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

Overview

IEC 60287-1-3:2023 is part of the IEC 60287 series for calculating cable current ratings. This part provides a rigorous method to compute current sharing between parallel single‑core cables and to calculate circulating current losses (including the sheath loss factor) for any number of conductors per phase and in any physical layout. The standard covers the mathematical formulation (including a matrix solution) for phase and sheath currents at a 100% load factor, with worked examples and coefficient tables. It is Edition 2.0 (2023) and updates the symbol list and computational approach from the earlier edition.

Key topics and technical requirements

• Scope and assumptions
  • Method applies to parallel single‑core cables of the same conductor cross‑section (equations can be adapted for unequal sizes).
  • Sheath losses are calculated assuming sheaths/screens are bonded at both ends.
  • Earth return paths are not modelled (their effect is typically small except in special low‑resistivity/low‑earthing‑resistance cases).
  • Calculations are set for 100% load factor.
• Impedance-based formulation
  • Uses conductor self and mutual reactance and resistance to build simultaneous complex equations for conductor and sheath loops.
  • The impedance voltages are eliminated using phase current constraints; results yield complex conductor currents and sheath circulating currents.
• Matrix solution & computational approach
  • The method typically produces a large system of complex linear equations (6·n for n cables per phase in a 3‑phase system) - computer solution is recommended.
  • Includes derivation, a support matrix [Z], support vectors, and iterative procedure guidance where thermal resistance depends on cable losses.
• Loss metrics
  • Computes sheath loss factor (λ′) and circulating current losses per sheath; includes examples, tables (e.g., coefficients α for hollow core conductors) and informative annexes.

Practical applications and who should use it

• Target users:
  • Cable designers, power system planners, utilities, consultants, manufacturers and installation engineers specifying or analyzing parallel single‑core cable systems.
• Typical applications:
  • Determining unequal current sharing in parallel runs.
  • Calculating circulating current losses for thermal rating, efficiency and lifecycle loss costing.
  • Supporting thermal performance assessments for buried cable groups (in conjunction with external thermal resistance calculations).
  • Informing protection coordination and sizing where mutual coupling impacts voltage drop and loss distribution.

Related standards

• IEC 60287 series (general current rating methodology)
• IEC 60287-1-2 - sheath eddy current losses for two circuits in flat formation
• IEC 60287-2-1:2023 - external thermal resistance methods for buried parallel cables (used iteratively with 1-3 results)

Keywords: IEC 60287-1-3:2023, current sharing, parallel single-core cables, circulating current losses, current rating calculation, sheath loss factor, mutual reactance, matrix solution.

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
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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 small
extent on a limited number of cases, where both very low soil electrical resistivity values and
low earthing conductor resistance values are simultaneously considered.
The conductor currents and sheath circulating currents in parallel single-core cables are
unlikely to be equal. Because of this, the external thermal resistance for buried parallel cables
should be calculated using the method set out in IEC 60287-2-1:2023, 4.2.3.2. Because the
external thermal resistance and sheath temperatures are functions of the power dissipation
from each cable in the group an iterative procedure to determine the circulating current losses
and the external thermal resistance should be adopted.

– 6 – IEC 60287-1-3:2023 © IEC 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

