T r a n s i e n T s in e l e c T r i c a l s y s T e m s A n A ly s i s , R e c o g n i t i o n , A n d M itigAtion J. C. Das New York Chicago San Francisco Lisbon London Madrid Mexico City Milan New Delhi San Juan Seoul Singapore Sydney Toronto Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved. Except as permitted under the United States Copyright Act of 1976, no part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without the prior written permis- sion of the publisher. ISBN: 978-0-07-162603-3 MHID: 0-07-162603-4 The material in this eBook also appears in the print version of this title: ISBN: 978-0-07-162248-6, MHID: 0-07-162248-9. All trademarks are trademarks of their respective owners. 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Under no circumstances shall McGraw-Hill and/or its licensors be liable for any indirect, incidental, special, punitive, consequential or similar damages that result from the use of or inability to use the work, even if any of them has been advised of the possibility of such damages. This limitation of liability shall apply to any claim or cause whatsoever whether such claim or cause arises in contract, tort or otherwise. To My Parents J. C. Das is currently Staff Consultant, Electrical Power Systems, AMEC Inc., Tucker, Georgia, USA. He has varied experience in the utility industry, industrial establishments, hydroelectric gen- eration, and atomic energy. He is responsible for power system studies, including short-circuit, load flow, harmonics, stability, arc- flash hazard, grounding, switching transients, and also, protective relaying. He conducts courses for continuing education in power systems and has authored or coauthored about 60 technical publica- tions. He is author of the book Power System Analysis, Short-Circuit, Load Flow and Harmonics (New York, Marcel Dekker, 2002); its second edition is forthcoming. His interests include power system transients, EMTP simulations, harmonics, power quality, protection, and relaying. He has published 185 electrical power systems study reports for his clients. He is a Life Fellow of the Institute of Electrical and Electronics Engineers, IEEE (USA), a member of the IEEE Industry Applications and IEEE Power Engineering societies, a Fellow of Institution of Engi- neering Technology (UK), a Life Fellow of the Institution of Engineers (India), a member of the Federation of European Engineers (France), and a member of CIGRE (France). He is a registered Professional Engineer in the states of Georgia and Oklahoma, a Chartered Engineer (C. Eng.) in the UK, and a European Engineer (Eur. Ing.). He received a MSEE degree from Tulsa University, Tulsa, Oklahoma in 1982 and BA (mathematics) and BEE degrees in India. A b o u t t h e A u t h o r Preface xiii c h a p T e r 1 i n T r o d u c T i o n T o T r a n s i e n T s 1-1 Classification of Transients 1 1-2 Classification with Respect to Frequency Groups 1 1-3 Frequency-Dependent Modeling 2 1-4 Other Sources of Transients 3 1-5 Study of Transients 3 1-6 TNAs—Analog Computers 3 1-7 Digital Simulations, EMTP/ATP, and Similar Programs 3 References 4 Further Reading 4 c h a p T e r 2 T r a n s i e n T s in l u m p e d c i r c u i T s 2-1 Lumped and Distributed Parameters 5 2-2 Time Invariance 5 2-3 Linear and Nonlinear Systems 5 2-4 Property of Decomposition 6 2-5 Time Domain Analysis of Linear Systems 6 2-6 Static and Dynamic Systems 6 2-7 Fundamental Concepts 6 2-8 First-Order Transients 11 2-9 Second-Order Transients 15 2-10 Parallel RLC Circuit 18 2-11 Second-Order Step Response 21 2-12 Resonance in Series and Parallel RLC Circuits 21 2-13 Loop and Nodal Matrix Methods for Transient Analysis 24 2-14 State Variable Representation 25 2-15 Discrete-Time Systems 28 2-16 State Variable Model of a Discrete System 30 2-17 Linear Approximation 30 Problems 31 Reference 32 Further Reading 32 c h a p T e r 3 c o n T r o l s y s T e m s 3-1 Transfer Function 33 3-2 General Feedback Theory 35 3-3 Continuous System Frequency Response 38 3-4 Transfer Function of a Discrete-Time System 38 3-5 Stability 39 3-6 Block Diagrams 41 3-7 Signal-Flow Graphs 41 3-8 Block Diagrams of State Models 