Probabilistic Transmission System Planning (Li/Transmission System Planning) || Frontmatter

PROBABILISTIC TRANSMISSION

SYSTEM PLANNING

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IEEE Press445 Hoes Lane

Piscataway, NJ 08854

IEEE Press Editorial BoardLajos Hanzo, Editor in Chief

R. Abari M. El-Hawary S. NahavandiJ. Anderson B. M. Hammerli W. ReeveF. Canavero M. Lanzerotti T. SamadT. G. Croda O. Malik G. Zobrist

Kenneth Moore, Director of IEEE Book and Information Services (BIS)

Technical ReviewersRoy Billinton

Lalit GoelMurty BhavarajuWenpeng Luan

A complete list of titles in the IEEE Press Series on Power Engineering appears at the end of this book.

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PROBABILISTIC TRANSMISSION

SYSTEM PLANNING

Wenyuan Li, Fellow, IEEE, EICBC Hydro, Canada

A JOHN WILEY & SONS, INC., PUBLICATION

IEEE-PRESS

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Copyright © 2011 by Institute of Electrical and Electronics Engineers. All rights reserved.

Published by John Wiley & Sons, Inc., Hoboken, New Jersey.Published simultaneously in Canada.

No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, (978) 750-8400, fax (978) 750-4470, or on the web at www.copyright.com. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, (201) 748-6011, fax (201) 748-6008, or online at http://www.wiley.com/go/permission.

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Library of Congress Cataloging-in-Publication Data is available.ISBN 978-0-470-63001-3

Printed in Singapore.

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Dedicated to Jun and my family

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vii

CONTENTS

Preface and Acknowledgments xxi

1 INTRODUCTION 11.1 Overview of Transmission Planning 1

1.1.1 Basic Tasks in Transmission Planning 1

1.1.2 Traditional Planning Criteria 3

1.2 Necessity of Probabilistic Transmission Planning 6

1.3 Outline of the Book 8

2 BASIC CONCEPTS OF PROBABILISTIC PLANNING 112.1 Introduction 11

2.2 Probabilistic Planning Criteria 12

2.2.1 Probabilistic Cost Criteria 12

2.2.2 Specifi ed Reliability Index Target 13

2.2.3 Relative Comparison 13

2.2.4 Incremental Reliability Index 13

2.3 Procedure of Probabilistic Planning 14

2.3.1 Probabilistic Reliability Evaluation 14

2.3.2 Probabilistic Economic Analysis 17

2.4 Other Aspects in Probabilistic Planning 17

2.5 Conclusions 18

3 LOAD MODELING 213.1 Introduction 21

3.2 Load Forecast 22

3.2.1 Multivariate Linear Regression 22

3.2.1.1 Regression Equation 22

3.2.1.2 Statistical Test of Regression Model 23

3.2.1.3 Regression Forecast 25

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3.2.2 Nonlinear Regression 26

3.2.2.1 Nonlinear Regression Models 26

3.2.2.2 Parameter Estimation of Models 27

3.2.3 Probabilistic Time Series 28

3.2.3.1 Conversion to a Stationary Time Series 29

3.2.3.2 Model Identifi cation 30

3.2.3.3 Estimating Coeffi cients of Models 31

3.2.3.4 Load Forecast Equation 32

3.2.3.5 A Posteriori Test of Load Forecast Accuracy 33

3.2.4 Neural Network Forecast 34

3.2.4.1 Feedforward Backpropagation Neural Network (FFBPNN) 34

3.2.4.2 Learning Process of FFBPNN 36

3.2.4.3 Load Prediction 37

3.3 Load Clustering 37

3.3.1 Multistep Load Model 37

3.3.2 Load Curve Grouping 40

3.4 Uncertainty and Correlation of Bus Loads 42

3.5 Voltage- and Frequency-Dependent Bus Loads 44

3.5.1 Bus Load Model for Static Analysis 45

3.5.1.1 Polynomial Bus Load Model 45

3.5.1.2 Exponential Bus Load Model 45

3.5.2 Bus Load Model for Dynamic Analysis 46

3.6 Conclusions 46

4 SYSTEM ANALYSIS TECHNIQUES 494.1 Introduction 49

4.2 Power Flow 50

4.2.1 Newton–Raphson Method 50

4.2.2 Fast Decoupled Method 51

4.2.3 DC Power Flow 52

4.3 Probabilistic Power Flow 53

4.3.1 Point Estimation Method 54

4.3.2 Monte Carlo Method 55

4.4 Optimal Power Flow (OPF) 57

4.4.1 OPF Model 58

4.4.2 Interior Point Method (IPM) 60

4.4.2.1 Optimality and Feasibility Conditions 60

4.4.2.2 Procedure of IPM 62

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4.5 Probabilistic Search Optimization Algorithms 64

