Power System Transients: Modelling Simulation and Applications

249 Pages·2023·16.696 MB·English

by  Gevork Gharehpetian, Atousa Yazdani, Behrooz Zaker

Power System
Transients
In this textbook, a variety of transient cases that have occurred or are possible to
occur in power systems are discussed and analyzed. It starts by categorizing tran-
sients’ phenomena and specifying unfavorable situations in power systems raised by
transients. It then moves on to different protective measures that have been imple-
mented in the system to prevent disasters caused by those transients. It also explains
different methodologies used to analyze transients in power systems.
This book discusses the modeling of components very extensively and provides
analysis cases to assess a wide variety of transients, their possible effects on the sys-
tem, and the types of protection commonly used for each case, along with methods for
designing a sound protection system.
FEATURES
• Detailed models of system components along with power systems com-
puter-aided design (PSCAD) implementation and analysis
• Comprehensive reference of transient cases in power systems along with
design considerations and protective solutions
• The cases are not limited to classical transients such as lightning strikes and
switching, but rather the book discusses transient cases that power system
operators and engineers have to deal with, such as ferroresonance, in detail,
accompanied by computer simulations
• A chapter on original materials related to transformer windings with induced
traveling waves
Power System Transients: Modelling Simulation and Applications provides a
comprehensive resource to mainly educate graduate students in the area of power
system transients. It also serves as a reference for industry engineers challenged by
transient problems in the system.

Power System
Transients
Modelling Simulation
and Applications
Gevork B. Gharehpetian
Atousa Yazdani
Behrooz Zaker
MATLAB® is a trademark of The MathWorks, Inc. and is used with permission. The MathWorks does not
warrant the accuracy of the text or exercises in this book. This book’s use or discussion of MATLAB®
software or related products does not constitute endorsement or sponsorship by The MathWorks of a
particular pedagogical approach or particular use of the MATLAB® software.
First edition published 2023
by CRC Press
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CRC Press is an imprint of Taylor & Francis Group, LLC
© 2023 Gevork B. Gharehpetian, Atousa Yazdani and Behrooz Zaker
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ISBN: 978-1-032-18558-3 (hbk)
ISBN: 978-1-032-18559-0 (pbk)
ISBN: 978-1-003-25513-0 (ebk)
DOI: 10.1201/9781003255130
Typeset in Times
by SPi Technologies India Pvt Ltd (Straive)
Contents
Preface .......................................................................................................................ix
Authors ....................................................................................................................xiii
Chapter 1 Overview ..............................................................................................1
1.1 Introduction ...............................................................................1
1.2 Categories of Transient Phenomenon in Power Systems ..........2
1.3 Transients and Their Effect on Design and Operation of
Power Systems ...........................................................................5
1.4 Catastrophic Cases .....................................................................5
1.4.1 High Voltage Transients ................................................5
1.4.1.1 Required Studies ...........................................5
1.4.1.2 Causes of Overvoltages ................................6
1.4.1.3 Insulation Coordination and System
Protection Against Transients .......................6
1.5 Overcurrent Transients ..............................................................7
1.5.1 Circuit Breaker Design .................................................7
1.5.2 Mechanical Stress .........................................................7
1.5.3 Thermal Stress ..............................................................7
1.6 Abnormal Waveforms ................................................................7
1.6.1 Importance of the Study ...............................................7
1.7 Electromechanical Transients ....................................................8
1.8 Study Techniques for Transient Studies ....................................9
1.8.1 Modeling and Simulation .............................................9
1.8.2 Simulations Tools .......................................................10
1.8.3 Important Considerations for Transient Analysis .......12
1.9 An Introduction to PSCAD/EMTDC ......................................12
Problems .............................................................................................13
Bibliography .......................................................................................13
Chapter 2 Traveling Waves .................................................................................15
2.1 Transmission Line Equations ..................................................16
2.1.1 Lossless Lines ............................................................19
2.1.2 Lossy Lines ................................................................21
2.2 Reflection Rules for Sinusoidal Waves ....................................26
2.2.1 Transmission Line Reflection .....................................26
2.2.2 End of the Line Reflection..........................................27
2.2.3 Reflection at the Beginning of the Line ......................30
2.2.4 Voltage Distribution across a Lossless Line ...............32
2.2.5 Frequency-dependent Wave Speed Propagation
Variation .....................................................................35
v
vi Contents
2.2.6 Frequency-dependent Characteristic Impedance
Variations ....................................................................39
2.3 Step-form Traveling Waves .....................................................40
2.3.1 Solving Equations ......................................................41
2.3.2 Current Equations (D’Alembert’s Solution)...............47
2.3.3 Forward and Backward Waves ...................................48
