EN 60909-0:2001

SLOVENSKI STANDARD
01-september-2002
1DGRPHãþD
SIST HD 533 S1:1998
.UDWNRVWLþQLWRNLYL]PHQLþQLKWULID]QLKVLVWHPLKGHO5DþXQDQMHWRNRY
Short-circuit currents in three-phase a.c. systems - Part 0: Calculation of currents
Kurzschlussströme in Drehstromnetzen - Teil 0: Berechnung der Ströme
Courants de court-circuit dans les réseaux triphasés à courant alternatif  Partie 0: Calcul
des courants
Ta slovenski standard je istoveten z: EN 60909-0:2001
ICS:
17.220.01 Elektrika. Magnetizem. Electricity. Magnetism.
Splošni vidiki General aspects
29.240.20 Daljnovodi Power transmission and
distribution lines
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

EUROPEAN STANDARD EN 60909-0
NORME EUROPÉENNE
EUROPÄISCHE NORM August 2001
ICS 17.220.01; 29.240.20 Supersedes HD 533 S1:1991
English version
Short-circuit currents in three-phase a.c. systems
Part 0: Calculation of currents
(IEC 60909-0:2001)
Courants de court-circuit dans les réseaux Kurzschlussströme in Drehstromnetzen
triphasés à courant alternatif Teil 0: Berechnung der Ströme
Partie 0: Calcul des courants (IEC 60909-0:2001)
(CEI 60909-0:2001)
This European Standard was approved by CENELEC on 2001-07-01. CENELEC members are bound to
comply with the CEN/CENELEC Internal Regulations which stipulate the conditions for giving this European
Standard the status of a national standard without any alteration.
Up-to-date lists and bibliographical references concerning such national standards may be obtained on
application to the Central Secretariat or to any CENELEC member.
This European Standard exists in three official versions (English, French, German). A version in any other
language made by translation under the responsibility of a CENELEC member into its own language and
notified to the Central Secretariat has the same status as the official versions.
CENELEC members are the national electrotechnical committees of Austria, Belgium, Czech Republic,
Denmark, Finland, France, Germany, Greece, Iceland, Ireland, Italy, Luxembourg, Netherlands, Norway,
Portugal, Spain, Sweden, Switzerland and United Kingdom.
CENELEC
European Committee for Electrotechnical Standardization
Comité Européen de Normalisation Electrotechnique
Europäisches Komitee für Elektrotechnische Normung
Central Secretariat: rue de Stassart 35, B - 1050 Brussels
© 2001 CENELEC - All rights of exploitation in any form and by any means reserved worldwide for CENELEC members.
Ref. No. EN 60909-0:2001 E
Foreword
The text of document 73/119/FDIS, future edition 1 of IEC 60909-0, prepared by IEC TC 73,
Short-circuit currents, was submitted to the IEC-CENELEC parallel vote and was approved by
CENELEC as EN 60909-0 on 2001-07-01.
This European Standard supersedes HD 533 S1:1991.
The following dates were fixed:
– latest date by which the EN has to be implemented
at national level by publication of an identical
national standard or by endorsement (d'op) 2002-04-01
– latest date by which the national standards conflicting
with the EN have to be withdrawn (dow) 2004-07-01
Annexes designated "normative" are part of the body of the standard.
In this standard, annexes A and ZA are normative.
Annex ZA has been added by CENELEC.
__________
Endorsement notice
The text of the International Standard IEC 60909-0:2001 was approved by CENELEC as a European
Standard without any modification.
__________
- 3 - EN 60909-0:2001
Annex ZA
(normative)
Normative references to international publications
with their corresponding European publications
This European Standard incorporates by dated or undated reference, provisions from other
publications. These normative references are cited at the appropriate places in the text and the
publications are listed hereafter. For dated references, subsequent amendments to or revisions of any
of these publications apply to this European Standard only when incorporated in it by amendment or
revision. For undated references the latest edition of the publication referred to applies (including
amendments).
NOTE When an international publication has been modified by common modifications, indicated by (mod), the relevant
EN/HD applies.
