IEC 60287-1-3:2023

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

IEC 60287-1-3:2023 provides a method for calculating the phase currents and circulating current losses in single-core cables arranged in parallel. The method described in this document can be used for any number of cables per phase in parallel in any physical layout. The phase currents can be calculated for any arrangement of sheath bonding. For the calculation of sheath losses, it is assumed that the sheaths are bonded at both ends. A method for calculating sheath eddy current losses in two circuits in flat formation is given in IEC 60287-1-2.

General Information

• Status: Published
• Publication Date: 21-May-2023
• ICS: 29.060.20 - Cables
• Technical Committee: TC 20 - Electric cables
• Drafting Committee: WG 19 - TC 20/WG 19
• Current Stage: PPUB - Publication issued
• Start Date: 09-Jun-2023
• Completion Date: 22-May-2023

Relations

• Revises: 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
• Effective Date: 05-Sep-2023

Standards Content (Sample)

IEC 60287-1-3 ®
Edition 2.0 2023-05
INTERNATIONAL
STANDARD
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
All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized in any form
or by any means, electronic or mechanical, including photocopying and microfilm, without permission in writing from
either IEC or IEC's member National Committee in the country of the requester. If you have any questions about IEC
copyright or have an enquiry about obtaining additional rights to this publication, please contact the address below or
your local IEC member National Committee for further information.

IEC Secretariat Tel.: [phone]
3, rue de Varembé [e-mail]
CH-1211 Geneva 20 www.iec.ch
Switzerland
About the IEC
The International Electrotechnical Commission (IEC) is the leading global organization that prepares and publishes
International Standards for all electrical, electronic and related technologies.

About IEC publications
The technical content of IEC publications is kept under constant review by the IEC. Please make sure that you have the
latest edition, a corrigendum or an amendment might have been published.

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details all new publications released. Available online and once
and French, with equivalent terms in 19 additional languages.
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(IEV) online.
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further assistance, please contact the Customer Service
Centre: [e-mail].
IEC 60287-1-3 ®
Edition 2.0 2023-05
INTERNATIONAL
STANDARD
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
INTERNATIONAL
ELECTROTECHNICAL
COMMISSION
ICS 29.060.20  ISBN 978-2-8322-6973-2

– 2 – IEC 60287-1-3:2023 © IEC 2023
CONTENTS
FOREWORD . 3
INTRODUCTION . 5
1 Scope . 6
2 Normative references . 6
3 Terms, definitions and symbols. 6
3.1 Terms and definitions . 6
3.2 Symbols . 6
4 Description of method . 7
4.1 General . 7
4.2 Outline of method . 8
4.3 Matrix solution . 11
Annex A (informative) Example calculations . 12
A.1 Overview. 12
A.2 Example 1 . 12
A.2.1 General . 12
A.2.2 Calculations . 13
A.3 Example 2 . 18
A.4 Example 3 . 18
A.5 Example 4 . 19
Annex B (informative) Example of the computation of the coefficient α for hollow core
conductors . 20
Bibliography . 21

Figure B.1 – Representation of a hollow core conductor. 20

Table 1 – Values of α for conductors . 10
Table A.1 – Sheath loss factor calculation according to IEC 60287-1-1 . 13
Table A.2 – Sheath current and sheath loss factor calculation per phase . 15
Table A.3 – Calculated values of d . 16
i,k
Table A.4 – Calculated values of zz . 16
Table A.5 – Array [Z] including coefficients for currents . 17
Table A.6 – Sheath current and sheath loss factor calculation per phase . 18
Table A.7 – Sheath current and sheath loss factor calculation per phase . 19
Table A.8 – Sheath current and sheath loss factor calculation per phase . 19

