IEC 61784-5-12/FRAGF

IEC/TR 61597

Provides informations with regards to conductors specified in IEC 61089. Such informations include properties of conductors and useful methods of calculations. It does not discuss all theories and available methods for calculating conductor properties, but provides users with simple methods that provide acceptable accuracies.[
]This publication has the status of a Technical Report - type 3.

-

La CEI 61784-5-12:2010 spécifie les profils d'installation applicables à la CPF 12 (EtherCAT ). Les profils d'installation sont spécifiés dans l'annexe. Cette annexe est lue conjointement à la CEI 61918:2010. La présente version bilingue (2012-02) correspond à la version anglaise monolingue publiée en 2010-07.

Vodniki za nadzemne vode – Izračuni za gole pletene vrvi

General Information

• Status: Published
• Publication Date: 22-Feb-2012
• ICS: 29.240.20 - Power transmission and distribution lines
• Technical Committee: SC 65C - Industrial networks
• Current Stage: MERGED - Merged project
• Completion Date: 23-Feb-2012
• Ref Project: SIST IEC/TR3 61597:1999 - Overhead electrical conductors - Calculation methods for stranded bare conductors

Relations

• Revised: IEC 61784-5-12:2018 - Industrial communication networks - Profiles - Part 5-12: Installation of fieldbuses - Installation profiles for CPF 12
• Effective Date: 05-Sep-2023

Standards Content (Sample)

SLOVENSKI STANDARD
SIST IEC/TR3 61597:1999
01-november-1999
9RGQLNL]DQDG]HPQHYRGH±,]UDþXQL]DJROHSOHWHQHYUYL
Overhead electrical conductors - Calculation methods for stranded bare conductors
Conducteurs pour lignes électriques aériennes - Méthodes de calcul applicables aux
conducteurs câblés
Ta slovenski standard je istoveten z: IEC/TR 61597
ICS:
29.240.20 Daljnovodi Power transmission and
distribution lines
SIST IEC/TR3 61597:1999 en
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

---------------------- Page: 1 ----------------------

SIST IEC/TR3 61597:1999

---------------------- Page: 2 ----------------------

SIST IEC/TR3 61597:1999


TECHNICAL IEC


REPORT – TYPE 3 TR 61597





First edition
1995-05


Overhead electrical conductors –
Calculation methods for stranded
bare conductors

© IEC 1995 Copyright - all rights reserved
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 the publisher.
International Electrotechnical Commission, 3, rue de Varembé, PO Box 131, CH-1211 Geneva 20, Switzerland
Telephone: [phone] Telefax: [phone] E-mail: [e-mail] Web: www.iec.ch
PRICE CODE
X
Commission Electrotechnique Internationale
International Electrotechnical Commission
МеждународнаяЭлектротехническаяКомиссия
For price, see current catalogue

---------------------- Page: 3 ----------------------

SIST IEC/TR3 61597:1999
1597 ©IEC:1995 - 3 -
CONTENTS
Page
FOREWORD 7
Clause
11
Scope
11 2 Symbols and abbreviations
11 2.1 Symbols and units
15 2.2 Abbreviations
15 3 Current carrying capacity
15 3.1 General
15
3.2 Heat balance equation
15
3.3 Calculation method
17 3.4 Joule effect
17
3.5 Solar heat gain
17
3.6 Radiated heat loss
17
3.7 Convection heat loss
19
3.8 Method to calculate current carrying capacity (CCC)
19 3.9 Determination of the maximum permissible aluminium temperature
19 3.10 Calculated values of current carrying capacity
21 Alternating current resistance, inductive and capacitive reactances
4
21
4.1 General
21 4.2 Alternating current (AC) resistance
23 4.3 Inductive reactance
27
4.4 Capacitive reactance
27
4.5 Table of properties
27 5 Elongation of stranded conductors
27
5.1 General
29
5.2 Thermal elongation
33 Stress-strain properties 5.3
35 5.4 Assessment of final elastic modulus
41
6 Conductor creep
41 General 6.1
41
6.2 Creep of single wires
43
6.3 Total conductor creep
45 6.4 Prediction of conductor creep
45
6.5 Creep values

