobs from central bases called depots, then, they visit the

damaged elements to perform repairs and after finishing their jobs they travel back

to their central stations where they started. The travelling and repair times have

been considered in the model. The rapier teams can carry a certain amount of re-

sources to perform their jobs. The State-of-the-Art k-means clustering algorithm

was used to help finding the optimal locations of each depot in the system among

clusters.Using this algorithm can assure that the repair teams are strategically lo-

cated which will enhance the recovery rate of the system. When a system element

get damaged, the TSRRP algorithm can find the repair teams and system gener-

ators scheduling. It is important to mention that generators damages are ignored

in this study, as it is sensible to presume that on-site repair teams will handle their

damages. A similar study [138] tried to implement the same approach. We found

out that the paper has major errors and mistakes in formulating the problem and

presenting results. Thus, in our study, we tried to enhance and verify the approach

by testing it on a different transmission system and justify the obtained results

well.

The developed approach is assessed using the standard IEEE 30-bus power trans-

mission system. We have compared the TSRRP results with a standard method

where the RRC and power-flow optimisation are decoupled.

3.1.2 Proposed Approach

The developed approach consists of two stages: distributing central stations (de-

pots) by elements clustering, and TSRRP. Every central station (depot) has a


number of repair crews/teams available along with needed resources such as man-

power, equipment, vehicles, etc. to manage the damages to the system. Every

depot is positioned by the k-means clustering method, where depots locations are

the midpoints of each cluster. A State-of-the-Art k-means clustering algorithm was

developed in such it considers the number of depots and the locations of power

system elements.

Figure 3.1: K-Means Clustering Algorithm Procedure.

When a power outage happen, a damage assessment study is to be done to specify

the damaged elements state and predict the time needed for repairs. Afterwards,

it is time to send the repair teams to the sites of damages to repair and restore/re-

cover damaged system elements. Every repair team travels through an optimised

route to reach the damaged elements. Fig. 3.2 gives an example of the TSRRP.

Figure 3.2: Example of repair crews routing and service restoration.

3.1.3 Mathematical Formulation

A co-optimisation frame for the TSRRP is implemented and a MILP problem.

Where it couples the power transmission system operational aspects and RRC

problem. Maximising the loads pickup subject to sizes and importance was our


objective function as shown in (3.1). The optimisation problem can be formulated

as follows:

max∑∀t

∑∀i∈ΩB

ωDi ρi,tPDi,t (3.1)

0 ≤ PGi,t ≤ Pmax

i , ∀i ∈ ΩB, t (3.2)

− uLkPmaxk ≤ Pk,t ≤ uLkP

maxk , ∀k, t (3.3)

Bk (θi,t − θj,t)− PLk,t ≥ −

(1− uLk,t

)M, ∀k, t (3.4)

Bk (θi,t − θj,t)− PLk,t ≤

(1− uLk,t

)M, ∀k, t (3.5)∑

k∈K(i,.)

Pk,t + PGi,t =

∑k∈K(.,i)

Pk,t + ρi,tPDi,t ,

∀i ∈ ΩB, t

(3.6)

ρi,t+1 ≥ ρi,t , ∀i ∈ ΩB, t (3.7)∑j∈N\i

xi,j,c −∑

j∈N\i

xj,i,c = 0 , ∀c ∈ RC, i ∈ N (3.8)

∑j∈N\0

x0,j,c −∑

j∈N\0

xj,0,c = 1 , ∀c ∈ RC (3.9)

∑j∈N\dp,c∈RC

xj,dp,c = nc (3.10)

∑c∈RC

yi,c = 1 , ∀i ∈ N (3.11)

yi,c =∑

j∈N\0,i

xi,j,c , ∀c ∈ RC, i ∈ N (3.12)

ResCc ≥∑∀i∈N

ResNi yi,c , ∀c (3.13)

ATi,c + ri,c + tri,j,c − ATj,c ≤ (1− xi,j,c)M ,

∀i ∈ N\ dp , j ∈ N, c ∈ RC(3.14)

∑∀t

fi,t = 1 , ∀i ∈ N (3.15)

∑∀t

tfi,t ≥∑c∈RC

(ATi,c + ri,cyi,c) , ∀i ∈ N (3.16)

∑∀t

tfi,t ≤∑c∈RC

(ATi,c + ri,cyic) + 1− ε, ∀i ∈ N (3.17)


0 ≤ ATi,c ≤ yi,cM , ∀i ∈ N, c ∈ RC (3.18)

zi,t ≤t−1∑τ=1

fi,t , ∀i ∈ N, t (3.19)

nbiuBi,t ≥

∑k∈BUi

uLk,t,∀i ∈ NB, t (3.20)

uLk,t ≤ zk,t , ∀k, t (3.21)

uBi,t ≤ zi,t , ∀i ∈ NB, t (3.22)

fi,t, uBi,t, u

Lk,t, xi,j,c, yi,c,

zi,t, ρi,t ∈ 0, 1 , ∀c, t, k, i ∈ N(3.23)

3.1.3.1 Power System Operation

Power system must satisfy its operation constraints, such as thermal limits, power-

flow, power balance etc. DCOPF model is utilised to program the power trans-

mission system operational aspects. Constraints (3.2) and (3.3) represents the

generators and lines thermal limits. A binary changeable variable that represent

transmission line status is multiplied by the thermal limit constraint to force the

power-flow in the line to zero in case the line is damaged. The power-flow approxi-

mation DCOPF is modelled in (3.4) and (3.5). Using big M, the above-mentioned

constraints make sure when a certain line is out of service, its bus angles is not

constrained. By constraint (3.6) the power balance in every point is enforced.

Also, it is assumed that if a certain load is restored, its supply of power stays, that

was enforced by (3.7).

3.1.3.2 Routing Repair Crews

The RRC goal is to obtain the best route for every repair team to navigate to

fix damaged elements at approached points/nodes. The points in every area are

specified in a general set N = 0, 1, ..., dp, where 0 and dp represent the start and

return points. NB and NL are the subsets that contain the affected busbars and

lines. Set RC represents repair teams in every area. ri,c is the needed repair time

for every damaged element. The needed time by each repair team to move from a

damaged element to another is indicated by tri,j,c. If the crew c moves from node i

to node j then xi,j,c equals to one. The binary variable yi,c equal to 1 if the repair

team c visits point i. ATi,c indicates the arrival time of the repair crew c at node


i. The direction-flow constraints represented in (3.8) and (3.9) make sure when

a repair crew arrives to point i it leaves that point, and assures that the repair

team will not return to its start point. Constraints (3.10) and (3.11) ensures that

each repair team starts from a certain depot then travels back to it. Constraint

(3.12) presumes that each damage is repaired by one team only. Constraint (3.13)

guarantees that if team c navigates via direction xi,j, then the binary variable yi,j

equals to one.

3.1.3.3 Availability of Resources

Constraint (3.14) represent the resources constraint, which ensures that every

repair crew has the required resources from their depots to perform their tasks.

3.1.3.4 Evaluating Damages

The required time to fix a damaged element in the system that is represented by

the binary variable tfi,t , is found through summing the travelling times and fixing

times. Constraint (3.15) represent time of arrival of each crew at every point in

the region. If the binary variable tfi,t equals to one, then the damage element is

restored. Constraint (3.16) makes sure that tfi,t equals to one when the element

is fixed only.

Constraints (3.17)-(3.18) represent the recovering time [tfi,t] . If point i is not

reached by team c then ATi,c equals to zero, that is represented by constraint

(3.19), that is important as that ATi,c will not conflict with constraint (3.17).

Constraint (3.20) implies that the recovered element stays ON for the subsequent

time frames, where zi,t equals to one implies that element i is ready. Constraint

(3.21) serves to de-energise all transmission lines linked to a damaged busbar.

Constraints (3.22) and (3.23) link the RRC problem with the power transmission

system operational constraints by setting uLk,t and uBi,t to zero if the damaged

component is not fixed.

3.1.3.5 Decoupling Approach

In order to assess our approach we used a commonly used decoupling approach

to compare the results with. Many research efforts in the literature decouples the


TSRRP into two subproblems, optimising the RRC first then optimising the power

flow in the system. The RRC is formulated as follows:

min∑∀t

∑i∈N

t fi,t (3.24)

Subject to

Constraints (3.8)− (3.20)

fi,t, xi,j,c, yi,c, zi,t ∈ 0, 1 , ∀c, t, i ∈ N (3.25)

Where the objective function is to minimise the time of restoration as presented in

(3.24). And when finding and completing the predicted times of restoration and

the schedules of routes for repair crews, the results of the binary variable zi,t are

to be utilised in optimising the power-flow of the system, that was modelled as

follows:

max Equation (3.1)

Subject to



uBi,t, uLk,t,∈ 0, 1 , ∀t, k, i ∈ NB (3.26)

The Decoupling Approach splits the RRC and power flow optimisation problems,

which in many cases cannot assure the optimality of solutions.

3.1.4 Results and discussion

The developed model is assessed on the standard IEEE 30-bus power transmission

system [139] as shown in Fig. 3.3. The k-means algorithm is programmed in

MATLAB and the MILP model is formulated in AMPL and resolved by CPLEX

12.9.0.0 on a PC with Intel® Core i7-8650U 1.90GHz 2.11GHz CPU and 8 GB

RAM. The time needed to repair a damaged element depends on the repair crew

skills. The travelling time, as the travelled distance dependant, varies from few

minutes to a number of hours. The time scale is 30hours with a 1-hour time-step.


Figure 3.3: IEEE 30-bus transmission system.

3.1.4.1 Depots Distributing

Step one is to assign the locations of depots using the k-means clustering algorithm.

It was assumed that the positions of buses and line are given. Also, it was supposed

that the X and Y coordination of several locations are given and select to place

two depots for repair crew. The clustering process is completed and its findings

are presented in Fig. 3.4. Depot number one is placed in the midst of buses 22

and 24, and depot two is placed in the midst of buses 4 and 6.

3.1.4.2 Results using TSRRP Approach

To make it easy to understand, we have randomly picked 5 buses and 5 lines to

be considered damaged components. Seventeen transmission lines linked to five


Figure 3.4: Cluster assignments and depots.

Table 3.1: Locations and capacity of the generators.

affected busbars are considered out of service. It was assumed that each depot of

the two available has two repair crews and every repair team is able to take 30

resources units. Generators dataset are shown in Table 3.1, also the required data

of loads and lines in given in [139].

Table 3.2: Summary of damaged components.

Table 3.2 shows the affected elements in the system. The required resources and

repair times for each crew is specified randomly among repair crews. The trans-

mission system repair and restoration problem is solved using the TSRRP model

illustrated in Section 3.1.3. The solution was obtained in 46 seconds. Table 3.3


reveals the found route for every repair team. Repair team 1 fixes the damaged

transmission line between buses 6 and 28 after 8 hours. This damage is prioritised

as the generator at bus 11 is out of service till this damage is repaired. Afterwards,

the same repair team moves to line 27 and fix it, that is finished after 14 hours.