Publication Year Title EN/HD Year
IEC 60038 (mod) 1983 Nominal voltages for low-voltage public HD 472 S1 1989
electricity supply systems
IEC 60050-131 1978 International Electrotechnical --
Vocabulary (IEV)
Chapter 131: Electric and magnetic
circuits
IEC 60050-151 1978 Chapter 151: Electrical and magnetic--
devices
IEC 60050-195 1998 Chapter 195: Earthing and protection--
against electric shock
1)
IEC 60056 (mod) 1987 High-voltage alternating-current circuit- HD 348 S7 1998
breakers
IEC 60071-1 1993 Insulation co-ordination EN 60071-1 1995
Part 1: Definitions, principles and rules
IEC 60781 1989 Application guide for calculation of HD 581 S1 1991
short-circuit currents in low-voltage
radial systems
IEC 60865-1 1993 Short-circuit currents - Calculation of EN 60865-1 1993
effects
Part 1: Definitions and calculation
methods
2)
IEC 60909-1 Short-circuit currents calculation in--
three-phase a.c. systems
Part 1: Factors for the calculation of
short-circuit currents in three-phase
a.c. systems according to IEC 60909-0

1)
HD 348 S7 is based on IEC 60056:1987 + A3:1996.
2)
To be published.
Publication Year Title EN/HD Year
IEC 60909-2 1992 Electrical equipment - Data for short---
circuit current calculations in
accordance with IEC 60909
IEC 60909-3 1995 Part 3: Currents during two separate--
simultaneous single phase line-to-earth
short circuits and partial short-circuit
currents flowing through earth
2)
IEC 60909-4 Part 4: Examples for the calculation of--
short-circuit currents
IEC 60949 1988 Calculation of thermally permissible--
short-circuit currents, taking into
account non-adiabatic heating effects
IEC 60986 1989 Guide to the short-circuit temperature--
limits of electric cables with a rated
voltage from 1,8/3 (3,6) kV to
18/30 (36) kV
2)
To be published.
NORME CEI
INTERNATIONALE IEC
60909-0
INTERNATIONAL
Première édition
STANDARD
First edition
2001-07
Courants de court-circuit dans les réseaux
triphasés à courant alternatif –
Partie 0:
Calcul des courants
Short-circuit currents in three-phase
a.c. systems –
Part 0:
Calculation of currents
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60909-0  IEC:2001 – 3 –
CONTENTS
FOREWORD. 9
1 General . 13
1.1 Scope .13
1.2 Normative references . 15
1.3 Definitions . 17
1.4 Symbols, subscripts and superscripts. 25
1.4.1 Symbols . 25
1.4.2 Subscripts . 29
1.4.3 Superscripts . 31
2 Characteristics of short-circuit currents: calculating method. 31
2.1 General.31
2.2 Calculation assumptions. 35
2.3 Method of calculation . 35
2.3.1 Equivalent voltage source at the short-circuit location . 35
2.3.2 Application of symmetrical components . 41
2.4 Maximum short-circuit currents . 45
2.5 Minimum short-circuit currents . 47
3 Short-circuit impedances of electrical equipment. 47
3.1 General.47
3.2 Network feeders . 49
3.3 Transformers . 51
3.3.1 Two-winding transformers . 51
3.3.2 Three-winding transformers . 53
3.3.3 Impedance correction factors for two- and three-winding
network transformers . 57
3.4 Overhead lines and cables . 59
3.5 Short-circuit limiting reactors . 61
3.6 Synchronous machines . 61
3.6.1 Synchronous generators . 61
3.6.2 Synchronous compensators and motors . 65
3.7 Power station unit . 65
3.7.1 Power station units with on-load tap-changer. 65
3.7.2 Power station units without on-load tap-changer. 69
3.8 Asynchronous motors. 71
3.8.1 General . 71
3.8.2 Contribution to short-circuit currents by asynchronous motors . 73
3.9 Static converters. 77
3.10 Capacitors and non-rotating loads . 77
4 Calculation of short-circuit currents . 79
4.1 General.79
4.2 Initial symmetrical short-circuit current I ′′ . 83
k
60909-0  IEC:2001 – 5 –
4.2.1 Three-phase short circuit. 83
4.2.2 Line-to-line short circuit . 95
4.2.3 Line-to-line short circuit with earth connection. 99
4.2.4 Line-to-earth short circuit .101
4.3 Peak short-circuit current i .101
p
4.3.1 Three-phase short circuit.101
4.3.2 Line-to-line short circuit .105
4.3.3 Line-to-line short circuit with earth connection.105
4.3.4 Line-to-earth short circuit .107
4.4 DC component of the short-circuit current .107
...........................................................107
4.5 Symmetrical short-circuit breaking current I
b
4.5.1 Far-from-generator short circuit .107
4.5.2 Near-to-generator short circuit .109
..........................................................................117
4.6 Steady-state short-circuit current I
k