2.3.4 Reflection Rules for Step Waves ................................50
2.3.5 Loss Consideration in Line ........................................54
2.4 PSCAD Examples ...................................................................54
Problems .............................................................................................63
Bibliography .......................................................................................64
Chapter 3 Lattice Diagram and Its Applications .................................................65
3.1 Traveling Wave as a Function of Time and Location ..............65
3.2 Cable Connection to Transmission Line ..................................71
3.3 Closing Resistance Circuit Breakers .......................................74
3.3.1 Source Internal Resistance .........................................74
3.3.2 Dead Line Connection to Live Line ...........................75
3.4 Reflection in Branches .............................................................78
3.5 Special Cases in Reflection .....................................................79
3.5.1 Capacitor Connection at the End of the Line .............79
3.5.2 Inductors Connection at the End of the Line ..............83
3.5.3 Parallel LC Connection at the End of the Line ..........86
3.5.4 Series LC Connection at the End of the Line .............90
3.5.5 Combination of Inductors and Capacitors in the
Middle of the Line ......................................................92
3.6 PSCAD Examples ...................................................................94
3.6.1 Overhead Line and Cable Connection ........................94
3.7 Closing Breaker in Line Energization .....................................95
3.8 Capacitor Connection at the End of the Line ..........................95
3.9 Inductor Connection at the End of the Line ............................97
3.10 Parallel Filter LC Connection at the End of the Line ..............97
Problems ...........................................................................................105
Bibliography .....................................................................................105
Chapter 4 Lightning-Induced Transients ..........................................................107
4.1 Introduction ...........................................................................107
4.2 General Characteristics of Lightning Surges .........................113
4.3 Types of Stroke ......................................................................115
4.3.1 Direct Stroke to Phase Conductor ............................115
4.3.2 Ground Conductor or Tower Stroke .........................116
4.3.3 Nearby Strokes .........................................................118
4.4 System Response to Voltage Arbitrary Pulses .......................118
4.5 Application of Lattice Diagram .............................................121
4.6 Tower Modeling for Transient Studies ..................................124
Contents vii
4.7 PSCAD Examples .................................................................129
Problems ...........................................................................................131
Bibliography .....................................................................................132
Chapter 5 Energization Overvoltages ...............................................................133
5.1 Source-type Effect .................................................................133
5.1.1 Step Source Energization through Inductance .........134
5.1.2 Sinusoidal Source Energization through
Inductance ................................................................136
5.1.3 Line Energization through Energized Lines .............138
5.1.4 Source Energization through Inductance
Adjacent to Parallel Lines ........................................140
5.2 Asynchronous Closing of Three Phase Circuit Breaker
Contactors ..............................................................................141
5.3 Reactive Compensation .........................................................143
5.4 Trapped Charge .....................................................................144
5.5 System Losses .......................................................................146
5.6 Switching Location ................................................................146
5.7 Terminal Type of Effects .......................................................148
5.8 Capacitive Bank Closing .......................................................157
5.9 PSCAD Examples .................................................................159
5.9.1 Sinusoidal Source Energization through
Inductance ................................................................159
5.9.2 Source Energization through Inductance
Adjacent to Parallel Lines ........................................160
5.9.3 Terminal-type Effects ...............................................162
Problems ...........................................................................................165
Bibliography .....................................................................................167
Chapter 6 Transients Induced by De-energization ............................................169
6.1 Transient Recovery Voltages .................................................169
6.2 Rate of Rise of Recovery Voltage ..........................................172
6.3 Current Injection Methodology .............................................173
6.4 Factors Affecting Transient Recovery Voltages .....................175
6.4.1 Power Factor Effect on Transient Recovery
Voltages ....................................................................175
6.4.2 Natural Frequency Effect on Transient Recovery
Voltages ....................................................................175
6.4.3 Effect of Existence of Two Natural Frequencies
on Transient Recovery Voltages ...............................176
6.4.4 Damping Effect on Transient Recovery Voltages .....178
6.4.5 Effect of Type of Short Circuit .................................178
6.4.6 Arc Voltage Effect on TRV .......................................179
6.5 Fault Interruption in a Short Line ..........................................179
6.6 Magnetizing Current Chopping .............................................182
viii Contents
6.7 Residual Flux Effect on Transformer Inrush Current ............185
