Đang tải... (xem toàn văn)
In 1997 the authors of this book, J. Machowski, J.W. Bialek and J.R. Bumby, published a book entitled Power System Dynamics and Stability. That book was well received by readers who toldus that it was used regularly as a standard reference text both in academia and in industry. Some 10 years after publication of that book we started work on a second edition. However, we quickly realized that the developments in the power systems industry over the intervening years required a large amount of new material. Consequently the book has been expanded by about a third and the word Control in the new title, Power System Dynamics: Stability and Control, reflects the fact that a large part of the new material concerns power system control: flexible AC transmission systems (FACTS), wide area measurement systems (WAMS), frequency control, voltage control, etc. The new title also reflects a slight shift in focus from solely describing power system dynamics to the means of dealing with them. For example, we believe that the new WAMS technology is likely to revolutionize power system control. One of the main obstacles to a wider embrace of WAMS by power system operators is an acknowledged lack of algorithms which could be utilized to control a system in real time. This book tries to fill this gap by developing a number of algorithms for WAMSbased realtime control.
POWER SYSTEM DYNAMICS Stability and Control Second Edition Jan Machowski Warsaw University of Technology, Poland Janusz W Bialek The University of Edinburgh, UK James R Bumby Durham University, UK POWER SYSTEM DYNAMICS POWER SYSTEM DYNAMICS Stability and Control Second Edition Jan Machowski Warsaw University of Technology, Poland Janusz W Bialek The University of Edinburgh, UK James R Bumby Durham University, UK This edition first published 2008 C 2008 John Wiley & Sons, Ltd Registered office John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex, PO19 8SQ, United Kingdom For details of our global editorial offices, for customer services and for information about how to apply for permission to reuse the copyright material in this book please see our website at www.wiley.com The right of the author to be identified as the author of this work has been asserted in accordance with the Copyright, Designs and Patents Act 1988 All rights reserved No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, except as permitted by the UK Copyright, Designs and Patents Act 1988, without the prior permission of the publisher Wiley also publishes its books in a variety of electronic formats Some content that appears in print may not be available in electronic books Designations used by companies to distinguish their products are often claimed as trademarks All brand names and product names used in this book are trade names, service marks, trademarks or registered trademarks of their respective owners The publisher is not associated with any product or vendor mentioned in this book This publication is designed to provide accurate and authoritative information in regard to the subject matter covered It is sold on the understanding that the publisher is not engaged in rendering professional services If professional advice or other expert assistance is required, the services of a competent professional should be sought Library of Congress Cataloging-in-Publication Data Machowski, Jan Power system dynamics: stability and control / Jan Machowski, Janusz W Bialek, James R Bumby – 2nd ed p cm Rev ed of: Power system dynamics and stability / Jan Machowski, Janusz W Bialek, James R Bumby 1997 Includes bibliographical references and index ISBN 978-0-470-72558-0 (cloth) Electric power system stability Electric power systems–Control I Bialek, Janusz W II Bumby, J R (James Richard) III Title TK1010.M33 2008 621.319 1–dc22 2008032220 A catalogue record for this book is available from the British Library ISBN 978-0-470-72558-0 Typeset in 9/11pt Times New Roman by Aptara Inc., New Delhi, India Printed in Great Britain by Antony Rowe Ltd, Chippenham, Wiltshire Contents About the Authors Preface xiii xv Acknowledgements xix List of Symbols xxi PART I INTRODUCTION TO POWER SYSTEMS 1.1 1.2 1.3 Introduction Stability and Control of a Dynamic System Classification of Power System Dynamics Two Pairs of Important Quantities: Reactive Power/Voltage and Real Power/Frequency 1.4 Stability of a Power System 1.5 Security of a Power System 1.6 Brief Historical Overview 3 9 12 Power System Components 2.1 Introduction 2.1.1 Reliability of Supply 2.1.2 Supplying Electrical Energy of Good Quality 2.1.3 Economic Generation and Transmission 2.1.4 Environmental Issues 2.2 Structure of the Electrical Power System 2.2.1 Generation 2.2.2 Transmission 2.2.3 Distribution 2.2.4 Demand 2.3 Generating Units 2.3.1 Synchronous Generators 2.3.2 Exciters and Automatic Voltage Regulators 2.3.3 Turbines and their Governing Systems 2.4 Substations 2.5 Transmission and Distribution Network 2.5.1 Overhead Lines and Underground Cables 2.5.2 Transformers 2.5.3 Shunt and Series Elements 2.5.4 FACTS Devices 15 15 15 16 16 16 16 18 18 19 19 19 20 21 25 35 35 35 36 41 43 Contents vi 2.6 Protection 2.6.1 Protection of Transmission Lines 2.6.2 Protection of Transformers 2.6.3 Protection of Busbars 2.6.4 Protection of Generating Units 2.7 Wide Area Measurement Systems 2.7.1 WAMS and WAMPAC Based on GPS Signal 2.7.2 Phasors 2.7.3 Phasor Measurement Unit 2.7.4 Structures of WAMS and WAMPAC The Power System in the Steady State 3.1 Transmission Lines 3.1.1 Line Equations and the π -Equivalent Circuit 3.1.2 Performance of the Transmission Line 3.1.3 Underground Cables 3.2 Transformers 3.2.1 Equivalent Circuit 3.2.2 Off-Nominal Transformation Ratio 3.3 Synchronous Generators 3.3.1 Round-Rotor Machines 3.3.2 Salient-Pole Machines 3.3.3 Synchronous Generator as a Power Source 3.3.4 Reactive Power Capability Curve of a Round-Rotor Generator 3.3.5 Voltage–Reactive Power Capability Characteristic V(Q) 3.3.6 Including the Equivalent Network Impedance 3.4 Power System Loads 3.4.1 Lighting and Heating 3.4.2 Induction Motors 3.4.3 Static Characteristics of the Load 3.4.4 Load Models 3.5 Network Equations 3.6 Power Flows in Transmission Networks 3.6.1 Control of Power Flows 3.6.2 Calculation of Power Flows PART II 54 54 56 57 57 58 58 59 61 62 65 65 66 67 72 72 72 74 76 76 83 89 91 95 100 104 105 106 110 111 113 118 118 122 INTRODUCTION TO POWER SYSTEM DYNAMICS Electromagnetic Phenomena 4.1 Fundamentals 4.2 Three-Phase Short Circuit on a Synchronous Generator 4.2.1 Three-Phase Short Circuit with the Generator on No Load and Winding Resistance Neglected 