IEC 61784-5-12/FRAGF

SLOVENSKI STANDARD
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
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

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.
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1597 ©IEC:1995 - 3 -
CONTENTS
Page
FOREWORD 7
Clause
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
3.2 Heat balance equation
3.3 Calculation method
17 3.4 Joule effect
3.5 Solar heat gain
3.6 Radiated heat loss
3.7 Convection heat loss
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
4.1 General
21 4.2 Alternating current (AC) resistance
23 4.3 Inductive reactance
4.4 Capacitive reactance
4.5 Table of properties
27 5 Elongation of stranded conductors
5.1 General
5.2 Thermal elongation
33 Stress-strain properties 5.3
35 5.4 Assessment of final elastic modulus
6 Conductor creep
41 General 6.1
6.2 Creep of single wires
6.3 Total conductor creep
45 6.4 Prediction of conductor creep
6.5 Creep values
-5-
1597 ©IEC:1995
Page
Clause
7 Loss of strength
49 8 Calculation of maximum conductor length on drums
Basis of calculation 8.1
51 8.2 Packing factor
53 8.3 Space between last conductor layer and lagging
8.4 Numerical example
Annexes
A Current carrying capacity
B Resistance, inductive and capacitive reactance of conductors
C Bibliography
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.

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.

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

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

- 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.

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
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)

- 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)
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:
/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.

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.
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)
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
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)

- 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.

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)

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
Aluminium wires Steel wires ASIA, K
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
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.

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 = (Ea
If Aa/A and ASIA are respectively defined as as and as (aluminium and steel areas
expressed as percentage of the total conductor area), then equation (24) can be rewritten:
E=Ea aa +Es as (25)
Equation (25) can be used to establish the final elastic modulus of elasticity of the composite
conductor after being subjected to tension because during unloading the behaviour of the
conductor becomes elastic.
(es), equation (21) can
Since aluminium wires are subjected to creep and settlement strain
be rewritten in order to include the effect of this additional creep strain Ec:
/11a Ea FS/ As ES (26)
F/A E = Fa + Ec =
1597 ©IEC:1995 - 35 -
Resolving equations (19) and (26) leads to the following results:
Fa = F Ea Aa (1 - ec Es As/F)/E A (27)
Fs = FEs As (1 +ec Ea Aa/F)/EA (28)
E = (Ea as + ES as)/(1 + ec Ea Aa/F) (29)
When equations (27), (28) and (29) are compared with equations (22), (23) and (24), the
following results can be derived:
creep of aluminium wires reduces the tensile load carried by these wires and
-
transfers this load to steel wires. The amount of reduction in the tension of aluminium
Fa in equation (27) from Fa in equation (22) which
wires can be obtained by subtracting
corresponds to:
A = (Ea Aa E As) ec/E A (30)
a
- the tension in aluminium wires decreases with creep. Under extreme conditions
aluminium wires will not carry any tensile load, i.e. when
F/Es As (31)
ec=
In this case, aluminium wires become completely slack and all the conductor tension is
transferred to the steel core. The same condition can result from using conductors at
very high temperatures in the order of 125 °C to 150 °C.
Recent studies have indicated that in multiple-layer conductors, the aluminium wires can
carry some compressive load (stresses not exceeding 5 MPa to 10 MPa) before birdcaging
which can force the steel core to carry more tension than the total conductor tension.
For practical reasons, compressive stresses can be neglected unless the suspended
conductor is expected to be subjected to very high temperatures.
5.4 Assessment of final elastic modulus
The final modulus of elasticity of conductors can be derived from equation (25) (E = Ea as
+ Es as) where Ea and Es are respectively the aluminium and steel moduli.
If the aluminium and steel wires of a conductor were straight solid wires, their corresponding
s = 207 000 MPa given in IEC 888 and 889
moduli of elasticity of Ea = 68 000 MPa and E
could have been used directly in equation (25).
However, since wires are helically wound, a unit elongation along the axis of the conductor
leads to less strain in the axis of the wire and thus reduces the effective modulus of
elasticity.
Furthermore, the radial compression between layers at contact points of wires tends also
to generate strain along the axis of the conductor.
For the above reasons, the modulus of elasticity of the aluminium portion tends to
decrease with increasing number of layers and wires. The same applies to steel wire
layers, but to a lesser degree, due to the surface hardness at contact points.

