Power System Control and Stability

by Vittal, Vijay; Mccalley, James D.; Anderson, Paul M.; Fouad, A. A.

• ISBN13: 9781119433712
• ISBN10: 1119433711
• Edition: 3rd
• Format: Hardcover
• Copyright: 2019-10-15
• Publisher: Wiley-IEEE Press

Summary

The third edition of the landmark book on power system stability and control, revised and updated with new material 

The revised third edition of Power System Control and Stability continues to offer a comprehensive text on the fundamental principles and concepts of power system stability and control as well as new material on the latest developments in the field. The third edition offers a revised overview of power system stability and a section that explores the industry convention of q axis leading d axis in modeling of synchronous machines.

In addition, the third edition focuses on simulations that utilize digital computers and commercial simulation tools, it offers an introduction to the concepts of the stability analysis of linear systems together with a detailed formulation of the system state matrix. The authors also include a revised chapter that explores both implicit and explicit integration methods for transient stability. Power System Control and Stability offers an in-depth review of essential topics and:

• Discusses topics of contemporary and future relevance in terms of modeling, analysis and control
• Maintains the approach, style, and analytical rigor of the two original editions
• Addresses both power system planning and operational issues in power system control and stability
• Includes updated information and new chapters on modeling and simulation of round-rotor synchronous machine model, excitation control, renewable energy resources such as wind turbine generators and solar photovoltaics, load modeling, transient voltage instability, modeling and representation of three widely used FACTS devices in the bulk transmission network, and the modeling and representation of appropriate protection functions in transient stability studies
• Contains a set of challenging problems at the end of each chapter

Written for graduate students in electric power and professional power system engineers, Power System Control and Stability offers an invaluable reference to basic principles and incorporates the most recent techniques and methods into projects.

Author Biography

VIJAY VITTAL, PhD, is an Ira A. Fulton Chair Professor at the School of Electrical, Computer and Energy Engineering at Arizona State University. He is a Fellow of IEEE and a member of the U.S. National Academy of Engineering and has more than 35 years experience in teaching and research related to power system dynamics and control.

JAMES D. MCCALLEY, PhD, is an Anson Marston Distinguished Professor at Iowa State University. Dr. McCalley, a Fellow of the IEEE, was an industry engineer from 1985-1990 performing dynamic analysis of the Western US Interconnection. He has been on the faculty at Iowa State University since 1992 performing research and instruction in power system planning and dynamic analysis.

PAUL M. ANDERSON, PhD, served as a professor of engineering at Iowa State University, Arizona State University, and as a visiting professor at Washington State University. Dr. Anderson passed away in 2011.

A. A. FOUAD was Anson Marston Distinguished Professor Emeritus of Engineering at Iowa State University. He had more than 40 years experience in power system dynamics in teaching, research, and in industry. Dr. Fouad passed away in 2017.