44 3-9 State Diagrams of Differential Equations 45 3-10 Steady-State Errors 47 3-11 Frequency-Domain Response Specifications 49 3-12 Time-Domain Response Specifications 49 3-13 Root-Locus Analysis 50 3-14 Bode Plot 55 3-15 Relative Stability 58 3-16 The Nyquist Diagram 60 3-17 TACS in EMTP 61 Problems 61 References 63 Further Reading 63 c h a p T e r 4 M o d e l i n g o f T r a n s m i s s i o n L i n e s a n d C a b l e s f o r T r a n s i e n T S T u d i e s 4-1 ABCD Parameters 65 4-2 ABCD Parameters of Transmission Line Models 67 4-3 Long Transmission Line Model-Wave Equation 67 4-4 Reflection and Transmission at Transition Points 70 4-5 Lattice Diagrams 71 4-6 Behavior with Unit Step Functions at Transition Points 72 4-7 Infinite Line 74 4-8 Tuned Power Line 74 4-9 Ferranti Effect 74 4-10 Symmetrical Line at No Load 75 4-11 Lossless Line 77 4-12 Generalized Wave Equations 77 4-13 Modal Analysis 77 C o n t e n t s v vi c o n t e n t s 6-12 Interruptions of Capacitance Currents 144 6-13 Control of Switching Transients 147 6-14 Shunt Capacitor Bank Arrangements 150 Problems 152 References 153 Further Reading 153 c h a p T e r 7 s w i T c h i n g T r a n s i e n T s a n d T e m p o r a r y o v e r v o lT a g e s 7-1 Classification of Voltage Stresses 155 7-2 Maximum System Voltage 155 7-3 Temporary Overvoltages 156 7-4 Switching Surges 157 7-5 Switching Surges and System Voltage 157 7-6 Closing and Reclosing of Transmission Lines 158 7-7 Overvoltages Due to Resonance 164 7-8 Switching Overvoltages of Overhead Lines and Underground Cables 165 7-9 Cable Models 166 7-10 Overvoltages Due to Load Rejection 168 7-11 Ferroresonance 169 7-12 Compensation of Transmission Lines 169 7-13 Out-of-Phase Closing 173 7-14 Overvoltage Control 173 7-15 Statistical Studies 175 Problems 179 References 180 Further Reading 180 c h a p T e r 8 c u r r e n T i n T e r r u p T i o n in ac c i r c u i T s 8-1 Arc Interruption 181 8-2 Arc Interruption Theories 182 8-3 Current-Zero Breaker 182 8-4 Transient Recovery Voltage 183 8-5 Single-Frequency TRV Terminal Fault 186 8-6 Double-Frequency TRV 189 8-7 ANSI/IEEE Standards for TRV 191 8-8 IEC TRV Profiles 193 8-9 Short-Line Fault 195 8-10 Interruption of Low Inductive Currents 197 8-11 Interruption of Capacitive Currents 200 8-12 Prestrikes in Circuit Breakers 200 8-13 Breakdown in Gases 200 4-14 Damping and Attenuation 79 4-15 Corona 79 4-16 Transmission Line Models for Transient Analysis 81 4-17 Cable Types 85 Problems 89 References 89 Further Reading 89 c h a p T e r 5 l i g h T n i n g s T r o k e s , s h i e l d i n g , a n d b a c k f l a s h o v e r s 5-1 Formation of Clouds 91 5-2 Lightning Discharge Types 92 5-3 The Ground Flash 92 5-4 Lightning Parameters 94 5-5 Ground Flash Density and Keraunic Level 98 5-6 Lightning Strikes on Overhead lines 99 5-7 BIL/CFO of Electrical Equipment 100 5-8 Frequency of Direct Strokes to Transmission Lines 102 5-9 Direct Lightning Strokes 104 5-10 Lightning Strokes to Towers 104 5-11 Lightning Stroke to Ground Wire 107 5-12 Strokes to Ground in Vicinity of Transmission Lines 107 5-13 Shielding 108 5-14 Shielding Designs 110 5-15 Backflashovers 113 Problems 117 References 121 Further Reading 121 c h a p T e r 6 T r a n s i e n T s o f s h u n T c a p a c i T o r b a n k s 6-1 Origin of Switching Transients 123 6-2 Transients on Energizing a Single Capacitor Bank 123 6-3 Application of Power Capacitors with Nonlinear Loads 126 6-4 Back-to-Back Switching 133 6-5 Switching Devices for Capacitor Banks 134 6-6 Inrush Current Limiting Reactors 135 6-7 Discharge Currents Through Parallel Banks 136 6-8 Secondary Resonance 136 6-9 Phase-to-Phase Overvoltages 139 6-10 Capacitor Switching Impact on Drive Systems 140 6-11 Switching of Capacitors with Motors 140 c o n t e n t s vii c h a p T e r 11 T r a n s i e n T b e h a v i o r o f i n d u c T i o n a n d s y n c h r o n o u s m o T o r s 11-1 Transient and Steady-State Models of Induction Machines 265 11-2 Induction Machine Model with Saturation 270 11-3 Induction Generator 271 11-4 Stability of Induction Motors on Voltage Dips 271 11-5 Short-Circuit Transients of an Induction Motor 274 11-6 