4.5.1 Genetic Algorithm (GA) 64

4.5.1.1 Fitness Function 65

4.5.1.2 Selection 65

4.5.1.3 Recombination 66

4.5.1.4 Mutation 67

4.5.1.5 Reinsertion 67

4.5.1.6 Procedure of Genetic Algorithm 68

4.5.2 Particle Swarm Optimization (PSO) 69

4.5.2.1 Inertia Weight Approach 70

4.5.2.2 Constriction Factor Approach 70

4.5.2.3 Procedure of PSO 71

4.6 Contingency Analysis and Ranking 72

4.6.1 Contingency Analysis Methods 72

4.6.1.1 AC Power-Flow-Based Method 72

4.6.1.2 DC Power-Flow-Based Method 73

4.6.2 Contingency Ranking 75

4.6.2.1 Ranking Based on Performance Index 75

4.6.2.2 Ranking Based on Probabilistic Risk Index 75

4.7 Voltage Stability Evaluation 76

4.7.1 Continuation Power Flow Technique 76

4.7.1.1 Prediction Step 77

4.7.1.2 Correction Step 78

4.7.1.3 Identifi cation of Voltage Collapse Point 78

4.7.2 Reduced Jacobian Matrix Analysis 78

4.8 Transient Stability Solution 80

4.8.1 Transient Stability Equations 80

4.8.2 Simultaneous Solution Technique 81

4.8.3 Alternate Solution Technique 82

4.9 Conclusions 83

5 PROBABILISTIC RELIABILITY EVALUATION 855.1 Introduction 85

5.2 Reliability Indices 86

5.2.1 Adequacy Indices 86

5.2.2 Reliability Worth Indices 88

5.2.3 Security Indices 89

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5.3 Reliability Worth Assessment 90

5.3.1 Methods of Estimating Unit Interruption Cost 90

5.3.2 Customer Damage Functions (CDFs) 91

5.3.2.1 Customer Survey Approach 91

5.3.2.2 Establishment of CDF 91

5.3.3 Application of Reliability Worth Assessment 92

5.4 Substation Adequacy Evaluation 93

5.4.1 Outage Modes of Components 94

5.4.2 State Enumeration Technique 95

5.4.3 Labeled Bus Set Approach 96

5.4.4 Procedure of Adequacy Evaluation 97

5.5 Composite System Adequacy Evaluation 99

5.5.1 Probabilistic Load Models 100

5.5.1.1 Load Curve Models 100

5.5.1.2 Load Uncertainty Model 100

5.5.1.3 Load Correlation Model 101

5.5.2 Component Outage Models 101

5.5.2.1 Basic Two-State Model 101

5.5.2.2 Multistate Model 101

5.5.3 Selection of System Outage States 102

5.5.3.1 Nonsequential Sampling 102

5.5.3.2 Sequential Sampling 103

5.5.4 System Analysis 103

5.5.5 Minimum Load Curtailment Model 1045.5.6 Procedure of Adequacy Evaluation 105

5.6 Probabilistic Voltage Stability Assessment 107

5.6.1 Optimization Model of Recognizing Power Flow Insolvability 108

5.6.2 Method for Identifying Voltage Instability 110

5.6.3 Determination of Contingency System States 1115.6.3.1 Selection of Precontingency System States 1115.6.3.2 Selection of Contingencies 112

5.6.4 Assessing Average Voltage Instability Risk 113

5.7 Probabilistic Transient Stability Assessment 114

5.7.1 Selection of Prefault System States 1145.7.2 Fault Probability Models 115

5.7.2.1 Probability of Fault Occurrence 115

5.7.2.2 Probability of Fault Location 115

5.7.2.3 Probability of Fault Type 115

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5.7.2.4 Probability of Unsuccessful Automatic Reclosure 116