6.8 Capacitive Current Interruption .............................................187
6.9 Disconnectors Opening .........................................................189
6.10 PSCAD Examples .................................................................191
6.10.1 Transient Recovery Voltages ....................................191
6.10.2 Effect of Existence of Two Natural Frequencies
on Transient Recovery Voltage .................................192
6.10.3 Magnetizing Current Chopping ................................192
Problems ...........................................................................................197
Bibliography .....................................................................................198
Chapter 7 Traveling Wave Influence on Power Transformers Windings ..........199
7.1 Winding Modeling without Mutual Inductances ...................199
7.1.1 Voltage Initial Distribution .......................................201
7.1.2 Equivalent Capacitance of the Winding at t = 0 .......204
7.1.3 Final Distribution .....................................................205
7.1.4 Solution for Main Partial Differential Equation .......205
7.1.5 Traveling Wave Response Justification ....................208
7.2 Winding Modeling with Mutual Coupling and
Resistances ............................................................................209
7.2.1 Winding Detailed Model ..........................................209
7.3 MATLAB®/Simulink® Example ............................................215
Problems ...........................................................................................217
Bibliography .....................................................................................218
Chapter 8 Ferroresonance .................................................................................219
8.1 Linear Circuit Resonance ......................................................220
8.2 Nonlinear Circuit Resonance .................................................222
8.2.1 Stability Assessment of Operating Points in a
Nonlinear Resonance Circuit....................................223
8.2.1.1 Effect of ω .................................................225
8.2.1.2 Effect of u ................................................226
0
8.3 Ferroresonance Practical Cases in Power Systems ................227
8.3.1 One Phase Open .......................................................227
8.3.2 Overload Relay Malfunction ....................................228
8.3.3 De-energization of One Circuit of Two-circuit
Transmission Line ....................................................228
8.3.4 Single-phase Fault and Capacitive Voltage
Transformer ..............................................................228
8.4 Simulations ............................................................................229
Problems ...........................................................................................229
Bibliography .....................................................................................232
Index ......................................................................................................................233
Preface
Over the years, utility engineers have been challenged by dealing with many of the
components discussed in the book.
Examples of those cases are not limited to line energization, equipment switching,
and many more contained in the book. Therefore, this will be a great reference for
their analysis and design adjustments. Also, the book serves the educational needs of
graduate students in the field of power engineering. The author has taught the course
for almost 20 years and now has received praise from European industries involved
in the concept. Throughout these years, the students have been challenged by finding
a comprehensive book that covers a large number of concepts in the area. The book
provides a concrete reference for people who are working in modeling and design of
power systems considering transients. The mentioned group of people can be as large
as graduate students, consultants, utility engineers, and more.
The book provides a comprehensive resource to mainly educate graduate students
in the area of power system transients. It also serves as a reference for industry engi-
neers challenged by transient problems in the system. The book starts by categoriz-
ing transients’ phenomena and specifying unfavorable situations in power systems
raised by transients. Then, it moves on to different protective measures that have
been implemented in the system to prevent disasters caused by those transients. It
also explains different methodologies used to analyze transients in power systems. A
variety of transient cases that occurred or are possible to occur in power systems are
discussed and analyzed in this textbook. The book discusses the modeling of compo-
nents very extensively and provides analysis cases to assess a wide variety of tran-
sients, their possible effects on the system, and types of protections commonly used
for each case along with methods in designing a sound protection system.
Modeling of system elements such as transmission lines and cables with fre-
quency dependency consideration is an integral part of the book. Detailed PSCAD
models of the system components are presented and are used in system-level analy-
ses. Modeling will be done in a multi-phase platform accommodating mathematical
models of various elements such as overhead lines, cables, transformers, and so on.
These models are built to accommodate system transients in time scales as small as
microseconds. Various issues caused by transients in power grids are explored and
simulated in detail such as transients in connection nodes of cables and transmission
lines, ferroresonance, and several other examples like this.
Low-frequency and mid-frequency transients such as inrush current, ferroreso-
nance, faulted line transients, and magnetizing current chopping are discussed and
analyzed. Also, high-frequency cases such as lightning strikes and switching tran-
sients are discussed, modeled, and analyzed.
The book covers deterministic and stochastic simulations and calculation method-
ologies and discusses how they are different, but eventually, the goal of presenting
the book is to use deterministic approaches in studying a variety of transient cases in
power systems.
ix