Starting Methods 274 11-7 Study of Starting Transients 278 11-8 Synchronous Motors 280 11-9 Stability of Synchronous Motors 284 Problems 288 References 291 Further Reading 291 c h a p T e r 12 p o w e r s y s T e m s T a b i l i T y 12-1 Classification of Power System Stability 293 12-2 Equal Area Concept of Stability 295 12-3 Factors Affecting Stability 297 12-4 Swing Equation of a Generator 298 12-5 Classical Stability Model 299 12-6 Data Required to Run a Transient Stability Study 301 12-7 State Equations 302 12-8 Numerical Techniques 302 12-9 Synchronous Generator Models for Stability 304 12-10 Small-Signal Stability 317 12-11 Eigenvalues and Stability 317 12-12 Voltage Stability 321 12-13 Load Models 324 12-14 Direct Stability Methods 328 Problems 331 References 331 Further Reading 332 c h a p T e r 13 e x c i T aT i o n s y s T e m s a n d p o w e r s y s T e m s T a b i l i z e r s 13-1 Reactive Capability Curve (Operating Chart) of a Synchronous Generator 333 13-2 Steady-State Stability Curves 336 13-3 Short-Circuit Ratio 336 13-4 Per Unit Systems 337 13-5 Nominal Response of the Excitation System 337 8-14 Stresses in Circuit Breakers 204 Problems 205 References 206 Further Reading 206 c h a p T e r 9 s y m m e T r i c a l a n d u n s y m m e T r i c a l s h o r T -c i r c u i T c u r r e n T s 9-1 Symmetrical and Unsymmetrical Faults 207 9-2 Symmetrical Components 208 9-3 Sequence Impedance of Network Components 210 9-4 Fault Analysis Using Symmetrical Components 211 9-5 Matrix Methods of Short-Circuit Current Calculations 221 9-6 Computer-Based Calculations 224 9-7 Overvoltages Due to Ground Faults 224 Problems 232 References 233 Further Reading 233 c h a p T e r 10 T r a n s i e n T b e h a v i o r o f s y n c h r o n o u s g e n e r a T o r s 10-1 Three-Phase Terminal Fault 235 10-2 Reactances of a Synchronous Generator 237 10-3 Saturation of Reactances 238 10-4 Time Constants of Synchronous Generators 238 10-5 Synchronous Generator Behavior on Terminal Short-Circuit 239 10-6 Circuit Equations of Unit Machines 244 10-7 Park’s Transformation 246 10-8 Park’s Voltage Equation 247 10-9 Circuit Model of Synchronous Generators 248 10-10 Calculation Procedure and Examples 249 10-11 Steady-State Model of Synchronous Generator 252 10-12 Symmetrical Short Circuit of a Generator at No Load 253 10-13 Manufacturer’s Data 255 10-14 Interruption of Currents with Delayed Current Zeros 255 10-15 Synchronous Generator on Infinite Bus 257 Problems 263 References 264 Further Reading 264 viii c o n t e n t s 15-9 Static Series Synchronous Compensator 416 15-10 Unified Power Flow Controller 419 15-11 NGH-SSR Damper 422 15-12 Displacement Power Factor 423 15-13 Instantaneous Power Theory 424 15-14 Active Filters 425 Problems 425 References 426 Further Reading 426 c h a p T e r 16 f l i c k e r , b u s T r a n s f e r , T o r s i o n a l d y n a m i c s , a n d o T h e r T r a n s i e n T s 16-1 Flicker 429 16-2 Autotransfer of Loads 432 16-3 Static Transfer Switches and Solid-State Breakers 438 16-4 Cogging and Crawling of Induction Motors 439 16-5 Synchronous Motor-Driven Reciprocating Compressors 441 16-6 Torsional Dynamics 446 16-7 Out-of-Phase Synchronization 449 Problems 451 References 451 Further Reading 452 c h a p T e r 17 i n s u l a T i o n c o o r d i n a T i o n 17-1 Insulating Materials 453 17-2 Atmospheric Effects and Pollution 453 17-3 Dielectrics 455 17-4 Insulation Breakdown 456 17-5 Insulation Characteristics—BIL and BSL 459 17-6 Volt-Time Characteristics 461 17-7 Nonstandard Wave Forms 461 17-8 Probabilistic Concepts 462 17-9 Minimum Time to Breakdown 465 17-10 Weibull Probability Distribution 465 17-11 Air Clearances 465 17-12 Insulation Coordination 466 17-13 Representation of Slow Front Overvoltages (SFOV) 469 17-14 Risk of Failure 470 17-15 Coordination for Fast-Front Surges 472 17-16 Switching Surge Flashover Rate 473 17-17 Open Breaker Position 474 13-6 Building Blocks of Excitation Systems 339 13-7 Saturation Characteristics of Exciter 340 13-8 Types of Excitation Systems 343 13-9 Power System Stabilizers 352 13-10 Tuning a PSS 355 13-11 Models of Prime Movers 358 13-12 Automatic