IEEE Power and Energy Society
Sponsored by the
Insulated Conductors Committee
IEEE
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IEEE Std 575™-2014
(Revision of
IEEE Std 575-1988)
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IEEE Guide for Bonding Shields and
Sheaths of Single-Conductor Power
Cables Rated 5 kV through 500 kV
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(Revision of
IEEE Std 575-1988)
IEEE Guide for Bonding Shields and
Sheaths of Single-Conductor Power
Cables Rated 5 kV through 500 kV
Sponsor
Insulated Conductors Committee
of the
IEEE Power and Energy Society
Approved 12 June 2014
IEEE-SA Standards Board
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IEEE Std 575™-2014
Keywords: bonding, cross bonding, distribution cable, grounding, high-voltage cable,
IEEE 575™, medium-voltage cable, power cable, sheath, sheath bonding, sheath voltage
limiters, shield, shield bonding, shield voltage limiters, single-point bonding, special bonding, SVL,
transmission cable
•
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Copyright © 2014 by The Institute of Electrical and Electronics Engineers, Inc.
All rights reserved. Published 18 September 2014. Printed in the United States of America.
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Abstract: The most common shield/sheath-bonding systems now in use on medium through
extra high-voltage (5 kV to 500 kV) single-conductor shielded power cables and the methods of
calculating the corresponding shield/sheath voltages and currents, when the cables are operated
as part of a three-phase system, with the neutral grounded directly or through an impedance, are
described in this guide.
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Updating of IEEE Standards documents
At the time this IEEE guide was completed, the C2 Cable System Bonding Working Group had the
following membership:
Michael D. Buckweitz, Chair
Thomas C. Champion, Vice Chair
Torben Aabo
Richard W. Allen, Jr.
Pierre Argaut
Ray Awad
Earle C. Bascom, III
Mohamed Chaaban
John H. Cooper
Dennis F. DeCosta
Swapan K. Dey
Anthony Ernst
William G. Hansen
Wolfgang B. Haverkamp
Dennis E. Johnson
Arthur J. Kroese
Frederic Lesur
Allen MacPhail
Neal K. Parker
Ray E. Saccany
William D. Wilkens
Jay A. Williams
The following members of the individual balloting committee voted on this guide. Balloters may have
voted for approval, disapproval, or abstention.
Saleman Alibhay
Senthil Kumar Asok Kumar
Peter Balma
Thomas Barnes
G. Bartok
Earle E. Bascom, III
Wallace Binder
William Bloethe
Kenneth Bow
Gustavo Brunello
William Bush
Mark Bushnell
William Byrd
John Cancelosi
Paul Cardinal
Weijen Chen
Robert Christman
Luis Coronado
Frank Di Guglielmo
Gary Donner
Randall Dotson
Dana Dufield
Donald Dunn
Gary Engmann
Cliff Erven
Dan Evans
Jorge Fernandez Daher
Rabiz Foda
David Garrett
David Gilmer
Edwin Goodwin
Todd Goyette
Randall Groves
Richard Harp
Timothy Hayden
Jeffrey Helzer
Steven Hensley
Lee Herron
Gary Heuston
Lauri Hiivala
Robert Hoerauf
Edward Jankowich
Dennis E. Johnson
A. Jones
Gael Kennedy
Yuri Khersonsky
Robert Kluge
Robert Konnik
Jim Kulchisky
Saumen Kundu
Chung-Yiu Lam
Michael Lauxman
Greg Luri
Glenn Luzzi
Arturo Maldonado
Michael Maytum
William McBride
Gary Michel
Daleep Mohla
Rachel Mosier
Jerry Murphy
Arun Narang
Dennis Neitzel
Arthur Neubauer
Michael Newman
Joe Nims
Gary Nissen
Lorraine Padden
Bansi Patel
vi
Copyright © 2014 IEEE. All rights reserved.
S. Patel
Percy Pool
Moises Ramos
Robert Resuali
Michael Roberts
Lei Rong
Thomas Rozek
Bartien Sayogo
Dennis Schlender
Hamid Sharifnia
Devki Sharma
Gil Shultz
Michael Smalley
Jerry Smith
John Spare
Nagu Srinivas
Gregory Stano
Ryan Stargel
Gary Stoedter
Peter Sutherland
David Tepen
Peter Tirinzoni
James Tomaseski
John Vergis
Mark Walton
Daniel Ward
Lee Welch
Yingli Wen
Kenneth White
Jonathan Woodworth
Jian Yu
Dawn Zhao
Tiebin Zhao
J. Zimnoch
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Participants
John Kulick, Chair
Jon Walter Rosdahl, Vice Chair
Richard H. Hulett, Past Chair
Konstantinos Karachalios, Secretary
Peter Balma
Farooq Bari
Ted Burse
Clint Chaplain
Stephen Dukes
Jean-Phillippe Faure
Gary Hoffman
Michael Janezic
Jeffrey Katz
Joseph L. Koepfinger*
David J. Law
Hung Ling
Oleg Logvinov
Ted Olsen
Glenn Parsons
Ron Peterson
Adrian Stephens
Peter Sutherland
Yatin Trivedi
Phil Winston
Don Wright
Yu Yuan
*Member Emeritus
Also included are the following nonvoting IEEE-SA Standards Board liaisons:
Richard DeBlasio, DOE Representative
Michael Janezic, NIST Representative
Don Messina
IEEE-SA Standards Technical Community
Malia Zaman
IEEE-SA Standards Technical Community
vii
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When the IEEE-SA Standards Board approved this guide on 12 June 2014, it had the following
membership:
This introduction is not part of IEEE Std 575™-2014, IEEE Guide for Bonding Shields and Sheaths of SingleConductor Power Cables Rated 5 kV through 500 kV.
This document is a revision of IEEE 575-1988, which had been reaffirmed multiple times without change
in years past. The current revision changes the document title to more appropriately reflect the intent of the
guide. Most clauses of the guide were revised and updated to better clarify recommendations and
procedures. Advances in computer technology now allow many of the equations to be programmed and
solved rapidly using software that can analyze the corresponding circuit configuration and make
recommendations for application of specialized bonding. Considerations for shield/sheath optimization
have been included in Clause 5. A major addition is Annex F, which provides new information on current
and voltage distribution on cable shields/sheaths in situations involving installations with multiple cables
per phase.
viii
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Introduction
1. Overview .................................................................................................................................................... 1
1.1 Scope ................................................................................................................................................... 1
1.2 Purpose ................................................................................................................................................ 2
2. Normative references.................................................................................................................................. 2
3. Definitions .................................................................................................................................................. 2
3.1 Special terms........................................................................................................................................ 5
4. Background ................................................................................................................................................ 5
5. Shield optimization ..................................................................................................................................... 6
6. Special bonding techniques ........................................................................................................................ 7
6.1 Design .................................................................................................................................................. 9
6.2 Safety considerations for specially bonded cable systems ................................................................. 10
6.3 Single-point bonding ......................................................................................................................... 10
6.4 Impedance-bonding methods ............................................................................................................. 14
6.5 Cross bonding .................................................................................................................................... 15
6.6 Sheath sectionalizing joints ............................................................................................................... 20
6.7 Choice of bonding system ................................................................................................................. 20
6.8 Sheath standing voltage ..................................................................................................................... 22
6.9 Transient voltage analysis.................................................................................................................. 23
7. Sheath voltage limiters ............................................................................................................................. 24
7.1 Introduction ....................................................................................................................................... 24
7.2 Nonlinear resistances ......................................................................................................................... 25
7.3 Nonlinear resistances in series with spark gap .................................................................................. 25
7.4 Spark gaps ......................................................................................................................................... 25
7.5 Selection of shield/sheath voltage limiters ........................................................................................ 26
7.6 Use of shield/sheath voltage limiters ................................................................................................. 29
8. Effect on parallel communication and control cables ............................................................................... 29
8.1 Coupling ............................................................................................................................................ 30
8.2 Shielding ............................................................................................................................................ 30
8.3 Common-mode and metallic voltages ............................................................................................... 30
Annex A (informative) Bibliography ........................................................................................................... 32
Annex B (informative) Discussion of early practices and problems ............................................................ 35
Annex C (informative) Current practice for shield/sheath standing voltages ............................................... 36
Annex D (informative) Calculation of induced voltages .............................................................................. 39
Annex E (informative) Transient voltages and voltage withstand requirements of protective jackets ......... 44
Annex F (informative) Current and voltage distribution on cable shields/sheaths with
multiple cables per phase......................................................................................................................... 53
ix
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Contents
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IMPORTANT NOTICE: IEEE Standards documents are not intended to ensure safety, security, health,
or environmental protection, or ensure against interference with or from other devices or networks.
Implementers of IEEE Standards documents are responsible for determining and complying with all
appropriate safety, security, environmental, health, and interference protection practices and all
applicable laws and regulations.
This IEEE document is made available for use subject to important notices and legal disclaimers.
These notices and disclaimers appear in all publications containing this document and may
be found under the heading “Important Notice” or “Important Notices and Disclaimers
Concerning IEEE Documents.” They can also be obtained on request from IEEE or viewed at
http://standards.ieee.org/IPR/disclaimers.html.
1. Overview
Large investment costs, generally associated with the installation of underground transmission circuits,
typically mandate optimizing cable operation from the standpoint of efficiency and power throughput
capacity. With the popularity of single-conductor cables and the use of low loss, high dielectric-strength
insulating materials and improved cable jackets in the mid-1960s, and their application at sub-transmission
and transmission voltages, there is significant interest in the use of single-conductor cables and the
problems of the induced voltages and currents associated with their use. Many of these problems (for
example, failure of shield/sheath insulators, failure of cable jackets, and shield/sheath corrosion) have been
recognized since metallic-sheathed cables were first used, and the fundamentals of calculating shield/sheath
voltages and currents have been defined for many years. However, increasingly, ampacity requirements and
short-circuit capabilities of modern power systems have accentuated some problems, while improvements
in shield/sheath insulations have virtually eliminated others.
Thus it is evident that there is a need for some guidelines whereby the cable engineer can select the
shield/sheath-bonding method that best fits the needs of a particular installation.
1.1 Scope
This guide describes the most common special shield/sheath-bonding systems now in use on high-voltage
single-conductor shielded power cables and the methods of calculating shield/sheath voltages and currents,
particularly as applied to three-phase systems operating at 60 kV and above, with the cable neutral
grounded directly or as part of a special bonding system as described in the guide.
1
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IEEE Guide for Bonding Shields and
Sheaths of Single-Conductor Power
Cables Rated 5 kV through 500 kV
Although special bonding has been used predominantly in the past on higher voltage cable systems, more
recent attention to shield and sheath losses on distribution class cables has prompted users to consider
special bonding on lower voltage class cable systems as well. This is particularly applicable on the collector
systems for wind farms, where long cable runs interconnect the individual wind turbines. While this guide
on induced voltages and currents in metallic shields and sheaths is written largely around high-voltage
cables operating at 60 kV and above, the fundamental principles in this document apply equally to singleconductor medium-voltage shielded power cables when installed and operated as outlined in this guide.
The user is cautioned to make sure that the installation/operating design does not contravene any local or
national regulations.
1.2 Purpose
The purpose of this guide is to provide the cable engineer with recommendations for consideration when
designing new power cable delivery systems as well as evaluating existing cable systems. This guide
addresses the reduction of cable operational losses and increase in cable current carrying capacity through
use of special cable bonding and grounding methods. The guide will also assist the user in calculating the
standing shield/sheath voltages for various bonding and grounding methods.
2. Normative references
The following referenced documents are indispensable for the application of this document (i.e., they must
be understood and used, so each referenced document is cited in text and its relationship to this document is
explained). For dated references, only the edition cited applies. For undated references, the latest edition of
the referenced document (including any amendments or corrigenda) applies.
AEIC CS9, Specification for Extruded Insulation Power Cables and their Accessories Rated above 46 kV
through 345 kV ac. 1
ANSI/ICEA S-108-720, Standard for Extruded Insulation Power Cables Rated above 46 kV through
345 kV. 2
ICEA Publication P-32-382, Short-Circuit Characteristics of Insulated Cables. 3
IEC 60287-1, Electric cables—Calculation of the current rating—Part 1: Current rating equations (100%
load factor) and calculation of losses. 4
3. Definitions
For the purposes of this document, the following terms and definitions apply. The IEEE Standards
Dictionary Online should be consulted for terms not defined in this clause. 5
1
AEIC publications are available from the Association of Edison Illuminating Companies (http://www.aeic.org/).
ANSI publications are available from the American National Standards Institute (http://www.ansi.org/).
3
ICEA publications are available from the Insulated Cable Engineers Association (http://www.icea.net/).
4
IEC publications are available from the International Electrotechnical Commission (http://www.iec.ch/). IEC publications are also
available in the United States from the American National Standards Institute (http://www.ansi.org/).
5
IEEE Standards Dictionary Online subscription is available at:
http://www.ieee.org/portal/innovate/products/standard/standards_dictionary.html.
2
2
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IEEE Std 575-2014
IEEE Guide for Bonding Shields and Sheaths of Single-Conductor Power Cables Rated 5 kV through 500 kV
bonding lead: The insulated conductor connecting the shield/sheath of a shielded cable segment to an
adjacent cable segment or bonding accessory for the purpose of providing a fault current path. A bonding
lead may connect the shield/sheath of a cable segment or cable accessory to: (1) the shield/sheath on
another cable segment, (2) a cable accessory, such as a joint casing, a termination bell, or a link box, or (3)
a grounding point, such as a grounding bus, a ground rod, or a ground continuity conductor (GCC).
continuous cross bonding: A form of cross bonding applicable to circuits consisting of at least four minor
sections in which the cable metallic shields/sheaths are successively cross-bonded at each junction between
adjacent minor sections throughout the cable route. At each end of the route the shields/sheaths are solidly
bonded and grounded.
cross bonding: The form of special bonding in which the metallic shields/sheaths of different phase cables
in successive minor sections are cross connected in such a way so as to attain partial or full cancellation of
induced currents on the metallic shields/sheaths.
flat formation: Three cables laid in one plane with normally equal spacing between adjacent cables.
ground continuity conductor (GCC): A conductor laid parallel and in close proximity to a cross-bonded
or single-point bonded cable circuit to provide a continuous metallic ground connection between the
grounding systems at the ends of the cable route and along the run.
impedance bonding: A bonding scheme in which an impedance, such as a reactor or a resistance, is
inserted into the shield/sheath current path for the purpose of limiting fault currents or load losses.
insulated shield/sheath system: A cable system in which the metallic shield/sheath of each cable is
individually insulated throughout its length except where any necessary grounding or inter-shield/sheath
connections are made.
joint sleeve insulation: The external insulation applied over the metallic sheath/shield of a cable joint.
link box: A box in which bonding and grounding connections are made through removable links. The box
may also contain shield/sheath voltage limiters.
major section: A set of consecutive minor cable sections between solidly bonded shields/sheaths that are
connected in such a way so as to minimize cable shield/sheath current losses on each phase cable. For
three-phase systems, three consecutive minor sections are required to form a major section to minimize
shield/sheath currents on all three phases.
minor section: The length of cable between shield/sheath sectionalizing insulators, and between sheath
insulators and sheath end-bells at the cable terminations.
multiple single-point bonding: The form of special bonding in which the three cable shields/sheaths are
solidly bonded and grounded to a ground continuity conductor (GCC) at one end of a section, and
connected to ground through shield/sheath voltage limiters at the other end; done at multiple locations
along a route.
power frequency: The operating frequency of the ac power cable system.
NOTE—The basic principles presented in this guide apply to 50 Hz and 60 Hz systems once appropriate adjustments of
constants are made. Examples in this guide assume either a 50 Hz or 60 Hz frequency as indicated. 6
6
Notes in text, tables, and figures of a standard are given for information only and do not contain requirements needed to implement
this standard.
3
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IEEE Std 575-2014
IEEE Guide for Bonding Shields and Sheaths of Single-Conductor Power Cables Rated 5 kV through 500 kV
screening conductor: A conductor laid in parallel with a current-carrying loop and itself forming part of a
closed circuit in which induced currents can flow whose magnetic field will oppose the field of the currentcarrying loop.
sectionalized cross bonding: The form of cross bonding in which three consecutive minor sections are
taken to form a single cross-bonded unit (see major section). The three shields/sheaths are solidly bonded
at both ends of a major section and may be grounded at these points. At the two intermediate positions the
cables are transposed and the shields/sheaths are interconnected in such a way so that each continuous
shield/sheath circuit through the major section occupies the same geometrical position in the cable
formation. For long cable routes there will usually be a number of major sections.
sheath: Historically the term implied an extruded lead sheath that provided a moisture impervious barrier
for the inner cable core while simultaneously providing the requisite metallic shielding for the cable. More
recently extruded aluminum sheathing and copper foil laminates have been employed in order to provide
moisture tightness.
sheath interrupt: A break or interruption, incorporated into the metallic shield/sheath and semiconducting
shield of a cable at a joint in order to provide electrical isolation between adjacent cable shield sections.
sheath sectionalizing insulator: An insulating member inserted into the joint and metallic joint casing (if
present) in order to electrically isolate the shields of adjacent cable lengths, of the same phase, from each
other; typically this insulating member is a ring made of epoxy or porcelain.
sheath sectionalizing joint: A joint in which the metallic screen and metallic casing, if present, are
electrically interrupted by means of a shield/sheath sectionalizing insulator.
sheath standing voltage: The voltage to ground appearing on the metallic shield/sheath of a specially
bonded cable when balanced full-load currents are flowing in the cable conductors; typically specified at
the point along the cable length at which it is a maximum (that is, at the ungrounded extremity of a minor
section in the case of single-point bonding and at a cross-bonding point in the case of cross bonding). When
the voltages differ for the three-phase cables, the highest value is typically specified.
sheath voltage limiter (SVL): A surge protective device connected between the metallic shield/sheath and
ground on specially bonded cables to limit shield/sheath overvoltages during system transients.
shield: A non-moisture impervious metallic outer conductor of single conductor power cables, such as
concentric wires and concentric copper tapes, that provide grounding and a fault current path for the cable.
shield/sheath: See 3.1.
single-point bonding: The form of special bonding in which the three cable shields/sheaths of a minor
section are solidly bonded together and grounded at one point only. For long cable routes this may be
repeated a number of times. See also: multiple single-point bonding.
solid bond: A metallic connection between shields/sheaths or between shields/sheaths and ground.
special bonding: Methods of bonding and grounding the metallic shields/sheaths of single-conductor
cables so as to minimize the shield/sheath circulating currents resulting from induction of conductor
currents.
transposition of power cables: The practice of laying single-conductor cables so that each phase cable
successively occupies, optimally over equal lengths of the route, each of the three geometric lay positions
in the formation.
4
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IEEE Guide for Bonding Shields and Sheaths of Single-Conductor Power Cables Rated 5 kV through 500 kV
transposition of the parallel ground continuity conductor (GCC): The practice of laying a parallel
ground conductor alongside a minor section of untransposed power cables so that the conductor occupies
over half of the section’s length one position and over the other half occupies a symmetrically opposite
position.
trefoil: The formation of three cables positioned so that the cable centers are equidistant (when viewed in
cross section, lines drawn through the cable centers form an equilateral triangle).
uniform major section: A section consisting of three similar uniform minor subsections having equal
lengths.
3.1 Special terms
shield/sheath: For the purpose of this guide and in order to simplify the discussion, the terms sheath and
shield, as used in the context of this document, are intended to refer to the metallic, electrically conducting
portion of the cable sheath or shield and as such both terms are used interchangeably when referring to the
outer conductor of a single conductor medium- or high-voltage power cable.
4. Background
Single conductor medium- and high-voltage power cables employ a coaxial design essentially consisting of
a metallic center conductor surrounded by insulation and an outer metallic shield or sheath (outer
conductor). Semiconducting layers are provided at the interface between the conductor and the insulation,
and between the insulation and the metallic shield or sheath in order to provide a smooth electrical interface
for the insulation and thus establish a uniform electrical stress pattern within the insulation. Cable core
conductors are normally comprised of aluminum or copper wires but can be of solid construction.
Present day cable insulation materials generally consist of impregnated paper, ethylene propylene rubber
(EPR), or cross-linked polyethylene (XLPE). The cables are constructed with an outer metallic shield or
sheath, which is primarily comprised of one of the following:

