IEC 60287-1-1:2023

IEC 60287-1-1 ®
Edition 3.0 2023-05
COMMENTED VERSION
INTERNATIONAL
STANDARD
colour
inside
Electric cables – Calculation of the current rating –
Part 1-1: Current rating equations (100 % load factor) and calculation of losses –
General
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IEC 60287-1-1 ®
Edition 3.0 2023-05
COMMENTED VERSION
INTERNATIONAL
STANDARD
colour
inside
Electric cables – Calculation of the current rating –
Part 1-1: Current rating equations (100 % load factor) and calculation of losses –
General
INTERNATIONAL
ELECTROTECHNICAL
COMMISSION
ICS 29.060.20 ISBN 978-2-8322-7059-2
– 2 – IEC 60287-1-1:2023 CMV © IEC 2023
CONTENTS
FOREWORD .4
INTRODUCTION .6

1 General .
1 Scope .7
2 Normative references .7
3 Terms, definitions and symbols.8
3.1 Terms and definitions .8
3.2 Symbols .8
4 Permissible current rating of cables . 12
4.1 General . 12
4.2 Buried cables where drying out of the soil does not occur or cables in air . 12
4.2.1 AC cables . 12
4.2.2 DC cables up to 5 kV . 13
4.3 Buried cables where partial drying-out of the soil occurs . 14
4.3.1 AC cables . 14
4.3.2 DC cables up to 5 kV . 14
4.4 Buried cables where drying-out of the soil shall be avoided . 15
4.4.1 AC cables . 15
4.4.2 DC cables up to 5 kV . 15
4.5 Cables directly exposed to solar radiation. 15
4.5.1 General . 16
4.5.2 AC cables . 16
5 Calculation of losses . 16
5.1 AC resistance of conductor . 16
5.1.1 General . 16
5.1.2 DC resistance of conductor . 17
5.1.3 Skin effect factor y . 17
s
5.1.4 Proximity effect factor y for two-core cables and for two single-core
p
cables . 18
5.1.5 Proximity effect factor y for three-core cables and for three single-core
p
cables . 18
5.1.6 Skin and proximity effects in pipe-type cables . 19
5.2 Dielectric losses (applicable to AC cables only) . 19
5.3 Loss factor for sheath and screen (applicable to power frequency AC cables
only). 20
5.3.1 General . 20
5.3.2 Two single-core cables, and three single-core cables (in trefoil formation),
sheaths bonded at both ends of an electrical section . 21
5.3.3 Three single-core cables in flat formation, with regular transposition,
sheaths bonded at both ends of an electrical section . 22
5.3.4 Three single-core cables in flat formation, without transposition, sheaths
bonded at both ends of an electrical section . 22
5.3.5 Variation of spacing of single-core cables between sheath bonding points . 24
5.3.6 Effect of Milliken conductors . 24
5.3.7 Single-core cables, with sheaths bonded at a single point or cross-bonded . 25

5.3.8 Two-core unarmoured cables with common sheath . 28
5.3.9 Three-core unarmoured cables with common sheath . 28
5.3.10 Two-core and three-core cables with steel tape armour . 30
5.3.11 Cables with each core in a separate lead metallic sheath (SL type) and
armoured . 30
5.3.12 Losses in screen and sheaths of pipe-type cables . 31
5.4 Loss factor for armour, reinforcement and steel pipes (applicable to power
frequency AC cables only) . 31
5.4.1 General . 31
5.4.2 Non-magnetic armour or reinforcement . 32
5.4.3 Magnetic armour or reinforcement . 32
5.4.4 Losses in steel pipes . 37

Annex A (normative) Correction factor for increased lengths of individual cores within
multicore cables . 43
Bibliography . 44
List of comments . 45

Table 1 – Electrical resistivities and temperature coefficients of metals used . 38
Table 2 – Skin and proximity effects – Experimental values for the coefficients k and k . 39
s p
Table 3 – Values of relative permittivity and loss factors for the insulation of high-voltage
and medium-voltage cables at power frequency . 41
Table 4 – Absorption coefficient of solar radiation for cable surfaces . 42
Table A.1 – Values of factor C for different numbers of cores . 43
fL
– 4 – IEC 60287-1-1:2023 CMV © IEC 2023
INTERNATIONAL ELECTROTECHNICAL COMMISSION
____________
ELECTRIC CABLES –
CALCULATION OF THE CURRENT RATING –

