IEC TR 60865-2:2015

Short-circuit currents - Calculation of effects - Part 2: Examples of calculation

IEC TR 60865-2:2015(E) shows the application of procedures for the calculation of mechanical and thermal effects due to short circuits as presented in IEC 60865-1. Thus, this technical report is an addition to IEC 60865-1. It does not, however, change the basis for standardized procedures given in that publication. This second edition cancels and replaces the first edition published in 1994 and constitutes a technical revision. It includes the following changes. The determinations for auto reclosure together with rigid conductors have been revised. The configurations in cases of flexible conductor arrangements have been changed. The influence of mid-span droppers to the span has been included. For vertical cable-connection the displacement and the tensile force onto the lower fixing point may be calculated now. Additional recommendations for foundation loads due to tensile forces have been added. The subclause for determination of the thermal equivalent short-circuits current has been deleted (is part of IEC 60909-0:2001 now). The standard IEC 60865-1:2011 has been reorganized and some of the symbols have been changed to follow the conceptual characteristic of international standards.

General Information

• Status: Published
• Publication Date: 21-Apr-2015
• ICS: 01 - GENERALITIES. TERMINOLOGY. STANDARDIZATION. DOCUMENTATION
• ICS: 17.220.01 - Electricity. Magnetism. General aspects
• ICS: 29.240.20 - Power transmission and distribution lines
• Technical Committee: TC 73 - Short-circuit currents
• Current Stage: PPUB - Publication issued
• Start Date: 15-Apr-2015
• Completion Date: 22-Apr-2015

Standards Content (Sample)

IEC TR 60865-2
®

Edition 2.0 2015-04
TECHNICAL
REPORT



Short-circuit currents – Calculation of effects –
Part 2: Examples of calculation
IEC TR 60865-2:2015-04(en)

---------------------- Page: 1 ----------------------
THIS PUBLICATION IS COPYRIGHT PROTECTED
Copyright © 2015 IEC, Geneva, Switzerland

All rights reserved. Unless otherwise specified, 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
either IEC or IEC's member National Committee in the country of the requester. If you have any questions about IEC
copyright or have an enquiry about obtaining additional rights to this publication, please contact the address below or
your local IEC member National Committee for further information.


IEC Central Office Tel.: [phone]
3, rue de Varembé Fax: [phone]
CH-1211 Geneva 20 [e-mail]
Switzerland www.iec.ch

About the IEC
The International Electrotechnical Commission (IEC) is the leading global organization that prepares and publishes
International Standards for all electrical, electronic and related technologies.

About IEC publications
The technical content of IEC publications is kept under constant review by the IEC. Please make sure that you have the
latest edition, a corrigenda or an amendment might have been published.

IEC Catalogue - webstore.iec.ch/catalogue Electropedia - www.electropedia.org
The stand-alone application for consulting the entire The world's leading online dictionary of electronic and
bibliographical information on IEC International Standards, electrical terms containing more than 30 000 terms and
Technical Specifications, Technical Reports and other definitions in English and French, with equivalent terms in 15
documents. Available for PC, Mac OS, Android Tablets and additional languages. Also known as the International
iPad. Electrotechnical Vocabulary (IEV) online.

IEC publications search - www.iec.ch/searchpub IEC Glossary - std.iec.ch/glossary
The advanced search enables to find IEC publications by a More than 60 000 electrotechnical terminology entries in
variety of criteria (reference number, text, technical English and French extracted from the Terms and Definitions
committee,…). It also gives information on projects, replaced clause of IEC publications issued since 2002. Some entries
and withdrawn publications. have been collected from earlier publications of IEC TC 37,

77, 86 and CISPR.
IEC Just Published - webstore.iec.ch/justpublished

Stay up to date on all new IEC publications. Just Published IEC Customer Service Centre - webstore.iec.ch/csc
details all new publications released. Available online and If you wish to give us your feedback on this publication or
also once a month by email. need further assistance, please contact the Customer Service
Centre: [e-mail].