Concentrically applied copper wires, aluminum wires, or helically applied copper tapes

Extruded lead or aluminum sheathes

Longitudinally applied corrugated copper tapes sealed at the overlap

Longitudinally applied thin copper or aluminum foil laminates sealed at the overlap

Combination of wires with any of the above copper tapes
NOTE—Since this document deals primarily with the electrical aspects of shields and sheaths, and to simplify the
discussion, the cable metallic shields or sheaths will be referred to interchangeably as the shield or sheath unless
otherwise indicated.
Covering the metallic shield/sheath is normally an insulating jacket typically consisting of extruded
polyethylene (PE) or comparable electrically insulating jacketing material, which protects the underlying
metallic shield/sheath from electrolysis.
The magnetic field resulting from current flow through the core conductor couples the metallic
shield/sheath and any other adjacent conductors. If the shield is also part of a continuous closed loop
electric path, transformer action induces a current flow in the coupled shield/sheath and other adjacent
conductors. Resistive losses due to the circulating currents in the shield then contribute to the temperature
rise of the cable, limiting the amount of current that can be carried by the cable and reducing cable
5
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IEEE Std 575-2014
IEEE Guide for Bonding Shields and Sheaths of Single-Conductor Power Cables Rated 5 kV through 500 kV
efficiency. Conversely, if the electric path is interrupted through use of special bonding techniques, the
shield/sheath circulating currents will be reduced or eliminated resulting in greater loading capability for
the cable but at the disadvantage of developing a rise in shield/sheath voltage. Consequently, special
bonding and grounding arrangements have been developed to limit the magnitude of sheath voltages and to
minimize the flow of circulating currents.
To assure proper performance of specially bonded systems, the jacket’s electrical integrity should be
checked as part of factory testing and upon installation. To ensure that an adequate ground is available for
field testing of the cable jacket in the field, the outer surface of the jacket is either coated during
manufacture with a graphite coating or alternatively a semiconducting layer is extruded overall during
manufacture. Typical field practices include testing the jacket’s integrity by subjecting the jacket to a 10 kV
dc test for one minute as follows:
a)
After delivery and prior to installation
b)
Immediately after laying each cable length
c)
After cable jointing (splicing)
d)
As part of final commissioning of the circuit
e)
Periodically thereafter as part of a routine maintenance program as recommended by the
manufacturer
CAUTION
It is essential with specially bonded cable systems to ensure that all disconnecting links are properly
reconnected after completion of the jacket tests or any other related testing. Operation of cables with
shields/sheaths improperly connected (grounded) will often result in cable failure. To obviate this potential
risk, formal link box commissioning, inspection, certification, and
link box locking procedures should be established.
Safety and cost considerations often do not justify application of special bonding for cable operation below
transmission voltage class. Many distribution cable installations are also multipoint grounded because they
are installed in random lay with communication cables and the installations are governed by Accredited
Standards Committee C2-2012, National Electrical Safety Code® (NESC®) [B1] Rule 354D. 7 Conversely,
on higher voltage power cable systems that carry large bulk of power, it is often economical and practical
to employ special bonding in order to limit shield/sheath losses and thus maximize loading capability.
For distribution class cables, the metallic shield is for the most part normally installed multipoint solidly
grounded. This is due to safety concerns associated with making sure that all shield components of a
specially bounded distribution cable would remain effectively insulated in the field after installation/during
operation. The initial installation cost and additional maintenance associated with specially bonded
installations makes this option often also less economically attractive for distribution class feeders, which
have relatively lower power transfer requirements as compared to their transmission class counterpart. Thus
special bonding techniques may be justified in some instances on distribution class feeders once safety
aspects have been adequately addressed and the additional initial installation and subsequent maintenance
costs have been effectively considered.
5. Shield optimization
For distribution class cables, shield losses can sometimes be reduced by increasing the shield impedance
through a reduction of the metal content of the shield. However, this approach is generally limited by fault
current magnitude and duration requirements for the shield. The fault duration requirement will need to
7
The numbers in brackets correspond to those of the bibliography in Annex A.
6
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IEEE Guide for Bonding Shields and Sheaths of Single-Conductor Power Cables Rated 5 kV through 500 kV
consider any delay introduced by failure of the primary circuit protection and dependence on a backup
protection scheme. Cable designs typically specify a maximum temperature on the shield under this worstcase condition. The required amount of metal in the shield is then specified as a fraction of the crosssectional area of the core conductor. For example, the shield can be full, 1/2, 1/3, 1/6, or even 1/12 the
cross-sectional area of the core conductor. Designs with large surface areas compared to the volume of
metal allow for increased heat dissipation into surrounding materials through thermal conduction. Thin
corrugated shields tend to incorporate the highest shield to core conductor ratios because of the very large
surface area presented for the minimum amount of metal present. The design results in some of the highest
heat dissipation for the amount of metal included in the shield while reducing resistive losses by exhibiting
high impedance. The most commonly used shield configuration for distribution class cables is concentric
wires.
Incorporating an impervious moisture barrier into the design of a transmission class cable is an important
requirement. For this reason, transmission cables have historically employed tubular lead sheaths because
these could be readily extruded as a continuous, uninterrupted layer over the cable core while
simultaneously providing the requisite metallic shield. More recent moisture-tight designs have often
replaced lead with extruded corrugated aluminum sheaths and various combinations of corrugated and flat
copper tapes in conjunction with copper wires. Where extruded metallic sheaths are not part of the design,
metallic shields are supplemented with moisture-tight alternative polymeric and other designs in order to
assure the high degree of operational reliability required of a transmission cable. Balancing the choices
between designs, materials, electrical properties, and economics in the selection of the cable metallic
shields/sheaths is referred to as shield optimization.
In many early cable designs, the shield was exposed and in direct contact with the earth, water, mud, and
conduit. This resulted in corrosion problems caused by ac electrolysis, leading to shield damage. Early
efforts to limit such damage placed restriction on the maximum magnitude of shield/sheath voltage,
limiting these voltages to the range from about 12 V to 17 V. Newer cable designs generally include an
outer jacket that is insulating and the likelihood of corrosion is thus effectively eliminated as long as the
jacket remains intact. Since application of special bonding results in the build-up of significant voltage
levels on the shield during faults and other abnormal operating conditions, designs take advantage of the
state-of-the-art electrical insulating properties for the jacket to meet needed voltage withstand requirements.
A graphite coating or an outer semiconductive layer is usually applied over the jacket at the factory to
allow for testing of the jacket’s electrical integrity.
6. Special bonding techniques
With heavier loads on single conductor cable circuits, shield circulating current losses resulting from
multipoint solidly bonded and grounded systems can be excessive for the intended application. To mitigate
these losses, alternative shield grounding methods are available, and these are collectively referred to as
special bonding techniques. Because long circuits and high currents tend to be more common on
transmission class circuits, special bonding techniques tend to be more applicable on these types of circuits.
However, special bonding techniques can be applied on distribution circuits when operating conditions
dictate a reduction in circuit losses.
Shield losses also increase with the spacing between cables, particularly when multiple point grounded,
single-conductor cables are installed with wide spacing, such as when cables are placed in separate ducts or
when they are direct buried in spaced configurations. When cables are spaced apart, significantly higher
currents flow on the shield of solidly grounded systems, resulting in higher induced shield circulating
current losses. Increased spacing decreases the effects of mutual heating but increases the effect of
magnetic coupling and therefore, increases shield circulating current losses resulting in lower current
ratings. The purpose of special shield bonding is to eliminate or significantly reduce shield circulating
current losses on single-conductor cables.
7
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IEEE Guide for Bonding Shields and Sheaths of Single-Conductor Power Cables Rated 5 kV through 500 kV
Some special bonding options include the following:

Single-point bonding

Multiple single-point bonding

Impedance bonding

Sectionalized cross bonding

Continuous cross bonding
The simplest and most effective method of special shield bonding is single-point bonding, in which one end
of the circuit is grounded and the other end is isolated from ground. The maximum cable section length is
governed by the permissible shield standing voltage allowed at the isolated end. For typically permitted
shield voltage rise levels (i.e., no higher than about 200 V), this method is generally employed on line
lengths of up to about 2 km (1.2 mi).
For longer line lengths or when shield voltages become excessive due to very high fault currents, cross
bonding is generally preferred and is the most widely used form of special bonding. (Note, however, that
most ac submarine cable circuits are solidly bonded because it is not practical to install shield break
insulators along their run). The shields of cross-bonded cables are generally expected to be nominally at
ground potential, but specially bonded systems can have appreciable voltages with respect to ground, even
under normal load conditions. Under some circumstances, even solidly bonded and grounded shields can
develop voltages well above ground potential along the circuit run. With present day jacketing materials
and appropriate jacket thicknesses, some utilities have allowed shield standing voltages as high as 600 V
under normal operation on specially bonded transmission class cable systems. See Annex B for additional
information.
An alternative scheme that can be applied to long line lengths is multiple single-point bonding. Single-point
bonding should always employ a separate ground-return conductor, except for the case where a circuit is
installed totally within a station area having a ground grid that provides a low impedance return ground
path.
In all cases, special shield bonding designs must effectively address the following functions:

Provide grounding for the cable

Maintain a continuous fault-current return path either through the shield/sheath and/or a ground
continuity conductor (GCC)

Limit normal steady-state shield voltages to acceptable and safe levels

Significantly reduce or eliminate shield losses

Limit transient overvoltages to acceptable levels in combination with surge protective devices
To meet these requirements, special bonding techniques are used that divide the cable shield into a number
of sections along the cable run, using shield sectionalizing joints. The length of each section is determined
by the permissible shield voltage under normal and fault conditions. Shield sectionalizing is normally
accomplished at joint and termination locations where access to the shield is readily available. The ability
to site joints and terminations at a particular location affects the system shield voltages and currents that
will develop, and can affect the type of shield bonding selected. Complete suppression of circulating shield
currents may not always be possible because of practical limitations imposed on cable lengths by the
spacing of manholes and other access points. In these cases, it may be necessary to calculate the residual
shield currents and assess their effect on the cable rating.
8
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IEEE Guide for Bonding Shields and Sheaths of Single-Conductor Power Cables Rated 5 kV through 500 kV
Special bonding designs depend in part on the insulating properties of a cable jacket to withstand induced
voltages. Jackets for specially bonded cable systems typically incorporate an outer conductive layer, such
as a graphite coating, to allow periodic testing of the jacket integrity and thus assure proper in service
performance. However, the jacket is only part of the bonding system and proper design and coordination
with other components, such as shield interrupts, link boxes, and shield voltage limiters (SVLs) is
necessary in order to arrive at the proper design for a specially bonded system. The design and ratings of
these components is determined based on factors such as the following:

Maximum allowable magnitude of steady-state shield voltage

Maximum allowable magnitude of transient shield voltage under fault conditions

Dielectric breakdown voltage (puncture voltage) of the cable jacket under fault conditions