4.2.2 Including the Effect of Winding Resistance 4.2.3 Armature Flux Paths and the Equivalent Reactances 4.2.4 Generator Electromotive Forces and Equivalent Circuits 4.2.5 Short-Circuit Currents with the Generator Initially on No Load 4.2.6 Short-Circuit Currents in the Loaded Generator 4.2.7 Subtransient Torque 127 127 129 129 133 134 140 146 149 150 Contents vii 4.3 Phase-to-Phase Short Circuit 4.3.1 Short-Circuit Current and Flux with Winding Resistance Neglected 4.3.2 Influence of the Subtransient Saliency 4.3.3 Positive- and Negative-Sequence Reactances 4.3.4 Influence of Winding Resistance 4.3.5 Subtransient Torque 4.4 Synchronization 4.4.1 Currents and Torques 4.5 Short-Circuit in a Network and its Clearing 152 153 156 159 160 162 163 164 166 Electromechanical Dynamics – Small Disturbances 5.1 Swing Equation 5.2 Damping Power 5.2.1 Damping Power at Large Speed Deviations 5.3 Equilibrium Points 5.4 Steady-State Stability of Unregulated System 5.4.1 Pull-Out Power 5.4.2 Transient Power–Angle Characteristics 5.4.3 Rotor Swings and Equal Area Criterion 5.4.4 Effect of Damper Windings 5.4.5 Effect of Rotor Flux Linkage Variation 5.4.6 Analysis of Rotor Swings Around the Equilibrium Point 5.4.7 Mechanical Analogues of the Generator–Infinite Busbar System 5.5 Steady-State Stability of the Regulated System 5.5.1 Steady-State Power–Angle Characteristic of Regulated Generator 5.5.2 Transient Power–Angle Characteristic of the Regulated Generator 5.5.3 Effect of Rotor Flux Linkage Variation 5.5.4 Effect of AVR Action on the Damper Windings 5.5.5 Compensating the Negative Damping Components 169 169 172 175 176 177 177 179 184 186 187 191 195 196 196 200 202 205 206 Electromechanical Dynamics – Large Disturbances 6.1 Transient Stability 6.1.1 Fault Cleared Without a Change in the Equivalent Network Impedance 6.1.2 Short-Circuit Cleared with/without Auto-Reclosing 6.1.3 Power Swings 6.1.4 Effect of Flux Decrement 6.1.5 Effect of the AVR 6.2 Swings in Multi-Machine Systems 6.3 Direct Method for Stability Assessment 6.3.1 Mathematical Background 6.3.2 Energy-Type Lyapunov Function 6.3.3 Transient Stability Area 6.3.4 Equal Area Criterion 6.3.5 Lyapunov Direct Method for a Multi-Machine System 6.4 Synchronization 6.5 Asynchronous Operation and Resynchronization 6.5.1 Transition to Asynchronous Operation 6.5.2 Asynchronous Operation 6.5.3 Possibility of Resynchronization 207 207 207 212 215 215 216 220 222 223 225 227 228 230 237 239 240 241 242 References 615 Cushing, E.W., Drechsler, G.E., Killgoar, W.P et al (1972) Fast valving as an aid to power system transient stability and prompt resynchronization and rapid reload after full load rejection IEEE Transactions on Power Apparatus and Systems, PAS-91 (2), 1624–36 Dahl, O.G.C (1938) Electric Power Circuits – Theory and Applications, McGraw-Hill, New York Dandeno, P and Kundur, P (1973) Non-iterative transient stability program including the effects of variable load voltage characteristics IEEE Transactions on Power Apparatus and Systems, PAS-92 (5) Debs, A.S (1988) Modern Power System Control and Operation, Kluwer Academic De Mello, F.P and Concordia, C (1969) Concepts of synchronous machine stability as affected by excitation control IEEE Transactions on Power Apparatus and Systems, PAS-88 (4), 316–29 De Mello, R.W., Podmore, R and Stanton, K.N (1975) Coherency based dynamic equivalents: applications in transient stability studies PICA Conference Di Caprio, U and Marconato, R (1975) A novel criterion for the development of multi-area simplified models oriented to on-line evaluation of power system dynamic security Proceedings of the PSCC, Cambridge, UK Dimo, P (1971) L’analyse Nodale des Reseaux D’energie, Eyrolles, Paris Dommel, H.W and Sato, N (1972) Fast transient stability solution IEEE Transactions on Power Apparatus and Systems, PAS-91 (4), 1643–50 Dopazo, J.F., Dwarakonath, M.H., Li, J.J and Sasson, A.M (1977) An external system equivalent model using real-time measurements for system security evaluation IEEE Transactions on Power Apparatus and Systems, PAS-96 Duff, I.S., Erisman, A.M and Reid, J.K (1986) Direct Methods for Sparse Matrices, Oxford University Press Dunlop, R.D., Gutman, R and Marchenko, R.P (1979) Analytical development of loadability characteristic for EHV and UHV transmission lines IEEE Transactions on Power Apparatus and Systems, PAS-98, 606–17 Dy Liacco, T.E (1968) Control of Power Systems via Multi-Level Concept, Report SRC-68-19, Case Western Reserve University Edelmann, H (1963) Berechung elektrischer Verbundnetze, Springer-Verlag, Berlin Edelmann, H (1974) Direkte Verfahren der Netzanalyse mit sparlichen Matritzen Nachrichtechnische Zeitschrift, Heft 2–3 Ekanayake, J., Holdsworth, L and Jenkins, K (2003a) Control of DFIG wind turbines IEE Power Engineer, 17 (1), 28–32 Ekanayake, J., Holdsworth, L., Wu, X G and Jenkins, K (2003b) Dynamic modelling of doubly fed induction generator wind turbines IEEE Transactions on Power Systems, 18 (2), 803–9 El-Abiad, A.H (1983) Power System Analysis and Planning, Hemisphere, Washington, DC and London Elgerd, O (1982) Electric Energy Systems Theory: An Introduction, 2nd edn, McGraw-Hill, New York Elkraft Systems (2003) Power failure in Eastern Denmark and Southern Sweden on 23 September 2003 EPRI (1991) Flexible AC Transmission Systems (FACTS) Scoping study, EPRI Report EL-6943, Final Report on RP3022-02 by GE EPRI (1999) Decentralized Damping of Power Swings – Feasibility Study, Final Report TR-112417 Erlich, I., Kretschmann, J., Fortmann, J et al (2007) Modelling of wind turbines based on doubly-fed induction generators for power system stability studies IEEE Transactions on Power Systems, 22 (3), 909–19 Estanqueiro, A (2007) A dynamic wind generation model for power system studies IEEE Transactions on Power Systems, 22 (3), 920–8 Fahlen, N.T (1973) Series capacitors in power transmission: design and experience International Conference on High Voltage DC and/or AC Power Transmission, London, IEE Conference Publication No 107 Fahlen, N.T (1981) EHV series capacitor equipment protection and control IEE Proceedings, 128 (Pt C) Feng, X., Lubosny, Z and Bialek, J.W (2007) Dynamic Equivalent of a Network with High Penetration of Distributed Generation, IEEE PowerTech Conference Fouad, A.A and Vittal, V (1992) Power System Transient Stability Analysis Using the Transient Energy Function Method, Prentice Hall, Englewood Cliffs, NJ Garmond, A.J and Podmore, R (1978) Dynamic aggregation of generating unit models IEEE Transactions on Power Apparatus and Systems, PAS-97 (4) Giles, R.L (1970) Layout of E.H.V Substations, Cambridge