Optimization of power system operation

OPTIMIZATION OF POWER

SYSTEM OPERATION

IEEE Press

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Piscataway, NJ 08854

IEEE Press Editorial Board

Tariq Samad, Editor in Chief

George W. Arnold Mary Lanzerotti Linda Shafer

Dmitry Goldgof Pui-In Mak MengChu Zhou

Ekram Hossain Ray Perez George Zobrist

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

Technical Reviewers

Malcom Irving, University of Birmingham

Kit Po Wong, The University of Western Australia

OPTIMIZATION OF POWER

SYSTEM OPERATION

Second Edition

JIZHONG ZHU

Copyright © 2015 by The Institute of Electrical and Electronics Engineers, Inc.

Published by John Wiley & Sons, Inc., Hoboken, New Jersey. All rights reserved

Published simultaneously in Canada

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Library of Congress Cataloging-in-Publication Data is available:

Zhu, Jizhong, 1961-

Optimization of power system operation / Jizhong Zhu. – Second edition.

pages cm – (IEEE Press series on power engineering)

Summary: “Addresses advanced methods and optimization technologies and their applications in power

systems”– Provided by publisher.

ISBN 978-1-118-85415-0 (hardback)

1. Electric power systems–Mathematical models. 2. Mathematical optimization. I. Title.

TK1005.Z46 2015

621.3101′

5196–dc23

2014023096

Printed in the United States of America

10 9 8 7 6 5 4 3 2 1

To My Wife and Son

CONTENTS

PREFACE xvii

PREFACE TO THE FIRST EDITION xix

ACKNOWLEDGMENTS xxi

AUTHOR BIOGRAPHY xxiii

CHAPTER 1 INTRODUCTION 1

1.1 Power System Basics 2

1.1.1 Physical Components 2

1.1.2 Renewable Energy Resources 6

1.1.3 Smart Grid 6

1.2 Conventional Methods 7

1.2.1 Unconstrained Optimization Approaches 7

1.2.2 Linear Programming 7

1.2.3 Nonlinear Programming 7

1.2.4 Quadratic Programming 8

1.2.5 Newton’s Method 8

1.2.6 Interior Point Methods 8

1.2.7 Mixed-Integer Programming 8

1.2.8 Network Flow Programming 9

1.3 Intelligent Search Methods 9

1.3.1 Optimization Neural Network 9

1.3.2 Evolutionary Algorithms 9

1.3.3 Tabu Search 9

1.3.4 Particle Swarm Optimization 10

1.4 Application of The Fuzzy Set Theory 10

References 10

CHAPTER 2 POWER FLOW ANALYSIS 13

2.1 Mathematical Model of Power Flow 13

2.2 Newton-Raphson Method 15

2.2.1 Principle of Newton-Raphson Method 15

2.2.2 Power Flow Solution with Polar Coordinate System 18

2.2.3 Power Flow Solution with Rectangular Coordinate System 23

2.3 Gauss-Seidel Method 31

2.4 P-Q Decoupling Method 33

2.4.1 Fast Decoupled Power Flow 33

2.4.2 Decoupled Power Flow without Major Approximation 40

2.5 DC Power Flow 43

2.6 State Estimation 44

vii

viii CONTENTS

2.6.1 State Estimation Model 44

2.6.2 WLS Algorithm for State Estimation 46

Problems and Exercises 48

References 49

CHAPTER 3 SENSITIVITY CALCULATION 51

3.1 Introduction 51

3.2 Loss Sensitivity Calculation 52

3.3 Calculation of Constrained Shift Sensitivity Factors 56

3.3.1 Definition of Constraint Shift Factors 56

3.3.2 Computation of Constraint Shift Factors 59

3.3.3 Constraint Shift Factors with Different References 65

3.3.4 Sensitivities for the Transfer Path 67

3.4 Perturbation Method for Sensitivity Analysis 68

3.4.1 Loss Sensitivity 68

3.4.2 Generator Shift Factor Sensitivity 69

3.4.3 Shift Factor Sensitivity for the Phase Shifter 69

3.4.4 Line Outage Distribution Factor (LODF) 70

