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 ¿d and ¿q for a Cylindrical Rotor Machine: The Two-Axis Model 150
4.15.4 Neglecting Amortisseur Effects and ¿d and ¿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, ZL = RL + j0 170
5.4.2 General Case: ZL 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 ¿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 Gx(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
