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PART Ⅰ GENERAL BACKGROUND 3

1 GENERAL CHARACTERISTICS OF MODERN POWER SYSTEMS 3

1.1 Evolution of electric power systems 3

1.2 Structure of the power system 5

1.3 Power system control 8

1.4 Design and operating criteria for stability 13

References 16

2 INTRODUCTION TO THE POWER SYSTEM STABILITY PROBLEM 17

2.1 Basic concepts and definitions 17

2.1.1 Rotor angle stability 18

2.1.2 Voltage stability and voltage collapse 27

2.1.3 Mid-term and long-term stability 33

2.2 Classification of stability 34

2.3 Historical review of stability problems 37

References 40

PART Ⅲ EQUIPMENT CHARACTERISTICS AND MODELLING 45

3 SYNCHRONOUS MACHINE THEORY AND MODELLING 45

3.1 Physical description 46

3.1.1 Armature and field structure 46

3.1.2 Machines with multiple pole pairs 49

3.1.3 MMF waveforms 49

3.1.4 Direct and quadrature axes 53

3.2 Mathematical description of a synchronous machine 54

3.2.1 Review of magnetic circuit equations 56

3.2.2 Basic equations of a synchronous machine 59

3.3 The dq0 transformation 67

3.4 Per unit representation 75

3.4.1 Per unit system for the stator quantities 75

3.4.2 Per unit stator voltage equations 76

3.4.3 Per unit rotor voltage equations 77

3.4.4 Stator flux linkage equations 78

3.4.5 Rotor flux linkage equations 78

3.4.6 Per unit system for the rotor 79

3.4.7 Per unit power and torque 83

3.4.8 Alternative per unit systems and transformations 83

3.4.9 Summary of per unit equations 84

3.5 Equivalent circuits for direct and quadrature axes 88

3.6 Steady-state analysis 93

3.6.1 Voltage,current,and flux linkage relationships 93

3.6.2 Phasor representation 95

3.6.3 Rotor angle 98

3.6.4 Steady-state equivalent circuit 99

3.6.5 Procedure for computing steady-state values 100

3.7 Electrical transient performance characteristics 105

3.7.1 Short-circuit current in a simple RL circuit 105

3.7.2 Three-phase short-circuit at the terminals of a synchronous machine 107

3.7.3 Elimination of dc offset in short-circuit current 108

3.8 Magnetic saturation 110

3.8.1 Open-circuit and short-circuit characteristics 110

3.8.2 Representation of saturation in stability studies 112

3.8.3 Improved modelling of saturation 117

3.9 Equations of motion 128

3.9.1 Review of mechanics of motion 128

3.9.2 Swing equation 128

3.9.3 Mechanical starting time 132

3.9.4 Calculation of inertia constant 132

3.9.5 Representation in system studies 135

References 136

4 SYNCHRONOUS MACHINE PARAMETERS 139

4.1 Operational parameters 139

4.2 Standard parameters 144

4.3 Frequency-response characteristics 159

4.4 Determination of synchronous machine parameters 161

References 166

5 SYNCHRONOUS MACHINE REPRESENTATION IN STABILITY STUDIES 169

5.1 Simplifications essential for large-scale studies 169

5.1.1 Neglect of stator pψ terms 170

5.1.2 Neglecting the effect of speed variations on stator voltages 174

5.2 Simplified model with amortisseurs neglected 179

5.3 Constant flux linkage model 184

5.3.1 Classical model 184

5.3.2 Constant flux linkage model including the effects of subtransient circuits 188

5.3.3 Summary of simple models for different time frames 190

5.4 Reactive capability limits 191

5.4.1 Reactive capability curves 191

5.4.2 V curves and compounding curves 196

References 198

6 AC TRANSMISSION 199

6.1 Transmission lines 200

6.1.1 Electrical characteristics 200

6.1.2 Performance equations 201

6.1.3 Natural or surge impedance loading 205

6.1.4 Equivalent circuit of a transmission line 206

6.1.5 Typical parameters 209

6.1.6 Performance requirements of power transmission lines 211

6.1.7 Voltage and current profile under no-load 211

6.1.8 Voltage-power characteristics 216

6.1.9 Power transfer and stability considerations 221

6.1.10 Effect of line loss on V-P and Q-P characteristics 225

6.1.11 Thermal limits 226

6.1.12 Loadability characteristics 228

6.2 Transformers 231

