Power system transients theory and applications By Akihiro Ametani and Naoto Nagaoka and Yoshihiro Baba and Teruo Ohno

POWER SYSTEM

TRANSIENTS
Theory and Applications

AKIHIRO AMETANI • NAOTO NAGAOKA
YOSHIHIRO BABA • TERUO OHNO

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Power SyStem

tranSientS
Theor y and Applications

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Power SyStem

tranSientS
theor y and Applications

Akihiro AmetAni

nAoto nAgAokA
Yoshihiro BABA
teruo ohno

Boca Raton London New York

CRC Press is an imprint of the
Taylor & Francis Group, an informa business

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pedagogical approach or particular use of the MATLAB® software.

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Contents
Introduction............................................................................................................xv
List of Symbols..................................................................................................... xix
List of Acronyms.................................................................................................. xxi
International Standards.................................................................................... xxiii
1. Theory of Distributed-Parameter Circuits and the
Impedance/Admittance Formulas................................................................1
1.1Introduction............................................................................................1
1.2 Impedance and Admittance Formula.................................................2
1.2.1 Conductor Internal Impedance Zi..........................................3
1.2.1.1 Derivation of an Approximate Formula................3

1.2.1.2 Accurate Formula by Schelkunoff..........................6
1.2.2 Outer-Media Impedance Z0.....................................................8
1.2.2.1 Outer-Media Impedance..........................................8
1.2.2.2 Overhead Conductor................................................9
1.2.2.3 Pollaczek’s General Formula for Overhead,
Underground, and Overhead/Underground
Conductor Systems.................................................. 14
1.2.3Problems................................................................................... 16
1.3 Basic Theory of Distributed-Parameter Circuit............................... 17
1.3.1 Partial Differential Equations of Voltages
and Currents........................................................................... 17
1.3.2 General Solutions of Voltages and Currents....................... 18
1.3.2.1 Sinusoidal Excitation.............................................. 18
1.3.2.2 Lossless Line............................................................ 21
1.3.3 Voltages and Currents on a Semi-Infinite Line.................. 23
1.3.3.1 Solutions of Voltages and Currents...................... 23
1.3.3.2 Waveforms of Voltages and Currents................... 24
1.3.3.3 Phase Velocity.......................................................... 25
1.3.3.4 Traveling Wave........................................................ 27
1.3.3.5 Wave Length............................................................ 28
1.3.4 Propagation Constants and Characteristic Impedance...... 28
1.3.4.1 Propagation Constants........................................... 28
1.3.4.2 Characteristic Impedance...................................... 31
1.3.5 Voltages and Currents on a Finite Line............................... 32
1.3.5.1 Short-Circuited Line............................................... 32
1.3.5.2 Open-Circuited Line............................................... 35
1.3.6Problems................................................................................... 38

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1.4

1.5

1.6

Multiconductor System....................................................................... 38
1.4.1 Steady-State Solutions............................................................ 38
1.4.2 Modal Theory.......................................................................... 41
1.4.2.1 Eigenvalue Theory.................................................. 41
1.4.2.2 Modal Theory..........................................................44
1.4.2.3 Current Mode........................................................... 45
1.4.2.4 Parameters in Modal Domain............................... 46
1.4.3 Two-Port Circuit Theory and Boundary Conditions......... 48
1.4.3.1 Four-Terminal Parameter....................................... 48
1.4.3.2 Impedance/Admittance Parameters.................... 50
1.4.4 Modal Distribution of Multiphase Voltages
and Currents............................................................................ 52
1.4.4.1 Transformation Matrix........................................... 52
1.4.4.2 Modal Distribution................................................. 53
1.4.5Problems................................................................................... 55
Frequency-Dependent Effect.............................................................. 56
1.5.1 Frequency Dependence of Impedance................................ 56
1.5.2 Frequency-Dependent Parameters....................................... 58

