IEC 60287-2-1:2023

Electric cables - Calculation of the current rating - Part 2-1: Thermal resistance - Calculation of thermal resistance

IEC 60287-2-1:2023 is solely applicable to the conditions of steady-state operation of cables at all alternating voltages, and direct voltages up to 5 kV, buried directly in the ground, in ducts, in troughs or in steel pipes, both with and without partial drying-out of the soil, as well as cables in air. The term "steady state" is intended to mean a continuous constant current (100 % load factor) just sufficient to produce asymptotically the maximum conductor temperature, the surrounding ambient conditions being assumed constant.

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 60287-2-1:2015 - Electric cables - Calculation of the current rating - Part 2-1: Thermal resistance - Calculation of the thermal resistance
• Effective Date: 05-Sep-2023

Standards Content (Sample)

IEC 60287-2-1 ®
Edition 3.0 2023-05
INTERNATIONAL
STANDARD
Electric cables – Calculation of the current rating –
Part 2-1: Thermal resistance – Calculation of thermal resistance

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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(IEV) online.
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further assistance, please contact the Customer Service
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IEC 60287-2-1 ®
Edition 3.0 2023-05
INTERNATIONAL
STANDARD
Electric cables – Calculation of the current rating –

Part 2-1: Thermal resistance – Calculation of thermal resistance

INTERNATIONAL
ELECTROTECHNICAL
COMMISSION
ICS 29.060.20  ISBN 978-2-8322-6981-7

– 2 – IEC 60287-2-1:2023 © IEC 2023
CONTENTS
FOREWORD . 4
INTRODUCTION . 6
1 Scope . 7
2 Normative references . 7
3 Terms, definitions and symbols . 8
3.1 Terms and definitions. 8
3.2 Symbols . 8
4 Calculation of thermal resistances . 11
4.1 Thermal resistance of the constituent parts of a cable, T , T and T . 11
1 2 3
4.1.1 General . 11
4.1.2 Thermal resistance between one conductor and sheath T . 11
4.1.3 Thermal resistance of any generic annular layer . 15
4.1.4 Thermal resistance between sheath and armour T . 15
4.1.5 Thermal resistance of outer covering (serving) T . 16
4.1.6 Pipe-type cables . 17
4.2 External thermal resistance T . 17
4.2.1 Cables laid in free air. 17
4.2.2 Single isolated buried cable . 19
4.2.3 Groups of buried cables (not touching) . 19
4.2.4 Groups of buried cables (touching) equally loaded . 22
4.2.5 Cables in buried troughs . 24
4.2.6 Cables in ducts or pipes . 24
4.2.7 Cables or conduits laid in a medium of different thermal resistivity . 26
5 Digital calculation of quantities given graphically . 27
5.1 General . 27
5.2 Geometric factor G for two-core belted cables with circular conductors . 27
5.3 Geometric factor G for three-core belted cables with circular conductors . 28
5.4 Thermal resistance of three-core screened cables with circular conductors
compared to that of a corresponding unscreened cable . 29
5.5 Thermal resistance of three-core screened cables with sector-shaped
conductors compared to that of a corresponding unscreened cable. 30
5.6 Curve for G for obtaining the thermal resistance of the filling material
between the sheaths and armour of SL and SA type cables . 31
5.7 Calculation of Δθ by means of a diagram . 32
s
Annex A (informative) Correction factor for increased lengths of individual cores within
multicore cables . 46
Bibliography . 47

Figure 1 – Diagram showing a group of q cables and their reflection in the ground-air
surface . 36
Figure 2 – Geometric factor G for two-core belted cables with circular conductors
(see 4.1.2.2.2) . 37
Figure 3 – Geometric factor G for three-core belted cables with circular conductors
(see 4.1.2.2.4) . 38
Figure 4 – Thermal resistance of three-core screened cables with circular conductors
compared to that of a corresponding unscreened cable (see 4.1.2.3.1) . 39

Figure 5 – Thermal resistance of three-core screened cables with sector-shaped
conductors compared to that of a corresponding unscreened cable (see 4.1.2.3.3) . 40
Figure 6 – Geometric factor G for obtaining the thermal resistances of the filling
material between the sheaths and armour of SL and SA type cables (see 4.1.2.5) . 41
Figure 7 – Heat dissipation coefficient for black surfaces of cables in free air, laying
conditions 1 to 4 . 42
Figure 8 – Heat dissipation coefficient for black surfaces of cables in free air, laying
conditions 5 to 8 . 43
Figure 9 – Heat dissipation coefficient for black surfaces of cables in free air, laying
conditions 9 and 10 . 44
Figure 10 – Graph for the calculation of external thermal resistance of cables in air . 45

Table 1 – Thermal resistivities of materials . 33
Table 2 – Extended values of the geometric factor for duct banks and backfills. 34
Table 3 – Values for constants Z, E and C for black surfaces of cables in free air . 35
g
Table 4 – Absorption coefficient of solar radiation for cable surfaces . 36
Table 5 – Values of constants U, V and Y . 36
Table A.1 – Values of C for different cases . 46
fL
– 4 – IEC 60287-2-1:2023 © IEC 2023
INTERNATIONAL ELECTROTECHNICAL COMMISSION
____________
ELECTRIC CABLES –
CALCULATION OF THE CURRENT RATING –

Part 2-1: Thermal resistance –
Calculation of thermal resistance

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 60287-2-1 has been prepared by IEC technical committee 20: Electric cables. It is an
International Standard.
This third edition cancels and replaces the second edition published in 2015. This edition
constitutes a technical revision.
This edition includes the following significant technical changes with respect to the previous
edition:
a) thorough redefinition of symbols used across the IEC 60287 and IEC 60853 series to realign
and unify definitions, eliminate inconsistencies and to improve cross-use of the different
parts of both IEC 60287 and IEC 60853 series;
b) improvement in the identification of tabulated materials and introduction of new materials in
the tables;
c) introduction of generic annular layers to improve thermal modelling of existing and future
cables designs;
d) improved calculation of T in the case of directly buried cables;
e) introduction of corrective factors, on relevant calculated physical characteristics to take into
account the effect of multicore lay-lengths; a dedicated annex to highlight correction factors
for different numb
...