5.7.2.5 Probability of Fault Clearing Time 116

5.7.3 Selection of Fault Events 117

5.7.4 Transient Stability Simulation 117

5.7.5 Assessing Average Transient Instability Risk 118

5.8 Conclusions 120

6 ECONOMIC ANALYSIS METHODS 1236.1 Introduction 123

6.2 Cost Components of Projects 124

6.2.1 Capital Investment Cost 124

6.2.2 Operation Cost 124

6.2.3 Unreliability Cost 125

6.3 Time Value of Money and Present Value Method 125

6.3.1 Discount Rate 125

6.3.2 Conversion between Present and Future Values 126

6.3.3 Cash Flow and Its Present Value 127

6.3.4 Formulas for a Cash Flow with Equal Annual Values 128

6.3.4.1 Present Value Factor 129

6.3.4.2 End Value Factor 129

6.3.4.3 Capital Return Factor 129

6.3.4.4 Sinking Fund Factor 130

6.3.4.5 Relationships between the Factors 130

6.4 Depreciation 131

6.4.1 Concept of Depreciation 131

6.4.2 Straight-Line Method 132

6.4.3 Accelerating Methods 133

6.4.3.1 Declining Balance Method 133

6.4.3.2 Total Year Number Method 134

6.4.4 Annuity Method 135

6.4.5 Numerical Example of Depreciation 135

6.5 Economic Assessment of Investment Projects 137

6.5.1 Total Cost Method 137

6.5.2 Benefi t/Cost Analysis 139

6.5.2.1 Net Benefi t Present Value Method 139

6.5.2.2 Benefi t/Cost Ratio Method 139

6.5.3 Internal Rate of Return Method 140

6.5.4 Length of Cash Flows 141

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6.6 Economic Assessment of Equipment Replacement 142

