Overhead electrical conductors - Calculation methods for stranded bare conductors

IEC 61597:2021(E) which is a Technical Report provides information with regard to conductors specified in IEC 61089 and other aluminium and aluminium steel conductors. 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
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.
This second edition cancels and replaces the first edition published in 1995. This edition constitutes a technical revision.
This edition includes the following significant technical changes with respect to the previous edition:
a) Addition of Clause 2 and Clause 3 since the “Normative references” and “Terms and definitions” clauses are mandatory elements of the text according to the new IEC template.
b) In Clause 6, addition of new kinds of aluminium alloy and aluminium clad steel and their values of temperature coefficients of resistance.
c) In Clause 6, addition of guidelines for the calculation of AC resistance taken into account hysteresis and eddy current losses.
d) In Clause 7, addition of the values of coefficient of linear expansion of aluminium alloy conductor aluminium-clad steel reinforced series.
e) Deletion of Clause 8 “Calculation of maximum conductor length on drums” in the last version.
f) Annex A, replaced by “A practical example of CCC calculation”.
g) Annex B, replaced by “Indicative conditions for CCC calculation”.

General Information

Status
Published
Publication Date
28-Jun-2021
Current Stage
PPUB - Publication issued
Completion Date
29-Jun-2021
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IEC TR 61597
Edition 2.0 2021-06
TECHNICAL
REPORT
Overhead electrical conductors – Calculation methods for stranded bare
conductors
IEC TR 61597:2021-06(en)
---------------------- Page: 1 ----------------------
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---------------------- Page: 2 ----------------------
IEC TR 61597
Edition 2.0 2021-06
TECHNICAL
REPORT
Overhead electrical conductors – Calculation methods for stranded bare
conductors
INTERNATIONAL
ELECTROTECHNICAL
COMMISSION
ICS 29.240.20 ISBN 978-2-8322-9938-8

Warning! Make sure that you obtained this publication from an authorized distributor.

® Registered trademark of the International Electrotechnical Commission
---------------------- Page: 3 ----------------------
– 2 – IEC TR 61597:2021 © IEC 2021
CONTENTS

FOREWORD ........................................................................................................................... 4

1 Scope .............................................................................................................................. 6

2 Normative references ...................................................................................................... 6

3 Terms and definitions ...................................................................................................... 6

4 Symbols, units and abbreviated terms ............................................................................. 7

4.1 Symbols and units................................................................................................... 7

4.2 Abbreviated terms ................................................................................................... 8

5 Current carrying capacity ................................................................................................. 8

5.1 General ................................................................................................................... 8

5.2 Heat balance equation ............................................................................................ 8

5.3 Calculation method ................................................................................................. 9

5.4 Joule effect ............................................................................................................. 9

5.5 Solar heat gain ....................................................................................................... 9

5.6 Radiated heat loss .................................................................................................. 9

5.7 Convection heat loss ............................................................................................. 10

5.8 Method to calculate current carrying capacity (CCC) ............................................. 10

5.9 Determination of the maximum permissible aluminium temperature ....................... 10

5.10 Calculated values of current carrying capacity ...................................................... 11

6 Alternating current resistance, Inductive and capacitive reactances ............................... 11

6.1 General ................................................................................................................. 11

6.2 Alternating current (AC) resistance ....................................................................... 11

6.3 Inductive reactance ............................................................................................... 12

6.4 Capacitive reactance ............................................................................................ 14

7 Elongation of stranded conductors ................................................................................. 14

7.1 General ................................................................................................................. 14

7.2 Thermal elongation ............................................................................................... 15

7.3 Stress-strain properties ......................................................................................... 18

7.4 Assessment of final elastic modulus ...................................................................... 20

8 Conductor creep ............................................................................................................ 22

8.1 General ................................................................................................................. 22

8.2 Creep of single wires ............................................................................................ 23

8.3 Total conductor creep ........................................................................................... 24

8.4 Prediction of conductor creep ............................................................................... 24

8.5 Creep values ........................................................................................................ 24

9 Loss of strength ............................................................................................................. 25