University Press, Cambridge Glebov [Glˆ bov], I.A (1970) Excitation systems of generators with controlled rectifiers, Nauka, Leningrad (in e Russian) Gless, G.E (1966) Direct method of Liapunov applied to transient power system stability IEEE Transactions on Power Apparatus and Systems, PAS-85 (2) 616 References Glover, J.D and Sarma, M (1994) Power System Analysis and Design, 2nd edn, PWS, Boston Grainger, J.J and Stevenson, W.D (1994) Power System Analysis, McGraw-Hill Grebe, E., Handschin, E., Haubrich, H.J and Traeder, G (1979) Dynamische Langezeitstabilitat von Netzen Elektrizitatswirtschaft, 78, Heft 19 Greenwood, A (1971) Electrical Transients in Power Systems, Wiley-Interscience Gross, C.A (1986) Power System Analysis, 2nd edn, John Wiley & Sons, Inc., New York Gubina, F., Bakic, K., Omahen, P., Hrovatin, J and Jakl, F (1994) Economical, planning and operational aspects of East-West power transmission over the Slovenian power network 35th CIGRE Session, Paris Gubina, F., Omahen, P and Machowski, J (1987) Dynamic properties of a power system equivalent model for transient stability studies 34th Congress on Electronics, MELECON’87, Rome, Italy, pp 577–80 Hacaturov [Haˇ aturov], A.A (1969) Asynchronous connection and re-synchronisation in electric power systems, c Energia, Moscow (in Russian) Hammons, T.J and Winning, D.J (1971) Comparisons of synchronous machine models in the study of the transient behaviour of electrical power systems Proceedings of the IEE, 118 (10) Handschin, E and Stephanblome, T (1992) New SMES strategies as a link between network and power plant control International IFAC Symposium on Power Plants and Power System Control, Munich, Germany Harkopf, T (1978) Simulation of power system dynamics using trapezoidal rule and Newton’s method Proceedings of the PSCC Conference, Darmstadt Harris, M.R., Lawrenson, P.J and Stephenson, J.M (1970) Per Unit Systems with Special Reference to Electrical Machines, Cambridge University Press Hassenzahl, W.V (1983) Superconducting magnetic energy storage Proceedings of the IEEE, 71, 1089–8 Haubrich, H.J and Fritz, W (1999) Study on Cross-Border Electricity Transmission Tariffs by order of the European Commission, DG XVII/C1 Aachen Hicklin, J and Grace, A (1992) Simulink, MathWorks Inc Hill, D.J (1993) Nonlinear dynamic load models with recovery for voltage stability studies IEEE Transactions on Power Systems, PWRS-8 (1), 166–76 Hingorani, N.G and Gyugyi, L (2000) Understanding FACTS Concepts and Technology of Flexible AC Transmission Systems, IEEE Press Holdsworth, L., Jenkins, N and Strbac, G (2001) Electrical Stability of Large, Offshore Wind Farms, IEE Conference on AC–DC Power Transmission Holdsworth, L., Wu, X.G., Ekanayake, J and Jenkins, K (2003) Comparison of fixed speed and doubly-fed induction wind turbines during power system disturbances IEE Proceedings – Generation, Transmission and Distribution, 150 (3), 343–52 Hughes, F.M., Anaya-Lara, O., Jenkins, N and Strbac, G (2006) A power system stabilizer for DFIG-based wind generation IEEE Transactions on Power Systems, 21 (2) Humpage, W.D and Stott, B (1965) Predictor-corrector methods of numerical integration in digital computer analysis of power system transient stability IEE Proceedings, 112, 1557–65 Humpage, W.D., Wong, K.P and Lee, Y.W (1974) Numerical integration algorithms in power-system dynamic analysis IEE Proceedings, 121, 46773 ă Huwer, R (1992) Robuste Power System Stabilizer fur Mehrmaschinennetze, PhD Thesis, Universită t a Kaiserslautern IEEE Committee Report (1968) Computer representation of excitation systems IEEE Transactions on Power Apparatus and Systems, PAS-87 (6), 1460–4 IEEE Committee Report (1969) Recommended phasor diagrams for synchronous machines IEEE Transactions on Power Apparatus and Systems, PAS-88 (11), 1593–610 IEEE Committee Report (1973a) Excitation system dynamic characteristic IEEE Transactions on Power Apparatus and Systems, PAS-92 (1) IEEE Committee Report (1973b) Dynamic models for steam and hydroturbines in power system studies IEEE Transactions on Power Apparatus and Systems, PAS-92 (6), 1904–15 IEEE Committee Report (1973c) System load dynamics simulation effects and determination of load constants IEEE Transactions on Power Apparatus and Systems, PAS-92 (2), 600–9 IEEE Committee Report (1981) Excitation system models for power system stability studies IEEE Transactions on Power Apparatus and Systems, PAS-100 (2), 494–509 IEEE Committee Report (1991) Dynamic models for fossil fuelled steam units in power system studies IEEE Transactions on Power Systems, PWRS-6 (2), 753–61 References 617 IEEE Committee Report (1992) Hydraulic turbine and turbine control models for system dynamic studies IEEE Transactions on Power Systems, PWRS-7 (1), 167–79 IEEE Committee Report (1994) Static VAR compensator models for power flow and dynamic performance simulation IEEE Transactions on Power Systems, PWRS-9 (1), 229–40 IEEE Power System Relaying Committee Report (1977) Out-of-step relaying for generators IEEE Transactions on Power Apparatus and Systems, PAS-96 (5), 1556–4 IEEE Power System Relaying Comittee Power swing and out-of-step considerations on transmission lines A report to the Power System Relaying Committee of IEEE Power Engineering Society http://www133.pair com/psrc/ (Published Reports/Line protections) IEEE Std 122-1985 IEEE Recommended Practice for Functional and Performance Characteristics of Control Systems for Steam Turbine-Generators Units, IEEE Power Engineering Society IEEE Std 421.5-1992 IEEE Recommended Practice for Excitation System Models for Powers System Stability Studies, IEEE Power Engineering Society IEEE Task Force on Load Representation for Dynamic Performance (1993) Load representation for dynamic performance analysis IEEE Transactions on Power Systems, PWRS-8 (2), 472–82 IEEE Task Force on Load Representation for Dynamic Performance (1995) Standard load models for power flow and dynamic performance simulation IEEE Transactions on Power Systems, PWRS-10 (3), 1302–12 IEEE Working Group on Prime Mover and Energy Supply Models for System Dynamic Performance Studies (1994) Dynamic models for combined cycle power plants in power system studies IEEE Transaction on Power Systems, PWRS-9 (3), 1698–708 IEEE Working Group Report of panel discussion (1986) Turbine fast valving to aid system stability: benefits and other considerations IEEE Transactions on Power Systems, PWRS-1 (2), 143–53 Iliceto, F and Cinieri, E (1977) Comparative analysis of series and shunt compensation schemes for AC transmission systems IEEE Transactions on Power Apparatus and Systems, PAS-96 (1), 