---------------------- Page: 2 ----------------------
IEC TR 60865-2

®


Edition 2.0 2015-04




TECHNICAL



REPORT



















Short-circuit currents – Calculation of effects –

Part 2: Examples of calculation


























INTERNATIONAL

ELECTROTECHNICAL


COMMISSION





ICS 17.220.01; 29.240.20 ISBN 978-2-8322-2551-6



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


® Registered trademark of the International Electrotechnical Commission

---------------------- Page: 3 ----------------------
– 2 – IEC TR 60865-2:2015 © IEC 2015
CONTENTS
FOREWORD . 5
1 Scope . 7
2 Normative references . 7
3 Symbols and units . 7
4 Example 1 – Mechanical effects on a 10 kV arrangement with single rigid
conductors . 8
4.1 General . 8
4.2 Data . 9
4.3 Normal load case: Conductor stress and forces on the supports caused by
dead load . 9
4.4 Exceptional load case: Effects of short-circuit currents . 10
4.4.1 Maximum force on the central main conductor . 10
4.4.2 Conductor stress and forces on the supports . 11
4.5 Conclusions . 13
5 Example 2 – Mechanical effects on a 10 kV arrangement with multiple rigid
conductors . 14
5.1 General . 14
5.2 Data (additional to the data of Example 1) . 14
5.3 Normal load case: Conductor stress and forces on the supports caused by
dead load . 15
5.4 Exceptional load case: Effects of short-circuit currents . 15
5.4.1 Maximum forces on the conductors . 15
5.4.2 Conductor stress and forces on the supports . 16
5.5 Conclusions . 20
6 Example 3. – Mechanical effects on a high-voltage arrangement with rigid
conductors . 20
6.1 General . 20
6.2 Data . 21
6.3 Normal load case: Conductor stress and forces on the supports caused by

dead load . 22
6.4 Exceptional load case: Effects of short-circuit currents . 23
6.4.1 Maximum force on the central main conductor . 23
6.4.2 Conductor stress and forces on the supports . 23
6.4.3 Conclusions . 29
7 Example 4. – Mechanical effects on a 110 kV arrangement with slack conductors . 30
7.1 General . 30
7.2 Data . 31
7.3 Electromagnetic load and characteristic parameters . 32
7.4 Tensile force F during short-circuit caused by swing out . 34
t,d
7.5 Dynamic conductor sag at midspan . 35
7.6 Tensile force F after short-circuit caused by drop . 36
f,d
7.7 Horizontal span displacement b and minimum air clearance a . 36
h min
7.8 Conclusions . 36
8 Example 5. – Mechanical effects on strained conductors . 37
8.1 General . 37
8.2 Common data . 37
8.3 Centre-line distance between sub-conductors a = 0,1 m . 38
s

---------------------- Page: 4 ----------------------
IEC TR 60865-2:2015 © IEC 2015 – 3 –
8.3.1 Electromagnetic load and characteristic parameters . 38
8.3.2 Tensile force F during short-circuit caused by swing out . 41
t,d
8.3.3 Dynamic conductor sag at midspan . 41
8.3.4 Tensile force F after short-circuit caused by drop . 42
f,d
8.3.5 Horizontal span displacement b and minimum air clearance a . 43
h min
8.3.6 Pinch force F . 43
pi,d
8.3.7 Conclusions . 43
8.4 Centre-line distance between sub-conductors a = 0,4 m . 44
s
8.4.1 Preliminary remarks . 44
8.4.2 Characteristic dimensions and parameters . 44
8.4.3 Pinch force F . 45
pi,d
8.4.4 Conclusions . 47
9 Example 6 – Mechanical effects on strained conductors with dropper in the middle
of the span . 47
9.1 General . 47
9.2 Common data . 48
9.3 Plane of the dropper parallel to the main conductors . 48
9.3.1 General . 48
9.3.2 Current flow along the whole length of the main conductor span . 49
9.3.3 Current flow along half of the length of the main conductor and along the
dropper . 57
9.4 Plane of the dropper perpendicular to the main conductors . 64
9.4.1 General . 64
9.4.2 Current flow along the whole length of the main conductor span . 64
9.4.3 Current flow along half of the length of the main conductor and along the
dropper . 69
10 Example 7 – Mechanical effects on vertical main conductors (droppers) . 77
10.1 General . 77
10.2 Data . 77
10.3 Short-circuit tensile force and maximum horizontal displacement . 78
10.4 Pinch force . 78
10.4.1 Static tensile force regarding droppers . 78
10.4.2 Characteristic dimensions and parameters . 79
10.4.3 Pinch force F . 80
pi,d
10.5 Conclusions . 81
11 Example 8 – Thermal effect on bare conductors . 81
11.1 General . 81
11.2 Data . 81
11.3 Calculations . 82
11.4 Conclusion . 82
Bibliography . 83