6.2.1 Representation of two-winding transformers 232

6.2.2 Representation of three-winding transformers 240

6.2.3 Phase-shifting transformers 245

6.3 Transfer of power between active sources 250

6.4 Power-flow analysis 255

6.4.1 Network equations 257

6.4.2 Gauss-Seidel method 259

6.4.3 Newton-Raphson（N-R）method 260

6.4.4 Fast decoupled load-flow（FDLF）methods 264

6.4.5 Comparison of the power-flow solution methods 267

6.4.6 Sparsity-oriented triangular factorization 268

6.4.7 Network reduction 268

References 269

7 POWER SYSTEM LOADS 271

7.1 Basic load-modelling concepts 271

7.1.1 Static load models 272

7.1.2 Dynamic load models 274

7.2 Modelling of induction motors 279

7.2.1 Equations of an induction machine 279

7.2.2 Steady-state characteristics 287

7.2.3 Alternative rotor constructions 293

7.2.4 Representation of saturation 296

7.2.5 Per unit representation 297

7.2.6 Representation in stability studies 300

7.3 Synchronous motor model 306

7.4 Acquisition of load-model parameters 306

7.4.1 Measurement-based approach 306

7.4.2 Component-based approach 308

7.4.3 Sample load characteristics 310

References 312

8 EXCITATION SYSTEMS 315

8.1 Excitation system requirements 315

8.2 Elements of an excitation system 317

8.3 Types of excitation systems 318

8.3.1 DC excitation systems 319

8.3.2 AC excitation systems 320

8.3.3 Static excitation systems 323

8.3.4 Recent developments and future trends 326

8.4 Dynamic performance measures 327

8.4.1 Le??ge-signal Performance measures 327

8.4.2 Small-signal performance measures 330

8.5 Control and protective functions 333

8.5.1 AC and DC regulators 333

8.5.2 Excitation system stabilizing circuits 334

8.5.3 Power system stabilizer（PSS） 335

8.5.4 Load compensation 335

8.5.5 Underexcitation limiter 337

8.5.6 Overexcitation limiter 337

8.5.7 Volts-per hertz limiter and protection 339

8.5.8 Field-shorting circuits 340

8.6 Modelling of excitation systems 341

8.6.1 Per unit system 342

8.6.2 Modelling of excitation system components 347

8.6.3 Modelling of complete excitation systems 362

8.6.4 Field testing for model development and verification 372

References 373

9 PRIME MOVERS AND ENERGY SUPPLY SYSTEMS 377

9.1 Hydraulic turbines and governing systems 377

9.1.1 Hydraulic turbine transfer function 379

9.1.2 Nonlinear turbine model assuming inelastic water column 387

9.1.3 Governors for hydraulic turbines 394

9.1.4 Detailed hydraulic system model 404

9.1.5 Guidelines for modelling hydraulic turbines 417

9.2 Steam turbines and governing systems 418

9.2.1 Modelling of steam turbines 422

9.2.2 Steam turbine controls 432

9.2.3 Steam turbine off-frequency capability 444

9.3 Thermal energy systems 449

9.3.1 Fossil-fuelled energy systems 449

9.3.2 Nuclear-based energy systems 455

9.3.3 Modelling of thermal energy systems 459

References 460

10 HIGH-VOLTAGE DIRECT-CURRENT TRANSMISSION 463

10.1 HVDC system configurations and components 464

10.1.1 Classification of HVDC links 464

10.1.2 Components of HVDC transmission system 467

10.2 Converter theory and performance equations 468

10.2.1 Valve characteristics 469

10.2.2 Converter circuits 470

10.2.3 Converter transformer rating 492

10.2.4 Multiple-bridge converters 493

10.3 Abnormal operation 498

10.3.1 Arc-back（backfire） 498

10.3.2 Commutation failure 499

10.4 Control of HVDC systems 500

10.4.1 Basic principles of control 500

10.4.2 Control implementation 514

10.4.3 Converter firing-control systems 516

10.4.4 Valve blocking and bypassing 520

10.4.5 Starting, stopping, and power-flow reversal 521

10.4.6 Controls for enhancement of ac system performance 523

10.5 Harmonics and filters 524

10.5.1 AC side harmonics 524

10.5.2 DC side hermonics 527

10.6 Influence of ac system strength on ac/dc system interaction 528

10.6.1 Short-circuit ratio 528

10.6.2 Reactive power and ac system strength 529

10.6.3 Problems with low ESCR systems 530

