Power system stability and control by prabha kundur

Copyrtylfted Mÿlenal ELECTRIC 'POWER RESEARCH INSTITUTE Power System Engineering Series ower System Stability and Control PRABHA KUNDUR tai|)yr(T)hin)iH)fitwJ Mafoiwl Library of Coairni ('ÿCllifii|-«? fono or h> toy mom or tweed in dm bate or (he pubfedher retneval system, Md*** dK pnee wrote* perouisaon of ? 19 ISBN TV It) II DOOTKX09I7AS4J J | M7ÿ33«l-X tpwiv i nj{ prvfacfk*r rddor far tW fool war /forwtf A war frcwaJd Wwdl OawfandL and At Pnm'ed and fa*nd by MR Dotwtit) A Sam Company hrormiCKin contained n dus work his been obtained by McGrawHill, Inf fn*m metes believed to be reliable However, neither McGraw-Hill nor its authors rxx its editors gvinntoc (he accuracy be cornpkientsi of any irtfOrraalion pubtefced herein arid neither McGraw-Hill nor its authors shall be responsible for in> mors, esrtryvKmy or damages arirtuÿ om of use of dm aaformiwo This work it pgfetabed the underflardipt dm McGraw-Hill and its authors are supply m$ inrormaeie* but are nee anemj*ini to reader eptmeerat oe other profcsworwJ services If such services are required, the nutitance of an ippmpmie pmfotuafuJ dkxdd be toughL Co|»iK>hfotd Malk-ital Contents FOREWORD xix PREFACE xxi PART I GENERAL BACKGROUND GENERAL CHARACTERISTICS OF MODERN POWER SYSTEMS 1.1 Evolution of electric power systems Structure of the power system Power system control 1.3 Design and operating criteria for stability 1.4 References 13 16 INTRODUCTION TO THE POWER SYSTEM STABILITY PROBLEM 17 Basic concepts and definitions 2.1.1 Rotor angle stability 2.1.2 Voltage stability and voltage collapse 2.1.3 Mid-term and long-term stability 2.2 Classification of stability Historical review of stability problems 2.3 References 17 2.1 vii 18 27 33 34 37 40 Contents viii PART II EQUIPMENT CHARACTERISTICS AND MODELLING SYNCHRONOUS MACHINE THEORY AND MODELLING 45 3.1 46 46 49 49 53 54 56 59 67 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 Physical description 3.1.1 Armature and field structure 3.1.2 Machines with multiple pole pairs 3.1.3 MMF waveforms 3.1.4 Direct and quadrature axes Mathematical description of a synchronous machine 3.2.1 Review of magnetic circuit equations 3.2.2 Basic equations of a synchronous machine The dqO transformation Per unit representation Per unit system for the stator quantities 3.4.1 Per unit stator voltage equations 3.4.2 3.4.3 Per unit rotor voltage equations Stator flux linkage equations 3.4.4 Rotor flux linkage equations 3.4.5 3.4.6 Per unit system for the rotor Per unit power and torque 3.4.7 3.4.8 Alternative per unit systems and transformations Summary of per unit equations 3.4.9 Equivalent circuits for direct and quadrature axes Steady-state analysis 3.6.1 Voltage, current, and flux linkage relationships 3.6.2 Phasor representation 3.6.3 Rotor angle 3.6.4 Steady-state equivalent circuit 3.6.5 Procedure for computing steady-state values Electrical transient performance characteristics 3.7.1 Short-circuit current in a simple RL circuit 3.7.2 Three-phase short-circuit at the terminals of a synchronous machine 3.7.3 Elimination of dc offset in short-circuit current Magnetic saturation 3.8.1 Open-circuit and short-circuit characteristics Representation of saturation in stability studies 3.8.2 Improved modelling of saturation 3.8.3 Equations of motion 75 75 76 77 78 78 79 83 83 84 88 93 93 95 98 99 100 105 105 107 108 110 110 112 117 128 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 SYNCHRONOUS MACHINE PARAMETERS 139 Operational parameters 4.1 Standard parameters 4.2 Frequency-response characteristics 4.3 Determination of synchronous machine parameters 4.4 References 139 144 159 161 166 SYNCHRONOUS MACHINE REPRESENTATION IN STABILITY STUDIES 5.1 Simplifications essential for large-scale studies Neglect of stator p\\f terms 5.1.1 5.1.2 Neglecting the effect of speed variations on stator voltages Simplified model with amortisseurs neglected 5.2 Constant flux linkage model 5.3 5.3.1 Classical model 5.3.2 Constant flux linkage model including the effects of subtransient circuits Summary of simple models for different time frames 5.3.3 Reactive capability limits 5.4 5.4.1 Reactive capability curves V curves and compounding curves 5.4.2 References 128 128 132 132 135 136 169 169 170 174 179 184 184 188 190 191 191 196 198 AC TRANSMISSION 199 6.1 200 200 201 205 206 209 Transmission lines 6.1.1 Electrical characteristics 6.1.2 Performance equations Natural or surge impedance loading 6.1.3 6.1.4 Equivalent circuit of a transmission line 6.1.5 Typical parameters x Contents 6.2 6.3 6.4 6.1.6 Performance requirements of power transmission lines Voltage and current profile under no-load 6.1.7 6.1.8 Voltage-power characteristics 6.1.9 Power transfer and stability considerations 6.1.10 Effect of line loss on V-P and Q-P characteristics 6.1.11 Thermal limits 6.1.12 Loadability characteristics Transformers 6.2.1 Representation of two-winding transformers Representation of three-winding transformers 6.2.2 Phase-shifting