EN 60865-1:1993

SLOVENSKI STANDARD
01-oktober-1998
.UDWNRVWLþQLWRNL5DþXQDQMHXþLQNRYGHO'HILQLFLMHLQUDþXQVNLSRVWRSNL,(&

Short-circuit currents - Calculation of effects -- Part 1: Definitions and calculation
methods
Kurzschlußströme - Berechnung der Wirkung -- Teil 1: Begriffe und
Berechnungsverfahren
Courants de court-circuit - Calcul des effets -- Partie 1: Définitions et méthodes de calcul
Ta slovenski standard je istoveten z: EN 60865-1:1993
ICS:
17.220.01 Elektrika. Magnetizem. Electricity. Magnetism.
Splošni vidiki General aspects
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

INTERNATIONAL IEC
STANDARD 60865-1
Second edition
1993-09
Short-circuit currents –
Calculation of effects –
Part 1:
Definitions and calculation methods

 IEC 1993 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
PRICE CODE
XA
Commission Electrotechnique Internationale
International Electrotechnical Commission
МеждународнаяЭлектротехническаяКомиссия
For price, see current catalogue

IEC Publication 865-1
Publication 865-1 de la CEI
(Second edition 1993)
(Deuxième édition 1993)
Courants de court-circuit -
Short-circuit currents -
Calcul des effets Calculation of effects
Partie 1: Définitions et méthodes de calcul Part 1: Definitions and calculation methods
C O R R I G E N D U M 1
Page 65, table 2
Page 64, tableau 2
In the third column, for a line-to-line short
Dans la troisième colonne, pour un court-
circuit biphasé, au lieu de: circuit, instead of:
1,8
1,8
lire: read:
- (dash)
- (un tiret)
Page 74, figure 2 Page 75, figure 2
Sur la gauche des dessins, ajouter: Add, at the left-hand side of the drawings:
a) a)
and b) respectively.
et b) respectivement.
Page 104, annexe A, article A.2 Page 105, annex A, clause A.2
Replace the last line of the existing equation
Remplacer la dernière ligne de l’équation
existante par la nouvelle ligne suivante: by the following new line:
& (a/d) + 1 a/d (a/d) -1  Oa/d • b/d ⎞
2 arctan - 2 arctan + arctan
⎠
b/d b/d b/d  6
⎭
Mars 1995 March 1995
– 3 –
865-1 ©IEC:1993
CONTENTS
Page
FOREWORD 7
Section 1: General
Clause
1.1 Scope and object 9
1.2 Normative references 9
11 1.3 Equations, symbols and units
1.3.1 Symbols for section 2 – Electromagnetic effects
1.3.2 Symbols for section 3 – Thermal effects
1.4 Definitions
1.4.1 Definitions for section 2 – Electromagnetic effects
1.4.1.1 Main conductor
1.4.1.2 Sub-conductor
1.4.1.3 Fixed support
1.4.1.4 Simple suppo
rt
1.4.1.5 Connecting piece
1.4.1.6 Short-circuit tensile force, F t
1.4.1.7 Drop force, Ff
1.4.1.8 Pinch force, Fpi
Tkl 21
1.4.1.9 Duration of the first short-circuit current flow,
1.4.2 Definitions for section 3 - Thermal effects
1.4.2.1 Thermal equivalent short-time current,
'th
1.4.2.2 Rated short-time withstand current,
Ithr
Sth 21
1.4.2.3 Thermal equivalent short-time current density,
titt, for conductors 21
1.4.2.4 Rated short-time withstand current density, S

Tk 21
1.4.2.5 Duration of short-circuit current,
1.4.2.6 Rated short time, Tkr 21
The electromagnetic effect on rigid conductors
Section 2:
and flexible conductors
2.1 General 23
2.1.1 Influence on stress reduction
2.1.2 Consideration of automatic reclosing
2.2 Rigid conductor arrangements
2.2.1 Calculation of electromagnetic forces
2.2.1.1 Calculation of peak force between the main conductors during a three-phase
short circuit 25
2.2.1.2 Calculation of peak force between the main conductors during a line-to-line
short circuit 25
s between coplanar sub-conductors 25
2.2.1.3 Calculation of peak value of for ce
ce between main conductors and between sub-conductors
2.2.1.4 Effective distan
865-1 © IEC:1993 – 5 –
Clause Page
an forces on supports 27
2.2.2 Calculation of stresses in rigid conductors d
2.2.2.1 General 27
2.2.2.2 Calculation of stresses in rigid conductors
q of main conductors composed of sub-conductors 31
2.2.2.3 Section modulus and factor
2.2.2.4 Permitted conductor stress
2.2.2.5 Calculation of forces on supports of rigid conductors
2.2.2.6 Calculation with special regard to conductor oscillation
2.3 Flexible conductor arrangements
2.3.1 General 37
37 2.3.2 Effects on main conductors
2.3.2.1 Characteristic dimensions and parameters
circuit caused by swing out (short-circuit
2.3.2.2 Tensile force Ft during short
tensile force)
Ff after short circuit caused by drop (drop force)
2.3.2.3 Tensile force
minimum air clearance amjn 45
2.3.2.4 Horizontal span displacement b h and
2.3.3 Tensile force Fri caused by the pinch effect
2.3.3.1 Characteristic dimensions and parameters
2.3.3.2 Tensile force F in the case of clashing sub-conductors
e of non-clashing sub-conductors 51
2.3.3.3 Tensile force Fri in the cas
2.4 Structure loads due to electromagnetic effects
connectors 53
2.4.1 Design load for post isulators, their suppo rts and
connectors, with tensile forces
2.4.2 Design load for structu res, insulators and
transmitted by insulator chains
2.4.3 Design load for foundations
3: The thermal effect on bare conductors and electrical equipment
Section
3.1 General 57
3.2 Calculation of temperature rise