10.6.4 Solutions to problems associated with weak systems 531

10.6.5 Effective inertia constant 532

10.6.6 Forced commutation 532

10.7 Responses to dc and ac system faults 533

10.7.1 DC line faults 534

10.7.2 Converter faults 535

10.7.3 AC system faults 535

10.8 Multiterminal HVDC systems 538

10.8.1 MIDC network configurations 539

10.8.2 Control of MTDC systems 540

10.9 Modelling of HVDC systems 544

10.9.1 Representation for power-flow solution 544

10.9.2 Per unit system for dc quantities 564

10.9.3 Representation for stability studies 566

References 577

11 CONTROL OF ACTIVE POWER AND REACTIVE POWER 581

11.1 Active power and frequency control 581

11.1.1 Fundamentals of speed governing 582

11.1.2 Control of generating unit power output 592

11.1.3 Composite regulating characteristic of power systems 595

11.1.4 Response rates of turbine-governing systems 598

11.1.5 Fundamentals of automatic generation control 601

11.1.6 Implementation of AGC 617

11.1.7 Underfrequency load shedding 623

11.2 Reactive power and voltage control 627

11.2.1 Production and absorption of reactive power 627

11.2.2 Methods of voltage control 628

11.2.3 Shunt reactors 629

11.2.4 Shunt capacitors 631

11.2.5 Series capacitors 633

11.2.6 Synchronous condensers 638

11.2.7 Static var systems 639

11.2.8 Principles of transmission system compensation 654

11.2.9 Modelling of reactive compensating devices 672

11.2.10 Application of tap-changing transformers to transmission systems 678

11.2.11 Distribution system voltage regulation 679

11.2.12 Modelling of transformer ULTC control systems 684

11.3 Power-flow analysis procedures 687

11.3.1 Prefault power flows 687

11.3.2 Postfault power flows 688

References 691

PART Ⅲ SYSTEM STABILITY:physical aspects,analysis,and improvement 699

12 SMALL-SIGNAL STABILITY 699

12.1 Fundamental concepts of stability of dynamic systems 700

12.1.1 State-space representation 700

12.1.2 Stability of a dynamic system 702

12.1.3 Linearization 703

12.1.4 Analysis of stability 706

12.2 Eigenproperties of the state matrix 707

12.2.1 Eigenvalues 707

12.2.2 Eigenvectors 707

12.2.3 Modal matrices 708

12.2.4 Free motion of a dynamic system 709

12.2.5 Mode shape,sensitivity,and participation factor 714

12.2.6 Controllability and observability 716

12.2.7 The concept of complex frequency 717

12.2.8 Relationship between eigenproperties and transfer functions 719

12.2.9 Computation of eigenvalues 726

12.3 Small-signal stability of a single-machine infinite bus system 727

12.3.1 Generator represented by the classical model 728

12.3.2 Effects of synchronous machine field circuit dynamics 737

12.4 Effects of excitation system 758

12.5 Power system stabilizer 766

12.6 System state matrix with amortisseurs 782

12.7 Small-signal stability of multimachine systems 792

12.8 Special techniques for analysis of very large systems 799

12.9 Characteristics of small-signal stability problems 817

References 822

13 TRANSIENT STABILITY 827

13.1 An elementary view of transient stability 827

13.2 Numerical integration methods 836

13.2.1 Euler method 836

13.2.2 Modified Euler method 838

13.2.3 Runge-Kutta（R-K）methods 838

13.2.4 Numerical stability of explicit integration methods 841

13.2.5 Implicit integration methods 842

13.3 Simulation of power system dynamic response 848

13.3.1 Structure of the power system model 848

13.3.2 Synchronous machine representation 849

13.3.3 Excitation system representation 855

13.3.4 Transmission network and load representation 858

13.3.5 Overall system equations 859

13.3.6 Solution of overall system equations 861

13.4 Analysis of unbalanced faults 872

13.4.1 Introduction to symmetrical components 872

13.4.2 Sequence impedances of synchronous machines 877

13.4.3 Sequence impedances of transmission lines 884

13.4.4 Sequence impedances of transformers 884

13.4.5 Simulation of different types of faults 885

13.4.6 Representation of open-conductor conditions 898