3.4.5 Outage Transfer Distribution Factor (OTDF) 70

3.5 Voltage Sensitivity Analysis 71

3.6 Real-Time Application of the Sensitivity Factors 73

3.7 Simulation Results 74

3.7.1 Sample Computation for Loss Sensitivity Factors 75

3.7.2 Sample Computation for Constrained Shift Factors 81

3.7.3 Sample Computation for Voltage Sensitivity Analysis 85

3.8 Conclusion 86

Problems and Exercises 88

References 88

CHAPTER 4 CLASSIC ECONOMIC DISPATCH 91

4.1 Introduction 91

4.2 Input–Output Characteristics of Generator Units 91

4.2.1 Input–Output Characteristic of Thermal Units 91

4.2.2 Calculation of Input–Output Characteristic Parameters 93

4.2.3 Input–Output Characteristic of Hydroelectric Units 95

4.3 Thermal System Economic Dispatch Neglecting Network Losses 97

4.3.1 Principle of Equal Incremental Rate 97

4.3.2 Economic Dispatch without Network Losses 99

4.4 Calculation of Incremental Power Losses 105

4.5 Thermal System Economic Dispatch with Network Losses 107

4.6 Hydrothermal System Economic Dispatch 109

4.6.1 Neglecting Network Losses 109

4.6.2 Considering Network Losses 114

4.7 Economic Dispatch by Gradient Method 116

4.7.1 Introduction 116

4.7.2 Gradient Search in Economic Dispatch 116

CONTENTS ix

4.8 Classic Economic Dispatch by Genetic Algorithm 123

4.8.1 Introduction 123

4.8.2 GA-Based ED Solution 124

4.9 Classic Economic Dispatch by Hopfield Neural Network 128

4.9.1 Hopfield Neural Network Model 128

4.9.2 Mapping of Economic Dispatch to HNN 129

4.9.3 Simulation Results 132

Appendix A: Optimization Methods Used in Economic Operation 132

A.1 Gradient Method 132

A.2 Line Search 135

A.3 Newton-Raphson Optimization 135

A.4 Trust-Region Optimization 136

A.5 Newton–Raphson Optimization with Line Search 137

A.6 Quasi-Newton Optimization 137

A.7 Double Dogleg Optimization 139

A.8 Conjugate Gradient Optimization 139

A.9 Lagrange Multipliers Method 140

A.10 Kuhn–Tucker Conditions 141

Problems and Exercises 142

References 143

CHAPTER 5 SECURITY-CONSTRAINED ECONOMIC DISPATCH 145

5.1 Introduction 145

5.2 Linear Programming Method 145

5.2.1 Mathematical Model of Economic Dispatch with Security 145

5.2.2 Linearization of ED Model 146

5.2.3 Linear Programming Model 149

5.2.4 Implementation 150

5.2.5 Piecewise Linear Approach 156

5.3 Quadratic Programming Method 157

5.3.1 QP Model of Economic Dispatch 157

5.3.2 QP Algorithm 158

5.3.3 Implementation 160

5.4 Network Flow Programming Method 162

5.4.1 Introduction 162

5.4.2 Out-of-kilter Algorithm 164

5.4.3 N Security Economic Dispatch Model 171

5.4.4 Calculation of N−1 Security Constraints 174

5.4.5 N−1 Security Economic Dispatch 176

5.4.6 Implementation 178

5.5 Nonlinear Convex Network Flow Programming Method 183

5.5.1 Introduction 183

5.5.2 NLCNFP Model of EDC 184

5.5.3 Solution Method 189

5.5.4 Implementation 194

5.6 Two-Stage Economic Dispatch Approach 197

5.6.1 Introduction 197

5.6.2 Economic Power Dispatch—Stage One 197

x CONTENTS

5.6.3 Economic Power Dispatch—Stage Two 198

5.6.4 Evaluation of System Total Fuel Consumption 200

5.7 Security Constrained Economic Dispatch by Genetic Algorithms 201

Appendix A: Network Flow Programming 202

A.1 The Transportation Problem 203

A.2 Dijkstra Label-Setting Algorithm 209

Problems and Exercises 210

References 212

CHAPTER 6 MULTIAREAS SYSTEM ECONOMIC DISPATCH 215