Crew 2 goes the path N2 → N7 → N4 → N5 and finishes fixing jobs after 29

hours. The damage N5 is fixed at another time due to the fact that total it does

not affect the amount of restored loads. Repair crew 3 is assigned to fix N9 and

N3 , and Crew 4 is scheduled to fix N6 and N1. Whole loads are supplied after

16hours, that is accomplished by fixing N2, N3, N6 to N10. The other elements

are fixed in the sake of restoring the full system. Table 3.3 presents a time-frame

of the availability of all restored elements. All damages are fixed after 29 hours.

Table 3.3: Repair crews path for TSRRP.

Table 3.4: Times when each component is available for TSRRP (variable zi,t).


3.1.4.3 Results using Decoupling Approach

To prove the good performance of the developed TSRRP model. We have com-

pared the solution with the Decoupling Approach method presented in Section

3.1.3.5. The repair crews routing sequence is shown in Table 3.5.

Table 3.5: Repair crews path for decoupling approach.

Table 3.6: Times when each component is available for decoupling approach(variable zi,t).


Figure 3.5: Total restored loads for TSRRP and Decoupling Approach.

3.1.5 Conclusion and future work

This section presented a co-optimisation approach for transmission system repair

and restoration problem. The study proposed a MILP formulation to coordinate

repair crews and system generators to pick-up the maximum possible loads after a

damage. The developed model was implemented on an IEEE 30-bus power trans-

mission system. The findings are compared to a different optimisation method.

The results prove the advantages of the developed approach (TSRRP) in restoring

all loads in 16 hours comparing to 20 hours in Decoupling Approach.

Currently, the industry depends on power system operators and power engineers

experience in case of a power outage to optimise the power-flow for the system

and the repair crews dispatching process. A co-optimised approach such as the

proposed TSRRP can enhance the process of power system repair and restoration

after damages as shown in this study.

Possible future work includes using new and more accurate approximation of the

AC optimal power flow such as linear-programming models (LPAC) [140], and

many others [141] that incorporate reactive power and voltage magnitudes in a

linear power-flow approximation. Also, implementing the developed approach in

electrical distribution systems with the presence of distributed generators. As well

as, implementing the proposed approach on larger systems that simulates real life

scenarios.


3.2 Advanced Approach for Solving Power Trans-

mission System Repair and Restoration

3.2.1 Introduction

Climate change and the increase in natural disasters induced by bad weather

illustrates the need of new and more accurate methods to restore electric power

systems. The literature has several research efforts that tackles the power system

restoration [132], however, more high-level research on new restoration schemes is

needed.

The focus of this study is optimising the power-flow in transmission system, and

routing repair crews (RRC) optimally. The problem was first examined in [133],

the study suggested a multi-stage style that decouples the power-flow and RRC

problems. The paper proposed two sub-problems to find a minimised set of ele-

ments that could lead in recovering the system to its full capacity, and discover an

optimised restoration order that could help to minimise the outage duration. Ref-

erence [134] has provided an extension for this study, by proposing a randomised

adjustable vehicle decomposition method in order to solve large-scale problems.

In this study, we present an advanced and more accurate method for solving the

power transmission system repair and restoration (TSRR) with no decomposition.

A mixed integer linear program (MILP) is modelled to pickup as much loads

as possible. The more accurate and advanced linear approximation of power-

flow LPAC optimal power-flow (LPAC-OPF) is used to represent the operation

constraints of the power transmission system. The RRC to damages problem was

modelled as a vehicle routing problem (VRP). Where the VRP is modelled as a

combinatorial optimisation and integer programming approach that seeks finding

the a fleet of vehicles best route [135], [136], [137].

Repair teams start their jobs from central bases called depots, then, they visit the

damaged elements to perform repairs and after finishing their jobs they travel back

to their central stations where they started. The travelling and repair times have

been considered in the model. The rapier teams can carry a certain amount of re-

sources to perform their jobs. The State-of-the-Art k-means clustering algorithm

was used to help finding the optimal locations of each depot in the system among

clusters.Using this algorithm can assure that the repair teams are strategically lo-

cated which will enhance the recovery rate of the system. When a system element


get damaged, the TSRRP algorithm can find the repair teams and system gener-

ators scheduling. It is important to mention that generators damages are ignored

in this study, as it is sensible to presume that on-site repair teams will handle their

damages. A similar study [138] tried to implement the same approach. We found

out that the paper has major errors and mistakes in formulating the problem and

presenting results. Thus, in our study, we tried to enhance and verify the approach

by testing it on a different transmission system and justify the obtained results

well.

The developed approach is assessed using the standard IEEE 30-bus power trans-

mission system. We have compared the TSRRP results with a standard method

where the RRC and power-flow optimisation are decoupled.

3.2.2 Proposed Method

The proposed method comprises of two phases: distributing depots by clustering

repair crews, and TSRR. Every crew depot has its assets such as manpower, gear,

repair vehicles, etc. and a number of repair teams offered to handle the damages

to the network. The repair crews depots are distributed using state-of-art k-means

algorithm, where the spots of depots are the centres of the clusters. The k-means

clustering procedure was created in such it takes into account the number of depots

and the positions of power system parts.

Figure 3.6: K-Means Clustering Algorithm Procedure.

Once a power outage happens in the system, a damage assessment study is to be

done. The aim of this analysis is to investigate and determine the damaged parts

state and forecast the required repair times.


Afterwards, the accessible repair teams are to be sent to the damaged elements

locations to repair and restore the power network. Each repair team has an op-

timised direction to go to the damaged parts. Fig. 3.7 gives an example of the

TSRR.

Figure 3.7: Example of TSRR operation.

3.2.3 Problem Formulation

A co-optimisation frame for the TSRRP is implemented and a MILP problem.

Where it couples the power transmission system operational aspects and RRC

problem. Maximising the loads pickup subject to sizes and importance was our

objective function as shown in (3.27). The optimisation problem can be formulated

as follows:

max∑∀t

∑∀i∈ΩB

ωDi ρi,tpDi,t (3.27)

0 ≤ pGi,t ≤ pmaxi , ∀i ∈ G, t (3.28)

− uLk pmaxk ≤ pk,t ≤ uLk pmaxk , ∀k, t (3.29)

− uLk qmaxk ≤ qk,t ≤ uLk qmaxk , ∀k, t (3.30)

qgn = 0 , ∀n ∈ N\G (3.31)

qn =

n6=m∑m∈N

−qTnm + qδnm , ∀n ∈ G (3.32)

θ0s = 0 , φs = 0 (3.33)

pn =

n6=m∑m∈N

pTnm , ∀n ∈ N , n 6= s (3.34)


qn =

n6=m∑m∈N

qTnm + qδnm , ∀n ∈ N , n 6= s , n /∈ G , ∀(n,m), (m,n) ∈ L (3.35)

[pTnm](k,t) = |V Tn |2gnm − |V T

n ||V Tm |(gnmcosnm + bnm(θ0

n − θ0m)) ≥

−(1− uLk,t

)M, ∀k, t

(3.36)

[pTnm](k,t) = |V Tn |2gnm − |V T

n ||V Tm |(gnmcosnm + bnm(θ0

n − θ0m)) ≤(

1− uLk,t)M, ∀k, t

(3.37)

[qTnm](k,t) = −|V Tn |2bnm − |V T

n ||V Tm |(gnm(θ0

n − θ0m)− bnmcosnm) ≥

−(1− uLk,t

)M, ∀k, t

(3.38)

[qTnm](k,t) = −|V Tn |2bnm − |V T

n ||V Tm |(gnm(θ0

n − θ0m)− bnmcosnm) ≤(

1− uLk,t)M, ∀k, t

(3.39)

qδnm = −|V tn |bnm(φn − φm)− (|V t

n | − |V tm|)bnmφn (3.40)

cosnm = PWLA((cos(θ0n − θ0

m),−π/3 , π/3)) (3.41)∑k∈K(i,.)

pk,t + pGi,t =∑

k∈K(.,i)

pk,t + ρi,tpDi,t ,

∀i ∈ G, t(3.42)

ρi,t+1 ≥ ρi,t , ∀i ∈ G, t (3.43)∑j∈N\i

xi,j,c −∑

j∈N\i

xj,i,c = 0 , ∀c ∈ RC, i ∈ N (3.44)

∑j∈N\0

x0,j,c −∑

j∈N\0

xj,0,c = 1 , ∀c ∈ RC (3.45)

∑j∈N\dp,c∈RC

xj,dp,c = nc (3.46)

∑c∈RC

yi,c = 1 , ∀i ∈ N (3.47)

yi,c =∑

j∈N\0,i

xi,j,c , ∀c ∈ RC, i ∈ N (3.48)

ResCc ≥∑∀i∈N

ResNi yi,c , ∀c (3.49)

ATi,c + ri,c + tri,j,c − ATj,c ≤ (1− xi,j,c)M ,

∀i ∈ N\ dp , j ∈ N, c ∈ RC(3.50)

∑∀t

fi,t = 1 , ∀i ∈ N (3.51)

Chapter 3. Mathematical Applications on Power System Repair andRestoration 48∑

∀t

tfi,t ≥∑c∈RC

(ATi,c + ri,cyi,c) , ∀i ∈ N (3.52)

∑∀t

tfi,t ≤∑c∈RC

(ATi,c + ri,cyic) + 1− ε, ∀i ∈ N (3.53)

0 ≤ ATi,c ≤ yi,cM , ∀i ∈ N, c ∈ RC (3.54)

zi,t ≤t−1∑τ=1

fi,t , ∀i ∈ N, t (3.55)

nbiuBi,t ≥

∑k∈BUi

uLk,t,∀i ∈ NB, t (3.56)

uLk,t ≤ zk,t , ∀k, t (3.57)

uBi,t ≤ zi,t , ∀i ∈ NB, t (3.58)

fi,t, uBi,t, u

Lk,t, xi,j,c, yi,c,

zi,t, ρi,t ∈ 0, 1 , ∀c, t, k, i ∈ N(3.59)

3.2.3.1 Operation of Power Transmission System

Power transmission system must has its operation/processing constraints met, such

as system thermal limits, power-flow, power-balance etc. The LPAC-OPF model

is applied to program the power transmission system operation. Constraints (3.28)

and (3.29) characterizes the output restrictions of generators and transmission lines

respectively. A binary adjustable variable that symbolise the status of the trans-

mission line is multiplied by the thermal limit constraint to drive the power-flow in

the line to zero in case the line is damaged. The power-flow linear approximation

LPAC is modelled in LPAC Constraints presented in Section 3.2.3. Using big M,

the above-mentioned constraints make sure when a certain line is out of service,

its bus angles is not constrained. By constraint (3.42) the power balance in every

point is enforced. Also, it is assumed that if a certain load is restored, its supply

of power stays, that was enforced by (3.43).

