book

Power System Transients, 2nd Edition

by Akihiro Ametani, Naoto Nagaoka, Yoshihiro Baba, Teruo Ohno, Koichi Yamabuki

November 2016

Intermediate to advanced

600 pages

18h 45m

English

CRC Press

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Cover
Half Title
Title Page
Copyright Page
Contents (1/2)
Contents (2/2)
Preface
Authors
List of Symbols
List of Acronyms

International Standards
1 Theory of Distributed-Parameter Circuits and Impedance/ Admittance Formulas
1.1 Introduction
1.2 Impedance and Admittance Formulas
1.2.1 Conductor Internal Impedance Z[sub(i)]
1.2.1.1 Derivation of an Approximate Formula1.2.1.2 Accurate Formula by Schelkunoff
1.2.2 Outer-Media Impedance Z[sub(0)] (1/2)
1.2.2.1 Outer-Media Impedance1.2.2.2 Overhead Conductor
1.2.2 Outer-Media Impedance Z[sub(0)] (2/2)
1.2.2.3 Pollaczek’s General Formula for Overhead, Underground, and Overhead/Underground Conductor Systems
Problems
1.3 Basic Theory of Distributed-Parameter Circuit
1.3.1 Partial Differential Equations of Voltages and Currents
1.3.2 General Solutions of Voltages and Currents
1.3.2.1 Sinusoidal Excitation1.3.2.2 Lossless Line
1.3.3 Voltages and Currents on a Semi-Infinite Line
1.3.3.1 Solutions of Voltages and Currents1.3.3.2 Waveforms of Voltages and Currents1.3.3.3 Phase Velocity1.3.3.4 Traveling Wave
1.3.3.5 Wavelength
1.3.4 Propagation Constants and Characteristic Impedance1.3.4.1 Propagation Constants1.3.4.2 Characteristic Impedance
1.3.5 Voltages and Currents on a Finite Line (1/2)
1.3.5.1 Short-Circuited Line1.3.5.2 Open-Circuited Line
1.3.5 Voltages and Currents on a Finite Line (2/2)
Problems
1.4 Multiconductor System1.4.1 Steady-State Solutions
1.4.2 Modal Theory (1/2)
1.4.2.1 Eigenvalue Theory1.4.2.2 Modal Theory
1.4.2 Modal Theory (2/2)
1.4.2.3 Current Mode1.4.2.4 Parameters in Modal Domain
1.4.3 Two-Port Circuit Theory and Boundary Conditions
1.4.3.1 Four-Terminal Parameter1.4.3.2 Impedance/Admittance Parameters
1.4.4 Modal Distribution of Multiphase Voltages and Currents
1.4.4.1 Transformation Matrix1.4.4.2 Modal Distribution
Problems
1.5 Frequency-Dependent Effect
1.5.1 Frequency Dependence of Impedance
1.5.2 Frequency-Dependent Parameters (1/3)
1.5.2.1 Frequency Dependence1.5.2.2 Propagation Constant1.5.2.3 Characteristic Impedance
1.5.2 Frequency-Dependent Parameters (2/3)
1.5.2.4 Transformation Matrix1.5.2.5 Line Parameters in the Extreme Case
1.5.2 Frequency-Dependent Parameters (3/3)
1.5.3 Time Response (1/2)
1.5.3.1 Time-Dependent Responses1.5.3.2 Propagation Constant: Step Response1.5.3.3 Characteristic Impedance1.5.3.4 Transformation Matrix
1.5.3 Time Response (2/2)
Problems
1.6 Traveling Wave1.6.1 Reflection and Refraction Coefficients
1.6.2 Thevenin’s Theorem
1.6.2.1 Equivalent Circuit of a Semi-Infinite Line1.6.2.2 Voltage and Current Sources at the Sending End1.6.2.3 Boundary Condition at the Receiving End1.6.2.4 Thevenin’s Theorem
1.6.3 Multiple Reflection
1.6.4 Multiconductors (1/3)
1.6.4.1 Reflection and Refraction Coefficients1.6.4.2 Lossless Two-Conductor Systems1.6.4.3 Consideration of Modal Propagation Velocities
1.6.4 Multiconductors (2/3)
1.6.4.4 Consideration of Losses in a Two- Conductor System
1.6.4 Multiconductors (3/3)