Flashover voltage of the shield joint insulator (shield interrupt) under fault conditions
6.1 Design
In the design of special sheath-bonding arrangements, consideration must be given to the following aspects:
a)
Cable sheaths on short transmission cable circuits and most distribution circuits are usually
expected to be nominally at ground potential. However, in a specially bonded system the
shields/sheaths can have appreciable voltages with respect to ground and shields/sheaths should
never be assumed to be at ground potential. Appropriate precautions must be taken to ensure that
personnel are aware of the potential hazard and proper safety procedures. Consideration should be
given to effective installation of appropriate barriers, warning devices, etc., as warranted by
expected shield/sheath voltages.
b)
Complete suppression of circulating shield/sheath currents may not always be possible because of
practical difficulties in the choice of cable lengths and cable spacing. It is then necessary to
calculate the residual sheath currents and assess their effect on the cable rating.
d)
The use of special bonding gives rise to sheath overvoltages during system transients and faults,
and the magnitudes of those overvoltages must be considered in the design of the cable system. For
higher voltage systems, a shield/sheath voltage limiter will be generally needed and in all cases
consideration must be given to the coordination of the jacket insulation levels, the voltages to
which the jacket will be subjected, and the characteristics of surge voltage protective devices.
e)
Failure of a part of the jacket or of a sheath voltage limiter (SVL) can result in excessive
shield/sheath currents and losses and cause overheating of the cables. Consideration must therefore
be given to the duty imposed on the shield/sheath voltage-limiting device and to the monitoring and
maintenance of the complete systems.
For single-conductor cable circuits carrying currents in excess of about 500 A, special bonding is often
economically desirable as the reduction in losses allows an appreciably smaller conductor size to be used.
Very often, employing special bonding will permit the use of a single cable per phase installation where,
otherwise, multiple cables per phase would be required with the use of solid bonding. There is no clear-cut
load level at which special bonding should be introduced and the extra cost of the larger conductor cable or
multiple cables per phase system needed for a solidly bonded system must be weighed against the cost of
the additional equipment and the maintenance cost arising from the greater complexity of a specially
bonded system.
The use of special bonding gives rise to high shield overvoltages during system transients and faults.
Failure of components employed in special bonding systems can result in significant shield currents and
losses leading to cable overheating. The magnitude of overvoltages must be considered during system
design and the protective capabilities of SVLs properly coordinated with the expected shield insulation
9
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IEEE Guide for Bonding Shields and Sheaths of Single-Conductor Power Cables Rated 5 kV through 500 kV
levels. Prudent circuit design requires that consideration be given to the duty imposed on the shieldvoltage-limiting device and to periodic monitoring and maintenance of the complete system during
operation
6.2 Safety considerations for specially bonded cable systems
WARNING
Potentially hazardous voltages can be present on the exposed portions of the metallic shields/sheaths of
high-voltage cables, the outer surface of conducting cable jackets, the conductor of bonding cables, the
conductor of grounding leads, across exposed shield/sheath interrupts, the SVLs, and various hardware
connections within the link boxes and other equipment connected to or associated with specially bonded
cable systems. Appropriate precautions must be taken to provide access control to these areas to ensure that
safety procedures are followed in order to protect both personnel and equipment.
Exposed portions of the metallic shield, sheath, bond cable, or other conductive connections in electrical
contact with the cable’s shield/sheath, or bond cable of a specially bonded cable system, should never be
assumed to be at ground potential. The allowable shield/sheath voltage at full load varies considerably
among utilities and among countries. The shield/sheath voltage will be significantly higher during system
transients and short circuit conditions. As a consequence, appropriate protection and precautions must be
taken to ensure that personnel who may come into contact with any of the above conductive components
are familiar with the design, take adequate protection against potentially related hazards, and follow proper
safety procedures.
6.3 Single-point bonding
The simplest form of special bonding consists in grounding the sheaths of the three cables at only one
common point (for all three cables) along the cable run. In these types of installations, a voltage is induced
on the sheath of the cable during operation, progressively increasing with distance away from the grounded
point and reaching a maximum at the farthest point away from the grounded end. The sheaths must
therefore be adequately insulated from ground by means of an effective insulating jacket. Since there is no
continuous closed loop electrical path for the shield/sheath, current does not flow longitudinally along the
shields/sheaths and shield circulating current losses are thus eliminated (sheath eddy losses will still be
present).
SVLs should always be used if the expected surge voltage level exceeds 75% of the BIL of the jacket or of
the shield/sheath sectionalizing insulator.
10
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IEEE Guide for Bonding Shields and Sheaths of Single-Conductor Power Cables Rated 5 kV through 500 kV
E (V/km); I = 1000 A
400
Outer cables of group
in flat formation
300
200
Cables in trefoil and center
cable of group in flat formation
100
f = 60 Hz
0
1
2
3
5
7
10
20
30
50
Ratio S/d
Figure 1 —Induced shield/sheath voltage gradient for a conductor current of 1000 A
6.3.1 Shield/sheath standing voltages
Values of sheath standing voltage can be found using Figure 1.
As an example, for a typical circuit having a conductor current I = 1000 A and S/d = 2
where
S
d
is the center-to-center cable spacing
is the mean sheath diameter
The shield/sheath voltage will be 103 V/km (166 V/mi) and 138 V/km (222 V/mi) for trefoil and flat
formations, respectively, under normal three-phase operation. It should be also recognized that the
shield/sheath voltages will be significantly higher during system transients and short circuit conditions.
6.3.2 Multiple lengths
When the circuit length is such that the sheath-standing voltage limitation is exceeded when the ground is
connected at one end of the circuit, the ground connection may be moved to some other location along the
circuit run, for example, the center of the length. The shield/sheath standing voltage on each of the two
sections thus formed is then correspondingly reduced. When the circuit is too long to be dealt with by this
means, it may be sectionalized by the use of shield/sheath sectionalizing joints (multiple single-point
bonding) so that the shield/sheath standing voltage for each minor section is within the limitation imposed.
6.3.3 Parallel ground continuity conductor
During a ground fault on the power system, the zero-sequence current carried by the cable conductors
returns by whatever external paths are available. Since a single-point, bonded cable shield/sheath is
grounded at one position only, it cannot, except in the case of a cable fault, carry any of the returning
current. This being so, unless some parallel external conductor is available or is provided to serve as an
alternative path, the return current can flow only by way of the ground itself. Because the resistivity of the
11
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IEEE Guide for Bonding Shields and Sheaths of Single-Conductor Power Cables Rated 5 kV through 500 kV
ground is very high compared with that of good conductors, the return current is widely diffused through
the ground and the mean effective depth of the current is hundreds of meters deep. Because the returning
current path is significantly remote from the cable, the voltage induced along parallel conductors, including
the cable shields/sheaths, tend to be very high.
Furthermore, in the absence of a parallel GCC, the occurrence of a ground fault in the immediate vicinity of
a cable could cause a major difference in potential to arise between the two ends of a cable system.
Depending to some extent on the particular design of the voltage limiters employed, hazards could then
ensue to personnel or equipment.
Accordingly, it is recommended that single-point bonded and multiple single-point bonded cable
installations be provided with a parallel GCC that is grounded at both ends of the route as shown in Figure
2. The spacing of this conductor from the cable circuit should be sufficiently close to limit the voltage rise
of the shield/sheath to an acceptable level during a single-phase fault. The size of this conductor must be
adequate to carry the full, expected fault current for the cable system.
Although a GCC is not required for cross-bonded systems since the cable shields/sheaths form an end-toend path for fault currents, many utilities, especially those in the U.S., do install GCCs to insure a solid
end-to-end conductor, and to give a low impedance connection point for grounding the shield/sheath
voltage limiters and cable shields/sheaths in vaults. Note that circulating currents can be induced in the
GCCs, especially in imbalanced cross-bonded systems, and the resulting losses should be considered when
calculating cable ampacity.
The parallel GCC is usually insulated so as to avoid any corrosion risk since it will be subjected to voltage
induction from the power cables in the same way as any other parallel conductor. To avoid circulating
currents and losses in this conductor, it is preferable, when the power cables are not transposed, to
transpose the parallel GCC as shown in Figure 2, using the methods described in Annex D, D.3.
Figure 2 —Transposition of parallel ground continuity conductor to reduce induced
shield/sheath voltages on power cables in flat or trefoil formation
12
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6.3.4 Circuit arrangements
The application of single-point bonding to single length circuits is shown in Figure 3 and to multiple length
circuits in Figure 4. These diagrams do not show the disconnecting boxes to permit testing of the
shield/sheath insulation.
(a) End-point bonding
(b) Midpoint Bonding
NOTE―Other patterns of ground conductor transposition may be used. See Annex D, D.4.
Figure 3 —Single-point bonding diagrams for circuits comprised of only one cable length
Figure 4 —Single-point bonding diagram for a circuit comprised of three cable lengths
13
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IEEE Guide for Bonding Shields and Sheaths of Single-Conductor Power Cables Rated 5 kV through 500 kV
6.4 Impedance-bonding methods
In impedance-bonding methods, the cable shield/sheath sections are bonded together in some manner
through an inserted impedance. This impedance can consist of simple reactors or of devices such as
saturable reactors and bonding transformers. In all these methods a certain amount of shield/sheath current
is permitted so as to reduce losses and shield/sheath voltages. To provide ground connections, the
impedance devices are typically designed with center taps or grounding points.
At one time resistors were used, however, in general, resistance bonding is not practical, since the resistors
have to be sized to take the fault currents and they are considered very large for high fault currents.
Although a partial suppression of induced shield/sheath voltages is obtained using impedance-bonding
methods, there are a number of disadvantages that limit the application of these methods. The principal
disadvantages are as follows:
a)
Additional vault space is required.
b)
The impedance devices are relatively expensive since they must be designed to withstand fault
currents.
c)
In normal operation, 3rd harmonics can be introduced into the shield/sheath, and these can cause
interference on nearby telephone lines.
d)
Stray direct currents entering through the grounding can cause saturation of the iron cores and upset
the operation of the reactors or transformers.
6.4.1 Description of transformer shield/sheath bonding for single-conductor cables
Another special shield/sheath bonding method to minimize induced shield/sheath currents is called
transformer shield/sheath bonding. In the transformer shield/sheath bonding method, both ends of each
cable shield/sheath are electrically connected to a three-phase shield/sheath bonding transformer as shown
in Figure 5.
MANHOLE
Sheath Interrupt
MANHOLE
Cable Sheath
Sheath Interrupt
Sheath Voltage Limiters
SBT
Local
Driven
Ground
SBT
SBT
Sheath Bonding
Transformers
SBT
Local
Driven
Ground
Figure 5 —Schematic of transformer shield/sheath bonding
The shield/sheath-bonding transformer is a specially wound transformer (Figure 6) that is electrically the
same as a zigzag grounding transformer. This type of transformer is designed to give a high impedance
between the three shield/sheath connections (A, B, and C) and ground (N) when the voltages applied to
terminals A, B, and C are balanced three-phase voltages. The shield/sheath bonding transformer has a low
14
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IEEE Guide for Bonding Shields and Sheaths of Single-Conductor Power Cables Rated 5 kV through 500 kV
impedance between any of the three shield/sheath bonding terminals (A, B, and C) and ground (N) if a
single-phase or zero sequence voltage is applied. In other words, the shield/sheath bonding transformer is a
high impedance to ground for positive sequence voltages and a low impedance to ground for zero sequence
voltages applied to the terminals A, B, and C.
A
B
C
N
Steel Core
Figure 6 —Schematic of shield/sheath bonding transformer
During normal cable operation the induced shield/sheath voltages on the three cable shields/sheaths are
approximately equal and 120 electrical degrees out of phase. Consequently, there is very little current that
flows through the cable shields/sheaths to ground via the shield/sheath bonding transformers. Single-lineto-ground fault conditions produce a zero sequence voltage that appears across the bonding transformer and
the fault flows to ground through relatively low impedance. The shield/sheath bonding transformers must
be designed so that they will not saturate as a result of induced shield/sheath voltages produced by normal
and short-term emergency operating currents.
The cable shields/sheaths are also connected to local ground by means of shield/sheath voltage limiters (see
Figure 5). The shield/sheath voltage limiters protect the cable jackets, shield/sheath interrupts, and the
shield/sheath bonding transformer from transient overvoltages.
The primary advantage of the shield/sheath bonding transformer scheme is that it is effective in limiting
induced shield/sheath currents regardless of whether or not the distances between cable vaults are equal or
unequal. The primary disadvantage of the shield/sheath bonding transformer scheme is that additional
space is required in the joint vaults to accommodate the additional components (compared to other special
shield/sheath bonding methods). The cost of the equipment for implementing transformer bonding is also
generally higher than single-point or cross-bonding schemes.
6.5 Cross bonding
6.5.1 Basic circuit arrangement
Cross bonding consists essentially in sectionalizing the shields/sheaths into minor sections and cross
connecting them so as to approximately neutralize the total induced voltage in three consecutive sections,
as shown in Figure 7.
With untransposed cables, as illustrated in Figure 7, it is impossible to achieve an exact balance of induced
shield/sheath voltages unless the cables are laid in trefoil. When, for the reasons given in Annex D, D.3, the
15
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IEEE Guide for Bonding Shields and Sheaths of Single-Conductor Power Cables Rated 5 kV through 500 kV
cable conductors are transposed at each joint position, the induced shield/sheath voltages will be
neutralized irrespective of cable formation provided the three minor sections are identical. Figure 8 shows
how this can be accomplished for a circuit consisting of three minor sections. The shields/sheaths are
bonded and grounded at both ends of the route. In this arrangement, the three minor sections together are
referred to as a major section.
Transposition is preferred in order to provide the best balance of the shield/sheath voltages. However,
practical difficulties that lie with transposing large and heavy high-voltage cables generally prevent these
from being installed in a transposed configuration.
Figure 7 —Cross-bonded cables without transposition
Figure 8 —Cross-bonded cables with transposition
6.5.2 Longer cable circuits
Cross bonding can be extended to longer cable circuits by the methods described in 6.5.3 through 6.5.7.
6.5.3 Sectionalized cross bonding
This cross-bonding system is often called Kirke-Searing bonding, although the system used by Searing and
Kirke [B45] did not involve transposition of cables. When the number of minor sections is divisible exactly
by three, the circuit can be arranged to consist of one or more major sections in series. At the junction of
two major sections and at the ends of the circuit, the shields/sheaths are bonded together and grounded,
although the grounds at the junctions of major sections will generally be only local ground rods and the
GCC if one is provided. (See Figure 9 in which each separate major section is connected as in Figure 8).
16
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IEEE Guide for Bonding Shields and Sheaths of Single-Conductor Power Cables Rated 5 kV through 500 kV
*
*
*
*
*
*
NOTE―Asterisk (*) indicates that these joints can be without shield/sheath sectionalizing insulators and may be
connected directly to the local ground.
Figure 9 —Sectionalized cross-bonded cable with three major sections
6.5.4 Modified sectionalized cross bonding
In this modified version of the sectionalized cross-bonding system, it is not necessary to have the number
of minor sections exactly divisible by three. Balanced voltage conditions within a given major section
consisting of four minor sections can be achieved by subdividing one minor section into two subsections, as
follows:
a)
One short length (or subsection) followed by two equal lengths (or minor sections) with another
short length (or subsection) completing the major section; the combined length of the two
subsections should be equal to the length of one minor section as shown on Figure 10 and
Figure 11.
b)
One short length (or subsection) followed by one longer length (or minor section) then another
short length (or subsection) followed by one longer length (or minor section) to complete the major
section; the two longer lengths (or minor sections) should be equal and the combined length of the
two subsections should be equal to the length of one minor section as shown on Figure 12 and
Figure 13. In this case, the first cross bonding must be reversed.
17
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IEEE Guide for Bonding Shields and Sheaths of Single-Conductor Power Cables Rated 5 kV through 500 kV
L1 and L2 = Length of subsections
L = Length of minor sections
L1 + L 2 = L
Figure 10 —Modified sectionalized cross-bonding type without transpositions
L1 and L2 = Length of subsections
L = Length of minor sections
L1 + L 2 = L
Figure 11 —Modified sectionalized cross-bonding type with transpositions
L1 and L2 = Length of subsections
L = Length of minor sections
L1 + L 2 = L
Figure 12 —Modified sectionalized cross-bonding type without transpositions
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IEEE Guide for Bonding Shields and Sheaths of Single-Conductor Power Cables Rated 5 kV through 500 kV
L1 and L2 = Length of subsections
L = Length of minor sections
L1 + L 2 = L
Figure 13 —Modified sectionalized cross-bonding type with transpositions
6.5.5 Continuous cross bonding
In this system the shields/sheaths are cross-bonded at the end of each minor section throughout the whole
cable route. The three shields/sheaths are bonded and grounded at the two ends of the route only, as shown
in Figure 14. It is again generally desirable that the cables are transposed so that each conductor occupies
each of the three positions for one third of the total length. The number of matched minor sections should
preferably be exactly divisible by three, but this becomes less important as the total number of minor
sections increases (see 6.5.7).
Figure 14 —Continuous cross bonding
6.5.6 Mixed systems
When the number of minor sections is not exactly divisible by three, the system can consist of a mixture of
Kirke-Searing (regular and modified) and single-point bonded lengths. When necessary, on account of a
large number of minor sections having unequal lengths, the cross bonding can be of the continuous type.
Figure 15 shows the arrangement of a final single-point bonded length at the end of a cross-bonded system.
19
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Figure 15 —Termination of cross-bonded system with single-point bonded length
6.5.7 Imbalanced systems
It is not generally possible to divide the route length into exactly matched minor section lengths, nor is it
always possible to maintain a constant spacing of the cables throughout the route. In continuous crossbonded systems, it may also be desirable to have a total number of minor sections not exactly divisible by
three. In practical systems, there is therefore generally some imbalance, and it may be necessary to
calculate the circulating shield/sheath currents that are present so as to assess their effect on the cable
rating. See IEC 60287-1, Kuwahara and Doench [B32], and Annex D for methods of calculation. 8
6.6 Sheath sectionalizing joints
When the shield/sheath losses of single-conductor cables must be reduced or eliminated, shield/sheath
sectionalizing joints are required for interrupting the electrical continuity of the shield/sheath circuit. To
perform their function satisfactorily there are several major factors involved in the design of these joints.
Mechanically, they must be rugged, impervious to moisture, and fluid tight under all operating conditions.
Electrically, they must be designed to withstand the voltage stresses occurring under fault, lightning, and
switching surge conditions or be effectively protected by suitable surge protective devices. This subject is
discussed in more detail in Annex C.
6.7 Choice of bonding system
Impedance bonding methods are generally considered less satisfactory than the other methods described.
For this reason these methods are not recommended for general use.
Bonding transformers can be economical in some isolated cases such as when:
8
a)
Suitable balancing for cross bonding is impossible and single-point bonding is unacceptable (that
is, no empty duct is available for a GCC).
b)
A spare cable (a fourth cable for a single circuit or a seventh cable for a double circuit) is installed;
in this case, reconnecting the cross bonding whenever the spare cable is needed is a lengthy and
complex operation, whereas reconnecting of bonding transformers is simple and straightforward.
Information on references can be found in Clause 2.
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IEEE Guide for Bonding Shields and Sheaths of Single-Conductor Power Cables Rated 5 kV through 500 kV
Users of this method may refer to 6.4.1 and Halperin, Clem, and Miller [B23], Halperin and Miller [B24],
Watson and Erven [B47], Wollaston and Kidd [B49], and Report No. 55-286 [B39].
Further discussion will therefore be limited to consideration of the other bonding methods.
6.7.1 Use of single-point bonding
A minimum of three minor sections is needed to form a cross-bonded system. Hence, cross bonding is not
applicable to cable circuits comprised of only one or two lengths of cable, and for such circuits, singlepoint bonding would be employed unless it were feasible to reconfigure the circuit into three minor
sections.
For longer cable systems, multiple single-point bonding can also be employed in lieu of cross bonding.
This is especially useful when a spare cable is installed in addition to the phase cables (a fourth cable in the
case of a single circuit or a seventh cable in for a double circuit line), or where the section lengths are very
unequal.
6.7.2 Advantages of cross bonding
Although the cable shields/sheaths of a single-point bonded system are generally of a cross-sectional area
and conductivity that makes them quite capable of carrying short-circuit currents due to through faults in
the power system, they are unable to do so because they are grounded at one point only. A parallel GCC is
therefore recommended (see 6.3.3), and this adds appreciably to the cost of the cable system.
The principal advantage of cross bonding is that, while induced shield/sheath currents are inhibited during
normal balanced load operation, the shields/sheaths do form a continuous path from end to end of the cable
circuit and are grounded at both ends. Shield/sheath currents can, therefore, flow during ground faults, and
the necessity for the parallel GCC is removed. In addition to the economy achieved by the elimination of
the ground conductor, the cable shields/sheaths function more effectively as screening conductors during
ground faults than a parallel GCC. Hence, the voltages induced in parallel cables, communication lines,