Table of Contents

Foreword xiii

Preface xv

About the Authors xvii

Part I Introduction

Chapter 1 Power System Stability 3

1.1 Introduction 3

1.2 Requirements of a Reliable Electrical Power Service 4

1.3 Statement of the Problem 5

1.3.1 Definition of Stability 5

1.3.2 Classification of Stability Problems 6

1.3.3 Description of Stability Phenomenon 6

1.4 Effect of Impact on System Components 7

1.4.1 Loss of Synchronism 8

1.4.2 Synchronous Machine During a Transient 8

1.5 Methods of Simulation 10

1.5.1 Linearized System Equations 10

1.5.2 Large System with Nonlinear Equations 11

1.6 Planning and Operating Standards 11

Chapter 2 The Elementary Mathematical Model 19

2.1 Swing Equation 19

2.2 Units 21

2.3 Mechanical Torque 22

2.3.1 Unregulated Machines 22

2.3.2 Regulated Machines 24

2.4 Electrical Torque 26

2.4.1 Synchronous Torque 26

2.4.2 Other Electrical Torques 27

2.5 Power-Angle Curve of a Synchronous Machine 27

2.5.1 Classical Representation of a Synchronous Machine in Stability Studies 28

2.5.2 Synchronizing Power Coefficients 29

2.6 Natural Frequencies of Oscillation of a Synchronous Machine 30

2.7 System of One Machine Against an Infinite Bus: The Classical Model 31

2.8 Equal Area Criterion 37

2.8.1 Critical Clearing Angle 38

2.8.2 Application to a One-Machine System 39

2.8.3 Equal Area Criterion for a Two-Machine System 39

2.9 Classical Model of a Multimachine System 40

2.10 Classical Stability Study of a Nine-Bus System 42

2.10.1 Data Preparation 43

2.10.2 Preliminary Calculations 45

2.11 Shortcomings of the Classical Model 51

2.12 Block Diagram of One Machine 53

Chapter 3 System Response to Small Disturbances 61

3.1 Introduction 61

3.2 Types of Problems Studied 62

3.2.1 System Response to Small Impacts 62

3.2.2 Distribution of Power Impacts 62

3.3 The Unregulated Synchronous Machine 63

3.3.1 Demagnetizing Effect of Armature Reaction 64

3.3.2 Effect of Small Changes of Speed 65

3.4 Modes of Oscillation of an Unregulated Multimachine System 66

3.5 Regulated Synchronous Machine 73

3.5.1 Voltage Regulator with One Time Lag 73

3.5.2 Governor with One Time Lag 75

3.6 Distribution of Power Impacts 76

3.6.1 Linearization 77

3.6.2 A Special Case: t = 0⁺ 78

3.6.3 Average Behavior Prior to Governor Action (t = t₁) 79

Part II Electrical and Electromagnetic Dynamic Performance

Chapter 4 The Synchronous Machine 91

4.1 Introduction 91

4.2 Park’s Transformation 91

4.3 Flux Linkage Equations 94

4.3.1 Stator Self-Inductances 94

4.3.2 Rotor Self-Inductances 95

4.3.3 Stator Mutual Inductances 95

4.3.4 Rotor Mutual Inductances 95

4.3.5 Stator-to-Rotor Mutual Inductances 95

4.3.6 Transformation of Inductances 96

4.4 Voltage Equations 97

4.5 Formulation of State-Space Equations 99

4.6 Current Formulation 100

4.7 Per-Unit Conversion 101

4.7.1 Choosing a Base for Stator Quantities 102

4.7.2 Choosing a Base for Rotor Quantities 103

4.7.3 Comparison with Other Per-Unit Systems 104

4.7.4 The Correspondence of Per-Unit Stator EMF to Rotor Quantities 107

4.8 Normalizing the Voltage Equations 108

4.9 Normalizing the Torque Equations 113

4.9.1 The Normalized Swing Equation 114

4.9.2 Forms of the Swing Equation 114

4.10 Torque and Power 115

4.11 Equivalent Circuit of a Synchronous Machine 117

4.12 The Flux Linkage State-Space Model 119

4.12.1 The Voltage Equations 120

4.12.2 The Torque Equation 120

4.12.3 Machine Equations with Saturation Neglected 121

4.12.4 Treatment of Saturation 123

4.13 Load Equations 124

4.13.1 Synchronous Machine Connected to an Infinite Bus 124

4.13.2 Current Model 126

4.13.3 The Flux Linkage Model 127

4.14 Subtransient and Transient Inductances and Time Constants 131

4.14.1 Time Constants 133

4.15 Simplified Models of the Synchronous Machine 136

4.15.1 Neglecting Damper Windings: The E^’_q (One-Axis) Model 137

4.15.2 Voltage Behind Subtransient Reactance: The E^” Model 142

4.15.3 Neglecting λ_d and λ_q for a Cylindrical Rotor Machine: The Two-Axis Model 150