6.1 Introduction 215

6.2 Economy of Multiareas Interconnection 215

6.3 Wheeling 220

6.3.1 Concept of Wheeling 220

6.3.2 Cost Models of Wheeling 222

6.4 Multiarea Wheeling 225

6.5 Maed Solved by Nonlinear Convex Network Flow Programming 226

6.5.1 Introduction 226

6.5.2 NLCNFP Model of MAED 227

6.5.3 Solution Method 231

6.5.4 Test Results 232

6.6 Nonlinear Optimization Neural Network Approach 235

6.6.1 Introduction 235

6.6.2 The Problem of MAED 235

6.6.3 Nonlinear Optimization Neural Network Algorithm 237

6.6.4 Test Results 241

6.7 Total Transfer Capability Computation in Multiareas 244

6.7.1 Continuation Power Flow Method 245

6.7.2 Multiarea TTC Computation 246

Appendix A: Comparison of Two Optimization Neural Network Models 248

A.1 For Proposed Neural Network M-9 248

A.2 For Neural Network M-10 in Reference [27] 249

Problems and Exercises 250

References 251

CHAPTER 7 UNIT COMMITMENT 253

7.1 Introduction 253

7.2 Priority Method 253

7.3 Dynamic Programming Method 256

7.4 Lagrange Relaxation Method 259

7.5 Evolutionary Programming-Based Tabu Search Method 263

7.5.1 Introduction 263

7.5.2 Tabu Search Method 265

7.5.3 Evolutionary Programming 266

7.5.4 Evolutionary Programming-Based Tabu-Search for Unit

Commitment 268

7.6 Particle Swarm Optimization for Unit Commitment 269

7.6.1 Algorithm 269

CONTENTS xi

7.6.2 Implementation 271

7.7 Analytic Hierarchy Process 273

7.7.1 Explanation of Proposed Scheme 274

7.7.2 Formulation of Optimal Generation Scheduling 274

7.7.3 Application of AHP to Unit Commitment 278

Problems and Exercises 293

References 295

CHAPTER 8 OPTIMAL POWER FLOW 297

8.1 Introduction 297

8.2 Newton Method 298

8.2.1 Neglecting Line Security Constraints 298

8.2.2 Consider Line Security Constraints 304

8.3 Gradient Method 307

8.3.1 OPF Problem without Inequality Constraints 307

8.3.2 Consider Inequality Constraints 311

8.4 Linear Programming OPF 312

8.5 Modified Interior Point OPF 314

8.5.1 Introduction 314

8.5.2 OPF Formulation 315

8.5.3 IP OPF Algorithms 317

8.6 OPF with Phase Shifter 328

8.6.1 Phase Shifter Model 330

8.6.2 Rule-Based OPF with Phase Shifter Scheme 332

8.7 Multiple Objectives OPF 337

8.7.1 Formulation of Combined Active and Reactive Dispatch 338

8.7.2 Solution Algorithm 344

8.8 Particle Swarm Optimization For OPF 346

8.8.1 Mathematical Model 346

8.8.2 PSO Methods [59,71–75] 348

8.8.3 OPF Considering Valve Loading Effects 354

Problems and Exercises 359

References 359

CHAPTER 9 STEADY-STATE SECURITY REGIONS 365

9.1 Introduction 365

9.2 Security Corridors 366

9.2.1 Concept of Security Corridor [4,5] 366

9.2.2 Construction of Security Corridor [5] 368

9.3 Traditional Expansion Method 371

9.3.1 Power Flow Model 371

9.3.2 Security Constraints 372

9.3.3 Definition of Steady-State Security Regions 372

9.3.4 Illustration of the Calculation of Steady-State Security Region 373

9.3.5 Numerical Examples 374

9.4 Enhanced Expansion Method 374

9.4.1 Introduction 374

9.4.2 Extended Steady-State Security Region 375

xii CONTENTS

9.4.3 Steady-State Security Regions with N−1 Security 377

9.4.4 Consideration of the Failure Probability of Branch Temporary

Overload 377

9.4.5 Implementation 378

9.4.6 Test Results and Analysis 380

9.5 Fuzzy Set and Linear Programming 385

9.5.1 Introduction 385

9.5.2 Steady-State Security Regions Solved by Linear