1597 ©IEC:1995 - 37 -
The ideal way to generate the stress-strain characteristics of the aluminium portion of a
conductor is to perform stress-strain tests as suggested in IEC 1089.
In the absence of such data, values found in the technical literature can be used in order
to obtain approximate stress-strain calculations of conductors. These values are based on
one of the following methods:
average the values obtained from tests of similar stranding and generalize the
a)
results. Values given in table 3 are based on published curves of the Aluminum
Association [1] and should represent a good approximation in the absence of direct test
data.
use equation (25) and assume Ea = 55 000 MPa and Es
b) = 190 000 MPa constant7).
The results of this method are given in table 4 and agree to within 5 % of those
obtained in method a).
c) start from the modulus of single steel and aluminium wires and reduce them by the
following factors: 0,80 to 0,90 for Al wires, 0,85 to 0,95 for A2 and A3 wires, and 0,90
to 0,95 for steel wires.
It is however noted that variations in the final modulus of elasticity in the order of 5 %
usually lead to final sag variations less than 1 %.
7) Except for single, steel wire core where ES = 207 000 MPa.

1597 © IEC:1995 - 39 -
Table 3 - Typical stress -strain data of stranded conductors
based on published test results
Strain of conductor in %
Conductor data
Stress levels
Final
MPa
modulus
Type Ax Sx
MPa x 10 3
25 50 75 100 125 150
0,17 0,26 0,39
7 0 63,3 0,05 0,11 0,58
19 0 61,2 0,05 0,11 0,18 0,27 0,41 0,60
0 0,05 0,11 0,18 0,27 0,41 0,60
Ax') 37 58,9
61 0 58,3 0,06 0,12 0,20 0,30 0,44 0,64
6 0,04 0,08 0,11 0,15 0,20 0,25
1 79,0
0,27
18 1 68,0 0,05 0,10 0,15 0,21 0,36
22 7 71,0 0,05 0,09 0,15 0,20 0,25 0,33
0,09 0,14 0,18 0,23 0,28
26 7 74,2 0,05
45 7 64,5 0,06 0,11 0,16 0,22 0,29 0,38
7 0,05 0,10 0,15 0,20 0,26 0,33
54 67,1
Ax/Sxy 54 19 69,7 0,05 0,09 0,14 0,19 0,25 0,31
72 7 61,1 0,07 0,12 0,18 0,24 0,31 0,41
0,12 0,18 0,24 0,32 0,42
72 19 61,0 0,07
84 7 66,6 0,05 0,09 0,15 0,21 0,28 0,36
0,09 0,14 0,20 0,27 0,35
84 19 66,5 0,05
Values derived for A1, but can also be used for A2 and A3 in the absence of relevant
test data.
Table 4 - Final modulus of elasticity calculated with
Es = 190 000 MPa8)
Ea = 55 000 MPa and
Aluminum Steel Elasticity
ratio ratio modulus in
Aluminium wires Steel wires
as as
MPa x 103
0,857 0,143 76,7
6 1
18 1 0,947 0,053 63,1
22 7 0,910 0,090 67,1
7 0,860 0,140 73,9
45 7 0,935 0,065 63,7
54 7 0,885 0,115 70,5
54 19 0,888 0,112 70,2
72 7 0,959 0,041 60,6
0,959 0,041 60,5
72 19
84 7 0,923 0,077 65,4
0,075 65,2
84 19' 0,925
8) Except for single-wire steel core where Es = 207 000 MPa.

