Power System Dynamics Stability and Control

An authoritative guide to the most up-to-date information on power system dynamics

The revised third edition of Power System Dynamics and Stability contains a comprehensive, state-of-the-art review of information on the topic. The third edition continues the successful approach of the first and second editions by progressing from simplicity to complexity. It places the emphasis first on understanding the underlying physical principles before proceeding to more complex models and algorithms. The book is illustrated by a large number of diagrams and examples.

The third edition of Power System Dynamics and Stability explores the influence of wind farms and virtual power plants, power plants inertia and control strategy on power system stability. The authors—noted experts on the topic—cover a range of new and expanded topics including: 

• Wide-area monitoring and control systems.
• Improvement of power system stability by optimization of control systems parameters.
• Impact of renewable energy sources on power system dynamics.
• The role of power system stability in planning of power system operation and transmission network expansion.
• Real regulators of synchronous generators and field tests.
• Selectivity of power system protections at power swings in power system.
• Criteria for switching operations in transmission networks.
• Influence of automatic control of a tap changing step-up transformer on the power capability area of the generating unit.
• Mathematical models of power system components such as HVDC links, wind and photovoltaic power plants. 
• Data of sample (benchmark) test systems.

Power System Dynamics: Stability and Control, Third Edition is an essential resource for students of electrical engineering and for practicing engineers and researchers who need the most current information available on the topic.

Jan Machowski is Full Professor at the Warsaw University of Technology, Faculty of Electrical Engineering, Poland.

Zbigniew Lubosny is Full Professor at Gdansk University of Technology, Faculty of Electrical and Control Engineering, Poland.

Janusz W. Bialek, formerly Professor at Durham University and Edinburgh University, UK.

James R. Bumby, formerly Reader at Durham University, UK.

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

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