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