4.6.1 Three-phase short circuit of one generator or one power station unit .117
4.6.2 Three-phase short circuit in non-meshed networks.121
4.6.3 Three-phase short circuit in meshed networks.123
4.6.4 Unbalanced short circuits.123
4.6.5 Short circuits at the low-voltage side of transformers, if one line conductor
is interrupted at the high-voltage side .125
4.7 Terminal short circuit of asynchronous motors.127
4.8 Joule integral and thermal equivalent short-circuit current .129
Annex A (normative) Equations for the calculation of the factors m and n .137
Figure 1 – Short-circuit current of a far-from-generator short circuit with
constant a.c. component (schematic diagram).31
Figure 2 – Short-circuit current of a near-to-generator short circuit with
decaying a.c. component (schematic diagram).33
Figure 3 – Characterization of short circuits and their currents.37
′′
Figure 4 – Illustration for calculating the initial symmetrical short-circuit current I
k
in compliance with the procedure for the equivalent voltage source .39
Figure 5 – Short-circuit impedances of a three-phase a.c. system at
the short-circuit location F.43
Figure 6 – System diagram and equivalent circuit diagram for network feeders .49
Figure 7 – Three-winding transformer (example) .55
Figure 8 – Phasor diagram of a synchronous generator at rated conditions .63
Figure 9 – Example for the estimation of the contribution from the asynchronous motors
in relation to the total short-circuit current.75
Figure 10 – Diagram to determine the short-circuit type (figure 3) for the highest
short-circuit current referred to the symmetrical three-phase short-circuit current at
the short-circuit location when the impedance angles of the sequence
impedances Z , Z , Z are identical .81
(1) (2) (0)
Figure 11 – Examples of single-fed short circuits.85
Figure 12 – Example of a non-meshed network .89

60909-0  IEC:2001 – 7 –
Figure 13 – Short-circuit currents and partial short-circuit currents for three-phase
short circuits between generator and unit transformer with or without on-load tap-changer,
or at the connection to the auxiliary transformer of a power station unit and at the
auxiliary busbar A .89
Figure 14 – Example of a meshed network fed from several sources.97
Figure 15 – Factor κ for series circuit as a function of ratio R/X or X/R.101
Figure 16 – Factor μ for calculation of short-circuit breaking current I .111
b
Figure 17 – Factor q for the calculation of the symmetrical short-circuit breaking
current of asynchronous motors .113
Figure 18 – λ and λ factors for cylindrical rotor generators .119
min max
Figure 19 – Factors λ and λ for salient-pole generators .119
min max
Figure 20 – Transformer secondary short circuits, if one line (fuse) is opened on the
high-voltage side of a transformer Dyn5 .125
Figure 21 – Factor m for the heat effect of the d.c. component of the short-circuit current
(for programming, the equation for m is given in annex A).131
Figure 22 – Factor n for the heat effect of the a.c. component of the short-circuit current
(for programming, the equation for n is given in annex A) .133
Table 1 – Voltage factor c.41
Table 2 – Factors α and β for the calculation of short-circuit currents with equation (90)
Rated transformation ratio t = U /U .127
r rTHV rTLV
Table 3 – Calculation of short-circuit currents of asynchronous motors in the case of
a short circuit at the terminals (see 4.7) .129

60909-0  IEC:2001 – 9 –
INTERNATIONAL ELECTROTECHNICAL COMMISSION
____________
SHORT-CIRCUIT CURRENTS IN THREE-PHASE AC SYSTEMS –
Part 0: Calculation of currents
FOREWORD
1) The IEC (International Electrotechnical Commission) is a worldwide organization for standardization comprising
all national electrotechnical committees (IEC National Committees). The object of the IEC is to promote
international co-operation on all questions concerning standardization in the electrical and electronic fields. To
this end and in addition to other activities, the IEC publishes International Standards. Their preparation is
entrusted to technical committees; any IEC National Committee interested in the subject dealt with may
participate in this preparatory work. International, governmental and non-governmental organizations liaising
with the IEC also participate in this preparation. The IEC collaborates closely with the International Organization
for Standardization (ISO) in accordance with conditions determined by agreement between the two organizations.