1.5.2.1 Frequency-Dependent Effect................................. 58
1.5.2.2 Propagation Constant............................................. 59
1.5.2.3 Characteristic Impedance...................................... 61
1.5.2.4 Transformation Matrix...........................................63
1.5.2.5 Line Parameters in the Extreme Case.................. 68
1.5.3 Time Response........................................................................ 70
1.5.3.1 Time-Dependent Responses.................................. 70
1.5.3.2 Propagation Constant: Step Response................. 71
1.5.3.3 Characteristic Impedance...................................... 72
1.5.3.4 Transformation Matrix........................................... 74
1.5.4Problems...................................................................................77
Traveling Wave.....................................................................................77
1.6.1 Reflection and Refraction Coefficients.................................77
1.6.2 Thevenin’s Theorem............................................................... 79
1.6.2.1 Equivalent Circuit of a Semi-Infinite Line........... 79
1.6.2.2 Voltage and Current Sources at the
Sending End............................................................. 79
1.6.2.3 Boundary Condition at the Receiving End.......... 79
1.6.2.4 Thevenin’s Theorem................................................ 82
1.6.3 Multiple Reflection..................................................................84
1.6.4Multiconductors...................................................................... 88
1.6.4.1 Reflection and Refraction Coefficients................. 88
1.6.4.2 Lossless Two Conductors....................................... 88
1.6.4.3 Consideration of Modal
Propagation Velocities..........................................91
1.6.4.4 Consideration of Losses in a
Two-Conductor System.......................................... 96
1.6.4.5 Three-Conductor System....................................... 99

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1.6.4.6 Cascaded System Composed of the
Different Numbers of Conductors...................... 102
1.6.5Problems................................................................................. 103
1.7 Nonuniform Conductors.................................................................. 104
1.7.1 Characteristic of Nonuniform Conductors....................... 105
1.7.1.1 Nonuniform Conductor....................................... 105
1.7.1.2 Difference from Uniform Conductors................ 108
1.7.2 Impedance and Admittance Formulas.............................. 109
1.7.2.1 Finite-Length Horizontal Conductor................. 109
1.7.2.2 Vertical Conductor................................................ 112
1.7.3 Line Parameters.................................................................... 114
1.7.3.1 Finite Horizontal Conductor............................... 114
1.7.3.2 Vertical Conductor................................................ 117
1.7.3.3 Nonparallel Conductor......................................... 119
1.7.4Problems................................................................................. 119
1.8 Introduction of EMTP....................................................................... 122
1.8.1Introduction........................................................................... 122
1.8.1.1 History of a Transient Analysis........................... 122
1.8.1.2 Background of EMTP........................................... 123
1.8.1.3 EMTP Development.............................................. 124
1.8.2 Basic Theory of EMTP.......................................................... 124
1.8.2.1 Representation of a Circuit Element by a
Current Source and a Resistance........................ 126
1.8.2.2 Composition of Nodal Conductance.................. 128

1.8.3 Other Circuit Elements........................................................ 129
1.8.4 Solutions of the Problems.................................................... 131
References...................................................................................................... 136
2. Transients on Overhead Lines.................................................................. 141
2.1Introduction........................................................................................ 141
2.2 Switching Surge on Overhead Line................................................. 142
2.2.1 Basic Mechanism of Switching Surge................................ 142
2.2.2 Basic Parameters Influencing Switching Surge................ 143
2.2.2.1 Source Circuit........................................................ 143
2.2.2.2Switch...................................................................... 146
2.2.2.3Transformer............................................................ 147
2.2.2.4 Transmission Line................................................. 147
2.2.3 Switching Surges in Practice............................................... 148
2.2.3.1 Classification of Switching Surges...................... 148
2.2.3.2 Basic Characteristic of Closing Surge:
Field Test Results................................................... 149
2.2.3.3 Closing Surge on a Single-Phase Line................ 151
2.2.3.4 Closing Surges on a Multiphase Line................. 153
2.2.3.5 Effect of Various Parameters on
Closing Surge..................................................... 162