1 Scope
This part of IEC 60287 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.
2 Normative references
There are no normative references in this document.
3 Terms, definitions and symbols
3.1 Terms and definitions
No terms and definitions are listed in this document.
ISO and IEC maintain terminology databases for use in standardization at the following
addresses:
• IEC Electropedia: available at https://www.electropedia.org/
• ISO Online browsing platform: available at https://www.iso.org/obp
3.2 Symbols
d external diameter of the conductor, mm
c
d mean diameter of sheath or screen, mm
s
f system frequency, Hz
n number of cables per phase
c
axial spacing between conductors, mm
D
mn
[I] support vector used in the calculation of current in 4.3
I current in the conductor of cable n , A
nc c
I circulating current in the sheath of cable n , A
snc c
[Q] support matrix used in the calculation of current in 4.3
R resistance of a conducting element, Ω/m
R AC resistance of conductor at maximum operating temperature, Ω/m
c
R AC resistance of the cable sheath or screen at their maximum operating temperature,
s
Ω/m
X apparent mutual reactance of a pair of conductors
i,k
[Z] support matrix used in the calculation of current in 4.3
ΔV conductor voltage drop, V
Α coefficient depending on the construction of the conductor
λ′ sheath loss factor of cable n due to circulating currents
nc c
−1
Ω angular frequency of system (2πf), s
NOTE Subscripts m, n, i and k are used in the following only to denote rows and columns of matrices and therefore
to identify specific matrix elements. They do not correspond to the respective symbols used in other parts of the
IEC 60287 series for identifying physical quantities.
4 Description of method
4.1 General
The method calculates the proportion of the phase current carried by each parallel conductor
and the circulating current in the sheath of each cable. The loss factor (λ’) for each case is then
calculated as the ratio of the losses in a sheath caused by circulating currents to the losses in
the conductor of that cable.
The method of calculation set out in 4.2 and 4.3 only considers voltage drop along the
conductors. Any unbalance in the load which would lead to unbalanced phase currents is
ignored.
The equations to be solved for the unknown currents in the parallel conductors and their sheaths
are built up from a consideration of the basic formulae for the impedance associated with a loop
consisting of two long conductors lying parallel to each other and the formulae for the mutual
impedance between a loop and an adjacent conductor. Consideration of these equations leads
to a system of simultaneous equations for the impedance voltage for all the conductors and
sheaths in a three-phase parallel cable system. The impedance voltages for all conductors in
parallel in the same phase are equal. Also for the conductors representing the bonded sheaths
the
...

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 precludes the use of manual calculations and solution by computer is
recommended. For n cables per phase having metallic sheaths in a three-phase system there
c
are 6 n · n equations containing the same number of complex variables.
c
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 may 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
may 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
small extent on a limited number of cases, where both very low soil electrical resistivity values
and low earthing conductor resistance values are simultaneously considered. 2
The conductor currents and sheath circulating currents in parallel single-core cables are
unlikely to be equal. Because of this, the external thermal resistance for buried parallel cables
should be calculated using the method set out in IEC 60287-2-1:2023, 4.2.3.2. Because the
external thermal resistance and sheath temperatures are functions of the power dissipation
from each cable in the group it is necessary to adopt an iterative procedure to determine the
circulating current losses and the external thermal resistance should be adopted.

– 6 – IEC 60287-1-3:2023 CMV © IEC 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

1 Scope
This part of IEC 60287 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.
2 Normative references
The following referenced documents are indispensable for the application of this document. For
dated references, only the edition cited applies. For undated references, the latest edition of
the referenced document (including any amendments) applies.
IEC 60287-1-2:1993, Electric cables – Calculation of the current rating – Part 1: Current rating
equations (100 % load factor) and calculation of losses – Section 2: Sheath eddy current loss
factors for two circuits in flat formation
IEC 60287-2-1:1994, Electric cables – Calculation of the current rating – Part 2: Thermal
resistance – Section 1: Calculation of thermal resistance
There are no normative references in this document.
3 Terms, definitions and symbols
3.1 Terms and definitions
No terms and definitions are listed in this document.
ISO and IEC maintain terminology databases for use in standardization at the following
addresses:
• IEC Electropedia: available at https://www.electropedia.org/
• ISO Online browsing platform: available at https://www.iso.org/obp
3.2 Symbols
d external diameter of the conductor, mm
c
d mean diameter of sheath or screen, mm
s
f system frequency, Hz
i, k elements in the series of conductors