3.2.3.2 Repair Crews Routing

The RRC purpose is to obtain the best route for every repair team to navigate to

fix damaged elements at approached points/nodes. The points in every area are

specified in a general set N = 0, 1, ..., dp, where 0 and dp represent the start and

return points. NB and NL are the subsets that contain the affected busbars and


lines. Set RC represents repair teams in every area. ri,c is the needed repair time

for every damaged element. The needed time by each repair team to move from

a damaged element to another is indicated by tri,j,c. If the crew c moves from

node i to node j then xi,j,c equals to one. The binary variable yi,c equal to 1 if

the repair team c visits point i. ATi,c indicates the arrival time of the repair crew

c at node i. The direction-flow constraints represented in (3.44) and (3.45) make

sure when a repair crew arrives to point i it leaves that point, and assures that

the repair team will not return to its start point. Constraint (3.46) ensures that

each repair team starts from a certain depot then travels back to it. Constraint

(3.48) presumes that each damage is repaired by one team only. Constraint (3.47)

guarantees that if team c navigates via direction xi,j, then the binary variable yi,j

equals to one.

3.2.3.3 Resources Availability

Constraint (3.49) represent the resources constraint, which ensures that every

repair crew has the required resources from their depots to perform their tasks.

3.2.3.4 Damages Evaluation

The required time to fix a damaged element in the system that is represented by

the binary variable tfi,t , is found through summing the travelling times and fixing

times. Constraint (3.50) represent time of arrival of each crew at every point in

the region. If the binary variable tfi,t equals to one, then the damage element is

restored. Constraint (3.51) makes sure that tfi,t equals to one when the element

is fixed only.

Constraints (3.52)-(3.53) represent the recovering time [tfi,t] . If point i is not

reached by team c then ATi,c equals to zero, that is represented by constraint

(3.54), that is important as that ATi,c will not conflict with constraint (3.51).

Constraint (3.55) implies that the recovered element stays ON for the subsequent

time frames, where zi,t equals to one implies that element i is ready. Constraint

(3.56) serves to de-energise all transmission lines linked to a damaged busbar.

Constraints (3.57) and (3.58) link the RRC problem with the power transmission

system operational constraints by setting uLk,t and uBi,t to zero if the damaged

component is not fixed.


3.2.3.5 Decoupling Methodology

To test our proposed method we used a known approach that is commonly used to

compare our results with. Lots of studies in the literature decouples the TSRR into

two subproblems, optimising the RRC problem first then optimising the power-

flow in the network. The RRC is prepared as follows:

min∑∀t

∑i∈N

t fi,t (3.60)

Subject to


fi,t, xi,j,c, yi,c, zi,t ∈ 0, 1 , ∀c, t, i ∈ N (3.61)

Where the objective function is to minimise the time of restoration as presented in

(3.60). And when finding and completing the predicted times of restoration and

the schedules of routes for repair crews, the results of the binary variable zi,t are

to be utilised in optimising the power-flow of the system, that was modelled as

follows:

max Equation (3.27)

Subject to



uBi,t, uLk,t,∈ 0, 1 , ∀t, k, i ∈ NB (3.62)

This Decoupling Style divides the RRC and power-flow optimisation processes.

That is usually found to be less accurate and cannot guarantee the optimality of

results.


3.2.4 Results and discussion

The developed model is assessed on the standard IEEE 30-bus power transmission

system [139] as shown in Fig. 3.8. The k-means algorithm is programmed in

MATLAB and the MILP model is formulated in AMPL and resolved by CPLEX

12.9.0.0 on a PC with Intel® Core i7-8650U 1.90GHz 2.11GHz CPU and 8 GB

RAM. The time needed to repair a damaged element depends on the repair team

abilities. The travelling time, as the travelled distance dependant, varies from few

minutes to a number of hours. The time limit is chosen to be 30 hours with a

one-hour step.

Figure 3.8: IEEE 30-bus transmission system.


Figure 3.9: Cluster assignments and depots.

3.2.4.1 Depots Allocation

Step one is to assign the locations of depots using the k-means clustering algorithm.

It was assumed that the positions of buses and line are given. Also, it was supposed

that the X and Y coordination of several locations are given and select to place

two depots for repair crew. The clustering process is completed and its findings

are presented in Fig. 3.9. Depot number one is placed in the midst of buses 22

and 24, and depot two is placed in the midst of buses 4 and 6.

The results for depots allocation is persistent with the first study presented in

Section 3.1, which is sensible because we used the same state-of-the-art clustering

algorithm on the same system.

Table 3.7: Location and capacity of system generators.

3.2.4.2 TSRR Methodology Results

To make it easy to illustrate our study, we have arbitrarily picked 5 buses and

5 transmission lines to be deemed damaged parts. 17 lines linked to 5 damaged


busbars are de-energised. It was presumed that every depot of the two offered has

two repair teams and every repair team can have 30 pieces of resources. Generators

information are provided in Table 3.7, and the needed data about loads and lines

can be obtained from [139].

Table 3.8: Damages numbers and damaged elements.

Table 3.8 lists the damaged parts in the network. The necessary resources and

repair times for every team is listed at random with repair teams. The repair

and restoration is solved with the TSRR version illustrated in Section 3.2.3. The

solution was found in 40 seconds.


Table 3.9 introduce the observed route for every repair team. Table 3.10 displays

the time when every element is accessible. All damages are fixed after 22 hours.

Table 3.9: Repair crews paths for TSRR.

Table 3.10: The time when each element is available for TSRR (variable zi,t).


3.2.4.3 Decoupling (Route First) Methodology Results

To validate the good implementation of the created TSRR version. We have

compared the solution with the Decoupling Approach method AKA (Route First)

introduced in Section 3.2.3.5. The repair crews routing directions of the Route

First method is displayed in Table 3.11.

Table 3.11: Repair crews paths for Decoupling Methodology.

Table 3.12: The time when each component is available for DecouplingMethodology (variable zi,t).


Figure 3.10: Total restored loads for TSRR and Decoupling Methodologies.

3.2.5 Conclusion

This study introduced a co-optimisation style for power transmission system repair

and restoration using an advanced and more accurate model for the power-flow.

The study suggested a MILP template to manage repair teams and network gen-

erators to pick-up the maximum feasible loads after a damage. The template

was applied using a more accurate and advanced linear approximation of optimal

power flow (LPAC-OPF) compared to the commonly used model DCOPF that was

published in [142] and presented in Section 3.2 of this thesis. The created model

was applied on a modified IEEE 30-bus power transmission system. The findings

is compared with a different commonly used optimisation method (Route First).

The outcomes prove the improvements and accuracy of the created methodology

(TSRR) in re-establishing all loads in 22 hours comparing to 23 hours in the

Decoupling Approach.

The reader can observe that using the more accurate and advanced linear model

of power-flow (LPAC-OPF) has enhanced the TSRRP results in both of the opti-

misation methods and helped to restore the system in shorter time comparing to

the DCOPF model.

At Present, the industry hinges on power system operators and power engineers

experiences when a power outage happens, in order to optimise the repair and

restoration of the power network. A co-optimised approach such as the proposed

TSRR combined with more accurate and advanced model for the power-flow can

enhance the practice of power system repair and restoration after damages as

demonstrated in this chapter’s sections.

Chapter 4

Reliability Analysis in Power

System Restoration

In this chapter, a very important aspect of PSR will be presented and discussed

(Reliability Analysis).

4.1 Introduction

The power distribution system is considered the main important part of power

system as it has to fed the load directly. These loads are the residential, com-

mercial and industrial. In these loads-based distribution systems, the reliability

of the residential distribution system is lesser as compared to the commercial and

industrial. The quality of power feeding to these loads has gained importance due

to the introduction of deregulated electricity to these loads. The cost of operation

of these systems also includes the reliability cost nowadays. The cost is paid by

the utility companies if the grid is less reliable. This cost is yielded by the utilities

directly in the form of compensation paid to customers or indirectly by some other

means [143]. There are certain parameters regarded as the reliability indices that

are adopted for the reliability assessment of power distribution system. These are

system average interruption frequency index (SAIFI), system average interrup-

tion duration index (SAIDI) and energy not supplied (ENS). These reliability

indices are accessed with different techniques presented in the literature. The

techniques involve both simulation and analytical methods. The most commonly

used simulation technique is the Monte Carlo Simulations and these determine

the system reliability on the basis of system failures history and maintenance data

57

Chapter 4. Reliability Analysis in Power System Restoration 58

[144]. Contrarily, these reliability indices do not include the non-component-based

failures such as cold load pickups or embedded failures of the system. Thus, from

this fact it is clear that these reliability indices do not completely represent the

reliability of the distribution system.

The thermostatic controlled loads are responsible for the occurrence of cold load

events and these require a high sudden load demand. It will result in single step

restoration of the system and in many cases of the restoration it is impossible.

These high stresses on the system will lead to a violated operation of the system

and will not follow the required protection limits. In the absence of proper planning

for the cold load pickups, the equipment associated with this operation will be

damaged. In addition to these damages, it also causes unnecessary restoration

that are not acceptable for the proper operation of system within its stability

limits. However, the system restoration is possible only with the help of the low

concentration of total connected load (TCL) and low power demands for the TCL.

The other procedure for the restoration of the system dynamics is the sectionalising

of the system [145].

The CLPU phenomenon in power distribution systems was first time presented in

1979. The physical model of the load facing CLPU was developed and is presented

in [122]. The factors affecting the CLPU in power distribution system are presented

in [146]. The factors that causes the occurrence of these events involve the system

outage duration, ambient temperature, thermostat setting, thermal insulation of

house and the customer behaviour. The CLPU studies on the main distribution

transformer of the system are presented in [147]. From these studies it is found

that voltage limits following CLPU are violated but no other protection limits are

affected. In [148] the exponential decay studies are performed on the distribution

transformer facing CLPU and it is suggested to enhance the transformer size after

restoration because of thermal stresses faced by transformer during the process

of restoration. Thus, with these outcomes and several damages and effects faced

due to CLPU an optimal research technique was introduced that addressed these

transformer constraints. It resulted in the formation of artificial neural network-

based algorithms that addressed these problems. Firstly, Genetic Algorithm (GA)

was opted in order to solve these problems [145]. The other scheme introduced was

the adjacent pairwise interchange for optimal restoration when subjected to these

cold load pickup events [31]. The GA is also capable for optimal restoration of the

system when it is also using distributed generation and the thermal stresses it has

to face with cold load pickups. The Monte Carlo simulations for the determination

of the stochastic behaviour of loads and its impacts on the optimal restoration of


the system are presented in [149]. These simulations are also utilised in order to

find the other reliability indices and is presented in [31]. The SAIFI calculations

were made in [150] and also the effects of cold load pickups were found. On the

other hand, the SAIDI calculations were made on the similar platform but no

CLPU were found. This represents that these calculations are varyingly affected

by the dynamic nature of the CLPU.