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2.3

2.4

2.5

2.6

Fault Surge.......................................................................................... 166
2.3.1 Fault Initiation Surge............................................................ 166
2.3.2 Characteristic of a Fault Initiation Surge........................... 169
2.3.2.1 Effect of Line Transposition................................. 169
2.3.2.2 Overvoltage Distribution..................................... 169
2.3.3 Fault-Clearing Surge............................................................ 172
Lightning Surge.................................................................................. 175
2.4.1 Mechanism of Lightning Surge Generation..................... 177
2.4.2 Modeling of Circuit Elements............................................. 179
2.4.2.1 Lightning Current................................................. 179
2.4.2.2 Tower and Gantry................................................. 180
2.4.2.3 Tower Footing Impedance................................... 182
2.4.2.4 Arc Horn................................................................. 184
2.4.2.5 Transmission Line................................................. 185
2.4.2.6Substation............................................................... 185
2.4.3 Lightning Surge Overvoltage.............................................. 185
2.4.3.1 Model Circuit......................................................... 185
2.4.3.2 Lightning Surge Overvoltage.............................. 187
2.4.3.3 Effect of Various Parameters............................... 188
Theoretical Analysis of Transients: Hand Calculations............... 194
2.5.1 Switching Surge on an Overhead Line.............................. 195
2.5.1.1 Traveling Wave Theory........................................ 195
2.5.1.2 Lumped-Parameter Equivalent with
Laplace Transform................................................. 202

2.5.2 Fault Surge............................................................................. 206
2.5.3 Lightning Surge.................................................................... 208
2.5.3.1 Tower Top Voltage................................................. 208
2.5.3.2 Two-Phase Model.................................................. 208
2.5.3.3 No Back Flashover................................................. 210
2.5.3.4 Case of a Back Flashover...................................... 212
2.5.3.5 Consideration of Substation................................. 212
Frequency-Domain Method of Transient Simulations......................215
2.6.1Introduction........................................................................... 215
2.6.2 Numerical Fourier/Laplace Transform............................. 215
2.6.2.1 Finite Fourier Transform...................................... 215
2.6.2.2 Shift of Integral Path: Laplace Transform.......... 217
2.6.2.3 Numerical Laplace Transform: Discrete
Laplace Transform................................................. 218
2.6.2.4 Odd-Number Sampling: Accuracy
Improvement.......................................................... 218
2.6.2.5 Application of FFT: Fast Laplace
Transform (FLT)..................................................... 221
2.6.3 Transient Simulation............................................................ 228
2.6.3.1 Definition of Variables.......................................... 228

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2.6.3.2 Subroutine to Prepare F(ω)................................... 229
2.6.3.3 Subroutine FLT...................................................... 230

2.6.3.4 Remarks of the Frequency-Domain
Method.. .......................................................... 230
References...................................................................................................... 230
3. Transients on Cable Systems..................................................................... 233
3.1Introduction........................................................................................ 233
3.2 Impedance and Admittance of Cable Systems..............................234
3.2.1 Single-Phase Cable................................................................234
3.2.1.1 Cable Structure......................................................234
3.2.1.2 Impedance and Admittance................................234
3.2.2 Sheath Bonding..................................................................... 235
3.2.3 Homogeneous Model of a Cross-Bonded Cable............... 238
3.2.3.1 Homogeneous Impedance and Admittance....... 238
3.2.3.2 Reduction of Sheath.............................................. 243
3.2.4 Theoretical Formula of Sequence Currents...................... 246
3.2.4.1 Cross-Bonded Cable.............................................. 246
3.2.4.2 Solidly Bonded Cable............................................ 251
3.3 Wave Propagation and Overvoltages.............................................. 256
3.3.1 Single-Phase Cable................................................................ 256
3.3.1.1 Propagation Constant........................................... 256
3.3.1.2 Example of Transient Analysis............................ 258
3.3.2 Wave Propagation Characteristic....................................... 260
3.3.2.1 Impedance: R, L..................................................... 263
3.3.2.2 Capacitance: C........................................................ 264
3.3.2.3 Transformation Matrix......................................... 264
3.3.2.4 Attenuation Constant and
Propagation Velocity............................................. 264
3.3.3 Transient Voltage................................................................... 265
3.3.4 Limitation of the Sheath Voltage........................................ 269
3.3.5 Installation of SVLs.............................................................. 271
3.4 Studies on Recent and Planned EHV AC Cable Projects............. 272

