Power System Wide–area Stability Analysis and Control

JING MA, PhD, is a professor in the School of Electrical and Electronic Engineering at North China Electric Power University, Beijing, China. He is a lead member of the National Science and Technology Support Program of China and a consultant with the China Electric Power Research Institute. Dr. Ma pioneered the application of Guardian Map Theory, Perturbation Theory, and the Markov model for the analysis of large time-varying, strong time-delay and high uncertainties into power system stability analysis process. He has innovated robust and adaptive control strategies using Federated Kalman Filters, Dual Youla Parameterization and Classification and Regression Tree to establish a wide-area control system with high accuracy and efficiency.

About the Author ix

Preface xi

1 Basic Theories of Power System Security Defense 1

1.1 Introduction 1

1.2 Power System Reliability and Stability 2

1.2.1 Reliability of Power System 2

1.2.2 Stability of Power System 4

1.3 Three Defense Lines in the Power System 7

1.3.1 Classification of Disturbance in the Power System 7

1.3.2 Power System Operation State 8

1.3.3 Three Defense Lines in Power System Stability Control 10

1.3.4 Functions of Defense System 12

1.4 Summary 15

References 15

2 Power System Analysis and Control Theory 17

2.1 Introduction 17

2.2 Mathematical Model of Power System 17

2.2.1 Mathematical Model of Synchronous Generator 17

2.2.2 Mathematical Model of Excitation System 22

2.2.3 Mathematical Model of Prime Mover and Speed Governor 24

2.2.4 Mathematical Model of Load 27

2.3 Power System Stability Analysis Method 29

2.3.1 Time‐Domain Simulation Method 29

2.3.2 Eigenvalue Analysis Method 31

2.3.3 Transient Energy Function Method 33

2.4 Automatic Control Theory 33

2.4.1 Classical Control Theory 34

2.4.2 Modern Control Theory 35

2.4.3 Large System Theory and Intelligent Control Theory 36

2.5 Summary 38

References 38

3 Wide‐Area Information Monitoring 41

3.1 Introduction 41

3.2 Test System 41

3.2.1 Four‐Generator Two‐Area System 41

3.2.2 Sixteen‐Generator System 42

3.2.3 Western Electricity Coordinating Council 43

3.3 Optimal Selection of Wide‐Area Signal 44

3.3.1 Wide‐Area Signal Selection Method Based on the Contribution Factor 44

3.3.2 Simulation Verification 48

3.4 Optimal Selection of Wide‐Area Controller 57

3.4.1 Mathematical Background 57

3.4.2 Example Test System 62

3.4.3 GPSS Based on Collocated Controller Design 63

3.4.4 Testing Results and Analysis 64

3.5 Summary 70

References 71

4 Stability Analysis of Stochastic System 73

4.1 Introduction 73

4.2 Stability Analysis of Stochastic Parameter System 74

4.2.1 Interval Model and Second‐Order Perturbation Theory‐Based Modal Analysis 74

4.2.2 Power System Small‐Signal Stability Region Calculation Method Based on the Guardian Map Theory 82

4.3 Stability Analysis of Stochastic Structure System 102

4.3.1 Model‐Trajectory‐Based Method for Analyzing the Fault System 102

4.3.2 Angle Stability Analysis of Power System Considering Cascading Failure 119

4.4 Stability Analysis of Stochastic Excitation System 137

4.4.1 Model of Multiple Operating Conditions System Considering the Stochastic Characteristic of Wind Speed 137

4.4.2 Simulation Analysis 146

4.5 Summary 152

References 153

5 Stability Analysis of Time‐Delay System 155

5.1 Introduction 155

5.2 Stability Analysis of a Non‐Jump Time‐Delay System 156

5.2.1 Stochastic Stability Analysis of Power System with Time Delay Based on Itô Differential 156

5.2.2 Stochastic Time‐Delay Stability Analysis of a Power System with Wind Power Connection 168

5.3 Stability Analysis of a Jump Time‐Delay System 182

5.3.1 Jump Power System Time‐Delay Stability Analysis Based on Discrete Markov Theory 182

5.3.2 Time‐Delay Stability Analysis of Power System Based on the Fault Chains and Markov Process 196

5.4 Summary 208

Appendix A 209

References 210

6 Wide‐Area Robust Control 213

6.1 Introduction 213

6.2 Robust Control for Internal Uncertainties 214

6.2.1 Multiobjective Robust H 2 /H ∞ Control Considering Uncertainties for Damping Oscillation 214

6.2.2 Robust H 2 /H ∞ Control Strategy Based on Polytope Uncertainty 221

6.3 Optimal Robust Control 226

6.3.1 Wide‐Area Damping Robust Control Based on Nonconvex Stable Region 226

6.3.2 Wide‐Area Damping Robust H 2 /H ∞ Control Strategy Based on Perfect Regulation 236

6.4 Error Tracking Robust Control 243

6.4.1 Control Algorithm 245

6.4.2 Simulation Verification 248

6.5 Summary 251

References 252

7 Wide‐Area Adaptive Control 253

7.1 Introduction 253

7.2 Adaptive Control Considering Operating Condition Identification 254

7.2.1 Federated Kalman Filter Based Adaptive Damping Control of Inter‐Area Oscillations 254

7.2.2 Classification and Regression Tree Based Adaptive Damping Control of Inter‐Area Oscillations 268

7.3 Adaptive Control Considering Controller Switching 288

7.3.1 Dual Youla Parameterization Based Adaptive Wide‐Area Damping Control 288

7.3.2 Continuous Markov Model Based Adaptive Control Strategy for Time‐Varying Power System 303

7.3.3 Discrete Markov Model Based Adaptive Control Strategy of Multiple‐Condition Power System 318

7.3.4 Adaptive Controller Switching Considering Time Delay 327

7.4 Summary 339

References 340

Index 341