2) The formal decisions or agreements of the IEC on technical matters express, as nearly as possible, an international
consensus of opinion on the relevant subjects since each technical committee has representation from all
interested National Committees.
3) The documents produced have the form of recommendations for international use and are published in the form of
standards, technical specifications, technical reports or guides and they are accepted by the National Committees
in that sense.
4) In order to promote international unification, IEC National Committees undertake to apply IEC International
Standards transparently to the maximum extent possible in their national and regional standards. Any divergence
between the IEC Standard and the corresponding national or regional standard shall be clearly indicated in the
latter.
5) The IEC provides no marking procedure to indicate its approval and cannot be rendered responsible for any
equipment declared to be in conformity with one of its standards.
6) Attention is drawn to the possibility that some of the elements of this International Standard may be the subject of
patent rights. The IEC shall not be held responsible for identifying any or all such patent rights.
International Standard IEC 60909-0 has been prepared by IEC technical committee 73: Short-
circuit currents.
This first edition cancels and replaces IEC 60909 published in 1988 and constitutes a technical
revision.
The text of this standard is based on the following documents:
FDIS Report on voting
73/119/FDIS 73/121/RVD
Full information on the voting for the approval of this standard can be found in the report on
voting indicated in the above table.
Annex A forms an integral part of this standard.

60909-0  IEC:2001 – 11 –
This part of IEC 60909 shall be read in conjunction with the International Standards, Technical
Reports and Technical Specifications mentioned below:
– IEC TR 60909-1,— Short-circuit current calculation in three-phase a.c. systems – Part 1:
Factors for the calculation of short-circuit currents in three-phase a.c. systems according
1)
to IEC 60909-0
– IEC TR3 60909-2:1992, Electrical equipment – Data for short-circuit current calculations in
accordance with IEC 60909
– IEC 60909-3:1995, Short-circuit current calculation in three-phase a.c. systems – Part 3:
Currents during two separate simultaneous single-phase line-to-earth short circuits and
partial short-circuit currents following through earth
– IEC TR 60909-4:2000, Short-circuit current calculation in three-phase a.c. systems – Part 4:
Examples for the calculation of short-circuit currents
The committee has decided that the contents of this publication will remain unchanged until 2007.
At this date, the publication will be
• reconfirmed;
• withdrawn;
• replaced by a revised edition, or
• amended.
The contents of the corrigendum of February 2002 have been included in this copy.
________
1)
To be published.
60909-0  IEC:2001 – 13 –
SHORT-CIRCUIT CURRENTS IN THREE-PHASE AC SYSTEMS –
Part 0: Calculation of currents
1 General
1.1 Scope
This part of IEC 60909 is applicable to the calculation of short-circuit currents:
• in low-voltage three-phase a.c. systems
• in high-voltage three-phase a.c. systems
operating at a nominal frequency of 50 Hz or 60 Hz.
Systems at highest voltages of 550 kV and above with long transmission lines need special
consideration.
This part of IEC 60909 establishes a general, practicable and concise procedure leading to results,
which are generally of acceptable accuracy. For this calculation method, an equivalent voltage source at
the short-circuit location is introduced. This does not exclude the use of special methods, for example the
superposition method, adjusted to particular circumstances, if they give at least the same precision. The
superposition method gives the short-circuit current related to the one load flow presupposed. This
method, therefore, does not necessarily lead to the maximum short-circuit current.
This part of IEC 60909 deals with the calculation of short-circuit currents in the case of balanced
or unbalanced short circuits.
In case of an accidental or intentional conductive path between one line conductor and local
earth, the following two cases must be clearly distinguished with regard to their different
physical properties and effects (resulting in different requirements for their calculation):
• line-to-earth short circuit, occurring in a solidly earthed neutral system or an impedance
earthed neutral system;
• a single line-to-earth fault, occurring in an isolated neutral earthed system or a resonance
earthed neutral system. This fault is beyond the scope of, and is therefore not dealt with in,
this standard.
For currents during two separate simultaneous single-phase line-to-earth short circuits in an
isolated neutral system or a resonance earthed neutral system, see IEC 60909-3.
Short-circuit currents and short-circuit impedances may also be determined by system tests, by
measurement on a network analyzer, or with a digital computer. In existing low-voltage systems
it is possible to determine the short-circuit impedance on the basis of measurements at the
location of the prospective short circuit considered.

