# IEC 60865-1:2011

(Main)## Short-circuit currents - Calculation of effects - Part 1: Definitions and calculation methods

## Short-circuit currents - Calculation of effects - Part 1: Definitions and calculation methods

IEC 60865-1:2011 is applicable to the mechanical and thermal effects of short-circuit currents. It contains procedures for the calculation of: the electromagnetic effect on rigid conductors and flexible conductors, the thermal effect on bare conductors. For cables and insulated conductors, reference is made, for example, to IEC 60949 and IEC 60986. For the electromagnetic and thermal effects in d.c. auxiliary installations of power plants and substations reference is made to IEC 61660-2. Only a.c. systems are dealt with in this standard. This third edition cancels and replaces the second edition published in 1993 and constitutes a technical revision. The main changes with respect to the previous edition are:

- The determinations for automatic reclosure together with rigid conductors have been revised.

- 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 now be calculated. 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 (it is now part of IEC 60909-0). The regulations for thermal effects of electrical equipment have been deleted. The standard has been reorganized and some of the symbols have been changed to follow the conceptual characteristic of international standards.

## Courants de court-circuit - Calcul des effects - Partie 1: Définitions et méthodes de calcul

La CEI 60865-1:2011 s'applique aux effets mécaniques et thermiques des courants de court-circuit. Elle contient les modes opératoires de calcul de: l'effet électromagnétique sur les conducteurs rigides et souples; l'effet thermique sur les conducteurs nus. Pour les câbles et les conducteurs isolés, se référer par exemple à la CEI 60949 et à la CEI 60986. Pour les effets électromagnétiques et thermiques dans les installations auxiliaires alimentées en courant continu dans les centrales et les postes, il est fait référence à la CEI 61660-2. Seuls les systèmes alimentés en courant alternatif sont abordés dans la présente norme. Cette troisième édition annule et remplace la deuxième édition parue en 1993 et constitue une révision technique. Les modifications principales par rapport à l'édition précédente sont les suivantes:

- Les déterminations liées à la refermeture automatique ainsi qu'aux conducteurs rigides ont été révisées.

- L'influence des billettes de support en milieu de portée sur la portée a été incluse. Pour le raccordement de câbles verticaux, le déplacement et la force de traction sur le point de fixation le plus bas peuvent à présent être calculés. Des recommandations supplémentaires liées aux charges pour les fondations dues aux forces de traction ont été ajoutées. Le paragraphe relatif à la détermination du courant de court-circuit thermique équivalent a été supprimé (il fait à présent partie de la CEI 60909-0). Les régulations concernant les effets thermiques du matériel électrique ont été supprimées. La norme a été restructurée et certains symboles ont été modifiés afin de mieux correspondre aux caractéristiques conceptuelles des normes internationales.

### General Information

### Standards Content (Sample)

IEC 60865-1

®

Edition 3.0 2011-10

INTERNATIONAL

STANDARD

NORME

INTERNATIONALE

Short-circuit currents – Calculation of effects –

Part 1: Definitions and calculation methods

Courants de court-circuit – Calcul des effects –

Partie 1: Définitions et méthodes de calcul

IEC 60865-1:2011

---------------------- Page: 1 ----------------------

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---------------------- Page: 2 ----------------------