transformers 6.2.3 Transfer of power between active sources Power-flow analysis 6.4.1 Network equations Gauss-Seidel method 6.4.2 Newton-Raphson (N-R) method 6.4.3 6.4.4 Fast decoupled load-flow (FDLF) methods Comparison of the power-flow solution methods 6.4.5 Sparsity-oriented triangular factorization 6.4.6 6.4.71 Network reduction References 211 211 216 221 225 226 228 231 232 240 245 250 255 257 259 260 264 267 268 268 269 POWER SYSTEM LOADS 271 7.1 271 272 274 279 279 287 293 296 297 300 306 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 Per unit representation 7.2.5 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 Sample load characteristics 7.4.3 References 306 306 308 310 312 xi Contents EXCITATION SYSTEMS Excitation system requirements Elements of an excitation system Types of excitation systems DC excitation systems 8.3.1 8.3.2 AC excitation systems 8.3.3 Static excitation systems 8.3.4 Recent developments and future trends Dynamic performance measures 8.4 8.4.1 Large-signal performance measures Small-signal performance measures 8.4.2 Control and protective functions 8.5 AC and DC regulators 8.5.1 8.5.2 Excitation system stabilizing circuits Power system stabilizer (PSS) 8.5.3 8.5.4 Load compensation 8.5.5 Underexcitation limiter 8.5.6 Overexcitation limiter 8.5.7 Volts-per-hertz limiter and protection Field-shorting circuits 8.5.8 Modelling of excitation systems 8.6 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 8.1 8.2 8.3 PRIME MOVERS AND ENERGY SUPPLY SYSTEMS 9.1 9.2 315 315 317 318 319 320 323 326 327 327 330 333 333 334 335 335 337 337 339 340 341 342 347 362 372 373 377 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 Detailed hydraulic system model 9.1.4 404 9.1.5 Guidelines for modelling hydraulic turbines 417 Steam turbines and governing systems 418 9.2.1 Modelling of steam turbines 422 9.2.2 Steam turbine controls 432 Steam turbine off-frequency capability 9.2.3 444 Contents xii 9.3 Thermal 9.3.1 9.3.2 9.3.3 References energy systems Fossil-fuelled energy systems Nuclear-based energy systems Modelling of thermal energy systems 10 HIGH-VOLTAGE DIRECT-CURRENT TRANSMISSION 10.1 10.2 10.3 10.4 10.5 10.6 10.7 HVDC system configurations and components 10.1.1 Classification of HVDC links 10.1.2 Components of HVDC transmission system Converter theory and performance equations 10.2.1 Valve characteristics 10.2.2 Converter circuits 10.2.3 Converter transformer rating 10.2.4 Multiple-bridge converters Abnormal operation 10.3.1 Arc-back (backfire) 10.3.2 Commutation failure Control of HVDC systems 10.4.1 Basic principles of control 10.4.2 Control implementation 10.4.3 Converter firing-control systems 10.4.4 Valve blocking and bypassing 10.4.5 Starting, stopping, and power-flow reversal 10.4.6 Controls for enhancement of ac system performance Harmonics and filters 10.5.1 AC side harmonics 10.5.2 DC side harmonics Influence of ac system strength on ac/dc system interaction 10.6.1 Short-circuit ratio 10.6.2 Reactive power and ac system strength 10.6.3 Problems with low ESCR systems 10.6.4 Solutions to problems associated with weak systems 10.6.5 Effective inertia constant 10.6.6 Forced commutation Responses to dc and ac system faults 10.7.1 DC line faults 10.7.2 Converter faults 10.7.3 AC system faults 449 449 455 459 460 463 464 464 467 468 469 470 492 493 498 498 499 500 500 514 516 520 521 523 524 524 527 528 528 529 530 531 532 532 533 534 535 535 References 163 [24] H.F Martin, D.N Tapper and T.M Alston, "Sustained Fast Valving Applied to TVA's Watts Bar Nuclear Units," Paper 76-JPGC-PWR-5, presented at the 1976 Joint Power Generation Conference, Buffalo, N.Y., September 1976, ASME Trans., Series A, Vol 99, No 1, 1977 [25] P.L McGaha and T.L Dresner, "A Nuclear Steam Turbine Intercept Valve and Control System for Fast Valving," Paper presented at the 1977 Joint Power Generation Conference, Long Beach, Calif, September 1977 [26] L Edwards, R.J Thomas, D.C Hogue, P Hughes, W Novak, G Weiss and J.E, Welsh, "Sustained Fast Valving at TVA's Cumberland Steam Plant: Background and Test Results," Proceeding of the American Power Conference, Vol 43, pp 142-152, April 1981 [27] IEEE Working Group Report of panel discussion, "Turbine Fast Valving to Aid System Stability: Benefits and Other Considerations," IEEE Trans., Vol PWRS-1, pp 143-153, February 1986 [28] W.A Morgan, H.B Peck, D.R Holland, F.A Cullen, and J.B Ruzek, "Modern Stability Aids for Calvert Cliffs Units," IEEE Trans., Vol PAS-90, pp 1-10, January/February 1971 [29] P Kundur and J.P Bayne, "A Study of Early Valve Actuation Using Detailed Prime Mover and Power System Simulation," IEEE Trans., Vol PAS-94, pp 1275-1287, July/August 1975 [30] D.L Osborn, "Fast Valving and Neutral Resistor Application on a 600 MW Fossil Unit," Paper A76608-0, presented at the 1976 Joint Power Generation Conference, Buffalo, N.Y., September 1976 [31] N.J Balu, "Fast Turbine Valving and Independent Pole Tripping Breaker Applications for Plant Stability," IEEE Trans., Vol