3.4.1 Recent Cable Projects........................................................... 273
3.4.2 Planned Cable Projects......................................................... 275
3.5 Cable System Design and Equipment Selection............................ 277
3.5.1 Study Flow............................................................................. 277
3.5.2 Zero-Missing Phenomenon................................................. 278
3.5.2.1 Sequential Switching............................................ 280
3.5.3 Leading Current Interruption............................................. 281
3.5.4 Cable Discharge....................................................................284
3.6 EMTP Simulation Test Cases............................................................ 285
References...................................................................................................... 287

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4. Transient and Dynamic Characteristics of New Energy Systems..... 291
4.1 Wind Farm.......................................................................................... 291
4.1.1 Model Circuit of Wind Farm............................................... 291
4.1.2 Steady-State Analysis........................................................... 294
4.1.2.1 Cable Model........................................................... 294
4.1.2.2 Charging Current.................................................. 298
4.1.2.3 Load-Flow Calculation......................................... 301
4.1.3 Transient Calculation........................................................... 303
4.2 Power-Electronics Simulation by EMTP.........................................306
4.2.1 Simple-Switching Circuit.....................................................306
4.2.2 Switching-Transistor Model................................................ 307
4.2.2.1 Simple-Switch Model............................................308

4.2.2.2 Switch with Delay Model..................................... 312
4.2.3MOSFET................................................................................. 314
4.2.3.1 Simple Model......................................................... 315
4.2.3.2 Modified Switching Device Model..................... 316
4.2.3.3 Simulation Circuit and Results........................... 321
4.2.4 Thermal Calculation............................................................. 329
4.3 Voltage Regulation Equipment Using Battery in a DC
Railway System.................................................................................. 331
4.3.1Introduction........................................................................... 331
4.3.2 Feeding Circuit...................................................................... 333
4.3.3 Measured and Calculated Results...................................... 336
4.3.3.1 Measured Results.................................................. 336
4.3.3.2 Calculated Results of Conventional System...... 336
4.3.3.3 Calculated Results with
Power Compensator......................................... 340
4.4 Concluding Remarks.........................................................................343
References......................................................................................................344
5. Numerical Electromagnetic Analysis Methods and Their
Applications to Transient Analyses.........................................................345
5.1Fundamentals.....................................................................................345
5.1.1 Maxwell’s Equations.............................................................345
5.1.2 Finite-Difference Time-Domain Method..........................346
5.1.3 Method of Moments............................................................. 355
5.2Applications........................................................................................ 363
5.2.1 Grounding Electrodes.......................................................... 363
5.2.2 Transmission Towers............................................................ 367
5.2.3 Distribution Lines: Lightning-Induced Surges................. 371
5.2.4 Transmission Lines: Propagation of Lightning
Surges in the Presence of Corona....................................... 375
5.2.5 Power Cables: Propagation of Power Line