1.6.4.5 Three-Conductor Systems1.6.4.6 Cascaded System Composed of Different Numbers of Conductors
Problems
1.7 Nonuniform Conductors
1.7.1 Characteristic of Nonuniform Conductors
1.7.1.1 Nonuniform Conductors1.7.1.2 Difference from Uniform Conductors
1.7.2 Impedance and Admittance Formulas (1/2)
1.7.2.1 Finite-Length Horizontal Conductor1.7.2.2 Vertical Conductor
1.7.2 Impedance and Admittance Formulas (2/2)
1.7.3 Line Parameters (1/2)
1.7.3.1 Finite Horizontal Conductor1.7.3.2 Vertical Conductor1.7.3.3 Nonparallel Conductor
1.7.3 Line Parameters (2/2)
Problems
1.8 Introduction to EMTP
1.8.1 Introduction1.8.1.1 History of Transient Analysis1.8.1.2 Background of the EMTP1.8.1.3 EMTP Development
1.8.2 Basic Theory of the EMTP
1.8.2.1 Representation of a Circuit Element by a Current Source and Resistance1.8.2.2 Composition of Nodal Conductance
1.8.3 Other Circuit Elements
Solutions to Problems
References
2 Transients on Overhead Lines
2.1 Introduction
2.2 Switching Surge on Overhead Lines
2.2.1 Basic Mechanism of A Switching Surge
2.2.2 Basic Parameters Influencing Switching Surges
2.2.2.1 Source Circuit2.2.2.2 Switch
2.2.2.3 Transformer
2.2.2.4 Transmission Line2.2.3 Switching Surges in Practice (1/4)2.2.3.1 Classification of Switching Surges2.2.3.2 Basic Characteristics of a Closing Surge: Field Test Results
2.2.3 Switching Surges in Practice (2/4)
2.2.3.3 Closing Surge on a Single Phase Line2.2.3.4 Closing Surges on a Multiphase Line
2.2.3 Switching Surges in Practice (3/4)
2.2.3.5 Effect of Various Parameters on a Closing Surge
2.2.3 Switching Surges in Practice (4/4)
2.3 Fault Surge
2.3.1 Fault Initiation Surge
2.3.2 Characteristic of a Fault Initiation Surge
2.3.2.1 Effect of Line Transposition2.3.2.2 Overvoltage Distribution
2.3.3 Fault-Clearing Surge (1/2)
2.3.3 Fault-Clearing Surge (2/2)
2.4 Lightning Surge
2.4.1 Mechanism of Lightning Surge Generation
2.4.2 Modeling of Circuit Elements (1/2)
2.4.2.1 Lightning Current2.4.2.2 Tower and Gantry2.4.2.3 Tower Footing Impedance2.4.2.4 Arc Horn
2.4.2 Modeling of Circuit Elements (2/2)
2.4.2.5 Transmission Line
2.4.2.6 Substation2.4.3 Simulation Result of A Lightning Surge (1/2)2.4.3.1 Model Circuit2.4.3.2 Lightning Surge Overvoltage2.4.3.3 Effect of Various Parameters
2.4.3 Simulation Result of A Lightning Surge (2/2)
2.5 Theoretical Analysis of Transients: Hand Calculations
2.5.1 Switching Surge on an Overhead Line (1/2)
2.5.1.1 Traveling Wave Theory
2.5.1 Switching Surge on an Overhead Line (2/2)
2.5.1.2 Lumped Parameter Equivalent with Laplace Transform
2.5.2 Fault Surge
2.5.3 Lightning Surge (1/2)
2.5.3.1 Tower-Top Voltage2.5.3.2 Two-Phase Model2.5.3.3 No BFO2.5.3.4 Case of a BFO2.5.3.5 Consideration of Substation
2.5.3 Lightning Surge (2/2)
2.6 Frequency-Domain (FD) Method of Transient Simulations
2.6.1 Introduction2.6.2 Numerical Fourier/Laplace Transform2.6.2.1 Finite Fourier Transform2.6.2.2 Shift of Integral Path: Laplace Transform2.6.2.3 Numerical Laplace Transform: Discrete Laplace Transform2.6.2.4 Odd-Number Sampling: Accuracy Improvement
2.6.2.5 Application of Fast Fourier Transform FFT: Fast Laplace Transform (FLT)
2.6.3 Transient Simulation
2.6.3.1 Definition of Variables2.6.3.2 Subroutine to Prepare F( ω)