-41 -
1597 © IEC:1995
6 Conductor creep
6.1 General
A conductor suspended between two suppo rts will in time get an increase in sag which
must be considered by the transmission line engineer in order to satisfy the required
ground and crossing clearances. This additional sag is caused by a characteristic of the
material called creep, normally defined as the long-term change in shape depending on
applied forces.
Many investigations have been made throughout the world to calculate or measure the
creep in conductors in order to predict the final elongation and thus the final sag.
A general finding is that the total elongation for conductors can be divided into two
different parts: One being mainly a geometric settlement when wires are tightened
together initiating stresses at wire cross-over points. The other is regarded as a pure
metallurgical creep within the wires.
Note that a more detailed information on conductor creep is currently being studied
by IEC/TC7.
6.2 Creep of single wires
ain load is applied and the elongation is recorded
When creep testing a conductor, a ce rt
versus the time. If the elongation is plotted on a double logarithmic diagram the readings
will likely follow a straight line as in figure 1.
This is also the case when testing only an aluminium wire.

43 -
1597 © IEC:1995 -
Log (creep strain)
- 1,90
- 1,95
- 2,00
- 2,05
-2,10
- 2,15
-2,20
- 2,25
- 2,30
- 2,35
0,1 10 100 1 000
Time (hours)
/EC 275/95
Figure 1 - Typical creep curve
The equation for the straight line is:
xlg
lg ec= lg a+b t (32)
(33)
or e = a x tb
The constants a and b are only valid for given load history and temperatures.
6.3 Total conductor creep
The total creep elongation for different loads and temperature has been shown to follow
equation (34):
ec =Kcxe^Tx6wxtµ (34)
where
Kc is the creep coefficient depending mainly on number of wires in the conductor
is the coefficient for the temperature (T) dependence
• is the coefficient for the stress (a) dependence
dependence
is the coefficient for the time (t)
In order to determine these coefficients, tests must be made according to a very precise
rtion of the creep will take place in the
procedure. The reason for this is that a large po
very beginning of the test. The method for loading the conductor and starting the reading
of the elongation must therefore be accurate.

