power system stability and control - gbv
TRANSCRIPT
POWER SYSTEM STABILITY AND CONTROL
•
P. KUNDUR Vice-President, Power Engineering Powertech Labs Inc., Surrey, British Columbia
Formerly Manager Analytical Methods and Specialized Studies Department Power System Planning Division, Ontario Hydro, Toronto, Ontario
and
Adjunct Professor Department of Electrical and Computer Engineering
U I I I V t M b l i y Ul I U I U I U U , I U I U M I U , W l l l d l l U
Edited by Neal J. Balu Mark G. Lauby Power System Planning and Operations Electrical Systems Division Electric Power Research Institute 3412 Hillview Avenue Palo Alto, California
Program
-McGraw-Hill, Inc. New York San Francisco Washington, D.C. Auckland Bogota Caracas Lisbon London Madrid Mexico City Milan Montreal New Delhi San Juan Singapore Sydney Tokyo Toronto
Contents
xix
xxi
FOREWORD
PREFACE
PART I GENERAL BACKGROUND
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
VII
viii Contents
PART II EQUIPMENT CHARACTERISTICS AND MODELLING
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 dqO 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 instability studies 112 3.8.3 Improved modelling of saturation 117
3.9 Equations of motion 128
Contents ix
3.9.1 3.9.2 3.9.3 3.9.4 3.9.5
References
Review of mechanics of motion Swing equation Mechanical starting time Calculation of inertia constant Representation in system studies
128 128 132 132 135 136
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 p\\i 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 Electrical characteristics 200 Performance equations 201 Natural or surge impedance loading 205 Equivalent circuit of a transmission line 206 Typical parameters 209
6.1.1 6.1.2 6.1.3 6.1.4 6.1.5
X Contents
6.2
6.3 6.4
6.1.6 6.1.7 6.1.8 6.1.9 6.1.10 6.1.11 6.1.12
Performance requirements of power transmission lines Voltage and current profile under no-load Voltage-power characteristics Power transfer and stability considerations Effect of line loss on V-P and Q-P characteristics Thermal limits Loadability characteristics
Transformers 6.2.1 Representation of two-winding transformers 6.2.2 Representation of three-winding transformers 6.2.3 Phase-shifting transformers Transfer of power between active sources Power-flow analysis 6.4.1 Network equations 6.4.2 Gauss-Seidel method 6.4.3 Newton-Raphson (N-R) method 6.4.4 Fast decoupled load-flow (FDLF) methods 6.4.5 Comparison of the power-flow solution methods 6.4.6 Sparsity-oriented triangular factorization 6.4.7 Network reduction
References
7 POWER SYSTEM LOADS
211
211
216
221
225
226
228
231
232
240
245
250
255
257
259
260
264
267
268
268
269
271
7.1 Basic load-modelling concepts 7.1.1 Static load models 7.1.2 Dynamic load models
7.2 Modelling of induction motors 7.2.1 Equations of an induction machine 7.2.2 Steady-state characteristics 7.2.3 Alternative rotor constructions 7.2.4 Representation of saturation 7.2.5 Per unit representation 7.2.6 Representation in stability studies
7.3 Synchronous motor model 7.4 Acquisition of load-model parameters
7.4.1 Measurement-based approach 7.4.2 Component-based approach 7.4.3 Sample load characteristics
References
271
272
274 279 279 287 293
296
297
300
306
306
306 308 310 312
Contents xi
8 EXCITATION SYSTEMS 315
8.1 Excitation system requirements 8.2 Elements of an excitation system 8.3 Types of excitation systems
8.3.1 DC excitation systems 8.3.2 AC excitation systems 8.3.3 Static excitation systems 8.3.4 Recent developments and future trends
8.4 Dynamic performance measures 8.4.1 Large-signal performance measures 8.4.2 Small-signal performance measures
8.5 Control and protective functions 8.5.1 AC and DC regulators 8.5.2 Excitation system stabilizing circuits 8.5.3 Power system stabilizer (PSS) 8.5.4 Load compensation 8.5.5 Underexcitation limiter 8.5.6 Overexcitation limiter 8.5.7 Volts-per-hertz limiter and protection 8.5.8 Field-shorting circuits