60909-0  IEC:2001 – 15 –
The calculation of the short-circuit impedance is in general based on the rated data of the
electrical equipment and the topological arrangement of the system and has the advantage of
being possible both for existing systems and for systems at the planning stage.
In general, two short-circuit currents, which differ in their magnitude, are to be calculated:
• the maximum short-circuit current which determines the capacity or rating of electrical
equipment; and
• the minimum short-circuit current which can be a basis, for example, for the selection of
fuses, for the setting of protective devices, and for checking the run-up of motors.
NOTE The current in a three-phase short circuit is assumed to be made simultaneously in all poles. Investigations of
non-simultaneous short circuits, which may lead to higher aperiodic components of short-circuit current, are beyond
the scope of this standard.
This standard does not cover short-circuit currents deliberately created under controlled
conditions (short-circuit testing stations).
This part of IEC 60909 does not deal with the calculation of short-circuit currents in installations
on board ships and aeroplanes.
1.2 Normative references
The following normative documents contain provisions which, through reference in this text,
constitute provisions of this part of IEC 60909. For dated references, subsequent amendments to,
or revisions of, any of these publications do not apply. However, parties to agreements based on
this part of IEC 60909 are encouraged to investigate the possibility of applying the most recent
editions of the normative documents indicated below. For undated references, the latest edition
of the normative document referred to applies. Members of IEC and ISO maintain registers of
currently valid International Standards.
IEC 60038:1983, IEC standard voltages
IEC 60050(131):1978, International Electrotechnical Vocabulary – Chapter 131: Electric and
magnetic circuits
IEC 60050(151):1978, International Electrotechnical Vocabulary – Chapter 151: Electric and
magnetic devices
IEC 60050-195:1998, International Electrotechnical Vocabulary – Part 195: Earthing and
protection against electric shock
IEC 60056:1987, High-voltage alternating-current circuit-breakers
IEC 60071-1:1993, Insulation coordination – Part 1: Definitions, principles and rules
IEC 60781:1989, Application guide for calculation of short-circuit currents in low-voltage radial
systems
IEC 60865-1:1993, Short-circuit currents – Calculation of effects – Part 1: Definitions and calculation
methods
60909-0  IEC:2001 – 17 –
IEC TR 60909-1, Short-circuit currents calculation in three-phase a.c. systems – Part 1: Factors
1)
for the calculation of short-circuit currents in three-phase a.c. systems according to IEC 60909-0
IEC TR3 60909-2:1992, Electrical equipment – Data for short-circuit current calculations in
accordance with IEC 60909
IEC 60909-3:1995, Short-circuit current calculation in three-phase a.c. systems – Part 3:
Currents during two separate simultaneous single phase line-to-earth short circuits and partial
short-circuit currents flowing through earth
IEC TR 60909-4:2000, Short-circuit current calculation in three-phase a.c. systems – Part 4:
Examples for the calculation of short-circuit currents
IEC 60949:1988, Calculation of thermally permissible short-circuit currents, taking into
account non-adiabatic heating effects
IEC 60986:1989, Guide to the short-circuit temperature limits of electrical cables with a rated
voltage from 1,8/3 (3,6) kV to 18/30 (36) kV
1.3 Definitions
For the purposes of this part of IEC 60909, the definitions given in IEC 60050(131) and the
following definitions apply.
1.3.1
short circuit
accidental or intentional conductive path between two or more conductive parts forcing the
electric potential differences between these conductive parts to be equal or close to zero
1.3.1.1
line-to-line short circuit
accidental or intentional conductive path between two or more line conductors with or without
earth connection
1.3.1.2
line-to-earth short circuit
accidental or intentional conductive path in a solidly earthed neutral system or an impedance
earthed neutral system between a line conductor and local earth
1.3.2
short-circuit current
over-current resulting from a short circuit in an electric system
NOTE It is necessary to distinguish between the short-circuit current at the short-circuit location and partial short-
circuit currents in the network branches (see figure 3) at any point of the network.
________
1)
To be published.