2.6.3.3 Subroutine FLT
2.6.4 Remarks of the FD MethodAppendix 2A
References
3 Transients on Cable Systems
3.1 Introduction
3.2 Impedance and Admittance of Cable Systems
3.2.1 Single-Phase Cable3.2.1.1 Cable Structure3.2.1.2 Impedance and Admittance
3.2.2 Sheath Bonding
3.2.3 Homogeneous Model of a Cross-Bonded Cable (1/2)
3.2.3.1 Homogeneous Impedance and Admittance
3.2.3 Homogeneous Model of a Cross-Bonded Cable (2/2)
3.2.3.2 Reduction of the Sheath
3.2.4 Theoretical Formula of Sequence Currents (1/2)
3.2.4.1 Cross-Bonded Cable
3.2.4 Theoretical Formula of Sequence Currents (2/2)
3.2.4.2 Solidly Bonded Cable
3.3 Wave Propagation and Overvoltages
3.3.1 Single-Phase Cable3.3.1.1 Propagation Constant3.3.1.2 Example of Transient Analysis
3.3.2 Wave Propagation Characteristics
3.3.2.1 Impedance: R, L3.3.2.2 Capacitance: C
3.3.2.3 Transformation Matrix
3.3.2.4 Attenuation Constant and Propagation Velocity3.3.3 Transient Voltage
3.3.4 Limitations of the Sheath Voltage
3.3.5 Installation of SVLs
3.4 Studies on Recent and Planned EHV AC Cable Projects
3.4.1 Recent Cable Projects
3.4.2 Planned Cable Projects
3.5 Cable System Design and Equipment Selection3.5.1 Study Flow
3.5.2 Zero-Missing Phenomenon
3.5.2.1 Sequential Switching
3.5.3 Leading Current Interruption
3.5.4 Cable Discharge
3.6 EMTP Simulation Test CasesProblem 1
Problem 2
References
4 Transient and Dynamic Characteristics of New Energy Systems
4.1 Wind Farm4.1.1 Model Circuit of a Wind Farm
4.1.2 Steady-State Analysis (1/2)
4.1.2.1 Cable Model4.1.2.2 Charging Current
4.1.2 Steady-State Analysis (2/2)
4.1.2.3 Load-Flow Calculation
4.1.3 Transient Calculation
4.2 Power-Electronics Simulation Using the EMTP
4.2.1 Simple Switching Circuit
4.2.2 Switching Transistor Model (1/2)
4.2.2.1 Simple Switch Model
4.2.2 Switching Transistor Model (2/2)
4.2.2.2 Switch with Delay Model
4.2.3 Metal Oxide Semiconductor Field-Effect Transistor (1/3)
4.2.3.1 Simple Model4.2.3.2 Modified Switching Device Model
4.2.3 Metal Oxide Semiconductor Field-Effect Transistor (2/3)
4.2.3.3 Simulation Circuit and Results
4.2.3 Metal Oxide Semiconductor Field-Effect Transistor (3/3)
4.2.4 Thermal Calculation
4.3 Voltage-Regulation Equipment Using Battery in a DC Railway System
4.3.1 Introduction
4.3.2 Feeding Circuit
4.3.3 Measured and Calculated Results (1/2)
4.3.3.1 Measured Results4.3.3.2 Calculated Results of the Conventional System4.3.3.3 Calculated Results with Power Compensator
4.3.3 Measured and Calculated Results (2/2)
4.4 Concluding Remarks
References
5 Numerical Electromagnetic Analysis Methods and Their Application in Transient Analyses
5.1 Fundamentals5.1.1 Maxwell’s Equations
5.1.2 Finite-Difference Time-Domain Method (1/2)
5.1.2 Finite-Difference Time-Domain Method (2/2)
5.1.3 Method of Moments (1/2)
5.1.3 Method of Moments (2/2)
5.2 Applications
5.2.1 Grounding Electrodes
5.2.2 Transmission Towers
5.2.3 Distribution Lines: Lightning-Induced Surges
5.2.4 Transmission Lines: Propagation of Lightning Surges in the Presence of Corona (1/2)
5.2.4 Transmission Lines: Propagation of Lightning Surges in the Presence of Corona (2/2)
5.2.5 Power Cables: Propagation of Power Line Communication Signals
5.2.6 Air-Insulated Substations
