Electric Power System Planning : Issues, Algorithms and Solutions

Power Systems

For further volumes:

http://www.springer.com/series/4622

Hossein Seifi • Mohammad Sadegh Sepasian

Electric Power System

Planning

Issues, Algorithms and Solutions

123

Prof. Hossein Seifi

Faculty of Electrical and Computer

Engineering

Tarbiat Modares University

PO Box 14115-194

Tehran

Iran

e-mail: [email protected]

Dr. Mohammad Sadegh Sepasian

Power and Water University of Technology

PO Box 16765-1719

Tehran

Iran

e-mail: [email protected]

ISSN 1612-1287 e-ISSN 1860-4676

ISBN 978-3-642-17988-4 e-ISBN 978-3-642-17989-1

DOI 10.1007/978-3-642-17989-1

Springer Heidelberg Dordrecht London New York

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Preface

One of the largest, or perhaps, the largest scale system ever made, is the electric

grid with its numerous components, called a power system. Over decades, power

systems have evolved to the systems which may cover countries or even

continents.

From one side, the behaviors, modeling and operation of the basic components

of a power system should be understood and recognized. That is why so many

books are published to address such issues.

On the other hand, once the system as a whole is observed, its analysis,

operation and planning deserve special considerations. While analysis and to some

extent, operation of power systems have received attention in literature and in

terms of text books, power system planning is not rich from this viewpoint. This

book is intended to cover this issue.

While the importance of power system planning can not be overstated, writing a

text book on this issue is not an easy task due to some, but not limited to, reasons

as follows

• Planning horizon is from short to long periods. The issues of concern are not the

same; although some may be similar.

• Utilities and experts may think of a specific planning term quite differently. For

instance, one may think of long-term power system planning to cover 20 years

onward, while the other may consider it as 5–15 years.

• While the basics of say, load flow in a book on power system analysis, or

Automatic Generation Control (AGC) in a book on power system operation, are

essentially the same on similar books, the algorithms and the methodologies

used in power system planning may be utility or even case dependent.

The book is intended to cover long-term issues of power system planning,

mainly on transmission and sub-transmission levels. However, the reader would

readily recognize that some of the chapters may also be used for mid-term or even

short-term planning, perhaps with some modifications. In terms of the long-term

planning itself, the algorithms presented are mainly so designed that they may be

used for various time frames. However, enough input data should be available;

v

which may be unavailable for very long-term periods. Regarding the methodolo￾gies and the algorithms, the chapters are arranged in a case independent manner

and the algorithms are formulated in the ways that the readers can readily modify

them according to their wishes.

We envision two groups of audiences for this book. The first consists of final

year BSc or graduate students with a major in power systems. The second group

consists of professionals working in and around the power industry especially in

planning departments.

To bridge the gap between formal learning of the algorithms and deep under￾standing of the materials, some Matlab M-file codes are generated and attached in

Appendix L. They are based on the materials developed within the chapters and

easy to follow. Once referred to any of the above codes within the chapters, it is

shown as [#X.m; Appendix L: (L.Y)], where X stands for M-file name and Y

stands for the relevant section number. These codes may be accessed through the

publisher website, too. They are used to solve some of the examples within and

some of the problems at the end of the chapters. However, we should emphasize

that they are not designed as commercial software and the instructors may ask the

students to modify them and the professionals may improve them to meet their

special requirements.

Some numerical examples are solved within the chapters. Although we have

tried to use realistic input parameters, especially economic parameters are quite

case dependent. That is why, an artificial monetary unit abbreviated as R is used to

refer to economic values.

We were fortune to make the most benefits of our both academic and profes￾sional positions in preparing the book. The first author is a professor of the Faculty

of Electrical and Computer Engineering at Tarbiat Modares University (TMU)

(Tehran/Iran). TMU is only involved in graduate studies. He has supervised or has

under supervision more than 80 MSc and PhD students. At the same time, he has

founded a National Research Center (Iran Power System Engineering Research

Center, IPSERC) as an affiliated center to TMU, for which he is acting as the head.