3.2.1 General 57
3.2.2 Calculation of thermal equivalent short-time current
rated short-time withstand current density
3.2.3 Calculation of temperature rise and
for conductors
3.2.4 Calculation of the thermal short-circuit strength for different durations
of the short-circuit current
3.2.4.1 Electrical equipment
3.2.4.2 Conductors
TABLES
FIGURES
ANNEXES
A Equations for calculation of diagrams
Fpl in the case of
B Iteration-procedure for calculation of factor rl for the tensile force
non-clashing bundled conductors according to IEC 865, 2.3.3.3 equation (62)

865-1 ©IEC:1993 – 7 –
INTERNATIONAL ELECTROTECHNICAL COMMISSION
CIRCUIT CURRENTS – CALCULATION OF EFFECTS –
SHORT -
Part 1: Definitions and calculation methods
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
and electronic fields. To this
international cooperation on all questions concerning standardization in the electrical
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
rnational Organization for Standardization
participate in this preparation. The IEC collaborates closely with the Inte
(ISO) in accordance with conditions determined by agreement between the two organizations.
The formal decisions or agreements of the IEC on technical matters, prepared by technical committees on which all
2)
the National Committees having a special interest therein are represented, express, as nearly as possible, an
international consensus of opinion on the subjects dealt with.
dards, technical repo rts or
rnational use published in the form of st an
3) They have the form of recommendations for inte
they are accepted by the National Committees in that sense.
guides and
rnational
ational unification, IEC National Committees undertake to apply IEC Inte
4) In order to promote inte rn
dards. Any divergence
dards transparently to the maximum extent possible in their national and regional st an
Stan
dard shall be clearly indicated in the latter.
dard and the corresponding national or regional st an
between the IEC St an
International Standard IEC 865-1 has been prepared by IEC technical committee 73: Short-
circuit currents.
the first edition published in 1986 and constitutes
This second edition cancels and replaces
a technical revision.
the following documents:
The text of this standard is based on
rt on Voting
DIS Repo
73(CO)16 73(CO)18
rt
the approval of this standard can be found in the repo
Full information on the voting for
on voting indicated in the above table.
rt of this standard.
Annex A forms an integral pa
Annex B is for information only.
rts, under the general title: Short-circuit currents –
IEC 865 consists of the following pa
Calculation of effects:
– Part 1: 1993: Definitions and calculation methods;
2: 1994: Examples of calculation (in preparation).
– Part
865-1 ©IEC:1993 – 9 –
SHORT-CIRCUIT CURRENTS – CALCULATION OF EFFECTS –
Part l: Definitions and calculation methods
Section 1: General
1.1 Scope and object
ational Standard is applicable to the mechanical and thermal effects of short-
This Intern
circuit currents. It contains standardized procedures for the calculation of the effects of the
short-circuit currents in two sections as follows:
Section 2 - The electromagnetic effect on rigid conductors and flexible conductors.
–
electrical equipment.
- Section 3 - The thermal effect on bare conductors and
insulated conductors reference is made, for example, to IEC 949 and IEC 986.
For cables and
including 420 kV are dealt with in this
Only a.c. systems for rated voltages up to and
standard.
The following points should particularly be noted:
The calculation of short-circuit currents should be based on IEC 909.
1)
dard depends on the protection concept and
2) Short-circuit duration used in this st an
should be considered in that sense.
and contain
3) These standardized procedures are adjusted to practical requirements
simplifications with safety margins. Testing or more detailed methods of calculation or
both may be used.
dard, for arrangements with rigid conductors, only the
4) an
In section 2 of this st
stresses caused by short-circuit currents are calculated. Furthermore, other stresses can
exist, e.g. caused by dead-load, wind, ice, operating forces, earthquake. The
rt of an agree-
combination of these loads with the short-circuit loading should be pa
ment and/or be given by standards, e.g. erection-codes.
exible conductors include the effects of dead-
The tensile forces in arrangements with fl
load. With respect to the combination of other loads the considerations given above
are valid.
1.2 Normative references
The following normative documents contain provisions which, through reference in this
ational Standard. At the time of publication, the
text constitute provisions of this Inte rn
editions indicated were valid. All normative documents are subject to revision, and pa rties
ational Standard are encouraged to investigate the possi-
rn
to agreements based on this Inte
bility of applying the most recent editions of the normative documents indicated below.
rnational Standards.