Generation Control 358 13-13 On-Line Security Assessments 361 Problems 362 References 362 Further Reading 363 c h a p T e r 14 T r a n s i e n T b e h a v i o r o f T r a n s f o r m e r s 14-1 Frequency-Dependent Models 365 14-2 Model of a Two-Winding Transformer 365 14-3 Equivalent Circuits for Tap Changing 367 14-4 Inrush Current Transients 368 14-5 Transient Voltages Impacts on Transformers 368 14-6 Matrix Representations 371 14-7 Extended Models of Transformers 373 14-8 EMTP Model FDBIT 380 14-9 Sympathetic Inrush 382 14-10 High-Frequency Models 383 14-11 Surge Transference Through Transformers 384 14-12 Surge Voltage Distribution Across Windings 389 14-13 Duality Models 389 14-14 GIC Models 391 14-15 Ferroresonance 391 14-16 Transformer Reliability 394 Problems 395 References 396 Further Reading 396 c h a p T e r 15 p o w e r e l e c T r o n i c e q u i p m e n T a n d FaCTS 15-1 The Three-Phase Bridge Circuits 397 15-2 Voltage Source Three-Phase Bridge 401 15-3 Three-Level Converter 402 15-4 Static VAR Compensator (SVC) 405 15-5 Series Capacitors 408 15-6 FACTS 414 15-7 Synchronous Voltage Source 414 15-8 Static Synchronous Compensator 415 c o n t e n t s ix c h a p T e r 20 s u r g e a r r e s T e r s 20-1 Ideal Surge Arrester 525 20-2 Rod Gaps 525 20-3 Expulsion-Type Arresters 526 20-4 Valve-Type Silicon Carbide Arresters 526 20-5 Metal-Oxide Surge Arresters 529 20-6 Response to Lightning Surges 534 20-7 Switching Surge Durability 537 20-8 Arrester Lead Length and Separation Distance 539 20-9 Application Considerations 541 20-10 Surge Arrester Models 544 20-11 Surge Protection of AC Motors 545 20-12 Surge Protection of Generators 547 20-13 Surge Protection of Capacitor Banks 548 20-14 Current-Limiting Fuses 551 Problems 554 References 555 Further Reading 555 c h a p T e r 21 T r a n s i e n T s in g r o u n d i n g s y s T e m s 21-1 Solid Grounding 557 21-2 Resistance Grounding 560 21-3 Ungrounded Systems 563 21-4 Reactance Grounding 564 21-5 Grounding of Variable-Speed Drive Systems 567 21-6 Grounding for Electrical Safety 569 21-7 Finite Element Methods 577 21-8 Grounding and Bonding 579 21-9 Fall of Potential Outside the Grid 581 21-10 Influence on Buried Pipelines 583 21-11 Behavior Under Lightning Impulse Current 583 Problems 585 References 585 Further Reading 586 c h a p T e r 22 l i g h T n i n g p r o T e c T i o n o f s T r u c T u r e s 22-1 Parameters of Lightning Current 587 22-2 Types of Structures 587 22-3 Risk Assessment According to IEC 588 22-4 Criteria for Protection 589 22-5 Protection Measures 592 22-6 Transient Behavior of Grounding System 594 17-18 Monte Carlo Method 474 17-19 Simplified Approach 474 17-20 Summary of Steps in Insulation Coordination 475 Problems 475 References 476 Further Reading 476 c h a p T e r 18 g a s -i n s u l a T e d s u b s T aT i o n s —v e r y f a s T T r a n s i e n T s 18-1 Categorization of VFT 477 18-2 Disconnector-Induced Transients 477 18-3 Breakdown in GIS—Free Particles 480 18-4 External Transients 481 18-5 Effect of Lumped Capacitance at Entrance to GIS 482 18-6 Transient Electromagnetic Fields 483 18-7 Breakdown in SF 6 483 18-8 Modeling of Transients in GIS 484 18-9 Insulation Coordination 487 18-10 Surge Arresters for GIS 488 Problems 493 References 493 Further Reading 494 c h a p T e r 19 T r a n s i e n T s a n d s u r g e p r o T e c T i o n in l o w -v o l T a g e s y s T e m s 19-1 Modes of Protection 495 19-2 Multiple-Grounded Distribution Systems 495 19-3 High-Frequency Cross Interference 498 19-4 Surge Voltages 499 19-5 Exposure Levels 499 19-6 Test Wave Shapes 500 19-7 Location Categories 502 19-8 Surge Protection Devices 505 19-9 SPD Components 508 19-10 Connection of SPD Devices 512 19-11 Power Quality Problems 516 19-12 Surge Protection of Computers 517 19-13 Power Quality for Computers 520 19-14 Typical Application of SPDs 520 Problems 523 References 523 Further Reading 524 [...]