m, n elements in the series of cables
p n number of cables per phase
c
D axial spacing between conductors, mm
mn
[I] support vector used in the calculation of current in 4.3
I current in the conductor of cable p n , A
pnc c
I circulating current in the sheath of cable p n , A
spnc c
[Q] support matrix used in the calculation of current in 4.3
R resistance of a conducting element, Ω/m
R AC resistance of conductor at maximum operating temperature, Ω/m
c
R AC resistance of the cable sheath or screen at their maximum operating temperature,
s
Ω/m
X apparent mutual reactance of a pair of conductors
i,k
[Z] support matrix used in the calculation of current in 4.3
ΔV conductor voltage drop, V
αΑ coefficient depending on the construction of the conductor
λ’ sheath loss factor of cable p n due to circulating currents
pnc c
−1
ωΩ angular frequency of system (2πf), s
NOTE Subscripts m, n, i and k are used in the following only to denote rows and columns of matrices and therefore
to identify specific matrix elements. They do not correspond to the respective symbols used in other parts of the
IEC 60287 series for identifying physical quantities.
4 Description of method
4.1 General
The method calculates the proportion of the phase current carried by each parallel conductor
and the circulating current in the sheath of each cable. The loss factor (λ’) for each case is then
calculated as the ratio of the losses in a sheath caused by circulating currents to the losses in
the conductor of that cable.
The method of calculation set out in 4.2 and 4.3 only considers voltage drop along the
conductors. Any unbalance in the load which would lead to unbalanced phase currents is
ignored.
The equations to be solved for the unknown currents in the parallel conductors and their sheaths
are built up from a consideration of the basic formulae for the impedance associated with a loop
consisting of two long conductors lying parallel to each other and the formulae for the mutual
impedance between a loop and an adjacent conductor. Consideration of these equations leads
to a system of simultaneous equations for the impedance voltage for all the conductors and
sheaths in a three-phase parallel cable system. The impedance voltages for all conductors in
parallel in the same phase are equal. Also for the conductors representing the bonded sheaths
the voltages are equal. Hence the impedance voltages can be eliminated from the equations.
The sum of the currents in the parallel conductors is equal to either the known phase current or
zero for the sheaths. This provides the additional information needed required for the solution
of the simultaneous equations.
It should be noted that all the currents are complex quantities containing both real and imaginary
parts.
The mutual impedance between conductors is a function of their relative positions. Hence, if
the relative positions of the cables vary along the route, or the sheaths are cross-bonded, then

– 8 – IEC 60287-1-3:2023 CMV © IEC 2023
the impedance for each section shall be calculated individually and the vector results summed
in order to obtain the total impedance of each loop. If the route length is very short, then
significant errors may can occur in the calculated result due to the change in the relative
positions of the cables as they approach the terminations.
The equations set out in this document can also be used to calculate the current sharing
between cables without a metallic sheath or armour and between cables with the sheaths
connected together at one end only, single-point bonded. For such calculations, the circulating
current in each sheath is zero. Where cable sheaths are bonded at one end only, the standing
voltage at the open circuit end of the sheath can also be determined using this method of
calculation.
For the method set out in this document, it is recommended that the solution of the equations
is achieved by a process of matrix algebra. This has the advantage that the solution achieved
is unique and not a function of an iterative process.
4.2 Outline of method
The loss factor for the sheath in a given cable in a parallel circuit is given by:
 I 
R
sp
s
 
′
λ = (1)
p
 
I R
p c
 
where
λ′ is the sheath loss factor of cable p due to circulating currents;
p
I is the circulating current in the sheath of cable p, in A;
sp
I is the current in the conductor of cable p, in A;
p
R is the resistance of sheath at operating temperature, in Ω/m;
s
R is the a.c. resistance of conductor at operating temperature, in Ω/m.
c
 
I
R
s n
c s
′   (1)
λ =
n
c
 
IR
n c
c
 
The currents I and I are obtained by solution of equations of the following form where
spnc pnc
there are pn conductors in parallel and a total of n 6 · n conductors in a three-phase system.
c c
To simplify matters, both the phase conductors and the sheaths are referred to as conductors.
The phase conductor currents are I , I , etc. The sheath currents are I , I , I ,
1 2 3pnc+1 3pnc+2 3pnc+3
etc.
For convenience in the calculations, the following notation is used:
Cable references
Circuit 1 … i … pn
c
Phase R 1 … i … pn
c
Phase S pn + 1 … pn + i … 2pn
c c c
Phase T 2pn + 1 … 2pn + i … 3pn
c c c
The conductors can then be identified as follows:

