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Power System Modeling, Computation, and Control

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Power System Modeling, Computation, and Control

Joe H. Chow, Juan J. Sanchez-Gasca, Luigi Vanfretti

ISBN: 978-1-119-54687-0 January 2020 Wiley-IEEE Press 640 Pages

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Description

Provides students with an understanding of the modeling and practice in power system stability analysis and control design, as well as the computational tools used by commercial vendors

Bringing together wind, FACTS, HVDC, and several other modern elements, this book gives readers everything they need to know about power systems. It makes learning complex power system concepts, models, and dynamics simpler and more efficient while providing modern viewpoints of power system analysis.

Power System Modeling, Computation, and Control provides students with a new and detailed analysis of voltage stability; a simple example illustrating the BCU method of transient stability analysis; and one of only a few derivations of the transient synchronous machine model. It offers a discussion on reactive power consumption of induction motors during start-up to illustrate the low-voltage phenomenon observed in urban load centers. Damping controller designs using power system stabilizer, HVDC systems, static var compensator, and thyristor-controlled series compensation are also examined. In addition, there are chapters covering flexible AC transmission Systems (FACTS)—including both thyristor and voltage-sourced converter technology—and wind turbine generation and modeling.

  • Simplifies the learning of complex power system concepts, models, and dynamics
  • Provides chapters on power flow solution, voltage stability, simulation methods, transient stability, small signal stability, synchronous machine models (steady-state and dynamic models), excitation systems, and power system stabilizer design
  • Includes advanced analysis of voltage stability, voltage recovery during motor starts, FACTS and their operation, damping control design using various control equipment, wind turbine models, and control
  • Contains numerous examples, tables, figures of block diagrams, MATLAB plots, and problems involving real systems
  • Written by experienced educators whose previous books and papers are used extensively by the international scientific community

Power System Modeling, Computation, and Control is an ideal textbook for graduate students of the subject, as well as for power system engineers and control design professionals.