---------------------- Page: 4 ----------------------

SIST IEC/TR3 61597:1999
-5-
1597 ©IEC:1995
Page
Clause
47
7 Loss of strength
49 8 Calculation of maximum conductor length on drums
49
Basis of calculation 8.1
51 8.2 Packing factor
53 8.3 Space between last conductor layer and lagging
53
8.4 Numerical example
Annexes
55
A Current carrying capacity
69
B Resistance, inductive and capacitive reactance of conductors
85
C Bibliography

---------------------- Page: 5 ----------------------

SIST IEC/TR3 61597:1999
O IEC:1995 - 7 -
1597 0
INTERNATIONAL ELECTROTECHNICAL COMMISSION
OVERHEAD ELECTRICAL CONDUCTORS -
CALCULATION METHODS FOR STRANDED
BARE CONDUCTORS
FOREWORD
1) The IEC (International Electrotechnical Commission) is a worldwide organization for standardization
comprising all national electrotechnical committees (IEC National Committees). The object of the IEC is to
promote international cooperation on all questions concerning standardization in the electrical and
electronic fields. To this end and in addition to other activities, the IEC publishes International Standards.
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. The 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 the IEC on technical matters, prepared by technical committees on
a special interest therein are represented, express, as nearly as
which all the National Committees having
possible, an international consensus of opinion on the subjects dealt with.
They have the form of recommendations for international use published in the form of standards, technical
3)
reports or guides and they are accepted by the National Committees in that sense.
unification, IEC National Committees undertake to apply IEC International
4) In order to promote international
Standards transparently to the maximum extent possible in their national and regional standards. Any
divergence between the IEC Standard and the corresponding national or regional standard shall be clearly
indicated in the latter.
The main task of IEC technical committees is to prepare International Standards. In
exceptional circumstances, a technical committee may propose the publication of a technical
report of one of the following types:
type 1, when the required support cannot be obtained for the publication of an
•
International Standard, despite repeated efforts;
type 2, when the subject is still under technical development or where for any
•
other reason there is the future but not immediate possibility of an agreement on an
International Standard;
type 3, when a technical committee has collected data of a different kind from that
•
which is normally published as an International Standard, for example "state of the a rt".
Technical reports of types 1 and 2 are subject to review within three years of publication to
decide whether they can be transformed into International Standards. Technical repo rts of
type 3 do not necessarily have to be reviewed until the data they provide are considered
to be no longer valid or useful.
IEC 1597, which is a technical repo rt of type 3, has been prepared by IEC technical
committee 7: Overhead electrical conductors.

---------------------- Page: 6 ----------------------

SIST IEC/TR3 61597:1999
1597 © IEC:1995 - 9 -
The text of this technical report is based on the following documents:
Report on voting
Committee draft
7(SEC)466 7(SEC)471
Full information on the voting for the approval of this technical repo rt can be found in the
repo rt on voting indicated in the above table.
This technical report is an informative companion to IEC 1089: Round wire concentric lay
overhead electrical conductors.
This document is a Technical Repo rt of type 3. It is intended to provide additional
technical information on conductors specified in IEC 1089.
Various conductor properties and calculation methods are given in this document. These
are normally found in a number of references, but rarely condensed in a single document.
It is noted that all definitions given in IEC 1089 apply equally to this document.
Annexes A, B and C are for information only.

---------------------- Page: 7 ----------------------

SIST IEC/TR3 61597:1999
1597 ©IEC:1995 - 11 -
OVERHEAD ELECTRICAL CONDUCTORS -
CALCULATION METHODS FOR STRANDED
BARE CONDUCTORS
1 Scope
This document provides information with regard to conductors specified in IEC 1089. Such
information includes properties of conductors and useful methods of calculation.
The following chapters are included in this document:
current carrying capacity of conductors: Calculation method and typical example
-
- alternating current resistance, inductive and capacitive reactances
elongation of conductors: Thermal and stress-strain data
-
- conductor creep
- loss of strength of aluminium wires due to high temperatures
- calculation of maximum conductor length in a drum
It is noted that this document does not discuss all theories and available methods for
calculating conductor properties, but provides users with simple methods that provide
acceptable accuracies.
2 Symbols and abbreviations
2.1 Symbols and units
A cross-sectional area of the conductor (mm2)
Aa aluminium wires
AS steel wires
B Internal width of a drum (m)
D conductor diameter (m)
d1, d2 outside and inside diameter of a drum (m)
E modulus of elasticity of complete conductor (MPa)
E a aluminium wires
E steel wires
f frequency (Hz)
F tensile force in the complete conductor (kN)
Fa in the aluminium wires
FS in steel wires
conductor current (A)
relative rigidity of steel to aluminum wires
Kc
creep coefficient
Ke emissivity coefficient in respect to black body

