Cable System Transients - Akihiro Ametani - E-Book

Cable System Transients E-Book

Akihiro Ametani

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Beschreibung

A systematic and comprehensive introduction to electromagnetic transient in cable systems, written by the internationally renowned pioneer in this field * Presents a systematic and comprehensive introduction to electromagnetic transient in cable systems * Written by the internationally renowned pioneer in the field * Thorough coverage of the state of the art on the topic, presented in a well-organized, logical style, from fundamentals and practical applications * A companion website is available

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Table of Contents

Cover

Title Page

Copyright

About the Authors

Preface

Acknowledgements

Chapter 1: Various Cables Used in Practice

1.1 Introduction

1.2 Land Cables

1.3 Submarine Cables

1.4 Laying Configurations

References

Chapter 2: Impedance and Admittance Formulas

2.1 Single-core Coaxial Cable (SC Cable)

2.2 Pipe-enclosed Type Cable (PT Cable)

2.3 Arbitrary Cross-section Conductor

2.4 Semiconducting Layer Impedance

2.5 Discussion of the Formulation

2.6 EMTP Subroutines “Cable Constants” and “Cable Parameters”

Appendix 2.AImpedance of an SC Cable Consisting of a Core, a Sheath and an Armor

Appendix 2.BPotential Coefficient

Appendix 2.CInternal Impedances of Arbitrary Cross-section Conductor

Appendix 2.DDerivation of Semiconducting Layer Impedance

References

Chapter 3: Theory of Wave Propagation in Cables

3.1 Modal Theory

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

3.3 Three-phase Underground SC Cables

3.4 Effect of Various Parameters of an SC Cable

3.5 Cross-bonded Cable

3.6 PT Cable

3.7 Propagation Characteristics of Intersheath Modes

References

Chapter 4: Cable Modeling for Transient Simulations

4.1 Sequence Impedances Using a Lumped PI-circuit Model

4.2 Electromagnetic Transients Program (EMTP) Cable Models for Transient Simulations

4.3 Dommel Model

4.4 Semlyen Frequency-dependent Model

4.5 Marti Model

4.6 Latest Frequency-dependent Models

References

Chapter 5: Basic Characteristics of Transients on Single-phase Cables

5.1 Single-core Coaxial (SC) Cable

5.2 Pipe-enclosed Type (PT) Cable – Effect of Eccentricity

5.3 Effect of a Semiconducting Layer on a Transient

References

Chapter 6: Transient on Three-phase Cables in a Real System

6.1 Cross-bonded Cable

6.2

Tunnel-installed 275 kV Cable

6.3 Cable Installed Underneath a Bridge

6.4 Cable Modeling in EMTP Simulations

6.5 Pipe-enclosed Type (PT) Cable

6.6 Gas-insulated Substation (GIS) – Overhead Cables

Appendix 6.A

Appendix 6.B

References

Chapter 7: Examples of Cable System Transients

7.1 Reactive Power Compensation

7.2 Temporary Overvoltages

7.3 Slow-front Overvoltages

7.4 Leading Current Interruption

7.5 Zero-missing Phenomenon

7.6 Cable Discharge

References

Chapter 8: Cable Transient in Distributed Generation System

8.1 Transient Simulation of Wind Farm

8.2 Transients in a Solar Plant

References

Index

End User License Agreement

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Guide

Cover

Table of Contents

Preface

Begin Reading

List of Illustrations

Chapter 1: Various Cables Used in Practice

Figure 1.1 Five principles for the future grid expansion (from [2])

Figure 1.2 Grid expansion plan based on Principle C (from [2])

Figure 1.3 Single-core XLPE cable. Courtesy of VISCAS Corporation

Figure 1.4 Stranded conductor. Courtesy of VISCAS Corporation

Figure 1.5 Segmental conductor. Courtesy of VISCAS Corporation

Figure 1.6 Copper wire sheath. Courtesy of VISCAS Corporation

Figure 1.7 SCOF cable. Courtesy of VISCAS Corporation

Figure 1.8 HPOF cable. Courtesy of VISCAS Corporation

Figure 1.9 HVAC submarine cable. Courtesy of VISCAS Corporation

Figure 1.10 MI cable. Courtesy of Nexans

Figure 1.11 Flat formation (a) and trefoil formation (b)

Figure 1.12 Solid bonding

Figure 1.13 Solid bonding of a submarine cable

Figure 1.14 Single-point bonding (two sections)

Figure 1.15 Single-point bonding (two sections) with ECC and SVLs

Figure 1.16 Cross bonding (three sections)