Preface xvii

1 Introduction 1

1.1 Electrification 1

1.2 Generation, Transmission and Distribution Systems 2

1.2.1 Central Generating Station Model 2

1.2.2 Renewable Generation 4

1.2.3 Smart Grid 5

1.3 Time Scales 5

1.3.1 Dynamic Phenomena 6

1.3.2 Measurements and Data 7

1.3.3 Control Functions and System Operation 7

1.4 Organization of the Book 8

Part I System Concepts

2 Steady-State Power Flow 13

2.1 Introduction 13

2.2 Power Network Elements and Admittance Matrix 14

2.2.1 Transmission Lines 14

2.2.2 Transformers 15

2.2.3 Per Unit Representation 16

2.2.4 Building the Network Admittance Matrix 17

2.3 Active and Reactive Power Flow Calculations 19

2.4 Power Flow Formulation 23

2.5 Newton-Raphson Method 24

2.5.1 General Procedure 25

2.5.2 NR Solution of Power Flow Equation 26

2.6 Advanced Power Flow Features 32

2.6.1 Load Bus Voltage Regulation 32

2.6.2 Multi-Area Power Flow 33

2.6.3 Active Line Power Flow Regulation 34

2.6.4 Dishonest Newton-Raphson Method 35

2.6.5 Fast Decoupled Loadflow 35

2.6.6 DC Power Flow 36

2.7 Summary and Notes 37

2.8 Appendix 2.A: Two-Winding Transformer Model 37

2.9 Appendix 2.B: LU Decomposition and Sparsity Methods 42

2.10 Appendix 2.C: Power Flow and Dynamic Data for the 2-Area, 4-Machine System 45

2.11 Problems 46

3 Steady-State Voltage Stability Analysis 53

3.1 Introduction 53

3.2 Voltage Collapse Incidents 54

3.2.1 Tokyo, Japan: July 23, 1987 55

3.2.2 US Western Power System: July 2, 1996 55

3.3 Reactive Power Consumption on Transmission Lines 56

3.4 Voltage Stability Analysis of a Radial Load System 61

3.4.1 Maximum Power Transfer 66

3.5 Voltage Stability Analysis of Large Power Systems 68

3.6 Continuation Power Flow Method 72

3.6.1 Continuation Power Flow Algorithm 74

3.7 An AQ-Bus Method for Solving Power Flow 76

3.7.1 Analytical Framework for AQ-Bus Method 77

3.7.2 AQ-Bus Formulation for Constant-Power-Factor Loads 78

3.7.3 AQ-Bus Algorithm for computing voltage stability margins 79

3.8 Power System Components Affecting Voltage Stability 84

3.8.1 Shunt Reactive Power Supply 84

3.8.2 Under-Load Tap Changer (ULTC) 86

3.9 Hierarchical Voltage Control 88

3.10 Voltage Stability Margins and Indices 89

3.10.1 Voltage Stability Margins 89

3.10.2 Voltage Sensitivities 90

3.10.3 Singular Values and Eigenvalues of the Power Flow Jacobian Matrix 91

3.11 Summary and Notes 92

3.12 Problems 92

4 Power System Dynamics and Simulation 97

4.1 Introduction 97

4.2 Electromechanical Model of Synchronous Machines 98

4.3 Single-Machine Infinite-Bus (SMIB) System 101

4.4 Power System Disturbances 105

4.4.1 Fault-On Analysis 105

4.4.2 Post-Fault Analysis 108

4.4.3 Other Types of Faults 110

4.5 Simulation Methods 110

4.5.1 Modified Euler Methods 111

4.5.2 Adams-Bashforth Second-Order Method 114

4.5.3 Selecting Integration Stepsize 115

4.5.4 Implicit Integration Methods 117

4.6 Dynamic Models of Multi-Machine Power Systems 119

4.6.1 Constant-Impedance Loads 120

4.6.2 Generator Current Injections 121

4.6.3 Network Equation Extended to the Machine Internal Node 122

4.6.4 Reduced Admittance Matrix Approach 123

4.6.5 Method for Dynamic Simulation 123

4.7 Multi-Machine Power System Stability 128

4.7.1 Reference Frames for Machine Angles 129

4.8 Power System Toolbox 130

4.9 Summary and Notes 133

4.10 Problems 134

5 Direct Transient Stability Analysis 137

5.1 Introduction 137

5.2 Equal-Area Analysis of a SMIB System 138

5.2.1 Power-Angle Curve 138

5.2.2 Fault-On and Post-Fault Analysis 140

5.3 Transient Energy Functions 142

5.3.1 Lyapunov Functions 143

5.3.2 Energy Function for SMIB Electromechanical Model 143

5.4 Energy Function Analysis of a Disturbance Event 146

5.5 SMIB Model Phase Portrait and Region of Stability 151

5.6 Direct Stability Analysis using Energy Functions 153

5.7 Energy Functions for Multi-Machine Power Systems 155

5.7.1 Direct Stability Analysis for Multi-machine Systems 158

5.7.2 Computation of Critical Energy 159

5.8 Dynamic Security Assessment 162

5.9 Summary and Notes 163

5.10 Problems 163

6 Linear Analysis and Small-Signal Stability 165

6.1 Introduction 165

6.2 Electromechanical Modes 166

6.3 Linearization 167

6.3.1 State-Space Models 167

6.3.2 Input-Output Models 169

6.3.3 Modal Analysis and Time-Domain Solutions 169

6.3.4 Time Response of Linear Systems 171

6.3.5 Participation Factors 174

6.4 Linearized Models of Single-machine Infinite-Bus Systems 175