5.2.7 Wind-Turbine Generator Towers
References
6 Electromagnetic Disturbances in Power Systems and Customer Homes
6.1 Introduction
6.2 Disturbances in Power Stations and Substations
6.2.1 Statistical Data of Disturbances6.2.1.1 Overall Data6.2.1.2 Disturbed Equipment
6.2.1.3 Incoming Surge Routes
6.2.2 Characteristics of Disturbances (1/2)6.2.2.1 Characteristics of LS Disturbances6.2.2.2 Characteristics of SS Disturbances
6.2.2 Characteristics of Disturbances (2/2)
6.2.2.3 SSs in DC Circuits
6.2.3 Influence, Countermeasures, and Costs of Disturbances
6.2.3.1 Influence of Disturbances on Power System Operation6.2.3.2 Conducted Countermeasures6.2.3.3 Cost of Countermeasures
6.2.4 Case Studies (1/2)
6.2.4.1 Case No. 16.2.4.2 Case No. 2
6.2.4 Case Studies (2/2)
6.2.4.3 Case No. 3
6.2.5 Concluding Remarks
6.3 Disturbances in Customers’ Home Appliances6.3.1 Statistical Data of Disturbances
6.3.2 Breakdown Voltage of Home Appliances
6.3.2.1 Testing Voltage
6.3.2.2 Breakdown Test
6.3.3 Surge Voltages and Currents to Customers Due to Nearby Lightning (1/3)6.3.3.1 Introduction6.3.3.2 Model Circuits for Experiments and EMTP Simulations
6.3.3 Surge Voltages and Currents to Customers Due to Nearby Lightning (2/3)
6.3.3.3 Experimental and Simulation Results
6.3.3 Surge Voltages and Currents to Customers Due to Nearby Lightning (3/3)
6.3.3.4 Concluding Remarks
6.3.4 LS Incoming from a Communication Line (1/2)6.3.4.1 Introduction6.3.4.2 Protective Device6.3.4.3 Lightning Surges
6.3.4 LS Incoming from a Communication Line (2/2)
6.3.4.4 Concluding Remarks
6.4 Analytical Method of Solving Induced Voltages and Currents
6.4.1 Introduction
6.4.2 F-Parameter Formulation for Induced Voltages and Currents
6.4.2.1 Formulation of F-Parameter6.4.2.2 Approximation of F-Parameters6.4.2.3 Cascaded Connection of Pipelines
6.4.3 Application Examples (1/3)
6.4.3.1 Single Section Terminated by R[sub(1)]and R[sub(2)]
6.4.3 Application Examples (2/3)
6.4.3.2 Two-Cascaded Sections of a Pipeline (Problem 6.1)
6.4.3 Application Examples (3/3)
6.4.3.3 Three-Cascaded Sections of a Pipeline (Problem 6.1)
6.4.4 Comparison with a Field Test Result (1/2)
6.4.4.1 Comparison with EMTP Simulations6.4.4.2 Field Test Results
6.4.4 Comparison with a Field Test Result (2/2)
6.4.5 Concluding Remarks
Solution to Problem 6.1
Appendix 6A (1/2)
Appendix 6A (2/2)
References
7 Grounding
7.1 Introduction
7.2 Grounding Methods
7.2.1 Gas Pipeline
7.2.2 Transmission Towers and GWs
7.2.3 Underground Cable
7.2.4 Buildings
7.2.5 Distribution Lines and Customer’s House
7.3 Modeling for Steady-State and Transient Analysis
7.3.1 Analytical/Theoretical Model7.3.1.1 Steady-State
7.3.2 Modeling for EMTP Simulation
7.3.3 Numerical Electromagnetic Analysis
7.4 Measurement of Transient Responses on Various Grounding Electrodes
7.4.1 Transient Response Measurements on Multiple Vertical Electrodes and FDTD Simulations (1/3)
7.4.1.1 Experimental Conditions7.4.1.2 Measuring Instruments7.4.1.3 Measured Results7.4.1.4 Experiments and FDTD Simulations
7.4.1 Transient Response Measurements on Multiple Vertical Electrodes and FDTD Simulations (2/3)
7.4.1.5 A Study of Mutual Coupling by FDTD Simulations