6.6.1 Replacement Delay Analysis 142

6.6.2 Estimating Economic Life 143

6.7 Uncertainty Analysis in Economic Assessment 144

6.7.1 Sensitivity Analysis 145

6.7.2 Probabilistic Analysis 145

6.8 Conclusions 147

7 DATA IN PROBABILISTIC TRANSMISSION PLANNING 1497.1 Introduction 149

7.2 Data for Power System Analysis 150

7.2.1 Equipment Parameters 150

7.2.1.1 Parameters of Overhead Line 150

7.2.1.2 Parameters of Cable 152

7.2.1.3 Parameters of Transformer 153

7.2.1.4 Parameters of Synchronous Generator 155

7.2.1.5 Parameters of Other Equipment 155

7.2.2 Equipment Ratings 155

7.2.2.1 Current Carrying Capacity of Overhead Line 157

7.2.2.2 Current Carrying Capacity of Cable 158

7.2.2.3 Loading Capacity of Transformer 159

7.2.3 System Operation Limits 161

7.2.4 Bus Load Coincidence Factors 161

7.3 Reliability Data in Probabilistic Planning 163

7.3.1 General Concepts of Reliability Data 163

7.3.2 Equipment Outage Indices 164

7.3.2.1 Outage Duration (OD) 165

7.3.2.2 Outage Frequency (OF) 166

7.3.2.3 Unavailability (U) 167

7.2.3.4 Calculating Equipment Outage Indices 167

7.2.3.5 Examples of Equipment Outage Indices 169

7.3.3 Delivery Point Indices 171

7.3.3.1 Defi nitions of Delivery Point Indices 172

7.3.3.2 Examples of Delivery Point Indices 175

7.4 Other Data 176

7.4.1 Data of Generation Sources 176

7.4.2 Data for Interconnections 177

7.4.3 Data for Economic Analysis 177

7.5 Conclusions 178

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CONTENTS xiii

8 FUZZY TECHNIQUES FOR DATA UNCERTAINTY 1818.1 Introduction 181

8.2 Fuzzy Models of System Component Outages 182

8.2.1 Basic Fuzzy Models 183

8.2.1.1 Fuzzy Model for Repair Time 183

8.2.1.2 Fuzzy Model for Outage Rate 185

8.2.1.3 Fuzzy Model for Unavailability 186

8.2.2 Weather-Related Fuzzy Models 186

8.2.2.1 Exposure to One Weather Condition 186

8.2.2.2 Exposure to Two Weather Conditions 187

8.2.2.3 Exposure to Multiple Weather Conditions 188

8.3 Mixed Fuzzy and Probabilistic Models for Loads 190

8.3.1 Fuzzy Model for Peak Load 190

8.3.2 Probabilistic Model for Load Curve 190

8.4 Combined Probabilistic and Fuzzy Techniques 192

8.4.1 Probabilistic Representation for Region-Divided Weather States 192

8.4.2 Hybrid Reliability Assessment Method 193

8.4.2.1 Evaluating Membership Functions of Reliability Indices 193

8.4.2.2 Defuzzifi cation of Membership Functions 196

8.5 Example 1: Case Study Not Considering Weather Effects 196

8.5.1 Case Description 196

8.5.2 Membership Functions of Reliability Indices 198

8.6 Example 2: Case Study Considering Weather Effects 202

8.6.1 Case Description 202

8.6.2 Membership Functions of Reliability Indices 204

8.6.3 Comparisons between Fuzzy and Traditional Models 211

8.7 Conclusions 212

9 NETWORK REINFORCEMENT PLANNING 2159.1 Introduction 215

9.2 Probabilistic Planning of Bulk Power Supply System 216

9.2.1 Description of Problem 216

9.2.2 Economic Comparison between Two Options 217

9.2.3 Reliability Evaluation Method 217

9.2.4 Reliability Comparison between Two Options 219

9.2.4.1 Data Preparation 219

9.2.4.2 EENS (Expected Energy Not Supplied) Indices 220

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9.2.5 Effect of the Existing HVDC Subsystem 221

9.2.5.1 Comparison between Cases with and without the Existing HVDC 221

9.2.5.2 Effect of Replacing a Reactor of the Existing HVDC 222

9.2.5.3 Comparison between the 230-kV AC Line and Existing HVDC 223

9.2.6 Summary 224

9.3 Probabilistic Planning of Transmission Loop Network 225


9.3.2 Planning Options 225

9.3.3 Planning Method 227

9.3.3.1 Basic Procedure 227

9.3.3.2 Evaluating Unreliability Cost 227

9.3.3.3 Evaluating Energy Loss Cost 228

9.3.3.4 Evaluating Annual Investment Cost 229

9.3.3.5 Calculating Present Values of Costs 229

9.3.4 Study Results 229

9.3.4.1 Unreliability Costs 229

9.3.4.2 Energy Loss Costs 230

9.3.4.3 Cash Flows of Annual Investments 231

9.3.4.4 Benefi t/Cost Analysis 232

9.3.5 Summary 234

9.4 Conclusions 234

10 RETIREMENT PLANNING OF NETWORK COMPONENTS 23710.1 Introduction 237

10.2 Retirement Timing of an Aged AC Cable 238


10.2.2 Methodology in Retirement Planning 239


10.2.2.2 Evaluating Parameters in the Weibull Model 240

10.2.2.3 Evaluating Unavailability of System Components 241

10.2.2.4 Evaluating Expected Damage Cost Caused by End-of-Life Failure 241

10.2.2.5 Economic Analysis Approach 243

10.2.3 Application to Retirement of the Aged AC Cable 244

10.2.3.1 α and β in the Weibull Model 244

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10.2.3.2 Unavailability Due to End-of-Life Failure 244