Reference of a phase conductor = reference of the cable
Reference of a sheath conductor = reference of the cable + 3pn
c
For each phase the current is given by:
p
I [1 + j 0]      = I
R k
∑
k =1
2 p
I [− 0,5 − j 0,866] = I
S k
∑
k =p+1
3 p
I [− 0,5 + j 0,866] = I
T k
∑
k =2 p+1
n
c
Ij1+=0      I
[ ]
∑
Rk
k1=
2n
c
Ij[−0,5 − 0,866] = I
Sk∑ (2)
k1n+
c
3n
c
Ij−0,5 + 0,866 = I
[ ]
Tk∑
k2n+1
c
The above Equations (2) assume forward phase rotation. If the phase rotation is not known, the
calculation shall be carried out for both forward and reverse phase rotations.
For conductor loops representing the sheaths, the current is given by:
6 p
0 + j 0 = I
k
∑
k=3 p+1
6n
c
00+=j I
(3)
∑ k
k3n+1
c
The voltage drop in each conductor is then
– for the conductors of phase R:
6 p
∆V = Z × I
R i,k k
∑
k =1
=
=
=
– 10 – IEC 60287-1-3:2023 CMV © IEC 2023
6n
c
ΔV ZI× (4)
∑
R i,k k
k1=
for i = 1 to pn ;
c
– for the conductors of phase S:
6 p
∆V = Z × I
S i,k k
∑
k =1
6n
c
ΔV ZI× (5)
S ∑ i,k k
k1=
for i = pn + 1 to 2pn ;
c c
– for the conductors of phase T:
6 p
∆V = Z × I
T i,k k
∑
k =1
6n
c
ΔV ZI× (6)
T ∑ i,k k
k1=
for i = 2pn + 1 to 3pn ;
c c
– for the sheath conductors:
6 p
∆V = Z × I
A ∑ i,k k
k =1
6n
c
ΔV ZI× (7)
∑
A i,k k
k1=
for i = 3pn + 1 to 6pn .
c c
Eliminating the voltage drop from this set of equations leads to (6pn – 4) equations having the
c
following form:
6 p
0 + j 0 = zz × I
i,k k
∑
k =3 p+1
=
=
=
=
6n
c
00+= j zz× I (8)
∑
i,k k
k1=
where zz =Z − Z =R+ jX
i,k i,k i+1,k i,k i,k
and R is defined as follows:
i ≠ k i ≠ k− 1
R = 0 if  R = 0 if
For the phase conductors (refer to array [Z] in Example 1)
R = R if i = k and i ≤ 3pn   R = – R if i = k – 1 and i ≤ 3pn
c c c c
For the sheath conductors (refer to array [Z] in Example 1)
R = R if i = k and i > 3pn   R = – R if i = k – 1 and i > 3pn
s c s c
X is regarded as a reactance and is defined as follows:
i,k
d
−7 i+1,k
X = 2ω10 ln
 (9)
i,k

d
i,k

where
if i ≠ k , then d = D = axial spacing between cables m and n,
i,k m,n
with m = i if i ≤ 3pn  m = i – 3pn if i > 3pn
c c c
and n = k if k ≤ 3pn  n = k – 3pn if k > 3pn
c c c
d
c
d = α
If i = k  and i ≤ 3pn then
i,k
c
d
s
d =
If i = k  and i > 3pn  then
i,k
c
where
ω = 2πf
f is the frequency, in Hz;
d is the diameter of the conductor, in mm;
c
d is the mean diameter of the sheath, in mm;
s
α is the coefficient depending on the construction of the conductor, see table 1.
For appropriate values of coefficient α see Table 1.

– 12 – IEC 60287-1-3:2023 CMV © IEC 2023
Table 1 – Values of α for conductors
Number of wires
Value of α
1 (solid) 0,779
3 0,678
7 0,726
19 0,758
37 0,768
61 0,772
91 0,774
127 0,776
The values given in Table 1 are applicable to non-compacted conductors. For compacted
conductors α = 0,779 should be used. The values for hollow conductors are dependent on the
inner and outer diameters of the conductor. An example of the calculation of α for hollow
conductors is given in Annex B.
4.3 Matrix solution
In general the equations developed will be of the form:
Q = f (Z × I )
n n n
Q f Z× I
( )
where the values for Q are given by the left-hand side of Equations (2), (3) and (8). The value
for Z are the coefficients of I in these equations, and the values for I are the unknown currents
n n
in the conductors and sheaths.
In matrix form the equations become:
Q ZI×
[ ] [ ] [ ]
where [Z] is a square matrix of the coefficients of I to I in Equations (2), (3) and (8).
1 nk
In order to solve the unknown currents [I] the equation is written as:
−1
[I ] = [Z] × [Q]
−1
where [Z] is the inverse matrix of [Z].
Example calculations using the matrix solution are given in Annex A.