... currents, voltages, speeds, frequency, torques, in the electrical systems is the main objective of transient analysis and simulation of transients in power systems 1-1 Classification of Transients Broadly, the transients are studied in two categories, based upon their origin: 1. Of atmospheric origin, that is, lightning 2. Of switching origin, that is, all switching operations, load rejection, and faults... Feb 2001 M Zitnik, “Numerical Modeling of Transients in Electrical Systems, ” Uppsal Dissertations from the Faculty of Science and Technology (35), Elanders Gutab, Stockholm, 2001 Chapter 2 Transients in Lumped Circuits In this chapter the transients in lumped, passive, linear circuits are studied Complex electrical systems can be modeled with certain constraints and interconnections of passive system... phenomena giving rise to transients in a certain group is indicated This classification is more appropriate from system modeling considerations and is proposed by CIGRE Working Group 33.02.1 Transients in the frequency range of 100 kHz to 50 MHz are termed very fast transients (VFT), also called very fast front transients These belong to the highest range of transients in power systems According to IEC... understanding the nature and impact of transients The transient analyses must account for special modeling and frequency-dependent behavior and are important in the context of modern power systems of increasing complexity Often, it is difficult to predict intuitively that a transient problem exists in a certain section of the system Dynamic modeling in the planning stage of the systems may not be fully investigated... Groups The study of transients in power systems involves frequency range from dc to about 50 MHz and in specific cases even more Table 1-2 gives the origin of transients and most common frequency ranges Usually, transients above power frequency involve electromagnetic phenomena Below power frequency, electromechanical transients in rotating machines occur Table 1-3 shows the division into four groups,... generation of transients: 1. Electromagnetic transients Generated predominantly by the interaction between the electrical fields of capacitance and magnetic fields of inductances in the power systems The electromagnetic phenomena may appear as traveling waves on transmission lines, cables, bus sections, and oscillations between inductance and capacitance 2. Electromechanical transients Interaction... electrical components The three-step process is: 1. On-site measurements 2. Determining the frequency dependent models 3. Simulation and modeling from the original waveform Yet, in common use, the term transients embraces overvoltages of various origins, transients in the control systems, transient and dynamic stability of power systems, and dynamics of the power system on short circuits, starting... Introduction to Transients Electrical power systems are highly nonlinear and dynamic in nature: circuit breakers are closing and opening, faults are being cleared, generation is varying in response to load demand, and the power systems are subjected to atmospheric disturbances, that is, lightning Assuming a given steady state, the system must settle to a new acceptable steady state in a short duration Thus,... Domain Analysis of Linear Systems We can study the behavior of an electrical system in the time domain A linear system can be described by a set of linear differential or difference equations (App C) The output of the system for some given inputs can be studied If the behavior of the system at all points in the system is to be studied, then a mathematical description of the system can be obtained in. .. disturbance at one point to be transmitted to the other point Thus, we deal with space variable in addition to independent time variable The equations describing distributed parameter systems are partial differential equations All systems are in fact, to an extent, distributed parameter systems The power transmission line models are an example Each elemental section of the line has resistance, inductance, shunt . flash hazard, grounding, switching transients, and also, protective relaying. He conducts courses for continuing education in power systems and has authored. and transients in transmission lines, transformers, rotat- ing machines, electronic equipment, FACTs, bus transfer schemes, grounding systems, gas insulated