pipe lines, fences, etc., are less during ground faults in a cross-bonded system than for a similar single-point
bonded system.
6.7.3 Choice of cross-bonded system
For long cable circuits, there is a choice between sectionalized cross bonding (see 6.5.3 and 6.5.4) and
continuous cross bonding (see 6.5.5). The relative advantages are as follows.
6.7.3.1 Advantages of sectionalized cross bonding
a)
Since each major section forms a separate electrical mesh, it is relatively straightforward to
calculate the shield/sheath currents when the lengths or spacing of the minor sections are not
uniform.
In a non-uniform section having an equilateral cable configuration, the ratio of shield/sheath loss
with cross bonding to that with solid bonding is given by Equation (1):
x
= [1 − 3(λ1λ2 + λ1λ3 + λ2 λ3 )]
y
(1)
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where
x
is cross-bonded loss
y
is solidly bonded loss
λ1, λ2, λ3 are per unit lengths of the three minor sections; that is: λ1+λ2+λ3=1
EXAMPLE: When λ1 = 0.4, λ2 = 0.2, λ3 =0.4, the loss with cross-bonded shields/sheaths is 4% of
the loss compared with solidly bonded shields/sheaths.
b)
The shield/sheath bond at the junction of each major section allows fault current due to a cable
failure to be distributed among the three shields/sheaths except within the major section containing
the fault.
c)
The shield/sheath bonds and grounds at the junction of major sections tend to reduce transient
shield/sheath voltages.
d)
The number of shield/sheath voltage limiters required is reduced.
e)
The shield/sheath bonds at the junction of major sections ensure that there will be no charging
current flow beyond the neutral points of the bonds irrespective of any inequality in the lengths of
the minor sections.
6.7.3.2 Advantages of continuous cross bonding
a)
The effects of non-uniform minor sections can be reduced when they form part of a total
shield/sheath circuit containing a number of sections. It may also be possible to use a total number
of sections not exactly divisible by three.
b)
It is possible to monitor shield/sheath currents throughout the whole circuit, irrespective of the
number of minor sections, at one point along the length.
c)
At least for low resistance faults, the monitoring of the shield/sheath insulation and shield/sheath
voltage limiters becomes easier because there are only two shield/sheath bonds and ground links to
be removed, even on a long circuit, to enable tests to be applied from the ends of the cable circuit.
6.8 Sheath standing voltage
6.8.1 Single-point bonding
Figure 1 shows the shield/sheath voltages per kilometer due to balanced loads in the cable conductors.
6.8.2 Sectionalized cross bonding
In a minor section, the shield/sheath standing voltage per kilometer will be as stated in Figure 1 and the
longest minor section should be taken for calculating the maximum standing voltage. With the modified
bonding method described in item a) in 6.5.4, the maximum standing voltage thus calculated is reduced as
much as 13% (see Annex D, D.4). This maximum reduction applies when the two short lengths (or
subsections) are equal (that is, L1 = L2 = 0.5L). See Figure 10 and Figure 11.
When the major section is non-uniform, the shield/sheath standing voltage can be taken as that calculated
for the longer of the two grounded minor section lengths. When the non-uniformity causes appreciable
shield/sheath current, there will be some reduction of the shield/sheath standing voltage.
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6.8.3 Continuous cross bonding
When the whole system between shield/sheath bonds consists of a number of uniform minor sections
exactly divisible by three and the cables are transposed so that each conductor occupies each of the three
positions for one third of the total length, then no shield/sheath current flows, and the maximum
shield/sheath standing voltages per kilometer for each section are as stated in Figure 1. In a practical system
having variable lengths of minor sections, the shield/sheath standing voltage can be taken as that calculated
for the longest minor section length. The shield/sheath standing voltages are reduced when appreciable
shield/sheath current flows.
6.8.4 Double-circuit systems
Where two closely spaced circuits are present, the shield/sheath standing voltages are modified by the
presence of the second circuit.
Because of the infinite variety of geometrical arrangements coupled with differences in individual cable
loading and phase rotation, a universal solution to shield/sheath standing voltages on multiple circuits
cannot be given here. Some of the more common double-circuit geometries are described in Kuwahara and
Doench [B32] and Simmons [B46].
A general solution requires the use of a digital computer and linear algebra. However, when discretion is
used in the selection of phase rotation and position, the effect of adjacent circuits does not significantly
increase standing voltages provided these circuits have equal or lower balanced phase currents.
A solution to a simple parallel double circuit is given in Annex D, D.2.4.
6.9 Transient voltage analysis
It is well known (Marti, Grainger, and Morched [B34] and Itoh, Nagaoka, and Ametiani [B29]) that
relatively high shield/sheath transient voltages can occur when transmission cable shields/sheaths are
single-point bonded or cross-bonded to minimize induced shield/sheath currents. A study by Ontario Hydro
(Erven and Ringler [B19]) reported that the shield/sheath to ground voltages at cross-bonding locations can
reach 20% of the magnitude of the incoming surge on the main conductors, while voltages across the
shield/sheath joint insulators can reach 40% the magnitude of the incoming surge. These transient
overvoltages are typically caused by the following:
a)
Lightning current impulses entering an underground cable system from overhead lines
b)
Fault conditions
c)
Switching transients, such as line energization
Sheath voltage limiters (SVLs) are commonly used to limit the voltage of the cable shields/sheaths during
transient overvoltage conditions; however, the amount of energy that the SVLs must dissipate increases
with lower protective levels and increased distances between SVLs.
The shield/sheath overvoltages are primarily the result of two factors. The first is the mutual coupling
among the cable phases that occurs when the magnetic flux created by one cable links the other cables in
the same trench. The second transient overvoltage phenomenon is caused by the discontinuity to traveling
waves presented by the shield/sheath interrupts. Traveling waves created by lightning, switching, and faults
reflect at the shield/sheath interrupts, resulting in superposition of the incident and reflected waves.
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IEEE Guide for Bonding Shields and Sheaths of Single-Conductor Power Cables Rated 5 kV through 500 kV
While it is possible to estimate the power frequency component of fault-current-initiated shield/sheath
overvoltages using methods described in the other sections of this guide, more sophisticated calculation
tools are required to accurately model transient shield/sheath voltages and to determine the amount of
energy that SVLs must dissipate due to high frequency (i.e., traveling wave) transients. Prior to the
development of computer simulation tools for power systems electrical transients, such as the
electromagnetic transients program (EMTP), it was common practice to make conservative assumptions
when specifying equipment for shield/sheath transient overvoltage protection for cross-bonded and singlepoint bonded cable systems (Dommel [B15]). However, with the trend to longer distances between SVLs
and increased standing voltage limits (Emin, Basak, and Ferguson [B17]), it is often necessary to perform
EMTP simulations to determine maximum overvoltages and SVL energy dissipation requirements (Erven
and Ringler [B19]).
In general, an electromagnetic transients computer program that is capable of modeling frequency
dependent effects (see Emin, Basak, and Ferguson [B17]) is required to accurately calculate energy
dissipation requirements of SVLs when special shield/sheath bonding methods are used.
7. Sheath voltage limiters
7.1 Introduction
Sheath voltage limiters (SVLs) have been developed to protect shield/sheath sectionalizing insulators and
cable jackets from flashovers or punctures caused by transient overvoltages typically associated with the
following:
a)
Lightning
b)
Switching surges
c)
Faults
The use of shield/sheath voltage limiters reduces the likelihood of failures for shield/sheath insulators and
cable jackets, which was a problem encountered in early installations that utilized special bonding
techniques.
The three main types of shield/sheath voltage limiters are as follows:
1)
Nonlinear resistances, such as metal oxide varistors (MOVs)
2)
Nonlinear resistances, such as silicone carbide (SiC) blocks, in series with spark gaps
3)
Spark gaps
The introduction of MOVs into shield/sheath voltage limiter applications offered a number of advantages
over older limiter designs incorporating SiC and/or spark gaps. MOV designs offer faster response to
transients, a more compact design, and better ac voltage withstand recovery following a transient. Because
of these characteristics, MOV based shield/sheath voltage limiters have rapidly displaced other designs.
Some limiter designs utilized commercially available metal oxide surge arresters in either a porcelain or
polymer housing or a specially designed housing containing MOVs.
Because shield/sheath voltage limiters and associated components can be installed in underground vaults or
other outdoor environment, and thus be exposed to weather, moisture, or flooding, these devices should be
protected by a suitable casing or encapsulation that permits continuous, proper operation under potentially
adverse conditions. Appropriate access control to the devices should be provided for periodic checks and
maintenance of the units.
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IEEE Guide for Bonding Shields and Sheaths of Single-Conductor Power Cables Rated 5 kV through 500 kV
7.2 Nonlinear resistances
Nonlinear resistances, such as MOVs, can provide good protection from transient voltages. MOVs exhibit a
conduction curve with a sharply defined knee that breaks the curve into two linear resistance segments.
Conduction current is very small below the knee as applied voltage rises. Once the knee is crossed, current
through the device rises rapidly for a small increase in applied voltage. This “voltage clamping” effect
shunts overvoltages through the device. MOVs do, however, have a limited capacity to absorb energy,
being a thermally limited device, and are not designed to carry the actual 50 Hz/60 Hz fault current. They
must be sized to withstand 60 Hz fault-current overvoltages due to system faults external to the cable
circuit, although they are not typically expected to survive overvoltages resulting from faults internal to the
cable circuit. The surge energy and 50 Hz/60 Hz voltages, to which the resistor is subjected, dictate the
required characteristics of the limiter. Distribution class arresters are often adequate for the surge energy
requirements when selected to withstand the power-frequency fault voltage without discharging.
Current solid-state SVLs employ for the most part metal oxide varistors zinc oxide (MOV-ZnO)
technology. The MOV provides continuous operation under applied service voltage and has negligible
power dissipation. Because MOV resistance below the operation threshold is very high, MOVs can allow
jacket testing without the need to physically disconnect the SVL. Care must be exercised to stay below the
temporary overvoltage capability of the MOV device to prevent damage during high-voltage diagnostic
testing.
Progress in the development of MOV-ZnO technology has essentially eliminated the use of other nonlinear resistance and spark gap type SVLs in favor of MOVs. Currently available compact MOV SVLs
have a high transient energy withstand capability (kJ/kV) and allow a direct connection of SVLs to the lead
of a sectionalized joint or base of termination with the other end directly connected to the GCC.
7.3 Nonlinear resistances in series with spark gap
Nonlinear resistance devices like SiC-based materials exhibit an approximately exponential conduction
curve without a sharp transition threshold. Consequently, the device may conduct considerable current at
normal operating voltages. To limit these energy losses, spark gaps should be inserted in series with the SiC
voltage limiter. The voltage flashover characteristics of the gap will control the initiation of conduction
while the SiC will provide the needed voltage recovery characteristics. In such designs, although the SiCbased limiter will spark over with a minimum of overvoltage on steeply rising waves, its response will be
slowed by the spark gap. The primary advantage of this approach is an improvement in voltage-withstand
performance under 50 Hz/ 60Hz overvoltage conditions but at the cost of a slower response for fast risetime transient overvoltages and the design should be carefully evaluated for the intended application. In
contrast, MOV voltage limiters based on ZnO technology have a sharply defined voltage transition
threshold and do not therefore require the use of a spark gap.
7.4 Spark gaps
The spark gap is the oldest and simplest of the three types of voltage limiters, and it has some
disadvantages. Spark gaps can be physically damaged by high 50 Hz/60 Hz currents following initial spark
over (metal vaporizes off the gap electrodes) and the gap response is slow, particularly to very steeply
rising transient overvoltages. If the gap length is increased so that 50 Hz/60 Hz fault-current voltages will
not maintain an arc, the protection level of the spark gap will be decrease, particularly for steeply rising
voltage waves. Some of the simplest spark gap designs incorporated two metal spheres separated by an air
gap. The spark gap flashover characteristics depend on the characteristics of the material within the air gap.
When the gap is in ambient air, outdoor pollution or changing moisture content in the air can change the
surge voltage withstand characteristics of the gap, which could cause flashover at normal operating
voltages. To minimize the problem, limiter gaps can be sealed through encapsulation.
25
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IEEE Guide for Bonding Shields and Sheaths of Single-Conductor Power Cables Rated 5 kV through 500 kV
A spark gap developed by Ontario Hydro (see Report No. 66-242 [B41]) is claimed to provide improved
surge protection reliability compared to a simple spark gap. The electrode arrangement of the spark gap
(referred to as a ring gap) is designed to cause a motoring action of the arc that eliminates serious erosion
of the electrodes. These spark gaps are capable of conducting arcs of high current densities without
deterioration of the electrodes, and are used for protecting cable shields/sheaths at the terminals on circuits
up to 10 km in length.
Spark gaps require periodic inspection and maintenance. Gaps should only be used to protect single-point
bonded circuits at the terminations, where the gap is readily accessible. Gaps should not be used in crossbonded systems where the gaps can be installed in underground boxes that are relatively inaccessible.
7.5 Selection of shield/sheath voltage limiters
In selecting a shield/sheath voltage limiter, the following criteria should be considered:
a)
The limiter should be suitable for continuous operation with an applied voltage equal to the
shield/sheath standing voltage under either normal or emergency loads (6.9).
b)
The surge voltage limiter must be designed to dissipate the energy associated with the transient
overvoltages impressed upon it.
c)
The limiter and the shield/sheath joint insulator must be able to withstand the 50 Hz/60 Hz
overvoltages resulting from system faults, including external cable faults. Caution should be used in
the selection of nonlinear resistance-type limiters to ensure that they can handle
50 Hz/60 Hz induced overvoltages as discussed in 7.2 (see Annex D).
d)
For nonlinear resistance-type (MOV) limiters, a maximum time should be specified for the duration
of the 50 Hz/60 Hz overvoltage resulting from fault currents external to the cable. In order to allow
for breaker reclosure, the time typically considered is twice that of the maximum fault clearing time
of the system.
e)
When calculating 50 Hz/60 Hz voltages appearing across shield/sheath voltage limiters, allowance
should be made for the limiters that are star or delta connected.
A nonlinear resistance-type limiter should be able to absorb, without damage, the energy dissipated due to
switching, including switching associated with a fault external to the cable circuit. Experience and
calculations indicate that the energy dissipated in the nonlinear resistances due to switching is not an
important design criterion for typical cross-bonded circuits. However, for long single-point bonded circuits
or lengths of single-point bonded cable that terminates long circuits, the switching surge energy can be
important, and calculations should be made for these cases (see EPRI Project RP-7893-1 [B18], Buller
[B9], and Hassler, Potter, Reid, and Secrest [B25]). The calculations should be performed using a
computer, since manual methods cannot readily be used because of the presence of the nonlinear circuit
element. Typical switching transient waveshapes should be assumed. See Ball and Occhini [B6], Ball,
Occhini, and Luoni [B7], Clark and Shanklin [B13], Haga and Kusano [B22], Halperin, Clem, and Miller
[B23], Kuwahara and Doench [B32], Ogorodnikov [B36], Watson and Erven [B47], Report No. 66-242
[B41], Report No. 55-286 [B39], and Report No. 62-78 [B40].
7.5.1 Link boxes
7.5.1.1 Introduction
In order to facilitate the installation, protection, and connection of SVLs, various outer coverings or
housings are available. At present the following options are predominantly used to protect or house SVLs
and connection links:
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a)
b)
Heat shrinkable tubing
Box-type enclosures (fiberglass, stainless steel, or non-corroding cast iron)
One of the principal features of link boxes is that these can be provided with a water tight seal. The degree
of water tightness can be specified based on external water pressure requirements according to NEMA
Type 4X or IEC 60059 (IP Class). Link boxes are expected to be corrosion resistant and match different
installation requirements such as pole or gantry mounting, placement in vaults or shallow pits, or at times to
be even direct buried. AEIC CS9 also provides some guidance on the selection of link boxes.
7.5.1.2 Heat shrinkable insulation housing
This provides one of the simplest and effective means of moisture protection. An adhesive coated heat
shrinkable polymeric sleeve seals the MOV and insulated ground cable(s) to protect the SVL and cable
connections from the elements.
7.5.1.3 Box-type enclosures
A box-type enclosure can house the SVL(s), copper links, ground cable terminals, and cable entry sockets.
The enclosure may be constructed of fiberglass, stainless steel, or non-corroding cast iron. The cable entry
should be designed to accommodate either coaxial insulated cable lead connections or single-conductor
insulated cables as required. All mechanical box fasteners should be made of stainless steel to alleviate
potential corrosion problems. The cable lead entry socket seals and lugs should be watertight and sealed at
the transition between the lug barrel and the core insulation. In addition to the cable entry socket seals, it is
essential that the cable lugs be watertight and sealed at the transition between the lug barrel and core
insulation. Water tight seals should be tested to a maximum external pressure of 100 kPa (14.5 psig). When
appropriately designed, the enclosure can be direct buried or located inside an underground vault or
concrete pit for mechanical protection and subsequent accessibility. Metal box enclosures may be installed
on a gantry or pole since these provide a more durable and vandal resistant enclosure than fiberglass. The
design of the enclosure should also incorporate an interlock system that provides entry only with an
appropriate tool/key to prevent inadvertent or improper connection settings.
Hazardous voltage can be present within the SVL enclosure. It is, therefore, important to follow appropriate
safety procedures to protect personnel accessing the enclosure.
7.5.2 Bonding leads
Connection between SVLs and the shield/sheath of a power cable requires proper insulation coordination,
taking into account insulation withstand of bonding leads, shields/sheaths, insulators, and the protective
level of the shield/sheath voltage limiters. In general, it is desirable to keep bonding lead lengths as short as
possible to provide proper protection against steep fronted overvoltages. Bonding leads should preferably
use a low surge impedance coaxial cable design. When the use of coaxial leads is impractical due to
equipment or other physical constraints, the following guidelines are suggested as a means of limiting surge
protection:
a)
For lead lengths of up to 3 m (10 ft), non-twisted pair of single-conductor cables can generally be
employed without too much protection compromise.
b)
For bonding lead lengths of between 3 m to 10 m (10 ft to 33 ft), use of twisted pair of singleconductor cables may be employed. Alternatively, when twisting is impractical, paralleling of leads
with periodic ties to keep leads in close proximity to one another as much as possible should be
employed.
27
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IEEE Guide for Bonding Shields and Sheaths of Single-Conductor Power Cables Rated 5 kV through 500 kV
c)
For bonding lead lengths of between 10 m to 15 m (33 ft to 49 ft), coaxial designs are strongly
suggested.
d)
Bonding lead lengths greater than 15 m (49 ft) should be avoided.
Bonding leads should be as a minimum insulated as 600 V class cables and sized based on fault current
duty. ICEA Publication P-32-382 provides a method for determining conductor size as a function of short
circuit rating requirements. AEIC CS9 also provides some general guidance on the selection of bonding
leads.
For lower impedance and faster transient response, the bonding lead constructions in Table 1 are suggested.
Table 1 ―Recommended bonding lead constructions
Single-conductor bonding cable
Coaxial bonding cable
Size of inner
XLPE/EPR/PVC
and outer Cu
insulation thickness
conductor
Inner layer
Outer layer
(Size of each)
(mm/mils)
(mm/mils)
(kcmil)
Copper
conductor
size
(kcmil)
XLPE/EPR/PVC
insulation
thickness
(mm/mils)
69
115 to 138
161 to 230
4/0
500
750
3.3/130
3.3/130
3.3/130
4/0
500
750
4.4/175
4.4/175
4.4/175
3.3/130
3.3/130
3.3/130
345 to 500
1000
3.3/130
1000
6.6/260
3.3/130
System kV
The bonding cable insulation material(s) should be UV resistant and if feasible, the outer most layer of the
coaxial design as well as that of the single-conductor cable should preferably be coated with a
semiconducting layer of graphite or an extruded semiconducting polymeric layer in order to facilitate field
testing.
The minimum recommended Basic Impulse Level (BIL) withstand of shield/sheath interrupts is as shown
in Table 2.
Table 2 ―BIL withstand for shield/sheath interrupts
BIL withstand of joint shield interrupts
Peak kV of 1.2 × 50 μs wave
System kV
Across halves
Each half to ground
69 to 138
161 to 230
60
80
30
40
345 to 500
120
60
7.5.3 Power cable jackets
From an electrical standpoint, the principal function of the power cable jacket on a specially bonded cable
system is to electrically isolate the cable shield/sheath from ground. Depending on the system design,
sustained voltage levels comparable to those seen on secondary cables can be realized on the metallic
shield during normal operation and transient voltage levels in the 100 kV range and higher can be attained
during lightning, switching, or fault conditions. These voltages can result from a local ground potential rise
relative to a remote ground and may not be limited by surge protective devices depending on the circuit
configuration. Under some conditions, a back flash can occur from the surrounding earth to the remotely
grounded cable shield/sheath, leading to a puncture of the jacket material. Consequently, the jacket
electrical insulating integrity needs to be checked periodically in order to assure operational reliability.
28
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To achieve a reasonable likelihood for maintaining jacket integrity, an extruded layer of insulating grade
polyethylene (PE), polyvinylchloride (PVC) or equivalent jacketing material is typically provided over the
metallic shield/sheath in accordance with ANSI/ICEA S-108-720. The jacketing material needs to possess
the appropriate dimensional and physical characteristics for the intended application and should be UV
resistant. An insulating jacket should also preferably be coated with a semiconducting layer of graphite or
an extruded semiconducting polymeric layer in order to facilitate electrical field testing of the jacket prior
to and after installation, and periodically thereafter.
7.6 Use of shield/sheath voltage limiters
7.6.1 Single-point bonded cables
SVLs are connected between the non-solidly-grounded end of the power cable shield/sheath and ground. A
separate limiter is connected to the cable shield/sheath at the base of each non-solidly-grounded cable
termination or non-solidly-grounded side of a joint shield interrupt with the opposite cable end or side of a
shield interrupt being solidly grounded. Generally, the end of the cable circuit that is liable to be subjected
to the higher incoming transient voltages, due to lightning or switching, should be grounded. However,