Communication Signals....................................................... 379

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5.2.6 Air-Insulated Substations.................................................... 385
5.2.7 Wind Turbine Generator Towers........................................ 387
References...................................................................................................... 389
6. Electromagnetic Disturbances in Power Systems
and Customers............................................................................................. 393
6.1Introduction........................................................................................ 393
6.2 Disturbances in Power Stations and Substations.......................... 394
6.2.1 Statistical Data of Disturbances.......................................... 394
6.2.1.1 Overall Data........................................................... 394
6.2.1.2 Disturbed Equipments......................................... 395
6.2.1.3 Surge Incoming Route.......................................... 397
6.2.2 Characteristics of Disturbances.......................................... 397
6.2.2.1 Characteristics of Lightning
Surge Disturbances............................................... 397
6.2.2.2 Characteristics of Switching
Surge Disturbances............................................... 398
6.2.2.3 Switching Surge in DC Circuits.......................... 402
6.2.3 Influence, Countermeasures, and
Costs of Disturbances........................................................... 403
6.2.3.1 Influence of Disturbances on Power
System Operation.................................................. 403

6.2.3.2 Countermeasures Carried Out............................405
6.2.3.3 Cost of Countermeasures..................................... 406
6.2.4 Case Studies........................................................................... 407
6.2.4.1 Case No. 1...............................................................408
6.2.4.2 Case No. 2............................................................... 410
6.2.4.3 Case No. 3............................................................... 411
6.2.5 Concluding Remarks............................................................ 412
6.3 Disturbances in Customers and Home Appliances...................... 413
6.3.1 Statistical Data of Disturbances.......................................... 413
6.3.2 Breakdown Voltage of Home Appliances......................... 415
6.3.2.1 Testing Voltage....................................................... 415
6.3.2.2 Breakdown Test..................................................... 416
6.3.3 Surge Voltages and Currents into Customers due to
Nearby Lightning................................................................. 416
6.3.3.1Introduction........................................................... 416
6.3.3.2 Model Circuits for Experiments and
EMTP Simulations................................................ 417
6.3.3.3 Experimental and Simulation Results................425
6.3.3.4 Concluding Remarks............................................ 429
6.3.4 Lightning Surge Incoming from a
Communication Line............................................................ 429
6.3.4.1Introduction........................................................... 429

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6.3.4.2 Protective Device...................................................430
6.3.4.3 Lightning Surge.....................................................430
6.3.4.4 Concluding Remarks............................................433
6.4 Analytical Method of Solving Induced
Voltages and Currents...................................................................... 435
6.4.1Introduction........................................................................... 435
6.4.2 F-Parameter Formulation for Induced
Voltages and Currents.......................................................... 439
6.4.2.1 Formulation of F-Parameter................................. 439
6.4.2.2 Approximation of F-Parameters..........................440
6.4.2.3 Cascaded Connection of Pipelines.....................440
6.4.3 Application Examples.......................................................... 441
6.4.3.1 Single Section Terminated by R1 and R 2............ 441
6.4.3.2 Two-Cascaded Sections of a Pipeline
(Problem 6.1)...........................................................446
6.4.3.3 Three-Cascaded Sections of a Pipeline.............. 453
6.4.4 Comparison with a Field-Test Result.................................454
6.4.4.1 Comparison with EMTP Simulations................454
6.4.4.2 Field-Test Result.....................................................454
6.4.5 Concluding Remarks............................................................ 459
Solution of Problem 6.1................................................................................ 460
Appendix 6.A.1Test Voltage for Low-Voltage Control
Circuits in Power Stations and Substations
(JEC-0103-2004)............................................................461
6.A.2Traveling Wave Solution................................................464
6.A.3 Boundary Conditions and Solutions of a Voltage
and a Current...................................................................464
6.A.4 Approximate Formulas for Impedance
and Admittance.............................................................. 465
6.A.5 Accurate Solutions for Two-Cascaded Sections......... 466