PAS-99, pp 1330-1342, July/August 1980 [32] R.M Maliszewski, B.M Pasternack, and R.D Rana, "Temporary Fast Turbine Valving on the AEP System," Proceedings of the American Power Conference, ÿ Vol 44, pp 118-125, 1982 [33] T.D Younkins, J.H Chow, A.S Brower, J Kure-Jensen, and J.B Wagner, "Fast Valving with Reheat and Straight Condensing Steam Turbines," IEEE Trans., Vol PWRS-2, pp 397-405, May 1987 [34] P Kundur, R.E Beaulieu, C Munro, and P.A Starbuck, "Steam Turbine Fast Valving: Benefits and Technical Considerations," ST267 position paper, 164 Methods of Improving Stability Chap 17 presented at the Canadian Electrical Association, spring meeting, March 1986 [35] R.H Hillery and E.D Holdup, "Load Rejection Testing of Large Thermal Electric Generating Units," IEEE Trans., Vol PAS-87, pp 1440-1453, June 1968 [36] V.F Carvalho, "Use of Generator and Customer Load Rejection to Increase Power Transfer Limits," CIGRE Paper 32-79-00-56, presented at the Study Committee 32 Meeting, Minneapolis, Minn., 1979 [37] P Kundur and W.G.T Hogg, "Use of Generation Rejection in Ontario Hydro to Increase Power Transfer Capability," Paper presented at panel session on generator tripping, IEEE PES winter meeting, New York, January /February 1982 [38] R.G Farmer, "Independent Detection Scheme to Initiate Western System Islanding for Pacific AC Intertie Outages," Paper presented at the panel session on controlled separation and load shedding, IEEE PES summer meeting, July 1985 [39] C.W Taylor, F.R Nassief, and R.L Cresap, "Northwest Power Pool Transient Stability and Load Shedding Controls for Generation-Load Imbalances," IEEE Trans., Vol PAS-100, pp 3486-3495, July 1981 [40] D.C Lee and P Kundur, "Advanced Excitation Control for Power System Stability Enhancement," CIGRE 38-01, 1986 [41] C.W Taylor, J.R Mechenbier, and C.E Matthews, "Transient Excitation Boosting at Grand Coulee Third Power Plant: Power System Application and Field Test," Paper 92 SM 533-0 PWRS, presented at the IEEE PES summer meeting, Seattle, July 12-16, 1992 [42] IEEE Committee Report, "Dynamic Performance Characteristics of North American HVDC Systems for Transient and Dynamic Stability Evaluations," IEEE Trans., Vol PAS-100, pp 3356-3364, July 1981 [43] IEEE Committee Report, "HVDC Controls for System Dynamic Performance," IEEE Trans., Vol PWRS-6, No 2, pp 743-752, May 1991 [44] C.E Grund, G.D Breuer, and R.P Peterson, "AC/DC System Dynamic Performance - Transient Stability Augmentation with Dynamic Reactive Power Compensation," IEEE Trans., Vol PAS-99, pp 1493-1502, July/August 1980 [45] P.L Dandeno, A.N Karas, K.R McClymont, and W Watson, "Effect of High- References 165 Speed Rectifier Excitation Systems on Generator Stability Limits," IEEE Trans,, Vol PAS-87, pp 190-201, January 1968 [46] W Watson and G Manchur, "Experience with Supplementary Damping Signals for Generator Static Excitation Systems," IEEE Trans,, Vol PAS-92, pp 199-203, January/February 1973 [47] W Watson and M.E Coultes, "Static Exciter Stabilizing Signals on Large Generators - Mechanical Problems," IEEE Trans., Vol PAS-92, pp 204-211, January/February 1973 [48] P Kundur, D.C Lee, and H.M Zein El-Din, "Power System Stabilizers for Thermal Units: Analytical Techniques and On-Site Validation," IEEE Trans., Vol PAS-100, pp 81-95, January 1981 [49] F.P deMello, L.N Hannett, and J.M Undrill, "Practical Approaches to Supplementary Stabilizing from Accelerating Power," IEEE Trans., Vol PAS97, pp 1515-1522, September/October 1978 [50] D.C Lee, R.E Beaulieu, and J.R.R Service, "A Power System Stabilizer Using Speed and Electrical Power Inputs - Design and Field Experience," IEEE Trans., Vol PAS-100, pp 4151-4167, September 1981 [51] E.V Larsen and D.A Swan, "Applying Power System Stabilizers, Parts I, II, and III," IEEE Trans., Vol PAS-100, pp 3017-3046, June 1981 [52] F.P deMello, J.S Czuba, P.A Ruche, and J Willis, "Developments in Application of Stabilizing Measures through Excitation Control," CIGRE Paper 38-05, 1986 [53] P Kundur, M Klein, G.J Rogers, and M.S Zywno, "Application of Power System Stabilizers for Enhancement of Overall System Stability," IEEE Trans., Vol PWRS-4, pp 614-626, May 1989 [54] M Klein, G.J Rogers, S Moorty, and P Kundur, "Analytical Investigation of Factors Influencing Power System Stabilizer Performance," IEEE Trans., Vol EC-7, pp 382-388, September 1992 [55] Canadian Electrical Association Report, "Investigation of Low Frequency Inter-Area Oscillation Problems in Large Interconnected Power Systems," Report of Project 294 T 622, prepared by Ontario Hydro, 1993 [56] E.V Larsen and J.H Chow, "SVC Control Design for System Dynamic Performance," IEEE Special Symposium on Application of SVS for System 1166 Methods of Improving Stability Chap 17 Dynamic Performance, Publication 87TH0187-5-PWR, 1987 [57] N Martins and L.T.G Lima, "Determination of Suitable Locations of PSS and SVC for Damping Electromechanical Oscillations in Large Power System," Proceedings of the 1989 Power Industry Computer Application