=
=
Annex A
(informative)
Example calculations
A.1 Introduction Overview
The cable dimensions used in these examples are arbitrary and do not represent any particular
type of cable.
It is assumed that the relative positions of the cables do not change over the length of the run.
It is also assumed that the bonding conductors have an impedance which is negligible compared
with the impedance of the conductors. The skin and proximity effects on AC resistance are
ignored. The various impedance values calculated in these examples are for 1 000 m long
cables.
These examples assume a supply frequency of 50 Hz.
The cable and installation parameters are as follows:
Copper conductor diameter: 32,8 mm
−6
Conductor resistance at 20 °C:
28,3 · 10 Ω/m
Maximum operating temperature: 70 °C
−6
Conductor resistance at 70 °C:
33,86 · 10 Ω/m
Number of wires in conductor: 127
Conductor coefficient for 127 strands: 0,776
−3
Aluminium sheath resistance at 20 °C:
0,18 · 10 Ω/m
Mean diameter of sheath: 48 mm
Sheath temperature: 60 °C
−3
Sheath resistance at 60 °C:
0,209 · 10 Ω/m
A.2 Example 1
A.2.1 General
The cables are laid in flat formation at 200 mm between centres with two cables per phase and
no neutrals. The cable arrangement is as follows:
Cable 1 Cable 3 Cable 5 Cable 6 Cable 4 Cable 2
R1 S1 T1 T2 S2 R2
For convenience in the calculation, the conductors and sheath of each cable are numbered so
that the conductors are numbered 1 to 6 and the sheaths 7 to 12. The first cable will have
conductor 1 and sheath 7. The second cable being 2, 8, etc. This gives a total of 12 conductors
in this example.
– 14 – IEC 60287-1-3:2023 CMV © IEC 2023
For a single circuit installed in flat formation at 200 mm centres, with one cable per phase, the
sheath loss factors calculated in accordance with IEC 60287-1-1 are:
Table A.1 – Sheath loss factor calculation according to IEC 60287-1-1
Outer Middle Outer
1,99 1,50 2,62
These values are similar to the values obtained in Examples 1 and 2, but significantly different
from those obtained in Example 4.
A.2.2 Calculations
The zero co-ordinates (0,0) can be fixed at any point, but it is convenient to take the axis of the
lower left-hand cable as (0,0). The cable co-ordinates are entered into the array S below:
x y
0 0 Cable 1, phase R
1 000 0 Cable 2, phase R
S = 200 0 Cable 3, phase S
800 0 Cable 4, phase S
400 0 Cable 5, phase T
600 0 Cable 6, phase T
The axial cable spacings are calculated using the following equation:
m = 1 to 6  n = 1 to 6
2 2
D = (S − S ) − (S − S )
m,n m,1 n,1 m,2 n,2
D SS− + S− S
( ) ( )
m,n m,1 n,1 m,2 n,2
The spacings are given in the array D below:
0 1 000 200 800 400 600
1 000 0 800 200 600 400
D = 200 800 0 600 200 400
800 200 600 0 400 200
400 600 200 400 0 200
600 400 400 200 200 0
Clearly this array is symmetrical about its diagonal and it is not necessary to calculate the
spacing between cables m and n as well as between cables n and m.
This array is then modified to include all the values of d required to calculate X . The modified
ji,k i,k
array is given in Table A.1.
The effective reactances X are calculated using Equation (9):
i,k
=

d
−7 i+1,k
X = 2ω10 ln
i,k

d
i,k

The coefficients, zz, for the right-hand side of Equation (8) are calculated as follows and are
given in the array zz, as shown in Table A.4.