when the ground resistance is very much lower at one end, it is preferable to ground the shield/sheath at
that end instead. It may also be preferable to install the shield/sheath voltage limiter inside a substation or
other protected location, since there is some risk of explosive failure of the limiter. In any case, sheath joint
insulator, cross-bonding location, or surge voltage limiter should not be accessible to the public due to
safety considerations.
7.6.2 Cross-bonded systems
In direct-buried installations, cross-bonding connections are made with links in surface link boxes, so that
individual cable shields/sheaths can readily be isolated for voltage testing of cable jackets. The
shield/sheath voltage limiters are then located in or adjacent to the link boxes so that maintenance is
possible by removing the link box cover. In these installations, the connections between the buried joint
and the link box may be as long as 10 m (33 ft) but should not exceed 15 m (49 ft). Remote placement of
the link box decreases the effectiveness of surge protection on the shield/sheath because lead lengths
become longer and introduce additional voltage drop between the shield/sheath of the power cable and the
surge voltage limiter. This can introduce sufficient voltage drop to limit the effectiveness of the SVL and
cause shield/sheath sectionalizing insulator failure or cable jacket puncture. Bonding leads should be of the
low surge-impedance coaxial cable type and as short as possible to minimize the effect of the connections
on the efficiency of the shield/sheath voltage limiters. The bond leads must be capable of carrying the
system short-circuit currents.
In tunnels or other installations where the joints are in vaults, the shield/sheath voltage limiters should be
connected across the shield/sheath sectionalizing insulators with relatively short leads whenever feasible.
The cross-bonding leads should also be as short as possible to minimize the effect of frontal wave surges,
and the conductor cross section must be adequate to carry system short-circuit currents.
8. Effect on parallel communication and control cables
Power cables can inductively influence the currents and voltages on the shields/sheaths of communication
and control cables when these are located in close proximity to power cables, even when special bonding
methods are applied. The magnitude of voltages and currents induced in communication and control cables
can be evaluated as described in Annex D. Annex D, D.3, provides guidelines for use in reducing such
29
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IEEE Guide for Bonding Shields and Sheaths of Single-Conductor Power Cables Rated 5 kV through 500 kV
interference based on optimization by transposition of circuit geometry. Some additional factors
influencing coupled interference are briefly examined in the following subclauses.
8.1 Coupling
The coupling of the power circuit to the communication and control circuit is evaluated in terms of the
mutual impedance. Residual or zero-sequence components of the power circuit often have a ground return
(that is, overhead lines). The induced currents in the communication and control cable shield/sheath also
return through the ground. Although most of the zero-sequence components of buried power cable typically
return through the shield/sheath or separate neutral conductor, some portion can return through the ground.
These factors introduce uncertainties in the calculations of the mutual impedance, which can, however, be
calculated with reasonable accuracy using Carson’s equation (see Carson [B10]). Since the magnitude of
the ground return current has a relatively large effect on the mutual impedance, the approximation that all
zero-sequence current returns through the shield/sheath cannot be made.
While the coupling of the fundamental power frequency under steady-state balanced conditions can be
minimized by suitable transposition, odd triple harmonics (3rd, 9th, 15th, etc.) can be present that add in
phase, and therefore, are not neutralized by circuit geometry.
8.2 Shielding
The design of the communication and control cable shield/sheath and other outer coverings is a
fundamental factor in the reduction of the voltage induced in the communication and control cable pairs.
The reduction factor (often referred to as shielding factor) is defined as the ratio of the induced
electromotive force (emf) between the cable conductors and ground to the longitudinal emf that is induced
when metallic cable coverings are absent. It can be expressed (where nonmagnetic materials are used) as
shown in Equation (2).
ru =
R
R 2 + (ωLe )
(2)
2
where
ru
R
ω
Le
is the reduction factor of the communication cable
is the dc resistance of the grounded metallic cable coverings including the ground resistances,
Ω/km
is the angular frequency = 2πf
is the inductance of the ground circuit, H/km (approximately 2 mH/km)
From Equation (2), it can be seen that the induced longitudinal or common mode voltage on the enclosed
pairs of the cable is equal to the IR drop in the shield/sheath ground circuit, including the grounding
resistances. It is, therefore, fundamental to provide low-resistance grounds. The use of magnetic materials
for outer coverings improves the shielding efficiency substantially, unless the magnetic field strength
results in saturation.
8.3 Common-mode and metallic voltages
The common mode voltage or longitudinal voltage is the voltage between the cable pairs and ground. It is
the prime consideration relative to connected equipment or personnel hazards and is of prime significance
during faults in the power system. The so called metallic voltage is the voltage between the two wires of a
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pair and is manifested by pair to ground imbalance that converts the longitudinal voltage to a transverse
voltage. It is associated with noise introduced into the communication circuit. When the affected pair is
used in a protective circuit for power circuit relaying, false tripping of a protected power circuit can occur.
Objectionable audio noise can be introduced into voice frequency circuits at quite low field strengths by
power frequency harmonics. Similarly, disruptive signals can be introduced onto control cables by these
same harmonics.
The audio effect is the consequence of the response of the human ear, the sensitivity of which increases
rapidly from 50 Hz/60 Hz to 1000 Hz.
It becomes evident that the inductive effects on parallel telephone and control cables are dependent on
many factors, including circuit geometries, mutual impedance, frequency, ground resistivity, shield factors,
wave shape, design of connected equipment, and the like. Quantitative estimations are facilitated by
computer. In unusual situations, where established practice is not applicable, verification by field tests may
be required (see Klewe [B31] and Wollaston and Kidd [B49]).
31
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Annex A
(informative)
Bibliography
Bibliographical references are resources that provide additional or helpful material but do not need to be
understood or used to implement this standard. Reference to these resources is made for informational use
only.
[B1] Accredited Standards Committee C2-2012, National Electrical Safety Code® (NESC®). 9, 10
[B2] Adamson, C., Taha, H., and Wedepohl, L. M., “Comparative Steady-State Performance of CrossBonded Cable Systems,” Proceedings IEEE, vol. 115, no. 8, pp. 1147–1156, August 1968.
[B3] Adamson, C., Taha, H., and Wedepohl, L. M., “Determination of the Open-Circuit Sheath Voltages
of Cable Systems,” Proceedings IEEE, vol. 115, no. 8, pp. 1137–1146, August 1968.
[B4] Arnold, A. H., “The Impedances of a Three-Phase Line of Single-conductor Lead Covered Cables
Arranged in a Plane, with the Middle Cable Equidistant from the Two Outer Cables,” Journal IEEE,
vol. 67, pp. 90–96, 1929.
[B5] Arnold, A. H., “The Theory of Sheath Losses in Single-conductor Lead-Covered Cables,” Journal
IEEE, vol. 67, pp. 69–89, 1929.
[B6] Ball, E. H., and Occhini, E., “Overvoltages in the Sheaths of High-Voltage Cables Due to Special
Sheath Bonding Connections,” IEEE Winter Power Meeting, 1964.
[B7] Ball, E. H., Occhini, E., and Luoni, G., “Sheath Overvoltages in High-Voltage Cables Due to Special
Sheath Bonding Connections,” IEEE Transactions on Power Apparatus and Systems, vol. PAS-84,
pp. 974–988, 1965.
[B8] Berke, L. R., Geer, Jr., E. W., and Tucker, D. R., “Staged Fault Testing of Leased Audio-Tone
Relaying Channels Subject to Ground Potential Rise and Induced Voltage,” IEEE Transactions on Power
Apparatus and Systems, vol. PAS – 92, no. 1, pp. 89–97, Jan./Feb. 1973.
[B9] Buller, F. H., “A Technique for Calculating Inductance, Reactance, Impedance, and Sheath Voltage
of Single-Conductor Cable in Duct Banks,” General Electric Review, vol. 52, pp. 40–44, March 1949.
[B10] Carson, J. R., “Wave Propagation in Overhead Wires with Ground Return,” Bell System Technical
Journal, vol. 5, pp. 539–554, Oct. 1926.
[B11] Chaaban, M., “Calculation of Current Distribution and Sheath Losses in Cable Installation with
Several Cables per Phase,” Presentation at the ICC Spring Meeting, Colorado Springs, Colorado, May
2002.
[B12] Clark, D. J., and Seth, I. P., “Cross Bonding Single-Core Power Cables,” Electrical Review,
pp. 237–242, Feb 10, 1961.
[B13] Clark, W. S., and Shanklin, G. B., “High Tension Single-conductor Cables for Polyphase Systems,”
Transactions AIEE, vol. 38, p. 917, 1919.
[B14] “Design of Special Bonded Cable Systems,” Paper presented by Working Group 07 of Study
Committee No. 21, Electra, May 1973, pp. 55–81 and “Design of Specially Bonded Cable Circuits, Part II,
Second Report of Working Group 07 of Study Committee No. 21, Electra, no. 47, July 1976.
9
National Electrical Safety Code and NESC are registered trademarks and service marks of The Institute of Electrical and Electronics
Engineers, Inc.
10
The NESC is available from The Institute of Electrical and Electronics Engineers (http://standards.ieee.org/).
32
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IEEE Guide for Bonding Shields and Sheaths of Single-Conductor Power Cables Rated 5 kV through 500 kV
[B15] Dommel, H. W., “The EMTP Theory Book, Second Edition,” The University of British Columbia,
1994.
[B16] Dunsheath, P., “33 kV Cables with Metal-Sheathed Cores, with Special Reference to the S.I. Type,”
Journal IEEE, vol. 65, pp. 469–478, 1927.
[B17] Emin, Z., Basak, P. K., and Ferguson, C., “Simulation Studied to Improve Design for Mid-Life
275 kV Cable Refurbishment,” paper submitted to IEEE Aug. 2001.
[B18] EPRI Project RP-7893-l, Accessories for Specially Bonded Extruded Dielectric Transmission Cable
Systems, Electric Power Research Institute, Palo Alto, CA.
[B19] Erven, C. C., and Ringler, K. G., “Development of Improved Sheath Crossbonding Joint Protectors
for Self Contained Underground Cables,” Report for the Canadian Electrical Association, DEA No. 072 T
223, Ontario Hydro Research Division, 1986.
[B20] Fallou, M., “Application of Symmetrical Components to the Calculation of the Voltage Rise of
Metallic Single Core Cable Sheaths Due to Short Circuit from Phase-to-Ground,” General Electric, vol. 27,
no. 6, pp. 358–364, 1963.
[B21] Fisher, H. W., “Losses, Induced Volts and Amperes in Armor and Lead Cover of Cables,” AIEE
Transactions, vol. 29, Part II, pp. 747–767, 1989.
[B22] Haga, K and Kusano, T., “Surge Phenomena on the Sheaths of Cross-Bonded, Three-Phase Cable
Systems,” Journal Institute of Electrical Engineers of Japan, p. 1580, 1959.
[B23] Halperin, H., Clem, J. C., and Miller, K. W., “Transient Voltages on Bonded Cable Sheaths,” AIEE
Transactions, vol. 54, pp. 73–82, 1935.
[B24] Halperin H., and Miller, K. W., “Reduction of Sheath Losses in Single-Conductor Cables,” AIEE
Transactions, vol. 48, pp. 299–416, April 1929.
[B25] Hassler, S. P., et al., “M.O.V. Arrester Protection of Shield Interrupts, on 138 kV Extruded
Dielectric Cables,” IEEE Transactions on Power Apparatus and Systems, vol. PAS-103, pp. 3334–3341,
Nov. 1984.
[B26] Hassler, S. P., et al., “Shield Interrupt Overvoltages on 138 kV Extruded Dielectric Cables,” IEEE
Transactions on Power Apparatus and Systems, vol. PAS-103, pp. 3327–3333, Nov. 1984.
[B27] IEC 60287-1-3:2002, Electric cables, Calculation of the current rating, Part 1–3: Current rating
equations (100% load factor) and calculation of losses–Current sharing between parallel single-core cables
and calculation of circulating current losses.
[B28] “Induced Voltages in the Sheaths of Cross-Bonded AC Cables,” Proceedings IEEE, vol. 113, no. 12,
pp. 1990–1994, Dec. 1966.
[B29] Itoh, Y., Nagaoka, N., and Ametiani, A., “Transient Analysis of a Cross-bonded Cable System
Underneath a Bridge,” IEEE Transactions on Power Delivery, Vol. 5, No. 2, April 1950.
[B30] Kellam, B., Report No. 62-1, Problems and Experiences with Protective Jackets on Metal-Sheathed
Cables, Ontario Hydro Research Division, Toronto, Ontario, Canada.
[B31] Klewe, H. R. S., Interference between Power Systems and Telecommunication Lines, London,
Arnold, 1958.
[B32] Kuwahara, K., and Doench, C., “Evaluation of Power Frequency Sheath Currents and Voltages in
Single-conductor Cables for Various Sheath-Bonding Methods,” IEEE Transactions on Power Apparatus
and Systems, Special Supplement, Item 3784, pp. 206–235, 1963.
[B33] Lodwig, S. G., “Matrix Methods for Determining Voltages and Currents in Cross-bonded 138 kV
XLPE Transmission Circuits,” Minutes of the Insulated Conductor Committee, Charlotte, North Carolina,
May 1999.
[B34] Marti, L., Grainger, T. E., and Morched, A., “Sheath Overvoltages In HV Underground Cables,”
CIGRE Paper 33-201, 1996.
33
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[B35] Miller, K. W., “Sheath Currents, Sheath Losses, Induced Sheath Voltages and Apparent Conductor
Impedances of Metal-Sheathed Cables Carrying Alternating Currents,” Electric Engineering Thesis,
University of Illinois, 1929.
[B36] Ogorodnikov, V. E., “Surges on Metallic Cable Sheaths,” Canadian Electrical Association Winter
Meeting, Paper, Montreal, 1964.
[B37] Petty, K. A., “Calculation of Current Division in Parallel Single-Conductor, Power Cables for
Generating Station Applications,” Proceedings of the IEEE/PES 1989 Summer Meeting, Long Beach,
California, July 9–14, 1989.
[B38] Pirelli, High-voltage Cable Standards, Volume II, 1988.
[B39] Report No. 55-286, Cable Sheath Bonding Methods, Ontario Hydro Research Division, Toronto,
Ontario, Canada.
[B40] Report No. 62-78, Protection of Sheath Insulating Joints on High-Voltage Cable Circuits, Ontario
Hydro Research Division, Toronto, Ontario, Canada.
[B41] Report No. 66-242, A Spark Gap for Protection of Underground Cable Sheaths at the Terminal,
Ontario Hydro Research Division, Toronto, Ontario, Canada.
[B42] Rhodes, D. G., and Wright A., “Induced Voltages in the Sheaths of Cross-Bonded AC Cables,”
Proceedings IEEE, vol. 113 (1), pp. 99–110, 1966.
[B43] Riley, B. W., “Estimation of Voice Frequency Noise in Communication Circuits,” Proceedings of
the 19th International Wire and Cable Symposium, Atlantic City, pp. 144–154, Dec. 1970.
[B44] Schurig, O. R., Kuehni, H. P., and Buller, F. H., “Losses in Armored Conductor Lead Covered AC
Cables,” AIEE Transactions, vol. 48, pp. 417–435, April 1929.
[B45] Searing, H. R., and Kirke, W. B., “Reduction of Sheath Losses in Single-Conductor Cable,”
Electrical World, vol. 92, pp. 685–688, Oct. 6, 1928.
[B46] Simmons, D. M., “Calculation of Electrical Problems of Underground Cables,” The Electric Journal,
vol. 29, May-Nov. 1932.
[B47] Watson, W., and Erven, C. C., “Surge Potentials on Underground Cable Sheath and Joint
Insulation,” AIEE Transactions, pp. 239–249, June 1963.
[B48] Wedmore, G. B., Morgan, P. D., and Whitehead, S., “A Critical Study of a Three-Phase System of
Unarmored Single-Conductor Cables, from the Standpoint of the Power Losses, Line Constants, and
Interference with Communication Circuits,” Journal IEEE, vol. 67, pp. 359 – 434, 1929.
[B49] Wollaston, F. D., and Kidd, K. H., “Cable Sheath Jacket Requirements to Withstand Abnormal
Voltage Stresses,” AIEE Transactions on Power Apparatus and Systems, part III, pp. 1116–1123, Feb.
1962.
[B50] Woodland Jr. F., “Electrical Interference Aspects of Buried Electric Power and Telephone Lines,”
IEEE Transactions on Power Apparatus and Systems, vol. PAS-89, no. 2, pp. 275–280, Feb. 1970.
34
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Annex B
(informative)
Discussion of early practices and problems
Early self-contained cables were insulated with a combination of oil and paper and were constructed with a
metallic sheath, which acted both as a barrier to moisture ingress and as a return path for fault currents. The
most common sheathing material was lead, and outside of the U.S. these cables were frequently installed
with a protective jacket with the sheaths solidly grounded.
In North America, they were usually installed in ducts and underground vaults often without a protective
jacket. In Europe, particularly in Britain, cables were often armored and directly buried. Many of these
directly buried cables were protected with hessian wrappings and bituminous compounds. As a general
rule, power losses in the sheaths were recognized but accepted.
As system voltages and currents increased, these losses assumed a greater importance, and various methods
of reducing these losses were devised over the years from 1910 to the mid-1930s. Most of these methods
required the use of insulators inserted in the sheaths to break the sheath circuit into smaller electrical
sections.
Although these systems were reasonably successful, the sheath insulators were often a source of problems
because of leaks that permitted cable oils to leak out and moisture to penetrate the cables.
Because of factors, such as ac corrosion and personnel safety, and also because of a natural reluctance to
depart too far from the practice of solidly grounding the sheaths, a sheath voltage limit of approximately
12 V to 17 V seems to have been commonly adopted in the early days.
35
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Annex C
(informative)
Current practice for shield/sheath standing voltages
C.1 North American practice
C.1.1 United States
There are currently no generally accepted limits for maximum steady-state sheath standing voltage levels
used in the U.S. Through the late 1960s, limits of up to about 17 V were imposed on non-jacketed lead
sheathed cables in order to protect the bare lead against electrolytic corrosion. Subsequently when jacketed
cable designs were introduced, steady-state sheath voltage design limits were increased to
65 V to 90 V, although there has not been much evidence to substantiate this use in the past.
Due to the lack of maximum sheath voltage limits in industry standards, current practice in the U.S. varies
significantly among electric utilities. However, there has been a trend to increase the normal operating
condition sheath voltage limits during the past decade. Most single-conductor underground cable systems
with a length of greater than several thousand feet are designed with a maximum sheath voltage of 100 V to
200 V during normal operating conditions. Sheath voltages during emergency operating conditions are
generally limited to voltages of less than 275 V. However, at least one underground cable system was
designed with a maximum sheath voltage of 447 V during emergency operating conditions.
Some examples of current U.S. practices are as follows:
a)
A 138 kV XLPE cable system installed by one utility with cross-bonded sheath was designed for a
maximum induced sheath voltage of 202 V. The maximum sheath section length for this cable
system is 3035 ft and the rated current is 1400 A.
b)
A 120 kV XLPE cable system installed by another utility utilizes single-point bonding and was
designed for a maximum voltage during normal operating conditions of 163 V. The maximum
sheath voltage during emergency operating conditions can be as high as 447 V. The maximum
sheath section length for this cable system is 7279 ft. The maximum currents during normal and
emergency operating conditions are 510 A and 1400 A, respectively.
C.1.2 Canada
In Canada, practice varies from province to province. In their installations of underground low-pressure
fluid-filled (LPFF) cables, one utility utilizes the sectionalized cross-bonding method to minimize sheath
losses and also provide a low-impedance path for fault current. At all cross-bonded positions, 3 kV
lightning arresters were installed to minimize the effects of transient overvoltage on the sheath and joint
casing insulation.
Until about the 1990s, the practice was to limit sheath bonding and grounding arrangements such that the
standing sheath voltage at maximum load current did not exceed 100 V to ground at any point along the
cable.
In more recent years, with increased load current demands, longer circuit length installations, and present
day single-conductor high-voltage cable designs, the standing voltage levels are being designed to operate
in some instances with maximum standing voltages of up to 600 V. To ensure the system will adequately
36
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withstand anticipated transient overvoltages, the components on the circuit acted on by these overvoltages
are subjected to specified withstand levels with respect to ac and impulse voltages.
One utility has installed cross-bonded cable systems in the past without any sheath sectionalizing joint
insulator protection. However, some joint insulators failed in service, causing the system to be considered
unsatisfactory for use without some method of joint insulator protection. Subsequently, the utility adapted
the use of single-point bonding with ring gaps at the terminals. Standing sheath voltages of 300 V to 400 V
on emergency load were permitted at the terminals.
One rather unusual method of bonding had been successfully employed by another utility for cable routes
with unequal lengths between underground vaults and can be described as a modified sectionalized crossbonding scheme and described in detail in 6.5.4 of this guide.
C.2 Practices outside of North America
C.2.1 Great Britain
In Britain, cables have from very early days employed some form of outer jacket over the sheath. Initially
these were constructed by lapping various layers of self-vulcanizing rubbers and PVC in conjunction with
bitumen compounds in hessian tapes. Because these were electrically sound and of reasonable electrical
strength, it was judged that, even when special bonding came into vogue, there was little likelihood of
sheath voltages ever becoming high enough to puncture any form of anticorrosion jackets. Polyvinyl
chloride, polyethylene, and high-density polyethylene extruded jackets have replaced these more
complicated constructions.
Special bonding circuits were introduced into Britain in the late 1950s, at which time the maximum
standing sheath voltage was limited to 50 V for below ground applications and to 25 V at the terminations.
These maximum permissible levels were mandated by the central electricity generating board (CEGB) from
1959 to 1965, and subsequently increased to 65 V on cable sheaths in below ground installations. The
reason for selecting 50 V in the 1950s is not clear, but it was increased to 65 V because it was affecting
cable shipping lengths and increasing circuit installation costs.
The 65 V value is commonly used, except in special cases and in CEGB-owned tunnel installations. The
River Severn cable circuit, for example, operates with an induced sheath voltage of 100 V at full load along
the route, but the voltage on the sheath at the terminations is limited to 25 V.
C.2.2 Netherlands
In the Netherlands, a recognized limit on sheath voltages has not been agreed upon. The maximum sheath
voltage currently reported as being used in the Netherlands for 400 kV extruded dielectric cables with
polymeric cable jackets is 400 V.
C.2.3 France
In France, a value of 125 V was originally considered taking into account the risk of fatal contact but a
conservative value of 50 V was adopted as a first step. In 1987, some tests showed that a value of 200 V
would be acceptable even in the case of a sheath fault if protection devices were installed but with the
specific requirement that personnel avoid contact with any related cable system components that could
develop a voltage. In 1994 a maximum value of 400 V was permitted under normal operation but in
practice this limit is generally not reached due to other design considerations that include: typical length of
37
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elementary sections, load current design in the order of about 2000 A, and short-circuit current design
criteria of about 30 kA.
C.2.4 Norway
In Norway, a fixed voltage limit has not been agreed upon, but in practice a sheath voltage limit of 60 V is
used.
C.2.5 Italy
In Italy, a fixed voltage value has not been agreed upon, but exposed metal parts are typically limited to
approximately 25 V.
C.2.6 Japan
In Japan, designs typically employ standing voltages of up to 200 V.
C.2.7 Other countries
Table C.1―Shield/sheath standing voltage limits in some other countries
UAE/Dubai
132
Shield/sheath
voltage limit
(V)
65
UAE/Other locations
132
12
Country
Rated system voltage
(kV)
Oman
132
65
Saudi Arabia
132
100
Saudi Arabia
230 to 380
200
Turkey
154
150
Turkey
380
200
Kuwait
275
65
Kuwait
400
200
Singapore
66
60
Singapore
230
120
Australia
132
150
Australia
330
250
South Korea
154 to 345
100
38
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Annex D
(informative)
Calculation of induced voltages
D.1 Induced voltages—general
Any conductor p, lying parallel with a set of three conductors carrying balanced three-phase currents, will
have a voltage gradient Ep induced along its length, given by Equation (D.1):
1
 S ap S cp
E p = jωI b 2 × 10 −7  log e 
 S 2
2
 bp