Over the last few years, IPSERC has been actively involved in more than 60

strategic planning studies for major Iranian electric utilities. His vast experiences

within IPSERC are properly reflected in various chapters. Some commercial

software is also developed, now used by some of Iranian utilities. The Iranian

electric power industry ranks nearly 8th in the world, in terms of the generation

capacity (roughly 57 GW, 2010) and his experiences are based on this rather large

scale system.

The second author is a faculty member at Power and Water University of

Technology (PWUT) and a senior expert in IPSERC since its foundation. PWUT is

affiliated to the Ministry of Energy of the country with vast experiences in terms of

practical issues.

Many individuals and organizations have made the writing of this book pos￾sible. We are deeply grateful to the experts in Iranian electric power industry who

graciously discussed and helped our understanding of practical issues and their

requirements. We enjoyed marvelous learning opportunity through carrying out

vi Preface

the strategic planning studies for this industry. Mr Rae, Mr Akhavan (both

from Tavanir), Dr Zangene, Mrs Zarduzi (both from Tehran Regional Electric

Utility), Mr Zeraat-Pishe, Mr Asiae (both from Fars Regional Electric Utility),

Mr Arjomand, Mr Torabi, Mr Ghasemi (all from Hormozgan Regional Electric

Utility), Mr Mehrabi (from Yazd Regional Electric Utility), Mrs Ghare-Toghe

(from Mazandaran Regional Electric Utility) are only a few among many others.

Mr Saburi (from Tavanir) provided us some useful data for a part of Chap. 4.

However, we should especially thank Dr Ahmadian for his support in founding

IPSERC from the Ministry of Energy viewpoint. Special thanks are due to

Mr Mohseni Kabir, who was and is still acting as the deputy in planning affairs of

Tavanir (Tavanir is the holding company of Iranian power industry). Besides very

useful technical discussions with him, he also greatly helped bridge Tavanir with

IPSERC.

Within IPSERC, many individuals have contributed developing the software;

employed in the studies, discussing with the industry experts, etc. To name a few,

Dr Akbari, Dr Yousefi, Dr Haghighat, Mr Khorram, Mr Elyasi, Mr Roustaei,

Mrs Hajati, Mr Sharifzadeh, Mr Shaffee-Khah deserve special thanks.

Our gratitude also extends to all others who, somehow, participated in the

development of the book-particularly our students who never cease to ask

challenging questions-and to our friends who offered encouragement and support.

Mr Daraeepour developed the Matlab M-files codes. Dr Sheikh-al-Eslam,

Dr Akbari, Dr Dehghani, Mr Elyasi, Mrs Hajati, Mr Roustaei, Mr Khorram,

Mr Velayati, Mr Sharif-Zadeh, Mr Karimi reviewed the chapters, solved some

examples, devised some problems and provided us useful suggestions and

comments. Mrs Najafi and Mrs Tehrani did an excellent job in typing the whole

manuscript.

One name deserves special gratitude. We deeply owe Mr Elyasi for an excellent

task of reviewing, typesetting, organizing the manuscript and careful editing of the

book. He did a really marvelous task in a very nice and efficient manner.

Sincere thanks are due to Prof. Christoph Baumann and his colleagues, from

Springer, for their support in the preparation of the book. Finally, we should thank

our families who graciously accepted us as part-time family members during the

course of this book.

We should mention that a review of the chapters is provided in Chap. 1.

Although the book is intended to be a text book, power system planning is a

research-oriented topic, too. That is why; we have also added a chapter, to cover

research issues.

Finally, we should mention that although we have attempted to review the

materials so that they are, hopefully, error free, some may still exist. Please feel

free to email us feedback including errors, comments, opinions, or any other useful

information. These suggestions from the readers for improving the book clarity

and accuracy will be greatly welcomed.