---------------------- Page: 8 ----------------------

SIST IEC/TR3 61597:1999
1597 © IEC:1995 - 13 -
K9 layer factor
kp factor due to packing a conductor in a drum
ks factor due to void between conductor and planking
L maximum conductor length in a drum (m)
Nu Nusselt number
convection heat loss (W/m)
P conv
P. Joule losses (W/m)
radiation heat loss (W/m)
grad
solar radiation heat gain (W/m)
Pso^
r conductor radius (m)
Re Reynolds number
RT electrical resistance of conductor at a temperature T (S2/m)
s Stefan-Boltzmann constant (5,67 x 10 -8 W.m 2.K-4)
Si intensity of solar radiation (W/m2)
t time (h)
T temperature (K)
T1 ambient temperature (K)
T2 final equilibrium temperature (K)
v wind speed in m/s
coiling volume in a drum (m3)
Vdr
X capacitive reactance, calculated for 0,3 m spacing (MS .km)
Xi inductive reactance calculated for a radius of 0,3 m (S2/km)
a temperature coefficient of electrical resistance (K-1)
as ratio of aluminium area to total conductor area
as ratio of steel area to total conductor area
coefficient of linear expansion of conductor in K-1
for aluminum
13aa
for steel
Ps
Ax general expression used to express the increment of variable x
e general expression of strain (unit elongation)
e elastic strain of aluminium wires
a
ec creep and settlement strain
elastic strain of steel wires
e
E thermal strain
T
coefficient for temperature (7) dependence in creep calculations
4)
y solar radiation absorption coefficient
thermal conductivity of air film in contact with the conductor (W.m 1.K-1)
coefficient for time (t) dependence in creep calculations
a stress (MPa)
yr coefficient for stress (a) dependence in creep calculations

---------------------- Page: 9 ----------------------

SIST IEC/TR3 61597:1999
- 15 -
1597 ©IEC:1995
2.2 Abbreviations
CCC current carrying capacity (A)
GMR geometric mean radius of the conductor (m)
3 Current carrying capacity
3.1 General
The current carrying capacity (CCC) of a conductor is the maximum steady-state current
inducing a given temperature rise in the conductor, for given ambient conditions.
The CCC depends on the type of conductor, its electrical resistance, the maximum
allowable temperature rise and the ambient conditions.
3.2 Heat balance equation
The steady-state temperature rise of a conductor is reached whenever the heat gained
by the conductor from various sources is equal to the heat losses. This is expressed by
equation (1) as follows:
Pj +
P
(1)
sol = Prad + Pconv
where
Pj is the heat generated by Joule effect
Psol is the solar heat gain by the conductor surface
the heat loss by radiation of the conductor
P is
r ad
" is the convection heat loss
cony
Note that magnetic heat gain (see 4.1, 4.2 and 4.3), corona heat gain, or evaporative heat
loss are not taken into account in equation (1).
Calculation method
3.3
In the technical literature there are many methods of calculating each component of
equation (1). However, for steady-state conditions, there is reasonable agreement be-
tween the currently available methods' ) and they all lead to current carrying capacities
within approximately 10 %.
Technical Report IEC 943 provides a detailed and general method to compute temperature
rise in electrical equipment. This method is used for calculating the current carrying
capacity of conductors included in this document. Note that CIGRÉ has published a
detailed method for calculating CCC in Electra No. 144, October 1992.
1) Various methods were compared to IEC 943, IEEE, practices in Germany, Japan, France, etc.