60909-0  IEC:2001 – 19 –
1.3.3
prospective (available) short-circuit current
current that would flow if the short circuit were replaced by an ideal connection of negligible
impedance without any change of the supply (see note of 1.1)
1.3.4
symmetrical short-circuit current
r.m.s. value of the a.c. symmetrical component of a prospective (available) short-circuit current
(see 1.3.3), the aperiodic component of current, if any, being neglected
1.3.5
initial symmetrical short-circuit current I ′′
k
r.m.s. value of the a.c. symmetrical component of a prospective (available) short-circuit current
(see 1.3.3), applicable at the instant of short circuit if the impedance remains at zero-time value
(see figures 1 and 2)
1.3.6
′′
initial symmetrical short-circuit power S
k
′′
fictitious value determined as a product of the initial symmetrical short-circuit current I
k
′′ ′′
(see 1.3.5), the nominal system voltage U (see 1.3.13) and the factor 3: S = 3 U I
n n
k k
′′
NOTE The initial symmetrical short-circuit power S is not used for the calculation procedure in this standard.
k
′′
If S is used in spite of this in connection with short-circuit calculations, for instance to calculate the internal
k
impedance of a network feeder at the connection point Q, then the definition given should be used in the following
form: S′′ = 3 U I′′ or Z = cU / S′′ .
kQ nQ kQ Q nQ kQ
1.3.7
decaying (aperiodic) component i of short-circuit current
d.c.
mean value between the top and bottom envelope of a short-circuit current decaying from an
initial value to zero according to figures 1 and 2
1.3.8
peak short-circuit current i
p
maximum possible instantaneous value of the prospective (available) short-circuit current
(see figures 1 and 2)
NOTE The magnitude of the peak short-circuit current varies in accordance with the moment at which the short
circuit occurs. The calculation of the three-phase peak short-circuit current i applies to the line conductor and to the
p
instant at which the greatest possible short-circuit current exists. Sequential short circuits are not considered.
1.3.9
symmetrical short-circuit breaking current I
b
r.m.s. value of an integral cycle of the symmetrical a.c. component of the prospective short-
circuit current at the instant of contact separation of the first pole to open of a switching device
1.3.10
steady-state short-circuit current I
k
r.m.s. value of the short-circuit current which remains after the decay of the transient phenomena
(see figures 1 and 2)
60909-0  IEC:2001 – 21 –
1.3.11
symmetrical locked-rotor current I
LR
highest symmetrical r.m.s. current of an asynchronous motor with locked rotor fed with rated
voltage U at rated frequency
rM
1.3.12
equivalent electric circuit
model to describe the behaviour of a circuit by means of a network of ideal elements
[IEV 131-01-33]
1.3.13
nominal system voltage U
n
voltage (line-to-line) by which a system is designated, and to which certain operating
characteristics are referred
NOTE Values are given in IEC 60038.
1.3.14
equivalent voltage source cU / 3
n
voltage of an ideal source applied at the short-circuit location in the positive-sequence system
for calculating the short-circuit current according to 2.3. This is the only active voltage of the
network
1.3.15
voltage factor c
ratio between the equivalent voltage source and the nominal system voltage U divided by 3.
n
The values are given in table 1
NOTE The introduction of a voltage factor c is necessary for various reasons. These are:
– voltage variations depending on time and place,
– changing of transformer taps,
– neglecting loads and capacitances by calculations according to 2.3.1,
– the subtransient behaviour of generators and motors.
1.3.16
subtransient voltage E″″ of a synchronous machine
″″
r.m.s. value of the symmetrical internal voltage of a synchronous machine which is active behind
′′
the subtransient reactance X at the moment of short circuit
d
1.3.17
far-from-generator short circuit
short circuit during which the magnitude of the symmetrical a.c. component of the prospective
(available) short-circuit current remains essentially constant (see figure 1)
1.3.18
near-to-generator short circuit
short circuit to which at least one synchronous machine contributes a prospective initial
symmetrical short-circuit current which is more than twice the machine's rated current, or a short
circuit to which asynchronous motors contribute more than 5 % of the initial symmetrical short-
circuit current I ′′ without motors (see figure 2)
k
60909-0  IEC:2001 – 23 –
1.3.19
short-circuit impedances at the short-circuit location F
1.3.19.1
positive-sequence short-circuit impedance Z of a three-phase a.c. system
(1)
impedance of the positive-sequence system as viewed from the short-circuit location (see 2.3.2
and figure 5a)
1.3.19.2
negative-sequence short-circuit impedance Z of a three-phase a.c. system
(2)
impedance of the negative-sequence system as viewed from the short-circuit location (see 2.3.2
and figure 5b)
1.3.19.3
zero-sequence short-circuit impedance Z of a three-phase a.c. system
(0)
impedance of the zero-sequence system as viewed from the short-circuit location (see 2.3.2 and
figure 5c). It includes three times the neutral-to-earth impedance Z
N
1.3.19.4
short-circuit impedance Z of a three-phase a.c. system
k
abbreviated expression for the positive-sequence short-circuit impedance Z according to
(1)
1.3.19.1 for the calculation of three-phase short-circuit currents
1.3.20
short-circuit impedances of electrical equipment
1.3.20.1
positive-sequence short-circuit impedance Z of electrical equipment
(1)
ratio of the line-to-neutral voltage to the short-circuit current of the corresponding line conductor
of electrical equipment when fed by a symmetrical positive-sequence system of voltages (see
clause 2 and IEC 60909-4)
NOTE The index of symbol Z may be omitted if there is no possibility of confusion with the negative-sequence
(1)
and the zero-sequence short-circuit impedances.