Tehran, May 2011 Hossein Seifi

Mohammad Sadegh Sepasian

Preface vii

Contents

1 Power System Planning, Basic Principles................... 1

1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Power System Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.3 Power System Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.4 Power System Studies, a Time-horizon Perspective . . . . . . . . 4

1.5 Power System Planning Issues . . . . . . . . . . . . . . . . . . . . . . . 7

1.5.1 Static Versus Dynamic Planning . . . . . . . . . . . . . . . 8

1.5.2 Transmission Versus Distribution Planning . . . . . . . . 8

1.5.3 Long-term Versus Short-term Planning . . . . . . . . . . . 9

1.5.4 Basic Issues in Transmission Planning . . . . . . . . . . . 10

1.6 A Review of Chapters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2 Optimization Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.2 Problem Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.2.1 Problem Definition . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.2.2 Problem Modeling . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.3 Solution Algorithms, Mathematical Versus Heuristic

Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.3.1 Mathematical Algorithms . . . . . . . . . . . . . . . . . . . . 20

2.3.2 Heuristic Algorithms. . . . . . . . . . . . . . . . . . . . . . . . 24

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

3 Some Economic Principles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

3.2 Definitions of Terms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

3.3 Cash-flow Concept . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

3.3.1 Time Value of Money. . . . . . . . . . . . . . . . . . . . . . . 33

3.3.2 Economic Terms . . . . . . . . . . . . . . . . . . . . . . . . . . 34

ix

3.4 Economic Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

3.4.1 Present Worth Method . . . . . . . . . . . . . . . . . . . . . . 36

3.4.2 Annual Cost Method. . . . . . . . . . . . . . . . . . . . . . . . 38

3.4.3 Rate of Return Method . . . . . . . . . . . . . . . . . . . . . . 38

3.4.4 A Detailed Example . . . . . . . . . . . . . . . . . . . . . . . . 39

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

4 Load Forecasting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

4.2 Load Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

4.3 Load Driving Parameters. . . . . . . . . . . . . . . . . . . . . . . . . . . 47

4.4 Spatial Load Forecasting . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

4.5 Long Term Load Forecasting Methods . . . . . . . . . . . . . . . . . 50

4.5.1 Trend Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

4.5.2 Econometric Modeling . . . . . . . . . . . . . . . . . . . . . . 51

4.5.3 End-use Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 51

4.5.4 Combined Analysis. . . . . . . . . . . . . . . . . . . . . . . . . 52

4.6 Numerical Examples. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

4.6.1 Load Forecasting for a Regional Utility . . . . . . . . . . 52

4.6.2 Load Forecasting of a Large Scale Utility . . . . . . . . . 56

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

5 Single-bus Generation Expansion Planning . . . . . . . . . . . . . . . . . 69

5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

5.2 Problem Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

5.3 Problem Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

5.4 Mathematical Development . . . . . . . . . . . . . . . . . . . . . . . . . 75

5.4.1 Objective Functions . . . . . . . . . . . . . . . . . . . . . . . . 75

5.4.2 Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

5.5 WASP, a GEP Package. . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

5.5.1 Calculation of Costs . . . . . . . . . . . . . . . . . . . . . . . . 78

5.5.2 Description of WASP-IV Modules . . . . . . . . . . . . . . 80

5.6 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

Problems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

6 Multi-bus Generation Expansion Planning. . . . . . . . . . . . . . . . . . 89

6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

6.2 Problem Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

6.3 A Linear Programming (LP) Based GEP. . . . . . . . . . . . . . . . 91

6.3.1 Basic Principles . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

6.3.2 Mathematical Formulation . . . . . . . . . . . . . . . . . . . . 95

6.4 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

x Contents