References...................................................................................................... 467
7. Problems and Application Limits of Numerical Simulations............ 471
7.1 Problems of Existing Impedance Formulas Used in
Circuit Theory–Based Approaches.................................................. 471
7.1.1 Earth-Return Impedance..................................................... 471
7.1.1.1 Carson’s Impedance.............................................. 471
7.1.1.2 Basic Assumption of the Impedance.................. 472
7.1.1.3 Nonparallel Conductor......................................... 472
7.1.1.4 Stratified Earth....................................................... 473
7.1.1.5 Earth Resistivity and Permittivity...................... 473
7.1.2 Internal Impedance.............................................................. 473
7.1.2.1 Schelkunoff’s Impedance..................................... 473
7.1.2.2 Arbitrary Cross-Section Conductor.................... 473

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7.1.2.3 Semiconducting Layer of Cable.......................... 474
7.1.2.4 Proximity Effect..................................................... 474
7.1.3 Earth-Return Admittance.................................................... 474
7.2 Existing Problems in Circuit Theory–Based
Numerical Analysis........................................................................... 475
7.2.1 Reliability of a Simulation Tool........................................... 475
7.2.2 Assumption and Limit of a Simulation Tool.................... 475
7.2.3 Input Data.............................................................................. 476
7.3 Numerical Electromagnetic Analysis for Power

System Transients............................................................................... 476
References...................................................................................................... 477

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Introduction
When lightning strikes a building or a transmission tower, an electric current
flows into its structures, which are made of electrically conductive materials
such as steel and copper. The electric current produces a high voltage called
“overvoltage” (or abnormal voltage), which can damage or break electrical
equipment installed in the building or in the power transmission system.
The breakdown may shut down the electrical room of the building, resulting
in a blackout of the whole building. If the breakdown occurs in a substation
in a high-voltage power transmission system, a city where electricity is supplied by the substation can experience a blackout. An overvoltage can also
be generated by switching operations of a circuit breaker or a load switch,
which is electrically the same as a breaker in a house.
A phenomenon during the time period in which an overvoltage occurs
due to lightning or switching operation is called transient, while electricity
being supplied under normal circumstances is called steady state. In general, a transient dies out and reaches a steady state within approximately
10 μs (10−6 s) in the lightning transient case and within approximately 10 ms
(10−3 s) in the switching transient case. Occasionally, a transient sustains for
a few seconds if it involves resonant oscillation of circuit parameters (mostly
inductance and capacitance) or mechanical oscillation of the steel shaft of a
generator (called subsynchronous resonance).
In order to design the electrical strength of electrical equipment and to
ensure human safety during a transient, it is crucial to perform a transient

analysis, especially in the field of electric power engineering.
Chapter 1 of this book describes a transient on a single-phase line from the
physical viewpoint and how this is solved analytically by an electric circuit
theory. The impedance and the admittance formulas of an overhead line are
described. Simple formulas that can be calculated using a pocket calculator
are also explained so that a transient can be analytically evaluated. Since a real
power line is three-phase, theory that deals with multiphase lines is presented.
Finally, the book describes how to tackle a real transient in a power system.
Chapter 1 also presents the well-known simulation tool electromagnetic
transients program (EMTP), originally developed by the US Department of
Energy, Bonneville Power Administration, which is useful in dealing with a
real transient in a power system.
Chapter 2 describes wave propagation characteristics and transients in
an overhead transmission line. The distributed-parameter circuit theory
is applied to solve the transients analytically. The EMTP is then applied to
calculate transients in a power system composed of an overhead line and
a substation. Various simulation examples are demonstrated, together with
comparison with field test results.
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Chapter 3 discusses transients in a cable system. A cable system is, in general, more complicated than an overhead line system, because one phase of
the cable is composed of two conductors called the metallic core and metallic
sheath. The former carries a current and the latter behaves as an electromagnetic shield against the core current. Another reason why a cable system is
complicated is that most long cables are cross-bounded, that is, the metallic