Conference, pp 74-82, May 1989 Index AC/DC system interaction, 528 influence of ac system strength, 528 AC excitation system, 318, 320 rotating rectifier system, 322 stationary rectifier system, 320 AC exciter, 353 AESOPS, 800 Alternative transformations, 83 Amortisseurs, 47, 782 Amplidyne voltage regulator, 319 Amplidyne, 320 Arc-back, 498 Area control error, 606 Area frequency-response characteristic, 607 Armature current limit, 191 Armature time constant, 161 Asymptotic stability, 702 Asynchronous link, 464 Attenuation constant, 203 Automatic generation control, 377, 601 control performance criteria, 618 effect of speed-governor dead band, 622 emergency mode operation, 621 frequency of AGC execution, 619 implementation of, 617 in interconnected power systems, 601 in isolated power systems, 601 167 performance of, 610, 621 tuning, 621 Automatic line reclosing, 922 Autotransformer, 23 Average direct voltage of dc converters, with ignition delay, 475 with no ignition delay, 473 Backswing, 1106 Baum, F.G., 665 Bias factor, 606, 607 Bipolar HVDC link, 465 Blinders, 920 Boiler, 451 drum type, 451 once-through, 451 Boiler-following mode of control, 453 BPA, 1104, 1106 Braking resistor, 1106 Brushless excitation system, 322 Bulk power system, Bundled conductor, 230 Bus classification, 255 Bypass valve, 498 168 CANDU reactor, 457 control modes, 457 Centre of inertia, 946 Characteristic harmonics, 525 Characteristic impedance of a line, 203 Commutating voltage, 481 Commutation angle, 479 Commutation failure, 499, 537 double, 500 Commutation in dc converters, 473 Commutation overlap, 479, 482 Complex frequency, 717 Complex turns ratio of transformers, 245 Composite regulating characteristic, 595 Composition of load, 271 Compounding curve of synchronous machine, 126, 197 Concordia, C., 728 Contingency, extreme, 14 normal design, 13 Continuation parameter 1015 Continuation power-flow analysis, 1012 Control mode, 25 Control of HVDC system, 500 augmenting transient stability, 1125 Controllability, 16 Controlled system separation, 1120 Converter, 467 Converter circuit, 470 Converter faults, 535 Converter firing control system, 516 Converter theory, 468 Converter transformer, 470 Critical operating condition, 965 Crowbar, 340 d-q transformation of induction machine equations, 283 Damper winding, 47 Damping coefficient, 1029 Dashpot bypass, 400, 1085 DC braking torque, 173 DC excitation system, 318, 319 DC line faults, 533 deMello, F.P., 728 Design criteria for stability, 13 Direct (d) axis, 53 Direct method, 706, 941 Direct offset current, 108 Discharge lamp, 275 Discharge lighting load, 278 Discontinuous excitation control, 1124 Displacement factor, 479 Distance relay characteristics, 905 Distribution system, feeder regulation, 680 substation bus regulation, 680 voltage regulation, 679 Disturbance, 18 dqO transformation of synchronous machine equations, 67, 73 Dynamic braking, 1106 Dynamic overvoltage, 530 Edison, T., Effective short-circuit ratio, 529 Eigenvalue, 707 computation of, 726 eigenvalue and stability, 711 sensitivity, 714 Eigenvector, 707, 714 calculation of, 806 left eigenvector, 708 right eigenvector, 707 Elastic strain, 1063 Electrical centre, 916 Electrical island, 1074 Electromagnetic transient program, 1065 End region heating limit, 194 Equal-area criterion, 83 Equations of motion of synchronous machines, 128_ Index Equidistant pulse control system, 519 Equilibrium point, 701 Equivalent commutating resistance, 485 ETMSP, 274 Euler method of integration, 836 EUROSTAG, 1087 Excitation control design, 1131 Excitation system, 315, 1121 ac regulator, 333 basic function, 315 ceiling current, 328 ceiling voltage, 328 control and protective functions, 333 dc regulator, 333 discontinuous control, 1124 effect on small-signal stability, 758 elements of, 317 high initial response, 328, 1121 line-drop compensator, 318, 336 load compensator, 318, 335, 361 modelling of, 341 nominal response, 328 performance measures, 327, 330 per unit system, 342 reactive-current compensator, 336 requirements, 315, 317 stabilizing circuits, 334, 357 types of, 318 voltage response time, 328 voltage time response, 328 Exciter, 318 Exciter mode, 1044 Explicit integration method, 841, 861 Extinction advance angle, 487 Extinction angle, 480 Extinction delay angle, 487 Fast decoupled load flow, 264 Fast-valving, 1110 Fault, simulation of, 885 Fault-clearing time, 911 Ferranti effect, 215, 629 Field current limit, 192 Field current limiter, 318, 339, 370 Field shorting circuit, 340 representation of, 857 Finite stability, 702 Flue gas system, 451 Forced commutation, 532 Fossil-fuelled power plant, 449 Francis turbine, 378 Free motion of a dynamic system, 709 Frequency bias setting, 619 Frequency bias tie line control, 606 Frequency control, 581 Frequency dependency of load, 273 Frequency response, calculation of, 807 characteristics of synchronous machine, 159 Fuel system, 450 Full-wave bridge circuit, 470 Furnace, 449 Gauss-Seidel method, 259, 267 Gear method, 1087 Generator