Optimisation algorithms are used to solve these problems. An advanced Light-

ning Search Algorithm (LSA) is presented in this research in order to tackle this

problem. This algorithm is also based on natural optimisations and possess sim-

ilar but fast and advanced operational behaviour to the GA and Particle Swarm

Optimisation (PSO) algorithm. This LSA algorithm is applied to several electrical

applications and analysed in the papers [[151],[152],[31]]. This research algorithm

formulates the research problem that includes the cold load pickup (CLPU) and

includes the reliability indices of SAIDI, CAIDI and ENS. The occurrence

rate is also determined by the utilisation of CLPU and it includes the SAIFI

calculations for the system as well, that yields the system optimal performance.

This chapter is formulated in different sections and first of all includes the design

of utility scheme that is capable of bearing CLPU events. The reliability indices of

the power distribution system had been determined on the basis of the stochastic

behaviour of the load, system protection and stable operation of the system. Then

the A-LSA algorithm will be used to solve the problem in the form of complex

optimisation problem and optimises the restoration time of the system. The re-

sults taken from these simulations shows that the proposed strategy is a powerful

solution in order to get efficient and robust operation when subjected to cold load

pickup events. The results are also compared with the previously proposed (LSA)

form [153] and it confirms the effectiveness of the proposed methodology.

4.2 Load Modelling

The load for this research will be modelled stochastically. The stochastic modelling

of the load is made by the utilisation of the time of use curves (TOU). The Amer-

ican houses utilisation of the energy is presented in [154] and it is collected for the

research purpose by NREL (National Renewable Energy Laboratory). These mea-

surements are hourly rate energy utilisation measurements. These hourly delayed

exponential model of the utilisation of energy with cold load pickup is presented

in the figure below:


Figure 4.1: A general figure for delayed exponential model with CLPU.

The AC load of the residential distribution system depends on the ambient tem-

perature, the probability of the use of curves are formulated and are presented

below:

AC Load Status =

Prob > 0 if T > TU or T < TD

Prob = 0 otherwise

As the AC load modelled above is dependent on the lower and higher values of

the temperature, the TU is presenting the upper limit of the temperature while

the TD is representing the lower limit of the temperature. The probability of the

utilisation of AC loads increases as the dead environmental time increases. The

dead ambient time is the difference of the high ambient time and lower ambient

time. Initially, the TOU curves are developed for all the electric appliances and

these curves are adjusted for the two commonly used multipliers. The multipliers

for which the power distribution system is modelled are the demand factor and load

factor. After this, the number of units are found for each load of the residential

distribution system. The number of AC loads utilised in this study are the 70

percent of the load point divided by the power rating of the power device. Thus,

for 1MW load 580 loads are used with 1.2kW each of the AC load point. The

reactive power compensation of the system is also of the importance as the power

factor for the system load usage is almost about 0.8 to 0.9 and the fall in the power

factor of the system requires the reactive power compensation so that the system

may operate within its stable operating limits. The exponential model of the load

is shown in Fig. 4.1 and the mathematical modelling of the load with the CLPU

points is presented below:

S(t) = SD + (SU −SD)e−α(t−t1)u(t− t1) +SD([1−u(t− t1)]u(t− (Ri− ti))) (4.1)


In the equation above the α represents the decay factor and state as the rate

of decay. The diversified demand before the outages of the equipment from the

power distribution system is represented as SD. The undiversified demand after

the restoration of the system from the outages faced due to the CLPU is states

the power SU . Thus, the total SU power can be represented in the form of below:

SU = kSDTCL + SDNTCL (4.2)

The factor ‘k′ in the above equation is presented in the form below:

k =ln( toutage

0.107)

1.101(4.3)

It states the empirical relation when the CLPU events has been occurred in the

system and the relation exist between the outage duration and demand taken

by the load. The factor ‘k′ is representing the increase in the demand. This

increase in the demand is only affected by the load variation possessed by the

TCL. This demand variation is also shown in the Figure 4.1 presented above. The

other important parameters variation caused by the customer behaviour, thermal

variation due to variation in the ambient temperature are presented in the research

paper [122].

4.3 Problem Formulation

4.3.1 Mathematical Formulation

The optimal restoration plan is considered during the mathematical formulation

for the reliability indices measurements with the inclusion of the CLPU events.

The failure is faced in the system and after elapsing this failure time, the program

is modelled to run for a suitable time for restoring the load affected by such events.

The mathematical problem formulated for this purpose is presented below:

min

(k∑1

TTRl −k∑1

TTRi

)(4.4)


In this statement the TTR represents the time to restore the ith load point when

the ‘k′ number of load points are out of service. The adjusted TTR is the sum of

the total TTR considering them without CLPU and the additional time that is

to be waived by the system for the restoration. Thus, we can say that this is sum

of multiple at the different load points and can be written in the form presented

below.

k∑1

TTRl =k∑1

TTRi + tr1 + tr2 + tr3 · · ·+ trn (4.5)

Thus, our objective function can be rewritten in the form presented below:

min (tr1 + tr1 + tr1 + . . . trn) (4.6)

All the reliability indices SAIDI, CAIDI and ENS are minimised with the min-

imisation of the restoration time followed by the technique presented in this re-

search. However, the SAIFI is not affected if the number of failures is not affected.

The above research problem is subjected to following constraints:

The maximum loading on the transformer should not exceed the 125 percent

of the provided rating. This is regarded as the protection system constraint:

ST ≤ 1.25pu (4.7)

The voltage of the system should not vary above and below the 5 percent

of the rated voltage value. This is regarded as the operational constraint of

the system:

0.95 ≤ Vi ≤ 1.05 ,∀i ∈ [1, N ] (4.8)

The reliability indices of the power distribution system for the complete time

assessment with the cold load pickup points of the different load points are stated

in the statements given below:

SAIFI =Total number of all interruptions

Total number of customers connected=

∑Ni

NT

(4.9)


SAIDI =Total duration of all interruptions

Total number of customers connected=

∑OiNi

NT

(4.10)

CAIDI =SAIDI

SAIFI(4.11)

Thus, the ENS reliability index of the system can be stated as shown in (4.12).

ENS =∑

PiOi (4.12)

In the above equations the NT is the total number of customers at each load point

and Ni is stating the total number of the interruptions and the average power that

would be supplied during interruption is presented as Pi. When CLPU events are

faced by the system then duration of restoration of the system is changed and it

is represented as Oi.

4.3.2 Selected Test System

In this study the radial power distribution system is presented and this system is

shown in the figure presented below. The feeders presented in this distribution

system has the property that it can restore all the feeders at once. The main

transformer of the feeder is of main importance and its total size is determined by

the running the load model. The maximum duration for this is presented for the

time period of 20 years.

Figure 4.2: Radial power distribution system.

The power demand of this system is 6.74MVA and this is 60 minutes power de-

mand, thus, it utilises the standard size transformer of 5MVA. If the protection

constraints of the system are considered then the required power for the system

will be 8.125MVA at the required full load current value of 125 percent.


The power required in the distribution system will be 8MVA for the load flow

analysis of the system. The length of the main feeder in this system is 600m. This

complete feeder length is further divided into four sections. The other sections of

the distribution system are of 200m and these sections include 1,2,3,8,9 and 10

load points. All other remaining sections of the distribution system are taken as

300m and these are underground cables.

4.4 Proposed Methodology

4.4.1 Monte Carlo Platform

The methodology in order to perform these simulations is presented in the chart

given below. The reliability indices are found by the usage of the MC platform.

The simulation is carried for the period of 200 years. The up status for the

electrical appliances is considered at the beginning of the simulations (T = 0),

The uniformly distributed generated unit is utilised to find the time to repair and

time to fail.

TTR =−1

rln(U) (4.13)

TTF =−1

γln(U) (4.14)

Initially, the simulations are carried out for the period of 200 years without con-

sidering the CLPU and the system analysis is performed and then the TTR is

found with inclusion of the CLPU events. This includes the optimal restoration

plan that is capable to reduce the restoration time such that it does not violates

the opted constraints. The A-LSA algorithm is utilised to calculate these TTR

and TTF . These time to restore and time to fail modified values with the help of

the A-LSA algorithm will be injected back to the power distribution system and

it enhances the operation capability of the system.

4.4.2 LSA and A-LSA Optimisation Platform

The optimal restoration of each outage at any load point in the power distribution

system is done by the utilisation of the Lightening Search Algorithm (LSA) and


the advanced A-LSA. They both works with uniform initialisation with random

population. This uniformly initialised population is regarded as the transition

projectiles. The A-LSA algorithm is capable to produce the results in a step wise

sequence and the nth step of the A-LSA algorithm for the presented system is

given as:

ESLn = [tr1, tr2, tr3 + . . . trn] (4.15)

This is representing the system of ‘k′ load points (LP) and the outage is faced

radially in this system. This can be elaborated in such a way that LP8, LP9 and

LP10 will be simultaneously affected with the outage faced at the load point 8.

The transition periods of the projectiles in the A-LSA algorithm will be tr8tr9 and

tr10. As the outage is occurred at the load point 8, the tr8 will be in the duration

from 0 to tr. Then further tr9 will lie in the duration from tr8 and TM . On the

other hand, the tr10 will occupy the duration from tr9 and TM . These transitions

are followed in the form of step ladder. The ‘n′ multiple step ladders adopted by

the A-LSA algorithm are presented in the equation below:

ESLs = [esl1, esl2, esl3 + . . . esln] (4.16)

Thus, the exponentially distribution of the objective function can be presented as:

rn+1ri = rnri ± exprand(u) (4.17)

In the best step ladder, the difference between the reference projectile and depen-

dent projectile is represented as ‘u′ and is utilised in the equation above. The

best projectile ladder regarded as the lead projectile is in the form of the normal

distribution function is presented in the equation below:

rn+1ri = rnri ± normrand(u, σ) (4.18)

The α is the scaling parameters in the equation above. This utilises the forking

process of lightning search algorithm. The forking is the secondary process of the

A-LSA algorithm, it redirects to search and yields different solutions within the

prescribed space of the system. There are two ways to perform forking within the

A-LSA algorithm.


A general flow chart of the developed advanced lighting algorithm is presented in

the figure below [155]. This algorithm contains some additional steps as compared

to the previously proposed LSA algorithm used in our main comparative reference

[153] in order to enhance the efficiency of the solution of the investigated problem.

Figure 4.3: General flowchart represents the fundamental mechanisms for theAdvanced LSA Algorithm.


4.5 Results and Analysis

4.5.1 Load Model Results

The load model results of the power distribution system are taken on the basis of

the time to use (TOU) curves of the electrical appliances. These TOU curves are

yielded from the multiplication of load factor with the demand factor. This value

is measured to have a value of 0.285 in Saudi Arabia. The thermostat settings

possess the upper and lower values of temperature. The upper temperature of

TU = 22o and the lower values of the temperature is TD = 20o. The measured

TOU curves for the different electric appliances are presented in the figure below.

Figure 4.4: Time to Use (TOU) curves of different customers.