Figure 1 – Conductor arrangement . 8
Figure 2 – Position of the sub-conductors and connecting pieces . 14
Figure 3 – Two-span arrangement with tubular conductors. 21
Figure 4 – Arrangement with slack conductors . 31
Figure 5 – Arrangement with strained conductors . 37
Figure 6 – Arrangement with strained conductors and droppers in midspan. Plane of the

droppers parallel to the main conductors . 47

---------------------- Page: 5 ----------------------
– 4 – IEC TR 60865-2:2015 © IEC 2015
Figure 7 – Possible arrangement of perpendicular droppers in three-phase system and
two-line system . 64
Figure 8 – Arrangement with strained conductors . 77

---------------------- Page: 6 ----------------------
IEC TR 60865-2:2015 © IEC 2015 – 5 –
INTERNATIONAL ELECTROTECHNICAL COMMISSION
____________

SHORT-CIRCUIT CURRENTS –
CALCULATION OF EFFECTS

Part 2: Examples of calculation

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.
7) No liability shall attach to IEC or its directors, employees, servants or agents including individual experts and
members of its technical committees and IEC National Committees for any personal injury, property damage or
other damage of any nature whatsoever, whether direct or indirect, or for costs (including legal fees) and
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.
The main task of IEC technical committees is to prepare International Standards. However, a
technical committee may propose the publication of a technical report when it has collected
data of a different kind from that which is normally published as an International Standard, for
example "state of the art".
IEC TR 60865-2, which is a technical report, has been prepared by IEC technical
committee 73: Short-circuit currents.
This second edition cancels and replaces the first edition published in 1994. This edition
constitutes a technical revision.
This edition includes the following significant technical changes with respect to the previous
edition.
a) The determinations for auto reclosure together with rigid conductors have been revised.

---------------------- Page: 7 ----------------------
– 6 – IEC TR 60865-2:2015 © IEC 2015
b) The configurations in cases of flexible conductor arrangements have been changed.
c) The influence of mid-span droppers to the span has been included.
d) For vertical cable-connection the displacement and the tensile force onto the lower fixing
point may be calculated now.
e) Additional recommendations for foundation loads due to tensile forces have been added.
f) The subclause for determination of the thermal equivalent short-circuits current has been
deleted (is part of IEC 60909-0:2001 now).
g) The standard IEC 60865-1:2011 has been reorganized and some of the symbols have been
changed to follow the conceptual characteristic of international standards.
The text of this technical report is based on the following documents:
Enquiry draft Report on voting
73/168/DTR 73/173/RVC

Full information on the voting for the approval of this technical report can be found in the report
on voting indicated in the above table.
This publication has been drafted in accordance with the ISO/IEC Directives, Part 2.
A list of all parts in the IEC 60865 series, published under the general title Short-circuit
currents – Calculations of effects, can be found on the IEC website.
The committee has decided that the contents of this publication will remain unchanged until the
stability date indicated on the IEC website under "http://webstore.iec.ch" in the data related to
the specific publication. At this date, the publication will be
• reconfirmed,
• withdrawn,
• replaced by a revised edition, or
• amended.
A bilingual version of this publication may be issued at a later date.

---------------------- Page: 8 ----------------------
IEC TR 60865-2:2015 © IEC 2015 – 7 –
SHORT-CIRCUIT CURRENTS –
CALCULATION OF EFFECTS

Part 2: Examples of calculation



1 Scope
The object of this part of IEC 60865, which is a Technical Report, is to show the application of
procedures for the calculation of mechanical and thermal effects due to short circuits as
presented in IEC 60865-1. Thus, this technical report is an addition to IEC 60865-1. It does not,
however, change the basis for standardized procedures given in that publication.
The following points should particularly be noted:
a) The examples in this Technical Report illustrate how to make the calculations according to
IEC 60865-1 in a simplified and easy-to-follow manner. They are not intended as a check
for computer programs.
b) The numbers in parentheses at the end of the equations refer to the equations in
IEC 60865-1:2011.
c) The system voltages are referred to as nominal voltages.
d) The results are rounded to three significant digits.
e) Short-circuit effects appear as exceptional load in addition to the mechanical loads of the
normal operation of a switchgear. In the following examples with rigid conductors, a
possible static preloading is therefore calculated too. Depending on whether it concerns the
load of the normal operation or the load during the short-circuit different safety factors
come to use. The height of these factors has been chosen typically and is recommended
for the use. However, other safety factors may be necessary depending on the safety
concept.
2 Normative references
IEC 60865-1:2011, Short-Circuit Currents – Calculation of Effects – Part 1: Definitions and
calculation methods
IEC 60909-0:2001, Short-circuit currents in three-phase AC systems – Part 0: Calculation of
currents
3 Symbols and units
For symbols and units, reference is made to IEC 60865-1:2011.
In addition, the following symbols are used:
F Dead load (characteristic value) N
str,k
F Dead load (design value) N
str,d
Force on support of rigid conductors (design value) due to dead load
F N
st,r,d
h , h Height of the substructure, insulator m
S I
H Horizontal component of the force at the lower fixing point of one sub-
s
N
conductor of a dropper

