Voltage Stability of Electric Power Systems – Thierry V. Cutsem, Costas Vournas – 1st Edition

PREFACE xi

Part I COMPONENTS AND PHENOMENA

1 INTRODUCTION 3
1.1 Why another Book? 3
1.2 Voltage Stability 4
1.3 Power System Stability Classification 7
1.4 Structure of this Book 10
1.5 Notation 12

2 TRANSMISSION SYSTEM ASPECTS 13
2.1 Single-Load Infinite-Bus System 13
2.2 Maximum Deliverable Power 15
2.3 Power-Voltage Relationships 22
2.4 Generator Reactive Power Requirement 25
2.5 A First Glance at Instability Mechanisms 26
2.6 Effect of Compensation 31
2.7 VQ Curves 38
2.8 Effect of Adjustable Transformer Ratios 41
2.9 Problems 44

3 GENERATION ASPECTS 47
3.1 A review of synchronous machine theory 47
3.2 Frequency and voltage controllers 64
3.3 Limiting devices affecting voltage stability 73
3.4 Voltage-reactive power characteristics of synchronous generators 78
3.5 Capability curves 86
3.6 Effect of machine limitations on deliverable power 89
3.7 Problems 91

4 LOAD ASPECTS 93
4.1 Voltage Dependence of Loads 94
4.2 Load Restoration Dynamics 97
4.3 Induction Motors 99
4.4 Load Tap Changers 113
4.5 Thermostatic Load Recovery 123
4.6 Generic Aggregate Load Models 126
4.7 HVDCLinks 131
4.8 Problems 132

Part II INSTABILITY MECHANISMS AND ANALYSIS METHODS 135

5 MATHEMATICAL BACKGROUND 137
5.1 Differential Equations (qualitative theory) 137
5.2 Bifurcations 153
5.3 Differential-Algebraic Systems 161
5.4 Multiple time scales 166

6 MODELLING: SYSTEM PERSPECTIVE 175
6.1 Outline of a general dynamic model 175
6.2 Network modelling 178
6.3 A detailed example 184
6.4 Time-scale decomposition perspective 193
6.5 Equilibrium equations for voltage stability studies 194
6.6 Detailed example (continued): equilibrium formulation 206
6.7 Number-Crunching Problem 210

7 LOADABILITY, SENSITIVITY AND BIFURCATION ANALYSIS 213
7.1 Loadability Limits 214
7.2 Sensitivity Analysis 223
7.3 Bifurcation Analysis 226
7.4 Eigenvector and Singular Vector Properties 246
7.5 Loadability or Bifurcation Surface 249
7.6 Loadability Limits in the Presence of Discontinuities 255
7.7 Problems 260

8 INSTABILITY MECHANISMS AND COUNTERMEASURES 263
8.1 Types of Countermeasures 263
8.2 Classification of Instability Mechanisms 265
8.3 Examples of Short-term Voltage Instability 269
8.4 Countermeasures to Short-term Instability 275
8.5 Case Studies of Long-term Voltage Instability 277
8.6 Corrective Actions against Long-term Instability 286
8.7 Problems 297 9

9 CRITERIA AND METHODS FOR VOLTAGE SECURITY ASSESSMENT 299
9.1 Voltage Security: Definitions and Criteria 299
9.2 Contingency Evaluation 304
9.3 Loadability Limit Computation 322
9.4 Secure Operation Limit Determination 334
9.5 Eigenanalysis for Instability Diagnosis 338
9.6 Examples from a Real-life System 343
9.7 Real-time Issues 356
REFERENCES 359
INDEX 377