The results of stochastic model of residential distribution system based on the

above presented (TOU) curves are presented in the figure below. These stochastic

curves are taken for two different load picks on the different time durations, i.e.

for Summer and Winter days. For the Winter day it is taken for January 1 and

for Summer day it is taken for August 1. This is incorporating human behaviour

that is directly incorporated with the ambient temperature effect of the system

TOU curves that caused by the heating and cooling phenomenon of the system.

The simulation is carried for 200 years and load demand for every minute over

this duration is produced at each load point. The cold load pickup model of the

test system is presented in the figure below. This modelling is done with the

time deviation of δt = 30min with the α parameter variation of 0.5hr−1. From

the curves, it can be concluded that, at the restored points, the power demand is


Figure 4.5: Model for Summer day and Winter day.

enhanced two times than the normal power demand. Thus, it results in the increase

of power demand on the main distribution transformer of the power system.

Figure 4.6: CLPU curves of the distribution system.

4.5.2 Optimal Restoration of One Outage Resulting in CLPU

The peak demand that occurs due to the outages in the system results in violation

of protection and operational limits of the system. But this does not happen with

all the outages that causes the peak rise in the system peak power limits that

violates the prescribed system limits. The 3485879-minute event in the system

duration is the point at which the failure faced and it tripped the load points LP1,

LP2 and LP3. In this case the power was supposed to restored after 482 minutes.

This was actually the outage faced due to outage of section 1. The low TCL

concentration was main responsible for this outage. From Fig. 4.7 it is observed

that with this outage no violation limit is made and no CLPU event is happened

and it takes just a single step to restore to original point. This phenomenon of

restoration is presented in the figure:


Figure 4.7: Low TCL demand and restoration after extended outage.

The outage occurred at the time 36630989 is important as at this point cable

of section 8 faces an outage and this part remains out of the system for almost

5hrs. It has been observed that in this outage all the peak points were recovered

within voltage stability limits. The voltage limits were violated as the system lower

voltage limit is fallen below the 0.9487. Thus, the A-LSA algorithm proposed for

this outage works for the optimal restoration of the system. Thus, the A-LSA

algorithm is powerful algorithm for optimal restoration when system is subjected

to outages.

Figure 4.8: Low bus voltage restoration without planning.

The A-LSA algorithm is the optimisation algorithm and run for five times for the

optimal restoration for such outage with different parameters followed. It followed

the generation number 100, population number 50, forking probability 0.01, chan-

nel time 10 and maximum restoration 500 minutes. The optimal restoration plan

for the affected load points is in the form of summary presented in Table 4.1:.

The optimal restoration with the Advanced Lightning Search Algorithm is shown

in Fig. 4.9. However, optimal restoration with power and voltage profile is pre-

sented in the Fig 4.8. This restores the maximum power without violation of


Table 4.1: Results for A-LSA and LSA optimisation algorithms.

voltage and power constraints and limits of the system.

Figure 4.9: Optimal load restoration with A-LSA algorithm.

The comparison of the advanced lightning search algorithm and conventional light-

ening search algorithm is presented in Fig. 4.10. The convergence rate of the

advanced lightening search algorithm is faster than the previous presented algo-

rithm. Thus, this algorithm is capable to restore the outage values at a faster rate

as compared to the previous algorithm.

4.5.3 Reliability Assessment Results

In order to assess the reliability of the system, different analysis are performed.

This includes the inclusion of system failures and unavailability at different load

points. The 10 different load points are included for this simulation study. This

simulation is carried in the duration from 15684183 to 15685455 minutes. In this

duration, the affected elements of the system are main transformer, feeder circuit


Figure 4.10: Comparison of converging between the Advanced LSA and pre-vious LSA algorithm.

Table 4.2: Results for A-LSA and LSA optimisation algorithms.

breaker, main circuit breaker, section 8, 9 and 10 of the system. It is observed

that the outage faced at section 8 of system caused the load outage of the section

10 of the system due to radial nature of the system. The reliability indices are

calculated.

The reliability indices determined and the calculated values for these indices are

presented in the table below:

Table 4.3: Reliability indices values for A-LSA and LSA optimisation algo-rithms.

In Table 4.3, the reliability indices i.e. SAIDI, SAIFI, CAIDI and ENS are

increasing and this verifies that these are real time values and present the real time


Figure 4.11: For sample duration, status of sections 9 and 10, and LP10.

simulations. And this is summarised in the table presented above. The reliability

indices are also calculated for the time variation of different values, i.e. for the

time 20 minutes, 30 minutes and 60 minutes for restoring the equipment without

violating the system operating and protection limits as presented in Table 4.4.

4.6 Discussion

In this chapter the reliability indices are calculated for a typical power distribution

system with cold load pickup points. The 200 years simulation is carried out

in order to find the reliability indices for the system. The A-LSA algorithm is

used for the optimal restoration of the system after it has subjected to outages

or contingencies. These reliability indices parameters of the system include the

SAIFI, CAIDI, SAIDI, and ENS measurements.


Table 4.4: Reliability indices values for A-LSA and LSA optimisation algo-rithms for different procedures.

The reliability effect was about 66kWh/year with an average of 19.806 minutes

per failure with considering the cold load pickups. However, this time is subjected

to variation when larger power systems are considered. The occurrence of the

CLPU in the system is an important phenomenon that directly affects the optimal

restoration of the system. The CLPU failures in the SAIFI calculations are

performed by considering every CLPU failure. Thus, with this environment of

calculation only SAIFI calculations of the system are affected. The optimal

restoration is regarded with multiple time schedules. If 20min restoration plan is

adopted then the SAIDI calculations varies by 27.7 kWh/year for the durations

of 7 minutes. The other time variation is presented in the table presented above.

The optimal restoration is obtained with the adoption of A-LSA algorithm for the

system optimal recovery. The robustness comparison of A-LSA is made with the

LSA algorithm and the A-LSA algorithm is found be effective in every aspect of

the operation of the system facing the CLPU events.

4.7 Conclusion

In this chapter the reliability assessment of power distribution system is per-

formed. The key parameters that are considered for this study are SAIFI,

SAIDI, CAIDI and ENS. These parameters are initially measured with LSA al-

gorithm and the optimal restoration of the power distribution system is analysed.

Then the algorithm is modified to A-LSA as presented in the flow chart above, this

was found to improve all of these parameters and system dynamic behaviour when


the system is subjected to cold load pickups. All of these dynamic operational pro-

cedures are verified by implementing this algorithm on the power distribution in

MATLAB. Thus, this modified advanced lighting search algorithm is found to be

effective in restoring the power distribution system when it is subjected to cold

load pickups.

Chapter 5

Statistical Analysis for Power

System Outages

In this chapter, a related subject to PSR will be presented and discussed. (Outages

Analysis).

5.1 Introduction

There is a big debate around the world among policy makers for the benefits

of smart grid technologies to the power grid. Thus, as a result, it is our rule as

researchers to study and analyse the problem in a scientific and data-driven way in

order to guide the policy makers to make the right and optimal decisions towards

the power grid future. This study is aimed to be directed to the Australian power

grid, but the results could be generalised to any power grid around the world.

Studying power outages events can enable us to investigate important queries such

as if the power outages are decreasing with the increasing deployment of smart grid

technologies. There has been a large amount of money deployed by governments

to fund smart grid assets around the world. The goal of these investments is

to increase the reliability of electric systems. Many studies on power outages

usually focus on large individual events because of the discomfort they cause to

the public and the large media attention for such events. This attention may

help in discovering the root-causes in specific events, however, it may not show

other hidden issues that affects the power grid. A potion of these underlying

75

Chapter 5. Statistical Analysis for Power System Outages 76

issues comprise of weather vulnerabilities, human error, equipment failure, and

infrastructure failure.

Analysing power outages trends through time will give us the opportunity to ex-

plore important trends like the frequency/magnitude of power outages, time of a

year, time of a day and the geographical positions of these events. All of these

rising queries and more can be investigated using the appropriate dataset from

official references, in our case, the Australian Energy Market Operator (AEMO)

and electricity service providers over Australia.

In this chapter, we will examine power outages data in Australia, and investi-

gate trends of magnitude, frequency, duration, and geographic positions. We will

also study states and utilities reliability data trends in an attempt to find a cor-

relation between states, utilities, reliability indices and smart grid technologies

investments. After that, recommendations will be provided to regulators, utilities

and official references to use resources more efficiently and enable new researchers

in this field to analyse smart grid investments data more efficiently in future.

In this introductory Section, we will study the power industry facts, which gives

an idea about where the power industry in Australia headed. We will start by the

following four points.

The number of customers is increasing over time.

The total electricity generated annually has increased over time.

A relationship between the number of customers and electricity generation

annually exists.

The price of electricity of cents/kWh is increasing over time.

The following graphs answer these points.


Figure 5.1: Figure showing the increase of customers number in millions byyear.

Figure 5.2: The Australian total electricity generation by year in GWh.


Figure 5.3: The relationship between the number of costumers and the elec-tricity generation.

Figure 5.4: The average household electricity bills annually and the averagecommercial and industrial prices from 2007-17 by ACCC.


5.2 Background

5.2.1 Smart Grid

Smart grid is a future goal for almost all traditional power grid utilities in the

world. It is a broad concept, which means generally making the power grid smarter

and dynamic by making it easy to monitor and control through adding smart grid

technologies such as Advanced Metering Infrastructure (AMI), grid-scale energy

storage systems such as large-scale batteries, and renewable energy sources (RES)

such as solar panels and wind turbines.

5.2.2 Smart Grid Investments in Australia

As an extreme continent, with unpredictable weather, aged power grids infras-

tructure and constantly changing electricity market, and with the fact that robust

supply of electricity is essential for Australia’s economic growth, it made it an

urgent task for Australia to have a long-term power grid strategy. Thus, it started

investing its smart grid technologies and investigating their benefits to the current

aged power grid.

Australia has made a first step into this concept by accomplishing the Smart Grid

Smart City (SGSC) project which started in 2010 and finished at 2014 and cost

about AU(Dollars)100m government funds. The SGSC project analysis indicated

that adding smart grid technologies to the power grid will improve the grid re-

liability and the utilities operations. And the project’s cost-benefits assessments

predicted more than AU(Dollars)27bn economic benefits over the next twenty

years and lower network charges if smart grid technologies and improved tariffs

were rolled out [1] .

The study also examined and recommended technologies such as fault detection,

isolation and restoration (FDIR), which allows operators to rapidly recognise any

fault in the grid by their exact source and location. This technology allows grid

operators to isolate the faulted section of the grid and restore power to costumers

in healthy sections, which can be done remotely in some cases [1].

The SGSC project included deployment of other smart grid technologies and ap-

plications such as in Table 5.1.


Table 5.1: Smart grid applications deployed in the SGSC project [1].

As per the current dynamics between the decreased forecasted electricity demand

and the growing number of customers in Australia, the network service providers

were able to delay some capital investment. Yet, maintaining and replacing aged

elements in the network is becoming more of a serious matter. The state-wide

blackout in South Australia on 28 September 2016 due to a storm damaging the

transmission infrastructure is one example [156].

