IEC 60287-2-1:2015

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

IEC 60287-2-1:2015 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. This part of IEC 60287 provides formulae for thermal resistance. This second edition of IEC 60287-2-1 cancels and replaces the first edition, published in 1994, Amendment 1:2001, Amendment 2:2006 and Corrigendum 1:2008. This edition includes the following significant technical changes with respect to the previous edition:
a) inclusion of a reference to the use of finite element methods where analytical methods are not available for the calculation of external thermal resistance;
b) explanation about SL and SA type cables;
c) calculation method for T3 for unarmoured three-core cables with extruded insulation and individual copper tape screens on each core;
d) change of condition for X in 5.4;
e) inclusion of constants or installation conditions for water filled ducts in Table 4.

Câbles électriques - Calcul du courant admissible - Partie 2-1: Résistance thermique - Calcul de la résistance thermique

IEC 60287-2-1:2015 s'applique uniquement au fonctionnement en régime permanent des câbles de toutes tensions alternatives et de tensions continues jusqu'à 5 kV, enterrés directement dans le sol, placés dans des fourreaux, des caniveaux ou des tubes d'acier, avec ou sans assèchement partiel du sol, ainsi que les câbles posés à l'air libre. On entend par "régime permanent" la circulation continue d'un courant constant (facteur de charge 100 %) juste suffisant pour atteindre asymptotiquement la température maximale de l'âme en supposant que les conditions du milieu ambiant restent inchangées. La présente partie de l'IEC 60287 fournit des formules pour la résistance thermique. Cette seconde édition de l'IEC 60287-2-1 annule et remplace la première édition, publiée en 1994, l'Amendement 1:2001, l'Amendement 2:2006 et le Corrigendum 1:2008. Cette édition inclut les modifications techniques majeures suivantes par rapport à l'édition précédente:
a) ajout d'une référence à l'utilisation des méthodes des éléments finis dans le cas où des méthodes analytiques ne sont pas disponibles pour le calcul de la résistance thermique externe;
b) explication sur les câbles triplombs et sous gaines d'aluminium individuelles;
c) méthode de calcul de T3 pour les câbles tripolaires non armés à isolation extrudée et écrans individuels constitués de bandes en cuivre disposés sur chaque conducteur;
d) changement de condition de X en 5.4;
e) ajout des valeurs des constantes ou conditions d'installation des fourreaux remplis d'eau au Tableau 4.

General Information

• Status: Published
• Publication Date: 08-Apr-2015
• ICS: 01 - GENERALITIES. TERMINOLOGY. STANDARDIZATION. DOCUMENTATION
• ICS: 29.060.20 - Cables
• Technical Committee: TC 20 - Electric cables
• Drafting Committee: WG 19 - TC 20/WG 19
• Current Stage: DELPUB - Deleted Publication
• Start Date: 29-Jan-2021
• Completion Date: 22-May-2023

Relations

• Revised: IEC 60287-2-1:2023 - Electric cables - Calculation of the current rating - Part 2-1: Thermal resistance - Calculation of thermal resistance
• Effective Date: 05-Sep-2023
• Revises: IEC 60287-2-1:1994 - Electric cables - Calculation of the current rating - Part 2: Thermal resistance - Section 1: Calculation of thermal resistance
• Effective Date: 05-Sep-2023
• Revises: IEC 60287-2-1:1994/AMD2:2006 - Amendment 2 - Electric cables - Calculation of the current rating - Part 2-1: Thermal resistance - Calculation of thermal resistance
• Effective Date: 05-Sep-2023
• Revises: IEC 60287-2-1:1994/AMD1:2001 - Amendment 1 - Electric cables - Calculation of the current rating - Part 2: Thermal resistance - Section 1: Calculation of thermal resistance
• Effective Date: 05-Sep-2023
• Revises: IEC 60287-2-1:1994/AMD2:2006/COR1:2008 - Corrigendum 1 - Amendment 2 - 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 2.0 2015-04
REDLINE 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

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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.