Members of IEC and ISO maintain registers of currently valid Inte

– 11-
865-1 ©IEC:1993
IEC 909: 1988, Short-circuit current calculation in three-phase a.c. systems.
IEC 949: 1988, Calculation of thermally permissible short-circuit currents, taking into
account non-adiabatic heating effects
IEC 986: 1989, Guide to the short-circuit temperature limits of electric cables with a
rated voltage from'] ,8/3 (3,6) kV to 18130 (36) kV
1.3 Equations, symbols and units
All equations used in this standard are quantity equations in which quantity symbols
represent physical quantities possessing both numerical values and dimensions.
-units concerned are given in the following
The symbols used in this standard and the SI
lists.
1.3.1 Symbols for section 2 - Electromagnetic effects
A s Cross-section of one sub-conductor m2
m
a Centre-line distance between conductors
m
a m Effective distance between neighbouring main conductors
m
Minimum air clearance
amie
m
as Effective distance between sub-conductors
ce between sub-conductor 1 and sub-conductor n m
al „ Centre-line distan
m
Centre-line distance between sub-conductors
al,
m
as,,,, Effective centre-line dist ance between the sub-conductors in the bundle
b Dimension of a sub-conductor perpendicular to the direction of the force m
be Equivalent static conductor sag at midspan m
m
bh Maximum horizontal displacement
Dimension of a main conductor perpendicular to the direction of the force m
bm
c Factor for the influence of connecting pieces
cth Material constant m4/(A2s)
CD Dilatation factor
CF Form factor 1
m
D Outer diameter of a tubular conductor
d Dimension of a sub-conductor in the direction of the force m
m
dm Dimension of a main conductor in the direction of the force
ds flexible conductor m
Diameter of a
N/m2
E Young's modulus
Es N/m2
Actual Young's modulus
865-1 © IEC:1993 – 13 –
rt circuit N
F Force acting between two parallel long conductors during a sho
Fd of rigid conductors (peak value) N
Force on support
Ff Drop force N
Fm rt circuit N
Force between main conductors during a sho
rt N
Fm2 Force between main conductors during a line-to-line sho circuit
Force on the central main conductor during a balanced three-phase
Fm3
short circuit N
circuit N
FS Force between sub-conductors during a sho rt
Static tensile force in flexible main conductor N
Fst
N
Ft Short-circuit tensile force
Fps Pinch force N
Characteristic electromagnetic force per unit length on flexible
F'
N/m
main conductors
Fv Short-circuit current force between the sub-conductors in a bundle N
Hz
f System frequency
Hz
Relevant natural frequency of a main conductor
Hz
Relevant natural frequency of a sub-conductor
fcs
f^ Factor characterising the contraction of the bundle
g Conventional value of acceleration of gravity m/s2
n
A
Ik3 Three-phase initial symmetrical short-circuit current (r.m.s.)
Ike Line-to-line initial symmetrical short-circuit current (r.m.s.) A
A Line-to-earth initial short-circuit current (r.m.s.)
IX!
A ip Peak short-circuit current
circuit A
ip2 Peak short-circuit current in case of a line-to-line sho rt
Peak short-circuit current in case of a balanced three-phase sho rt circuit A
ip3
A
i2 Instantaneous values of the currents in the conductors
J Second moment of main conductor area m4
JS Second moment of sub-conductor area m4
j Parameter determining the bundle configuration during short-circuit

current flow 1
k Number of sets of spacers or stiffening elements
k ln Factor for the effective distance between sub-conductor 1 and
sub-conductor n
Factor for effective conductor distance
kis
m
1 Centre-line distance between suppo rts
m
l^ Cord length of a flexible main conductor in the span
h Length of one insulator chain

– 15 –
865-1 © IEC:1993
is Centre-line distance between connecting pieces or between one
connecting piece and the adjacent suppo rt m
kg/m
Mass per unit length of main conductor
ms Mass per unit length of one sub-conductor kg/m
kg
mZ Total mass of one set of connecting pieces
1/N
N Stiffness norm of an installation with flexible conductors
n Number of sub-conductors of a main conductor
q Factor of plasticity
N/m2
R 02 Stress corresponding to the yield point
The ratio of electromechanical force on a conductor under short-circuit
conditions to gravity 1
rts of one span N/m
S Resultant spring constant of both suppo
s Wall thickness of tubes In
T Period of conductor oscillation s
s
Tk Duration of short-circuit current
Duration of the first short-circuit current flow s
Tkl
s
Time from short-circuit initiation until reaching
TPi Fpi
Resulting period of the conductor oscillation during the short-circuit
Tres
current flow s
rt 1
VF Ratio of dynamic and static force on suppo s
Vr Ratio of stress for a main conductor with and without three-phase automatic
reclosing 1
Vrs Ratio of stress for a sub-conductor with and without three-phase automatic
reclosing
V 6 Ratio of dynamic and static main conductor stress
Vas Ratio of dynamic and static sub-conductor stress
Centre-line distance between non-clashing sub-conductors during Ya
m
short-circuit current flow
Z Section modulus of main conductor m3
m3
ZS Section modulus of sub-conductor
rt 1
a Factor for force on suppo
Factor for main conductor stress
7 Factor for relevant natural frequency estimation
Angular direction of the force degrees
degrees
Sk Swing-out angle at the end of the short-circuit current flow
Sm Maximum swing-out angle degrees
Elastic expansion
Cela
Thermal expansion
Eth
– 17 –
865-1 © IEC:1993
pi Strain factor of the bundle contraction 1
Est' E
Stress factor of the flexible main conductor 1
rl Factor for calculating Fpi in the case of non-clashing sub-conductors 1
x 1
Factor for the calculation of the peak short-circuit current
H/m
Magnetic constant, permeability of vacuum Po
v i ,v2,v3 ,v4 ,ve Factors for calculating.