IEC 60865-1

®

Edition 3.0 2011-10

INTERNATIONAL

STANDARD

NORME

INTERNATIONALE

Short-circuit currents – Calculation of effects –

Part 1: Definitions and calculation methods

Courants de court-circuit – Calcul des effects –

Partie 1: Définitions et méthodes de calcul

INTERNATIONAL

ELECTROTECHNICAL

COMMISSION

COMMISSION

ELECTROTECHNIQUE

PRICE CODE

INTERNATIONALE

CODE PRIX XA

ISBN 978-2-88912-771-9

ICS 17.220.01; 29.240.20

® Registered trademark of the International Electrotechnical Commission

Marque déposée de la Commission Electrotechnique Internationale

---------------------- Page: 3 ----------------------

– 2 – 60865-1 IEC:2011

CONTENTS

FOREWORD . 4

1 Scope . 6

2 Normative references . 6

3 Terms, definitions, symbols and units . 7

3.1 Terms and definitions . 7

3.2 Symbols and units . 9

4 General . 12

5 Rigid conductor arrangements . 13

5.1 General . 13

5.2 Calculation of electromagnetic forces . 13

5.2.1 Calculation of peak force between the main conductors during a

three-phase short-circuit . 13

5.2.2 Calculation of peak force between the main conductors during a line-

to-line short-circuit . 13

5.2.3 Calculation of peak value of force between coplanar sub-conductors . 14

5.3 Effective distance between main conductors and between sub-conductors . 14

5.4 Calculation of stresses in rigid conductors . 16

5.4.1 Calculation of stresses . 16

5.4.2 Section modulus and factor q of main conductor composed of sub-

conductors . 17

5.4.3 Permitted conductor stress . 20

5.5 Structure loads due to rigid conductors . 21

5.6 Consideration of automatic reclosing . 21

5.7 Calculation with special regard to conductor oscillation . 22

5.7.1 General . 22

5.7.2 Determination of relevant natural frequency . 23

5.7.3 The factors V , V , V , V and V . 23

F σm σs rm rs

6 Flexible conductor arrangements . 26

6.1 General . 26

6.2 Effects on horizontal main conductors . 27

6.2.1 General . 27

6.2.2 Characteristic dimensions and parameter . 27

6.2.3 Tensile force F during short-circuit caused by swing out (short-

t,d

circuit tensile force) without dropper in midspan . 30

6.2.4 Dynamic change of sag due to elongation of conductor and change of

shape of the conductor curve . 31

6.2.5 Tensile force F during short-circuit caused by swing out (short-

t,d

circuit tensile force) with dropper in the middle of the span . 32

6.2.6 Tensile force F after short-circuit caused by drop (drop force) . 33

f,d

6.2.7 Horizontal span displacement b and minimum air clearance a . 33

h min

6.3 Effects on vertical main conductors (droppers) . 34

6.4 Effects on bundled conductors . 35

6.4.1 Characteristic dimensions and parameter . 35

6.4.2 Tensile force F in the case of clashing sub-conductors . 38

pi,d

6.4.3 Tensile force F in the case of non-clashing sub-conductors . 38

pi,d

6.5 Structure loads due to flexible conductors . 41

6.5.1 Design load for post insulators, their supports and connectors . 41

---------------------- Page: 4 ----------------------

60865-1 IEC:2011 – 3 –

6.5.2 Design load for structures, insulators and connectors with tensile

forces transmitted by insulator chains . 41

6.5.3 Design load for foundations . 42

7 The thermal effect on bare conductors . 42

7.1 General . 42

7.2 Calculation of thermal equivalent short-circuit current . 42

7.3 Calculation of temperature rise and rated short-time withstand current

density for conductors . 43

7.4 Calculation of thermal short-time strength for different durations of the short-

circuit . 44

Annex A (normative) Equations for calculation of diagrams . 46

Bibliography . 51

Figure 1 – Factor k for calculating the effective conductor distance . 15

1s

Figure 2 – Loading direction and bending axis for multiple conductor arrangements . 18

Figure 3 – Factor e for the influence of connecting pieces in Equation (17) . 24

Figure 4 – Factors V , V and V to be used with the three-phase and line-to-line

F σm σs

short-circuits . 25

Figure 5 – Factors V and V to be used with three-phase automatic reclosing . 26

rm rs

Figure 6 – Maximum swing out angle δ for a given maximum short-circuit duration T . 30

max k1

Figure 7 – Factor ψ for tensile force in flexible conductors . 31

Figure 8 – Geometry of a dropper . 33

Figure 9 – ν as a function of ν . 37

2 1

180°

Figure 10 – ν ·sin as a function of a /d . 37

3 s

n

Figure 11 – ξ as a function of j and ε . 38

st

Figure 12 – η as a function of j and ε . 41

st

Figure 13 – Relation between rated short-circuit withstand current density (T = 1 s)

kr

and conductor temperature . 44

Table 1 – Effective distance a between sub-conductors for rectangular cross-section

s

dimensions . 16

Table 2 – Maximum possible values of V V , V V , V V . 19

σm rm σs rs F rm

Table 3 – Factors α, β, γ for different busbar support arrangements . 20

Table 4 – Factor q . 22

Table 5 – Section moduli W of main conductors with two or more stiffening elements

m

between two adjacent supports. The stiffening elements are black. . 22

Table 6 – Recommended highest temperatures for mechanically stressed conductors

during a short-circuit . 43

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– 4 – 60865-1 IEC:2011

INTERNATIONAL ELECTROTECHNICAL COMMISSION

____________

SHORT-CIRCUIT CURRENTS –

CALCULATION OF EFFECTS –

Part 1: Definitions and calculation methods

FOREWORD

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

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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.

International Standard IEC 60865-1 has been prepared by IEC technical committee 73: Short-

circuit currents.

This third edition cancels and replaces the second edition published in 1993. This edition

constitutes a technical revision.