6.5 Linearized Models of Multi-Machine Systems 178

6.5.1 Synchronizing Torque Matrix and Eigenvalue Properties 180

6.5.2 Modeshapes and Participation Factors 181

6.6 Developing Linearized Models of Large Power Systems 184

6.6.1 Analytical Partial Derivatives 184

6.6.2 Numerical Linearization 188

6.7 Summary and Notes 190

6.8 Problems 191

Part II Synchronous Machine Models and their Control Systems

7 Steady-State Models and Operation of Synchronous Machines 197

Joe H Chow

7.1 Introduction 197

7.2 Physical Description 198

7.2.1 Amortisseur Bars 200

7.3 Synchronous Machine Model 200

7.3.1 Flux Linkage and Voltage Equations 201

7.3.2 Stator (Armature) Self and Mutual Inductances 203

7.3.3 Mutual Inductances between Stator and Rotor 204

7.3.4 Rotor Self and Mutual Inductances 205

7.4 Park Transformation 206

7.4.1 Electrical Power in dq0 Variables 209

7.5 Reciprocal, Equal Lad Per-Unit System 210

7.5.1 Stator Base Values 211

7.5.2 Stator Voltage Equations 212

7.5.3 Rotor Base Values 212

7.5.4 Rotor Voltage Equations 213

7.5.5 Stator Flux-Linkage Equations 214

7.5.6 Rotor Flux-Linkage Equations 214

7.5.7 Equal Mutual Inductance 214

7.6 Equivalent Circuits 219

7.6.1 Flux-Linkage Circuits 219

7.6.2 Voltage Equivalent Circuits 220

7.7 Steady-State Analysis 222

7.7.1 Open-Circuit Condition 222

7.7.2 Under-Load Condition 224

7.7.3 Drawing Voltage-Current Vector Diagrams 226

7.8 Saturation Effects 228

7.8.1 Representations of Magnetic Saturation 230

7.9 Generator Capability Curves 232

7.10 Summary and Notes 233

7.11 Problems 234

8 Dynamic Models of Synchronous Machines 237

Joe H Chow

8.1 Introduction 237

8.2 Machine Dynamic Response During Fault 238

8.2.1 DC Offset and Stator Transients 239

8.3 Transient and Subtransient Reactances and Time Constants 241

8.4 Subtransient Synchronous Machine Model 246

8.5 Other Synchronous Machine Models 253

8.5.1 Flux-Decay Model 253

8.5.2 Classical Model 255

8.6 dq-axes rotation between a generator and the system 255

8.7 Power System Simulation using Detailed Machine Models 257

8.7.1 Power System Simulation Algorithm 257

8.8 Linearized Models 259

8.9 Summary and Notes 261

8.10 Problems 262

9 Excitation Systems 265

9.1 Introduction 265

9.2 Excitation System Models 266

9.3 Type DC Exciters 267

9.3.1 Separately Excited DC exciter 268

9.3.2 Self-Excited DC Exciter 272

9.3.3 Voltage Regulator 273

9.3.4 Initialization of DC Type Exciters 274

9.3.5 Transfer Function Analysis 275

9.3.6 Generator and Exciter Closed-Loop System 278

9.3.7 Excitation System Response Ratios 280

9.4 Type AC Exciters 283

9.5 Type ST Excitation Systems 285

9.6 Load Compensation Control 288

9.7 Protective Functions 289

9.8 Summary and Notes 291

9.9 Appendix 9.A Anti-Windup Limits 291

9.10 Problems 292

10 Power System Stabilizers 295

10.1 Introduction 295

10.2 Single-Machine Infinite-Bus System Model 296

10.3 Synchronizing and Damping Torques 302

10.3.1 ∆ Te2 Under Constant Field Voltage 303

10.3.2 ∆ Te2 With Excitation System Control 304

10.4 Power System Stabilizer Design using Rotor Speed Signal 307

10.4.1 PSS Design Requirements 308

10.4.2 PSS Control Blocks 309

10.4.3 PSS Design Methods 312

10.4.4 Torsional Filters 318

10.4.5 PSS Field Tuning 319

10.4.6 Interarea Mode Damping 320

10.5 Other PSS Input Signals 320

10.5.1 Generator Terminal Bus Frequency 320

10.5.2 Electrical Power Output ∆ Pe 321

10.6 Integral-of-Accelerating-Power or Dual-Input PSS 322

10.7 Summary and Notes 324

10.8 Problems 325

11 Load and Induction Motor Models 327

Joe H Chow

11.1 Introduction 327

11.2 Static Load Models 329

11.2.1 Exponential Load Model 329

11.2.2 Polynomial Load Model 330

11.3 Incorporating ZIP Load Models in Dynamic Simulation and Linear Analysis 331

11.4 Induction Motors: Steady-State Models 336

11.4.1 Physical Description 337

11.4.2 Mathematical Description 337

11.4.3 Equivalent Circuits 342

11.4.4 Per-Unit Representation 344

11.4.5 Torque-Slip Characteristics 345

11.4.6 Reactive Power Consumption 347

11.4.7 Motor Startup 348

11.5 Induction Motors: Dynamic Models 350

11.5.1 Initialization 353

11.5.2 Reactive Power Requirement during Motor Stalling 356

11.6 Summary and Notes 358

11.7 Problems 359

12 Turbine-Governor Models and Frequency Control 361

12.1 Introduction 361

12.2 Steam Turbines 362

12.2.1 Turbine Configurations 362

12.2.2 Steam Turbine Governors 365

12.3 Hydraulic Turbines 367