10.2.3.3 Expected Damage Costs 245

10.2.3.4 Economic Comparison 246

10.2.4 Summary 247

10.3 Replacement Strategy of an HVDC Cable 247


10.3.2 Methodology in Replacement Strategy 249


10.3.2.2 Evaluating Capacity State Probability of HVDC Subsystem 250

10.3.2.3 Evaluating Reliability of Overall System 250

10.3.2.4 Benefi t/Cost Analysis of Replacement Strategies 251

10.3.3 Application to Replacement of the Damaged HVDC Cable 251

10.3.3.1 Study Conditions 251

10.3.3.2 Capacity Probability Distributions of HVDC Subsystem 252

10.3.3.3 EENS Indices of Supply System 254

10.3.3.4 Strategy Analysis of Three Replacement Options 255

10.3.4 Summary 257

10.4 Conclusions 257

11 SUBSTATION PLANNING 25911.1 Introduction 259

11.2 Probabilistic Planning of Substation Confi guration 260


11.2.2 Planning Method 261

11.2.2.1 Simplifi ed Minimum Cutset Technique for Reliability Evaluation 261

11.2.2.2 Economic Analysis Approach 265

11.2.3 Comparison between the Two Confi gurations 266

11.2.3.1 Study Conditions and Data 266

11.2.3.2 Reliability Results 267

11.2.3.3 Economic Comparison 270

11.2.3.4 Other Considerations 271

11.2.4 Summary 272

11.3 Transformer Spare Planning 272

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11.3.2 Method of Probabilistic Spare Planning 273


11.3.2.2 Reliability Evaluation Technique for a Transformer Group 274

11.3.2.3 Reliability Criterion 275

11.3.3 Actual Example 276

11.3.3.1 Case Description 276

11.3.3.2 Fixed Turn Ratio Transformer Group 276

11.3.3.3 On-Load Tap Changer (OLTC) Transformer Group 278

11.3.3.4 Combined Fixed Turn Ratio and OLTC Transformer Group 278

11.3.4 Summary 280


12 SINGLE-CIRCUIT SUPPLY SYSTEM PLANNING 28312.1 Introduction 283

12.2 Reliability Performance of Single-Circuit Supply Systems 285

12.2.1 Delivery Point Reliability Indices 285

12.2.2 Contributions of Different Components to Reliability Indices 286

12.3 Planning Method of Single-Circuit Supply Systems 288

12.3.1 Basic and Weighted Reliability Indices 288

12.3.1.1 Basic Reliability Indices 289

12.3.1.2 Weighted Reliability Index 292

12.3.2 Unit Incremental Reliability Value Approach 293

12.3.2.1 Annual Capital Investment 293

12.3.2.2 Unit Incremental Reliability Value 293

12.3.3 Benefi t/Cost Ratio Approach 294

12.3.3.1 Expected Damage Cost 294

12.3.3.2 Benefi t/Cost Ratio 295

12.3.4 Procedure of Single-Circuit Supply System Planning 296

12.4 Application to Actual Utility System 298

12.4.1 Short List Based on Weighted Reliability Index 298

12.4.2 Financial Justifi cation of Reinforcement 301

12.4.3 Ranking Priority of Single-Circuit Systems 302


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APPENDIX A ELEMENTS OF PROBABILITY THEORY AND STATISTICS 309A.1 Probability Operation Rules 309

A.1.1 Intersection 309

A.1.2 Union 310

A.1.3 Conditional Probability 310

A.2 Four Important Probability Distributions 310

A.2.1 Binomial Distribution 310

A.2.2 Exponential Distribution 311

A.2.3 Normal Distribution 311

A.2.4 Weibull Distribution 312

A.3 Measures of Probability Distribution 313

A.3.1 Mathematical Expectation 313

A.3.2 Variance and Standard Deviation 313

A.3.3 Covariance and Correlation Coeffi cient 314

A.4 Parameter Estimation 314

A.4.1 Maximum Likelihood Estimation 314

A.4.2 Mean, Variance, and Covariance of Samples 315

A.4.3 Interval Estimation 315

A.5 Monte Carlo Simulation 316

A.5.1 Basic Concept 316

A.5.2 Random-Number Generator 317

A.5.3 Inverse Transform Method 317

A.5.4 Three Important Random Variates 318

A.5.4.1 Exponential Distribution Random Variate 318

A.5.4.2 Normal Distribution Random Variate 318

A.5.4.3 Weibull Distribution Random Variate 319

APPENDIX B ELEMENTS OF FUZZY MATHEMATICS 321B.1 Fuzzy Sets 321

B.1.1 Defi nition of Fuzzy Set 321

B.1.2 Operations of Fuzzy Sets 322

B.2 Fuzzy Numbers 323

B.2.1 Defi nition of Fuzzy Number 323

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B.2.2 Arithmetic Operation Rules of Fuzzy Numbers 323