7.4.1 Transient Response Measurements on Multiple Vertical Electrodes and FDTD Simulations (3/3)
7.4.2 Theoretical Analysis of Transient Response (1/2)
7.4.2.1 Analytical Formula of Electrode Voltage7.4.2.2 Transient Voltage Waveform7.4.2.3 Analytical Investigation
7.4.2 Theoretical Analysis of Transient Response (2/2)
7.4.2.4 Circuit Parameters7.4.2.5 Wave Propagation Characteristic
7.4.2.6 Concluding Remarks
7.4.3 Investigation of Various Measured Results (1/2)7.4.3.1 Test Circuit7.4.3.2 Measured Results7.4.3.3 Discussion
7.4.3 Investigation of Various Measured Results (2/2)
7.4.3.4 Effect of Lead Wire
7.4.4 Reduction of Grounding Impedance: Effect of Electrode Shape (1/4)
7.4.4.1 Introduction7.4.4.2 Field Measurements
7.4.4 Reduction of Grounding Impedance: Effect of Electrode Shape (2/4)
7.4.4.3 FDTD Simulation
7.4.4 Reduction of Grounding Impedance: Effect of Electrode Shape (3/4)
7.4.4 Reduction of Grounding Impedance: Effect of Electrode Shape (4/4)
7.4.4.4 Summary
7.4.5 Transient Induced Voltage to Control Cable from Grounding Mesh (1/3)
7.4.5.1 Introduction7.4.5.2 Model Circuit7.4.5.3 No Mutual Coupling (Case X0-Lj)
7.4.5 Transient Induced Voltage to Control Cable from Grounding Mesh (2/3)
7.4.5 Transient Induced Voltage to Control Cable from Grounding Mesh (3/3)
7.4.5.4 With Mutual Coupling (Case X1-Lj)7.4.5.5 Conclusion
Appendix 7A
References
8 Problems and Application Limits of Numerical Simulations
8.1 Problems with Existing Impedance Formulas Used in Circuit Theory-Based Approaches8.1.1 Earth-Return Impedance8.1.1.1 Carson’s Impedance8.1.1.2 Basic Assumptions of Impedance8.1.1.3 Nonparallel Conductors
8.1.1.4 Stratified Earth
8.1.1.5 Earth Resistivity and Permittivity8.1.2 Internal Impedance8.1.2.1 Schelkunoff’s Impedance8.1.2.2 Arbitrary Cross-Section Conductor
8.1.2.3 Semiconducting Layer of Cables
8.1.2.4 Proximity Effect8.1.3 Earth-Return Admittance
8.2 Existing Problems in Circuit Theory-Based Numerical Analysis
8.2.1 Reliability of a Simulation Tool8.2.2 Assumptions and Limits of a Simulation Tool
8.2.3 Input Data
8.3 NEA for Power System Transients
References
Index (1/3)
Index (2/3)
Index (3/3)

Content preview from Power System Transients, 2nd Edition

41Theory of Distributed-Parameter Circuits and Impedance

IYVdx=−

∫

(1.118)

For a semi-innite line, substituting the rst equation of Equation 1.112

into Equation 1.118 gives

IYPPxV YP V

=− −−=

−−

()exp( )

// /12 12 12

(1.119)

Therefore, the characteristic impedance and admittance matrices are

found as

ZPYYYP

12 1

−−//

, (1.120)

This equation produces the same matrices as in Equation 1.113. For exam-

ple, for the characteristic admittance matrix:

YYPPYPPY PZYY

12 11 12 11 12 11 12 1

====

−−−−−−−−

−−

(( )) ()()((

))

−−

−

(

)

112

PZ ZP

(1.121)

The characteristic impedance and admittance matrices are symmetrical

matrices. For example, for the characteristic impedance matrix:

ZPYYPY

tttt t0

12 1112 112

====

−− −

()

///

(1.122)

Here, Y = Y

since Y is a symmet ...

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Power System Transients, 2nd Edition

by Akihiro Ametani, Naoto Nagaoka, Yoshihiro Baba, Teruo Ohno, Koichi Yamabuki

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