6.5 A Genetic Algorithm (GA) Based GEP. . . . . . . . . . . . . . . . . 98

6.6 Numerical Results for GA-based Algorithm. . . . . . . . . . . . . . 99

Problems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

7 Substation Expansion Planning . . . . . . . . . . . . . . . . . . . . . . . . . . 105

7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

7.2 Problem Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

7.3 A Basic Case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

7.3.1 Problem Description . . . . . . . . . . . . . . . . . . . . . . . . 106

7.3.2 Typical Results for a Simple Case . . . . . . . . . . . . . . 110

7.4 A Mathematical View . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

7.4.1 Objective Function . . . . . . . . . . . . . . . . . . . . . . . . . 114

7.4.2 Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

7.4.3 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . 115

7.4.4 Required Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116

7.5 An Advanced Case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117

7.5.1 General Formulation . . . . . . . . . . . . . . . . . . . . . . . . 117

7.5.2 Solution Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . 122

7.6 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124

7.6.1 System Under Study . . . . . . . . . . . . . . . . . . . . . . . . 124

7.6.2 Load Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125

7.6.3 Downward Grid . . . . . . . . . . . . . . . . . . . . . . . . . . . 125

7.6.4 Upward Grid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126

7.6.5 Transmission Substation . . . . . . . . . . . . . . . . . . . . . 126

7.6.6 Miscellaneous . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128

7.6.7 Results for BILP Algorithm. . . . . . . . . . . . . . . . . . . 128

7.6.8 Results for GA. . . . . . . . . . . . . . . . . . . . . . . . . . . . 129

Problems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131

8 Network Expansion Planning, a Basic Approach . . . . . . . . . . . . . 133

8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133

8.2 Problem Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133

8.3 Problem Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134

8.4 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140

8.4.1 Objective Function . . . . . . . . . . . . . . . . . . . . . . . . . 140

8.4.2 Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141

8.5 Solution Methodologies. . . . . . . . . . . . . . . . . . . . . . . . . . . . 142

8.5.1 Enumeration Method . . . . . . . . . . . . . . . . . . . . . . . 142

8.5.2 Heuristic Methods . . . . . . . . . . . . . . . . . . . . . . . . . 143

8.6 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149

8.6.1 Garver Test System . . . . . . . . . . . . . . . . . . . . . . . . 150

8.6.2 A Large Test System . . . . . . . . . . . . . . . . . . . . . . . 150

Contents xi

Problems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153

9 Network Expansion Planning, an Advanced Approach. . . . . . . . . 155

9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155

9.2 Problem Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155

9.3 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159

9.3.1 Basic Requirements . . . . . . . . . . . . . . . . . . . . . . . . 159

9.3.2 Objective Functions . . . . . . . . . . . . . . . . . . . . . . . . 162

9.3.3 Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164

9.4 Solution Methodology. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166

9.5 Candidate Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166

9.6 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168

Problems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171

10 Reactive Power Planning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173

10.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173

10.2 Voltage Performance of a System. . . . . . . . . . . . . . . . . . . . . 174

10.2.1 Voltage Profile. . . . . . . . . . . . . . . . . . . . . . . . . . . . 174

10.2.2 Voltage Stability . . . . . . . . . . . . . . . . . . . . . . . . . . 174

10.2.3 Voltage Performance Control Parameters . . . . . . . . . 176

10.2.4 Static Versus Dynamic Reactive Power Resources . . . 176

10.3 Problem Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178

10.4 Reactive Power Planning (RPP) for a System . . . . . . . . . . . . 182

10.4.1 Static Reactive Resource Allocation and Sizing . . . . . 182

10.4.2 Dynamic Reactive Resource Allocation and Sizing. . . 184