---------------------- Page: 9 ----------------------
– 8 – IEC TR 60865-2:2015 © IEC 2015
J Second moment of main conductor area with respect to the direction of
4
st,m
m
the dead load
I Steady-state short-circuit current (r.m.s) according to IEC 60909-0 A
k
l Effective length of a span m
eff
l Form factor of a span m
f
l Extend of one head armature and clamp m
h
m, n Factor for heat effect of the d.c. component and a.c. component 1
M , M Bending moment on the bottom on the substructure, insulator (design
S,d I,d
Nm
value)
V Vertical component of the force at the upper fixing point of one sub-
s
N
conductor of a dropper
W Section modulus of main conductor with respect to the direction of the
st,m 3
m
dead load
g Partial safety factor for action 1
F
Partial safety factor for material property 1
g
M
2
σ Bending stress caused by the dead load (design value) N/m
st,m,d
2
σ Bending stress caused by the dead load (characteristic value) N/m
st,m,k

4 Example 1 – Mechanical effects on a 10 kV arrangement with single rigid
conductors
4.1 General
The basis for the calculation in this example is a three-phase 10 kV busbar with one conductor
per phase. The conductors are continuous beams with equidistant simple supports. The
1
conductor arrangement is shown in Figure 1. According to IEC 61936-1 [1] , the calculation is
done for the normal load case considering the dead load of the busbar and the exceptional load
case considering the combination of effects of short-circuit currents and dead load.
c
m
g
a a
main conductor axis
IEC

Figure 1 – Conductor arrangement
______________
1
 The numbers in square brackets refer to the Bibliography.
b
m

---------------------- Page: 10 ----------------------
IEC TR 60865-2:2015 © IEC 2015 – 9 –
4.2 Data

Initial symmetrical three-phase short-circuit current (r.m.s.) ′′ 16 kA
I =
k
Factor for the calculation of the peak short-circuit current 1,35
k =
System frequency f 50 Hz
=
No automatic reclosing



Number of spans ≥ 3
Centre-line distance between supports l = 1 m
Centre-line distance between conductors a 0,2 m
=


Rectangular conductor EN AW-6101B T7

– Dimensions b 60 mm
=
m
c 10 mm
=
m
– Mass per unit length of main conductor 1,62 kg/m
m′ =
m
2
– Young’s modulus 70 000 N/mm
E =
2
– Stress corresponding to the yield point f = 120 N/mm to
y
2
180 N/mm
2
Conventional value of acceleration of gravity
g = 9,81 m/s


Partial safety factors; for example according to EN 1990 [2]
– Normal load case g = 1,35
F
1,1
g =
M
– Exceptional load case 1,0
g g =
F M
NOTE Safety factors differ in national standards.
4.3 Normal load case: Conductor stress and forces on the supports caused by dead
load
The dead load on the conductor is:
kg m
′
F = m lg= 1,62⋅⋅1,00 m 9,81= 15,9 N
str,k m
2
m
s
FF=g =1,35⋅=15,9 N 21,5 N
str,d F str,k
The conductor bending stress is:
Fl
15,9 N⋅1,00 m
str,k
62 2
s = = =0,33⋅=10 N/m 0,33 N/mm
st,m,k
−63
8W
8 ⋅⋅6 10 m
st,m
22
s =g s =1,35⋅=0,33 N/mm 0,45 N/mm
st,m,d F st,m,k
with

---------------------- Page: 11 ----------------------
– 10 – IEC TR 60865-2:2015 © IEC 2015
33
c b 0,,010 ⋅0 060
4 −74
mm
J m 1,8⋅10 m
st,m
12 12

−74
J
1,8 ⋅10 m
st,m −63
W 6⋅10 m
st,m
b /2 0,03 m
m
NOTE The equation for the calculation of s gives the maximum value for two spans. The actual value for
st,m,k
three or more spans is slightly lower.
The conductors have sufficient strength if
f
y
s ≤
st,m,d
g
M
with the lower value of f . The partial safety factors for normal load case g , g see 4.2. This
y F M
gives:
2
f
120 N/mm
y
22
s 0,45 N/mm less than 109 N/mm
st,m,d
g 1,1
M
The forces on the supports are in the direction of the dead load:
– for the outer supports (A) with α = 0,4, see IEC 60865-1:2011, Table 3:
A