Factor for calculating Fpi in the case of clashing sub-conductors 1
N/m2
am Bending stress caused by the forces between main conductors
as Bending stress caused by the forces between sub-conductors N/m2
N/m2
atot Resulting conductor stress
N/m2
Lowest value of a when Young's modulus becomes constant
afin
x Quantity for the maximum swing-out angle 1
Factors for the tensile force in a flexible conductor
(NV
1.3.2
Symbols for section 3 - Thermal effects
A Main conductor cross-section m2
Ik A
Steady-state short-circuit current (r.m.s.)
Ik Initial symmetrical short-circuit current (r.m.s.) A
A
Thermal equivalent short-time current (r.m.s.)
Ith
Individual thermal equivalent short-time current at repeated
Ithi
A
short-circuits (r.m.s.)
Rated short-time withstand current (r.m.s.) A
Ithr
K Factor for calculating S thr As°'S/m2
m Factor for the heat effect of the d.c. component
n Factor for the heat effect of the a.c. component
Sth Thermal equivalent short-time current density (r.m.s.) A/m2
) for 1 s A/m2
Rated short-time withstand current density (r.m. ․
Sthr
Tk Duration of short-circuit current s
rt circuits s
Tki Duration of individual short-circuit current flow at repeated sho
Tkr Rated short-time s
Ab Conductor temperature at the beginning of a sho rt circuit °C
Conductor temperature at the end of a sho rt circuit °C
ge
865-1 © IEC:1993 – 19 –
1.4 Definitions
For
the purpose of this standard the following definitions apply. Reference is made to IEV
(IEC 50) when applicable.
1.4.1
Definitions for section 2 – Electromagnetic effects
1.4.1.1 Main conductor
A conductor or an arrangement composed of a number of conductors which carries the
total current in one phase.
1.4.1.2 Sub-conductor
rtain part of the total current in one phase and is a
A single conductor which carries a ce
part of the main conductor.
1.4.1.3
Fixed support
A support of a rigid conductor which does not permit the conductor to move angularly at
the point of the suppo rt.
1.4.1.4 Simple support
A support of a rigid conductor which permits angular movement at the point of suppo rt.
1.4.1.5
Connecting piece
Any additional mass within a span which does not belong to the uniform conductor
material. This includes among others: Spacers, stiffening elements, bar overlappings,
branchings, etc.
1.4.1.5.1 Spacer
A mechanical element between sub-conductors, rigid or flexible, which, at the point of
installation, maintains the clearance between sub-conductors.
1.4.1.5.2
Stiffening element
A special spacer intended to reduce the mechanical stress of rigid conductors.
1.4.1.6
Short-circuit tensile force, Ft
Maximum tensile force in a flexible main conductor due to swing out reached during the
short
circuit.
NOTE - Peak forces can occur in the conductor anchors and connector bolts, which can be greater than
the short-circuit tensile forces. See clause 2.4.
1.4.1.7 Drop force, Ff
exible main conductor which occurs when the span drops
Maximum tensile force in a fl
down after swing out.
865-1 © IEC:1993 – 21 –
1.4.1.8
Pinch force,
Fpi
the attraction of the sub-
Maximum tensile force in a bundled flexible conductor due to
conductors in the bundle.
1.4.1.9
Duration of the first short-circuit current flow,
Tkl
e first breaking of the current.
The time interval between the initiation of the short circuit and th
1.4.2
Definitions for section 3 – Thermal effects
1.4.2.1 Thermal equivalent short-time current,
'th
thermal effect and the same duration as the
The r.m.s. value of current having the same
and may subside in time.
actual short-circuit current, which may contain d.c. component
NOTE - If repeated short circuits occur (resulting from repeated reclosures) a resulting thermal
equivalent short-time current is evaluated (see 3.2.2).
1.4.2.2 Rated short-time withstand current,
Ithr
rt time
The r.m.s. value of current that the electrical equipment can carry during a rated sho
under prescribed conditions of use and behaviour.
NOTES
1 It is possible to state several pairs of values of rated short-time withstand current and rated short
time; for thermal effect 1 s is used in most IEC specifications.
2 The rated short-time withstand current as well as the corresponding rated short time are stated by the
manufacturer of the equipment.
1.4.2.3 Thermal equivalent short-time current density, Sth
cross-section area of e conductor.