(
)


 + j 3 log  S cp
e

2
 S ap


 V/m


(D.1)
where
Ib
ω
Sap
Sbp
Scp
is the rms current (A) in conductor b
is the angular frequency of the system (2πf)
is the axial spacing of the parallel conductor and phase a conductor
is the axial spacing of the parallel conductor and phase b conductor
is the axial spacing of the parallel conductor and phase c conductor
These spacings may be in any convenient common unit.
It is assumed that the phase rotation is such that Ia = aIb and Ic = a2Ib
where
1
3
+j
2
2
Ib=Io(1+j0)
Io is the magnitude of the load current
a=−
Clearly, as the spacing of the parallel conductors increases in relation to the mutual spacing of the groups of
cables, the induced voltage tends to zero. Similarly, if the three cables of the group are regularly transposed
at even intervals, the induced voltages in the parallel conductor sum to zero over a complete cycle of
transposition.
D.2 Voltage gradients induced in the cable shield/sheath
The voltage gradient induced in a cable shield/sheath may be considered as a special case in which the
parallel conductor is a shield/sheath at a spacing from the conductor that it embraces equal to the mean
radius of the shield/sheath. When no other current-carrying conductor is in the vicinity, the three
shield/sheath voltage gradients for a group of cables in any formation carrying balanced three-phase
conductor currents are then given by the following equations.
39
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D.2.1 General case of any cable formation
 1
 2S 2 
3
 2 S 
Ea = jωI a 2 ×10 − 7 − log e  ab  + j
log e  ac  V/m
 dS ac 
2
 d 
 2


(
)
(D.2)
1
 S 
3
 4S S 
Eb = jωI b 2 ×10− 7  log e  ab2 bc  + j
log e  bc  V/m
2
 d

 2
 S ab 
(
)
(D.3)
 1
 2S 2 
3
 2 S 
Ec = jωI c 2 ×10 − 7 − log e  bc  − j
log e  ac  V/m
 dS ac 
2
 d 
 2


(D.4)
(
)
where
d
Sab
Sbc
Sac
is the geometric mean shield/sheath diameter (arithmetic mean may be assumed)
is the axial spacing of phases a and b
is the axial spacing of phases b and c
is the axial spacing of phases a and c
D.2.2 Trefoil formation single circuit
For cables in trefoil where Sab = Sbc = Sac, these equations reduce to Equation (D.5), Equation (D.6), and
Equation (D.7), as follows:
(
)
(D.5)
(
)
(D.6)
(
)
(D.7)
 1
3 
 2S 
Ea = jωI a 2 ×10 − 7  − + j
log e 
 V/m
 2

2 
 d 

 2S 
Eb = jωI b 2 ×10 − 7 log e 
 V/m
 d 
 1
3 
 2S 
V/m
log
Ec = jωI c 2 ×10− 7  − − j
 2
 e  d 
2


D.2.3 Flat formation single circuit
For the other common formation of cables laid flat in which the axial spacing of adjacent cables = S, the
shield/sheath voltage gradients are given by Equation (D.8), Equation (D.9), and Equation (D.10).
(
)
 1
S
3
4S 
V/m
Ea = jωI a 2 ×10− 7  − log e + j
log e
 2
d
d 
2

40
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(D.8)
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(
)
(
)
Eb = jωI b 2 ×10 − 7 log e
2S
V/m
d
(D.9)
 1
S
3
4S 
V/m
Ec = jωI c 2 ×10− 7  − log e − j
log e
 2
d
2
d 

(D.10)
D.2.4 Double-circuit systems
It is impossible in this guide to cover all possible combinations of geometry for multiple circuits but a
solution to a simple parallel double-circuit follows.
Assumptions:
a)
Three or six cables are connected in three-phase circuits.
b)
All conductor currents are equal in magnitude.
c)
For three cables—any arrangement is permissible. For six cables—point or line symmetry is
assumed. This means a line 0-0 or a point 0 can be placed between the two circuits so that the
distance from cable a1 to 0 equals the distance from cable a2 to 0, where a1 is the a phase of
Circuit 1 and a2 is the a phase of Circuit 2. The same must be true for cables b1 and b2 and c1 and
c2.
d)
Positive phase-sequence rotation (phase “A” leading) was assumed in the equations. The effect of
reversing phase sequence can be simulated on input to the program by interchanging cable
positions 1 and 3 and 4 and 6 in the context S1 through S9.
Conductor currents are as shown in Equation (D.11), Equation (D.12), and Equation (D.13):
1
3
(assigned to cables 1 and 4)
Ia = − + j
2
2
(D.11)
I b = 1 + j 0 (assigned to cables 2 and 5)
(D.12)
Ic = −
1
3
(assigned to cables 3 and 6)
−j
2
2
(D.13)
Open-circuit voltages on shields/sheaths to neutral are as shown in Equation (D.14), Equation (D.15), and
Equation (D.16):
Ea 0 = I a × jX aa + I b × jX ab + I c × jX ac V/m
(D.14)
Eb 0 = I a × jX ab + I b × jX bb + I c × jX bc V/m
(D.15)
Ec 0 = I a × jX ac + I b × jX bc + I c × jX cc V/m
(D.16)
41
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where the corresponding matrix impedances are as follows:
X aa = k log e
1
rsm × S14
(D.17)
X ab = k log e
1
S12 × S15
(D.18)
X ac = k log e
1
S13 × S16
(D.19)
X bb = k log e
1
rsm × S 25
(D.20)
X bc = k log e
1
S 23 × S35
(D.21)
X cc = k log e
1
rsm × S36
(D.22)
And where
k
S12
S23
S13
S14
S25
S36
S15
S35
S16
rsm
is a constant = 2×ω×10–7=1.257×f×10–6
is distance from cable 1 to cable 2 (meters)
is the distance from cable 2 to cable 3 (meters)
is the distance from cable 1 to cable 3 (meters)
is the distance from cable 1 to cable 4 (meters)
is the distance from cable 2 to cable 5 (meters)
is the distance from cable 3 to cable 6 (meters)
is the distance from cable 1 to cable 5 (meters)
is the distance from cable 3 to cable 5 (meters)
is the distance from cable 1 to cable 6 (meters)
is the mean shield/sheath radius (meters)
Figure 1 of this guide shows values of the shield/sheath voltage gradient calculated from D.2,
Equation (D.5), Equation (D.6), and Equation (D.7) for a single circuit in trefoil configuration or
Equation (D.8), Equation (D.9), and Equation (D.10) for a single circuit in flat formation as a function of
the ratio S/d.
D.3 Screening and transposition
The voltage gradients calculated by the equations in D.2 are due to the magnetic field of the three-phase
currents only. When any other current-carrying conductors are in the vicinity, these voltages will be
modified. In particular, if any parallel conductor is present that is bonded so as to carry induced current,
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then the voltage gradient in any other parallel conductor will be reduced. This reduction depends on the
disposition of the conductors and the impedance of the current-carrying loop of which the screening
conductor forms a part.
Power cables frequently have communication or protection cables laid with them in the same trench. It is
clearly desirable to reduce to a minimum the voltage induction in these parallel cables. When the
shields/sheaths of single-conductor power cables are continuous and grounded at both ends of the route,
they act as screening conductors and thus reduce somewhat the voltage induction in the parallel cables. In a
specially bonded system, however, the power cable shields/sheaths no longer carry currents, and hence the
screening effect is absent, at least for balanced loads in the power cables. (During imbalanced loads or
faults, sheath currents will flow in the case of cross-bonded cables, and hence an important screening effect
is present in this case. There will also generally be a screening effect due to the sheath or armor wires of the
parallel cable itself).
The voltage induction in parallel cables resulting from balanced loads can be reduced or eliminated by
transposition, and this is particularly desirable for specially bonded cables for the reasons previously given.
Transposition has the additional advantage of balancing the impedances of the three-phase cables. The
transposition of heavy power cables is not generally practicable except at joint positions, however, and
hence the complete transposition cycle of the three phases will occupy three cable lengths. For cable
circuits that consist of only one or two lengths, it is not usual to transpose the power cables, but the parallel
conductor may be transposed as indicated below.
Figure 2 shows the methods to be used for transposition of the parallel cable or conductor. When the power
cables are laid in flat formation with wide spacing, the parallel conductor should be between the power
cables at the position shown. If there is insufficient space between the power cables to adopt this position
precisely, the parallel conductor should still be between the power cables. If the cables are touching or in
trefoil, the parallel conductor should be laid immediately alongside the power cables. In all cases the
parallel conductor should be transposed at the center of the section length or route length to an identical
position on the other side of the formation.
D.4 Sheath standing voltages (see 6.8.2)
The two corresponding vector diagrams for the cross-bonded sections are shown in Figure D.1.
A
For Figure 7 and Figure 8
For Figure 10 and Figure 11
Figure D.1—Vector diagrams for cross-bonded sections
On both diagrams, point A corresponds to the grounded positions. In the first diagram the maximum
standing voltage will occur at point B and is of magnitude E, whereas in the second diagram the maximum
standing voltage will occur at point C and is of magnitude
100% or 13.4%.
43
(
3 2 E, then the voltage reduction is 1− 3 2
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Annex E
(informative)
Transient voltages and voltage withstand requirements of protective
jackets
E.1 Power frequency sheath overvoltages
E.1.1 General
System faults produce an initial transient overvoltage followed by a power-frequency shield/sheath
overvoltage caused by the passage of the fault current. This power frequency overvoltage is not generally
high enough to be important in relation to the shield/sheath insulation design, but, as it persists for the
duration of the fault, it can be important in relation to the duty requirements of the shield/sheath voltage
limiters.
The cable installation must clearly be capable of safely withstanding the effects of any fault in the system
external to the cables. A fault in the cables themselves inevitably involves repair work and hence it is not so
important if the shield/sheath insulation adjacent to the fault is also damaged. The shield/sheath bonding
design should preclude the damage cascading to other parts of the cable system. Following system faults,
shield/sheath voltage limiters can be damaged, requiring inspection and possible replacement. The
shield/sheath voltage gradients due to external faults are of three types as classified in Table E.1.
Table E.1—Sheath voltage gradient types
Sheath voltage
gradient type
Type 1
Fault current type
Three-phase symmetrical fault
Type 2
Phase-to-phase fault
Type 3
Single-phase to ground fault
The equations for each type of fault are described in E.1.3 and E.1.4.
In deriving these equations, the following simplifying assumptions are made:
a)
The short-circuit current is known and is unaffected in value by the characteristics of the cable
system.
b)
For phase-to-phase and single-phase ground faults, the current in the healthy phase conductor(s) is
negligible in comparison with the short-circuit current, except for the case of impedance grounding
of the neutral (see E.1.2).
c)
No other screening conductors are present (except for the parallel GCC in the case of single-phase
ground faults on single-point bonded systems).
d)
The system consists of balanced minor and major sections in the case of sectionalized cross
bonding and a number of uniform minor sections exactly divisible by three in the case of
continuous cross bonding. (For design purposes, it is satisfactory to use these simplified equations
also for practical systems in which imbalance does exist.)
44
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E.1.2 Neutral grounding
For three-phase symmetrical faults and phase-to-phase faults, no zero-sequence current flows. The
equations given in E.1.3 and E.1.4 for faults of this type are, therefore, equally applicable to systems having
the neutral directly grounded or to those having impedance or resonant grounding of the system.
For single-phase ground faults in systems having impedance or resonant grounding, it is no longer
permissible to ignore the normal load currents in the system. The calculation of shield/sheath voltages
during a single-phase ground fault therefore requires the superposition of the voltages due to the
symmetrical positive sequence load currents and those due to the fault currents. The voltages due to the
fault current can also be calculated by considering the asymmetrical fault currents as the superposition of
an asymmetrical positive sequence system and a zero-sequence system with currents of the same
magnitude. The superposition of these currents results in two currents of equal magnitude but separated in
phase by an angle of 60° flowing in the unfaulted phases, while the faulted phase remains without current.
The shield/sheath voltages resulting from these currents can all be calculated from the following equations
and superimposed. However, in general, for systems having impedance or resonant grounding of the
neutral, the shield/sheath voltages resulting from single-phase ground faults will be much lower than those
due to three-phase symmetrical faults or phase-to-phase faults, and hence for design purposes single-phase
ground faults in these systems can be ignored.
E.1.3 Single-point bonding
E.1.3.1 Three-phase symmetrical fault
The shield/sheath voltage gradients are given in D.2, using the appropriate value of I.
E.1.3.2 Phase-to-phase fault
In the general case of any cable formation, assuming a fault between phases a and b with no ground current
flowing, when Iab is the fault current, the shield/sheath voltage gradients are shown in Equation (E.1),
Equation (E.2), and Equation (E.3):
(
)
 2S 
Ea = jωI ab 2 ×10− 7 log e  ab  V/m
 d 
(E.1)
(
)
(E.2)
(
)
(E.3)
 2S 
Eb = − jωI ab 2 × 10 − 7 log e  ab  V/m
 d 
S 
Ec = − jωI ab 2 ×10− 7 log e  bc  V/m
 S ac 
This results in a maximum for the shields/sheaths of the outer cables laid in a flat arrangement as shown in
Equation (E.4):
(
)
 4S 
 V/m
Ea = − Eb = jωI ab 2 × 10 − 7 log e 

 d 
(E.4)
where S = spacing of adjacent phases
45
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E.1.3.3 Single-phase ground fault (solidly grounded neutral)
Precise calculation of shield/sheath overvoltages for underground-fault conditions requires a knowledge of
the proportion of the return current that flows in the ground itself and the proportion that returns by way of
the parallel GCC. This depends on a number of factors, which are not usually accurately known.
Fortunately, however, the overvoltages of practical interest are those between shields/sheaths and the
parallel GCC, and these can be simply calculated by the assumption that this conductor carries the whole of
the return current. This assumption is normally accurate and leads to shield/sheath overvoltages that are
slightly higher than those observed in practice.
For a ground fault in phase a, and the general case of any cable formation when Iag is the fault current, the
shield/sheath-to-ground conductor voltages are shown in Equation (E.5), Equation (E.6), and
Equation (E.7):