---------------------- Page: 10 ----------------------

SIST IEC/TR3 61597:1999

1597 © IEC:1995
- 17 -
3.4 Joule effect
Power losses P1 (W), due to Joule effect are given by equation (2):
P1
= 12
RT (2)
where
T
RT is the electrical resistance of conductor at a temperature 42/m)
I is the conductor current (A)
3.5 Solar heat gain
Solar heat gain, (W/m), is given by equation (3):
Psol
(3)
PsoI -yD Si
where
y is the solar radiation absorption coefficient
D is the conductor diameter (m)
SI is the intensity of solar radiation (W/m2)
3.6 Radiated heat loss
Heat loss by radiation, Prad (W), is given by equation (4):
=snDKe (T2 (4)
- T14-)
Prad
where
2
s is the Stefan-Boltzmann constant (5,67 x 10-8 W.m .K-4)
D is the conductor diameter (m)
Ke is the emissivity coefficient in respect to black body
T is the temperature (K)
T1 ambient temperature (K)
T2 final equilibrium temperature (K)
3.7 Convection heat loss
Only forced convection heat loss, ? is taken into account and is given by equation (5):
onv (W),
T1 )
Nu (T2 - n (5)
=
Pconv
where
is the thermal conductivity of the air film in contact with the conductor,
assumed constant and equal to: 0,02585 W.m 1.K-1
Nu is the Nusselt number, given by equation (6):
Nu = 0,65 Re 0 ' 2 + 0,23 Re 0 '61 (6)

---------------------- Page: 11 ----------------------

SIST IEC/TR3 61597:1999
- 19 —
1597 © IEC:1995
Re is the Reynolds number given by equation (7):
-1,78
- T1)]
Re = 1,644 x v D [(T1 + 0,5(T2 (7)
109
y is the wind speed in m/s
D is the conductor diameter (m)
T is the temperature (K)
T 1 ambient temperature (K)
T2 final equilibrium temperature (K)
3.8 Method to calculate current carrying capacity (CCC)
From equation (1), the steady-state current carrying capacity can be calculated:
1
2
/RT
=
(8)
/max rad + Pconv — Psol ) ]1
where
RT is the electrical resistance of conductor at a temperature T ()./m)
and and are calculated from equations (3), (4), and (5).
P
Psoi' Prad conv
Determination of the maximum permissible aluminium temperature
3.9
The maximum permissible aluminium temperature is determined either from the econo-
mical optimization of losses or from the maximum admissible loss of tensile strength in
aluminium.
In all cases, appropriate clearances under maximum temperature have to be checked and
maintained.
Calculated values of current carrying capacity
3.10
Equation (8) enables the current carrying capacity (CCC) of any conductor in any condition to
be calculated.
As a reference, the tables in annex A gives the CCC of the recommended conductor
sizes 2) under the following conditions. It is impo rtant to note that any change to these
conditions (specially with wind speed and ambient temperature) will result in different CCC
which will have to be recalculated according to above equation (8):
v = 1 m/s
- speed of cross wind (90° to the line),
- intensity of solar radiation, S i = 900 W/m2
- solar absorption coefficient, y = 0,5
e
emissivity with respect to black body, K = 0,6
- aluminium temperature T2 = 353 K and 373 K (equal to 80 °C and 100 °C)
1 = 293 K (= 20 °C)
- ambient temperature, T
- frequency = 50 Hz (values for 60 Hz are very close, usually within 2 %)
2)
In this document conductor sizes are those recommended in IEC 1089.

---------------------- Page: 12 ----------------------

SIST IEC/TR3 61597:1999
1597 ©IEC:1995 - 21 -
4 Alternating current resistance, inductive and capacitive reactances
4.1 General
The electrical resistance of a conductor is a function of the conductor material, length,
cross-sectional area and the effect of the conductor lay. In more accurate calculations, it
also depends on current and frequency.
The nominal values of DC resistance are defined in IEC 1089 at 20 °C temperature for a
range of resistance exceeding 0,02 0/km.
In order to evaluate the electrical resistance at other temperatures, a correction factor has
to be applied to the resistance at 20 °C.
The alternating current (AC) resistance at a given temperature T is calculated from the DC
T and considering the skin effect increment on
resistance, corrected to the temperature
the conductor that reflects the increased apparent resistance caused by the inequality of
current density.
The other important effects due to the alternating current are the inductive and capacitive
reactances. They can be divided into two terms: the first one due to flux within a radius
of 0,30 m and the second which represents the reactance between 0,30 m radius and the
equivalent return conductor. Only the first term of both reactances is listed in tables of
annex B.
The methods of calculation adopted in this clause are based on the Aluminum Electrical
Conductor Handbook of The Aluminum Association and on the Transmission Line
Reference Book for 345 kV and above of the Electric Power Research Institute (EPRI).
4.2 Alternating current (AC) resistance
The AC resistance is calculated from the DC resistance at the same temperature. The DC
resistance of a conductor increases linearly with the temperature, according to the
following equation:
+a(T2
(9)
RT1[l -TO ]
R1.2 =
where
is the DC resistance at temperature T1
RT1
RT2 is the DC resistance at temperature T2
a is the temperature coefficient of electrical resistance at temperature T1
In this chapter, corresponds to the DC resistance at 20 °C given in IEC 1089. The
RT1
temperature coefficients of resistance at 20 °C are the following:
- for type Al aluminium: a = 0,00403 K-1
a = 0,00360 K-1
- for types A2 and A3 aluminium:'
Based on these values at 20 °C, the DC resistances have been calculated for temperatures
of 50 °C, 80 °C and 100 °C.