B.2.2.1 Addition 323

B.2.2.2 Subtraction 323

B.2.2.3 Multiplication 323

B.2.2.4 Division 324

B.2.2.5 Maximum and Minimum Operations 324

B.2.3 Functional Operation of Fuzzy Numbers 324

B.3 Two Typical Fuzzy Numbers in Engineering Applications 325

B.3.1 Triangular Fuzzy Number 325

B.3.2 Trapezoidal Fuzzy Number 325

B.4 Fuzzy Relations 326

B.4.1 Basic Concepts 326

B.4.1.1 Refl exivity 327

B.4.1.2 Symmetry 327

B.4.1.3 Resemblance 327

B.4.1.4 Transitivity 327

B.4.1.5 Equivalence 327

B.4.2 Operations of Fuzzy Matrices 327

APPENDIX C ELEMENTS OF RELIABILITY EVALUATION 329C.1 Basic Concepts 329

C.1.1 Reliability Functions 329

C.1.2 Model of Repairable Component 330

C.2 Crisp Reliability Evaluation 331

C.2.1 Series and Parallel Networks 331

C.2.1.1 Series Network 331

C.2.1.2 Parallel Network 332

C.2.2 Minimum Cutsets 333

C.2.3 Markov Equations 333

C.3 Fuzzy Reliability Evaluation 335

C.3.1 Series and Parallel Networks Using Fuzzy Numbers 335

C.3.2 Minimum Cutset Approach Using Fuzzy Numbers 336

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C.3.3 Fuzzy Markov Models 338

C.3.3.1 Approach Based on Analytical Expressions 338

C.3.3.2 Approach Based on Numerical Computations 339

References 341

Index 349

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Transmission system planning is one of the most essential activities in the electric power industry. Billions of dollars are invested in electric utility systems through plan-ning activities every year. In the past and at present, transmission system planning is basically dominated by deterministic criteria and methods. However, there are a con-siderable number of uncertain factors in transmission systems, and therefore probabi-listic methods will provide planning solutions closer to reality. Fragmentary papers for probabilistic transmission planning have been published so far, but there has not been a book to systematically discuss the subject. The intent of this book is to fi ll the gap. It is important to appreciate that the purpose of introducing probabilistic models and techniques into transmission planning is not to replace but to enhance the existing deterministic criteria.

The book originated from my deep interest and involvement in this area. My tech-nical reports and papers formed core portions of the book, although general knowledge had to be included to ensure its systematization. All basic aspects in transmission plan-ning are covered, including load forecast and load modeling, conventional and special system analysis techniques, reliability evaluation, economic assessment, and data prep-aration and uncertainties, as well as various actual planning issues. The probabilistic concept is a main thread throughout the book and touches each chapter. It should be emphasized that probabilistic transmission planning is far beyond reliability evaluation, although the latter is one of most important procedures toward this direction. I have followed such a principle for book structure: any new contents associated with the subject are illustrated in detail, whereas for a topic for which readers can fi nd more information in other sources, an outline that is necessary for the book to stand alone is provided.

Materials in both theory and actual applications are offered. The examples in the applications are all based on real projects that have been implemented. I believe that the book will meet the needs of practicing engineers, researchers, professors, and gradu-ates in the power system fi eld.

I am indebted to many friends and colleagues. My special thankfulness goes to Roy Billinton, Paul Choudhury, Ebrahim Vaahedi, and Wijarn Wangdee for their con-tinuous support and encouragement in my daily work. The papers that I coauthored with them are parts of the materials used in the book. Some data and results in a few examples are based on Wijarn Wangdee ’ s reports.

PREFACE AND ACKNOWLEDGMENTS

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xxii PREFACE AND ACKNOWLEDGMENTS

Drs. Roy Billinton, Lalit Goel, Murty Bhavaraju, and Wenpeng Luan reviewed the book proposal/manuscript and provided many helpful suggestions. I would also thank all the individuals whose publications are listed in the References at the end of the book.

I am grateful for the cooperation and assistance received from the IEEE Press and John Wiley & Sons, especially Mary Mann and Melissa Yanuzzi.

Finally, I would like to thank my wife, Jun Sun, for her sacrifi ces and patience in the quite long time period during which I worked on the book.

W enyuan L i

Vancouver, Canada February 2011

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Documents

Probabilistic Transmission System Planning (Li/Transmission System Planning) || Frontmatter