Figure 1.17 Continuous sheath voltage in a major section of a cross-bonded cable

Figure 1.18 Cross bonding (three sections) with ECC and SVLs

Figure 1.19 Combination of cross bonding and single-point bonding

Chapter 2: Impedance and Admittance Formulas

Figure 2.1 An SC cable system: (a) SC cable cross section; and (b) system configuration

Figure 2.2 A PT cable

Figure 2.3 (a) Arbitrary cross-section conductor and (b) its equivalent cylindrical conductor

Figure 2.4 (a) Test circuit for cable A; (b) cross section of cable A; and (c) equivalent PT cable

Figure 2.5 CSZV cable: (a) cross section; and (b) equivalent cylindrical conductors

Figure 2.6 (a) Cross section of cable C; and (b) cross section of equivalent circular conductors

Figure 2.7 Calculated results by FEM (—) and approximate method (o) for cable C: (a) self-impedance ; and (b) mutual impedance

Z

m

=

R

m

+

jωL

m

Figure 2.8 Cross section of a two-layered conductor

Figure 2.9 Outer surface impedance of a solid two-layered conductor : (a) resistance vs. frequency; and (b) inductance vs. frequency. Case 1: Two-layered conductor: . Case 2: Inner conductor only: . Case 3: Outer conductor only:

a

=

b

= 9.9 cm,

c

= 10 cm,

ρ

= 10

−4

Ωm

Figure 2.10 Outer surface impedance of a hollow two-layered conductor: (a) resistance vs. frequency; and (b) inductance vs. frequency. Case 1: Two-layered conductor: . Case 2: Inner conductor only: . Case 3: Outer conductor only:

a

=

b

= 1.25 cm,

c

= 1.5 cm,

ρ

= 10

−5

Ωm

Figure 2.11 Cross section of an underground XLPE cable

Figure 2.12 Conductor internal impedance. Real part (top) and imaginary part (bottom): (a) as a function of resistivity ; and (b) as a function of thickness

d

(

ρ

= 0.01 Ωm)

Figure 2.13 Propagation constants of the coaxial mode of an underground cable . Attenuation constant (top), velocity (middle), and characteristic impedance (real part) (bottom): (a) as a function of resistivity ; and (b) as a function of frequency . Case 0: no semiconducting layer. Case 1: . Case 2: . Case 3:

ρ

= 100 Ωm

Figure 2.14 Frequency characteristic of coaxial mode : (a) attenuation constant; (b) velocity; and (c) characteristic impedance (real part) as a function of frequency. Case 1: neglecting the semiconducting layer impedance. Case 2: considering the semiconducting layer impedance

Figure 2.15 Effect of pipe thickness on the pipe inner surface impedance

Figure 2.16 Susceptances (imaginary ) of (A) underground and (B) overhead SC cables

Figure 2.17 Effect of sheath and armor on the internal impedances of SC cables. A, Core and its outer insulator; B, core, sheath and its outer insulator: and C, core, sheath, armor and its outer insulator

Figure 2.A.1 An equivalent circuit for impedances of an SC cable

Figure 2.B.1 An equivalent circuit for admittance of an SC cable

Figure 2.D.1 (a) Two-layered coaxial cylindrical conductor and (b) cylindrical coordinate

Chapter 3: Theory of Wave Propagation in Cables

Figure 3.1 A distributed-parameter circuit

Figure 3.2 Current direction for Z- and Y-parameters

Figure 3.3 Cross-section of an underground SC cable

Figure 3.4 Modal current distribution along an SC cable

Figure 3.5 Modal step responses of an underground SC cable with length of

x

= 30 km

Figure 3.6 A three-phase underground SC cable: (a) arrangement (flat); and (b) cross-section

Figure 3.7 Frequency dependence of modal characteristic impedance

Figure 3.8 Three-phase cable arrangement: (a) trefoil; and (b) vertical

Figure 3.9 Cross-bonded cable with one major section

Figure 3.10 Cross-bonded cable system with “

m

” major sections

Figure 3.11 Two major sections

Figure 3.12 One major section with one more cross-bonding joint

Figure 3.13 Equivalent lumped-parameter circuit

Figure 3.14 Tunnel-installed three-phase cable: (a) cable configuration; and (b) cross-section of a phase cable:

Figure 3.15 Configuration of a buried cable

Figure 3.16 Frequency responses of modal (a) attenuation and (b) propagation velocity on a solidly bonded cable

Figure 3.17 A three-phase underground PT cable

Figure 3.18 Propagation constants on a PT cable with symmentrically arranged three-phase cores (): (a) attenuation vs. frequency; and (b) propagation velocity vs. frequency