out-of-step protection, 925, 926 Generator tripping, 1118 Global stability, 702 Graetz bridge, 470 Harmonic resonance, 531 Harmonics in HVDC systems, ac side, 524 dc side, 526 Hazards of underfrequency operation, 624 High-cycle fatigue limit, 1063 High-speed fault clearing, 1104 High-speed line reclosure, 922, 1065 High value gate, 361 Homopolar HVDC link, 466 170 HVDC system, abnormal operation, 498 ac system faults, 535 classification, 464 components, 464, 467 configurations, 464 detailed flexible model, 569 functional block diagram, 567 guidelines for selection of modelling detail, 575 per unit system, 564 representation for power flow solution, 544 representation for stability studies, 566 response model, 566 reversal of power flow, 522 simple model, 566 supplementary control of, 1151 HVDC system control, 500 actual characteristics, 505 auxiliary controls for ac system, 512 basic means of, 502 basic principles, 500 basis for selection of, 502 blocking, 522 constant current, 504 constant extinction angle, 504 constant margin angle, 504 control characteristics, 503 control implementation, 514 current limits, 509 deblocking, 522 enhancement of ac system performance, 523 hierarchy, 515 power control, 512 tap changer control, 509 Hydraulic turbine, 377 classical transfer function, 383 governors for, 394 nonlinear model, 387 special characteristics, 384 Hydraulic turbine governors, 394 electrohydraulic governor, 399 mechanical-hydraulic governor, 396 PID governor, 404 tuning of, 399, 1081 Ideal no-load direct voltage, 475 Ignition advance angle, 487 Ignition delay angle, 487 Implicit integration method, 842, 862, 979 Impulse turbine, 377 Independent-pole operation, 1107 Individual phase control, 516 Induction generator, 280 Induction motor, 279 basic equations, 280 deep-bar rotor, 294 double squirrel-cage rotor, 293, 294 equivalent circuit, 289, 295 modelling of, 279 parameters, 304 per unit representation, 297 representation of saturation, 296 rotor constructions, 293 squirrel-cage rotor, 280 torque-slip characteristic, 290 wound rotor, 280, 293 Induction voltage regulator, 680 Inertia constant, 129, 132, 1027 Infinite bus, 728, 827 Initial pressure regulator, 443 Integrated boiler-turbine control, 454 Interarea mode, 25, 39, 817 Inverter control modes, 507 mode stabilization, 508 Inverter equivalent circuit, 490 Inverter operation, 486 Isochronous governor, 587 IV trigger, 442 Jacobian, 262, 264 Index Kalman, R.E., 717 Kaplan wheel, 378 K constants, 747, 748, 762 Linearization, 703 Line drop compensator, 682, 684 Line loadability, 228 Loadability curve, 228, 229 Load angle, 221 Load characteristics, 310 Load classes, 309 Load compensator, 361 Load components, 309 Load-frequency control, 377, 582, 601 Load modelling, 271 acquisition of parameters, 306 composite load model, 275 dynamic model, 272, 274 exponential model, 272 motor loads, 279 polynomial model, 273 static model, 272, 274 Load reference setpoint, 592 Load sharing by parallel units, 591 Load shedding, 623, 1020, 1120 LOADSYN, 309 Local mode, 25, 39, 817 Local stability, 702 Long-term dynamic response, 1085 simulation of, 1085 Long-term stability, 33, 1073, 1078 Loss-of-excitation protection, 337, 927, 1076 LOTDYS, 1087 Low value gate, 361 LTSP, 1087 Lyapunov's first method, 706 Lyapunov's second method, 706 Mason, C.R., 928 MASS, 795 Maximum excitation limiter, 318, 337 Mechanically switched capacitor, 652 Mercury-arc valve, 469 Metadyne, 320 Mho relay, 920 Mid-term stability, 33, 34, 1073, 1078 Miller, T.J.E., 655 Minimum excitation limiter, 337 Modal matrix, 708 Mode controllability matrix, 717 Mode observability matrix, 717 Mode shape, 714 Modified Arnoldi method, 807 Modified Euler method, 838 Mohave generation station, 1066 Monopolar HVDC link, 464, 465 Multiple bridge converters, 493 Multiterminal HVDC system, 466, 538 control of, 540 parallel connected system, 541 series connected system, 542 Natural load, 205 Navajo plant, 1061 Negative-sequence braking torque, 891 Nepier, J., 717 NERC, 13, 618 Network equations, 257 Network reduction, 268 Network-switching disturbance, effects on turbine-generator shafts, 1061 Newton-Raphson method, 260, 267 NGH scheme, 1061 Node admittance matrix, 257 Non-characteristic harmonics, 525 Non-windup limits, 359 Northeast blackout of Nov 1965, 38 NPCC, 13 Numerical integration, 836 Numerical stability, 837 1172 Observability, 716 Off-nominal turns ratio, 235 Ontario Hydro, 930, 1120, 1124 Open-conductor condition, 898 Operating criteria for stability, 13 Oscillatory instability, 23 Out-of-step blocking, 921 Out-of-step condition, 923 effect of, 923 Out-of-step relaying, 921 principle of, 921 Out-of-step tripping, 921 for generators, 924 Overexcitation limiter, 337, 370, 967 Overhead line, 200, 209 Overlap angle, 487 Partial load rejection, 1076 Participation factor, 715 PEALS, 799 Pearl Street Station, Per unit system, 75, 342, 564 Phase constant, 203 Phase variable, 775 Phase-shifting transformer, 245 representation of, 246 Plastic strain, 