---------------------- Page: 13 ----------------------

SIST IEC/TR3 61597:1999
1597 ©IEC:1995 - 23 -
The AC resistance of the conductor is higher than the DC resistance mainly because of
the "skin effect". The cause of this phenomenon can be explained by the fact that the inner
portion of the conductor has a higher inductance than the outer portion because the inner
portion experiences more flux linkages. Since the voltage drop along any length of
the conductor must be necessarily the same over the whole cross-section, there will be a
current concentration in the outer portion of the conductor, increasing the effective
resistance.
Various methods are available for computing the ratio between AC and DC resistances.
3' in the
The values given in annex B are based on one of the accepted methods [i]
industry for AC resistance.
For conductors having steel wires in the core (Ax/Sxy conductors), the magnetic flux in the
core varies with the current, thus the AC/DC ratio also varies with it, especially when the
number of aluminium layers is odd, because there is an unbalance of magnetomotive force
due to opposite spiralling directions of adjacent layers.
Although this magnetic effect may be significant in some single layer Ax/Sxy conductors
and moderate in 3-layer conductors, the values of AC resistances for these types of
conductors have been calculated without this influence. Further information and a more
complete comparison and evaluation of magnetic flux and unbalance of magnetomotive
force may be found in chapter 3 of the Aluminum Electrical Conductor Handbook.
There are other factors with minor influence on the conductor electrical AC resistance, e.g.
hysteresis and eddy current losses not only in the conductors but also in adjacent metallic
s but they are usually estimated by actual tests and their effects have not been taken
part
into account in this clause.
4.3 Inductive reactance
The inductive reactance of conductors is calculated considering the flux linkages caused
by the current flowing through the conductors. In order to make computations easier, the
inductive reactance is divided into two parts:
4) radius;
a) the one resulting from the magnetic flux within a 0,3 m
the one resulting from the magnetic flux from 0,3 m to the equivalent return
b)
conductor.
This separation of reactances was first proposed by Lewis [1 j and the 0,3 m radius has
been used by all designers and conductor manufacturers and is herein adopted in order to
allow a comparison between the characteristics of the new conductor series and old ones.
The advantages of this procedure are that part a) above is a geometric factor (function of
rt b) depends only on the separation between conductors
conductor dimensions) while pa
and phases of the transmission line. As stated earlier in this clause, only the first term a)
is herein listed and part b) can be obtained from the usual technical literature.
3) Figures in square brackets refer to bibliography in annex C.
Exact number is 0,3048.
4)