Figure 3.19 A PT cable with an asymmetrical configuration of inner conductors

Figure 3.20 Propagation constants on a PT cable with asymmetrically arranged three-phase cores (): (a) attenuation vs. frequency; and (b) propagation velocity vs. frequency

Figure 3.21 A PT cable with inner conductors consisting of a core and sheath

Figure 3.22 Propagation constants on a PT cable with symmetrically arranged three-phase SC cable consisting of a core and a metallic sheath : (a) attenuation vs. frequency; and (b) propagation velocity vs. frequency

Figure 3.23 An overhead pipe-type cable

Figure 3.24 Frequency characteristic of coaxial mode impedance

z

c

: (a) resistance vs. frequency; and (b) inductance vs. frequency

Figure 3.25 Frequency response of characteristic impedance

z

c

: (a)

Z

011

; and (b)

z

oc

Figure 3.26 Frequency characteristic of coaxial mode propagation constant: (a) attenuation constant vs. frequency; and (b) velocity vs. frequency

Figure 3.27 Effect of the permittivity of the pipe inner insulator corresponding to Figure 3.18: (a) attenuation vs. frequency; and (b) propagation velocity vs. frequency

Figure 3.28 Intersheath mode circuits: (a) first intersheath mode (mode 1); and (b) second intersheath mode (mode 2)

Figure 3.29 Equivalent intersheath mode circuits to those in Figure 3.28: (a) first intersheath mode; and (b) second intersheath mode

Figure 3.30 Underground three-phase XLPE cable: (a) cable cross section; and (b) conductor arrangement

Figure 3.31 Theoretical waveforms for the first intersheath mode: Case 1-0: (a) sending-end currents; (b) sending-end voltages; and (c) receiving-end voltages

Figure 3.32 Theoretical current and voltage waveforms for the second intersheath mode: Case 2-0: (a) sending-end currents; (b) phase-a voltages; and (c) phase-c voltages

Figure 3.33 EMTP simulation results for Case 3-0 when the voltage source in Figure 3.28b is being grounded corresponding to Figure 3.32: (a) sending-end currents; (b) phase-a voltages; and (c) phase-c voltages

Figure 3.34 EMTP simulation results for Case 2-S equivalent to a current source corresponding to Figure 3.32 (Case 2-0): (a) phase-a voltages; (b) phase-a currents; and (c) phase-c currents

Figure 3.35 Cross-bonded cable system with “

m

” major sections

Figure 3.36 Transient currents and voltages associated with the first intersheath mode (mode 1) on a 6 km solidly bonded cable: Case 1N-21: (a) sending-end currents; (b) sending-end voltages; and (c) receiving-end voltages

Figure 3.37 Transient currents and voltages associated with the first intersheath mode (mode 1) on a 6 km cross-bonded cable: Case 1X-21: (a) sending-end currents; (b) sending-end voltages; and (c) receiving-end voltages

Figure 3.38 Transient currents and voltages associated with the second intersheath mode (mode 2) on a 6 km cross-bonded cable: Case 1X-22: (a) sending-end currents; (b) sending-end voltages; and (c) receiving-end voltages

Figure 3.39 Frequency responses of modal (a) attenuation and (b) propagation velocity on the homogeneous model of a cross-bonded cable corresponding to Figure 3.16

Figure 3.40 Transient currents and voltages on a 6 km cross-bonded cable: Case 1X-1.(a) , (b) , and (c)

.

(—) Original cross-bonded cable; (---) homogeneous model

Figure 3.41 Transient currents and voltages associated with the first intersheath mode on a 18 km cross-bonded cable: Case 2X-21: (a) sending-end currents; (b) phase-a voltages; (c) phase-b voltages; and (d) phase-c voltages

Figure 3.42 Transient currents and voltages on a 18 km cross-bonded cable: Case 2X-1. (a) , (b) , and (c)

.

(—) Original cross-bonded cable; (---) homogeneous model

Figure 3.43 Transient currents and voltages of the earth-return mode: (a) solidly bonded cable: Case ; (b) one-major cross-bonded cable: Case ; and (c) three-major cross-bonded cable: Case

Chapter 4: Cable Modeling for Transient Simulations

Figure 4.1 One cable case

Figure 4.2 Single-core three-phase cable case

Figure 4.3 Cross-bonded cable case

Figure 4.4 Setup for measuring sequence currents for a solidly bonded cable: (a) positive-sequence current; and (b) zero-sequence current.