Annex A (informative) A practical example of CCC calculation ............................................. 27

A.1 Basic Assumptions ................................................................................................ 27

A.2 CCC calculation .................................................................................................... 27

Annex B (informative) Indicative conditions for CCC calculation ........................................... 29

Bibliography .......................................................................................................................... 30

Figure 1 – Typical creep curve .............................................................................................. 23

Figure 2 – Loss of strength of aluminium A1 as a function of temperature ............................. 26

Figure 3 – Loss of strength of aluminium A2 ......................................................................... 26

---------------------- Page: 4 ----------------------
IEC TR 61597:2021 © IEC 2021 – 3 –

Table 1 – Values of K for inductive reactance calculations .................................................. 13

Table 2 – Coefficient of linear expansion β of inhomogeneous conductors designated

Ax/Sxy .................................................................................................................................. 17

Table 3 – Coefficient of linear expansion β of inhomogeneous conductors designated

Ax/20SA ............................................................................................................................... 18

Table 4 – Typical stress-strain data of stranded conductors based on published test

results .................................................................................................................................. 21

Table 5 – Final modulus of elasticity calculated with E = 55000 MPa and

E = 190000 MPa ................................................................................................................. 22

Table 6 – Final modulus of elasticity calculated with E = 55000 MPa and

E = 159000 MPa (20SA) ....................................................................................................... 22

Table 7 – Indicative creep values of stranded conductors(25 %RTS, 20 ℃) .......................... 25

Table B.1 – Indicative conditions for CCC calculation ........................................................... 29

---------------------- Page: 5 ----------------------
– 4 – IEC TR 61597:2021 © IEC 2021
INTERNATIONAL ELECTROTECHNICAL COMMISSION
____________
OVERHEAD ELECTRICAL CONDUCTORS – CALCULATION
METHODS FOR STRANDED BARE CONDUCTORS
FOREWORD

1) The International Electrotechnical Commission (IEC) is a worldwide organization for standardization comprising

all national electrotechnical committees (IEC National Committees). The object of IEC is to promote

international co-operation on all questions concerning standardization in the electrical and electronic fields. To

this end and in addition to other activities, IEC publishes International Standards, Technical Specifications,

Technical Reports, Publicly Available Specifications (PAS) and Guides (hereafter referred to as “IEC

Publication(s)”). Their preparation is entrusted to technical committees; any IEC National Committee interested

in the subject dealt with may participate in this preparatory work. International, governmental and non-

governmental organizations liaising with the IEC also participate in this preparation. IEC collaborates closely

with the International Organization for Standardization (ISO) in accordance with conditions determined by

agreement between the two organizations.

2) The formal decisions or agreements of IEC on technical matters express, as nearly as possible, an international

consensus of opinion on the relevant subjects since each technical committee has representation from all

interested IEC National Committees.

3) IEC Publications have the form of recommendations for international use and are accepted by IEC National

Committees in that sense. While all reasonable efforts are made to ensure that the technical content of IEC

Publications is accurate, IEC cannot be held responsible for the way in which they are used or for any

misinterpretation by any end user.

4) In order to promote international uniformity, IEC National Committees undertake to apply IEC Publications

transparently to the maximum extent possible in their national and regional publications. Any divergence

between any IEC Publication and the corresponding national or regional publication shall be clearly indicated in

the latter.

5) IEC itself does not provide any attestation of conformity. Independent certification bodies provide conformity

assessment services and, in some areas, access to IEC marks of conformity. IEC is not responsible for any

services carried out by independent certification bodies.

6) All users should ensure that they have the latest edition of this publication.

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expenses arising out of the publication, use of, or reliance upon, this IEC Publication or any other IEC

Publications.

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.

IEC TR 61597 has been prepared by IEC technical committee 7: Overhead electrical
conductors. It is a Technical Report.

This second edition cancels and replaces the first edition published in 1995. This edition

constitutes a technical revision.