 2 S ag 2 
 V/m
Ea = I ag  Rg + jω 2 × 10 − 7 log e 
 drg 




(E.5)

 S ag Sbg
Eb = I bg  Rg + jω 2 × 10 − 7 log e 
 rg S ab



 V/m


(E.6)

 S ag S cg
Ec = I cg  Rg + jω 2 × 10 − 7 log e 


 rg S ac

 V/m


(E.7)
(
(
(
)
)
)
where
Sag, Sbg, Scg
Rg
rg
are geometric mean spacings between cables a, b, and c, respectively, and the ground
conductor
is the resistance of ground conductor in Ω/m
is the geometric mean radius of the ground conductor (for stranded conductors take
0.75 of the overall radius)
E.1.3.4 Magnitude of voltages
Typical maximum values of shield/sheath voltages calculated from these equations are given in Figure E.1
for a circuit in flat formation, for a current of 1000 A having a transposed ground conductor. For a threephase symmetrical fault, the maximum voltage is reached in the outer cables and is the same as in Figure 1
of this guide but increased for higher current. For the phase-to-phase fault, the highest shield/sheath voltage
results when the fault is between the outer cables so that Sac = 2S. For a ground fault assuming the ground
conductor to be laid as shown in Figure 2 of this guide, see Equation (E.8) and Equation (E.9).
Sag = Scg = S
(E.8)
Sbg = 0.7S
(E.9)
46
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600
d/rg=15
E (V/km); I = 1000 A
500
Single phase-toground fault
400
10
5
Phase-to-phase fault
300
Three-phase
symmetrical fault
200
100
f = 60 Hz
0
1
2
3
5
7
10
20
30
50
Ratio S/d
Figure E.1—Induced shield/sheath voltage gradient (sheath-to ground conductor)
for various faults in single-point bonded-cable system (flat formation)
The highest of the three-sheath voltages for a fault in phase a is Ea, and since the effect of Rc can generally
be neglected, the preceding equation for Ea can be expressed as shown in Equation (E.10):
 S  2 d 
Ea = jωI ag 2 × 10 − 7 log e  
 V/m
 d  rg 
(
)
(E.10)
Figure E.1 shows the effect of varying d/rg over a typical range of values. It is clear that the overvoltages
per meter due to the single-phase fault is much greater than for the other types of fault, for systems having
solidly grounded neutral. For systems having impedance or resonant grounding of the neutral, the phase-tophase fault is the most important.
E.1.4 Cross bonding
E.1.4.1 Three-phase symmetrical fault
The shield/sheath voltage gradients are given by Annex D, D.2.3, Equation (D.8), Equation (D.9), and
Equation (D.10), using the appropriate value of I and using the longest minor section length in the case of
sectionalized cross bonding or continuous cross bonding.
E.1.4.2 Phase-to-phase fault
It had been previously considered that this is a balanced condition with regard to induced shield/sheath
voltages, and as a result no shield/sheath currents would flow. This has been since reassessed and although
use of computer calculations is required to arrive at an exact solution, it is generally considered that
shield/sheath currents will flow and tend to reduce the induced sheath voltages below that of a three-phase
symmetrical fault. In the case of a two phase to ground fault, voltages between sheaths will be strongly
influenced by the grounding resistances.
47
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E.1.4.3 Single-phase ground fault
In this case, the returning current divides between the shields/sheaths and ground, and the calculation of
shield/sheath voltages becomes more complex. The effect of the ground currents is important in relation to
the voltages between shields/sheaths and ground, and to calculate these it is necessary to know the values
of ground resistivity and of ground-plate resistance appropriate to the circuit. The voltages between
shields/sheaths can be calculated as follows for a sectionalized cross-bonded system (the behavior of
continuously cross-bonded cables during faults of this type is still being studied).
E.1.4.3.1 Cables in trefoil
Figure E.2 shows a single major section of cables in trefoil having the shields/sheaths grounded at both
ends.
Figure E.2—Single major section of cross-bonded cables during single-phase fault
A current Ix circulates in the path formed by the three shields/sheaths and the ground and divides equally
between the three shield/sheath circuits.
The voltages induced in the three shields/sheaths of Figure E.2, minor Section No. 1 are as shown in
Equation (E.11), Equation (E.12), and Equation (E.13).
(
)
(E.11)
(
)
(E.12)
Ea =
Ix
Z ss + 2 Z sg − I (Z ss − Rs ) V/m
3
Eb =
Ix
Z ss + 2Z sg − IZ sg V/m
3
Ec = E g V/m
(E.13)
where
I
is the fault current as shown in Figure E.2
48
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IEEE Std 575-2014
IEEE Guide for Bonding Shields and Sheaths of Single-Conductor Power Cables Rated 5 kV through 500 kV
The voltages between shields/sheaths at the cross-bonding points are then shown in Equation (E.14),
Equation (E.15), and Equation (E.16).
(
)
Vab = Il Z sg − Z ss + Rs V
(E.14)
Vbc = 0 V
(E.15)
(
)
Vac = Il Z sg − Z ss + Rs V
(E.16)
where
Zss
is the self-impedance of the shield/sheath with ground return in Ω/m, by definition
(
)
2
Zss = jω 2 × 10 −7 log e  
d 
Zag
Rs
l
(E.17)
is the mutual impedance of shield/sheath with ground return in Ω/m
is the resistance of shield/sheath in Ω/m
is the length of minor section in m
These impedances are functions of frequency and of ground resistivity but in these equations this factor
disappears and
(
)
 2S 
Vab = jωIl 2 × 10 − 7 log e 
 V
 d 
(E.18)
Vbc = 0 V
(E.19)
Vac = −Vab V
(E.20)
E.1.4.3.2 Cables in flat formation
When the cables are laid flat, the current I no longer divides equally between the shields/sheaths, but it can
be assumed to do so with little error, assuming also that the ground plate resistances are zero.
 3Z ss − 3Rs + 2 Z oog + 4 Z oig
Ix = I
 3Z ss + 2 Z oog + 4 Z oig


 A


(E.21)
where
Zoog
is the mutual impedance between shields/sheaths of outer cables with ground return in Ω/m
49
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IEEE Std 575-2014
IEEE Guide for Bonding Shields and Sheaths of Single-Conductor Power Cables Rated 5 kV through 500 kV
(
)
Zoog = jω 2 × 10 − 7 log e
Zoig
1
2S
(E.22)
is the mutual impedance between shields/sheaths of inner and outer cables with ground return in
Ω/m
(
)
Zoig = jω 2 × 10 − 7 log e
1
S
(E.23)
Then
(
)
I

Ea =  x Z s + Z oog + Z oig − I (Z s − Rs ) V/m
3

(
(E.24)
)
Eb =
Ix
Z s − 2 Z oig − IZ oig V/m
3
Ec =
Ix
Z ss + Z oog + Z oig − IZ oog V/m
3
(
(E.25)
)
(
) (
(
) (
(E.26)
)
I

Vab = l  x Z oog − Z oig + I Z oig − Z ss + Rs  V
3


(E.27)
)
I

Vbc = l  x Z oig − 2Z oog + I Z oog − Z oig  V

3
[ (
Vac = l I x Z ss − Rs − Z oog
(E.28)
)] V/m
(E.29)
Substituting for Ix in the equations for Vab, Vbc,, and Vac gives Equation (E.30), Equation (E.31), and
Equation (E.32).
[(
Vab =
Il
Z oog + 2 Z oig − 3Z ss + 3Rs F
3
Vbc =
Il
2 Z oog − Z oig + 3Rs F V
3
Vac =
Il
I Z ss − Rs − Z oog
3
[(
[(
)] V
(E.30)
]
)
(E.31)
)] V
(E.32)
50
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IEEE Std 575-2014
IEEE Guide for Bonding Shields and Sheaths of Single-Conductor Power Cables Rated 5 kV through 500 kV
Where the factor F is defined as:
F=
(Z
oig
− Z oog )
(E.33)
3Z ss + 2 Z oog + 4 Z oig
and all terms containing Rs can generally be disregarded. Then,
 2(2 )1 / 3 S 
 V
Vab = jωIl 2 × 10 − 7 log e 


d


(
)
(E.34)
(
) ( )
(E.35)
(
)
(E.36)
Vbc = jωIl 2 × 10 −7 log e 2 2 / 3 V
 4S 
Vac = jωIl 2 × 10 − 7 log e 
 V
 d 
E.1.4.4 Magnitude of voltages
Figure E.3 shows these voltages between shields/sheaths at the cross-bond position per unit length of 1 m
of the minor section length calculated from the equations above for single-phase faults and compared with
the voltages due to three-phase symmetrical faults and for phase-to-phase faults and for a short-circuit
current of 1000 A. It is evident that the voltage due to the phase-to-phase fault is the greatest.
600
E (V/km); I = 1000 A
500
Three-phase fault
400
300
Single-phase fault
200
100
f = 60 Hz
0
1
2
3
5
7
10
20
30
50
Ratio S/d
Figure E.3—Maximum induced shield/sheath voltage gradients (sheath to sheath) for
various faults of sectionalized cross-bonded cable systems (flat formation)
51
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IEEE Std 575-2014
IEEE Guide for Bonding Shields and Sheaths of Single-Conductor Power Cables Rated 5 kV through 500 kV
The shield/sheath voltage limiter generally consists of a star connected device having the star point
grounded to a local ground. The resistance of these local ground plates is often high but some current will
flow into the ground during a single-phase fault. The calculation of these currents and of the voltages
between the shields/sheaths and the ground plates is complex and requires knowledge of the ground-plate
resistances and the ground resistivity along the cable route. These values are not generally known,
especially at the design stage, and hence it is usual to consider the duty of the shield/sheath voltage limiter
only in terms of the voltage between shields/sheaths. Experience and measurements indicate that the
shield/sheath-to-ground voltage rise is not generally sufficient to damage the shield/sheath voltage limiter,
but, when there is any doubt, the star point should not be grounded, when this is permissible, with respect
to transient overvoltages.
52
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IEEE Std 575-2014
IEEE Guide for Bonding Shields and Sheaths of Single-Conductor Power Cables Rated 5 kV through 500 kV
Annex F
(informative)
Current and voltage distribution on cable shields/sheaths with multiple
cables per phase
F.1 Scope and objectives
The previous IEEE guide (IEEE Std 575-1988) for shield/sheath-bonding methods was limited to the
calculation of induced voltages and currents in cables shields/sheaths of simple three-phase installations
having one cable per phase. It provided analytical equations to solve for the shield/sheath induced voltage
in case of single-point bonding and for the induced current in the case of bonding at both ends. It did not
address the cases of several cables per phase. Experience with such installation (see Adamson, Taha, and
Wedepohl [B3]) has shown that the current distribution in the individual cables is not uniform, leading to
excessive heating in some cases, and lower temperature rise in others. Also, the shield/sheath Joule losses
or induced voltages are very much affected by the relative location of individual cables in the duct bank.
The present document presents a general calculation method based on complex matrix algebra to help the
user solving any type of cable configuration in a duct bank. Once the system of equations is assembled, the
solution can be obtained readily by using a personal computer. As will be shown later, this method is quite
useful in finding the best arrangement of cables/phases in order to reduce the disparity in current
distribution between cables and to reduce the shield/sheath Joule losses.
F.2 Calculation methodology
The general method of calculating the induced currents and voltages in shields/sheaths is based on
Kirchhoff's laws. The first one states that at a given node in an electrical circuit, the sum of the currents
entering equals the sum of the currents leaving. The second stipulates that around any closed loop, the sum
of the potential differences across all elements is zero. The following shows the calculation methodology
applied on a three-phase circuit. It consists of two parallel cables per phase as shown in Figure F.1 and
Figure F.2. The main currents in each phase, IA, IB, and IC are known. The shields/sheaths are solidly
bonded at both ends, together with a parallel GCC. The number of unknowns in this case is 13, namely the
current in each individual conductors, the induced current in each shield/sheath, and the induced current in
the continuity conductor. Therefore, 13 equations are needed.
Applying Kirchhoff’s first law on the shield/sheath node gives us Equation (F.1):
∑I
n
= 0 = I na1 + I na 2 + I nb1 + I nb 2 + I nc1 + I nc 2 + I gw
(F.1)
Applying Kirchhoff’s first law on the node formed by conductors a1 and a2 gives us Equation (F.2):
I A = 1 + j 0 = I a1 + I a 2
(F.2)
Applying Kirchhoff’s first law on the node formed by conductors b1 and b2 gives us Equation (F.3):
I B = −0.5 − j 0.8666 = I b1 + I b 2
(F.3)
53
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IEEE Guide for Bonding Shields and Sheaths of Single-Conductor Power Cables Rated 5 kV through 500 kV
Figure F.1—Example of 6 parallel cables, 2 cables per phase
Figure F.2—Loops formed by the shields/sheaths of the installation shown in Figure F.1
54
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IEEE Guide for Bonding Shields and Sheaths of Single-Conductor Power Cables Rated 5 kV through 500 kV
Applying Kirchhoff’s first law on the node formed by conductors c1 and c2 gives us Equation (F.4):
I C = −0.5 + j 0.8666 = I c1 + I c 2
(F.4)
Applying Kirchhoff’s second law on the loop formed by both conductors of phase A gives us Equation
(F.5):
Z a1,a1 I a1 − Z a 2,a 2 I a 2 + Z na1,a1 I na1 + Z na 2,a1 I na 2 + Z na 2,a1 I a 2 + .... + Z c 2,a1 I c 2 + Z a1, gw I gw −
Z na1,a 2 I na1 − Z a1,a 2 I a1 − Z na 2,a 2 I na 2 − .... − Z c 2,a 2 I c 2 − Z a 2, gw I gw = 0
(F.5)
Similar equations can be derived for the other two loops of phase B and phase C. These loops yield a total
of three equations.
Applying Kirchhoff’s second law on the loop formed by the shield/sheath of the first cable of phase A and
the shield/sheath of the second cable of shield/sheath A gives us Equation (F.6):
Z na1,na1 I na1 − Z na 2,na 2 I na 2 + Z a1,na1 I a 2 + Z na 2,na1 I na 2 + Z a 2,na1 I a 2 + .... + Z c 2,na1 I c 2 + Z na1, gw I gw −
Z na1,na 2 I na1 − Z a1,na 2 I a1 − Z a 2,na 2 I a 2 − .... − Z c 2,na 2 I c 2 − Z na 2, gw I gw = 0
(F.6)
Similar equations can be derived for the remaining six loops, the last one being the loop formed by the
shield/sheath of the second cable of phase C and the continuity conductor.
A total of 13 equations are obtained. The system of equations, written in matrix form, is shown in
Figure F.3. The solution to these equations provides the current distribution in the conductors a1 to c2, the
induced current in the shields/sheaths na1 to nc2, and the induced current Igw in the GCC.
The residual voltage at the bonding node can be evaluated as shown in Equation (F.7):
Ena1 = Eres = L × (Z a1, na1I a1 + Z a 2, na1I a 2 + Z b1, na1I b1 + Z b 2, na1I b 2 + Z c1, na1I c1 + …..
+ Z c 2,na1 I c 2 + Z na1,na1 I na1 + Z na1,na 2 I na 2 + Z na1,nb1 I nb1 + Z na1,nb 2 I nb 2 + …..
+ Z na1,nc1 I nc1 + Z na1,nc 2 I nc 2 + Z na1, gw I gw
)
(F.7)
where
L
is the cable length in meters
Other symbols are summarized in Figure F.3.
55
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IEEE Guide for Bonding Shields and Sheaths of Single-Conductor Power Cables Rated 5 kV through 500 kV
I na1 


0

 (Zna1,na1 − Zna2,na1 ) (Zna1,na2 − Zna2,na2 ) •••• (Zna1,nc2 − Zna2,nc2 ) (Zna1,gw − Zna2,gw ) (Zna1,a1 − Zna2,a1 ) (Zna1,a2 − Zna2,a2 ) ••• (Zna1,c2 − Zna2,c2 ) I na2  
0

(Zna2,na1 − Znb1,na1 ) (Zna2,na2 − Znb1,na2 ) •••• (Zna2,nc2 − Znb1,nc2 ) (Zna2,gw − Znb1,gw ) (Zna2,a1 − Znb1,a1 ) (Zna2,a2 − Znb1,a2 ) ••• (Zna2,c2 − Znb1,c2 ) I nb1  
0

(Znb1,na1 − Znb2,na1 )(Znb1,na2 − Znb2,na2 ) •••• (Znb1,nc2 − Znb2,nc2 ) (Znb1,gw − Znb2,gw ) (Znb1,a1 − Znb2,a1 ) (Znb1,a2 − Znb2,a2 ) ••• (Znb1,c2 − Znb2,c2 ) I nb2  
0