12.3.1 Hydraulic Turbine Governors 373

12.3.2 Load Rejection of Hydraulic Turbines 375

12.4 Gas Turbines and Co-generation Plants 376

12.5 Primary Frequency Control 378

12.5.1 Isolated Turbine-Generator Serving Local Load 379

12.5.2 Interconnected Units 384

12.5.3 Frequency Response in US Power Grids 386

12.6 Automatic Generation Control 388

12.7 Turbine-Generator Torsional Oscillations and Subsynchronous Resonance 394

12.7.1 Torsional Modes 394

12.7.2 Electrical Network Modes 401

12.7.3 SSR Occurrence and Countermeasures 404

12.8 Summary and Notes 404

12.9 Problems 405

Part III Advanced Power System Topics

13 High-Voltage Direct-Current Transmission Systems 413

Joe H Chow

13.1 Introduction 413

13.1.1 HVDC System Installations and Applications 414

13.1.2 HVDC System Economics 417

13.2 AC/DC and DC/AC Conversion 418

13.2.1 AC-DC Conversion using Ideal Diodes 419

13.2.2 Three-Phase Full-Wave Bridge Converter 420

13.3 Line-Commutation Operation in HVDC Systems 424

13.3.1 Rectifier Operation 424

13.3.2 Inverter Operation 429

13.3.3 Multiple Bridge Converters 430

13.3.4 Equivalent Circuit 431

13.4 Control Modes 433

13.4.1 Mode 1: Normal Operation 434

13.4.2 Mode 2: Reduced-Voltage Operation 435

13.4.3 Mode 3: Transitional Mode 436

13.4.4 System Operation Under Fault Conditions 438

13.4.5 Communication Requirements 439

13.5 Multi-terminal HVDC Systems 439

13.6 Harmonics and Reactive Power Requirement 441

13.6.1 Harmonic Filters 441

13.6.2 Reactive Power Support 442

13.7 AC-DC Power Flow Computation 444

13.8 Dynamic Models 450

13.8.1 Converter Control 450

13.8.2 DC Line Dynamics 452

13.8.3 AC-DC Network Solution 453

13.9 Damping Control Design 455

13.10 Summary and Notes 460

13.11 Problems 461

14 Flexible AC Transmission Systems 465

14.1 Introduction 465

14.2 Static Var Compensator (SVC) 466

14.2.1 Circuit Configuration and Thyristor Switching 466

14.2.2 Steady-State Voltage Regulation and Stability Enhancement 468

14.2.3 Dynamic Voltage Control and Droop Regulation 474

14.2.4 Dynamic Simulation 479

14.2.5 Damping Control Design using SVC 481

14.3 Thyristor-Controlled Series Compensation (TCSC) 487

14.3.1 Fixed Series Compensation 488

14.3.2 TCSC Circuit Configuration and Switching 489

14.3.3 Voltage Reversal Control 490

14.3.4 Mitigation of Subsynchronous Oscillations 492

14.3.5 Dynamic Model and Damping Control Design 492

14.4 Shunt VSC Controllers 497

14.4.1 Voltage-Sourced Converters 498

14.4.2 Static Compensator 506

14.4.3 VSC HVDC Systems 511

14.5 Series and Coupled VSC Controllers 518

14.5.1 Static Synchronous Series Compensation 518

14.5.2 Unified Power Flow Controller (UPFC) 521

14.5.3 Interline Power Flow Controller (IPFC) 526

14.5.4 Dynamic Model 530

14.6 Summary and Notes 532

14.7 Problems 532

15 Wind Power Generation and Modeling 539

Juan J Sanchez-Gasca

15.1 Background 540

15.2 Wind Turbine Components 542

15.3 Wind Power 542

15.3.1 Blade Angle Orientation 545

15.3.2 Power Coefficient 547

15.4 Wind Turbine Types 549

15.4.1 Type 1 549

15.4.2 Type 2 549

15.4.3 Type 3 550

15.4.4 Type 4 551

15.5 Steady-State Characteristics 551

15.5.1 Type-1Wind Turbine 552

15.5.2 Type-2Wind Turbine 555

15.5.3 Example 15.3 555

15.5.4 Type-3 Wind Turbine 556

15.6 Wind Power Plant Representation 559

15.7 Overall Control Criteria for Variable Speed Wind Turbines 563

15.8 Wind Turbine Model for Transient Stability Planning Studies 566

15.8.1 Overall Model Structure 567

15.8.2 Generator/Converter Model 567

15.8.3 Electrical Control Model 569

15.8.4 Drive-Train Model 571

15.8.5 Torque Control Model 574

15.8.6 Aerodynamic Model 575

15.8.7 Pitch Controller 576

15.9 Plant-Level Control Model 581

15.9.1 Simulation Example 581

15.10 Summary and Notes 582

15.11 Problems 584

16 Power System Coherency and Model Reduction 587

16.1 Introduction 587

16.2 Interarea Oscillations and Slow Coherency 589

16.2.1 Slow Coherency 590

16.2.2 Slow Coherent Areas 593

16.2.3 Finding Coherent Groups of Machines 599

16.3 Generator Aggregation and Network Reduction 602

16.3.1 Generator Aggregation 603

16.3.2 Dynamic Aggregation 606

16.3.3 Load Bus Elimination 609

16.4 Simulation Studies 614

16.4.1 Singular perturbations method 616

16.5 Linear Reduced Model Methods 617

16.5.1 Modal truncation 618

16.5.2 Balanced Model Reduction method 618

16.6 Dynamic Model Reduction Software 619

16.7 Summary and Notes 619

16.8 Problems 620

References 623

Index 635