Power System Control and Stability

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 λd and λq for a Cylindrical Rotor Machine: The Two-Axis Model 150 4.15.4 Neglecting Amortisseur Effects and λd and λq 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 λAD 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