The main changes with respect to the previous edition are listed below:

• The determinations for automatic reclosure together with rigid conductors have been

revised.

• 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 now be calculated.

• Additional recommendations for foundation loads due to tensile forces have been added.

---------------------- Page: 6 ----------------------

60865-1 IEC:2011 – 5 –

• The subclause for determination of the thermal equivalent short-circuits current has been

deleted (it is now part of IEC 60909-0).

• The regulations for thermal effects of electrical equipment have been deleted.

• The standard has been reorganized and some of the symbols have been changed to

follow the conceptual characteristic of international standards.

The text of this standard is based on the following documents:

CDV Report on voting

73/152/CDV 73/153/RVC

Full information on the voting for the approval of this standard 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 of the IEC 60865 series, under the general title, Short-circuit currents –

Calculation 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 web site 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.

---------------------- Page: 7 ----------------------

– 6 – 60865-1 IEC:2011

SHORT-CIRCUIT CURRENTS –

CALCULATION OF EFFECTS –

Part 1: Definitions and calculation methods

1 Scope

This part of IEC 60865 is applicable to the mechanical and thermal effects of short-circuit

currents. It contains procedures for the calculation of

– the electromagnetic effect on rigid conductors and flexible conductors,

– the thermal effect on bare conductors.

For cables and insulated conductors, reference is made, for example, to IEC 60949 and

IEC 60986. For the electromagnetic and thermal effects in d.c. auxiliary installations of power

plants and substations reference is made to IEC 61660-2.

Only a.c. systems are dealt with in this standard.

The following points should, in particular, be noted:

a) The calculation of short-circuit currents should be based on IEC 60909. For the

determination of the greatest possible short-circuit current, additional information from

other IEC standards may be referred to, e.g. details about the underlying circuitry of the

calculation or details about current-limiting devices, if this leads to a reduction of the

mechanical stress.

b) Short-circuit duration used in this standard depends on the protection concept and should

be considered in that sense.

c) These standardized procedures are adjusted to practical requirements and contain

simplifications which are conservative. Testing or more detailed methods of calculation or

both may be used.

d) In Clause 5 of this standard, for arrangements with rigid conductors, only the stresses

caused by short-circuit currents are calculated. Furthermore, other stresses can exist, e.g.

caused by dead-load, wind, ice, operating forces or earthquakes. The combination of

these loads with the short-circuit loading should be part of an agreement and/or be given

by standards, e.g. erection-codes.

The tensile forces in arrangements with flexible conductors include the effects of dead-

load. With respect to the combination of other loads the considerations given above are

valid.

e) The calculated loads are design loads and should be used as exceptional loads without

any additional partial safety factor according to installation codes of, for example,

1

IEC 61936-1 [1] .

2 Normative references

The following referenced documents are indispensable for the application 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 60909 (all parts) Short-circuit current calculation in three-phase a.c. systems

—————————

1

Figures in square brackets refer to the bibliography.

---------------------- Page: 8 ----------------------

60865-1 IEC:2011 – 7 –

IEC 60909-0, Short-circuit currents in three-phase a.c. systems – Part 0: Calculation of

currents

IEC 60949, Calculation of thermally permissible short-circuit currents, taking into account

non-adiabatic heating effects

IEC 60986, Short-circuit temperature limits of electric cables with rated voltages from 6 kV

(U = 7,2 kV) up to 30 kV (U = 36 kV)

m m

IEC 61660-2, Short-circuit currents in d.c. auxiliary installations in power plants and

substations – Part 2: Calculation of effects

3 Terms, definitions, symbols and units

3.1 Terms and definitions

For the purposes of this document the following terms and definitions apply.

3.1.1

main conductor

conductor or arrangement composed of a number of conductors which carries the total current

in one phase

3.1.2

sub-conductor

single conductor which carries a certain part of the total current in one phase and is a part of

the main conductor

3.1.3

fixed support

support of a rigid conductor in which moments are imposed in the regarded plane

3.1.4

simple support

support of a rigid conductor in which no moments are imposed in the regarded plane

3.1.5

connecting piece

any additional mass within a span which does not belong to the uniform conductor material,

includingamong others, spacers, stiffening elements, bar overlappings, branchings, etc.