sheaths on phases a, b, and c in one cable section are connected to those of
phases b, c, and a in the next section. Each section is called a minor section
whose length ranges normally from approximately 100 m to 1 km. Three
minor sections compose one major section. The sheath impedances of three
phases thus become nearly equal to each other. Because of this, a transient on
a cable system is quite different from that on an overhead line system.
Similarly to Chapter 2, Chapter 4 analyzes the basic characteristic of wave
propagation on a cable based on the distributed-parameter circuit theory,
together with EMTP simulation examples. One of the most attractive subjects
in recent years has been so-called clean energy (or sustainable energy) and
smart grids. Wind farms and mega solar plants have become well known.
The chapter describes transients in wind farms based on EMTP simulations.
Since the output voltage of most wind generators is about 600 V, wind generators are connected to a low-voltage transmission (distribution) line. Also,
as their generating capacity is small, a number of wind generators are connected together in a substation, which allows the voltage to be stepped up for
power transmission, thus forming a wind farm. In the case of an off-shore
wind farm, the generated power is sent to an on-shore connection point
through submarine cables.
A transient analysis in wind farms, mega solars, and smart grids requires
a different approach in comparison to those in overhead lines and cables. A
transient in an overhead line and cable is directly associated with traveling
waves whose traveling time is in the order of 10 μs up to 1 ms; in most cases,
the maximum overvoltage appears within a few milliseconds. In contrast, a
transient in a wind farm involving power electronic circuits is affected by
the dynamic behavior of power transistors/thyristors, which is a basic element of the power electronic circuit.
In the case of photovoltaic (PV) generation, the output voltage and power
generation vary depending on the amount of sunshine the photo cells are
exposed to, which is based on the time of the day and the weather. A power
conditioner and a storage system such as a battery are thus essential to operate a PV system. In the last section, voltage regulation on equipment in a dc
railway is described when a lithium-ion battery is adopted, since this type of
battery is used as a storage element for PV and wind farm generation systems.

The first four chapters describe a transient analysis/simulation, which is
based on a circuit theory derived by a transverse electro-magnetic (TEM)
mode of wave propagation. When a transient involves a non-TEM mode of
wave propagation, a circuit theory–based approach cannot provide an accurate solution. Typical examples include arcing horn flashover considering

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mutual coupling between power lines and tower arms, a transient in a
grounding electrode, and an induced voltage from a lightning channel.
Solving this type of transient requires the use of numerical electromagnetic analysis (NEA). Chapter 5 first discusses the basic theory of NEA and
then describes various methods of NEA, for example, either in a frequency
domain or in a time domain. It provides a brief summary of the methods and
demonstrates application examples. Some of the examples compare field test
results with EMTP simulation results.
Chapter 6 further deals with electromagnetic compatibility (EMC)-related
problems in a low-voltage control circuit in a power station and a substation.
Electromagnetic disturbances experienced in Japanese utilities over a period
of ten years are summarized and categorized based on the cause, that is,
a lightning surge or a switching surge, and the incoming route. The influence of the disturbances on system operations and the countermeasures are
explained together with case studies. Also, disturbances due to lightning in
home appliances are explained based on collected statistical data, measured
results, and EMTP/FDTD simulation results. Finally, an analytical method
for evaluating electromagnetic-induced voltages on a telecommunication
line or a gas pipeline from a power line is described.
Nowadays, there are a number of numerical simulation tools that are used

worldwide to analyze transients in power systems. The most well known
among them is the EMTP. The accuracy and reliability of the original EMTP
have been confirmed by a number of test cases since 1968. However, no simulation tool can be perfect. Any simulation tool will have its own application
limits and restrictions. As mentioned previously, because the EMTP is based
on a circuit theory under the assumption of TEM mode propagation, it cannot provide an accurate solution for a transient associated with a non-TEM
mode propagation. Such application limits and restrictions are discussed in
Chapter 7 for both circuit theory–based approaches and NEA methods.
MATLAB® is a registered trademark of The MathWorks, Inc. For product
information, please contact:
The MathWorks, Inc.
3 Apple Hill Drive
Natick, MA 01760-2098 USA
Tel: 508-647-7000
Fax: 508-647-7001
E-mail:
Web: www.mathworks.com