zz R+ jX
i,k i,k i,k
where
i ≠ k i ≠ k− 1
R = 0 if R = 0 if
R = R if i = k and i ≤ 3pn R = –R if i = k – 1 and i ≤ 3pn
c c c c
R = R if i = k and i > 3pn R = –R if i = k – 1 and i > 3pn
s c s c
The coefficients for the current, I, for the right-hand side of Equations (2) and (3) are shown in
array H below;
1 1 0 0 0 0 0 0 0 0 0 0 Phase R
H = 0 0 1 1 0 0 0 0 0 0 0 0 Phase S
0 0 0 0 1 1 0 0 0 0 0 0 Phase T
0 0 0 0 0 0 1 1 1 1 1 1 Sheath

For convenience of calculation these coefficients are included in the same matrix as those
obtained from consideration of the conductor loops. The new array [Z] is given in Table A.5.
The values and coefficients for the left-hand side of Equations (2) and (3) are given in array [Q]
below:
–0,5 – 0,866j
–0,5 + 0,866j
[Q] = 0
The phase and sheath currents in each conductor can then be calculated by solving the
simultaneous equations set out in array [Z], Table A.3, and [Q] above. These currents are given
below in terms of the resistive and reactive components. Multiplying the inverse of matrix [Z] by
[Q] solves the equations.
=
– 16 – IEC 60287-1-3:2023 CMV © IEC 2023
0,5
0,5
–0,25 – 0,433j
–0,25 – 0,433j
–0,25 + 0,433j
[I] = –0,25 + 0,433j
–0,216 – 0,189 2j
–0,216 – 0,189 2j
–0,130 9 + 0,216 4j
–0,130 9 + 0,216 4j
0,346 9 – 0,027 2j
0,346 9 – 0,027 2j
The magnitude of the phase conductor and sheath currents together with the sheath loss factor
are given below, assuming a total phase current of 100 A.
Phase conductor current = I × 100 I ⋅100 ; Sheath current = I × 100 I ⋅100 ;
m
n 3 p+m sn
c c
I ⋅100 ⋅ R
(I × 100) × R
( )
ssn
3 p+m s
c
Loss factor = .
2 2
(I × 100) × R
m c IR⋅100 ⋅
( n ) c
c
Table A.2 – Sheath current and sheath loss factor calculation per phase
Sheath Sheath loss
Phase current
current factor
Cable 1, phase R 50 28,7 2,036
Cable 2, phase R 50 28,7 2,036
Cable 3, phase S 50 25,3 1,58
Cable 4, phase S 50 25,3 1,58
Cable 5, phase T 50 34,8 2,99
Cable 6, phase T 50 34,8 2,99
Table A.3 – Calculated values of d
ji,k
12,73 1 000 200 800 400 600 24 1 000 200 800 400 600
1 000 12,73 800 200 600 400 1 000 24 800 200 600 400
200 200800 12,73 600 200 400 200 200800 24 600 200 400
800 800200 600 12,73 400 200 800 800200 600 24 400 200
400 600 200 400 12,73 200 400 600 200 400 24 200
600 400 400 200 200 12,73 600 400 400 200 200 24
24 1 000 200 800 400 600 24 1 000 200 800 400 600
1 000 24 800 200 600 400 1 000 24 800 200 600 400
200 200800 24 600 200 400 200 200800 24 600 200 400
800 800200 600 24 400 200 800 800200 600 24 400 200
400 600 200 400 24 200 400 600 200 400 24 200
600 400 400 200 200 24 600 400 400 200 200 24