4.15.4 Neglecting Amortisseur Effects and λ_d and λ_q Terms: The One-Axis Model 153

4.15.5 Assuming Constant Flux Linkage in the Main Field Winding 154

4.16 Parameter Determination for Generator Dynamic Models 155

Chapter 5 The Simulation of Synchronous Machines 165

5.1 Introduction 165

5.2 Steady-State Equations and Phasor Diagrams 165

5.3 Machine Connected to an Infinite Bus Through a Transmission Line 168

5.4 Machine Connected to an Infinite Bus with Local Load at Machine Terminal 169

5.4.1 Special Case: The Resistive Load, Z_L = R_L + j0 170

5.4.2 General Case: Z_L Arbitrary 171

5.5 Determining Steady-State Conditions 172

5.5.1 Machine Connected to an Infinite Bus with Local Load 173

5.6 Examples 174

5.7 Initial Conditions for a Multimachine System 182

5.8 Determination of Machine Parameters from Manufacturers’ Data 183

5.9 Digital Simulation of Synchronous Machines 188

5.9.1 Digital Computation of Saturation 189

5.9.2 Updating λ_AD 192

Chapter 6 Load Modeling 199

6.1 Introduction 199

6.2 Static Load Models 200

6.3 Induction Motor Loads 203

6.3.1 Model Development of a Three-Phase Induction Machine 203

6.3.2 Representing Induction Machines in Stability Simulations 213

6.3.3 Stalled Motor Operation 215

6.4 Single-Phase Motors 216

6.4.1 Scroll Compressors 218

6.4.2 Point-on-Wave Effects 219

6.4.3 Dynamic Phasors 219

6.5 Power Electronic Loads 221

6.6 Self-Restoring Loads 224

6.7 Distributed Energy Resources 225

6.8 Composite Load Models 227

6.9 Data Development 229

6.9.1 Component Based 230

6.9.2 Measurement Based 232

Chapter 7 Simulation of Multimachine Systems 239

7.1 Introduction 239

7.2 Statement of the Problem 239

7.3 Matrix Representation of a Passive Network 240

7.3.1 Network in the Transient State 242

7.3.2 Converting to a Common Reference Frame 243

7.4 Converting Machine Coordinates to System Reference 244

7.5 Relation Between Machine Currents and Voltages 245

7.6 System Order 249

7.7 Machines Represented by Classical Methods 249

7.8 Linearized Model for the Network 252

7.9 Hybrid Formulation 258

7.10 Network Equations with Flux Linkage Model 260

7.11 Total System Equations 262

7.12 Alternating Solution Method 264

7.12.1 Nonlinear Loads 265

7.12.2 Network–Machine Interface 268

7.13 Simultaneous Solution Method 275

7.14 Design of Numerical Solvers 277

Chapter 8 Small-Signal Stability Analysis 281

8.1 Introduction 281

8.2 Fundamentals of Linear System Stability 282

8.3 Linearization of the Generator State-Space Current Model 284

8.4 Linearization of the Load Equation for the One-Machine Problem 288

8.5 Linearization of the Flux Linkage Model 293

8.6 State Matrix for Multimachine Systems 298

8.6.1 Formulation of the State Matrix 298

8.6.2 Representation of Static Loads in the State Matrix 300

8.7 Simplified Linear Model 312

8.7.1 The E' Equation 312

8.7.2 Electrical Torque Equation 313

8.7.3 Terminal Voltage Equation 314

8.7.4 Summary of Equations 315

8.7.5 Effect of Loading 318

8.7.6 Comparison with Classical Model 320

8.8 Block Diagrams 321

8.9 State-Space Representation of Simplified Model 322

Chapter 9 Excitation Systems 325

9.1 Simplified View of Excitation Control 325

9.2 Control Configurations 327

9.3 Typical Excitation Configurations 328

9.3.1 Primitive Systems 328

9.3.2 Type DC Excitation Control Systems with DC Generator-Commutator Exciters 332

9.3.3 Type AC Excitation Control Systems with Alternator-Rectifier Exciters 332

9.3.4 Type AC Excitation Control Systems with Alternator-SCR Exciter Systems 334

9.3.5 Type ST Excitation Control Systems with Compound-Rectifier Exciter Systems 335

9.3.6 Type ST Excitation Control System with Compound-Rectifier Exciter Plus Potential-Source-Rectifier Exciter 336

9.3.7 Type ST Excitation Control Systems with Potential-Source-Rectifier Exciter 336

9.4 Excitation Control System Definitions 337

9.4.1 Voltage Response Ratio 339

9.4.2 Exciter Voltage Ratings 341