At the same time, costumers are becoming more sensitive to electricity prices, and

aware of the competitive alternatives that are becoming more affordable such as,

residential solar PV installations, using more energy efficient appliances, thus, a

descending pressure on utilities energy demand is expected. All these elements

together, make the energy storage systems important in the transformation of the

Australian electricity industry. Australia was a world leader in the deployment of

the largest residential battery storage system in terms of power capacity in 2017

[157].

5.2.3 Environmental Reasons

Weather is an important factor in smart grid tendency around the world as the

climate change issue is becoming a world-wide issue. There is a big number if major

blackouts around the world that was caused mainly by severe weather conditions.

In Fig.5.5 below an average annual temperature change in the world for the past


167 years from 1850 to 2017. The figure indicates a change in the annual average

temperature in the world. Which supports the claims of climate change by many

organisations around the world [158].

Figure 5.5: Annual average temperature change in the world over 167 yearsperiod.

5.2.4 Weather Trends in Australia

As the world is trying to deal with the climate change issue, mitigate its reasons

and consequences, there become a noticeable political pressure in Australia to close

coal fired power plants and minimise the use of fusel fuels in electricity production.

It can be seen from Fig.5.6 that the climate change is real as the rise in sea surface

temperature in Australia started spiking from 1975 and kept rising in general

afterwards.


Figure 5.6: Annual sea surface temperature change in Australia over 118 yearsperiod .

5.2.5 The Australian Electricity Infrastructure

Figure 5.7: A map of electricity transmission lines in Australia.

The map in Fig. 5.7 shows the locations of Australia’s electricity transmission

lines. NSW, Queensland, Victoria, South Australia and Tasmania (via the under-

sea Basslink) are interconnected and make up the National Electricity Market


(NEM). Northern Territory has no available data, and the Western Australia is

considered an electricity island.

5.2.5.1 National Power Generation Data:

There was an opportunity to evaluate the performance of the Australian grid

when an Energy Matters contributor recorded the electricity generation data from

a published Australian reference [159]. The data were limited to 19.5 days starting

from Thursday 27 July 2017 at 19:30 to Wednesday 16 August 2017 at 07:45 (NEM

Time). The data shows the following generation resources table:

Table 5.2: Australia electricity generation data for the period of 27 July to 16August 2017.

The data shows large differences in generation mixes between different states. The

data also propose that Gas-Fired power plants are having difficulties balancing

irregular wind generation against demand in South Australia [159].

Figure 5.8: Australia total generation by source, 27 July to16 August, 2017.

The data are 5-minutes interval. They comprise generation differentiated by state

and source. The peak generation of (34,246MW) happened at 6:20pm NEM time

on 3 August 2017 [159]. Because Australia is an electricity island, the peak gen-

eration will be equal to the peak demand.


5.2.6 Australian Electric Infrastructure Security:

The important dual of reliability and security was getting an increasing attention

over the past few years because of the advanced cyber-attacks against important

infrastructure in different domains. These cyber-attacks may not only impact the

energy sector in Australia but have broader impacts on the nation’s economy,

public health and society [160].

Figure 5.9: Worldwide Cyber-Attacks events on critical infrastructure andindustrial control systems (ICS).

In response to the increasing threat landscape, AEMO has specially made a sector

wide Cyber Security project. Key considerations underneath its establishment

included [161]:

AEMO’s responsibility for maintaining the security of the grid means cyber

considerations are a material concern.

Finkel Recommendation 2.10 requires an annual report into the cyber secu-

rity preparedness of the National Electricity Market.

Increasing level of concern and urgency from Australian government agencies

(ASD, Critical Infrastructure Centre) in relation to cyber threats.

International events and incidents related to Energy Critical Infrastructure

that have been attributed to cyber threat actors such as those on the previous

slide.

The trend of increasing digitisation and automation of critical energy system

has increased the risk of disruption through cyber-attacks.


The project has mainly been started to deliver a tailored cyber security frame-

work, the Australian Energy Sector Cyber Security Framework (AESCSF), and

supporting tools to set the foundation for the future of energy cyber security in

Australia [161].

The administrative principles for the development of the AESCSF include:

Figure 5.10: The administrative principles for the development of theAESCSF.

The project has started with a Critical Assessment Tool (CAT), the purpose of

CAT is to determine the criticality of the entity, to rank entities within their

industry sub sector, and to assist in the determination of the target maturity

state for the entity [161].

Figure 5.11: Criticality scale and bands by energy market sub-sectors [160].


5.2.7 Cascading Outages

The definition of cascading outages by IEEE is: it is a sequence of events in which

an initial disturbance, or set of disturbances, triggers a sequence of one or more

dependent component outages [162].

The major cascading blackout happened in the NEM region was the state-wide

blackout in South Australia that occurred as a result of storm damage to electricity

transmission infrastructure on 28 September 2016.

Lessons learnt from cascading blackouts in South Australia and around the world:

Fault ride-through capability of renewable energy sources

Extreme weather

Incompatibility of UFLS with high RoCoF

Local voltage / reactive power support

Frequency support from renewable sources

Robustness of cyber security system

Hidden problems in protection schemes

Emergency load shedding

It is been noticed in many studies that the developing speed of cascading outages

are different in different stages, and that is due to protection scheme characteris-

tics and properties.

Important question: Is the reliability of the power system increasing

with the combined high penetration of renewable energy sources and

energy storage systems?

We could not find data to test this question as a hypothesis, however we found

many strong studies that indicate the benefit to system reliability when using

Battery-based energy storage systems, especially when the system has high pene-

tration of RES. Refer to [163] for more.


5.3 Study Questions

The National Electricity Market (NEM) covers the main 6 states where the ma-

jority of population lives. It interconnects the 6 eastern and southern states and

territories and delivers around 80 percent of all electricity consumption in Aus-

tralia [1]. In this research paper we will investigate the following hypotheses in

the NEM region majorly with the deployment of smart grid technologies.

5.3.1 Power Disturbances Hypotheses:

H1: The frequency of power outages is decreasing over time.

H2: The duration of power outages is decreasing over time.

H3: Weather is one of the main causes of outages in Australian power systems.

H4: The loss in MW by year is decreasing over time.

H5: There is a relationship between the number of customers and the magnitude

of the outage.

H6: There is a relationship between power outage duration and the magnitude of

the outage.

H7: The magnitude of power outages fits a power-law model.

H8: Outages greater than 5 GW are uncommon.

H9: The number of power outages is greater during specific times of a day.

H10: The number of power outages is greater during specific seasons of the year.

H11: The market impact of outages is increasing over time.

5.3.2 Reliability Hypotheses:

H12: SAIFI (frequency of outages reliability index) values vary from

state-to-state, utility-to-utility, and year from year.

H13: CAIDI (duration of outages reliability index) values vary from

state-to-state, utility-to-utility, and year from year.

H14: The frequency of power outages is decreasing with the deployment of smart

grid technologies.

H15: The duration of power outages is decreasing with the deployment of smart

grid technologies.


5.3.3 Used Statistical Methods:

A. Pearson Correlation Coefficient (PCC):

Correlation is a method for examining the relationship between two quan-

titative, continuous variables. PCC is a measure of the strength of the

association between two variables [164].

B. Power Law:

A power law is a relationship in which a relative variation in one quantity

leads to rise to a proportional relative variation in the other quantity, in-

dependent of the initial magnitude of those quantities. In other words, one

quantity changes as a power of the other [165].

C. Kolmogorov-Smirnov Test:

The Kolmogorov-Smirnov test (KS-test) attempts to find out if two datasets

differ significantly. The KS-test has the benefit of making no postulation

about the distribution of data [166].

D. Median Analysis:

Median analysis is a descriptive method, using two-way median analysis, for

example, we can find out if the median of magnitude loss events differ per

year between two groups. We can make a ”median scale” by ranking the

findings and then decide if those findings lay above or below the overall-

median [167].

E. Regression Analysis:

Regression analysis is an excellent statistical technique that allows examin-

ing the relationship between two or more variables. While there are differ-

ent types of regression analysis methods, their fundamental principle is to

observe the impact of one or more independent variables on a dependent

variable [168].

F. ANOVA:

The analysis of variance (ANOVA). ANOVA test is a statistical tool to com-

pare means in 3 or more population.

5.4 Research Hypotheses Analysis

H1: The frequency of power outages is decreasing over time.


From graph above we can see that the peak of frequency of power outages is in

2005. The lower frequency of power outages is in 2017. The graph show that the

frequency of power outages has negative trend, which indicates that the frequency

of power outages is decreasing over time. A formal analysis is conducted based on

the linear regression.

From output of linear regression above we can see that the coefficient yearly vari-

able is negative, which means if the year variable increases a year then the fre-

quency of power outages will be decreasing by -0.054. From the p-value of coef-

ficient yearly (6.9*10-7) and 95 percent confidence interval ((-0.065, -0.043)), we

can conclude that the frequency of power outages is significantly decreasing over

the time .

From the graph below we can see that the frequency of power outages is above

median on 2006 until 2011, and below median on 2012-2017. From the median

analysis, frequency of power outages indicates decreasing over the year. The result

is consistent with regression analysis above.


H2: The duration of power outages is decreasing over time.

From graph above we can see that the peak of duration of power outages is in

2005. The lower duration of power outages is in 2017. The graph shows that the

duration of power outages has negative trend, which indicates that the duration

of power outages is decreasing over time. A formal analysis is conducted based on

the linear regression.



able is negative, which means if the year variable increases a year then the duration

of power outages will be decreasing by -2.62. From the p-value of coefficient yearly

(0.0003) and 95 percent confidence interval ((-3.712, -1.528)), we can conclude that

the duration of power outages is significantly decreasing over time.

From the graph of median analysis we know that the duration of power outages

is above median on 2006 until 2011, and below median on 2012-2017. From the

median analysis, the duration of power outages is decreasing over time. The result

is consistent with regression analysis above.

H3: Weather is one of the main causes of outages in Australian power systems.

From the available data for AusGrid distribution network outages for the year

2016. We analysed the data and the conclusions are shown in the graph above.

The data indicates that faults are the major cause for outages in the Australian

distribution sector which resulted in about 53 percent of total outages while the

weather is the second major cause which resulted in about 38 percent of total


outages. The faults and weather together caused more than 90 percent of total

outrages.

Table 5.3: Descriptive Analysis Table For the USA Department of Energyoutages data from 2002 to 2019.

From table above we can observe that the mean is greater than the median, so the

distribution from variables magnitude, duration and customer is positive skewness.

The mode of three variables varies.

H4: The loss in MW by year is decreasing over time.

From the graph below we can see that the peak of magnitude is in 2002. The lower

magnitude is in 2019. But in 2011 the magnitude increases. The graph shows that

the magnitude of power outages is fluctuating and have negative trend, which

indicates that the magnitude is decreasing over time. To know if the decreasing is

significant or not, a formal analysis is conducted based on the linear regression.