167–79 Ili´ , M and Zaborszky, J (2000) Dynamics and Control of Large Electric Power Systems, John Wiley & Sons, c Inc., New York Ise, T., Murakami, Y and Tsuji, K (1986) Simultaneous active and reactive power control of superconducting magnetic storage using GTO converters IEEE Transactions on Power Delivery, PWRD-1 (1), 143–50 Jancke, G., Fahlen, N and Nerf, O (1975) Series capacitors in power systems IEEE Transactions on Power Apparatus and Systems, PAS-94, 915–25 Januszewski, M (2001) Transient Stability Enhancement by Using FACTS Devices, PhD Thesis, Warsaw University of Technology (in Polish) Jones, C.V (1967) The Unified Theory of Electrical Machines, Butterworth Kamwa, I and Grondin, R (1992) Fast adaptive scheme for tracking voltage phasor and local frequency in power transmission and distribution systems IEEE Transactions on Power Delivery, PWRD-7 (2), 789–95 ’ ˆ ’ Kazovskij, E.A., Danilˆ viˇ , A.B., Kaˆarskij, E.G and Rubisov, G.V (1969) Abnormal operating conditions of e c ˆ s large synchronous machines, Izdatelstvo Nauka, Leningradskoe Otdelenie, Leningrad (in Russian) Kehlhofer, R (1991) Combined-Cycle Gas and Steam Turbine Power Plants, The Fairmont Press, Librun, GA Kessel, P and Glavitsch, H (1986) Estimating the voltage stability of a power system IEEE Transactions on Power Delivery, PWRD-1 (3), 346–54 Kimbark, E.W (1995) Power System Stability, Vols I, II, III, John Wiley & Sons, Inc., New York, 1948, 1950, 1956, reprinted by IEEE in 1995 Kirby, N.M., Xu, L., Luckett, M and Siepmann, W (2002) HVDC transmission for large offshore wind farms IEE Power Engineering Journal, 16 (3), 135–41 Kirchmayer, L.K (1959) Economic Control of Interconnected Systems, John Wiley & Sons, Inc., New York ´ Kuczynski, R., Paprocki, R and Strzelbicki, J (2005) Defence and restoration of the Polish power system PSE-Operator, Konferencja Naukowa Rynek Energii (Conference Energy Market) ă Kulicke, B and Webs, A (1975) Elektromechanisches Verhalten von Turbosetzen bei Kurzschlussen in Kraftwerksnă he ETZ-A, 96, Heft a Kumano, S., Miwa, Y., Kokai, Y et al (1994) Evaluation of transient stability controller system model CIGRE Session 38-303 Kundur, P (1994) Power System Stability and Control, McGraw-Hill, New York Kundur, P., Lee, D.C and Zein El-Din, H.M (1981) Power system stabilizers for thermal units: analytical techniques and on-site validation IEEE Transactions on Power Apparatus and Systems, PAS-100, 8195 618 References ă Lă ge, K and Lambrecht, D (1974) Die Auswirkung dreipoliger Netzkurz-schlusse mit Kurzschlussfortschala tung auf die mechanische Beansprachung von Turbosă tzen ETZ-A, 95, Heft 10 a Lander, C.W (1987) Power Electronics, 2nd edn, McGraw-Hill Larsen, E.V and Swan, D.A (1981) Applying power system stabilizers, Parts I, II, and III IEEE Transactions on Power Apparatus and Systems, PAS-100, 3017–46 Lee, D.C., Beaulieu, R.E and Service, J.R.R (1981) A power system stabilizer using speed and electrical power inputs - design and field experience IEEE Transactions on Power Apparatus and Systems, PAS-100, 4151–67 Lee, S.T.Y and Schweppe, F.C (1973) Distance measures and coherency recognition for transient stability equivalents IEEE Transactions on Power Apparatus and Systems, PAS-92 (5), 1550–7 Leithead, W.E (1992) Effective wind speed models for simple wind turbines simulations Proceedings of the 14th Annual British Wind Energy Association Conference Leithead, W.E., Delasalle, S and Reardon, D (1991) Role and objectives of control for wind turbines IEE Proceedings C – Generation, Transmission and Distribution, 138 (2), 13548 ă Lof, P.A., Hill, D.J., Arnborg, S and Andersson, G (1993) On the analysis of long term voltage stability Electric Power and Energy Systems, 15 (4), 22937 ă Lof, P.A., Smed, T., Andersson, G and Hill, D.J (1992) Fast calculation of a voltage stability index IEEE Transactions on Power Systems, PWRS-7 (1), 54–64 Lubosny, Z and Bialek, J.W (2007) Supervisory control of a wind farm IEEE Transactions on Power Systems, 22 (2) ă Luders, G.A (1971) Transient stability of multimachine power system via the direct method of Lyapunov IEEE Transactions on Power Apparatus and Systems, PAS-90 (1) MacDonald, J (1994) Present phase-angle regulating transformer technology IEE Proceedings Colloquium Facts – the Key to Increased Utilisation of a Power System, pp 61–2 Machowski, J (1985) Dynamic equivalents for transient stability studies of electrical power systems International Journal of Electrical Power and Energy Systems, (4), 215–23 Machowski, J and Bernas, S (1989) Stany nieustalone i stabilnosc systemu elektroenergetycznego, Wydawnictwa Naukowo-Techniczne, Warszawa Machowski, J and Białek, J (2008) State-variable control of shunt FACTS devices using phasor measurements Electric Power System Research, 78 (1), 39–48 Machowski, J and Nelles, D (1992a) Optimal control of superconducting magnetic energy storage unit Electric Machines and Power Systems, 20 (6) Machowski, J and Nelles, D (1992b) Power system transient stability enhancement by optimal control of static VAR compensators International Journal of Electrical Power and Energy Systems, 14 (5) Machowski, J and Nelles, D (1993) Simple robust adaptive control of static VAR compensator European Transactions on Electric Power Engineering, (6) Machowski, J and Nelles, D (1994) Optimal modulation controller for superconducting magnetic energy storage International Journal of Electrical Power and Energy Systems, 16 (5) Machowski, J., Bialek, J.W and Bumby, J.R (1997) Power System Dynamics and Stability, John Wiley & Sons, Ltd, Chichester Machowski, J., Cichy, A., Gubina, F and Omahen, P (1986) Modified algorithm for coherency recognition in large electrical power systems IFAC Symposium on Power Systems and Power Plant Control, Beijing, China Machowski, J., Cichy, A., Gubina, F and Omahen, P (1988) External subsystem equivalent model for steadystate and dynamic security assessment IEEE Transactions on Power Systems, PWRS-3 (4) Machowski, J., Gubina, F and Omahen, P (1986) Power system transient stability studies by Lyapunov method using coherency based aggregation IFAC Symposium on Power Systems and Power Plant Control, Beijing, China Martin, H.F., Tapper, D.N and Alston, T.M (1976) Sustained fast valving applied to Tennessee Valley Authority’s Watts Bar Nuclear Units Transactions of the ASME Journal of Engineering for Power, Paper 76-JPGC-Pwr55 Masters, G.M (2004) Renewable and Efficient Electric Power Systems, Wiley–IEEE Press McDonald, J.D (2003) Electric Power Substations Engineering, CRC Press McPherson, G and Laramore, R.D (1990) Introduction to Electric Machines and