1063 Pole placement technique, 1147 Pole slipping, 916 Poles of a transfer function, 718 Potential energy boundary surface, 942, 943 Potier reactance, 119 Power load unbalance relay, 442 Power plant auxiliaries, effect of system islanding on, 1077 Power system control, hierarchy, 12 Power system operating states, 10, 1073 alert, 10, 1074, 1075 emergency, 11, 1074 in extremis, 11, 1074, 1075 normal, 10, 1074, 1075 restorative, 11, 1074, 1075 Power system stability, 17 basic concepts, 17 classification, 17, 34, 36 definition, 17 historical review, 37 Power system stabilizer, 318, 335, 766, 1121, 1128 alternative types of, 128 delta-omega, 1128 delta-P-omega, 1129 digital, 1131 frequency-based, 1130 Power transfer between two sources, factors influencing, 250 Power versus angle relationship, 20 Power-factor correction, 631, 632 Power-flow analysis, 255, 687 AGC response power flow, 690 governor response power flow, 690 inertial power flow, 690 postfault power flow, 688 prefault power flow, 687 PQ bus, 255, 264 Pressurized water reactor, 455 Propagation constant, 203 Propeller turbine, 378 PV bus, 255, 264 QR transformation method, 726 Quadrature (q) axis, 53 Quality of power supply, Q-V characteristics, 967 Reaction turbine, 377 Reactive-ampere limiter, 337 Reactive capability curves, 196 Reactive capability limits, 191 Reactive compensating devices, modelling of, 672 Index Reactive power, production and absorption, 627 Reactive power loss, 254 Rectifier equivalent circuit, 486 Reference frame transformation, 793 Regulated shunt compensation, 970, 1105 Relaying quantities during swings, 914 Reliability criteria, 13 Residue of a transfer function, 720 Richardson's formula, 841 Rigid-body mode, 1065 Rotor angle, 98 Rotor angle stability, 18 Runge-Kutta methods, 838 Saturation characteristics of synchronous machines, air-gap line, 10 improved modelling of, 117 incremental saturation, 745 open-circuit characteristic, 10 representation of, 112 saturation factor, 113, 114 short-circuit characteristic, 11 short-circuit ratio, 12 total saturation, 744 SCADA, 12 Secondary-arc extinction, 1107 Selective modal analysis, 799 Self-excitation, 10£2 Self-excited dc exciter, 352 Separately excited dc exciter, 347 Series capacitor, 633, 970, 1105 bypassing and reinsertion, 635 bypass protective schemes, 636 Severe system upset, 1073, case studies, 1087 hydro power plant response, 1081 nature of system response, 1073 thermal power plant response, 1079 Shaft system model, 1026 continuum model, 1026 lumped-mass model, 1026 Short-circuit ratio of ac system, 528 Shunt capacitor, 631, 969 Shunt reactor, 629 Signal washout, 770 Single-pole switching, 1107 Singular point, 701 type of, 712 Slack bus, 255 Sliding pressure mode, 454 Small-signal stability, 23, 228, 699 enhancement, 1127 Smoothed ACE, 618 Smoothing reactor, 467, 527 Sparse matrix methods, 268 Speed-changer motor, 592 Speed droop, 589, 590 Speed droop characteristic, 594 Speed regulation, 590 Speed voltage, SSR protection scheme, 1061 Stability of dynamic systems, 700, 702 Stable equilibrium point, 942 State matrix, 707 State space, 701 State-space representation, 700 State variable, 701 redundant, 798 Static excitation system, 318, 323 bus-fed, 323 compound controlled rectifier excitation system, 325 compound-source rectifier system, 324 field flashing, 326 potential-source control led-rectifler system, 323 transformer-fed, 323 Static var compensator, 639 application of, 654 supplementary control of, 1142 types of, 639 174 Static var system, 639 modelling of, 672 Stator decrement test, 162 St Clair curves, 228 Steam turbine, 418 cross-compound, 418 detailed generic model, 430 enhanced model, 430 modelling of, 422 non-reheat, 421 off-frequency capability, 444 reheat, 42 simplified transfer function, 427 tandem-compound, 18 Steam turbine bypass, 1081 Steam turbine controls, 432 digital electrohydraulic control, 442 electrohydraulic control, 439 emergency trip, 433 generic model, 444 mechanical-hydraulic control, 434 overspeed control, 433 overspeed trip, 433 Step voltage regulator, 681 Stiffness of differential equations, 841, 1087 Stiffness of power systems, 596 electrical, 1065 mechanical, 1065 torsional, 1027 Subsynchronous resonance, 638, 1025, 1050 countermeasures to, 1060 Subtransmission system, Surge impedance, 205 Surge impedance load, 205 Swing equation, 128, 131 Symmetrical components, 872 Synchronizing torque, 23, 751 Synchronous condenser, 638 Synchronous machine, 45 basic equations, 59 characteristics, 19 equivalent circuits, 88, 90 fault current, 107 magnetic saturation, 110 mechanical starting time, 132 modelling, 45 per unit equations, 84 per unit reactances, 87 phasor diagram, 181 phasor representation, 95 physical description, 46 rotor structure, 47 salient pole rotor, 47 solid round rotor, 48 Synchronous machine model, classical model, 184 representation in stability studies, 169 simplified models, 190 Synchronous machine parameters, 139 basic parameters, 139 determination of, 161 