10.4.3 Solution Procedure . . . . . . . . . . . . . . . . . . . . . . . . . 186

10.5 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187

10.5.1 Small Test System . . . . . . . . . . . . . . . . . . . . . . . . . 187

10.5.2 Large Test System . . . . . . . . . . . . . . . . . . . . . . . . . 189

Problems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194

11 Power System Planning in the Presence of Uncertainties . . . . . . . 197

11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197

11.2 Power System De-regulating . . . . . . . . . . . . . . . . . . . . . . . . 198

11.3 Power System Uncertainties. . . . . . . . . . . . . . . . . . . . . . . . . 199

11.3.1 Uncertainties in a Regulated Environment . . . . . . . . . 199

11.3.2 Uncertainties in a De-regulated Environment . . . . . . . 200

11.4 Practical Issues of Power System Planning

in a De-regulated Environment. . . . . . . . . . . . . . . . . . . . . . . 201

xii Contents

11.5 How to Deal with Uncertainties in Power System Planning . . . 204

11.5.1 Expected Cost Criterion . . . . . . . . . . . . . . . . . . . . . 205

11.5.2 Min-max Regret Criterion . . . . . . . . . . . . . . . . . . . . 206

11.5.3 Laplace Criterion . . . . . . . . . . . . . . . . . . . . . . . . . . 207

11.5.4 The Van Neuman–Morgenstern (VNM) Criterion. . . . 207

11.5.5 Hurwicz Criterion. . . . . . . . . . . . . . . . . . . . . . . . . . 207

11.5.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208

12 Research Trends in Power System Planning . . . . . . . . . . . . . . . . 209

12.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209

12.2 General Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209

12.3 References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210

12.3.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210

12.3.2 LF (2000 Onward) . . . . . . . . . . . . . . . . . . . . . . . . . 211

12.3.3 GEP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212

12.3.4 TEP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214

12.3.5 GEP and TEP . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218

12.3.6 RPP (2000 Onward) . . . . . . . . . . . . . . . . . . . . . . . . 218

12.3.7 Miscellaneous . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219

12.4 Exercise 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219

12.5 Exercise 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222

13 A Comprehensive Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223

13.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223

13.2 SEP Problem for Sub-transmission Level . . . . . . . . . . . . . . . 223

13.2.1 Basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223

13.2.2 System Under Study . . . . . . . . . . . . . . . . . . . . . . . . 224

13.2.3 Input Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224

13.2.4 Solution Information. . . . . . . . . . . . . . . . . . . . . . . . 224

13.2.5 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227

13.3 SEP Problem for Transmission Level . . . . . . . . . . . . . . . . . . 229

13.4 NEP Problem for Both Sub-transmission

and Transmission Levels . . . . . . . . . . . . . . . . . . . . . . . . . . . 233

13.5 RPP Problem for Both Sub-transmission

and Transmission Levels . . . . . . . . . . . . . . . . . . . . . . . . . . . 238

13.5.1 Results for 2011. . . . . . . . . . . . . . . . . . . . . . . . . . . 240

13.5.2 Results for 2015. . . . . . . . . . . . . . . . . . . . . . . . . . . 242

Appendix A: DC Load Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245

Appendix B: A Simple Optimization Problem . . . . . . . . . . . . . . . . . . 249

Appendix C: AutoRegressive Moving Average (ARMA) Modeling. . . . 259

Contents xiii

Appendix D: What is EViews. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261

Appendix E: The Calculations of the Reliability Indices . . . . . . . . . . . 263

Appendix F: Garver Test System Data. . . . . . . . . . . . . . . . . . . . . . . . 267

Appendix G: Geographical Information System . . . . . . . . . . . . . . . . 271

Appendix H: 84-Bus Test System Data. . . . . . . . . . . . . . . . . . . . . . . . 273

Appendix I: Numerical Details of the Basic Approach . . . . . . . . . . . . 285

Appendix J: 77-Bus Test System Data . . . . . . . . . . . . . . . . . . . . . . . . 287

Appendix K: Numerical Details of the Hybrid Approach . . . . . . . . . . 301

Appendix L: Generated Matlab M-files Codes . . . . . . . . . . . . . . . . . . 307

Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 369

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