IEC 60287-2-1 ®
Edition 3.0 2023-05
COMMENTED VERSION
INTERNATIONAL
STANDARD
colour
inside
Electric cables – Calculation of the current rating –
Part 2-1: Thermal resistance – Calculation of thermal resistance
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 60287-2-1 ®
Edition 3.0 2023-05
COMMENTED VERSION
INTERNATIONAL
STANDARD
colour
inside
Electric cables – Calculation of the current rating –
Part 2-1: Thermal resistance – Calculation of thermal resistance
INTERNATIONAL
ELECTROTECHNICAL
COMMISSION
ICS 29.060.20 ISBN 978-2-8322-7061-5
– 2 – IEC 60287-2-1:2023 CMV © IEC 2023
CONTENTS
FOREWORD .4
INTRODUCTION .7

1 Scope .8
2 Normative references .8
3 Terms, definitions and symbols.9
3.1 Terms and definitions .9
3.2 Symbols .9
4 Calculation of thermal resistances . 12
4.1 Thermal resistance of the constituent parts of a cable, T , T and T . 12
1 2 3
4.1.1 General . 12
4.1.2 Thermal resistance between one conductor and sheath T . 12
4.1.3 Thermal resistance of any generic annular layer . 16
4.1.4 Thermal resistance between sheath and armour T . 17
4.1.5 Thermal resistance of outer covering (serving) T . 17
4.1.6 Pipe-type cables . 18
4.2 External thermal resistance T . 18
4.2.1 Cables laid in free air. 18
4.2.2 Single isolated buried cable . 20
4.2.3 Groups of buried cables (not touching) . 21
4.2.4 Groups of buried cables (touching) equally loaded . 24
4.2.5 Buried pipes .
4.2.5 Cables in buried troughs . 26
4.2.6 Cables in ducts or pipes . 27
4.2.7 Cables or conduits laid in a medium of different thermal resistivity . 28
5 Digital calculation of quantities given graphically . 30
5.1 General . 30
5.2 Geometric factor G for two-core belted cables with circular conductors . 30
5.3 Geometric factor G for three-core belted cables with circular conductors . 32
5.4 Thermal resistance of three-core screened cables with circular conductors
compared to that of a corresponding unscreened cable . 33
5.5 Thermal resistance of three-core screened cables with sector-shaped
conductors compared to that of a corresponding unscreened cable . 35
5.6 Curve for G for obtaining the thermal resistance of the filling material between
the sheaths and armour of SL and SA type cables . 36
5.7 Calculation of Δθ by means of a diagram . 37
s
Annex A (informative) Correction factor for increased lengths of individual cores within
multicore cables . 52
Bibliography . 53
List of comments . 54

Figure 1 – Diagram showing a group of q cables and their reflection in the ground-air
surface . 42

Figure 2 – Geometric factor G for two-core belted cables with circular conductors
(see 4.1.2.2.2) . 43
Figure 3 – Geometric factor G for three-core belted cables with circular conductors
(see 4.1.2.2.4) . 44
Figure 4 – Thermal resistance of three-core screened cables with circular conductors
compared to that of a corresponding unscreened cable (see 4.1.2.3.1) . 45
Figure 5 – Thermal resistance of three-core screened cables with sector-shaped
conductors compared to that of a corresponding unscreened cable (see 4.1.2.3.3) . 46
Figure 6 – Geometric factor G for obtaining the thermal resistances of the filling material
between the sheaths and armour of SL and SA type cables (see 4.1.2.5) . 47
Figure 7 – Heat dissipation coefficient for black surfaces of cables in free air, laying
conditions 1 to 4. 48
Figure 8 – Heat dissipation coefficient for black surfaces of cables in free air, laying
conditions 5 to 8. 49
Figure 9 – Heat dissipation coefficient for black surfaces of cables in free air, laying
conditions 9 and 10 . 50
Figure 10 – Graph for the calculation of external thermal resistance of cables in air . 51

Table 1 – Thermal resistivities of materials . 39
Table 2 – Extended values of the geometric factor for duct banks and backfills . 40
Table 3 – Values for constants Z, E and gC for black surfaces of cables in free air . 40
g
Table 4 – Absorption coefficient of solar radiation for cable surfaces . 41
Table 5 – Values of constants U, V and Y . 42
Table A.1 – Values of C for different cases . 52
fL
– 4 – IEC 60287-2-1:2023 CMV © IEC 2023
INTERNATIONAL ELECTROTECHNICAL COMMISSION
____________
ELECTRIC CABLES –
CALCULATION OF THE CURRENT RATING –

Part 2-1: Thermal resistance –
Calculation of thermal resistance

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 60287-2-1:2023 edition 3.0
allows the user to identify the changes made to the previous IEC 60287-2-1:2015
edition 2.0. 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.

IEC 60287-2-1 has been prepared by IEC technical committee 20: Electric cables. It is an
International Standard.
This third edition cancels and replaces the second edition published in 2015. This edition
constitutes a technic
...