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

edition:

a) Addition of Clause 2 and Clause 3 since the “Normative references” and “Terms and

definitions” clauses are mandatory elements of the text according to the new IEC
template.

b) In Clause 6, addition of new kinds of aluminium alloy and aluminium clad steel and their

values of temperature coefficients of resistance.

c) In Clause 6, addition of guidelines for the calculation of AC resistance taken into account

hysteresis and eddy current losses.
---------------------- Page: 6 ----------------------
IEC TR 61597:2021 © IEC 2021 – 5 –

d) In Clause 7, addition of the values of coefficient of linear expansion of aluminium alloy

conductor aluminium-clad steel reinforced series.

e) Deletion of Clause 8 “Calculation of maximum conductor length on drums” in the last

version.
f) Annex A, replaced by “A practical example of CCC calculation”.
g) Annex B, replaced by “Indicative conditions for CCC calculation”.
The text of this Technical Report is based on the following documents:
Draft Report on voting
7/704/DTR 7/707/RVDTR

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 Technical Report 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/standardsdev/publications.

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.
---------------------- Page: 7 ----------------------
– 6 – IEC TR 61597:2021 © IEC 2021
OVERHEAD ELECTRICAL CONDUCTORS – CALCULATION
METHODS FOR STRANDED BARE CONDUCTORS
1 Scope

This document, which is a Technical Report, provides information with regard to conductors

specified in IEC 61089 and other aluminium and aluminium steel conductors. 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

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 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 TR 60943:1998, Guidance concerning the permissible temperature rise for parts of

electrical equipment, in particular for terminals
IEC TR 60943:1998/AMD1:2008

IEC 61089:1991, Round wire concentric lay overhead electrical stranded conductors

IEC 61089:1991/AMD1:1997

IEC 60104:1987, Aluminium-magnesium-silicon alloy wire for overhead line conductors

IEC 60889:1987, Hard-drawn aluminium wire for overhead line conductors
IEC 61232:1993, Aluminium-clad steel wires for electrical purposes

IEC 61395:1998, Overhead electrical conductors – Creep test procedures for stranded

conductors

IEC 62004:2007, Thermal-resistant aluminium alloy wire for overhead line conductor

3 Terms and definitions
No terms and definitions are listed in this document.

ISO and IEC maintain terminological databases for use in standardization at the following

addresses:
---------------------- Page: 8 ----------------------
IEC TR 61597:2021 © IEC 2021 – 7 –
• IEC Electropedia: available at http://www.electropedia.org/
ISO Online browsing platform: available at http://www.iso.org/obp
4 Symbols, units and abbreviated terms
4.1 Symbols and units
A cross-sectional area of the conductor (mm )
A cross-sectional area of aluminium wires (mm )
A cross-sectional area of steel wires (mm )
D conductor diameter (m)
E modulus of elasticity of complete conductor (MPa)
E modulus of elasticity of aluminium wires(MPa)
E modulus of elasticity of steel wires(MPa)
f frequency (Hz)
F tensile force in the complete conductor (kN)
F tensile force in the aluminium wires
F tensile force in steel wires
I conductor current (A)
K relative rigidity of steel to aluminium wires
K creep coefficient
K emissivity coefficient in respect to black body
K layer factor
Nu Nusselt number
P convection heat loss (W/m)
conv
P Joule losses (W/m)
P radiation heat loss (W/m)
rad
P solar radiation heat gain (W/m)
sol
r conductor radius (m)
R Reynolds number
R electrical resistance of conductor at a temperature T (Ω/m)
−8 −2 −4
s Stefan-Boltzmann constant (5,67×10 W·m ·K )
S intensity of solar radiation (W/m )
t time (h)
T temperature (K)
T ambient temperature (K)
T final equilibrium temperature (K)
v wind speed in m/s
capacitive reactance, calculated for 0,3 m spacing (MΩ·km)
X inductive reactance calculated for a radius of 0,3 m (Ω/km)
α temperature coefficient of electrical resistance (K )
α ratio of aluminium area to total conductor area
α ratio of steel area to total conductor area
β coefficient of linear expansion of conductor in K
---------------------- Page: 9 ----------------------
– 8 – IEC TR 61597:2021 © IEC 2021
β coefficient of linear expansion for aluminium in K
β coefficient of linear expansion for steel in K
Δx general expression used to express the increment of variable x
ε general expression of strain (unit elongation)
ε elastic strain of aluminium wires
ε creep and settlement strain of conductor
ε elastic strain of steel wires
ε thermal strain of conductor
Φ coefficient for temperature (T) dependence in creep calculations
γ solar radiation absorption coefficient
−1 −1
λ thermal conductivity of air film in contact with the conductor (W·m ·K )
μ coefficient for time (t) dependence in creep calculations
σ stress (MPa)
Ψ coefficient for stress (σ) dependence in creep calculations
4.2 Abbreviated terms
CCC current carrying capacity (A)
GMR geometric mean radius of the conductor (m)
5 Current carrying capacity
5.1 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.
5.2 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):