Transformers, 2nd edn, John Wiley & Sons, Inc., New York Miller, T.J.E (1982) Reactive Power Control in Electric Systems, John Wiley & Sons, Inc., New York References 619 Moussa, H.A.M and Yu, Y.N (1972) Improving power system damping through supplementary governor control PES Summer Meeting, Paper C 72 470-3 Muller, S., Deicke, M and De Donker, R.W (2002) Doubly fed induction generator systems IEEE Industry Applications Magazine, pp 26–33 Nagao, T (1975) Voltage collapse at load ends of power systems Electrical Engineering in Japan, 95 (4) National Grid Company (NGC) (1994) 1994 Seven Year Statement Nitta, T., Shirari, Y and Okada, T (1985) Power charging and discharging characteristics of SMES connected to artificial transmission line IEEE Transactions on Magnetics, 21 (2) Nogal, L (2008) Application of wide area measurements to stability enhancing control of FACTS devices installed in tie-lines PhD Thesis, Warsaw University of Technology (in Polish) Ogata, K (1967) State Space Analysis of Control Systems, Prentice Hall O’Kelly, D (1991) Performance and Control of Electrical Machines, McGraw-Hill Olas, A (1975) Synthesis of systems with prescribed trajectories Proceedings of Non-linear Vibrations, 16 Omahen, P (1991) Fast transient stability assessment using corrective PEBS method Proceedings of 6th IEEE Mediterranean Electrotechnical Conference, Vol 2, pp 1408–11 Omahen, P (1994) Unified Approach to Power System Analysis in its Multi-Time Scale Dynamic Response PhD Thesis, Warsaw University of Ethnology (in Polish) Omahen, P and Gubina, F (1992) Simulations and field tests of a reactor coolant pump emergency start-up by means of remote gas units IEEE Transactions on Energy Conversion, EC-7 (4), 691–7 Omahen, P and Gubina, F (1995) Experience with large power system dynamics model for security assessment CIGRE Power System Operation & Control Colloquium, Johannesburg/Cape Town Pai, M.A (1981) Power System Stability: Analysis by the direct method of Lyapunov, North-Holland, Amsterdam Pai, M.A (1989) Energy Function Analysis for Power System Stability, Kluwer Academic Park, R.H (1973) Fast turbine valving IEEE Transactions on Power Apparatus and Systems, PAS-92, 1065–73 Pavella, M., Ernst, D and Ruiz-Vega, D (2000) Transient Stability of Power Systems: A Unified Approach to Assessment and Control, Kluwer Academic Pavella, M and Murthy, P.G (1994) Transient Stability of Power Systems Theory and Practice, John Wiley & Sons, Ltd Phadke, A.G and Thorap, J.S (1988) Computer Relaying for Power Systems, John Wiley & Sons, Inc Phadke, A.G., Thorap, J.S and Adamiak, M.G (1983) A new measurement technique for tracking voltage phasors, local system frequency and rate of change of frequency IEEE Transactions on Power Apparatus and Systems, PAS-102 (5) Pissanetzky, S (1984) Sparse Matrix Technology, Academic Press Podmore, R (1978) Identification of coherent generators for dynamic equivalents IEEE Transactions on Power Apparatus and Systems, PAS-97, 1344–54 Press, W.H., Teukolsky, S.A., Vetterling, W.T and Flannery, B.P (1992) Numerical Recipes in C: The Art of Scientific Computing, 2nd edn, Cambridge University Press Racz, L.Z and Bokay, B (1988) Power System Stability, Kluwer Academic Rafian, M., Sterling, M.J.H and Irving, M.R (1987) Real time power system simulation IEE Proceedings, 134 (Pt C, 3), 206–23 Ramey, D.G and Skooglund, J.W (1970) Detailed hydrogovernor representation for system stability studies IEEE Transactions on Power Apparatus and Systems, PAS-89 (1), 106–12 Rasolomampionona, D.D (2000) Analysis of the power system steady-state stability: influence of the load characteristics Archives of Electrical Engineering, XLIX (191-1) Rasolomampionona, D.D (2007) Optimisation of parameters of TCPAR installed in tie lines with regard to their interaction with LFC Prace Naukowe Elektryka, z 134 Publishing House of the Warsaw University of Technology (in Polish) Riaz, M (1974) Hybrid-parameter models of synchronous machines IEEE Transactions on Power Apparatus and Systems, PAS-93, 84958 ă Rudenberg, R (1923) Elektrische Schaltvorgă nge und verwandte Stă rungserscheinungen in Starkstromanlagen, a o Julius Springer, Berlin ă Rudenberg, R (1950) Transient Performance of Electric Power Systems, McGraw-Hill, New York Saccomanno, F (2003) Electric Power System Control: Analysis and Control, Wiley–IEEE Press Schlueter, R.A., Ilu, T., Chang, J.C et al (1992) Methods for determining proximity to voltage collapse IEEE Transactions on Power Systems, PWRS-6 (2), 285–92 620 References Seshu, S and Reed, M.B (1961) Linear Graphs and Electrical Networks, Addison-Wesley Slootweg, J.G., de Hann, S.W.H., Polinder, H and Kling, W.L (2003) General model for representing variable speed wind turbines in power system dynamic simulations IEEE Transactions on Power Systems, 18 (1), 144–51 Slootweg, J.G., Polinder, H and Kling, W.L (2001) Dynamic modelling of a wind turbine with doubly fed induction generator Power Engineering Society Summer Meeting, IEEE paper 0-7803-7173-9/01 Song, Y.H and Johns, A.T (1999) Flexible AC transmission systems (FACTS) IEE Power and Energy Series 30, IEE: London Stalewski, A., Goody, J.L.H and Downes, J.A (1980) Pole-slipping protection 2nd International Conference on Developments in Power System Protection, IEE Conference Publication No 185 Stannard, N and Bumby, J.R (2007) Performance aspects of mains connected small scale wind turbines Proceedings of the IET – Generation, Transmission and Distribution, (2), 348–56 Stott, B (1974) Review of load flow calculation methods Proceedings of the IEEE, 62, 916–29 Stott, B (1979) Power system dynamic response calculations Proceedings of the IEEE, 67, 219–41 Strang, G (1976) Linear Algebra and Its Applications, Academic Press, New York Taylor, C.W (1994) Power System Voltage Stability, McGraw-Hill Taylor, C.W., Haner, J.M., Hill, L.A et al (1983) A new out-of-step relay with rate of change of apparent resistance augmentation IEEE Transactions on Power Apparatus and Systems, PAS-102 (3) Taylor, C.W., Haner, J.M and Laughlin, T.D (1986) Experience with the R-Rdot out-of-step relay IEEE Transactions on Power Delivery, PWRD-1 (2) Tewerson, R.P (1973) Sparse Matrices, Academic Press, New York Tinney, W.F., Brandwain, V and Chan, S.M (1985) Sparse vector methods IEEE Transactions on Power Apparatus and Systems, PAS-104, 295–301 Tinney, W.F and Bright, J.M (1986) Adaptive reductions for power equivalents IEEE Power Winter Meeting, Paper 86 WM Tinney, W.F., Powell, W.L and Peterson, N.M (1973) Sparsity oriented network reduction Proceedings of PICA Conference, Minneapolis, pp 385–90 Tinney, W.F and