The ratio of the thermal equivalent short-time current and the th
1.4.2.4 Rated short-time withstand current density, Sthr, for conductors
the rated
The r.m.s. value of the current density which a conductor is able to withstand for
short time.
NOTE - The rated short-time withstand current density is determined according to 3.2.
Tk
1.4.2.5 Duration of short-circuit current,
The sum of the time durations of the short-circuit current flow from the initiation of the
first sho rt circuit to the final breaking of the current in all phases.
1.4.2.6 Rated short time,
Tkr
The time duration for which:
– an electrical equipment can withstand a current equal to its rated short-time
withstand current;
a conductor can withstand a current density equal to its rated short-time withstand
–
current density.
865-1 © – 23 –
IEC:1993
Section 2: The electromagnetic effect on rigid conductors
and flexible conductors
2.1 General
With the calculation methods presented in this section, stresses in rigid conductors, tensile
forces in flexible conductors; forces on insulators and subst ructures, which might expose
them to bending, tension and/or compression, and span displacements of flexible
conductors can be estimated.
Electromagnetic forces are induced in conductors by the currents flowing through them.
Where such electromagnetic forces interact on parallel conductors, they cause stresses that
have to be taken into account at the substations. For this reason:
– the forces between parallel conductors are set forth in the following clauses;
the electromagnetic force components set up in conductors with bends and/or cross-
–
overs may normally be disregarded.
In the c ase of metal-clad systems, the change of the electromagnetic forces between the
conductors due to magnetic shielding can be taken into account. In addition, however, the
forces acting between each conductor and its enclosure and between the enclosures shall
be considered.
When parallel conductors are long compared to the distance between them, the forces will
be evenly distributed along the conductors and are given by the eqûation
I4o
(1)
F =
27c a 1 2
where
il and i2 are the instantaneous values of the currents in the conductors;
1 is the centre-line distance between the supports;
a is the centre-line distance between the conductors.
When the currents in the two conductors have the same direction, the forces are attractive.
When the directions of the currents are opposite, the forces are repulsive.
NOTE - For additional information see: CIGRÉ: The mechanical effects of short-circuit currents in
open air substations. Paris: CIGRÉ SC 23, WG 02, 1987.
2.1.1 Influences on stress reduction
When calculating the maximum possible short-circuit current, additional details of other
IEC standards may be considered if this results in stress reduction.
2.1.2 Consideration of automatic reclosing
Automatic reclosing shall be taken into account for rigid conductors only if three-phase
automatic reclosing is used.
865-1 © IEC:1993 – 25 –
2.2
Rigid conductor arrangements
2.2.1
Calculation of electromagnetic forces
2.2.1.1 Calculation of peak force between the main conductors during a three-phase
short circuit
In a three-phase system with the main conductors arranged with the same centre-line dis-
tances on the same plane, the maximum force acts on the central main conductor during a
three-phase sho rt circuit and is given by:
po 2 l
3 .
(2)
= a
2TC 2 P3 a
m
where
is the peak value of the short-circuit current in the case of a balanced three-phase short circuit. For
ip3
calculation, see IEC 909;
I is the maximum centre-line distance between supports;
is the effective distance between main conductors in 2.2.1.4.
am
NOTE - Equation (2) can also be used for calculating the resulting peak force when conductors with
m is the length of the side
circular cross-sections are in the corners of an equilateral triangle and where a
of the triangle.
2.2.1.2 Calculation of peak force between the main conductors during a line-to-line
short circuit
The maximum force acting between the conductors carrying the short-circuit current
circuit in a three-phase system or in a two-line single-phase-
during a line-to-line sho rt
system is given by:
l Po 2
(3)
Fm2
2n
lP2 am
where
is the peak short-circuit current in the case of a line-to-line short circuit;
ip2
1 is the maximum centre-line distance between supports;
a is the effective distance between main conductors in 2.2.1.4m
2.2.1.3 Calculation of peak value of forces between coplanar sub-conductors
The maximum force acts on the outer sub-conductors and is between two adjacent
connecting pieces given by:
I P l
F = ^0 I is (4)
2n n l as
where
n is the number of sub-conductors;
is the maximum existing centre-line distance between two adjacent connecting pieces;
Is
as is the effective distance between sub-conductors;
for a three-phase system or to ip2 for a two-line single-phase system.
ip is equal to ip3
865-1 © IEC:1993 – 27 –
2.2.1.4 Effective distance between main conductors and between sub-conductors
The forces between conductors carrying short-circuit currents depend on the geometrical
configuration and the profile of the conductors. For this reason the effective distance am
between main conductors has been introduced in 2.2.1.1 and 2.2.1.2 and the effective dis-
tance between sub-conductors in 2.2.1.3. They shall be taken as follows:
as
Effective distance am between coplanar main conductors with the centre-line distance a:
– Main conductors consisting of single circular cross-sections:

am = a
(5)
Main conductors consisting of single rectangular cross-sections and main conduc-
–
tors composed of sub-conductors with rectangular cross-sections:
a
ai„ – (6)
k12
k12 shall be taken from figure 1, with als = a, b = bm and d = dm.