𝑃𝑃 +𝑃𝑃 =𝑃𝑃 +𝑃𝑃 (1)
𝑗𝑗 sol rad conv
where
P is the heat generated by Joule effect
P is the solar heat gain by the conductor surface
sol
P is the heat loss by radiation of the conductor
rad
P is the convection heat loss
conv
e 6.1, 6.2 and 6.3), corona heat gain, or evaporative heat
Note that magnetic heat gain (se
loss are not taken into account in equation (1).
---------------------- Page: 10 ----------------------
IEC TR 61597:2021 © IEC 2021 – 9 –
5.3 Calculation method

In the technical literature there are many methods of calculating each component of equation

(1). However, for steady-state conditions, there is reasonable agreement between the

available methods and they all lead to current carrying capacities within approximately 10 %

for classical conductor in operational conditions (for example, conductor temperature below

100 ℃).

NOTE Various methods were compared to IEC 60943, IEEE, practices in Germany, Japan, France, etc.

IEC TR 60943 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 CIGRE has published a detailed method for calculating CCC in CIGRE TB 601 [4] .

5.4 Joule effect
Power losses P (W/m), due to Joule effect are given by equation (2):
𝑃𝑃 =𝑅𝑅 ⋅𝐼𝐼
(2)
𝑗𝑗 𝑇𝑇
where
R is the electrical resistance of conductor at a temperature T (Ω/m)
I is the conductor current (A), AC or DC
5.5 Solar heat gain
Solar heat gain, P (W/m), is given by equation (3):
sol
𝑃𝑃 =𝛾𝛾⋅𝐷𝐷⋅𝑆𝑆 (3)
sol 𝑖𝑖
where
γ is the solar radiation absorption coefficient
D is the conductor diameter (m)
S is the intensity of solar radiation (W/m )
5.6 Radiated heat loss
Heat loss by radiation, P (W/m), is given by equation (4):
rad
4 4
𝑃𝑃 =𝑠𝑠⋅𝜋𝜋⋅𝐷𝐷⋅𝐾𝐾 ⋅ (𝑇𝑇 −𝑇𝑇 ) (4)
rad 𝑒𝑒 2 1
where
−8 −2 −4
s is the Stefan-Boltzmann constant (5,67x10 W·m ·K )
D is the conductor diameter (m)
K is the emissivity coefficient in respect to black body
T ambient temperature (K)
___________
Numbers in square brackets refer to the bibliography.
---------------------- Page: 11 ----------------------
– 10 – IEC TR 61597:2021 © IEC 2021
T final equilibrium temperature (K)
5.7 Convection heat loss

Only forced convection heat loss, P (W), is taken into account and is given by equation (5):

conv
( )
𝑃𝑃 =𝜆𝜆𝜆𝜆𝜆𝜆𝑇𝑇 −𝑇𝑇 𝜋𝜋 (5)
conv 2 1
where

λ is the thermal conductivity of the air film in contact with the conductor. If assumed