Walker, J.W (1967) Direct solutions of sparse network equations by optimally ordered triangular factorization Proceedings of the IEEE, 55 (11), 1801–9 Tiranuchit, A and Thomas, R.J (1988) A posturing strategy action against voltage instabilities in electric power systems IEEE Transactions on Power Systems, PWRS-3 (1), 87–93 Troskie, H.J and de Villiers, L.N.F (2004) Impact of Long Duration Faults on Out-Of-Step Protection, ESCOM, South Africa UCTE (2007) Final Report System Disturbance on November 2006 UCTE Operation Handbook Load Frequency Control and Performance, Available at http://www.ucte.org/ Ulyanov [Ul’ˆ nov], S.A (1952) Short-circuits in electric power systems, Moscow and Leningrad (in Russian) a Undrill, J.M and Turner, A.E (1971) Construction of power system electromechanical equivalents by modal analysis IEEE Transactions on Power Apparatus and Systems, PAS-90 (5) Ungrad, H., Winkler, W and Wiszniewski, A (1995) Protection Techniques in Electrical Energy Systems, Marcel Dekker US–Canada Power System Outage Task Force (2004) Final Report on the August 14, 2003 Blackout in the United States and Canada Vaahedi, E., El-Kady, M.A., Libaque-Esaine, J.A and Carvalho, V.F (1987) Load models for largescale stability studies from end-user consumption IEEE Transactions on Power Systems, PWRS-2 (4), 864–2 Van Cutsem, T (1991) A method to compute reactive power margins with respect to voltage collapse IEEE Transactions on Power Systems, PWRS-6, 145–56 Van Cutsem, T and Vournas, C (1998) Voltage Stability of Electric Power Systems, Springer-Verlag Van Der Hoven, I (1957) Power spectrum of horizontal wind speed in the frequency range from 0.0007 to 900 cycles per hour American Journal of Meteorology, 14, 160–4 Venikov [Vˆ nikov], V.A (1958) Electromechanical transient processes in electric power systems, Gosudarstvennoe e Energeticeskoe Izdatelstvo, Moscow and Leningrad (in Russian) Venikov [Vˆ nikov], V.A (1964) Transient Phenomena in Electrical Power Systems, Pergamon Press, Oxford e Venikov [Vˆ nikov], V.A (1978a) Transient electromechanical processes in electric power systems, Vyssaa Skola, e Moscow (in Russian) Venikov [Vˆ nikov], V.A (1978b) Transient Processes in Electrical Power Systems, Mir, Moscow e References 621 Venikov [Vˆ nikov], V.A (1985) Transient electromechanical processes in electric power systems, Vyssaa Skola, e Moscow (in Russian) Voropaj, N.I (1975) Equivalencing of electric power systems under large disturbances Elektricestvo, No (in Russian) Vorley, D.H (1974) Numerical Techniques for Analysing the Stability of Large Power Systems PhD Thesis, University of Manchester Vournas, C.D., Nikolaidis, V.C and Tassoulis, A.A (2006) Postmortem analysis and data validation in the wake of the 2004 Athens Blackout IEEE Transactions on Power Systems, 21 (3) Wang, H.F., Hao, Y.S., Hogg, B.W and Yang, Y.H (1993) Stabilization of power systems by governor-turbine control Electrical Power & Energy Systems, 15 (6), 351–61 Wang, X (1997) Modal Analysis of Large Interconnected Power System, Reihe 6: Energietechnik, Nr 380, ă VDI-Verlag, Dusseldorf Ward, J.B (1949) Equivalent circuits for power flow studies AIEE Transactions on Power Apparatus and Systems, PAS-68, 373–82 Wasynczuk, O., Man, D.T and Sullivan, J.P (1981) Dynamic behaviour of a class of wind turbine generators during random wind fluctuations IEEE Transactions on Power Applications and Systems, PAS-100, 2837–45 Watson, W and Coultes, M.E (1973) Static exciter stabilizing signals on large generators – mechanical problems IEEE Transactions on Power Apparatus and Systems, PAS-92, 204–11 Weedy, B.M (1980) Underground Transmission of Electric Power, John Wiley & Sons, Ltd, Chichester Weedy, B.M (1987) Electric Power Systems, 3rd rev edn, John Wiley & Sons, Ltd, Chichester Weisman, J and Eckart, L.E (1985) Modern Plant Engineering, Prentice Hall, Englewood Cliffs, NJ Welfonder, E (1980) Regeldynamisches Zusammenvirken von Kraftwerken und Verbrauchern im Netzverbundbetrieb Elektrizită tswirtschaft, 79, Heft 20 a Westlake, A.J., Bumby, J.R and Spooner, E (1996) Damping the power angle oscillations of a permanent magnet synchronous generator with particular reference to wind turbine applications IEE Proceedings – Electric Power Applications, 143 (3) Willems, J.L (1970) Stability Theory of Dynamical Systems, Nelson, London Wilson, D., Bialek, J.W and Lubosny, Z (2006) Banishing blackouts IEE Power Engineering Journal 20 (2), 38–41 Witzke, R.L., Kresser, J.V and Dillard, J.K (1953) Influence of AC reactance on voltage regulation of 6-phase rectifiers AIEE Transactions, 72, 244–53 Wood, A.J and Wollenberg, B.F (1996) Power Generation Operation and Control, 2nd edn, John Wiley & Sons, Inc Wright, A and Christopoulos, C (1993) Electrical Power System Protection, Chapman and Hall, London Xiang, D., Ran, L., Tavner, P.J and Yang, S (2006) Control of a doubly fed induction generator in a wind turbine during grid fault ride-through IEEE Transactions on Energy Conversion, 21 (2), 652–62 Younkins, T.D., Chow, J.H., Brower, A.S et al (1987) Fast valving with reheat and straight condensing steam turbines IEEE Transactions on Power Systems, PWRS-2, 397–405 Yu, Y.N (1983) Electric Power System Dynamics, Academic Press, New York ˇ Zdanov [Zdanov], P.S (1948) Stability of electric power systems, Gosudarstvennoe Energeticeskoe Izdatelstvo, Moscow and Leningrad (in Russian) ˇ Zdanov [Zdanov], P.S (1979) Stability problems of electric power systems, Energia, Moscow (in Russian) ˇ Zukov [Zukov], L.A (1964) Simplified transformation of circuit diagrams of complex electric power systems Izvestia Akademii Nauk SSSR, Energetika i Transport, No (in Russian) Index a,b co-ordinates, 115 Acceleration area, 185, 209, 211 AC exciter Rotating, 22, 466 Static, 22, 468 Aggregation of generators, 567 of nodes, 562–563 Air-gap flux, 80 Alert state, 10 Amortisseurs, 21, 146, 172 Angle of attack, 273 Angular momentum, 171 Annual energy demand, 15 Aperiodic mode, 504 Area control error (ACE), 343 Armature Leakage, 85, 136 flux paths,134 short circuit current, 133 time constant, 133 winding, 21 reactance, 81, 85, 135 reaction, 21, 79 Asynchronous operation, 210, 239, 245, 251 torque, 172 Attenuation constant, 66 Automatic generator control (AGC), 336, 346 Auto-reclosing, 54, 212 Automatic voltage regulator (AVR) modelling, 462, 527 load compensation, 23, 462 limiters, 24, 200 influence on fault current, 150 influence on steady state stability, 196 influence on transient stability, 216 influence on voltage stability, 317 modelling, 462, 526 Autotransformer, 37 Auxiliary services, 20 Backward swing, 400 Bang-bang control, 