From output of linear regression below we can see that the coefficient yearly vari-


of power outages will be decreasing by -2206.2. From the p-value from coefficient

yearly (0.015) and 95 percent confidence interval ((-3901.38, -510.9)), We can con-

clude that the magnitude of power outages loss in MW is significantly decreasing

over time .

From the graph of median analysis we can observe that the magnitude value be-

low the median is increasing over the years. Then for the value below median it

is higher than values above the median, which means most of magnitude value is

below the median. The magnitude value below median in 2002-2008 is less than

in 2009-2019. It indicates that the magnitude is decreasing over the years. The

result is consistent with regression analysis above.


H5: There is a relationship between the number of customers and the magnitude

of the outage.

From graph above we can see that customers and magnitude have positive rela-

tionship if the value of log10(customers) above than 3. Then if we see the scatter

plot for log10(customers) below than 3, the points spread out, that indicates no

relationship for those data. So we exclude them for the next analysis.


From the graph above we get an indication that the magnitude has a relationship

with customers, to test if the relationship is significant or not, a formal analysis is

conducted based on the linear regression.

From output of linear regression above we can see that the coefficient log10(customer)

variable is positive, which means if the customers variable increases by 1 then the

magnitude will be increasing too. From the p-value from coefficient yearly (¡0.000)

and 95 percent confidence interval ((0.598, 0.726)), We can conclude that the mag-

nitude has a positive relationship with customers.

H6: There is a relationship between power outage duration and the magnitude of

the outage.

We want to know if there is a relationship between duration and magnitude of

outages, to do that we can use correlation analysis. To test if the correlation is

significant we can use Pearson correlation. The result from Pearson is p = 0.23


and p-value is < 0.000. which means p 6= 0 because the p-value < 0.05, so we have

evidence that magnitude has a relationship with duration.


H7: The magnitude of power outages fits a power-law model.

From the graph we can see that the distribution of outages magnitudes is highly

positive skewness. The graph shows the shape is likely to power law distribution.

To test our hypothesis that the magnitude fits a power law distribution, we used

Kolmogorov-Smirnov test. The Kolmogorov-Smirnov test was also used to test if

the magnitude fits with several other distributions such as Normal, Exponential,

LogNormal etc. Form the p-values in the table below, we can see only the p-value

from the power law is 0.96 while other p-values are much less than 0.05, indicating

that the magnitude does fit with power law distribution.


H8: Outages greater than 5 GW are uncommon.

From the table above, we can see that outages greater than 5 GW are uncommon

because they account only for 1.68 percent of total outages.

H9: The number of power outages is greater during specific times of a day.

We were able to get data for outages in AusGrid distribution network from 2012

to 2018. We divided the day to 4 periods as shown above. As can be seen in

the figure above, the number of outages is greater during specific times of a day.

Period 3 which is the peak hours was having the majority of power outages (about

34 percent) comparing to other periods. Then we compare period 3 with others

period to see if there is a significant difference of outages between period 3 and

any other period with the linear regression.


From results above we can see that the p-value for period 1, 2, and 4 is less than 5

percent, so we have evidence to say that the number of power outages in period 3

is significantly different form others periods. Thus, our finding indicates that the

number of power outages is greater during specific times of a day.

H10: The number of power outages is greater during specific seasons of the year.

We were able to get data for outages in AusGrid distribution network from 2012

to 2018. We divided the year to 4 seasons as shown above. As can be seen in

the figure above, the number of outages is greater during specific seasons of the

year. Summer season was having the majority of power outages (about 34 percent)

comparing to other seasons. Then we compare summer season with others seasons

to see if there is significant difference of outages between summer season and any

other seasons with the linear regression.


From results in the table above we can see that the p-value for Spring and Autumn

is lower than 5 percent, so we have evidence to say that the number of power out-

ages in summer season is significantly different from spring and autumn seasons,

but not with winter season.

H11: The market impact of power outages is increasing over time.

From graph above we can see that the peak of market impact is in 2006. The

lower market impact is in 2011.Then on 2016 the market impact is high again.

The graph shows that the market impact has negative trend starting from 2006

until 2011, then starting from 2012 the market impact is having a positive trend.


To know if the increasing is significant or not, a formal analysis is conducted based

on the regression model with a linear term and a quadratic term of year.

From output of regression model above we can see that the coefficient yearly vari-

able is negative and its corresponding p-value is lower than the level of significance

(5 percent). So the conclusion that the market impact of power outages is decreas-

ing over time is not significant.

In the median analysis we use data start from 2008 until 2016 to see if the market

impact is increasing or not in that period. From the graph above we can observe

that the market impact value below the median is increasing over the years. Then

for the value below median it is higher than value above the median, which means

most of market impact value is below the median. The market impact value below

median in 2008-2012 is greater than in 2013-2016. which indicates that the market

impact is increasing over the year. But the increase is not significant as we have

seen in regression model.

From the table below we can observe that the mean is greater than the median,

so the distribution from variables SAIFI, CAIDI are positive skewness. The mode


Table 5.4: Descriptive Analysis Table for SAIFI and CAIDI indices statisticsfor Australian power system data from 2006-2017.

of three variables varies. Also we can see that the median and mean values are

close in proximity suggesting that the data is fairly normally distributed.

SAIFI (frequency of outages reliability index.)

Figure 5.12: SAIFI index for each utility in NEM region


From our analysis we found that there is a variability from utility-to-utility, year-

to-year, and state-to-state.

Figure 5.13: Q-Q Plot for SAIFI index in each state.

Also, we can see from the Q-Q Plot that the SAIFI approximately follows a normal

distribution in each state.

CAIDI (duration of outages reliability index)

From our analysis we found that there is variability from utility-to-utility, year-

to-year, and state-to-state.


Figure 5.14: CAIDI index for each utility in NEM region.

Figure 5.15: Q-Q Plot for CAIDI index in each state.

Also, we can see from the Q-Q Plot that CAIDI approximately follows normal

distribution in each state.


H12: SAIFI (frequency of outages reliability index) values vary from state-to-state,

utility-to-utility, and year to year.

To test this hypothesis we use the analysis of variance (ANOVA). ANOVA test is

a statistical tool to compare means in 3 or more population.

From the table above, we can see that only the p-values for state to state and

utility to utility are less than 5 percent, so we have evidence to say that SAIFI

(frequency of outages reliability index) values vary significantly from state-to-state,

utility-to-utility, but not for year-to-year.

H13: CAIDI (duration of outages reliability index) values vary from state-to-state,

utility-to-utility, and year to year.

From the table above, we can see that only the p-values for state to state and

utility to utility are less than 5 percent, so we have evidence to say that CAIDI

(duration of outages reliability index) values vary significantly from state-to-state,

utility-to-utility, but not for year-to-year.


H14: The frequency of power outages is decreasing with the deployment of smart

grid technologies.


2010. The lower frequency of power outages is in 2017. The graph show that the

frequency of power outages has negative trend, which indicates that the frequency

of power outages is decreasing over time. To know if the decreasing is significant

or not, a formal analysis is conducted based on linear regression.

From output of linear regression we can see that the coefficient yearly variable is

negative, which means if the year variable increases a year then the frequency of

power outages will be decreasing by -0.054. To know if the decreasing is significant

or not, we can see the p-value from coefficient yearly (0.002). The p-value is lower

than level of significance (5 percent). So the conclusion is that the frequency of

power outages is significantly decreasing over time.

From the graph below we can observe that the frequency of power outages value

below the median is increasing over the years. Then for the value below median it

is higher than value above the median, which means most of frequency of power

outages value is below the median. The frequency of power outages value below


median in 2010-2014 is less than in 2015-2017. Which indicates that the frequency

of power outages is decreasing over the years. The result is consistent with regres-

sion analysis above. Thus we have an evidence to say that the frequency of power

outages is decreasing over time with the deployment of smart grid technologies

which started from 2010 to 2014.

H15: The duration of power outages is decreasing with the deployment of smart

grid technologies.



2011. The lower duration power outages is in 2013. The graph shows that the

duration of power outages has no clear trend, but we can notice that the duration

of power outages is slightly decreasing over time. To know if the decreasing is

significant or not, a formal analysis is conducted based on linear regression.



of power outages will be decreasing by -0.95. To know if the decreasing is signifi-

cant or not, we can see the p-value from coefficient yearly (0.362). The p-value is

greater than level of significance (5 percent). So the conclusion is that the duration

of power outages is not significantly decreasing over time.

From the graph above we can observe that the duration of power outages value

above the median is decreasing over the years. The duration of power outages

value above median in 2015-2017 is less than in 2010-2014. It indicates that the

duration of power outages is decreasing over the years. The result is not consistent

with regression analysis above. Thus we don’t have an evidence to say that the

duration of power outages is significantly decreasing over time with the deployment

of smart grid technologies that started from 2010 to 2014.


5.5 Discussion

This study has been done on the limited data available for power outages and

power system’s reliability indices. The hypotheses that are constructed to test

the Australian power system (mostly distribution networks), we were able to find

limited-but-enough data from 2006-2017 to test them. Other general hypotheses

we had to use the USA, Department of Energy (DOE) power outages data form

2002-2019 to test them, as they are considered confidential in the Australian power

system market. The analysis was done using R statistics software [169].

5.5.1 Power Disturbances Hypotheses:

Our analysis showed that the frequency of power outages is decreasing over time.

That could be explained by the effects of the significant network investment cycle,

smart grid technology deployment and changes to regulations. There is an evidence

that the duration of power outages is decreasing over time as well. Many potential

explanations of this finding include: adding more resources to reduce the power

restoration time, and using FDIR and AMI technologies to report power outages

faster so they can be fixed earlier.

When looking at the major causes of power outages in the Australian power sys-

tem, our findings indicate that the most common cause was equipment failure not

weather. It is important to mention that our analysis for this hypothesis were

made on data for the distribution system not the transmission system. It is to

our believe that the most common cause of power outages could be weather if

the analysis were done on transmission system data, as many good studies and

technical reports indicate. To test if the loss in MW by year is decreasing over

time we had to use the USA, DOE 2002-2019 data. Our finding was that the loss

in MW by year is significantly decreasing over time. The potential explanations

for these findings could be the same for previous ones.

When testing the relationship between the number of costumers and the magnitude

of a power outage, a reasonable correlation was found. Instinctively, it makes

sense that a larger power outage magnitude would impact a larger number of

customers. The outliers in the XY plot of log(magnitude) and log(costumers) could

be interpreted as large scale customers (industrial, commercial) that have large

loss but considered as only one costumer. We also tested if there is a relationship

between the power outage duration and the magnitude of the outage. Our finding


indicates that there was a significant correlation between the restoration time and

the size of the outage. That could be explained by the fact that a larger loss

indicates a probable larger damage to the network, and a larger damage would

intuitively need a larger restoration time and that’s a whole new problem (sending

repair crews, carrying resources, repair crew skills etc.).