1.3.20.2
negative-sequence short-circuit impedance Z of electrical equipment
(2)
ratio of the line-to-neutral voltage to the short-circuit current of the corresponding line conductor
of electrical equipment when fed by a symmetrical negative-sequence system of voltages
(see clause 2 and IEC 60909-4).
1.3.20.3
zero-sequence short-circuit impedance Z of electrical equipment
(0)
ratio of the line-to-earth voltage to the short-circuit current of one line conductor of electrical
equipment when fed by an a.c. voltage source, if the three paralleled line conductors are used for
the outgoing current and a fourth line and/or earth as a joint return (see clause 2 and IEC 60909-4)
1.3.21
subtransient reactance X ′′ of a synchronous machine
d
effective reactance at the moment of short circuit. For the calculation of short-circuit currents
′′
the saturated value of X is taken
d
NOTE When the reactance X ′′ in ohms is divided by the rated impedance Z = U /S of the synchronous
rG rG
d rG
machine, the result in per unit is represented by a small letter x′′ = X ′′ /Z .
rG
d d
60909-0  IEC:2001 – 25 –
1.3.22
minimum time delay t
min
shortest time between the beginning of the short-circuit current and the contact separation of the
first pole to open of the switching device
NOTE The time t is the sum of the shortest possible operating time of a protective relay and the shortest opening
min
time of a circuit-breaker. It does not take into account adjustable time delays of tripping devices.
1.3.23
thermal equivalent short-circuit current I
th
the r.m.s. value of a current having the same thermal effect and the same duration as the actual
short-circuit current, which may contain a d.c. component and may subside in time
1.4 Symbols, subscripts and superscripts
The equations given in this standard are written without specifying units. The symbols represent
physical quantities possessing both numerical values and dimensions that are independent of
units, provided a consistent unit system is chosen, for example the international system of units
(SI). Symbols of complex quantities are underlined, for example Z = R + jX.
1.4.1 Symbols
A Initial value of the d.c. component i
d.c.
a Complex operator
a A ratio between unbalanced short-circuit current and three phase short-circuit
current
c Voltage factor
cU / 3 Equivalent voltage source (r.m.s.)
n
E″ Subtransient voltage of a synchronous machine
f Frequency (50 Hz or 60 Hz)
I Symmetrical short-circuit breaking current (r.m.s.)
b
I Steady-state short-circuit current (r.m.s.)
k
I Steady-state short-circuit current at the terminals (poles)
kP
of a generator with compound excitation
′′
I Initial symmetrical short-circuit current (r.m.s.)
k
I Symmetrical locked-rotor current of an asynchronous motor
LR
I Rated current of electrical equipment
r
I Thermal equivalent short-circuit current
th
i d.c. component of short-circuit current
d.c.
i Peak short-circuit current
p
K Correction factor for impedances
m Factor for the heat effect of the d.c. component
n Factor for the heat effect of the a.c. component
p Pair of poles of an asynchronous motor
p Range of generator voltage regulation
G
p Range of transformer voltage adjustment
T
P Total loss in transformer windings at rated current
krT
P Rated active power of an asynchronous motor (P = S cos ϕ η )
rM rM rM rM rM
q Factor for the calculation of breaking current of asynchronous motors
q Nominal cross-section
n
60909-0  IEC:2001 – 27 –
R resp. r Resistance, absolute respectively relative value
R Resistance of a synchronous machine
G
R Fictitious resistance of a synchronous machine when calculating i
Gf p
′′
S Initial symmetrical short-circuit power (see 1.3.6)
k
S Rated apparent power of electrical equipment
r
t Minimum time delay
min
t Rated transformation ratio (tap-changer in main position); t ≥ 1
r r
T Duration of the short-circuit current
k
U Highest voltage for equipment, line-to-line (r.m.s.)