---------------------- Page: 14 ----------------------

SIST IEC/TR3 61597:1999
1597 © IEC:1995 - 25 -
The first step to determine the inductive reactance for 0,3 m radius is to calculate the
Geometric Mean Radius (GMR) of the conductor. The related expressions are the
following:
GMR= 0,5 D K9 (10)
where
GMR is the geometric mean radius of conductor (m)
D is the overall diameter of conductor (m)
Kg is the layer factor (ratio of radii [1])
The "K" 9 layer factor depends only on the type of conductor and geometry of layers
(number of layers and wires). The calculated values of "K9 " for the various stranding types
defined in this report are given in table 1.
Table 1 - Values of K9 for inductive reactance calculations
Aluminium Steel
Layer factor
K9
No. of No. of No. of No. of
layers
wires layers wires
6 1 1 - ')
1 - 0,7765
18 2
7 1 - - 0,7256
1 0,7949
22 2 7
1 0,8116
26 2 7
19 2 - - 0,7577
0,7678
37 3 - -
61 4 - - 0,7722
3 7 1 0,7939
45
54 3 7 1 0,8099
4 1 0,7889
72 7
84 4 7 1 0,8005
0,7743
91 5 - -
54 3 19 2 0,8099
2 0,7889
72 4 19
84 4 19 2 0,8005
* Values vary with the conductor size due to the presence of the
steel core. For individual conductors, K can be calculated from the
of
inductive reactance. The average value K9 for conductor sizes
with 6/1 stranding is 0,5090.
The inductive reactance for 0,3 m radius is then given by equation (11):
f /GMR) = 0,1736 (f/60) Ig (0,3/GMR) (11)
X = 4 x 10-4 7z In(0,3
where
X is the inductive reactance for 0,3 m radius (S2/km)
f is the frequency (Hz)
GMR is the geometric mean radius (m)

---------------------- Page: 15 ----------------------

SIST IEC/TR3 61597:1999
- 27 -
1597 ©IEC:1995
For conductors with steel core (Ax/Sxy designations), the magnetic flux in the core
depends on the current and this influence, as far as the inductive reactance is concerned,
can be considered negligible for conductors with three aluminium layers and more or with
even number of layers. For single-layer Ax/Sxy type, the effect is not negligible and Xi is
usually determined after tests on complete conductor samples.
As there are no available results from tests carried out on conductor samples of the new
for single-layer conductors has been estimated in comparison with
IEC series, Xi
experimental figures obtained for usual Ax/Sxy designations (old ACSR) at 25 °C,
published by the Aluminum Association. These values are accurate within 3 %.
4.4
Capacitive reactance
The capacitive reactance can also be divided into two parts:
a) the capacitive reactance for 0,3 m radius;
b) the capacitive reactance from 0,3 m to the equivalent return conductor.
Considering the same reason given in 4.3, only pa rt a) above is herein listed and pa rt b)
can be obtained from readily available technical literature.
As far as capacitive reactance is concerned, it is neither current nor steel wire dependent.
Hence the calculation is quite simple, depending only on the frequency and the conductor
dimensions, as shown in equation (12):
X^ = t) In (2 x 0,3/D) = 0,1099 (60 /f) Ig (2 x 0,3/D) (12)
(9/7c
where
; is the capacitive reactance for 0,3 m radius (MS2 • km)
f is the frequency (Hz)
D is the conductor diameter (m)
4.5 Table of properties
In annex B, there are two groups of tables calculated for frequencies of 50 Hz and 60 Hz.
The AC resistances have been calculated for temperatures of 20 °C, 50 °C, 80 °C and 100 °C.
Details concerning the conductors, for example wire diameters, cross-sectional areas, can
be obtained from IEC 1089.
5 Elongation of stranded conductors
5.1 General
of conductors can be caused by various sources such as:
Elongation5l
- elastic elongation
5) In this report, elongation is considered in a general way: it can either be positive or negative.

---------------------- Page: 16 ----------------------

SIST IEC/TR3 61597:1999
1597 ©IEC:1995 - 29 -
- thermal elongation
- creep
- elongation due to the slack in the wires during stranding
- radial compression and local indentation of conductor layers at wire contacts.
When a conductor is subjected to tensile forces, the distribution of stresses in its wires is
intimately related to the elongations listed above.
In this chapter, these elongations are discussed separately and, whenever applicable,
generalized models are proposed for each type of elongation.
It is noted that more detailed information on creep and conductor elongation is currently
being studied by IEC/TC7.
5.2 Thermal elongation
Changes in temperature will affect the length of a conductor. The thermal strain or unit
) of homogeneous aluminium conductors have the following format:
elongation (ET
= (3ae T (13)
ET
where
is the coefficient of linear expansion of conductor in K-1
for aluminium
la
for steel
Is
AT is the temperature T increment
For all conductors designated Al, A2, Al/A2 and Al/A3, the value of = 23 x 10-6 K-1 is
Ra
used.
For steel wires, the coefficient of linear expansion is considered equal to Rs = 11,5 x
Rs
#C 1
10-6 .
The thermal elongation of composite conductors (designation Ax/Sxy) is more complex to
establish because of the intimate relationship between elongations and stresses of
constituent wires.
Conductors used in overhead transmission lines are continuously subjected to mechanical
tension and, in most cases, both aluminium and steel wires share the total tension in
proportion to their relative rigidity.
When both aluminium and steel wires are subjected to tensile stresses, thermal strain and
tensile strain are related. In this case the following relations apply:
EFs s Es = 13 seT (applicable to steel po rtion) (14)
/A
rtion) AFa/Aa Ea = (3aLT (applicable to aluminium po (15)