Part 1-1: Current rating equations (100 % load factor)
and calculation of losses – General

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
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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 60287-1-1:2023 edition 3.0
allows the user to identify the changes made to the previous IEC 60287-1-1:2006+
AMD1:2014 edition 2.1. 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 60287-1-1 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 2006 and
Amendment 1:2014. 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; 1
b) 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 number of cores has been introduced (Annex A).
The text of this International Standard is based on the following documents:
Draft Report on voting
20/2096/FDIS 20/2103/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.

– 6 – IEC 60287-1-1:2023 CMV © IEC 2023
INTRODUCTION
This part of IEC 60287 contains formulae for the quantities R R , W , λ and λ .
C d 1 2
It contains methods for calculating the permissible current rating of cables from details of the
permissible temperature rise, conductor resistance, losses and thermal resistivities.
Formulae for the calculation of losses are also given.
The formulae in this document contain quantities which vary with cable design and materials
used. The values given in the tables are either internationally agreed, for example, electrical
resistivities and resistance temperature coefficients, or are those which are generally accepted
in practice, for example, thermal resistivities and permittivities of materials. In this latter
category, some of the values given are not characteristic of the quality of new cables but are
considered to apply to cables after a long period of use. In order that uniform and comparable
results may can be obtained, the current ratings should be calculated with the values given in
this document. However, where it is known with certainty that other values are more appropriate
to the materials and design, then these may be used, and the corresponding current rating
declared in addition, provided that the different values are quoted.
Quantities related to the operating conditions of cables are liable to vary considerably from one
country to another. For instance, with respect to the ambient temperature and soil thermal
resistivity, the values are governed in various countries by different considerations. Superficial
comparisons between the values used in the various countries may can lead to erroneous
conclusions if they are not based on common criteria: for example, there may can be different
expectations for the life of the cables, and in some countries design is based on maximum
values of soil thermal resistivity, whereas in others average values are used. Particularly, in the
case of soil thermal resistivity, it is well known that this quantity is very sensitive to soil moisture
content and may can vary significantly with time, depending on the soil type, the topographical
and meteorological conditions, and the cable loading.
The following procedure for choosing the values for the various parameters should, therefore,
be adopted.
Numerical values should preferably be based on results of suitable measurements. Often such
results are already included in national specifications as recommended values, so that the
calculation may can be based on these values generally used in the country in question; a
survey of such values is given in IEC 60287-3-1.
A suggested list of the information required to select the appropriate type of cable is given in
IEC 60287-3-1.
ELECTRIC CABLES –
CALCULATION OF THE CURRENT RATING –

Part 1-1: Current rating equations (100 % load factor)
and calculation of losses – General

1 General
1 Scope
This part of IEC 60287 is 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,
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 document provides formulae for current ratings and losses.
The formulae given are essentially literal and designedly leave open the selection of certain
important parameters. These may can be divided into three groups:
– parameters related to construction of a cable (for example, thermal resistivity of insulating
material) for which representative values have been selected based on published work;
– parameters related to the surrounding conditions, which may can vary widely, the selection
of which depends on the country in which the cables are used or are to will be used;
– parameters which result from an agreement between manufacturer and user and which
involve a margin for security of service (for example, maximum conductor temperature).
2 Normative references
The following documents are referred to in the text in such a way that some or all of their content
constitutes requirements 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 60027-3, Letter symbols to be used in electrical technology – Part 3: Logarithmic and
related quantities, and their units
IEC 60028:1925, International standard of resistance for copper
IEC 60141 (all parts), Tests on oil-filled and gas-pressure cables and their accessories
IEC 60228, Conductors of insulated cables
IEC 60287-1-3, 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 60287-2-1:2023, Electric cables – Calculation of the current rating – Part 2-1: Thermal
resistance – Calculation of the thermal resistance