9.4.3 Other Specifications 342

9.5 Voltage Regulator 344

9.5.1 Electromechanical Regulators 344

9.5.2 Early Electronic Regulators 345

9.5.3 Rotating Amplifier Regulators 345

9.5.4 Magnetic Amplifier Regulators 346

9.5.5 Digital Excitation Systems 348

9.6 Exciter Buildup 348

9.6.1 The DC Generator Exciter 348

9.6.2 Linear Approximations for DC Generator Exciters 356

9.6.3 The AC Generator Exciters 358

9.6.4 Solid-State Exciters 359

9.6.5 Buildup of a Loaded DC Exciter 360

9.6.6 Normalization of Exciter Equations 360

9.7 Limiting and Protection for Excitation Control Systems 361

9.7.1 Modeling Amplifier Limits 361

9.7.2 Control Limiters and Associated Protection 362

9.7.3 Volts per Hertz Protection 365

9.8 Excitation System Response 365

9.8.1 Noncontinuously Regulated Systems 365

9.8.2 Continuously Regulated Systems 369

9.9 State-Space Description of the Excitation System 379

9.9.1 Simplified Linear Model 381

9.9.2 Complete Linear Model 382

9.10 Computer Representation of Excitation Systems 389

9.10.1 Type DC1: DC Commutator Exciter 390

9.10.2 Type AC Systems: Alternator Supplied Rectifier Excitation Systems 393

9.10.3 Type AC1 System: Field-Controlled Alternator-Rectifier Excitation System 394

9.10.4 Type ST1 System: Controlled Rectifier System with Terminal Potential Supply Only 395

9.10.5 Type ST2 System: Static with Terminal Potential and Current Supplies 397

9.10.6 Type DC3 System: Noncontinuous Acting 399

9.11 Typical System Constants 400

9.12 The Effect of Excitation on Generator Performance 400

Chapter 10 The Effect of Excitation on Stability 409

10.1 Introduction 409

10.1.1 Transient Stability and Small-Signal Stability Considerations 410

10.2 Effect of Excitation on Generator Power Limits 411

10.3 Effect of the Excitation System on Transient Stability 415

10.3.1 The Role of the Excitation System in Classical Model Studies 415

10.3.2 Increased Reliance on Excitation Control to Improve Stability 417

10.3.3 Parametric Study 419

10.3.4 Reactive Power Demand During System Emergencies 421

10.4 Effect of Excitation on Small-Signal Stability 421

10.4.1 Examination of Small-Signal Stability by Routh’s Criterion 421

10.4.2 Further Considerations of the Regulator Gain and Time Constant 424

10.4.3 Effect on the Electrical Torque 425

10.5 Root-Locus Analysis of a Regulated Machine Connected to an Infinite Bus 426

10.6 Approximate System Representation 432

10.6.1 Approximate Excitation System Representation 432

10.6.2 Estimate of G_x(s) 433

10.6.3 The Inertial Transfer Function 437

10.7 Supplementary Stabilizing Signals 439

10.7.1 Block Diagram of the Linear System 439

10.7.2 Approximate Model of the Complete Exciter-Generator System 440

10.7.3 Lead Compensation 442

10.8 Linear Analysis of the Stabilized Generator 446

10.9 PSS Tuning in Multimachine Power Systems 448

10.10 Alternate Types of PSS 449

10.11 Digital Computer Transient Stability Studies 450

10.11.1 Effect of Fault Duration 452

10.11.2 Effect of the Power System Stabilizer 457

10.12 Some General Comments on the Effect of Excitation on Stability 459

Chapter 11 Dynamic Modeling and Representation of Renewable Energy Resources 463

11.1 Wind Turbine Generators 463

11.1.1 Type 1 WTGs 465

11.1.2 Type 2 WTGs 466

11.1.3 Type 3 WTGs 467

11.1.4 Type 4 WTGs 479

11.2 Photovoltaic Solar Plant Modeling 480

11.2.1 Generic Model of PV Solar Plant 480

11.2.2 Modified Generic Model of PV Solar Plant 481

Chapter 12 Voltage Stability 487

12.1 Modeling Requirements for Voltage Instability Analysis 487

12.2 Voltage Instability Analysis Using Time Domain Simulation 489

12.3 Dynamic VAr Planning and Optimization 493

12.3.1 Trajectory Sensitivity Analysis 493

12.3.2 Formulation of the VAr Optimization Problem 495

12.3.3 Implementation of the Dynamic VAr Optimization Approach 497

12.3.4 Application of Dynamic VAr Optimization Approach 499

Chapter 13 Dynamic Performance and Modeling of Flexible AC Transmission System(Facts) Components 503