Table A.4 – Calculated values of zz
0,033 9 + 0,274 2j −0,033 9−0,274 2j 0,087 1j −0,087 1j 0,025 5j −0,025 5j 0,234 3j −0,234 3j 0,087 1j −0,087 1j 0,025 5j −0,025 5j
0,087 1j −0,087 1j 0,033 9 + 0,242 1j −0,0339 − 0,242 1j 0,043 6j −0,043 6j 0,087 1j −0,087 1j 0,202 2j −0,202 2j 0,043 6j −0,043 6j
0,025 5j −0,025 5j 0,043 6j −0,043 6j 0,033 9 + 0,173 1j −0,033 9 − 0,173 1j 0,025 5j −0,025 5j 0,043 6j −0,043 6j 0,133 2j −0,133 2j
0,234 3j −0,234 3j 0,087 1j −0,087 1j 0,025 5j −0,022 5j 0,209 + 0,234 3j −0,209 − 0,234 3j 0,087 1j −0,087 1j 0,025 5j −0,022 5j
−0,101 1j 0,220 3j −0,220 3j 0,069j −0,069j 0 −0,101 1j 0,209 + 0,220 3j −0,209 − 0,220 3j 0,069j −0,069j 0
0,087 1j −0,087 1j 0,202 2j −0,202 2j 0,043 6j −0,043 6j 0,087 1j −0,087 1j 0,209 + 0,202 2j −0,209 − 0,202 2j −0,043 6j −0,043 6j
−0,043 6j 0,069j −0,069j 0,176 8j −0,176 8j 0 −0,043 6j 0,069j −0,069j 0,209 + 0,176 8j −0,209 − 0,176 8j 0
0,025 5j −0,025 5j 0,043 6j −0,043 6j 0,133 2j −0,133 2j 0,025 5j −0,025 5j 0,043 6j −0,0436j 0,209 + 0,133 2j −0,209 − 0,133 2j

– 18 – IEC 60287-1-3:2023 CMV © IEC 2023

Table A.5 – Array [Z] including coefficients for currents
0,033 9 + 0,274 2j –0,033 9 – 0,274 2j 0,087 1j –0,087 1j 0,025 5j –0,025 5j 0,234 3j –0,234 3j 0,087 1j –0,087 1j 0,025 5j –0,025 5j
1 1 0 0 0 0 0 0 0 0 0 0
0,087 1j –0,087 1j 0,033 9 + 0,242 1j –0,033 9 – 0,242 1j 0,043 6j –0,043 6j 0,087 1j –0,087 1j 0,202 2j –0,202 2j 0,043 6j –0,043 6j
0 0 1 1 0 0 0 0 0 0 0 0
0,025 5j –0,025 5j 0,043 6j –0,043 6j 0,033 9 + 0,173 1j –0,033 9 – 0,173 1j 0,025 5j –0,025 5j 0,043 6j –0,043 6j 0,133 2j –0,133 2j
0 0 0 0 1 1 0 0 0 0 0 0
0,234 3j –0,234 3j 0,087 1j –0,087 1j 0,025 5j –0,022 5j 0,209 + 0,234 3j –0,209 – 0,234 3j 0,087 1j –0,087 1j 0,025 5j –0,022 5j
–0,101 1j 0,220 3j –0,220 3j 0,069j –0,069j 0 –0,101 1j 0,209 + 0,220 3j –0,209 – 0,220 3j 0,069j –0,069j 0
0,087 1j –0,087 1j 0,202 2j –0,202 2j 0,043 6j –0,043 6j 0,087 1j –0,087 1j 0,209 + 0,202 2j –0,209 – 0,202 2j –0,043 6j
–0,043 6j
–0,043 6j 0,069j –0,069j 0,176 8j –0,176 8j 0 –0,043 6j 0,069j –0,069j 0,209 + 0,176 8j –0,209 – 0,176 8j 0
0,025 5j –0,025 5j 0,043 6j –0,043 6j 0,133 2j –0,133 2j 0,025 5j –0,025 5j 0,043 6j –0,043 6j 0,209 + 0,133 2j –0,209 – 0,133 2j
0 0 0 0 0 0 1 1 1 1 1 1
A.3 Example 2
In this example, the same cable data and spacing has been used as in Example 1, but the
phase rotation has been reversed.
The magnitude of the phase conductor and sheath currents together with the sheath loss factor
are given in Table A.6 below, assuming a total phase current of 100 A.
Table A.6 – Sheath current and sheath loss factor calculation per phase
Phase current Sheath current Sheath loss
factor
Cable 1, phase R 50 34,4 2,916
Cable 2, phase R 50 34,4 2,916
Cable 3, phase S 50 24,5 1,477
Cable 4, phase S 50 24,5 1,477
Cable 5, phase T 50 29,9 2,213
Cable 6, phase T 50 29,9 2,213

A.4 Example 3
In this example the same cable data has been used, but the six cables are now arranged in two
trefoil groups with 200 mm between centres of the groups. The arrangement is shown below:
R1 R2
S1 T1 T2 S2
The cable co-ordinates are as follows:
x y
30 52 Cable 1, phase R
230 52 Cable 2, phase R
D = 0 0 Cable 3, phase S
260 0 Cable 4, phase S
60 0 Cable 5, phase T
200 0 Cable 6, phase T
The magnitude of the phase conductor and sheath currents, together with the sheath loss factor
are given in Table A.7 below, assuming a total phase current of 100 A.