– 8 – IEC 60287-1-1:2023 CMV © IEC 2023
IEC 60502-1, Power cables with extruded insulation and their accessories for rated voltages
from 1 kV (Um = 1,2 kV) up to 30 kV (Um = 36 kV) – Part 1: Cables for rated voltages of 1 kV
(Um = 1,2 kV) and 3 kV (Um = 3,6 kV)
IEC 60502-2, Power cables with extruded insulation and their accessories for rated voltages
from 1 kV (Um = 1,2 kV) up to 30 kV (Um = 36 kV) – Part 2: Cables for rated voltages from 6
kV (Um = 7,2 kV) up to 30 kV (Um = 36 kV)
IEC 60889, Hard-drawn aluminium wire for overhead line conductors
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
The symbols used in this document and the quantities which they represent are given in the
following list.
AA cross-sectional area of the armour
mm
A
B , B coefficients (see 5.4.3) Ω/m
1 2
C capacitance per core F/m
C coefficient defined in 5.3.6
F
C coefficient to take into account the position of the neutral
fL
axis of the helically wound core in Annex A
C coefficient used in 5.3.7.1
gs
C length correction factor for considering laying up of cores
LL
C coefficient defined in 5.3.6
M1
C coefficient defined in 5.3.6
N
C coefficient defined in 5.3.4 Ω/m
P
C coefficient used in 5.3.7.2
p
C coefficient defined in 5.3.4 Ω/m
Q
C coefficient used in 5.3.7.2
q
*
external diameter of cable m
D
e
D diameter over insulation mm
i
*
diameter over the individual core of a multicore cable m
D
p
D external diameter of metal sheath mm
s
D diameter of the imaginary coaxial cylinder which just touches mm
oc
the crests of a corrugated sheath
D diameter of the imaginary cylinder which just touches the mm
it
inside surface of the troughs of a corrugated sheath

F coefficient defined in 2.3.5
H E intensity of solar radiation
W/m
e
H magnetizing force (see 5.4.3) A/m
H inductance of sheath H/m
s
components of inductance due to the steel wires (see 5.4.3) H/m

H , H , H
1 2 3
I current in one conductor (RMS value) A
I current in sheath (RMS value) A
S
*
axial cable length over which the cores make one full helical m
L
L
turn
M, N coefficients defined in 2.3.5

P, Q coefficients defined in 2.3.3
Ω/m
RR alternating current resistance of conductor at its maximum Ω/m
C
operating temperature per unit length of the cable
R AC resistance of armour at its maximum operating Ω/m
A
temperature per unit length of the cable
AC resistance of armour at 20 °C per unit length of the cable Ω/m
R
Ao
R equivalent AC resistance of sheath and armour in parallel Ω/m
e
R AC resistance of cable sheath or screen at their maximum Ω/m
s
operating temperature per unit length of the cable
AC resistance of cable sheath or screen at 20 °C per unit Ω/m
R
so
length of the cable
R′ DC resistance of conductor at maximum operating Ω/m
temperature per unit length of the cable
R DC resistance of conductor at 20 °C per unit length of the Ω/m
o
cable
T thermal resistance per core between conductor and sheath K · m/W
per unit length of the cable
T thermal resistance between sheath and armour per unit K · m/W
length of the cable
T thermal resistance of external serving per unit length of the K · m/W
cable
T thermal resistance of surrounding medium (ratio of cable K · m/W
surface temperature rise above ambient to the losses per
unit length)
*
# external thermal resistance in free air, adjusted for solar K · m/W
T T
radiation
T ′ thermal resistance between cable and duct (or pipe) K ∙ m/W
T ′′ thermal resistance of the duct (or pipe) K ∙ m/W
T ′′′ thermal resistance of the medium surrounding the duct (or K ∙ m/W
pipe)
U voltage between conductor and screen or sheath V
o
W losses in armour per unit length of the cable W/m
A
W losses in conductor per unit length of the cable W/m
c
W dielectric losses per unit length of the cable per phase W/m
d
– 10 – IEC 60287-1-1:2023 CMV © IEC 2023
W losses dissipated in sheath per unit length of the cable W/m
s
W total losses in sheath and armour per unit length of the cable W/m
(s+A)
X reactance of sheath (two-core cables and three-core cables Ω/m
in trefoil) per unit length of the cable
X reactance of sheath (cables in flat formation) Ω/m
X mutual reactance between the sheath of one cable and the Ω/m
m
conductors of the other two when cables are in flat
information
a shortest minor length in a cross-bonded electrical section m
having unequal minor lengths
distance between the axes of conductors and the axis of the mm
c
cable for three-core cables (= 0,55 r + 0,29 t for sector-
shaped conductors)
d mean diameter of sheath or screen mm
d′ mean diameter of sheath and reinforcement mm
d mean diameter of reinforcement mm
d mean diameter of armour mm
A
d external diameter of conductor mm
c
d′ external diameter of equivalent round solid conductor having mm
c
the same central duct as a hollow conductor
d internal diameter of pipe mm
d
d diameter of a steel wire mm
f
d internal diameter of hollow conductor mm
i
d major diameter of screen or sheath of an oval conductor mm
M
d minor diameter of screen or sheath of an oval conductor mm
m
d diameter of an equivalent circular conductor having the mm
x
same cross-sectional area and degree of compactness as
the shaped one
f system frequency Hz
g
s coefficient used in 2.3.6.1
kk factor used in the calculation of hysteresis losses in armour
f
or reinforcement (see 5.4.3.4)
k factor used in calculating x (proximity effect)
p p
k factor used in calculating x (skin effect)
s s
*
length of a cable section (general symbol, see 5.3.5) m
l l
natural logarithm (logarithm to base e, see IEC 60027-3)
ln
m
ω
–7
R
s
parameter used in calculation of eddy-current loss factor −7
10 m/Ω
n number of conductors in a cable
n number of steel wires in a cable (see 5.4.3)
p length of lay of a steel wire along a cable (see 5.4.3)
p, q coefficients used in 2.3.6.2