−1 −1

constant, it is equal to: 0,0258 5 W × m × K . If assumed variable, such equations can

be found in [4].
Nu is the Nusselt number, given by equation (6):
0.2 0.61
(6)
𝜆𝜆𝜆𝜆 = 0.65 𝑅𝑅𝑒𝑒 + 0.23 𝑅𝑅𝑒𝑒
Another expression of the Nusselt Number could be used and found in [4].
R is the Reynolds number given by equation (7):
1.78
9 −
(7)
𝑅𝑅𝑒𝑒 = 1,644 × 10𝑣𝑣⋅ 𝐷𝐷⋅ [𝑇𝑇 + 0.5(𝑇𝑇 −𝑇𝑇 )]
1 2 1
v is the wind speed in m/s
D is the conductor diameter (m)
T is the temperature (K)
T ambient temperature (K)
T final equilibrium temperature (K)
5.8 Method to calculate current carrying capacity (CCC)

From equation (1) the maximum permissible steady-state current carrying capacity can be

calculated:
1/2
𝐼𝐼 = [(𝑃𝑃 +𝑃𝑃 −𝑃𝑃 )/𝑅𝑅 ] (8)
max rad conv sol 𝑇𝑇
where
R is the electrical resistance of conductor at a temperature T (Ω/m)
P , P and P are calculated from equations (3), (4), and (5).
sol rad conv
5.9 Determination of the maximum permissible aluminium temperature

The maximum permissible aluminium temperature is determined either from the economical

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.

If needed, the equation of core temperature versus surface temperature can be found in [4].

---------------------- Page: 12 ----------------------
IEC TR 61597:2021 © IEC 2021 – 11 –
5.10 Calculated values of current carrying capacity

Equation (8) enables the current carrying capacity (CCC) of any conductor at any condition to

be calculated. Table B.1 gives indicative conditions in some countries and regions for CCC

calculation.
6 Alternating current resistance, Inductive and capacitive reactances
6.1 General

The electrical resistance of a conductor is a function of the conductor material, length, cross-

sectional area and 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 61089 at 20 °C temperature for a

range of resistance exceeding 0,02 Ω/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

resistance, corrected to the temperature T and considering the skin effect increment on 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.
The methods of calculation adopted in this clause refer to [1] and [5].
6.2 Alternating current (AC) resistance

The DC resistance of a conductor increases linearly with the temperature, according to the

following equation:
[ ( )]
𝑅𝑅 =𝑅𝑅 1 +𝛼𝛼𝑇𝑇 −𝑇𝑇 (9)
T2 T1 2 1
where
R is the DC resistance at temperature T
T1 1
R is the DC resistance at temperature T
T2 2
α is the temperature coefficient of electrical resistance at temperature T

In this clause, R corresponds to the DC resistance at 20 °C given in IEC 61089 and

IEC 62004. The temperature coefficients of resistance at 20 °C, which are given in IEC 60889,

IEC 60104 and IEC 61232, are the following:
– for type A1 aluminium: α= 0,004 03 K
– for type A2 aluminium: α= 0,003 60 K
– for type A3 aluminium: α= 0,003 60 K
– for type AT1 aluminium: α= 0,004 00 K
– for type AT2 aluminium: α= 0,003 60 K
---------------------- Page: 13 ----------------------
– 12 – IEC TR 61597:2021 © IEC 2021
– for type AT3 aluminium: α= 0,004 00 K
– for type AT4 aluminium: α= 0,003 83 K
– for type 20SA: α= 0,003 60 K
– for type 27SA: α= 0,003 60 K

Based on these values at 20°C, the DC resistances have been calculated for temperatures of

50°C, 80 °C and 100 °C.

The AC resistance is calculated from the DC resistance at the same temperature. Calculation

methods are in [1],[2],[3],[4]. Clause A.2 gives an example based on [1].

The AC resistance of the conductor is higher than the DC resistance at the same temperature.

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 ([1],

[2], [3], [4]).

For conductors having steel wires in the core (Ax/Sxy or Ax/xySA 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 spiraling 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 [1].

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

parts, and they can be estimated by actual tests. The method in [6] takes into account the

above factors.
6.3 Inductive reactance

The inductive reactance of conductors is calculated considering the flux linkages caused by

the current flowing through the conductors. In order
...

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