FF=α =0,4⋅=21,5 N 8,6 N
st,r,dA A str,d
– for the inner supports (B) with α = 1,1, see IEC 60865-1:2011, Table 3:
B
FF=α =1,1⋅=21,5 N 23,7 N
st,r,dB B str,d
NOTE In some standards the safety factors for the supports can include the partial safety factor g for action.
F
4.4 Exceptional load case: Effects of short-circuit currents
4.4.1 Maximum force on the central main conductor
The maximum electromagnetic force on the central main conductor is:
−7
2
m 3 l 4π ⋅10 Vs 3 1,00 m
23
0
Fi ⋅⋅ 30,6⋅10 A⋅ 803 N (2)
m3 p ( )
2ππ2 a 2 Am 2 0,202 m
m
where
3
iIk 2 ′′ 1,35⋅⋅2 16 kA 30,6 kA 30,6⋅10 A
pk
and the effective distance between the main conductors
a 0,20 m
a 0,202 m (6)
m
k 0,99
12
with k according to IEC 60865-1:2011, Figure 1 with a = a, b = b , c = c , for
12 1s s m s m
b /c = 60 mm/10 mm = 6, and a/c = 200 mm/10 mm = 20.
m m m
= ==
= = = =
= ==
== =
= = =
= = =

---------------------- Page: 12 ----------------------
IEC TR 60865-2:2015 © IEC 2015 – 11 –
4.4.2 Conductor stress and forces on the supports
4.4.2.1 General
The calculations can be made according to the following 4.4.2.2 or 4.4.2.3.
4.4.2.2 Simplified method
4.4.2.2.1 Conductor bending stress
The maximum bending stress is:
Fl 803 N⋅1,00 m
m3 62 2
s =V V β =1,0⋅⋅0,73 =73,3⋅10 N/m=73,3 N/mm (9)
m,d σm rm
−63
8W
8 ⋅⋅1 10 m
m
where
V V = 1,0 (V V ) according to IEC 60865-1:2011, Table 2
sm rm sm rm max
β = 0,73 according to IEC 60865-1:2011, Table 3

−8 4
J 0,5 ⋅10 m
−6 3
m
W = = = 1⋅10 m
m
c / 2 0,005 m
m
The busbar is assumed to withstand the short-circuit force if
ss+≤ qf (11)
m,d st,m,k y
with the lower value of f . s see 4.3. For rectangular cross-section q = 1,5, see
y st,m,k
IEC 60865-1:2011, Table 4. This gives:
2 2 2 22

ss+=73,3 N/mm+ 0,33 N/mm=73,6 N/mm less than qf=1,5⋅120 N/mm=180 N/mm
m,d st,m,k y
4.4.2.2.2 Forces on the supports
The equivalent static force on the supports is:
F = VV α F (15)
r,d F rm m3
According to IEC 60865-1:2011, Table 2, with the upper value of f and s = s + s it
y tot,d m,d st,m,k
is:
2
s
73,6 N/mm
tot,d
0,511
2
0,8 f
0,8 ⋅180 N/mm
y
Therefore, with a three-phase short-circuit we meet range 2 in IEC 60865-1:2011, Table 2,
s
tot,d
0,370 << 1
0,8 f
y
hence
==

---------------------- Page: 13 ----------------------
– 12 – IEC TR 60865-2:2015 © IEC 2015
0,8 f
1
y

VV 1,96
F rm
s 0,511
tot,d
For the outer supports (A) it is with α = 0,4, see IEC 60865-1:2011, Table 3:
A
F = VV α F = 1,96⋅⋅0,4 803 N= 630 N
r,dA F rm A m3
For the inner supports (B) it is with α = 1,1, see IEC 60865-1:2011, Table 3:
B
F VV α F 1,96⋅⋅1,1 803 N 1731N
r,dB F rm B m3
4.4.2.3 Detailed method
4.4.2.3.1 Relevant natural frequency f and factors V , V and V
cm F rm sm
The relevant natural frequency of the main conductor is:
10 2 −8 4
g E J 3,56 7 ⋅10 N/m ⋅0,5 ⋅10 m
m
f==⋅=52,3 Hz (16)
cm
22
′
m 1,62 kg/m
l
m
(1,00 m)
wh
...