r circumscribing radius of two- or three-sector shaped mm
conductors
s axial separation of conductors mm
s axial separation of two adjacent cables in a horizontal group mm
of three, not touching
s axial separation of cables (see 2.4.2) mm
axial spacing between adjacent cables in trefoil formation; mm
for cables in flat formation s is the geometric mean of the
three spacings
t insulation thickness between conductors mm
t thickness of the serving mm
t thickness of the sheath mm
s
v ratio of the thermal resistivities of dry and moist soils
(v = ρ /ρ )
d w
x argument of a Bessel function used to calculate proximity
p
effect
x argument of a Bessel function used to calculate skin effect
s
y proximity effect factor (see 5.1)
p
y skin effect factor (see 5.1)
s
α temperature coefficient of electrical resistivity at 20 °C, per I/K
kelvin
β coefficient used in 5.3.7.1
β angle between axis of armour wires and axis of cable (see
5.4.3)
γ angular time delay (see 5.4.3)
Δ ,Δ
coefficients used in 5.3.7.1
1 2
δ equivalent thickness of armour or reinforcement mm
A
tanδ loss factor of insulation
ε relative permittivity of insulation
ε permittivity of vacuum F/m
θ maximum operating temperature of conductor °C
θ ambient temperature °C
a
θ maximum operating temperature of armour °C
ar
θ maximum operating temperature of cable screen or sheath °C
sc
θ critical temperature of soil; this is the temperature of the °C
x
boundary between dry and moist zones
Δθ permissible temperature rise of conductor above ambient K
temperature
Δθ critical temperature rise of soil; this is the temperature rise K
x
of the boundary between dry and moist zones above the
ambient temperature of the soil
λ coefficient used in 5.3.7.1
λ , λ ratio of the total losses in metallic sheaths and armour
1 2
respectively to the total conductor losses (or losses in one
sheath or armour to the losses in one conductor)