Programming 385

9.5.3 Numerical Examples 389

Appendix A: Linear Programming 391

A.1 Standard Form of LP 391

A.2 Duality 394

A.3 The Simplex Method 397

Problems and Exercises 403

References 405

CHAPTER 10 APPLICATION OF RENEWABLE ENERGY 407

10.1 Introduction 407

10.2 Renewable Energy Resources 407

10.2.1 Solar Energy 407

10.2.2 Wind Energy 408

10.2.3 Hydropower 408

10.2.4 Biomass Energy 409

10.2.5 Geothermal Energy 409

10.3 Operation of Grid-Connected PV System 409

10.3.1 Introduction 409

10.3.2 Model of PV Array 410

10.3.3 Control of Three-Phase PV Inverter 411

10.3.4 Maximum Power Point Tracking 412

10.3.5 Distribution Network with PV Plant 412

10.4 Voltage Calculation of Distribution Network 414

10.4.1 Voltage Calculation without PV Plant 414

10.4.2 Voltage Calculation with PV Plant Only 415

10.4.3 Voltage Calculation of Distribution Feeders with PV Plant 415

10.4.4 Voltage Impact of PV Plant in Distribution Network 415

10.5 Frequency Impact of PV Plant in Distribution Network 417

10.6 Operation of Wind Energy [1,10–16] 420

10.6.1 Introduction 420

10.6.2 Operation Principles of Wind Energy 421

10.6.3 Types and Operating Characteristics of the Wind

Turbine 421

10.6.4 Generators Used in Wind Power 424

10.7 Voltage Analysis in Power System with Wind Energy 426

10.7.1 Introduction 426

10.7.2 Voltage Dip 427

10.7.3 Simulation Results 428

Problems and Exercises 432

References 434

CONTENTS xiii

CHAPTER 11 OPTIMAL LOAD SHEDDING 437

11.1 Introduction 437

11.2 Conventional Load Shedding 438

11.3 Intelligent Load Shedding 440

11.3.1 Description of Intelligent Load Shedding 440

11.3.2 Function Block Diagram of the ILS 442

11.4 Formulation of Optimal Load Shedding 443

11.4.1 Objective Function–Maximization of Benefit Function 443

11.4.2 Constraints of Load Curtailment 443

11.5 Optimal Load Shedding with Network Constraints 444

11.5.1 Calculation of Weighting Factors by AHP 444

11.5.2 Network Flow Model 445

11.5.3 Implementation and Simulation 446

11.6 Optimal Load Shedding without Network Constraints 451

11.6.1 Everett Method 451

11.6.2 Calculation of the Independent Load Values 455

11.7 Distributed Interruptible Load Shedding (DILS) 460

11.7.1 Introduction 460

11.7.2 DILS Methods 461

11.8 Undervoltage Load Shedding 467

11.8.1 Introduction 467

11.8.2 Undervoltage Load Shedding Using Distributed Controllers 468

11.8.3 Optimal Location for Installing Controller 471

11.9 Congestion Management 473

11.9.1 Introduction 473

11.9.2 Congestion Management in US Power Industry 473

11.9.3 Congestion Management Method 476

Problems and Exercises 480

References 481

CHAPTER 12 OPTIMAL RECONFIGURATION OF ELECTRICAL

DISTRIBUTION NETWORK 483

12.1 Introduction 483

12.2 Mathematical Model of DNRC 484

12.3 Heuristic Methods 486

12.3.1 Simple Branch Exchange Method 486

12.3.2 Optimal Flow Pattern 487

12.3.3 Enhanced Optimal Flow Pattern 487

12.4 Rule-Based Comprehensive Approach 488

12.4.1 Radial Distribution Network Load Flow 488

12.4.2 Description of Rule-Based Comprehensive Method 490

12.4.3 Numerical Examples 491

12.5 Mixed-Integer Linear-Programming Approach 492

12.5.1 Selection of Candidate Subnetworks 496

12.5.2 Simplified Mathematical Model 501

12.5.3 Mixed-Integer Linear Model 502

12.6 Application of GA to DNRC 504

12.6.1 Introduction 504