negative-sequence reactance, 878 operational parameters, 139 sequence impedances, 877 standard parameters, 147, 150 subtransient parameters, 144 synchronous parameters, 144 transient parameters, 144 Synchronous motor, 306 Synchronous speed, 47 System generation control, 10 System islanding, 1074 overgenerated island, 1076 undergenerated island, 1076 System restoration, 1077 Tap-changing transformer, 231, 678 application to transmission systems, 678 Taylor, C.W, 976 Terminal voltage limiter, 318, 1122 Thermostatically controlled load, 275, 277 Three-winding transformer, 240 Index equivalent circuit, 240 Thyristor-controlled reactor, 645 Thyristor-switched capacitor, 649 Thyristor valve, 469 Time deviation correction, 619 Torsional characteristics, 1026 examples of, 1035 hydro generator, 1067 turbine generator, 1026 Torsional fatigue, 1025, 1062 Torsional interaction, 1041 between closely coupled units, 1065 with generator excitation controls, 1041 with nearby dc converters, 1047 with power system controls, 1041 with speed governors, 1047 Torsional mode, 25 Torsional mode shape, 1034 Torsional natural frequency, 1034 Torsional oscillations, 1025 special problems, 1025 Torsional stiffness, 1027 Transformer, 231 n circuit representation, 236 equivalent circuit, 232, 234 representation of ONR, 235 sequence impedances, 884 zero-sequence equivalent, 886 Transformer voltage, 71, 109 Transient droop, 396 Transient energy function, 941 Transient energy margin, 943 Transient energy of a power system, 948 critical energy, 948 kinetic energy, 942, 948 potential energy, 942, 948 Transient sal iency, 184 Transient stability, 25, 38, 827 elementary view of, 827 enhancement, 1104 factors influencing, 83 Transmission control, 10 Transmission line, 200 175 classification of line length, 208 electrical characteristics, 200 equivalent circuit, 206 loadability, 228 performance requirements, 211 power transfer, 221 reactive power requirements, 224 sequence impedances, 884 stability considerations, 221 stability limits, 228 thermal limits, 226, 228 typical parameters, 208 voltage and current profile, 211 voltage drop limits, 228 voltage-power characteristics, 216 Transmission line protection, 903 directional comparison scheme, 909 distance relaying, 904 overcurrent relaying, 904 permissive overreaching scheme, 907 pilot-relaying schemes, 906 Transmission network classification, distribution system, subtransmission system, transmission system, Transmission system compensation, 654 degree of series compensation, 656 degree of shunt compensation, 656 effect on line voltage, 657 effect on maximum power, 657 regulated shunt compensation, 663 series compensation, 655 shunt compensation, 655 Trapezoidal integration method, 842 Triangular factorization, 268 Tripping to house load, 1077 TSEC, 1124 Turbine, hydraulic, 377 steam, 418 Turbine-following mode of control, 453 Two-winding transformer, 232 176 ULTC, 231,275,960 control system model, 684, 685 Unbalanced faults, 872 Underexcitation limiter, 318, 337 Underfrequency load shedding, 623, 1093 Underground cable, 201, 210 Undervoltage load shedding, 1020 Underwater cable, 463 Unstable equilibrium point, 949 V curve of a synchronous machine, 126, 197 Valve blocking, 520 Valve bypassing, 520 Valve characteristics, 469 Varistor, 340 VDCOL, 510,568 Vector power factor, 479 V/Hz limiter, 339, 340, 370 V/Hz protection, 340 Voltage avalanche, 960 Voltage collapse, 27, 959, 973 general characterization, 975 prevention of, 1019 typical scenario of, 973 Voltage control, 627 methods of, 628 objectives, 627 Voltage flicker, 531, 654 Voltage instability, 959 causes of, 965, 967 mechanism of, 977 proximity to, 977, 1006 Voltage stability, 27, 530, 959 basic concepts, 960 branch participation factor, 999 bus participation factor, 998 classification of, 976 effect of load characteristics, 979 effect of overexcitation limiter, 979 effect of transformer tap changer, 979 generator participation factor, 1000 large disturbance, 976 small disturbance, 976 Voltage stability analysis, 977 dynamic analysis, 978 IILSI algorithm, 1003 LOPSI algorithm, 1000 modelling requirements, 978 Q-V modal analysis, 993 static analysis, 990 transient state approximations, 1006 V-Q sensitivity analysis, 991 V-P characteristics, 963 Water hammer, 378 Water starting time, 382, 389 Wavelength 204 Windup limits, 358 Zeros of a transfer function, 18 Uopyncjliled Material Electrical Engineering Proven solutions to problems in electric power system stability and control Power System Stability and Control A Volume in the EPRI Power System Engineering Series Today's electric power systems are continually increasing in complexify due to interconnection growth, the use of new technologies, and financial and regulatory constraints Sponsored by the Electric Power Research Institute, this expert engi¬ neering guide helps you deal effectively with stability and control problems result¬ ing from these major changes in the industry Power System Stability and Control contains the handÿon