– 12 – IEC 60287-1-1:2023 CMV © IEC 2023
ratio of the losses in one sheath caused by circulating
′
λ
currents in the sheath to the losses in one conductor
′′ ratio of the losses in one sheath caused by eddy currents to
λ
the losses in one conductor
′ loss factor for the middle cable of three cables in flat
λ
1m
formation without transposition, with sheaths bonded at both
ends
loss factor for the outer cable with the greater losses of three
λ′
cables in flat formation without transposition, with sheaths
bonded at both ends
loss factor for the outer cable with the least losses of three
′
λ
cables in flat formation without transposition, with sheaths
bonded at both ends
µ relative magnetic permeability of armour material
µ longitudinal relative permeability
e
µ transverse relative permeability
t
ρ conductor resistivity at 20 °C Ω · m
ρ thermal resistivity of dry soil K · m/W
d
ρ thermal resistivity of moist soil K · m/W
w
ρ sheath resistivity at 20 °C Ω · m
s
σ absorption coefficient of solar radiation for the cable surface
ω angular frequency of system (2πf)
4 Permissible current rating of cables
4.1 General
When the permissible current rating is being calculated under conditions of partial drying out of
the soil, it is also necessary to calculate a rating for conditions where drying out of the soil does
not occur. The lower of the two ratings shall be used.
4.2 Buried cables where drying out of the soil does not occur or cables in air
4.2.1 AC cables
The permissible current rating of an AC cable can be derived from the expression for the
temperature rise above ambient temperature:
2 2 2
∆θ = (I R + ½ W ) T + [I R (1 + λ ) + W ] n T + [I R (1 + λ + λ ) + W ] n (T + T )
d 1 1 d 2 1 2 d 3 4
22 2
Δθ=(I R+ W )T++n[I R (1 λ )+ W ]T++n[I R (1 λ+ λ )+ W ](T+ T ) (1)
C d1 C 1 d2 C 1 2 d 3 4
where
I is the current flowing in one conductor (A);
Δθ is the conductor temperature rise above the ambient temperature (K);
NOTE The ambient temperature is the temperature of the surrounding medium under normal conditions, at a
situation in which cables are installed, or will be installed, including the effect of any local source of heat, but
not the increase of temperature in the immediate neighbourhood of the cables due to heat arising therefrom.

RR is the alternating current resistance per unit length of the conductor cable at maximum
C
operating temperature (Ω/m);
W is the dielectric loss per unit length of the cable for the insulation surrounding the conductor
d
(W/m);
T is the thermal resistance per unit length of the cable between one conductor and the sheath
(K · m/W);
T is the thermal resistance per unit length of the cable of the bedding between sheath and
armour (K · m/W);
T is the thermal resistance per unit length of the cable of the external serving of the cable
(K · m/W);
T is the thermal resistance per unit length between the cable surface and the surrounding
medium, as derived from IEC 60287-2-1 (K · m/W);
n is the number of load-carrying conductors in the cable (conductors of equal size and
carrying the same load);
λ is the ratio of losses in the metal sheath to total losses in all conductors in that cable;
λ is the ratio of losses in the armouring to total losses in all conductors in that cable.

The permissible current rating is obtained from Formula (1) as follows:
0,5
 ∆θ − W [0,5 T + n (T + T + T )] 
d 1 2 3 4
I =
 
RT + nR (1 + λ )Τ + nR (1 + λ + λ ) (T + T )
1 1 2 1 2 3 4
 
0,5
 Δθ -W 0,5 T + n (T +T +T ) 
[ ]
d 1 23 4
I = (2)
 
R T + nR (1+ λ ) T + nR (1+ λ +λ ) (T +T )
 
C 1 C1 2 C1 2 3 4
 
Where the cable is exposed to direct solar radiation, the formulae given in IEC 60287-2-1:2023,
4.2.1.2 shall be used.
The current rating for a four-core low-voltage cable may be taken to be equal to the current
rating of a three-core cable for the same voltage and conductor size having the same
construction, provided that the cable is used in a three-phase system where the fourth
conductor is either a neutral conductor or a protective conductor. When it is a neutral conductor,
the current rating applies to a balanced load.
4.2.2 DC cables up to 5 kV
The permissible current rating of a DC cable is obtained from the following simplification of the
AC Formula (2):
0,5

Δθ
I =

R'T + nR'T + nR'(T +T )
1 2 34
where
R′ is the direct current resistance per unit length of the conductor cable at maximum operating
temperature (Ω/m).
Where the cable is exposed to direct solar radiation, the formulae given in IEC 60287-2-1:2023,
4.2.1.2 shall be used.
– 14 – IEC 60287-1-1:2023 CMV © IEC 2023
4.3 Buried cables where partial drying-out of the soil occurs
4.3.1 AC cables
The following method shall be applied to a single isolated cable or circuit only, laid at
conventional depths. The method is based on a simple two-zone approximate physical model
of the soil where the zone adjacent to the cable is dried out whilst the other zone retains the
site's thermal resistivity, the zone boundary being on isotherm . This method is considered to
be appropriate for those applications in which soil behaviour is considered in simple terms only.
NOTE 1 Installations of more than one circuit as well as the necessary spacing between circuits are under
consideration.
Changes in external thermal resistance, consequent to the formation of a dry zone around a
single isolated cable or circuit, shall be obtained from the following Formula (3), compared with
Formula (2):
0,5
 