1597 ©IEC:1995 - 45 -
The coefficients Kc, 4), yr and µ are shown to depend upon the number of component wires
and their materials. This together with the fact that creep tests take a long time to perform
complicate the establishing of the creep equation coefficients.
6.4 Prediction of conductor creep
Different techniques have been used to predict the life-time creep for a conductor:
a) using a creep predictor formula as explained in 6.2 together with an anticipated
life-time history including different conductor conditions such as normal and overload
mechanical and temperature. Coefficients in the predictor creep formula must be
known.
b) using creep values from conductor creep tests made at actual mechanical and
temperature conditions under long time (normally more than two months) and
extrapolate the creep curve up to 10, 30 or 50 years. Normally the final sag calculation
is made by using the creep at 10 years. The reason for this is that the additional
creep from 10 to 50 years is relatively small and that a reasonable amount of the creep
may have been elapsed from the time of stringing up to the, time of clamping in the
conductor.
c) using creep values from accelerated conductor creep tests made at a higher
mechanical tension. The creep value at a certain time will then correspond to what is
known to be found under real conditions after 30 years.
For all these methods a final creep value is obtained. In order to simplify the conductor
sag calculation, the elongation due to creep can be simulated by a temperature difference
using the coefficient of linear expansion given in this document.
6.5 Creep values
The following creep values and correspondingly calculated temperature are typical. The
values have been taken as rounded mean values from many creep tests reported. It may
be pointed out that these values refer to ordinary conductors and ordinary stringing
tensions. In some cases especially designed conductors and/or prestress stringing
techniques significantly reduce the creep. Also abnormal conductor conditions such as, for
example, very high temperatures or high everyday tensions could be expected to increase
the creep more than that mentioned in table 5.
Table 5 - Typical creep values of stranded conductors
Estimated creep Equivalent temperature
Type of conductor after 10 years
difference
}gym/m
°C
Al 800 35
A2, A3 22
Al/A2, Al/A3 700 30
Al/Sxy 500 25
1597 ©IEC:1995 - 47 -
7 Loss of strength
The passage of electric current through a conductor causes a rise in temperature which
can have an annealing effect on aluminium and a combined annealing/over-ageing effect
on aluminium alloy, thus causing a loss of strength. The amount of strength that is lost
depends on the temperature and the duration, and the effect is cumulative: 10 hours each
year for 10 years has a similar effect to heating the conductor continuously for 100 hours
at the same temperature.
The loss of strength will vary with the method of manufacture and the values quoted in this
clause are for guidance only. For aluminium alloy the information provided covers only
wires which have received a heat treatment after drawing.
The percentage reduction in tensile strength of aluminium Al at different temperatures
and durations is shown in figure 2, while figure 3 shows the same for aluminium alloy
(finally heat-treated). These figures are based on data assembled from various sources
and test results. Note these values are not applicable to alloys which have not received
heat treatment after drawing or before stranding.
Information regarding loss of strength due to combinations of high temperatures of various
durations is not available from the industry.
It is normal practice to limit operating temperatures to about 80 °C and emergency load
temperatures to 125 °C.
Per cent remaining
strength
95 %
90 %
85 %
80 %
75 %
70%
65 %
60%
100 1 000
0,1 10 10 000
Time (hours)
/EC 276/95
Figure 2 - Loss of strength of aluminium Al as a function of temperature
NOTES applicable to figures 2 and 3:
1 Long-term exposure of aluminium wires to temperatures not exceeding 50 °C should not lead to any
practical loss of strength due to temperature.
2 At temperatures not exceeding 80 °C, the maximum loss of strength with time should not exceed 3 %
for aluminium alloy and is negligible for Al aluminium.

1597 © IEC:1995 - 49 -
Per cent remaining
80 °C
strength 100 %
95 %
125 °C
90 %
85%
80 %
75 %
70 %
150 °C
65 %
60 %
0,1 1 10 100 1 000
Time (hours)
277/95
IEC
Figure 3 - Loss of strength of aluminium A2
8 Calculation of maximum conductor length on drums
8.1 Basis of calculation
The coiling volume Vdr of a drum is given by equation (35). This volume is described in
figure 4.
= ( 7C d12 - 7t d2 2) B/4 (35)
Vdr
where
V dr is the coiling volume in a drum (m 3 )
d1 , d2 are the outside and inside diameters of a drum (m)
B is the internal width of a drum (m)
It is normal practice that the minimum inside drum diameter d2 be equal to at least
30 times the conductor diameter9).
9) Single, layer conductors may require higher values.

1597 © IEC:1995 -51 -
Vdr
d2
d^
IEC 278/95
Figure 4 - Coiling volume in a drum
8.2 Packing factor
The amount of conductor that can be coiled in a drum depends on the voids between turns
of the conductor. If the packing factor is defined as the ratio of available volume to the
total volume, two extreme cases can be considered, each one corresponding to a packing
factor as indicated in figures 5a and 5b.
The packing factor 10) k applicable to figure 5a (maximum void between conductor layers)
p
becomes equal to:
k = n/4 = 0,785 (36)
In case of figure 5b where the voids between conductors are minimum, k becomes equal
to:
kp = n/2 x 1,732 = 0,907 (37)
Usually, kp
= 0,87 is considered sufficient for practical operations.
IEC 279/95 IEC 280/95
Figure 5a - Maximum void Figure 5b - Minimum void
Figure 5 - Void between turns
10) This packing factor is valid for ratios of drum width to diameter of conductor in the order of 20 and more.

1597 ©IEC:1995 - 53 -
8.3 Space between last condu
...