---------------------- Page: 17 ----------------------

SIST IEC/TR3 61597:1999
1597 © IEC:1995 - 31 -
AF/A E= 13 AT (applicable to complete conductor) (16)
where
, O s are respectively increments in conductor, aluminium, and steel tensions
AF, AFa
is the coefficient of linear expansion of conductor in K-1 ((3a for aluminium
and (3 s for steel)
A is the cross-sectional area of the conductor (mm2)
Aa aluminium wires
As steel wires
AT is the temperature T increment
a s, equations (14), (15), and (16) can be reduced to:
Since AF= AF + AF
(3= (Ea 13a+EsAs(3s)/ EA
Aa
or
a Aa (3a 13 )/(Ea Aa
Q = (E
+ Es As s + Es As) (17)
If the relative rigidity of the steel section to the aluminum section is assumed to be K1 (that
is: K1 = Es As/ Ea Aa), equation (17) can thus be simplified to:
1 lis)/(1 + K1
13 = (aa + K ) (18)
The values of [3 given in table 2 for various conductor designations are based on
and calculated according to equation (18) for
13 = 23 x 10-6 K-1 and [3 = 11,5 x 10-6 K-1
a s
Ea = 55 000 MPa and Es = 190 000 MPa6) . -
In cases where tensile forces in aluminium wires are nil, the steel core carries all the
conductor tension. In such cases, the thermal elongation of the conductor is identical to
the elongation of the steel core alone, that is R = (3s.
Table 2 - Coefficient of linear expansion (3 of
Ax/Sxy
composite conductors designated
0
Aluminium wires Steel wires ASIA, K
1
10-6 K- 1
6 1 0,17 0,63 18,6
21,0
18 1 0,06 0,21
22 7 0,10 0,34 20,1
26 7 0,16 0,56 18,9
0,07 0,24 20,8
45 7
54 7 0,13 0,45 19,4
19 0,13 19,5
54 0,44
72 7 0,04 0,15 21,5
19 0,04 0,15 21,5
72
84 7 0,08 0,29 20,4
84 19 0,08 0,28 20,5
6) This figure is applicable to 7-wire and 19-wire cores. For larger cores, different values may have to be
used. For single wire steel core, ES = 207 000 MPa.

---------------------- Page: 18 ----------------------

SIST IEC/TR3 61597:1999
1597 © IEC:1995 - 33 -
5.3 Stress-strain properties
Stress-strain curves of conductors depend on the elasto-plastic behaviour of the
component wires, the geometric settlement and the metallurgical creep of wires. The first two
parameters are not time dependent on the opposite of the third one.
the conductor strain, stress-strain curves are
As a consequence of time dependency of
always associated with a time reference.
In some cases, two stress-strain curves are used to characterize behaviour of conductors.
The first one is the initial curve which includes the one-hour creep and the second one,
the final curve, which includes the 10-year creep at 20 °C.
In other cases, only a final curve is given and initial conditions are derived through a
temperature compensation. Furthermore, a separate creep curve is sometimes provided to
predict creep after any period of time.
The stress-strain behaviour of composite conductors (Ax/Sxy) depend on the properties of
the constituent wires, their number and layers.
In a conductor subjected to tensile loads, the total conductor tension, F, is equal to the
sum of tensions in the aluminium and steel portions (respectively Fa and Fs). Furthermore,
the total conductor elongation is equal to that of each component, i.e.:
F=Fa +Fs (19)
E = Ea = es (20)
FIAE = Fa/Aa Ea = FslAs ES (21)
Resolving equations (19) to (21), where it is assumed (in equation 21) that all components
behave elastically, leads to the following results:
Fa = F Ea Aa/EA (22)
Fs = F Es As/ EA (23)
Aa + ES A s)/ A (24)
E
...