Cable System Transients (eBook)

Akihiro Ametani, Doshisha University, Japan Teruo Ohno, Tokyo Electric Power Company, Japan Naoto Nagaoka, Doshisha University, Japan

Preface
A. Ametani

1. Various Cables Used in Practice
T. Ohno

1.1. Introduction

1.2. Land Cables

1.2.1 Introduction

1.2.2 XLPE cables

1.2.3 SCOF cables

1.2.4 HPOF cables

1.3. Submarine Cables

1.3.1 Introduction

1.3.2 HVAC submarine cables

1.3.3 HVDC submarine cables

1.4. Laying Configurations

1.4.1 Burial condition

1.4.2 Sheath bonding

1.5. References

2. Impedance and Admittance Formulas
A. Ametani

2.1 Single-Core Coaxial Cable (SC Cable)

2.1.1 Impedance

2.1.2 Potential coefficient

2.2 Pipe-Enclosed Type Cable (PT Cable)

2.2.1 Impedance

2.2.1.1 Pipe thickness assumed to be infinite

2.2.1.2 Pipe thickness being finite

2.2.2 Potential coefficient

2.2.2.1 Pipe thickness assumed to be infinite

2.2.2.2 Pipe thickness being finite

2.3 Arbitrary Cross-Section Conductor

2.3.1 Equivalent cylindrical conductor

2.3.2 Examples

2.3.2.1 Cable A

2.3.2.2 Cable B

2.3.2.3 Cable C

2.4 Semiconducting Layer Impedance

2.4.1 Derivation of impedance

2.4.2 Impedance of two-layered conductor

2.4.3 Discussion of the impedance formula

2.4.3.1 Comparison with the accurate formula in Appendix 2A.4

2.4.3.2 Comparison with Schelkunoff's formula

2.4.4 Admittance of semiconducting layer

2.4.5 Wave propagation characteristic of cable with core outer semiconducting layer

2.4.5.1 Impedance

2.4.5.2 Propagation constant

2.4.5.3 Effect of the semiconducting layer admittance

2.4.6 Concluding remarks

2.5 Discussion of the Formulation

2.5.1 Discussion of the formulas

2.5.2 Parameters influencing cable impedance and admittance

2.5.2.1 Stranded conductor

2.5.2.2 Enamel coated strand

2.5.2.3 Proximity effect between conductors

2.5.2.4 Snaking

2.5.2.5 Geometrical configuration

2.5.2.6 Physical parameters of a cable

2.6 EMTP Subroutines "Cable Constants" and "Cable Parameters"

2.6.1 Overhead line

2.6.2 Underground / overhead cable

2A Appendices

Appendix 2A.1 Impedance of an SC cable consisting of a core, a sheath and an armor