information you need to understand, model, analyze, and solve problems using the latest technical tools You'll learn about the structure of modern power systems, the different levels of control, and the nature of stability problems you face in your day-today work The book features a complete account of equipment characteristics and model¬ ing techniques Included is detailed coverage of generators, excitation systems, prime movers, ac and dc transmission, and system loads plus principles of octive ond reactive power control, and models for control equipment Different categories of power system stability are thoroughly covered with descriptions of numerous methods of onalysis and control meosures for mitigating the full spectrum of stability problems This comprehensive source "book is written from o pragmatic point of view, but without undue compromise in mathematical rigor Filled with illustrative examples, it gives the necessary bosic theory and insight into practical aspects — ISBN D-0?-D35ct5fi-X DC 07 McGraw-Hill, Inc Serving the Need lor Knowledge 1221 Avenue ot the America* New York NY 10020 [...]... System Generation Control Load frequency control with economic allocation Schedule Supplementary, control / Generating Unit Controls Prime mover and control T3 § § Shaft power fi 11 li Excitation system Field Generator current and control Voltage Speed S O 3? ec Speed /Power Electrical power Transmission Controls Reactive power and voltage control, HVDC transmission and associated controls Frequency... understand and challenging to analyze Electric power systems of the 21st century will present an even more formidable challenge as they are forced to operate closer to their stability limits I cannot think of a more qualified person than Dr Prabha Kundur to write a book on power system stability and control Dr Kundur is an internationally recognized authority on power system stability His expertise and. .. Generator power Figure 1.2 Subsystems of a power system and associated controls 10 General Characteristics of Modern Power Systems Chap 1 excitation control is to regulate generator voltage and reactive power output The desired MW outputs of the individual generating units are determined by the systemgeneration control The primary purpose of the system- generation control is to balance the total system. .. controllers are in turn supervised by system controllers at the operating centres The system- controller actions are coordinated by pool-level master controllers The overall control system is thus highly distributed, and relies on many different types of telemetering and control signals Supervisory Control and Data Acquisition (SCADA) systems provide information to indicate the system status State estimation... elements and their capabilities is essential for the understanding of system stability The representation of these elements by means of appropriate mathematical models is critical to the analysis of stability Chapters 3 to 10 are devoted to generators, excitation systems, prime movers, ac and dc transmission, and system loads Chapter 11 describes the principles of active power and reactive power control and. .. develops models for the control equipment Part III, comprising Chapters 12 to 17, considers different categories of power system stability Emphasis is placed on physical understanding of many facets of the stability phenomena Methods of analysis along with control measures for mitigation of stability problems are described in detail The notions of power system stability and power system control are closely... there are controllers operating directly on individual system elements In a generating unit these consist of prime mover controls and excitation controls The prime mover controls are concerned with speed regulation and control of energy supply system variables such as boiler pressures, temperatures, and flows The function of the 5ec 1 -3 Power System Control Frequency Tie flows Generator power System. .. interconnected power system is the largest and most complex machine ever devised by man It is truly amazing that such a system has operated with a high degree of reliability for over a century The robustness of a power system is measured by the ability of the system to operate in a state of equilibrium under normal and perturbed conditions Power system stability deals with the study of the behavior of power systems... 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 10.8 1 1 CONTROL OF ACTIVE POWER AND REACTIVE POWER Active power and frequency control 11.1.1 Fundamentals of speed governing 11.1.2 Control of... engineers and students in the field of power engineering Dr Neal J Balu Program Manager Power System Planning and Operations Electrical Systems Division Electric Power Research Institute Preface This book is concerned with understanding, modelling, analyzing, and mitigating power system stability and control problems Such problems constitute very important considerations in the planning, design, and operation