m
U Nominal system voltage, line-to-line (r.m.s.)
n
U Rated voltage, line-to-line (r.m.s.)
r
u Rated short-circuit voltage of a transformer in per cent
kr
u Short-circuit voltage of a short-circuit limiting reactor in per cent
kR
u Rated resistive component of the short-circuit voltage
Rr
of a transformer in per cent
u Rated reactive component of the short-circuit voltage
Xr
of a transformer in per cent
U , U , U Positive-, negative-, zero-sequence voltage
(1) (2) (0)
X resp. x Reactance, absolute respectively relative value
X resp. X Synchronous reactance, direct axis respectively quadrature axis
d q
X Fictitious reactance of a generator with compound excitation in the case of
dP
steady-state short circuit at the terminals (poles)
′′ ′′
X resp. X Subtransient reactance of a synchronous machine (saturated value), direct axis
d q
respectively quadrature axis
x Unsaturated synchronous reactance, relative value
d
x Saturated synchronous reactance, relative value, reciprocal of the saturated
d sat
no-load short-circuit ratio
Z resp. z Impedance, absolute respectively relative value
Z Short-circuit impedance of a three-phase a.c. system
k
Z Positive-sequence short-circuit impedance
(1)
Z Negative-sequence short-circuit impedance
(2)
Z Zero-sequence short-circuit impedance
(0)
η Efficiency of asynchronous motors
κ Factor for the calculation of the peak short-circuit current
λ Factor for the calculation of the steady-state short-circuit current
μ Factor for the calculation of the symmetrical short-circuit breaking current
–7
μ Absolute permeability of vacuum, μ = 4π ⋅ 10 H/m
0 0
ρ Resistivity
ϕ Phase angle
θ Conductor temperature at the end of the short circuit
e
01 Positive-sequence neutral reference
02 Negative-sequence neutral reference
00 Zero-sequence neutral reference

60909-0  IEC:2001 – 29 –
1.4.2 Subscripts
(1) Positive-sequence component
(2) Negative-sequence component
(0) Zero-sequence component
a.c Alternating current
d.c Direct current
f Fictitious
k or k3 Three-phase short circuit (see figure 3a)
k1 Line-to-earth short circuit, line-to-neutral short circuit (see figure 3d)
k2 Line-to-line short circuit (see figure 3b)
k2E resp. kE2E Line-to-line short circuit with earth connection (see figure 3c)
K Impedances or reactances calculated with an impedance correction factor K ,
T
K or K respectively K
G S SO
max Maximum
min Minimum
n Nominal value (IEV 151-04-01)
r Rated value (IEV 151-04-03)
rsl Resulting
t Transferred value
AT Auxiliary transformer
B Busbar
EEarth
F Short-circuit location
G Generator
HV High-voltage, high-voltage side of a transformer
LV Low-voltage, low-voltage side of a transformer
LLine
LR Locked rotor
L1, L2, L3 Line conductors of a three-phase a.c. system
M Asynchronous motor or group of asynchronous motors
M Without motor
MV Medium-voltage, medium-voltage side of a transformer
N Neutral of a three-phase a.c. system, starpoint of a generator or a transformer
P Terminal, pole
Q Feeder connection point
R Short-circuit limiting reactor
S Power station unit (generator and unit transformer with on-load tap-changer)
SO Power station unit (generator and unit transformer with constant transfor-
mation ratio or off-load taps)
T Transformer
60909-0  IEC:2001 – 31 –
1.4.3 Superscripts
″ Subtransient (initial) value
′ Resistance or reactance per unit length
b Before the short circuit
2 Characteristics of short-circuit currents: calculating method
2.1 General
A complete calculation of short-circuit currents should give the currents as a function of time at
the short-circuit location from the initiation of the short circuit up to its end, corresponding to the
instantaneous value of the voltage at the beginning of the short circuit (see figures 1 and 2).
Current
Top envelope
DC component i of the short-ciucuit current
d.c.
Time
Bottom envelope
′′
I = initial symmetrical sho
...