INTERNATIONAL ELECTROTECHNICAL COMMISSION
____________
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

FOREWORD
1) The International Electrotechnical Commission (IEC) is a worldwide organization for standardization comprising
all national electrotechnical committees (IEC National Committees). The object of IEC is to promote international
co-operation on all questions concerning standardization in the electrical and electronic fields. To this end and
in addition to other activities, IEC publishes International Standards, Technical Specifications, Technical Reports,
Publicly Available Specifications (PAS) and Guides (hereafter referred to as “IEC Publication(s)”). Their
preparation is entrusted to technical committees; any IEC National Committee interested in the subject dealt with
may participate in this preparatory work. International, governmental and non-governmental organizations liaising
with the IEC also participate in this preparation. IEC collaborates closely with the International Organization for
Standardization (ISO) in accordance with conditions determined by agreement between the two organizations.
2) The formal decisions or agreements of IEC on technical matters express, as nearly as possible, an international
consensus of opinion on the relevant subjects since each technical committee has representation from all
interested IEC National Committees.
3) IEC Publications have the form of recommendations for international use and are accepted by IEC National
Committees in that sense. While all reasonable efforts are made to ensure that the technical content of IEC
Publications is accurate, IEC cannot be held responsible for the way in which they are used or for any
misinterpretation by any end user.
4) In order to promote international uniformity, IEC National Committees undertake to apply IEC Publications
transparently to the maximum extent possible in their national and regional publications. Any divergence between
any IEC Publication and the corresponding national or regional publication shall be clearly indicated in the latter.
5) IEC itself does not provide any attestation of conformity. Independent certification bodies provide conformity
assessment services and, in some areas, access to IEC marks of conformity. IEC is not responsible for any
services carried out by independent certification bodies.
6) All users should ensure that they have the latest edition of this publication.
7) No liability shall attach to IEC or its directors, employees, servants or agents including individual experts and
members of its technical committees and IEC National Committees for any personal injury, property damage or
other damage of any nature whatsoever, whether direct or indirect, or for costs (including legal fees) and
expenses arising out of the publication, use of, or reliance upon, this IEC Publication or any other IEC
Publications.
8) Attention is drawn to the Normative references cited in this publication. Use of the referenced publications is
indispensable for the correct application of this publication.
9) Attention is drawn to the possibility that some of the elements of this IEC Publication may be the subject of patent
rights. IEC shall not be held responsible for identifying any or all such patent rights.
IEC 60287-1-3 has been prepared by IEC technical committee 20: Electric cables. It is an
International Standard.
This second edition cancels and replaces the first edition published in 2002. This edition
constitutes a technical revision.
This edition includes the following significant technical changes with respect to the previous
edition:
a) Change and update of list of symbols.

– 4 – IEC 60287-1-3:2023 © IEC 2023
The text of this International Standard is based on the following documents:
Draft Report on voting
20/2098/FDIS 20/2105/RVD
Full information on the voting for its approval can be found in the report on voting indicated in
the above table.
The language used for the development of this International Standard is English.
This document was drafted in accordance with ISO/IEC Directives, Part 2, and developed in
accordance with ISO/IEC Directives, Part 1 and ISO/IEC Directives, IEC Supplement, available
at www.iec.ch/members_experts/refdocs. The main document types developed by IEC are
described in greater detail at www.iec.ch/publications.
A list of all parts in the IEC 60287 series, published under the general title Electric cables –
Calculation of the current rating, can be found on the IEC website.
The committee has decided that the contents of this document will remain unchanged until the
stability date indicated on the IEC website under webstore.iec.ch in the data related to the
specific document. At this date, the document will be
• reconfirmed,
• withdrawn,
• replaced by a revised edition, or
• amended.
INTRODUCTION
When single-core cables are installed in parallel, it is possible that the load current will not
share equally between the parallel cables. The circulating currents in the sheaths of the parallel
cables will also differ. This is because a significant proportion of the impedance of large
conductors is due to self reactance and mutual reactance. Hence the spacing and relative
location of each cable will have an effect on the current sharing and the circulating currents.
The currents are also affected by phase rotation. The method described in this document can
be used to calculate the current sharing between conductors as well as the circulating current
losses.
There is no simple rule by which the circulating current losses of parallel cables can be
estimated. Calculation for each cable configuration should be applied. The principles and
impedance formulae involved are straightforward but the difficulty arises in solving the large
number of simultaneous equations generated. The number of equations to be solved generally
precludes the use of manual calculations and solution by computer is recommended. For n
c
cables per phase having metallic sheaths in a three-phase system there are 6 · n equations
c
containing the same number of complex variables.
For simplicity the equations set out in this document assume that the parallel conductors all
have the same cross-sectional area. If this is not the case, the equations should be adapted to
allow for different resistances for each conductor. The effect of neutral and earth conductors
can also be calculated by including these conductors in the appropriate loops. The method set
out in this document does not take account of any portion of the sheath circulating currents that
can flow through the earth or other extraneous paths. In this respect, the effect of earth return
path has been excluded for the purposes of the methodology described in the following, as it is
concluded that it can affect the magnitude of the resulting circulating currents only by a
...