– 20 – IEC 60287-1-3:2023 CMV © IEC 2023
Table A.7 – Sheath current and sheath loss factor calculation per phase
Phase current Sheath current Sheath loss
factor
Cable 1, phase R 50 13,9 0,474
Cable 2, phase R 50 13,9 0,474
Cable 3, phase S 50 13,8 0,468
Cable 4, phase S 50 13,8 0,468
Cable 5, phase T 50 14,1 0,492
Cable 6, phase T 50 14,1 0,492

A.5 Example 4
In this example, the same cable data has been used but the cables are now such that the
current sharing between phase conductors is not equal. The arrangement is shown below:
R1 R2 S1 S2 T1 T2
The cable co-ordinates are as follows:
x y
0 0 Cable 1, phase R
400 0 Cable 2, phase R
D = 800 0 Cable 3, phase S
1 200 0 Cable 4, phase S
1 600 0 Cable 5, phase T
2 000 0 Cable 6, phase T
The magnitude of the phase conductor and sheath currents together with the sheath loss factor
are given in Table A.8 below, assuming a total phase current of 100 A.
Table A.8 – Sheath current and sheath loss factor calculation per phase
Phase current Sheath current Sheath loss
factor
Cable 1, phase R 46,31 38,4 4,236
Cable 2, phase R 53,71 36,5 2,845
Cable 3, phase S 44,59 37,4 4,346
Cable 4, phase S 55,66 34,8 2,42
Cable 5, phase T 50,76 43,7 4,576
Cable 6, phase T 49,62 44,4 4,947

Comparison with Example 1 shows that the sheath losses for this cable arrangement are very
high. Because of this, arrangements where all the conductors of one phase are placed together
should be avoided.
Annex B
(informative)
Example of the computation of the coefficient α
for hollow core conductors
Consider a hollow core conductor with internal and external diameters d = 17,5 mm and
i
d = 33,8 mm, respectively. The following procedure can be used to calculate α.
c
Let a = d / d = 17,5 / 33,8 = 0,518. The hollow conductor can be replaced by an equivalent
i c
conductor with the inner radius a and the outer radius equal to 1, as shown in Figure B.1.
then:
If a fraction of the total current enclosed within the radius r is denoted by I
r
2 2
r − a
I =
r
1 − a
Figure B.1 – Representation of a hollow core conductor
The magnetic flux is proportional to I /r and the linkage flux, F, is equal to:
r
1 1
2 2 2 4
(r − a ) dr 0,25 − a + a (0,75 − ln a)
F = I dϕ = =
r m
∫ ∫ 2 2
r
2 2
(1 − a ) (1 − a )
0 0
2 4
0,25 − 0,518 + 0,518 (0,75 − ln 0,518)
= = 0,1551
(1 − 0,518 )
The coefficient α is then given by:
−0,1551
α e 0,856
==
– 22 – IEC 60287-1-3:2023 CMV © IEC 2023
Bibliography
IEC 60287-1-1:1994, Electric cables – Calculation of the current rating – Part 1-1: Current rating
equations (100 % load factor) and calculation of losses – General
IEC 60287-1-2, Electric cables – Calculation of the current rating – Part 1-2: Current rating
equations (100 % load factor) and calculation of losses – Sheath eddy current loss factors for
two circuits in flat formation
IEC 60287-2-1:2023, Electric cables – Calculation of the current rating – Part 2-1: Thermal
resistance – Calculation of thermal resistance

List of comments
1 To avoid the use of same symbol with different meanings or different symbols with the same
meaning across IEC 60287 standard series, some symbols have been changed. One of the
main new criteria is the use of capital letter "C" for all coefficients.
2 The text here complements the text above and provides an explanation for the exclusion of
earth return path from the methodology described in the following.

___________
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
– 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 .
...