coplanar sub-conductors of a main conductor:
Effective distance as between the n
Sub-conductors with circular cross-sections:
–
+
1 + 1 + 1 + . + 1 1 = 1 (7)
14 a1s aln
as a12 a 13 a
– Sub-conductors with rectangular cross-sections:
are given in table 1. For other distances and sub-conductor
Some values for as
dimensions the equation
+ kln _ _ k12 k13 + k14 kls
+
(8)
. . . . -} ^ . . .
a 13 a14 als a1n
12 a
k shall be taken from figure 1.
can be used. The values for
12 , k1n
2.2.2 Calculation of stresses in rigid conductors and forces on supports
2.2.2.1
General
The conductors may be supported in different manners, either fixed or simple or in a com-
rt and the number of supports, the
bination of both. Depending on the type of suppo
stresses in the conductors and the forces on the suppo rts will be different for the same
short-circuit current. The equations given also include the elasticity of the suppo rts.
The stresses in the conductors and the forces on the suppo rts also depend on the ratio
between the relevant natural frequency of the mechanical system and the electrical system
frequency. For example in the case of resonance or near to resonance, the stresses and
forces in the system may be amplified. If fc/f < 0,5 the response of the system decreases
and the maximum stresses are in the outer phases.

– 29 –
865-1 © IEC:1993
2.2.2.2
Calculation of stresses in rigid conductors
The assumption that the conductor is rigid means that the axial forces are disregarded.
Under this assumption the forces acting are bending forces and the general equation for
the bending stress caused by the forces between main conductors is given by:
(9)
V6,
Vr
Gin = R
8 Z
Fm3 of three-phase systems according to equation (2) or
where Fm is either the value
Fm2
of two-line single-phase systems according to equation (3).
is the section modulus of the main conductor and shall be calculated with respect to the
Z
direction of forces between main conductors.
The bending stress caused by the forces between sub-conductors is given by:
FS ls
6s as  Ks
= V
(10)
16;
where Fs according to equation (4) shall be used.
is the section modulus of the sub-conductor and shall be calculated with respect to the
ZS
direction of forces between sub-conductors.
(3 is a
are factors which take into account the dynamic phenomena, and
Va, Vos, V. and Vrs
s. The maximum possible values of
factor depending on the type and the number of suppo rt
[3 shall be taken from table 3.
Vo Vr and Vas Vrs shall be taken from table 2 and the factor
NOTE - For the beams in table 3 (except the single span beam with simple supports) the realistic ulti-
(3 given in table 3 and q given in table 4.
mate loads are calculated with the factors
Non-uniform spans in continuous beams may be treated, with sufficient degree of accuracy
by assuming the maximum span applied throughout. This means that:
s are not subjected to greater stress than the inner ones,
- the end support
span lengths less than 20 % of the adjacent ones shall be avoided. If that does not
–
prove to be possible, the conductors shall be decoupled using flexible joints at the
s. If there is a flexible joint within a span, the length of this span should be less
support
than 70 % of the lengths of the adjacent spans.
If it is not evident whether a beam is supported or fixed, the worst case shall be taken into
account.
For further consideration, see 2.2.2.6.

865-1 ©IEC:1993 – 31 –
Section modulus and factor q of main conductors composed of sub-conductors
2.2.2.3
The bending stress and consequently the mechanical withstand of the conductor depend on
the section modulus.
If the stress occurs in accordance with figure 2a), the section modulus Z is independent of
S of the
the number of connecting pieces and is equal to the sum of the section moduli Z
q has then the value 1,5 for
s with respect to the axis x-x). The factor
sub-conductors (Z
rectangular cross-sections and 1,19 for U and I sections.
in the case there is only one or no
If the stress occurs in accordance with figure 2b) and
ce, the section modulus Z is equal to the sum
stiffening element within a supported dist an
of the sub-conductors (Z s with respect to the axis y-y). The
of the section moduli Z s
and 1,83 for U and I sections.
factor q has then the value 1,5 for rectangular cross-sections
ce there are two or more stiffening elements, higher values
When within a supported distan
of section moduli may be used:
For main conductors composed of sub-conductors of rectangular cross-sections with
–
a space between the bars equal to the bar thickness, the section moduli are given in
table 5.
I cross-sections, 50 % of the section moduli
– For conductor groups having U and
with respect to the axis 0-0 should be used.
then has a value of 1,5 for rectangular cross-section and 1,83 for U and I
The factor q
sections.
2.2.2.4 Permitted conductor stress
A single conductor is assumed to withstand the short-circuit forces when:
am <_ q Rpo2
is the stress corresponding to the yield point.
where R p0 2
The factor q shall be taken from table 4, see also 2.2.2.3.
When a main conductor consists of two or more sub-conductors the total stress in the con-
ductor is given by:
(12)
tot-6mts
tm is the algebraic sum of am and as independent of the loading
NOTE - For rectangular cross-sections a
directions (see figure 2).