Appendix 2A.2 Potential coefficient

Appendix 2A.3 Internal impedances of arbitrary cross-section conductor

Appendix 2A.4 Derivation of semiconducting layer impedance

2.7 References

3. Theory of Wave Propagation in Cables
A. Ametani

3.1 Modal Theory

3.1.1 Eigenvalues and vectors

3.1.2 Calculation of a matrix function by eigenvalues/vectors

3.1.3 Direct application of eigenvalue theory to a multi-conductor system

3.1.4 Modal theory

3.1.4.1 Voltage

3.1.4.2 Current

3.1.4.3 Power

3.1.5 Formulation of multi-conductor voltages and currents

3.1.6 Boundary conditions and two-port theory

3.1.6.1 Reflection coefficient method

3.1.6.2 F-parameter method

3.1.6.3 Z- and Y-parameter methods

3.1.7 Problems

3.2 Basic Characteristics of Wave Propagation on Single-Phase SC Cables

3.2.1 Basic propagation characteristics for a transient

3.2.2 Frequency-dependent characteristics

3.2.2.1 Impedance of a single-phase SC cable

3.2.2.2 Transformation matrix

3.2.2.3 Attenuation and velocity

3.2.2.4 Characteristic impedance

3.2.3 Time response of wave deformation

3.3 Three-Phase Underground SC Cables

3.3.1 Mutual coupling between phases

3.3.2 Transformation matrix

3.3.3 Attenuation and velocity

3.3.4 Characteristic impedance

3.4 Effect of Various Parameters of an SC Cable

3.4.1 Buried depth 14h'>

3.4.2 Earth resistivity 14Ï?e'>

3.4.3 Sheath thickness 14d'>

3.4.4 Sheath resistivity 14Ï?s'>

3.4.5 Arrangement of a three-phase SC cable

3.5 Cross-Bonded Cable

3.5.1 Cross-bonded cable

3.5.2 Theoretical formulation of a cross-bonded cable

3.5.2.1 Rotation matrix

3.5.2.2 Accurate formulation by adopting a travelling-wave theory

3.5.2.3 Accurate formulation by Y-parameter

3.5.2.4 Approximate formulation

3.5.3 Homogeneous model of a cross-bonded cable

3.5.3.1 Impedance

3.5.3.2 Capacitance

3.5.3.3 Voltage transformation matrix 14A-1'>

3.5.3.4 Attenuation and velocity

3.5.4 Difference between tunnel-installed and buried cables

3.6 Pipe-Enclosed Type (PT) Cable

3.6.1 PT Cable

3.6.2 PT cable with finite-pipe thickness

3.6.2.1 Symmetrical configuration of inner conductors

3.6.2.2 Asymmetrical configuration of inner conductors

3.6.2.3 Inner conductors with core and sheath

3.6.3 Effect of eccentricity of inner conductor

3.6.3.1 Frequency responses of the impedance

3.6.3.2 Frequency responses of characteristic impedance

3.6.3.3 Propagation constant

3.6.3.4 Concluding remarks

3.6.4 Effect of the permittivity of the pipe inner insulator

3.6.5 Overhead PT cable

3.7 Propagation Characteristics of Intersheath Modes

3.7.1 Theoretical analysis of intersheath modes

3.7.1.1 Intersheath modes

3.7.1.2 Circuit for intersheath modes

3.7.1.3 Modal attenuation and velocity

3.7.1.4 Theoretical voltage and currents waveforms

3.7.2 Transients on a cross-bonded cable

3.7.2.1 One major section (x=6 km)

3.7.2.2 Three major section

3.7.3 Earth-return Mode

3.7.4 Concluding remarks

3.8 References

4. Cable Modeling for Transient Simulations
T. Ohno and A. Ametani

4.1 Sequence Impedances using a Lumped PAI-Circuit Model

4.1.1 Solidly-bonded cables

4.1.2 Cross-bonded cables

4.1.3 Derivation of sequence impedance formulas

4.1.3.1 Solidly-bonded cable

4.1.3.2 Cross-bonded cable

4.2 EMTP Cable Models for Transient Simulations

4.3 Dommel's Line Model

4.4 Semlyen Frequency-Dependent Model

4.4.1 Semlyen model

4.4.2 Linear model

4.5 Marti Model

4.6 Frequency-Dependent Model Using Vector Fitting

4.6.1 Basic theory

4.6.2 Frequency region partitioning algorithm

4.7 References

5. Basic Characteristics of Transients on Single-Phase Cables
A. Ametani

5.1 SC Cable

5.1.1 Experimental observations

5.1.1.1 Experimental circuit

5.1.1.2 Measured results

5.1.2 EMTP simulations

5.1.2.1 Model circuit

5.1.2.2 Simulation results

5.1.3 Theoretical analysis

5.1.3.1 Refraction coefficient matrix

5.1.3.2 Node voltage

5.1.4 Analytical evaluation of parameters

5.1.5 Analytical calculation of transient voltages

5.1.5.1 Case11-11 : 14Rc1=Rc2=Rs1=Rs2=0'>

5.1.5.2 Case11-33 : 14Rc1=Rc2=0, Rs1=Rs2=10 kâ"¦'> (nearly open-circuited)

5.1.5.3 Case12-11: 14Rc1=0 â"¦, Rc2=200 â"¦, Rs1=Rs2=0 â"¦'>

5.1.5.4 Case12-12: 14Rc1=0 â"¦, Rc2=200 â"¦, Rs1=0, Rs2=150 â"¦'>

5.1.5.5 Case12-13: 14Rc1=0, Rc2=200 â"¦, Rs1=0 â"¦, Rs2=10 kâ"¦'>

5.1.5.6 Case22-11: 14Rc1=Rc2=200 â"¦, Rs1=Rs2=0 â"¦'>

5.1.6 Concluding remarks

5.2 PT Cable . Effect of eccentricity

5.2.1 Model circuit for the EMTP simulation

5.2.2 Simulation results for step-function voltage source

5.2.2.1 Effect of the eccentricity

5.2.2.2 Effect of lead wire inductance

5.2.2.3 Effect of applied voltage waveform

5.2.3 FDTD simulation

5.2.3.1 Model circuit

5.2.3.2 Simulation results

5.2.4 Theoretical analysis

5.2.4.1 Steady-state solution in a frequency domain for a long time period

5.2.4.2 Traveling wave solutions for a small time period

5.2.5 Concluding remarks