IEC 60287-1-3 ®
Edition 2.0 2023-05
COMMENTED VERSION
INTERNATIONAL
STANDARD
colour
inside
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
All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized in any form
or by any means, electronic or mechanical, including photocopying and microfilm, without permission in writing from
either IEC or IEC's member National Committee in the country of the requester. If you have any questions about IEC
copyright or have an enquiry about obtaining additional rights to this publication, please contact the address below or
your local IEC member National Committee for further information.

IEC Secretariat Tel.: [phone]
3, rue de Varembé [e-mail]
CH-1211 Geneva 20 www.iec.ch
Switzerland
About the IEC
The International Electrotechnical Commission (IEC) is the leading global organization that prepares and publishes
International Standards for all electrical, electronic and related technologies.

About IEC publications
The technical content of IEC publications is kept under constant review by the IEC. Please make sure that you have the
latest edition, a corrigendum or an amendment might have been published.

IEC publications search - webstore.iec.ch/advsearchform IEC Products & Services Portal - products.iec.ch
The advanced search enables to find IEC publications by a
Discover our powerful search engine and read freely all the
variety of criteria (reference number, text, technical publications previews. With a subscription you will always have
committee, …). It also gives information on projects, replaced access to up to date content tailored to your needs.
and withdrawn publications.
Electropedia - www.electropedia.org
IEC Just Published - webstore.iec.ch/justpublished
The world's leading online dictionary on electrotechnology,
Stay up to date on all new IEC publications. Just Published
containing more than 22 300 terminological entries in English
details all new publications released. Available online and once
and French, with equivalent terms in 19 additional languages.
a month by email.
Also known as the International Electrotechnical Vocabulary

(IEV) online.
IEC Customer Service Centre - webstore.iec.ch/csc

If you wish to give us your feedback on this publication or need
further assistance, please contact the Customer Service
Centre: [e-mail].
IEC 60287-1-3 ®
Edition 2.0 2023-05
COMMENTED VERSION
INTERNATIONAL
STANDARD
colour
inside
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
INTERNATIONAL
ELECTROTECHNICAL
COMMISSION
ICS 29.060.20 ISBN 978-2-8322-7060-8

– 2 – IEC 60287-1-3:2023 CMV © IEC 2023
CONTENTS
FOREWORD .3
INTRODUCTION .5

1 Scope .6
2 Normative references .6
3 Terms, definitions and symbols.6
3.1 Terms and definitions .6
3.2 Symbols .6
4 Description of method .7
4.1 General .7
4.2 Outline of method .8
4.3 Matrix solution . 12

Annex A (informative) Example calculations . 13
A.1 Introduction Overview . 13
A.2 Example 1 . 13
A.2.1 General . 13
A.2.2 Calculations . 14
A.3 Example 2 . 19
A.4 Example 3 . 19
A.5 Example 4 . 20
Annex B (informative) Example of the computation of the coefficient α for hollow core
conductors . 21
Bibliography . 22
List of comments . 23

Figure B.1 – Representation of a hollow core conductor . 21

Table 1 – Values of α for conductors . 11
Table A.1 – Sheath loss factor calculation according to IEC 60287-1-1 . 14
Table A.2 – Sheath current and sheath loss factor calculation per phase . 16
Table A.3 – Calculated values of d . 17
ji,k
Table A.4 – Calculated values of zz . 17
Table A.5 – Array [Z] including coefficients for currents . 18
Table A.6 – Sheath current and sheath loss factor calculation per phase . 19
Table A.7 – Sheath current and sheath loss factor calculation per phase . 20
Table A.8 – Sheath current and sheath loss factor calculation per phase . 20