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IEC 60287-2-1 ®
Edition 2.0 2015-04
REDLINE 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 978-2-8322-2618-6

– 2 – IEC 60287-2-1:2015 RLV © IEC 2015

CONTENTS
FOREWORD . 4

INTRODUCTION . 6

1 General .

1 Scope . 7

2 Normative references . 7

3 Symbols . 8

4 Calculation of thermal resistances . 10
Thermal resistance of the constituent parts of a cable, T , T and T . 10
4.1 1 2 3
4.1.1 General . 10
4.1.2 Thermal resistance between one conductor and sheath T . 10
4.1.3 Thermal resistance between sheath and armour T . 14
4.1.4 Thermal resistance of outer covering (serving) T . 14
4.1.5 Pipe-type cables . 15
4.2 External thermal resistance T . 16
4.2.1 Cables laid in free air. 16
4.2.2 Single isolated buried cable . 17
4.2.3 Groups of buried cables (not touching) . 18
4.2.4 Groups of buried cables (touching) equally loaded . 20
4.2.5 Buried pipes . 22
4.2.6 Cables in buried troughs . 22
4.2.7 Cables in ducts or pipes . 22
5 Digital calculation of quantities given graphically . 24
5.1 General . 24
5.2 Geometric factor G for two-core belted cables with circular conductors . 24
5.3 Geometric factor G for three-core belted cables with circular conductors . 25
5.4 Thermal resistance of three-core screened cables with circular conductors
compared to that of a corresponding unscreened cable . 26
5.5 Thermal resistance of three-core screened cables with sector-shaped
conductors compared to that of a corresponding unscreened cable. 26
G
5.6 Curve for for obtaining the thermal resistance of the filling material
between the sheaths and armour of SL and SA type cables . 27
5.7 Calculation of ∆θ by means of a diagram . 28
s
Bibliography . 42

Figure 1 – Diagram showing a group of q cables and their reflection in the ground-air
surface . 32
Figure 2 – Geometric factor G for two-core belted cables with circular conductors (see
4.1.2.2.2) . 33
Figure 3 – Geometric factor G for three-core belted cables with circular conductors

(see 4.1.2.2.4) . 34
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) . 35
Figure 5 – Thermal resistance of three-core screened cables with sector-shaped
conductors compared with that of a corresponding unscreened cable (see 4.1.2.3.3) . 36
G
Figure 6 – Geometric factor for obtaining the thermal resistances of the filling
material between the sheaths and armour of SL and SA type cables (see 4.1.3.2) . 37

Figure 7 – Heat dissipation coefficient for black surfaces of cables in free air, laying

condition #1 to #4 . 38

Figure 8 – Heat dissipation coefficient for black surfaces of cables in free air, laying

condition #5 to #8 . 39

Figure 9 – Heat dissipation coefficient for black surfaces of cables in free air, laying
condition #9 to #10 . 40

Figure 10 – Graph for the calculation of external thermal resistance of cables in air . 41

Table 1 – Thermal resistivities of materials . 29

Table 2 – Values for constants Z, E and g for black surfaces of cables in free air . 30
Table 3 – Absorption coefficient of solar radiation for cable surfaces . 31
Table 4 – Values of constants U, V and Y . 31

– 4 – IEC 60287-2-1:2015 RLV © IEC 2015

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
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International Standard IEC 60287-2-1 has been prepared by IEC technical committee 20:
Electric cables.
This second edition of IEC 60287-2-1 cancels and replaces the first edition, published in

1994, Amendment 1:2001, Amendment 2:2006 and Corrigendum 1:2008. The document

20/1448/CDV, circulated to the National Committees as Amendment 3, led to the publication

of this new edition. This edition constitutes a technical revision.

This edition includes the following significant technical changes with respect to the previous

edition:
a) inclusion of a reference to the use of finite element methods where analytical methods are
not available for the calculation of external thermal resistance;
b) explanation about SL and SA type cables;
c) calculation method for T3 for unarmoured three-core cables with extruded in
...

