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.
International Electrotechnical Commission, 3, rue de Varembé, PO Box 131, CH-1211 Geneva 20, Switzerland
Telephone: +41 22 919 02 11 Telefax: +41 22 919 03 00 E-mail: inmail@iec.ch Web: www.iec.ch
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International Electrotechnical Commission
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For price, see current catalogue

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

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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 d
...