391, 397 Bandwidth of secondary control, 345 Betz limit, 266 Bias factors, 343, 366 Bifurcation point, 319 Blackouts, 323, 340 Blocking relay, 248 Boiler control, 475 boiler-follows-turbine, 475 turbine-follows-boiler, 475 integrated, 475 Braking resistor, 45, 49, 391 Buchholz protection, 57 Busbars, 35 protection, 57 Capacity factor, 269 Centre of power swing, 249 Classification of dynamics, Characteristic equation, 192, 492, 517, 602 Characteristic impedance, 67 Charging current line, 66 cable, 72 Classical model, 180, 456 Coherency, 567 based equivalents, 573 criterion, 571 electromechanical, 566 Power System Dynamics: Stability and Control, Second Edition Jan Machowski, Janusz W Bialek and James R Bumby C 2008 John Wiley & Sons, Ltd Index 624 Coherency (Continued ) exact, 567 recognition, 569 Combined cycle gas turbine (CCGT), 27 single shaft mode, 28 Combustion chamber, 27 Constant flux linkage, 127, 145, 153 Contingencies, Controller field-oriented, 289 vector, 289 Critical disturbance, fault clearing time, 210, 215, 230, 235 operating point, 176, 311 power demand, 310, 319 power state, 311 voltage, 311 Damped frequency, 611 Damper windings, 21,129, 136, 172, 186, 205 Damping coefficient, 171, 175, 193 power, 172, 240 ratio, 193, 256, 262, 611 torque, 205 Danish concept, 270 Decentralized control, 341 DC excitation system, 20, 463 DC offset, 129 Declaration area, 189, 209, 229 Defence plan, 347 Diagonalization, 496 Dimo’s method, 564 Direct method, 22, 230, 418 Disc averaging, 482 Discharge lighting, 105 Distance relay, 56 Distributed generation, 18 Distribution, 17, 19 Distribution transformer, 36 Disturbance critical, large, 207 small, 169 Dominant mode, 506 Droop, 32, 46, 336, 341 d,q axis, 76, 434 d,q to a,b transformation, 117, 436 0,d,q transformation, 436, 438 Economic dispatch, 336 Eigenvalues, 195, 491 Eigenvectors, 491 left and right hand, 492, 497 Electrical centre, 249 Electro-hydraulic governor, 29 Embedded generation, 18, 278 Emergency state, 10 Elimination of nodes, 230, 559 Energy function, 225 Environmental issues, 16 Exact coherency, 567 Excitation systems, 21, 384 load compensation, 23, 462 modelling, 462 Excitation transformer, 22, 40, 490 Extremis state, Equal-area criteria, 184, 209, 228, 388, 400, 419 Equilibrium point, 3, 176, 305, 339, 589 stable point, 178, 194, 306, 359 unstable point, 33, 178, 194, 306 Equivalents, 557 FACTS, 43, 119, 370, 391, 423,488 Fast-valving, 35, 244, 389 momentary, 389 sustained, 389 Fault clearing, 166, 168 critical clearing time, 210, 215 shunts, 208 unbalanced, 211 Feedback control, Fixed speed generator 269 Flux decrement145, 195, 215 Forward swing, 387, 400, 419, 423 Francis turbine, 476 Frequency collapse, 358, 363 Frequency control, 335 primary, 339, 346 secondary, 340, 346 tertiary, 345, 346 Frequency stiffness, 340 Fundamental system of solutions, 601 Gate turn-off thyristor, 44 Gas turbines, 26 Index Gauss-Seidel, 123 General solution, 602 Generating unit, 20 Generation characteristic, 336 Generator emfs, 78, 137, 143 establishing initial values, 143 subtransient, 140, 449 steady-state, 99, 447 transient, 142, 447 Generator equivalent circuits, 454 steady-state, 143 subtransient, 141, 143 transient, 142, 143 Generator reactance, 136, 138 Generator transformer21, 36 Generator tripping, 392 preventive, 393 restitutive, 394 Governor control valves, 26, 389, 471, 473 Governor systems, 32, 480 Heat recovery boiler, 27 Hybrid network equations, 116 Hydraulic turbines, 28 modelling, 476 transfer function, 479 Ideally stiff load, 300 Impulse turbine, 29 Incremental model, 371, 577 Induction generator, 265 doubly fed, 271 fixed speed, 269 variable speed, 271 Induction motor, 103, 282 easy starting, 107 equivalent circuit, 106 heavy-starting, 107 modelling, 485 slip, 106, 486 stalling voltage, 107 torque-slip curve, 106 Inertia coefficient, 172 Inertia constant, 171 Infinite busbar, 146, 163, 167, 173 Integration constants, 604 Intercept valves, 26, 389, 472 Interconnected systems, 340, 344, 364 Interface error, 353 625 Internal power factor angle, 82 Islanded systems, 335, 361 Jacobian, 116 Kaplan turbine, 29 Line trap, 55 Leakage flux, 72, 76, 459 Leakage reactance, 81, 460 Load angle, 68, 118 Load characteristics, 104, 110 effect of tap-changer, 111 frequency, 104, 112, 358 static, 110 voltage, 105, 107, 108, 110 Load modelling, 104, 111, 485 composite load, 104, 485 constant current, 111 constant power, 111 constant impedance, 105, 111, 324 exponential, 112 frequency dependent, 112 polynomial model, 111 stiffness, 321 voltage sensitivity, 105, 318 Load sensitivity frequency, 104, 339 voltage, 104 Load shedding, 348, 360 Load reference set point, 39 Local measurements, 400, 410, 421, 428 Logarithmic spiral, 613 Lyapunov’s first method, 513 Lyapunov’s second (direct) method, 222, 407 Magnetizing reactance, 106, 274 Main stop valves, 34 Matrix factorization, 547, 553 partial inversion, 543, 559, 600 Mechanical-hydraulic governor, 29, 470 Mechanical time constant, 171 Mho relay, 248, 250 Modal analysis, 513, 528, 570, 579 matrix, 501 reduction, 558 variables, 501, 580, 587 Mode shape, 254, 509 Index 626 Modulation controller, 47, 401, 404, 405 Multimachine systems, 220, 230, 307, 318, 352, 371, 491 Natural frequency, 193 damped/undamped, 193, 256, 262 Natural load, 67 Negative damping, 187, 204, 218, 384, 422 Network equations, 113, 442, 450, 546, 553 Network feasibility, 299, 317 Network loadability, 300 Network splitting, 251 Network reduction, 557–558 Newton method, 123, 539, 551 Nodal admittance matrix, 75, 113 Nodal impedance matrix, 114 Nodal network equations, 113 Nodes: PV, PQ, slack, 122 Non-intervention rule, 342 Normal state, 10 Nose curves, 301 Numerical integration, 536 Off-nominal transformation ratio, 72, 74 Oscillatory mode, 504 Out-of-step protection (relaying), 244 Out-of-step tripping, 245 Overexcitation, 103 Overhead line, 68 Park’s transformation, 438 Partial inversion, 543, 559, 600 Partially equidistant point, 590 Participation factor, 511 Particular solution, 606 Partitioned solution method, 541 Participation factor, 511, 588 Pelton Wheel, 28 Penstock, 28 Per unit systems, 439, 593 Pitch control, 237, 482 Phase angle regulator (TCPAR), 52, 370, 423 Phase constant, 66 Phase-shifting transformer , 40, 423, 488 Phasor Diagram, 86, 95, 141, 161, 180, 197, 288, 451 measurement unit (PMU), 61 Physical reduction, 558 Point of common connection, 278 Pole-slip protection, 245, 249 Potier reactance, 460 Power angle, 92, 97, 101, 171 Power-angle characteristic classical, 183 steady-state, 103 transient, 179, 183, 209 Power capability curve, 91 Power conditioning