About the Authors xix
List of Symbols & Abbreviations xxi
Part I Introduction to Power Systems 1
1 Introduction 3
1.1 Stability and Control of a Dynamic System 3
1.2 Classification of Power System Dynamics 5
1.3 Two Pairs of Important Quantities 7
1.4 Stability of a Power System 8
1.5 Security of a Power System 9
2 Power System Components 13
2.1 Introduction 13
2.2 Structure of the Electric Power System 14
2.3 Generating Units 17
2.4 Substations 33
2.5 Transmission and Distribution Network 34
2.6 Protection 49
2.7 Wide Area Measurement Systems 53
3 The Power System in the Steady State 57
3.1 Transmission Lines 57
3.2 Transformers 64
3.3 Synchronous Generators 68
3.4 Power System Loads 101
3.5 Network Equations 110
3.6 Power Flows in Transmission Networks 114
Part II Introduction to Power System Dynamics 123
4 Electromagnetic Phenomena 125
4.1 Fundamentals 125
4.2 Three-phase Short Circuit on a Synchronous Generator 130
4.3 Phase-to-phase Short Circuit 153
4.4 Switching Operations 164
4.5 Subsynchronous Resonance 191
5 Electromechanical Dynamics ¢" Small Disturbances 195
5.1 Swing Equation 195
5.2 Damping Power 195
5.3 Equilibrium Points 199
5.4 Steady-state Stability of Unregulated System 200
5.5 Steady-state Stability of the Regulated System 219
6 Electromechanical Dynamics ¢" Large Disturbances 229
6.1 Transient Stability 229
6.2 Swings in Multi-machine Systems 243
6.3 Direct Method for Stability Assessment 246
6.4 Synchronization 262
6.5 Asynchronous Operation and Resynchronization 264
6.6 Out-of-step Protection System 269
7 Wind Power 283
7.1 Wind Turbines 283
7.2 Generator Systems 287
7.3 Induction Machine Equivalent Circuit 291
7.4 Induction Generator Coupled to the Grid 294
7.5 Induction Generators with Slightly Increased Speed Range via External Rotor Resistance 297
7.6 Induction Generators with Significantly Increased Speed Range 299
7.7 Fully Rated Converter Systems (Wide Speed Control) 307
7.8 Peak Power Tracking of Variable Speed Wind Turbines 309
7.9 Connections of Wind Farms 309
7.10 Fault Behavior of Induction Generators 310
7.11 Influence of Wind Generators on Power System Stability 312
8 Voltage Stability 315
8.1 Network Feasibility 315
8.2 Stability Criteria 320
8.3 Critical Load Demand and Voltage Collapse 325
8.4 Static Analyses 332
8.5 Dynamic Analysis 342
8.6 Prevention of Voltage Collapse 348
8.7 Self-excitation of a Generator Operating on a Capacitive Load 349
9 Frequency Stability and Control 355
9.1 Automatic Generation Control 355
9.2 Stage I ¢" Rotor Swings in the Generators 368
9.3 Stage II ¢" Frequency Drop 371
9.4 Stage III ¢" Primary Control 373
9.5 Stage IV ¢" Secondary Control 378
9.6 Simplified Simulation Models 387
9.7 Series FACTS Devices in Tie-lines 392
9.8 Static Analysis by Snapshots of Power Flow 404
10 Stability Enhancement 407
10.1 Excitation Control System 408
10.2 Turbine Control System 415
10.3 Braking Resistors 419
10.4 Generator Tripping 421
10.5 Shunt FACTS Devices 423
10.6 Series Compensators 442
10.7 Unified Power Flow Controller 449
10.8 HVDC Links in Transmission Network 455
Part III Advanced Topics in Power System Dynamics 467
11 Advanced Power System Modeling 469
11.1 Synchronous Generator 469
11.2 Excitation Systems 496
11.3 Turbines and Turbine Governors 505
11.4 Wind Turbine Generator Systems and Wind Farms 522
11.5 Photovoltaic Power Plants 544
11.6 HVDC Links 548
11.7 Facts Devices 557
11.8 Dynamic Load Models 559
12 Steady-state Stability of Multi-machine Systems 561
12.1 Mathematical Background 561
12.2 Steady-state Stability of Unregulated System 580
12.3 Steady-state Stability of the Regulated System 589
13 Power System Dynamic Simulation 601
13.1 Numerical Integration Methods 602
13.2 The Partitioned Solution 606
13.3 The Simultaneous Solution Methods 618
13.4 Comparison Between the Methods 619
13.5 Modeling of Unbalanced Faults 620
13.6 Evaluation of Power System Dynamic Response 622
14 Stability Studies in Power System Planning 625
14.1 Purposes and Kinds of Analyses 625
14.2 Planning Criteria 629
14.3 Automation of Analyses and Reporting 641
15 Optimization of Control System Parameters 643
15.1 Grid Code Requirements 643
15.2 Optimization Methods 644
15.3 Linear Regulators 647
15.4 Optimal Regulators LQG, LQR, and LQI 681
15.5 Robust Regulators H2, h¢ 685
15.6 Nonlinear Regulators 693
15.7 Adaptive Regulators 694
15.8 Real Regulators and Field Tests 700
16 Wide-Area Monitoring and Control 709
16.1 Wide Area Measurement Systems 709
16.2 Examples of WAMS Applications 718
17 Impact of Renewable Energy Sources on Power System Dynamics 735
17.1 Renewable Energy Sources 735
17.2 Inertia in the Electric Power System 742
17.3 Virtual Inertia 758
18 Power System Model Reduction ¢" Equivalents 775
18.1 Types of Equivalents 775
18.2 Network Transformation 776
18.3 Aggregation of Generating Units 784
18.4 Equivalent Model of External Subsystem 785
18.5 Coherency Recognition 786
18.6 Properties of Coherency Based Equivalents 790
Appendix 809
A.1 Per-unit System 809
A.1.1 Stator Base Quantities 809
A.1.2 Power Invariance 811
A.1.3 Rotor Base Quantities 811
A.1.4 Power System Base Quantities 814
A.1.5 Transformers 815
A.2 Partial Inversion 816
A.3 Linear Ordinary Differential Equations 817
A.3.1 Fundamental System of Solutions 817
A.3.2 Real and Distinct Roots 819
A.3.3 Repeated Real Roots 820
A.3.4 Complex and Distinct Roots 821
A.3.5 Repeated Complex Roots 825
A.3.6 First-order Complex Differential Eq. 825
A.4 Prony Analysis 826
A.5 Limiters and Symbols in Block Diagrams 832
A.5.1 Addition, Multiplication, and Division 832
A.5.2 Simple Integrator 833
A.5.3 Simple Time Constant 833
A.5.4 Lead¢"lag Block 834
References 835
Index 847