We tested if the distribution of power outages magnitude data fits a power-law

model. Our finding indicates that the sizes of power outages fits a power-law

distribution model and does not fit other four distributions considered in this

paper. This test was made to verify previous research findings but on a new set

of data. Outages larger than 5 GW were found to be uncommon, and that could

be due to the large investments and modernisation on power system, mainly the

power system protection schemes, which would prevent/isolate cascading outages.

We tested if the frequency of power outages is greater during specific times of

the day and specific seasons of the year. Our findings indicate that the frequency

of power outages is time-of-a-day dependent and season-of-a-year dependent. It

seems that certain types of power outages are more likely to occur in certain times

of the day. The frequency of power outages was larger during peak hours (1pm-

6pm). This time slot is the one with the maximum expected electricity usage by

costumers. Thus, it is expected that the highest number of outages happen in

this time period. The number of power outages during summer (which is the peak

season followed by winter) is significantly higher than other seasons. This could

be driven by severe weather combined with a large demand on the network. It

has been suggested in many scientific articles and researches that climate change

is real and is causing severe weather situations, which has a large impact on our

power system. Last thing we tested that is related to power system disturbances

was the power outages market impact, which is a very important indicator for

power utilities that basically means the cost of a power outage to utilities and

costumers. Our analysis has shown that the market impact of power outages is

increasing over time, but the increase is not significant based on the limited data

we analysed.

5.5.2 Reliability Hypotheses:

In this part of the research we have analysed the power system reliability indices,

mainly SAIFI (frequency of outages reliability index) and CAIDI (duration of out-

ages reliability index). It must be mentioned that there are many other reliability


indices used in the power industry, but these two are the main ones and the ones

that we were able to find data to test.

There was enough data to test hypotheses 12 and 13, that SAIFI and CAIDI

vary from state-to-state, utility-to-utility and year-to-year. Our findings are that

SAIFI and CAIDI are significantly different from state-to-state and utility-to-

utility but not year-to-year. An explanation for these finding could be that each

state has different electricity providers and each electricity provider has different

set of equipment installed, age of equipment, number of costumers and network

topology.

We tested the impact of smart grid technologies deployment on power outages

frequency and duration. For this test we used data of the SGSC project that

was done on AusGrid network in NSW from 2010-2014. The initial analysis on

the limited available data showed that there was a reduction on the frequency of

power outages in AusGrid network with the deployment of smart grid technologies.

However, we found no significant reduction on the duration of power outages with

the deployment of smart grid technologies.

We must mention that there were many different approaches to tackle these hy-

potheses, but none of them would give us an affirm answer or a clear correlation

between the reduction in frequency and duration of power outages and the smart

grid technologies deployment. That is due to the mix of variables and factors

involved in SAIF and CAIDI behaviours in power system, which were mentioned

earlier in this discussion. However, the results are inspiring and these hypotheses

may be proved with more and detailed data in the future. Looking at the whole

dynamics of power systems and of SAIFI and CAIDI indices in power systems,

suggests that other factors could participate in their reduction and not only the

smart grid technologies deployments.

5.6 Conclusion and Recommendations

This chapter provided a detailed statistical analysis of power outages trends and

power system reliability metrics. We have stated the conclusions of each hypothesis

analysis we tested. Also, we illustrated and explained the scientific reasons that

support our findings in the discussion section. In this conclusion we will address

the variables that affected our analysis, such as the limited amount of detailed data

and the lack of cooperation form utilities in Australia. There were many factors


affected our ability to get solid conclusions about specific research hypothesis. We

have tried to correlate smart grid technologies deployments to the improvements

in power system reliability indices. That was a hard task given that many other

variables and factors could participate in the result we find. Utilities do not

provide detailed data for their smart grid technologies funding, or investments in

modernising their aged infrastructure broken down year by year. This led us to

use the SGSC project with its small scale and data availability limitations as an

indirect measure in our try to answer these questions.

We also wanted to study the impact of large-scale battery-based energy storage

systems to the power system’s reliability indices, but we found no sufficient data

to do such analysis. However, we found strong studies indicate its positive impact

and we mentioned them in previous sections of this paper. We were able to get

enough data to analyse the correlation of SAIFI and CAIDI by state, utility and

year and analyse them fully in their designated section.

Additionally, we have faced many difficulty variables in doing this study, as many

important information were not readily available, such as age of equipment, types

of smart grid technologies, type of transmission lines (overhead, underground),

type of area (rural or urban). Thus, it was hard to take these factors in con-

sideration as we perform our study. However, it is understandable that some of

these data were not made available publicly for security reasons, as they could be

misused by someone looking for a weakness in the power network.

Based on the available data, we were able to get to certain conclusions and rec-

ommendations for specific points. Equipment failure and severe weather were the

main causes of outages in Australian power system. Thus, it is important to rec-

ommend that along with the deployment of smart grid technologies, it is important

to reinforce and modernise the power system infrastructure to be more resilient

against severe weather. This could ease the repair problem aspects in a case of

power system restoration. Aging equipment need to be replaced. Power utilities

need to perform risk-analysis and cost-benefit analysis in order to decide which

equipment should be replaced first.

From time-of-a-day and season-of-a-year perspective, it is recommended to have

more repair crews ready in peak period of the day and in certain seasons that

have severe weather usually such as summer and winter based on the predictable

weather forecasting. Also, it makes sense to locate the repair depots and resources

optimally among the covered network especially near important and large loads

such as commercial and industrial costumers to insure they are better protected.


An agreement between large and important loads owners and power utilities could

be reached, for example the owners could install backup systems to protect them-

selves in return of discounted rates from utilities. Time-of-Use (TOU) pricing

scheme could be implemented to encourage costumers to use electricity more in

off-peak times, which may result in lower outages that are caused by large de-

mand on power. On the other hand, utilities are encouraged to increase supply

capacity in time windows that are likely to be impacted by power outages due to

high power demand. Intuitively, shorter power outages are preferred over longer

outages, thus, utilities are recommended to look for a good trade-off that come up

with a substantial reduction in longer power outages at a cost of frequent shorter

power outages.

Most power system regulators and utilities provide data in a research unfriendly

formats that need a lot of data management in order to make it suitable to be

imported to a software program to analyse the data. The data management must

be done manually which is a big waste of the researcher time. Many important

information and items are missed from the available data which highlights the

importance of data classification techniques and machine learning in order to cor-

rectly classify items. Dealing with such data needs a lot of work to manage them,

which may cause errors in analysing the data and wrong results in conclusion.

Governments, Academics, and power utilities are going to continue in their re-

search efforts that aim to find correlations between smart grid technologies de-

ployments, and power system reliability indices, which requires the availability of

detailed and readily accessible data from power system regulators and power utili-

ties, with the security concerns of making data publicly available, it is an essential

step to help researchers draw solid conclusions in this field.

Chapter 6

Conclusions and Future Work

In this chapter, the thesis research conclusions and findings will be presented

alongside with probable future work.

6.1 Conclusions

This thesis has developed and presented many important contributions to the PSR

field. Our findings were interesting and very useful to the PSR community and

their efforts to enhance the current practices in the field. We have developed and

presented a high-quality review to the best research efforts made to date in the

aim of easing and well illustrating the problem to new researchers. A systematic

and comprehensive literature review was presented in chapter two.

A major finding in this thesis is showing and proving that mathematical pro-

gramming is outperforming technique in solving PSRR and handling its daunting

computational complexity. A detailed studies and analysis are presented in chap-

ter three providing basic and advanced mathematical applications for the PSRR.

The chapter also provides readers with the ability to compare between different

power systems models in terms of performance with the trade-off factor between

computational easiness and accuracy in mind.

Another major finding was that the suitability and usefulness of Nature-inspired

optimisation techniques in power system reliability studies. Chapter four presents

a promising study for power system reliability in the restorative state under certain

conditions such as CLPU.

114

Chapter 6. Conclusions and Future Work 115

Another important findings in this thesis that were presented in chapter five for

power systems outages and smart grid investments in Australia. We have shown

the potential benefits of statistical analysis in power system studies. We have

developed and investigated many research hypotheses on power outages and sys-

tem reliability, and shown the potential benefits for smart grid technologies to the

power grid.

A complete and detailed list of findings are presented in each chapter’s conclusion.

6.2 Future Work

Based on our research efforts in this thesis, many questions arose and many in-

teresting research ideas have sparked. We have spotted several weak areas in the

PSR field. Thus, in terms of future work, we plan to extend our studies to all

aspects of the PSRRP and all areas of PSR. The following research subjects will

be investigated:

A historical review for major power system blackouts around the world.

Developing a more sophisticated optimisation method for a large-scale PSRRP.

Optimal allocation for black-start generators in power grid.

Investigating advanced optimisation techniques for restoration of large-scale

systems.

Transient stability in system restoration.

Protection schemes control in system restoration.

Vehicle routing strategies for large-scale systems.

Generation, transmission, distribution restoration strategies.

Investigating the optimal sequence to black-start a power system.

Developing a more accurate linear approximation of AC power-flow for sys-

tem restoration studies.

Developing a system operator training software for power system restoration.

Bibliography 116

Developing a more reliable communication scheme for power system opera-

tors that could make the disaster recovery operations optimal.

Investigating the physics of the power system and the logistics of the problem

in a more novel, advanced and applicable way, in the aim of producing a real

applicable research that could enhance disaster recovery approaches in power

systems and enhance people’s life.

Power system islanding coordination and synchronisation.

Rebuilding power system after a disaster.

Optimal sequential operation of switching devices.

Developing a machine learning framework for logistics operations time esti-

mation.

Efficient utilisation of mobile energy sources in power grid.

Studying the restoration problem with the existence of renewable energy

sources.

Power system stochastic storage problem optimisation.

We aim to collaborate with researchers and research centres interested in PSR

around the world in order to make novel and major contributions in this field in

future.

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Chapter 7

Appendix

7.1 Tools used in this Thesis

The following tools were used for the completion of this thesis research:

Python programming language.

Pyomo library in Python with appropriate solvers such as GLPK and IPOPT.

AMPL optimisation software with appropriate solvers.

MATLAB programming software.

A Power-Flow simulation software to adequately model the effects of each

restoration action on the system.

Microsoft Visio, Word, Excel and Power Point.

LaTex editing platform.

The General Algebraic Modeling System (GAMS).

R Programming language.

Relevant peer-reviewed journal and conference papers.

135

Appendix 136

7.2 Awards and Achievements

We have received the best paper and presentation award for our confer-

ence paper “Mathematical Approach for Solving Power Systems Repair and

Restoration Problem” from the Saudi Arabia Smart Grid conference in 2019.

In the making of this thesis research, we have studied and analysed about

300 relevant peer-reviewed journal and conference papers.

All research papers produced by this thesis were accepted and submitted at

prestigious conference and highly ranked journals.

In the making of this thesis research, we have collaborated with many experts

from the Australian industry along with experts from around the world, in

addition to a big benefit that we have studied, learned, and explored many

technical tools and programming languages.

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