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List of Symbols
The symbols used in this book are listed together with the proper units of
measurement, according to the International System of Units (SI).
Angular frequency
Conductance (admittance,
susceptance)
Conductivity

Current density
Decibel (dB)

Electric capacitance
Electric current
Electric field strength
Electric resistance
(impedance, reactance)
Frequency
Inductance: self, mutual
Length

Magnetic field strength
Magnetic flux
Magnetic flux density
Permeability
Permittivity
Potential difference,
voltage, electric potential
Power
Resistivity
Time, pulse rise time,
pulse width
Velocity

Radian per second (rad/s)
Siemens (S)

ω

Siemens per meter (S/m)
Ampere per square meter (A/m2)
Decibel is a dimensionless number
expressing the ratio of two power
levels, W1 to W2: dB = 10 log (W1/W2)
Further expressions of dB if both the
voltages (U1, U2) or currents (I1, I2) are
measured on the same impedance:
dB = 20 log (U1/U2) dB = 20 log (I1/I2)
Farad (F)
Ampere (A)
Volt per meter (V/m)
Ohm (Ω)

σ

Hertz (Hz)
Henry (H)
Meter (m)

f
L, M
d, D, R, x (distance)
r (radius)
ℓ (length)
h (height)
δ (skin depth)
λ (wavelength)
H
Φ

Ampere per meter (A/m)
Weber (Wb)
Tesla (T)
Henry per meter (H/m)
Farad per meter (F/m)
Volt

G (Y, B)

J

C
I
E
R (Z, X)

B
μ
ε
V, U

Watt (W)
Ohm meter (Ω·m)
Second (s)

P
ρ

Meter per second (m/s)

v

t, τ

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List of Acronyms
The following list includes the acronyms frequently used in this book:
AIS
Air insulated substation
ATP
Alternative transients program
CB
Circuit breaker
CM
Common mode
CT
Current transformer
DM
Differential mode
DSDisconnector
EHV
Extra-high voltage (330 kV ∼ 750 kV)
EMC

Electromagnetic compatibility
EMF
Electromotive force
EMI
Electromagnetic interference
EMTP
Electromagnetic transients program
ESD
Electrostatic discharge
GIS
Gas-insulated substation
GPR
Ground potential rise
HV
High voltage (1 kV ∼ 330 kV)
IC
Integrated circuit
IEC
International Electrotechnical Commission
IKL
Isokeraunic level
LPS
Lightning protection system
LS
Lightning surge
SPD
Surge protective device
SS
Switching surge
TE

Transverse electric
TEM
Transverse electromagnetic
TL
Transmission line
TLM
Transmission line model
TM
Transverse magnetic
UHV
Ultrahigh voltage (≥ 800 kV for ac and dc transmission)
UNIPEDEInternational Union of Producers and Distributors
of Electrical Energy
VT
Voltage transformer

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International Standards


1.IEC 61000-4-5, Electromagnetic Compatibility (EMC)—Part 4-5:
Testing and Measurement Technique—Surge Immunity Test, 2nd edn.,
2005.
2.IEC 60364-5-54, Low-Voltage Electrical Installations—Part 5-54:

Selection and Erection of Electrical Equipment—Earthing Arrangements
and Protective Conductors, Edition 3.0, 2011.
3.IEC 61000-4-3, Electromagnetic Compatibility (EMC)—Part 4-3: Testing
and Measurement Technique—Radiated, Radio Frequency Electromagnetic
Field Immunity Test, Edition 3.1, 2008.
4.IEC 60050-161, International Electrotechnical Vocabulary—Chapter 161:
Electromagnetic compatibility (EMC), 1st edn. (1990), Amendment 1
(1997), Amendment 2 (1988).
5. IEC 60050-604, International Electrotechnical Vocabulary—Chapter 604:
Generation, transmission and distribution of electricity—Operation.
Edition 1.0, 1987.

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