system, 48 Power flow, 118 Power invariance, 595 Power line carrier, 55 Power swing, 185, 191, 215, 219 detection, 248 Power system stability, angle, 9, 207 voltage, 9, 299 frequency, 9, 335 Power system stabilizer, 23, 47, 383, 429, 470 Power system structure, 19 Primary control, 339 Protection differential current, 54 directional comparison, 55 distance, 56 local back-up, 43 pole-slip, 244 remote back-up, 54 Pull-out power, 177 Quadrature booster, 40, 52 q axis, 76 Rayleigh distribution, 268 Reactive power, 70, 91, 109, 305 Regulation power, 344, 362 Reheat stop valves, 26 Reliability of supply, 15 Reluctance power, 91 Reserve of secondary control, 345 Resynchronization, 237, 393 Rotation matrix, 441 Rotational voltage, 87, 486 sampling, 482 Rotor angle, 101, 118, 170 Rotor screening, 135 Rotor swing, 184, 207, 218 Run-up control, 34 Roots distinct, 604 repeated, 605 Index Saturation characteristics, 458 factor, 459 parameter sensitivity, 461 Secondary control, 340 Security, assessment, 10 dynamic, 11 small signal, 10 static, 10 transient, 11 voltage, 10 Self-excitation, 329 synchronous, 332 asynchronous, 333 Sensitivity analysis, 319, 510 Series capacitor, 41 thyristor controlled (TCSC), 50, 416 Series transformer, 40 Servomotor, 26, 473 Short circuit current, 128, 134, 146, 149 in network, 167 power, 108, 396 reactance, 396 Shunt capacitor, 42, 45, 395 Shunt compensation, 41, 425 Shunt reactor, 25 Shut down wind speed, 267 Simulation methods partitioned (alternating), 541 simultaneous (combined), 553 Slack bus (node), 122 Slip frequency, 271 Small signal stability, 491 Sparse matrix, 114, 547, 560 Speed deviation, 170 Speed measuring device, 26 Speeder gear, 29 Speed-droop characteristic, 34, 336, 338 coefficient, 33 Speed reference set-point, 30 Speed ratio, 266 Spinning reserve, 337 Stability enhancement, 383 Stable equilibrium point, 181, 210, 227, 589 Stall control, 273 Standard form, 609 627 State control, 370, 410 matrix, 500 space equation, 515 steady, 65, 135 subtransient, 125, 140 transient, 135, 141 variable, 3, 397, 500, 541 vector, 3, 500 Static compensator (STATCOM), 47, 395, 327, 488 Static VAR compensator (SVC), 45, 395, 488 Steady-state stability, 69, 177, 196, 491 condition, 190, 517 limit, 178 margin, 178 regulated system, 196 unregulated system, 177 Steam turbine, 25 cross-compound, 26 condenser, 26 modelling, 470 non-reheat, 25 overspeed control, 34 regulated characteristic run-up control, 34 reheat, 25 stages, 25 tandem-compound, 25, 472 transfer function, 472 unregulated characteristic, 31 valves, 26, 389, 475 Step-up transformer, 18 Stiffness, 349, 344 Subtransmission network, 17 Subsynchronous resonance, 334 Substation, 21, 35 Subtransient reactance, 136 d axis, 136, 139 q axis, 137, 139 Subtransient saliency, 137, 148, 156 Subtransient time constant, 139 d axis, 139, 446 q axis, 139, 446 Superconducting magnetic energy storage (SMES), 49, 395 Supplementary control, 383 Surge impedance, 66 Surge impedance load (SIL), 67 Survival wind speed, 267 Swing equation, 169, 452, 514 Index 628 Swing frequency, 189 Symmetrical components, 158 Synchronization, 163, 237 condition, 239 currents, 164, 238 torque, 164, 238 Synchronous compensator, 42 Synchronous generator, 19 emfs, 85, 95, 99 equivalent circuits, 87, 100 leakage flux, 76 modelling, 433 on no-load, 77 parameters, 139 power supplied to system, 102, 103 protection, 57 round-rotor, 76 salient pole, 83 saliency, 76 steady state, 135 subtransient, 135 torque, 82, 88 transient state, 135 Synchronous reactance, 82 d axis, 85 q axis, 85 Synchronous speed, 28, 77, 163, 170, 239 Synchronizing power steady state, 178 transient, 184 Tap-changing transformers, 37 Tertiary control, 345 Thyristor, 43 conventional, 43 gate turn-off thyristor (GTO), 44 Tie-line, 17, 120, 342 control, 336, 343 oscillations, 364 Time constant, 128 armature, 133 d-axis, 133 mechanical, 171 q-axis, 138 Torque asynchronous, 172 in round-rotor generator, 82 in salient pole generator, 88 mechanical, 171 subtransient, 150 synchronous, 82, 88 Torque angle, 83 Torsional oscillation, 253 Torsional fatigue, 237, 253, 263 Tower shadow, 482 Trajectory, 3, 223, 567, 591 Transfer admittance, 231, 561 capability, 523 equivalent network, 207, 560 Transformation matrix, 437 Transformer emf, 442 Transformers, 36 booster, 40 π equivalent, 73 autotransformers, 41 core loss, 72 equivalent circuit, 73, 75 excitation current, 73 ideal, 73 leakage flux, 72 magnetization current, 72 modelling, 74 no-load test, 73 off-nominal taps, 74 phase shifting, 75 short-circuit test, 73 short-circuit voltage, 74 tap-changing, 37 three-winding transformers, 36 two-winding transformers, 36 unit transformer, 20 Transmission, 16 angle, 66 Transmission lines, 65 long, 66 lossless, 67 medium-length, 67 short-length, 67 π equivalent, 67 Transient droop, 479 Transient power angle, 178, 215 Transient reactance d axis, 136, 139, 444 q axis, 138, 139, 444 Transient saliency, 179, 455 Transient stability, 9, 207 margin, 210, 215 Transient time constant open-circuit, 139, 445 short-circuit, 139, 445 Index Trumpet characteristic, 349 Turbine governor, 19, 34, 470 modelling, 470 Turbogenerator, 20 Two-reaction theory, 84 Unbalanced faults, 211 Underexcitation, 103 Underdamped second – order system, 609 Underground cables, 35, 72 Unified power controller (UPFC), 52, 119, 423, 488 Uniform damping, 517 Unit transformer, 20 Unstable equilibrium point, 179, 195, 228, 589 Vandermonde’s determinant, 603 Vector control, 289 Voltage collapse, 299, 310, 312 Voltage sensitivities, 104 Voltage-sensitive loads, 315 Voltage source converter, 47 629 Voltage stability, 9, 299 criteria, 305 index, 320 proximity index, 320 Watt governor, 29 Water starting time, 474 Weibull distribution, 268 Wicket gates, 28 Wide area measurement system (WAMS), 58 monitoring, 59 measurement, protection, and control, (WAMPAC), 59, 378, 410 Wind power, 265 shear, 482 speed, 266, 482 turbines, 265, 481 Wronskian, 603 Zhukov’s method, 563 ... 7.9 .2 Variable-Speed Induction Generators 7.10 Influence of Wind Generators on Power System Stability 26 5 26 5 26 9 27 4 27 7 28 0 28 2 28 4 28 6 28 7 28 9 29 0 29 1 29 2 29 3 29 4 29 4 29 4 29 6 29 6 Voltage Stability. .. Operation and Resynchronization 6.5.1 Transition to Asynchronous Operation 6.5 .2 Asynchronous Operation 6.5.3 Possibility of Resynchronization 20 7 20 7 20 7 21 2 21 5 21 5 21 6 22 0 22 2 22 3 22 5 22 7 22 8 23 0 23 7... Quality 2. 1.3 Economic Generation and Transmission 2. 1.4 Environmental Issues 2. 2 Structure of the Electrical Power System 2. 2.1 Generation 2. 2 .2 Transmission 2. 2.3 Distribution 2. 2.4 Demand 2. 3