IEC 60287-2-1 ®
Edition 2.0 2015-04
INTERNATIONAL
STANDARD
NORME
INTERNATIONALE
Electric cables – Calculation of the current rating –
Part 2-1: Thermal resistance – Calculation of thermal resistance

Câbles électriques – Calcul du courant admissible –
Partie 2-1: Résistance thermique – Calcul de la résistance thermique

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
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International Standards for all electrical, electronic and related technologies.

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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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IEC 60287-2-1 ®
Edition 2.0 2015-04
INTERNATIONAL
STANDARD
NORME
INTERNATIONALE
Electric cables – Calculation of the current rating –

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

Câbles électriques – Calcul du courant admissible –

Partie 2-1: Résistance thermique – Calcul de la résistance thermique

INTERNATIONAL
ELECTROTECHNICAL
COMMISSION
COMMISSION
ELECTROTECHNIQUE
INTERNATIONALE
ICS 29.060.20 ISBN 978-2-8322-2583-7

– 2 – IEC 60287-2-1:2015 © IEC 2015
CONTENTS
FOREWORD. 4
INTRODUCTION . 6
1 Scope . 7
2 Normative references . 7
3 Symbols . 7
4 Calculation of thermal resistances . 10
Thermal resistance of the constituent parts of a cable, T , T and T . 10
4.1 1 2 3
4.1.1 General . 10
4.1.2 Thermal resistance between one conductor and sheath T . 10
4.1.3 Thermal resistance between sheath and armour T . 14
4.1.4 Thermal resistance of outer covering (serving) T . 14
4.1.5 Pipe-type cables . 15
4.2 External thermal resistance T . 16
4.2.1 Cables laid in free air . 16
4.2.2 Single isolated buried cable. 17
4.2.3 Groups of buried cables (not touching) . 18
4.2.4 Groups of buried cables (touching) equally loaded . 20
4.2.5 Buried pipes . 22
4.2.6 Cables in buried troughs . 22
4.2.7 Cables in ducts or pipes . 22
5 Digital calculation of quantities given graphically . 24
5.1 General . 24
5.2 Geometric factor G for two-core belted cables with circular conductors . 24
5.3 Geometric factor G for three-core belted cables with circular conductors . 25
5.4 Thermal resistance of three-core screened cables with circular conductors
compared to that of a corresponding unscreened cable . 26
5.5 Thermal resistance of three-core screened cables with sector-shaped
conductors compared to that of a corresponding unscreened cable . 26
G
5.6 Curve for for obtaining the thermal resistance of the filling material
between the sheaths and armour of SL and SA type cables . 27
5.7 Calculation of ∆θ by means of a diagram . 27
s
Bibliography . 42

Figure 1 – Diagram showing a group of q cables and their reflection in the ground-air
surface . 32
Figure 2 – Geometric factor G for two-core belted cables with circular conductors (see
4.1.2.2.2) . 33
Figure 3 – Geometric factor G for three-core belted cables with circular conductors
(see 4.1.2.2.4) . 34
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) . 35
Figure 5 – Thermal resistance of three-core screened cables with sector-shaped
conductors compared with that of a corresponding unscreened cable (see 4.1.2.3.3) . 36
G
Figure 6 – Geometric factor for obtaining the thermal resistances of the filling
material between the sheaths and armour of SL and SA type cables (see 4.1.3.2) . 37
Figure 7 – Heat dissipation coefficient for black surfaces of cables in free air, laying
condition #1 to #4 . 38

Figure 8 – Heat dissipation coefficient for black surfaces of cables in free air, laying
condition #5 to #8 . 39
Figure 9 – Heat dissipation coefficient for black surfaces of cables in free air, laying
condition #9 to #10 . 40
Figure 10 – Graph for the calculation of external thermal resistance of cables in air . 41

Table 1 – Thermal resistivities of materials . 29
Table 2 – Values for constants Z, E and g for black surfaces of cables in free air . 30
Table 3 – Absorption coefficient of solar radiation for cable surfaces . 31
Table 4 – Values of constants U, V and Y . 31

– 4 – IEC 60287-2-1:2015 © IEC 2015
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 internat
...