3.1.6

spacer

mechanical element between sub-conductors, rigid or flexible, which, at the point of

installation, maintains the clearance between sub-conductors

3.1.7

stiffening element

special spacer intended to reduce the mechanical stress of rigid conductors

3.1.8

relevant natural frequency

f

cm

first natural frequency of the free vibration of a single span beam without damping and natural

frequency of order ν of beams with ν spans without damping

---------------------- Page: 9 ----------------------

– 8 – 60865-1 IEC:2011

3.1.9

short-circuit tensile force

F

t,d

maximum tensile force (design value) in a flexible main conductor due to swing out reached

during the short-circuit

3.1.10

drop force

F

f,d

maximum tensile force (design value) in a flexible main conductor which occurs when the

span drops down after swing out

3.1.11

pinch force

F

pi,d

maximum tensile force (design value) in a bundled flexible conductor during the short-circuit

due to the attraction of the sub-conductors in the bundle

3.1.12

duration of the first short-circuit current flow

T

k1

time interval between the initiation of the short-circuit and the first breaking of the current

3.1.13

thermal equivalent short-circuit current

I

th

r.m.s. value of current having the same thermal effect and the same duration as the actual

short-circuit current, which can contain d.c. component and can subside in time

3.1.14

thermal equivalent short-circuit current density

S

th

ratio of the thermal equivalent short-circuit current and the cross-section area of the

conductor

3.1.15

rated short-time withstand current density, S , for conductors

thr

r.m.s. value of the current density which a conductor is able to withstand for the rated short

time

3.1.16

duration of short-circuit current

T

k

sum of the time durations of the short-circuit current flow from the initiation of the first short-

circuit to the final breaking of the current in all phases

3.1.17

rated short-time

T

kr

time duration for which a conductor can withstand a current density equal to its rated short-

time withstand current density

---------------------- Page: 10 ----------------------

60865-1 IEC:2011 – 9 –

3.2 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.

The symbols used in this standard and the SI-units concerned are given in the following lists.

2

A Cross-section of one main-conductor m

2

A Cross-section of one sub-conductor m

s

a Centre-line distance between conductors m

a Effective distance between main conductors m

m

a Minimum air clearance m

min

a Effective distance between sub-conductors m

s

a Centre-line distance between sub-conductor 1 and m

1n

sub-conductor n

a Centre-line distance between sub-conductors m

1s

b Maximum horizontal displacement m

h

b Dimension of a main conductor perpendicular to the direction of m

m

the force

b Dimension of a sub-conductor perpendicular to the direction m

s

of the force

C Dilatation factor 1

D

C Form factor 1

F

c Dimension of a main conductor in the direction of the force m

m

c Dimension of a sub-conductor in the direction of the force m

s

4 2

c Material constant m /(A s)

th

d Outer diameter of a tubular or flexible conductor m

2

E Young's modulus N/m

2

E Actual Young's modulus N/m

eff

e Factor for the influence of connecting pieces 1

F Force acting between two parallel long conductors during a short- N

circuit

Characteristic electromagnetic force per unit length on flexible N/m

F′

main conductors

F Force between main conductors during a short-circuit N

m

F Force between main conductors during a line-to-line short-circuit N

m2

F Force on the central main conductor during a balanced three- N

m3

phase short-circuit

F Force on support of rigid conductors (peak value, design value) N

r,d

F Drop force of one main conductor (design value) N

f,d

F Pinch force of one main conductor (design value) N

pi,d

F Force between sub-conductors during a short-circuit N

s

F Static tensile force of one flexible main conductor N

st

F Short-circuit tensile force of one main conductor (design value) N

t,d

---------------------- Page: 11 ----------------------

– 10 – 60865-1 IEC:2011

F Short-circuit current force between the sub-conductors in a bundle N

ν

f System frequency Hz

f Relevant natural frequency of a main conductor Hz

cm

f Relevant natural frequency of a sub-conductor Hz

cs

f Dynamic conductor sag at midspan m

ed

f Equivalent static conductor sag at midspan m

es

f Static conductor sag at midspan m

st

2

f Stress corresponding to the yield point N/m

y

2

g Conventional value of acceleration of gravity m/s

h Height of the dropper m

′′ Initial symmetrical three-phase short-circuit current (r.m.s.) A

I

k

′′ Initial line-to-earth short-circuit current (r.m.s.) A

I

k1

′′ Initial symmetrical line-to-line short-circuit current (r.m.s.) A

I

k2

I Thermal equivalent short-circuit current A

th

i Peak short-circuit current A

p

i Peak short-circuit current in case of a line-to-line short-circuit A

p2

i , i Instantaneous values of the currents in the conductors A

1 2

4

J Second moment of main conductor area m

m

4

J Second moment of sub-conductor area m

s

j Parameter determining the bundle configuration during short- 1

circuit current flow

k Number of sets of spacers or stiffening elements 1

k Factor for the effective distance between sub-conductor 1 and 1

1n

sub-conductor, n

k Factor for effective conductor distance 1

1s

l Centre-line distance

**...**

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