 (Z
I
)
)
(
(
−
−
•
•
•
•
−
−
−
−
•
•
•
−
Z
Z
Z
Z
Z
Z
Z
Z
Z
Z
Z
Z
Z
 nc1 
)(
) (
)(
)
)(
0

 Znb2,na1− Z nc1,na1 Znb2,na2 − Z nc2,na2 •••• Znb2,nc2 − Z nc1,nc2 Znb2,gw − Z nc1,gw Znb2,a1− Z nc1,a1 (Znb2,a2 − Z nc1,a2 ) ••• (Znb2,c2 − Z nc1,c2 ) I  
( nc1,nc2 nc2,nc2 ) ( nc1,gw nc2,gw ) ( nc1,a1 nc2,a1 ) nc1,a2 nc2,a2
nc2
nc1,c2 nc2,c2 
0


 ( nc1,na1 nc2,na1 ) ( nc1,na2 nc2,na2 )


0

 (Znc2,na1 − Zgw,na1 ) (Znc2,na2 − Zgw,na2 ) •••• (Znc2,nc2 − Zgw,nc2 ) (Znc2,gw − Zgw, gw ) (Znc2,a1 − Zgw,a1 )  Znc2,a2 − Zgw,a2  •••  Znc2,c2 − Zgw,c2   ×  I gw  = 
1. + 0J
••••
•••
1
1
1
1
0
0
0






I
a1
••••
•••
0
0
0
0
1
1
0
••••
•••
0
0
0
0
0
0
0
 I  − 0.5 − 0.866J 


••••
•••
0
0
0
0
0
0
1
 (Za1,na1 − Za2,na1 ) (Za1,na2 − Za2,na2 ) •••• (Za1,nc2 − Za2,nc2 ) (Za1,gw − Za2,gw ) (Za1,a1 − Za2,a1 ) (Za1,a2 − Za2,a2 ) ••• (Za1,c2 − Za2,c2 )   I a2  − 0.5 + 0.866J 
0

  b1  
 (Z
b1,na1 − Z b2,na1 ) (Z b1,na2 − Z b2,na2 ) •••• (Z b1,nc2 − Z b2,nc2 ) (Z b1, gw − Z b2, gw ) (Z b1,a1 − Z b2,a1 ) (Z b1,a2 − Z b2,a2 ) ••• (Z b1,c2 − Z b2,c2 )
0
I

 b2  

 Z
0
 ( c1,na1 − Zc2,na1 ) (Zc1,na2 − Zc2,na2 ) •••• (Zc1,nc2 − Zc2,nc2 ) (Zc1,gw − Zc2,gw ) (Zc1,a1 − Zc2,a1 ) (Zc1,a2 − Zc2,a2 ) ••• (Zc1,c2 − Zc2,c2 )   I c1  

I 
 c2 
where
Zna1,na2 is the mutual impedance between the shields/sheaths of cable 1 and cable 2 of phase A
Za1,nc2 is the mutual impedance between the conductor of cable 1 of phase A and the shield/sheath of cable 2 of phase C
Za1,a1 is the self-impedance between cable 1 and cable 2 of phase A
Zgw,nb1 is the mutual impedance between the ground conductor and the shields/sheaths of cable 1 of phase B
is the induced current in the shield/sheath of cable 1 of phase C
Inc1
is the current flowing in the conductor of cable 1 of phase A
Ia1
is the induced current in the GCC
Igw
RHS is the known phase currents (right hand side of matrix equation)
Figure F.3—System of equations describing the installation shown in Figure F.1
56
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IEEE Guide for Bonding Shields and Sheaths of Single-Conductor Power Cables Rated 5 kV through 500 kV
F.3 Single-point-bonding
Single-point-bonding is frequently used as an alternative to multiple point bonding, especially for short
cable lengths. This technique eliminates the induced currents in the various shields/sheaths but, at the same
time, causes a voltage rise along the shields/sheaths with the maximum occurring at the floating point. In
order to reduce this voltage, we install a GCC that runs parallel to the cables. This conductor should be
transposed at the mid-point location and solidly bonded to the ground at both ends. Figure F.4 shows a
sketch of single-point-bonding with continuity conductor. The induced voltages in shields/sheaths are
calculated as follows [see Equation (F.8) to Equation (F.14) and Table F.1]:
Figure F.4—Sketch of single-point-bonding
(ground continuity conductor position as shown in the profile view)
Z gw,na 
 Ena 
I A 




 
 Enb  = [Z M ] I B  + I gw • Z gw,nb 

E 
I 
Z
 nc 
 C
 gw,nc 
(F.8)
where
[ZM]
is the mutual impedance matrix between conductors a, b, c
and shields/sheaths na, nb, nc
(Z a ,na )
[Z M ] = (Z a,nb )
 (Z a ,nc )

(Z b,na ) (Z c,na )
(Z b,nb ) (Z c,nb )
(Z b,nc ) (Z c,nc )
(F.9)
where
Igw
is the induced current in the continuity ground conductor
57
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IEEE Guide for Bonding Shields and Sheaths of Single-Conductor Power Cables Rated 5 kV through 500 kV
I gw = −
1
Z gw, gw
Z a , gw
Z b, gw
Z c, gw
I A 
 
I B 
I 
 C
(F.10)
where
is the induced voltage in the shield/sheath na
Ena
Zgw,na is the mutual impedance between shield/sheath na and GCC gw
Za,nb is the mutual impedance between conductor a and shield/sheath nb (Ω/m)
 1
Z a , nb = j × 4πf ln
 S a nb
 ,

 × 10 − 7 (Ω/m)


(F.11)
 2
Z a , a = Rca + j × 4 πf ln
 αDca

−7
 × 10 (Ω/m)

(F.12)
 2
Z na , na = Rna + j × 4πf ln
 Dna

 × 10 − 7 (Ω/m

(F.13)
 2 
 × 10 − 7 (Ω/m)
Z gw, gw = Rgw + j × 4πf ln
 αDgw 


(F.14)
where
α
Dca
Dgw
Dna
f
Rca
Rgw
Rna
Sa,nb
Za,a
is the geometric mean diameter coefficient and is summarized in Table F.1
is the diameter of conductor a (mm)
is the diameter of ground conductor (mm)
is the average diameter of shield/sheath na (mm)
is the power frequency (Hz)
is the electrical resistance of conductor a (Ω/m)
is the electrical resistance of ground conductor (Ω/m)
is the electrical resistance of shield/sheath na (Ω/m)
is the axial spacing between conductor a and shield/sheath nb (mm)
is the self-impedance of conductor a
58
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IEEE Guide for Bonding Shields and Sheaths of Single-Conductor Power Cables Rated 5 kV through 500 kV
Table F.1—Values of α
Number of wires
Value of α
1
0.779
3
0.678
7
0.726
19
0.758
37
0.768
61
0.772
91
0.774
127
0.776
F.4 Cross bonding
Cross bonding of shields/sheaths eliminates or reduces significantly the circulating current in
shields/sheaths. The challenge is to insure that all minor sections are of the same length. Figure F.5 shows a
sketch of a cross-bonded cable installation. Figure F.6 is the equivalent electrical circuit on which we can
apply the Kirchhoff’s laws.
Figure F.5—Cross bonding of shields/sheaths
59
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IEEE Guide for Bonding Shields and Sheaths of Single-Conductor Power Cables Rated 5 kV through 500 kV
Figure F.6—Electrical circuit of shields/sheaths cross bonding
Kirchoff’s first law gives Equation (F.15):
Ina + Inb + Inc = 0
(F.15)
For the loop formed by the shield/sheath belonging initially to phase A and the shield/sheath belonging
initially to phase B, Kirchoff’s second law gives Equation (F.16):
(L1 + L2 + L3 )Z na ,na I na − (L1 + L2 + L3 )Z nb,nb I nb+ L1Z a ,na I A + L2 Z a ,nb I A + L3 Z a ,nc I A+
+ L1Z b , na I B + L2 Z b , nb I B + L3 Z b , nc I B + L1Z c , na I C + L2 Z c , nb I C + L3 Z c , nc I C +
+ L1Z na , nb I nb + L2 Z nb , nc I nb + L3 Z na , nc I nb + L1Z na , nc I nc + L2 Z na , nb I nc + L3 Z nb , nc I nc −
− (L1Z a , nb I A + L2 Z a , nc I A + L3 Z a , na I A ) − (L1Z b , nb I B + L2 Z b , nc I B + L3 Z b , na I B ) −
− (L1Z c , nb I C + L2 Z c , nc I C + L3 Z c , na I C ) − (L1Z na , nb I na + L2 Z nb , nc I na + L3 Z na , nc I na ) −
− (L1Z nb , nc I nc + L2 Z na , nc I nc + L3 Z na , nb I nc ) = 0
(F.16)
A similar equation can be derived for the other loop formed by the shields/sheaths of phase B and phase C.
The set of three equations can be solved to obtain the circulating currents in individual shields/sheaths.
The induced voltage along the shield/sheath, belonging initially to phase A, is determined as indicated in
the following F.4.1, F.4.2, and F.4.3.
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F.4.1 Along minor section #1 (L = 0 → L1)
Ena ,1 = L Z na , na
+ L Z a , na
Z b , na
Z na , nb
Z c , na
Z na , nc
 I na 
 
 I nb  +
I 
 nc 
I A 
 
 I B  + L • I gw • Z gw, na
I 
 C
(F.17)
F.4.2 Along minor section #2 (L = L1 → L2)
Ena , 2 = Ena ,1 + L Z na , nb
Z nb , nb
+ L Z a , nb
I A 
 
 I B  + L • I gw • Z gw, nb
I 
 C
Z b , nb
Z c , nb
Z nb , nc
 I nc 
 
 I na  +
I 
 nb 
(F.18)
F.4.3 Along minor section #3 (L = L2 → L3)
Ena ,3 = Ena , 2 + L Z na , na
Z na , nb
+ L Z a , na
I A 
 
 I B  + L • I gw • Z gw, nc
I 
 C
Z b , na
Z c , na
Z na , nc
 I na 
 
 I nb  +
I 
 nc 
(F.19)
The residual voltage at the bonding point of the major section is equal to Ena,3 at L = L3.
The induced voltage along the other shields/sheaths is calculated the same way.
F.5 Practical examples
The development outlined previously can be used to calculate the induced voltages and currents in complex
cable installations. The results can be used to optimize the cables/phases arrangement in a duct bank in the
case of parallel multi-cables per phase. Examples of two parallel cables per phase and six parallel cables
per phase with no GCCs are outlined as follows.
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F.5.1 Configuration optimization
F.5.1.1 Two cables per phase circuit
The following example is a three-phase circuit with two cables per phase, installed in flat formation with
shields/sheaths solidly bonded at both ends (see Figure F.7). The other characteristics are as follows:
Rconductor = 33.86E-6 Ω/m (1.03E-5 Ω/ft), Rsheath = 0.209E-3 Ω/m (6.37E-5 Ω/ft), Dconductor = 32.8 mm
(1.29 in)
Dsheath = 48 mm (1.89 in), 50 Hz, IA = IB = IC = 100 A, cable length = 1000 m (3281 ft)
Table F.2 shows, for this particular cables/phases arrangement, the current distribution in the individual
conductors and shields/sheaths and the shield/sheath loss factor, which is the ratio of losses in the
shield/sheath due to induced current to the losses in the conductor. It can be seen that the phase current is
not distributed uniformly as might be expected. It varies between 44.6 A and 55.7 A instead of a balanced
50 A in each one. This non-optimized arrangement impacts the losses in the shields/sheaths, giving a
maximum sheath loss factor of 4.95.
The shield/sheath loss factor being defined as shown in Equation (F.20):
λna =
I na2 Rna
(for shield/sheath na )
I ca2 Rca
(F.20)
where
Ina
Ica
Rna
Rca
is the current in shield/sheath na (A)
is the current in conductor ca (A)
is the electrical resistance of shield/sheath na (Ω/m)
is the electrical resistance of conductor ca (Ω/m)
(15.75 in)
Figure F.7—Cable configuration, two cables per phase, initial configuration
Table F.2—Currents and losses, initial configuration
Cable 1, Phase A
Phase current
(A)
46.3
Sheath current
(A)
38.4
Sheath loss factor
4.24
Cable 2, Phase A
53.7
34.3
2.85
Cable 3, Phase B
44.6
37.4
4.35
Cable 4, Phase B
55.7
34.8
2.42
Cable 5, Phase C
50.8
43.7
4.56
Cable 6, Phase C
49.6
44.4
4.95
62
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A better cables/phases arrangement, shown in Figure F.8, can improve the current distribution in the
conductors and reduce the losses in the shield/sheath as shown in Table F.3.
7.87 in
Figure F.8—Two cables per phase, alternate configuration 1
Table F.3—Currents and losses, alternate configuration 1
Cable 1, Phase A
Phase current
(Amps)
50
Sheath current
(Amps)
28.7
Cable 2, Phase B
50
28.7
2.04
Cable 3, Phase C
50
25.3
1.58
Cable 4, Phase C
50
25.3
1.58
Cable 5, Phase B
50
34.8
2.99
Cable 6, Phase A
50
34.8
2.99
Sheath loss factor
2.04
With this arrangement, the current is distributed uniformly among the individual conductors (50 A each)
and the losses in the shields/sheaths are reduced substantially.
An optimized trefoil configuration, as shown in Figure F.9, gives the best results (see Table F.4). In this
case, the shield/sheath losses are reduced significantly, down to 0.492 instead of 2.99.
(7.87 in)
(2.36 in)
Figure F.9—Two cables per phase, alternate configuration 2
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Table F.4—Currents and losses, alternate configuration 3
Cable 1, Phase A
Phase current
(A)
50
Sheath current
(A)
13.9
Cable 2, Phase A
50
13.9
0.474
Cable 3, Phase B
50
13.8
0.468
Cable 4, Phase B
50
13.8
0.468
Cable 5, Phase C
50
14.1
0.492
Cable 6, Phase C
50
14.1
0.492
Sheath loss factor
0.474
F.5.1.2 Six cables per phase circuit
The more cables per phase we have, the greater the probability to have an important imbalance in current
distribution among individual cables. Figure F.10 shows a real-life cable installation (see Petty [B37])
where the total load of a power generating station is carried by 18 cables (6 cables per phase). The
measured imbalance is 280%, resulting from one cable (#6) carrying much more power (270 A) than his
neighbor (#16), which carries 96 A only. The calculation, using the same methodology described
previously, gives an imbalance of 268%, assuming equal cable lengths.
190.5 mm
(7.5 in)
610 mm
(24 in)
190.5 mm
(7.5 in)
Figure F.10—Measured current distribution in a thermal generating station
A simple rearrangement in cables-phases as shown in Figure F.11 reduces significantly the imbalance in
current distribution and lowers the shield/sheath losses at the same time. In this case, the imbalance drops
to 119% and the maximum shield/sheath losses factor drops from 11.4 to 3.2.
64
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190.5 mm
(7.5 in)
610 mm
(24 in)
190.5 mm
(7.5 in)
Figure F.11—Current distribution in an optimized cables/phases configuration
F.5.2 Single-point-bonding
The following examples highlight the importance of transposing the GCC in order to reduce the induce
voltage along the shields/sheaths. It is the case of a real cable installation (see Pirelli [B38]) having the
following characteristics.
380 kV, 1200 mm2 (2400 kcmil) cable, 50 Hz, cable length = 1000 m (3281 ft)
#4/0 AWG ground conductor, 0.000173 Ω/m (5.27E-5 Ω/ft), shield/sheath diameter = 104 mm (4.1 in)
IA = IB = IC = 1675 A
F.5.3 Untransposed continuity conductor
Figure F.12 shows the arrangement of the cables and the GCC. The results for the induced voltage show a
maximum of 448 V for shield/sheath na, 184 V for shield/sheath nb, and 165 V for shield/sheath nc. The
induced current in the continuity conductor is equal to 614 A.
Figure F.12—Untransposed continuity conductor
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F.5.4 Transposed continuity conductor
Figure F.13 shows an optimized arrangement of the cables and the transposed GCC. The induced voltage in
shield/sheath na drops to 253 V, to 174 V for shield/sheath nb and increases to 213 V for shield/sheath nc.
The induced current in the continuity conductor drops to 68 A.
(1.0 ft)
in)
(3.5 in)
Figure F.13—Transposed continuity conductor
F.5.5 Bonding arrangements
F.5.5.1 Cross bonding
The following examples show the impact of shield/sheath cross bonding on losses. Two cases are
considered, one with perfect permutation (minor sections of equal length), the other with relatively bad
permutation. The characteristics of the installation are taken from an existing one (see Lodwig [B33]). The
cases involve the following parameters:
380 kV, 1200 mm2 cable (2400 kcmil), 60 Hz, cable length = 2100 m (6900 ft)
IA = IB = IC = 900 A
Cable spacing = 19 cm (7.5 in)
F.5.5.2 Perfect cross bonding
Figure F.14 shows the induced shield/sheath voltage along the cable route with perfect permutation (minor
section of 700 m (2297 ft) each). The maximum calculated voltage is 111 V and the residual voltage is
33 V. The circulating current in shields/sheaths is null.
66
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Copyrighted material licensed to Shann Chong Lew on 2014-09-24 for licensee's use only.
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IEEE Guide for Bonding Shields and Sheaths of Single-Conductor Power Cables Rated 5 kV through 500 kV
120
100
Sheath of phase A
Sheath of phase B
Sheath voltage (V)
80
60
Sheath of phase C
40
Residual voltage
20
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Distance (% of major section)
Figure F.14—Shield/sheath voltage with ideal permutation
F.5.5.3 Less than perfect cross bonding
Figure F.15 shows the induced shield/sheath voltage along the cable route with unequal minor sections,
namely 420 m (1378 ft) for #1, 630 m (2067 ft) for #2, and 1050 m (3445 ft) for #3. The maximum voltage
in this case increases to120 V and the residual voltage remains approximately the same.
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140
120
100
Sheath voltage (V)
Sheath of phase A
80
Sheath of phase B
60
Sheath of phase C
40
Residual voltage
20
0
0.0000
0.1000
0.2000
0.3000
0.4000
0.5000
0.6000
0.7000
0.8000
Distance (% of major section)
Figure F.15—Shield/sheath voltage with non-ideal permutation
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1.0000
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