CoverContentsForewordPrefacePART I GENERAL BACKGROUND1. GENERAL CHARACTERSTCS OF MODERN POWER SYSTEMS 3 1.1. Evolution of electric power systems1.2. Structure of the power system1.3. Power system control1.4. Design and operating criteria for stabilityReferences

2. INTRODUCTION TO THE POWER SYSTEM STABILITY PROBLEM 17 2.1. Basic concepts and definitions2.1.1. Rotor angle stability2.1.1. Voltage stability and voltage collapse2.1.3. Mid-term and long-term stability

2.2. Classification of stability2.3. Historical review of stability problemsReferences

PART II EQUIPMENT CHARACTERISTICS AND MODELLING3 SYNCHRONOUS MACHINE THEORY AND MODELLING 453.1. Physical description3.1.1. Armature and field structure3.1.2. Machines with multiple pole pairs3.1.3. MMF waveforms3.1.4. Direct and quadrature axes

3.2. Mathematical description of a synchronous machine3.2.1. Review of magnetic circuit equations3.2.2. Basic equations of a synchronous machine

3.3. The dq0 transformation3.4. Per unit representation3.4.1. Per unit system for the stator quantities3.4.2. Per unit stator voltage equations 3.4.3. Per unit rotor voltage equations3.4.4. Stator flux Linkage equations3.4.5. Rotor flux linkage equations3.4.6. Per unit system for the rotor 3.4.7. Per unit power and torque3.4.8. Alternative per unIt systems and transformations3.4.9. Summary of per unit equations

3.5. Equivalent circuits for direct and quadrature axes3.6. Steady-state analysis3.6.1 Voltage, current, and flux linkage relationships3.6.2 Phasor representation3.6.3 Rotor angle3.6.4 Steady-state equivalent circuit3.6.5 Procedure for computing steady-state values

3.7 Electrical transient performance characteristics3.7.1 Short-circuit current ia a simple RL circuit3.7.2 Three-phase short-circuit at the terminals of a synchronous machine3.7.3 Elimination of dc offset in short-circuit current

3.8 Magnetic saturation3.8.1 Open-circuit and short-circuit characteristics3.8.2 Representation of saturation in stability studies3.8.3 Improved modelling of saturation

3.9 Equations of motion3.9.1 Review of mechanics of motion3.9.2 Swing equation3.9.3 Mechanical starting time3.9.4 Calculation of inertia constant3.9.5 Representation in system studies

References

4 SYNCHRONOUS MACHINE PARAMETERS 1394.1 Operational parameters 1394.2 Standard parameters 1444.3 Frequency-response characteristics 1594.4 Determination of synchronous machine parameters 161References 166

5 SYNCHRONOUS MACHINE REPRESENTATION IN STABILITY STUDIES 1695.1 Simplifications essential for large-scale studies 169 5.1.1 Neglect of stator p 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 effcts 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 2116.1.7 Voltage and current profile under no-load 211 6.1.8 Voltage-power characteristics 2166.1.9 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 2316.2.1 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 2556.4.1 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 2717.1 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 2797.2.1 Equations of an induction machine 279 7.2.2 Steady-state characteristics 2877.2.3 Alternative rotor constructions 2937.2.4 Representation of saturation 2967.2.5 Per unit representation 2977.2.6 Representation in stability studies 300

7.3 Synchronous motor model 306 7.4 Acquisition of load-model parameters 3067.4.1 Measurement-based approach 306 7.4.2 Component-based approach 3087.4.3 Sample load characteristics 310

References 312

8 EXCITATION SYSTEMS 315 8.1 Excitation system requirements 315 8.2 Elements of an excitation system 3178.3 Types of excitation systems 318 8.3.1 DC excitation systems 3198.3.2 AC excitation systems 320 8.3.3 Static excitation systems 3238.3.4 Recent developments and future trends 326

8.4 Dynamic performance measures 327 8.4.1 Large-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 4559.3.3 Modelling of thermal energy systems 459

References 460

10 HIGH-VOLTAGE DIRECT-CURRENT TRANSMISSION 46310.1 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 49 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 harmonics 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 MTDC 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 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 severe 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