∆θ − W [0,5 T + n (T + T + vT )] + (v − 1) ∆θ
d 1 2 3 4 x
I =
 
R [T + n (1 + λ )Τ + n (1 + λ + λ ) (T + vT )]
 
1 1 2 1 2 3 4
 
0,5
ΔΔθ -W 0,5 T + n (T+T+ vT ) +−(v 1) θ 
[ ]
d 1 23 4 x
(3)
I =
 
R [T +n(1+ λ ) T + n(1+ λ + λ ) (T + vT )]
 C1 1 2 1 2 3 4 
 
where
v is the ratio of the thermal resistivities of the dry and moist soil zones (v = ρρ/ ) ;
dw
RR is the AC resistance of the conductor at its maximum operating temperature per unit length
C
of the cable (Ω/m);
ρ is the thermal resistivity of the dry soil (K · m/W);
d
ρ is the thermal resistivity of the moist soil (K · m/W);
w
θ is the critical temperature of the soil and temperature of the boundary between dry and
x
moist zones (°C);
θ
a is the ambient temperature (°C);
Δθ is the critical temperature rise of the soil. This is the temperature rise of the boundary
x
between the dry and moist zones above the ambient temperature of the soil (θ – θ ) (K);
x a
NOTE  T is calculated using the thermal resistivity of the moist soil (ρ ) using
4 w
IEC 60287-2-1:2023, 4.2.3.3. Mutual heating by modification of the temperature rise as in
IEC 60287-2-1:2023, 4.2.3.2 cannot be applied.
θ and ρ shall be determined from a knowledge of the soil conditions.
x d
NOTE 2 The choice of suitable soil parameters is under consideration. In the meantime, values may can be agreed
between the manufacturer and purchaser.
4.3.2 DC cables up to 5 kV
The permissible current rating of a DC cable is obtained from the following simplification of the
AC Formula (3):
___________
"Current ratings of cables buried in partially dried-out soil, Part 1": Electra No. 104, p. 11, January 1966
(in particular section 3 and Appendix 1).

0,5
 
ΔΔθv+−( 1) θ
x
I =
 
R′ T ++nT n ()T + vT
[ ]

12 3 4

where
R′ is the direct current resistance per unit length of the conductor cable at maximum operating
temperature (Ω/m).
When considering cable installations in pipes or ducts, the thermal resistance of the surrounding
is composed by three additive contributions of thermal resistances, i. e. that of the
medium T
′ ′′
medium inside the pipe, the pipe itself and the ambient medium around the pipe T , T and
4 4
′′′ ′′′
T , see IEC 60287-2-1. In that case only the contribution T is affected by drying out of the
4 4
soil and in the above two formulae the term vT shall be replaced by the term TT′ + ′′ + νT ′′′ .
4 44 4
4.4 Buried cables where drying-out of the soil shall be avoided
4.4.1 AC cables
Where it is desired that moisture migration be avoided by limiting the temperature rise of the
cable surface to not more than Δθ , the corresponding rating shall be obtained from:
x
0,5
 ∆θ − nW T 
x d 4
I =
 
( )
nRT 1+ λ + λ
 4 1 2 
0,5

Δθ − nW T
x d4
(4)
I =

nR T 1++λλ
( )

C4 1 2

However, depending on the value of Δθ this may can result in a conductor temperature which
x
exceeds the maximum permissible value. The current rating used shall be the lower of the two
values obtained, either from the above Equation (4) or from Equation (1).
The conductor resistance R R shall be calculated for the appropriate conductor temperature,
C
which may can be less than the maximum permitted value. An estimate of the operating
temperature shall be made and, if necessary, subsequently amended.
NOTE For four-core low-voltage cables, see the final paragraph in 4.2.1.
4.4.2 DC cables up to 5 kV
The permissible current rating of a DC cable shall be obtained from the following simplification
of the AC Formula (4):
0,5