865-1 © IEC:1993 – 33 –
The conductor is assumed to withstand the short-circuit forces when:

(13)
<_
atot Rp0.2
q
rt circuit does not affect the distance between sub-
It is necessary to verify that the sho
conductors too much, therefore a value
°s 5 Rpo 2 (14)
is recommended.
for different cross-sections are given. For
In table 4 the highest acceptable values for q
ent deformations may occur,
Rpo 2 small perman
am = q Rpo 2 respectively °tot =
q
ce between suppo rts for q-values according to table 4, which
approximately 1 % of the dist an
by this the minimum clearances between
do not jeopardize the safety of operation as long as
the earthed structure are not violated.
main conductors or between a main conductor and
Rpo 2, the standards often state ranges with mini-
NOTE - For the yield point of conductor materials,
mum and maximum values. If only such limit values rather than actual readings are available, the mini-
mum value should be used in 2.2.2.4 and the maximum value in table 2.
2.2.2.5 Calculation of forces on supports of rigid conductors
shall be calculated from:
The dynamic force Fd
VF Vr aFm (15)
Fd =
of three-phase systems according to equation (2) or
where Fm is either the value Fm3
Fm2
of two-line single-phase systems according to equation (3) shall be used.
VF Vr shall be taken from table 2.
The maximum possible values of
s and shall be taken from
is dependent on the type and the number of suppo rt
The factor a
table 3. Regarding the design load on post insulators and connectors, see clause 2.4.
For further consideration, see 2.2.2.6.
Calculation with special regard to conductor oscillation
2.2.2.6
6, V6s , VF, Vr and Vrs which take into
The equations in 2.2.2.2 and 2.2.2.5 contain factors V
account oscillatory nature of the stresses and forces.
The upper limits of these factors are given in table 2. Lower values than these are
permitted, if they are estimated by this subclause. It is necessary to calculate the relevant
taking into account the accuracy of the data.
natural frequency ff
865-1 © IEC:1993 – 35 –
2.2.2.6.1 Calculation of relevant natural frequency
The relevant natural frequency of a conductor can be calculated from:
EJ
(16)
m'
Equation (16) is directly applicable to main conductors consisting of single cross-sections.
s and is given in table 3.
The factor y is dependent on the type and number of suppo rt
If the main conductor is composed of sub-conductors of rectangular cross-section, the
relevant natural frequency of the main conductor shall be calculated from:
y EJS
(17)
fc=c12
m'
In the case of no connecting
The factor c shall be taken from graph b) or c) of figure 3.
pieces c = 1.
is calculated from
For a main conductor composed of sub-conductors of U and I sections fe
shall apply to the main conductor design.
equation (16): J and m'
tress, taking the relevant natural frequency into
For the calculation of sub-conductor s
account, the equation
3,5 6 \,/ EJS
(18)
f^s =
ls in:
shall be used.
J and Js are calculated according to figures 2 a) or 2 b).
NOTE - The second moments of area
2.2.2.6.2 VF , V6 , Vas , Vr and Vrs
The factors
as functions of the ratio fc/f and fcs/f, where f is the
The factors VF, V Vos , Vr and Vrs
system frequency, are a little different if a three-phase sho rt circuit or a line-to-line sho rt
circuit is to be concerned, and they are also dependent on the mechanical damping of the
conductor system. For practical calculations these factors shall be taken from figure 4.
NOTES
5 0,1 s can cause an appreciable reduction of the stress in structures with
1 Short-circuit duration T k
1.
flf -<
2 In the case of elastic supports the relevant natural frequency is lower than calculated with
equation (16). This is to be considered when using figure 4, if the value of fjf is greater than 2,4.
Vrs shall be taken from figure 5; in
For three-phase automatic reclosing, the factors V r and
other cases Vr = 1, Vrs = 1.
865-1 © IEC:1993 – 37 –
2.3 Flexible conductor arrangements
2.3.1 General
The maximum tensile forces due to the effect of a sho rt circuit on main conductors, are
determined after calculation of the characteristic parameters for the configuration and type
of short circuit as in 2.3.2.1. In a span there is a difference between the tensile force Ft
during the short circuit, as in 2.3.2.2, and the tensile force F f after the short circuit as in
2.3.2.3, when conductor drops back. In 2.3.3, the tensile force Fpi caused by the pinch
the
effect in the conductor bundles is calculated. The maximum ho rizontal displacement of the
span and
the minimum air clearance between conductors are determined in 2.3.2.4.
rt circuits
In installations with flexible conductors, the stresses occurring in line-to-line sho
and balanced three-phase sho rt circuits are approximately equal. However, for line-to-line
short
circuits, conductor swing out typically results in decreasing minimum clearances,
(i.e. when adjacent conductors carrying short-circuit current move towards one another
th center conduc-
after the short circuit). In the case of balanced three-phase sho rt circuit, e
tor moves only slightly because of its inertia and the alternating bidirectional forces which
an are therefore calculated for a line-to-line sho rt circuit.
act on it. Consequently F t, Ff d bh
dead-load.
The tensile forces F t, Ff and Fpi include the tensile forces caused by the
The following calculations shall be carried out on the basis of the static tensile force Fst
existing at the local minimum winter temperature, e.g. –20 °C, and also on the basis of the
maximum operating temperature, e.g. 60 °C. For each
static tensile force F at existing at the
tensile force, the worst case shall be taken into account for design purposes.