13.5 Performance of protective relaying 903

13.5.1 Transmission line protection 903

13.5.2 Fault-clearing times 911

13.5.3 Relaying quantities during swings 914

13.5.4 Evaluation of distance relay performance during swings 919

13.5.5 Prevention of tripping during transient conditions 920

13.5.6 Automatic line reclosing 922

13.5.7 Generator out-of-step protection 923

13.5.8 Loss-of-excitation protection 927

13.6 Case study of transient stability of a large system 934

13.7 Direct method of transient stability analysis 941

13.7.1 Description of the transient energy function approach 941

13.7.2 Analysis of practical power systems 945

13.7.3 Limitations of the direct methods 954

References 954

14 VOLTAGE STABILITY 959

14.1 Basic concepts related to voltage stability 960

14.1.1 Transmission system characteristics 960

14.1.2 Generator characteristics 967

14.1.3 Load characteristics 968

14.1.4 Characteristics of reactive compensating devices 969

14.2 Voltage collapse 973

14.2.1 Typical scenario of voltage collapse 974

14.2.2 General characterization based on actual incidents 975

14.2.3 Classification of voltage stability 976

14.3 Voltage stability analysis 977

14.3.1 Modelling requirements 978

14.3.2 Dynamic analysis 978

14.3.3 Static analysis 990

14.3.4 Determination of shortest distance to instability 1007

14.3.5 The continuation power-flow analysis 1012

14.4 Prevention of voltage collapse 1019

14.4.1 System design measures 1019

14.4.2 System-operating measures 1021

References 1022

15 SUBSYNCHRONOUS OSCILLATIONS 1025

15.1 Turbine-generator torsional characteristics 1026

15.1.1 Shaft system model 1026

15.1.2 Torsional natural frequencies and mode shapes 1034

15.2 Torsional interaction with power system controls 1041

15.2.1 Interaction with generator excitation controls 1041

15.2.2 Interaction with speed governors 1047

15.2.3 Interaction with nearby dc converters 1047

15.3 Subsynchronous resonance 1050

15.3.1 Characteristics of series capacitor-compensated transmission systems 1050

15.3.2 Self-excitation due to induction generator effect 1052

15.3.3 Torsional interaction resulting in SSR 1053

15.3.4 Analytical methods 1053

15.3.5 Countermeasures to SSR problems 1060

15.4 Impact of network-switching disturbances 1061

15.5 Torsional interaction between closely coupled units 1065

15.6 Hydro generator torsional characteristics 1067

References 1068

16 MID-TERM AND LONG-TERM STABILITY 1073

16.1 Nature of system response to severs upsets 1073

16.2 Distinction between mid-term and long-term stability 1078

16.3 Power plant response during severe upsets 1079

16.3.1 Thermal power plants 1079

16.3.2 Hydro power plants 1081

16.4 Simulation of long-term dynamic response 1085

16.4.1 Purpose of long-term dynamic simulations 1085

16.4.2 Modelling requirements 1085

16.4.3 Numerical integration techniques 1087

16.5 Case studies of severe system upsets 1088

16.5.1 Case study involving an overgenerated island 1088

16.5.2 Case study involving an undergenerated island 1092

References 1099

17 METHODS OF IMPROVING STABILITY 1103

17.1 Transient stability enhancement 1104

17.1.1 High-speed fault clearing 1104

17.1.2 Reduction of transmission system reactance 1104

17.1.3 Regulated shunt compensation 1105

17.1.4 Dynamic braking 1106

17.1.5 Reactor switching 1106

17.1.6 Independent-pole operation of circuit breakers 1107

17.1.7 Single-pole switching 1107

17.1.8 Steam turbine fast-valving 1110

17.1.9 Generator tripping 1118

17.1.10 Controlled system separation and load shedding 1120

17.1.11 High-speed excitation systems 1121

17.1.12 Discontinuous excitation control 1124

17.1.13 Control of HVDC transmission links 1125

17.2 Small-signal stability enhancement 1127

17.2.1 Power system stabilizers 1128

17.2.2 Supplementary control of static var compensators 1142

17.2.3 Supplementary control of HVDC transmission links 1151

References 1161

INDEX 1167