INTERNATIONAL ELECTROTECHNICAL COMMISSION
____________
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

FOREWORD
1) The International Electrotechnical Commission (IEC) is a worldwide organization for standardization comprising
all national electrotechnical committees (IEC National Committees). The object of IEC is to promote international
co-operation on all questions concerning standardization in the electrical and electronic fields. To this end and
in addition to other activities, IEC publishes International Standards, Technical Specifications, Technical Reports,
Publicly Available Specifications (PAS) and Guides (hereafter referred to as “IEC Publication(s)”). Their
preparation is entrusted to technical committees; any IEC National Committee interested in the subject dealt with
may participate in this preparatory work. International, governmental and non-governmental organizations liaising
with the IEC also participate in this preparation. IEC collaborates closely with the International Organization for
Standardization (ISO) in accordance with conditions determined by agreement between the two organizations.
2) The formal decisions or agreements of IEC on technical matters express, as nearly as possible, an international
consensus of opinion on the relevant subjects since each technical committee has representation from all
interested IEC National Committees.
3) IEC Publications have the form of recommendations for international use and are accepted by IEC National
Committees in that sense. While all reasonable efforts are made to ensure that the technical content of IEC
Publications is accurate, IEC cannot be held responsible for the way in which they are used or for any
misinterpretation by any end user.
4) In order to promote international uniformity, IEC National Committees undertake to apply IEC Publications
transparently to the maximum extent possible in their national and regional publications. Any divergence between
any IEC Publication and the corresponding national or regional publication shall be clearly indicated in the latter.
5) IEC itself does not provide any attestation of conformity. Independent certification bodies provide conformity
assessment services and, in some areas, access to IEC marks of conformity. IEC is not responsible for any
services carried out by independent certification bodies.
6) All users should ensure that they have the latest edition of this publication.
7) No liability shall attach to IEC or its directors, employees, servants or agents including individual experts and
members of its technical committees and IEC National Committees for any personal injury, property damage or
other damage of any nature whatsoever, whether direct or indirect, or for costs (including legal fees) and
expenses arising out of the publication, use of, or reliance upon, this IEC Publication or any other IEC
Publications.
8) Attention is drawn to the Normative references cited in this publication. Use of the referenced publications is
indispensable for the correct application of this publication.
9) Attention is drawn to the possibility that some of the elements of this IEC Publication may be the subject of patent
rights. IEC shall not be held responsible for identifying any or all such patent rights.
This commented version (CMV) of the official standard IEC 60287-1-3:2023 edition 2.0
allows the user to identify the changes made to the previous IEC 60287-1-3:2002
edition 1.0. Furthermore, comments from IEC TC 20 experts are provided to explain the
reasons of the most relevant changes, or to clarify any part of the content.
A vertical bar appears in the margin wherever a change has been made. Additions are in
green text, deletions are in strikethrough red text. Experts' comments are identified by a
blue-background number. Mouse over a number to display a pop-up note with the
comment.
This publication contains the CMV and the official standard. The full list of comments is
available at the end of the CMV.

– 4 – IEC 60287-1-3:2023 CMV © IEC 2023
IEC 60287-1-3 has been prepared by IEC technical committee 20: Electric cables. It is an
International Standard.
This second edition cancels and replaces the first edition published in 2002. This edition
constitutes a technical revision.
This edition includes the following significant technical changes with respect to the previous
edition:
a) Change and update of list of symbols. 1
The text of this International Standard is based on the following documents:
Draft Report on voting
20/2098/FDIS 20/2105/RVD
Full information on the voting for its approval can be found in the report on voting indicated in
the above table.
The language used for the development of this International Standard is English.
This document was drafted in accordance with ISO/IEC Directives, Part 2, and developed in
accordance with ISO/IEC Directives, Part 1 and ISO/IEC Directives, IEC Supplement, available
at www.iec.ch/members_experts/refdocs. The main document types developed by IEC are
described in greater detail at www.iec.ch/publications.
A list of all parts in the IEC 60287 series, published under the general title Electric cables –
Calculation of the current rating, can be found on the IEC website.
The committee has decided that the contents of this document will remain unchanged until the
stability date indicated on the IEC website under webstore.iec.ch in the data related to the
specific document. At this date, the document will be
• reconfirmed,
• withdrawn,
• replaced by a revised edition, or
• amended.
IMPORTANT – The "colour inside" logo on the cover page of this document indicates that it
contains colours which are considered to be useful for the correct understanding of its
contents. Users should therefore print this document using a colour printer.

INTRODUCTION
When single-core cables are installed in parallel, it is possible that the load current may will not
share equally between the parallel cables. The circulating currents in the sheaths of the parallel
cables will also differ. This is because a significant proportion of the impedance of large
conductors is due to self reactance and mutual reactance. Hence the spacing and relative
location of each cable will have an effect on the current sharing and the circulating currents.
The currents are also affected by phase rotation. The method described in this document can
be used to calculate the current sharing between conductors as well as the circulating current
losses.
There is no simple rule by which the circulating current losses of parallel cables can be
estimated. Calculation for each cable configuration is necessary should be applied. The
principles and impedance formulae involved are straightforward but the difficulty arises in
solving the large number of simultaneous equations generated. The number of equations to be
solved generally p
...