5.3 Effect of a Semiconducting Layer on a Transient

5.3.1 Step function voltage applied to a 2 km cable

5.3.2 5×70 ms impulse voltage applied to a 40 km cable

5.4 References

6. Transient on Three-Phase Cables in a Real System
A. Ametani

6.1 Cross-Bonded Cable

6.1.1 Field test on an 110 kV OF cable

6.1.2 Effect of cross-bonding

6.1.3 Effect of various parameters

6.1.4 Homogeneous model (See Section 3.5.3 of Chapter 3)

6.1.5 PAI-circuit model

6.2 Tunnel-Installed 275 kV Cable

6.2.1 Cable configuration

6.2.2 Effect of geometrical parameters on wave propagation

6.2.2.1 Effect of earth surface and wall thickness

6.2.2.2 Effect of cable configuration

6.2.2.3 Effect of cable arrangement

6.2.2.4 Effect of tunnel radius

6.2.2.5 Difference from a directly buried cable

6.2.3 Field test on 275 kV XLPE cable

6.2.3.1 Field test circuit

6.2.3.2 Comparison of calculated results with field test

6.2.3.3 Comparison with underground cable

6.2.3.4 Effect of cable parameter

6.2.4 Concluding remarks

6.3 Cable Installed Underneath a Bridge

6.3.1 Model system

6.3.2 Effect of an overhead cable and a bridge

6.3.2.1 Homogeneous system

6.3.2.2 Partially overhead cable

6.3.2.3 Effect of iron frameworks of a bridge

6.3.3 Effect of overhead lines on a cable transient

6.3.3.1 Double circuit operation of overhead line

6.3.3.2 Frequency-dependent effect of an overhead line

6.3.3.3 Effect of single-circuit operation of overhead lines

6.3.3.4 Effect of iron frameworks of a bridge

6.4 Cable Modeling in EMTP Simulations

6.4.1 Marti's and Dommel's cable models

6.4.2 Homogeneous cable model (See Section 3.5.3)

6.4.3 Effect of tunnel-installed cable

6.5 PT Cable

6.5.1 Field test on a 275 kV POF cable

6.5.2 Measured results

6.5.2.1 Pipe grounded

6.5.2.2 Pipe isolated

6.5.3 FTP simulation

6.5.3.1 Pipe grounded

6.5.3.2 Pipe isolated

6.5.3.3 Effect of sheath thickness

6.5.3.4 Effect of inner cable arrangement

6.6 Gas-Insulated Substation -- Overhead Cables

6.6.1 Basic characteristic of an overhead cable

6.6.2 Effect of spacer in a bus

6.6.2.1 Propagation parameters with a spacer

6.6.2.2 EMTP simiulation results

6.6.2.3 Case of short-length bus

6.6.2.4 Equivalent permittivity

6.6.3 Three-phase underground gas-insulated line

6.6.4 Switching surges in a 500 kV gas-insulated substation

6.6.4.1 A model GIS

6.6.4.2 EMTP simulation results

6.6.5 Basic characteristics of switching surges induced to a control cable

6.6.5.1 A model circuit

6.6.5.2 EMTP simulation results

6.6.5.3 Effect of spacers

6.A Appendices

Appendix 6A.1

Appendix 6A.2

6.7 References

7. Examples of Cable System Transients
T. Ohno

7.1 Reactive Power Compensation

7.2 Temporary Overvoltages

7.2.1 Series resonance overvoltage

7.2.1.1 Theoretical background

7.2.1.2 Analysis of examples

7.2.1.3 Dominant frequency in energization overvoltage

7.2.2 Parallel resonance overvoltage

7.2.2.1 Theory

7.2.2.2 Example of analysis

7.2.3 Overvoltage caused by system islanding

7.3 Slow-front Overvoltages

7.3.1 Line energization overvoltages from lumped source

7.3.1.1 Overview

7.3.1.2 Study conditions and parameters

7.3.1.3 Simulation results and statistical distributions

7.3.1.4 Concluding remarks

7.3.2 Line energization overvoltages from complex source

7.3.2.1 Study conditions

7.3.2.2 Simulation results and statistical distributions

7.3.3 Analysis of statistical distribution of energization overvoltages

7.3.3.1 Analysis on the highest overvoltages

7.3.3.2 Analysis on the effects of line length

7.3.3.3 Analysis on the effects of feeding network

7.3.3.4 Concluding remarks

7.4 Leading Current Interruption

7.5 Zero-missing Phenomenon

7.5.1 Zero-missing phenomenon and countermeasures

7.5.2 Sequential switching

7.6 Cable Discharge

7.7 References

8. Cable Transient in Distributed Generation System
N. Nagaoka

8.1 Transient Simulation of Wind Farm

8.1.1 Circuit diagram

8.1.2 Cable models and dominant frequency

8.1.3 Data for CABLE PARAMETERS

8.1.3.1 Declaration and miscellaneous data

8.1.3.2 Radii and physical constants

8.1.3.3 Position, earth resistivity and frequency

8.1.4 EMTP data structure

8.1.4.1 Miscellaneous data

8.1.4.2 Branch data

8.1.4.3 Switch data

8.1.4.4 Source data

8.1.4.5 Output specification

8.1.4.6 Plot specification

8.1.5 Results of pre-calculation

8.1.6 Cable energization

8.1.6.1 Data for transient simulation

8.1.6.2 Simulated results

8.2 Transients in a Solar Plant

8.2.1 Modeling of solar plant

8.2.1.1 Equivalent circuit of PV module

8.2.1.2 Cable model

8.2.2 Simulated results

8.2.2.1 Pre-calculation of current vs. voltage characteristic

8.2.2.2 Short circuit fault simulation

8.3 References

"Because the authors have included fundamental background theory, and much practical information, this book will be considered a reference standard on power cable transients for many years." (IEEE Electrical Engineering magazine, 1 January 2016)