∆θ
x
I =

nR′ T
4
The conductor resistance R′ shall be modified as in 4.3.2.
4.5 Cables directly exposed to solar radiation
Permissible current ratings
– 16 – IEC 60287-1-1:2023 CMV © IEC 2023
4.5.1 General
Taking into account the effect of solar radiation on a cable, the permissible current rating is
given by Formulae (5) and (6):
4.5.2 AC cables
0,5
* * *
 
∆θ − W [0,5 T + n (T + T + T )] − σ D H T
d 1 2 3 4 e 4
I =
 
*
RT + nR (1 + λ )Τ + nR (1 + λ + λ ) (T + T )
 
 1 1 2 1 2 3 4 
0,5
# *#
 
 
∆−θ W 0,5 T + n (TTT+ + ) − σ D E T
d 1 2 3 4 e e 4
   
(5)
I =
 # 
R T + nR (1+)λT + nR (1+ λ + λ ) (T + T )
C 1 C1 2 C1 2 3 4
 
 
DC cables up to 5 Kv
0,5
* *
 
∆θ − σ D H T
e 4
I =
 
*
R′ T + nR′Τ + nR′ (T + T )
 
 1 2 3 4 
0,5
*#
 
Δθ − σD E T
e e 4
(6)
I =  
#
R′′T + nR Τ + nR′ ()T + T
 
 1 2 34 
where
σ is the absorption coefficient of solar radiation for the cable surface (see Table 4);
HE is the intensity of solar radiation which should be taken as 1000 W/m² for most latitudes;
e
it is recommended that the local value should be obtained where possible;
#
*
T T is the external thermal resistance of the cable in free air, adjusted to take account of
solar radiation (see IEC 60287-2-1) (K · m/W);
*
D is the external diameter of the cable (m) for corrugated sheaths
e
* –3
D = (D + 2t ) ⋅ 10 (m);
e
oc 3
t is the thickness of the serving (mm).
5 Calculation of losses
5.1 AC resistance of conductor
5.1.1 General
The AC resistance per unit length of the conductor cable at its maximum operating temperature
is given by the following Formula (7), except in the case of pipe-type cables (see 5.1.6):
R = R′ (1 + y + y )
s p
R R'(1 + yy + )
(7)
C sp
=
where
RR is the alternating current resistance of the conductor at maximum operating temperature
C
per unit length of the cable (Ω/m); 2
R′ is the DC resistance of the conductor at maximum operating temperature per unit length of
the cable (Ω/m);
y is the skin effect factor;
s
y is the proximity effect factor.
p
5.1.2 DC resistance of conductor
The DC resistance per unit length of the conductor cable at its maximum operating temperature
θ is given by:
R′ = R [1 + α (θ – 20)]
o 20
RR' [1 + αθ ( – 20K)]
o 20
where
is the DC resistance of the conductor at 20 °C per unit length of the cable (Ω/m);
R
o
The value of R shall be derived directly from IEC 60228. Where the conductor size is
o
outside the range covered by IEC 60228, the value of R may can be chosen by agreement
o
between the manufacturer and purchaser. The conductor resistance should then be
calculated using the values of resistivity given in Table 1 and considering the length of the
conductor in the finished cable, see also Annex A.
α is the constant mass temperature coefficient at 20 °C per kelvin (see Table 1 for standard
values);
θ is the maximum operating temperature in degrees Celsius (this will be determined by the
type of insulation to be used); see appropriate IEC specification or national standard.
5.1.3 Skin effect factor y
s
The skin effect factor y is given by the following equations:
s
x
s
For 0 < x ≤ 2,8 y =
s s
192 + 0,8 x
s
For 2,8 < x ≤ 3,8 y =−−0,136 0,0177xx+ 0,0563
s s ss
For x > 3,8 yx0,354− 0,733
s ss
where
8πf
27−
x = 10 k ;
ss
′
R
f is the supply frequency in Hz.
Values for k are given in Table 2.
s
In the absence of alternative formulae, it is recommended that the formulae in 5.1.3 should be
used also for sector and oval-shaped conductors.
=
=
– 18 – IEC 60287-1-1:2023 CMV © IEC 2023
5.1.4 Proximity effect factor y for two-core cables and for two single-core cables
p
The proximity effect factor is given by:
4 2
x
d
p
c
y × 2,9
p 
s
192 + 0,8 x 
p
where
...