13.1 Introduction 503

13.2 Static VAr System 503

13.2.1 Stability Characteristics of an SVS 506

13.2.2 Positive-Sequence Transient Stability Model for SVS 509

13.3 Thyristor-Controlled Series Compensation 511

13.3.1 Operating Modes of a TCSC 512

13.3.2 Equipment Characteristics and Limiting Conditions 513

13.3.3 TCSC Model for Transient Stability Studies 515

13.4 Static Synchronous Compensator 517

13.4.1 Statcom Model for Transient Stability Studies 519

13.5 High Voltage DC Transmission 519

Chapter 14 Power System Protection and Monitoring Associated With Power System Stability 525

14.1 Introduction 525

14.2 Power System Protection Functions Associated with Transient Stability Analysis 527

14.2.1 Bulk Transmission Line Out-of-Step Protection 527

14.2.2 Generator Out-of-Step Protection 533

14.2.3 Undervoltage Load Shedding 533

14.2.4 Underfrequency Load Shedding 534

14.3 Special Protection Schemes 535

14.3.1 Generation Rejection and Load Shedding 535

14.3.2 Controlled Islanding and Load Shedding 535

14.4 Synchrophasor-Based Monitoring of Power System Stability 537

14.4.1 Online Dynamic Security Assessment Using Synchrophasor Measurements and Decision Trees 537

14.4.2 Island Formation Prediction Scheme Supported by PMU Measurements 539

14.4.3 Real-Time Voltage Security and Oscillation Monitoring Using PMU Measurements 540

Part III Mechanical Dynamic Performance

Chapter 15 Speed Governing 545

15.1 The Flyball Governor 546

15.2 The Isochronous Governor 551

15.3 Incremental Equations of the Turbine 553

15.4 The Speed Droop Governor 556

15.5 The Floating Lever Speed Droop Governor 561

15.6 The Compensated Governor 564

15.7 Electronic Governors 570

15.8 Governor Models for Transient Stability Simulations 571

Chapter 16 Steam Turbine Prime Movers 577

16.1 Introduction 577

16.2 Power Plant Control Modes 579

16.2.1 The Turbine-Following Control Mode 579

16.2.2 The Boiler-Following Control Mode 579

16.2.3 The Coordinated Control Mode 580

16.3 Thermal Generation 581

16.4 A Steam Power Plant Model 582

16.5 Steam Turbines 583

16.6 Steam Turbine Control Operations 590

16.7 Steam Turbine Control Functions 592

16.8 Steam Generator Control 604

16.9 Fossil-Fueled Boilers 605

16.9.1 Drum-Type Boilers 606

16.9.2 Once-Through Boilers 613

16.9.3 Computer Models of Fossil-Fueled Boilers 617

16.10 Nuclear Steam Supply Systems 620

16.10.1 Boiling Water Reactors 620

16.10.2 Pressurized Water Reactors 620

Chapter 17 Hydraulic Turbine Prime Movers 627

17.1 Introduction 627

17.2 The Impulse Turbine 627

17.3 The Reaction Turbine 629

17.4 Propeller-Type Turbines 631

17.5 The Deriaz Turbine 632

17.6 Conduits, Surge Tanks, and Penstocks 633

17.7 Hydraulic System Equations 639

17.8 Hydraulic System Transfer Function 644

17.9 Simplifying Assumptions 647

17.10 Block Diagram for a Hydro System 649

17.11 Pumped-Storage Hydro Systems 650

17.12 Representation of Hydro Turbines and Governors in Stability Studies 651

Chapter 18 Combustion Turbine and Combined-Cycle Power Plants 655

18.1 Introduction 655

18.2 The Combustion Turbine Prime Mover 655

18.2.1 Combustion Turbine Control 657

18.2.2 Off-Nominal Frequency and Voltage Effects 658

18.2.3 Nonlinear Governor Droop Characteristic 659

18.2.4 Recent Advances in Modeling Gas Turbines 660

18.3 The Combined-Cycle Prime Mover 663

18.3.1 Fuel and Air Controls 664

18.3.2 The Gas Turbine Power Generation 668

18.3.3 The Steam Turbine Power Generation 669

18.3.4 Recent Development in Modeling Combined-Cycle Plants 671

Appendix A 673

Appendix B 675

Appendix C 685

Appendix D 695

Appendix E 727

Appendix F 737

Appendix G 759

Appendix H 767

Appendix I 775

Appendix J 783

Index 793