8.6 Modelling of excitation systems 8.6.1 Per unit system 8.6.2 Modelling of excitation system components 8.6.3 Modelling of complete excitation systems 8.6.4 Field testing for model development and verification
References
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
tion
315 317 318 319 320 323 326 327 327 330 333 333 334 335 335 337 337 339 340 341 342 347 362 372 373
XII Contents
449 449 455 459 460
9.3 Thermal energy systems 9.3.1 Fossil-fuelled energy systems 9.3.2 Nuclear-based energy systems 9.3.3 Modelling of thermal energy systems
References
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 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
Contents л и i
538 539 540 544 -/"TT 544 564 566 577
10.8 Multiterminal HVDC systems 10.8.1 MTDC network configurations 10.8.2 Control of MTDC systems
10.9 Modelling of HVDC systems 10.9.1 Representation for power-flow solution 10.9.2 Per unit system for dc quantities 10.9.3 Representation for stability studies
References
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
XIV Contents
PART III SYSTEM STABILITY: physical aspects, analysis, and improvement
12 SMALL-SIGNAL STABILITY 699
12.1
12.2
12.3
12.4 12.5 12.6 12.7 12.8 12.9
Fundamental concepts of stability of dynamic systems 12.1.1 12.1.2 12.1.3 12.1.4
State-space representation Stability of a dynamic system Linearization Analysis of stability
Eigenproperties of the state matrix 12.2.1 12.2.2 12.2.3 12.2.4 12.2.5 12.2.6 12.2.7 12.2.8 12.2.9
Eigenvalues Eigenvectors Modal matrices Free motion of a dynamic system Mode shape, sensitivity, and participation factor Controllability and observability The concept of complex frequency
700 700 702 703 706 707 707 707 708 709 714 716 717
Relationship between eigenproperties and transfer functions 719 Computation of eigenvalues
Small-signal stability of a single-machine infinite bus system 12.3.1 12.3.2
Generator represented by the classical model Effects of synchronous machine field circuit dynamics
Effects of excitation system Power system stabilizer System state matrix with amortisseurs Small-signal stability of multimachine systems Special techniques for analysis of very large systems Characteristics of small-signal stability problems
References
726 727 728 737 758 766 782 792 799 817 822
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
Contents xv
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
xvi
14.2.3 Classification of voltage stability 14.3 Voltage stability analysis
14.3.1 Modelling requirements 14.3.2 Dynamic analysis 14.3.3 Static analysis 14.3.4 Determination of shortest distance to instability 14.3.5 The continuation power-flow analysis
14.4 Prevention of voltage collapse 14.4.1 System design measures 14.4.2 System-operating measures
References
15 SUBSYNCHRONOUS OSCILLATIONS
15.1 Turbine-generator torsional characteristics 15.1.1 Shaft system model 15.1.2 Torsional natural frequencies and mode shapes
15.2 Torsional interaction with power system controls 15.2.1 Interaction with generator excitation controls 15.2.2 Interaction with speed governors 15.2.3 Interaction with nearby dc converters
15.3 Subsynchronous resonance 15.3.1 Characteristics of series capacitor-compensated
transmission systems 15.3.2 Self-excitation due to induction generator effect 15.3.3 Torsional interaction resulting in SSR 15.3.4 Analytical methods 15.3.5 Countermeasures to SSR problems
15.4 Impact of network-switching disturbances 15.5 Torsional interaction between closely coupled units 15.6 Hydro generator torsional characteristics References
976 977 978 978 990 1007
1012
1019
1019
1021
1022
1025
1026
1026
1034
1041
1041
1047
1047
1050
1050
1052
1053
1053
1060
1061
1065
1067
1068
16 MID-TERM AND LONG-TERM STABILITY
16.1 Nature of system response to severe upsets 16.2 Distinction between mid-term and long-term stability 16.3 Power plant response during severe upsets
16.3.1 Thermal power plants 16.3.2 Hydro power plants
1073
1073
1078
1079
1079
1081
Contents xvii
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