NOTES
1 The following equations apply for span lengths up to approximately 60 m and ratios of sag to span-
length to approx. 8 %. For longer spans, the movement of the conductor can result in lower stresses than
calculated using the equations. If this can be proved by computation or measurement, lower loads may be
taken into account.
2 The following subclauses apply for horizontal spans in side-by-side configuration. Other configur-
ations may result in lower tensile forces. However, because of the complicated computation involved, it
is recommended to use the given equations for calculating these cases also.
3 The contribution of additional concentrated masses within the span to the gravitational force should
be considered.
4 For flexible conductors, magnification effect due to automatic reclosing need not be considered.
2.3.2 Effects on main conductor
The following subclauses apply to single conductors and to regular bundle configurations,
midpoints are located on a circle with equal distances between adjacent sub-
where the
conductors.
865-1 © IEC:1993 – 39 –
2.3.2.1 Characteristic dimensions and parameters
The characteristic electromagnetic load per unit length on flexible main conductors in
three-phase systems is given by:
(1Z3 )2
Ic
Po
(19)
F' 0,75
_
27c a 1
where
1k3 is the three-phase initial symmetrical short-circuit current (r.ms.);
a is the centre-line distance between main conductor mid-points;
1, is the cord length of the main conductor in the span.
rt insulators 1c = 1. For spans
For slack conductors which exert bending forces on the suppo
lc = I – 21i, where li is the length of one insulator chain.
with strained conductors
NOTES
2 in equation (19) by (1k2)2.
1 In the case of two-line single-phase systems replace 0,75(1k3)
2 The calculation procedure does not consider the contribution of the aperiodic component of the short-
circuit current. This will, however, significantly influence the result only if the duration of the short-
circuit current flow is less than 0,1 s. In this case reference is made to : CIGRÉ: The mechanical effects
of short-circuit currents in open air substations. Paris: CIGRÉ SC 23, WG 02, 1987.
The ratio of electromagnetic force under short-circuit conditions to the gravitational force
on a conductor is an impo rtant parameter given by:
F'
(20)
r =
n ms gn
and gives the direction of the resulting force exerted on the conductor:
(21)
S 1 = arctan r
The equivalent static conductor sag at midspan is given by
ms gn12
n
(22)
bc =
Fst
of the conductor oscillations is given by
The period T
(23)
and applies for small swing-out angles without current flow in the conductor.
of the conductor oscillation during the short-circuit current flow
The resulting period
Tres
is given by:
865-1 © IEC:1993 – 41 –
T
(24)
Tres
4^ ^2 81
1 +r2 1 – r 2
64 L 90°
where S i shall be given in degrees.
The stiffness norm is given by:
N= + (25)
n ESA$
SI
If the exact value of S is not known in equation (25), the value S = 105 N/m should be used
for slack conductors which exert bending forces on suppo rt insulators. For spans with
strained conductors specifications for S are under consideration.
Es
is the actual Young's modulus
sa  Fst
for <
°)
afin
^ nA nAs
s fm
(26)
for Fst >
afin
nAs
where
5  10' N 2 (27)
afin —
m
afin is the lowest value of a when Young's modulus becomes constant. The final Young's
modulus E for stranded conductors shall be used.
The stress factor of the main conductor is given by:
1)z
(ng n
ms
(28)
24 FtN
During or at the end of the short-circuit current flow, the span will have oscillated out of
the steady-state position to the angle given by:
Tki
1 _cos
F
S i [ 36O0.i1l for 0 < –< 0,5
Tres Tres
(29)
Tki
S1 for > 0,5
Tres
865-1 © IEC:1993 – 43 –
Insofar as the duration of the first short-circuit current flow as defined in 1.4.1.9 is
Tkl
known, the maximum swing-out angle
may be determined as per figure 6 or calculated
Sm
as given below. Otherwise, or if Tkl is greater than the value 0,4 T, then the value 0,4 T
shall be used for Tkl in equations (29), (32) and (37).
During or after the short-circuit current flow the span will have oscillated to the maximum
swing-out angle
Sm which is obtained as follows:
for
1– r sin Sk 05. Sk<_ 90°
X =
(30)
1–r for sk > 90°
and
1,25 arccos x for 0,766 <– x <– 1
(31)
10° + arccos x for –0,985 <_ x < 0,766
180° for x <-0,985
is the maximum value which can occur for the "worst case"
NOTE - The calculated swing-out angle d m
which is a short-circuit duration less than or equal to the stated short-circuit duration Tkl.
2.3.2.2
Tensile force Ft during short circuit caused by swing out
(short-circuit tensile force)
The load parameter cp is obtained as follows
3( J 1 + r2 – 1) for T
k 1 Tres / 4
(32)
for
3 (r sin Sk + cos Sk — 1) T
kl < Tres / 4
The factor llr and cp and is determined in figure 7. It can be calculated as a
is a function of
real solution of the equation
92 v3 + (p(2+C)tyr 2 + (1+2ij)W – C(2+(p) = 0 (33)
with 0<_yr <
...