Short-circuit currents in d.c. auxiliary installations in power plants and substations - Part 1: Calculation of short-circuit currents

Describes method for calculating short-circuit currents in d.c. auxilliary systems in power plants and substations, which can be equipped with the following equipment, acting as short-circuit current sources: - rectifiers in three-phase a.c. bridge connection for 50 Hz; - stationary lead-acid batteries; - smoothing capacitors; - d.c. motors with independent excitation Provides a generally applicable method of calculation which produces results of sufficient accuracy on the conservative side.

Kurzschlußströme in Gleichstrom-Eigenbedarfsanlagen in Kraftwerken und Schaltanlagen - Teil 1: Berechnung der Kurzschlußströme

Courants de court-circuit dans les installations auxiliaires alimentées en courant continu dans les centrales et les postes - Partie 1: Calcul des courants de court-circuit

Décrit une méthode de calcul des courants de court-circuit des réseaux auxiliaires en courant continu dans des centrales et des postes, qui peuvent être équipés des éléments suivants, agissant comme sources de courants de court-circuit: - redresseurs dans les ponts triphasés en courant alternatif pour 50 Hz; - batteries stationnaires au plomb; - condensateurs de lissage; - moteurs à courant continu avec excitation indépendante. Fournit une méthode générale de calcul donnant des résultats suffisamment précis et par excès.

Kratkostični toki v pomožnih enosmernih napeljavah elektrarn in transformatorskih postaj - 1. del: Računanje kratkostičnih tokov (IEC 61660-1:1997)

General Information

Status
Published
Publication Date
23-Jul-1997
Drafting Committee
Parallel Committee
Current Stage
6060 - Document made available
Due Date
24-Jul-1997
Completion Date
24-Jul-1997

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SLOVENSKI STANDARD
SIST EN 61660-1:1998
01-oktober-1998
.UDWNRVWLþQLWRNLYSRPRåQLKHQRVPHUQLKQDSHOMDYDKHOHNWUDUQLQ
WUDQVIRUPDWRUVNLKSRVWDMGHO5DþXQDQMHNUDWNRVWLþQLKWRNRY ,(&


Short-circuit currents in d.c. auxiliary installations in power plants and substations - Part

1: Calculation of short-circuit currents
Kurzschlußströme in Gleichstrom-Eigenbedarfsanlagen in Kraftwerken und
Schaltanlagen - Teil 1: Berechnung der Kurzschlußströme

Courants de court-circuit dans les installations auxiliaires alimentées en courant continu

dans les centrales et les postes - Partie 1: Calcul des courants de court-circuit

Ta slovenski standard je istoveten z: EN 61660-1:1997
ICS:
17.220.01 Elektrika. Magnetizem. Electricity. Magnetism.
Splošni vidiki General aspects
29.240.01 2PUHåMD]DSUHQRVLQ Power transmission and
GLVWULEXFLMRHOHNWULþQHHQHUJLMH distribution networks in
QDVSORãQR general
SIST EN 61660-1:1998 en

2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

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SIST EN 61660-1:1998
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SIST EN 61660-1:1998
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SIST EN 61660-1:1998
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SIST EN 61660-1:1998
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SIST EN 61660-1:1998
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SIST EN 61660-1:1998
NORME
CEI
INTERNATIONALE
IEC
61660-1
INTERNATIONAL
Première édition
STANDARD
First edition
1997-06
Courants de court-circuit dans les installations
auxiliaires alimentées en courant continu
dans les centrales et les postes –
Partie 1:
Calcul des courants de court-circuit
Short-circuit currents in d.c. auxiliary installations
in power plants and substations –
Part 1:
Calculation of short-circuit currents
 IEC 1997 Droits de reproduction réservés  Copyright - all rights reserved

Aucune partie de cette publication ne peut être reproduite ni No part of this publication may be reproduced or utilized in

utilisée sous quelque forme que ce soit et par aucun any form or by any means, electronic or mechanical,

procédé, électronique ou mécanique, y compris la photo- including photocopying and microfilm, without permission in

copie et les microfilms, sans l'accord écrit de l'éditeur. writing from the publisher.

International Electrotechnical Commission 3, rue de Varembé Geneva, Switzerland
Telefax: +41 22 919 0300 e-mail: inmail@iec.ch IEC web site http: //www.iec.ch
CODE PRIX
Commission Electrotechnique Internationale
PRICE CODE
International Electrotechnical Commission
Pour prix, voir catalogue en vigueur
For price, see current catalogue
---------------------- Page: 7 ----------------------
SIST EN 61660-1:1998
61660-1 © IEC:1997 – 3 –
CONTENTS
Page

FOREWORD ................................................................................................................... 5

Clause

1 General.................................................................................................................... 7

1.1 Scope and object ............................................................................................... 7

1.2 Normative references......................................................................................... 7

1.3 Definitions......................................................................................................... 9

1.4 Symbols and subscripts ..................................................................................... 11

2 Calculation of short-circuit currents........................................................................... 15

2.1 General............................................................................................................. 15

2.2 Calculating methods.......................................................................................... 21

2.3 Resistance and inductance of conductor ............................................................ 25

2.4 Rectifier............................................................................................................. 27

2.5 Battery............................................................................................................... 37

2.6 Capacitor........................................................................................................... 41

2.7 DC motor with independent excitation ................................................................ 49

3 Calculation of the total short-circuit current ............................................................... 59

3.1 Correction factor................................................................................................ 59

3.2 Superimposing the partial short-circuit currents at the short-circuit location ........ 61

3.3 Standard approximation function........................................................................ 63

Annex A – Equations for the calculation of λ , κ , κ and t
D D C pC .......................................... 67
---------------------- Page: 8 ----------------------
SIST EN 61660-1:1998
61660-1 © IEC:1997 – 5 –
INTERNATIONAL ELECTROTECHNICAL COMMISSION
____________
SHORT-CIRCUIT CURRENTS IN DC AUXILIARY INSTALLATIONS
IN POWER PLANTS AND SUBSTATIONS –
Part 1: Calculation of short-circuit 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 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 61660-1 has been prepared by IEC technical committee 73: Short-circuit

currents.
The text of this standard is based on the following documents:
FDIS Report on voting
73/84/FDIS 73/97/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 is for information only.

IEC 61660 consists of the following parts, under the general title: Short-circuit currents in d.c.

auxiliary installations in power plants and substations:
– Part 1: 1997, Calculation of short-circuit currents
– Part 2: 1997, Calculation of effects
– Part 3: 199X, Examples of calculations (in preparation).

The contents of the corrigenda of February 1999 and March 2000 have been included in this

copy.
---------------------- Page: 9 ----------------------
SIST EN 61660-1:1998
61660-1 © IEC:1997 – 7 –
SHORT-CIRCUIT CURRENTS IN DC AUXILIARY INSTALLATIONS
IN POWER PLANTS AND SUBSTATIONS –
Part 1: Calculation of short-circuit currents
1 General
1.1 Scope and object

This part of IEC 61660 describes a method for calculating short-circuit currents in d.c. auxiliary

systems in power plants and substations. Such systems can be equipped with the following

equipment, acting as short-circuit current sources:
– rectifiers in three-phase a.c. bridge connection for 50 Hz;
– stationary lead-acid batteries;
– smoothing capacitors;
– d.c. motors with independent excitation.

NOTE – Rectifiers in three-phase a.c. bridge connection for 60 Hz are under consideration. The data of other

equipment may be given by the manufacturer.

This standard is only concerned with rectifiers in three-phase a.c. bridge connection. It is not

concerned with other types of rectifiers.

The purpose of the standard is to provide a generally applicable method of calculation which

produces results of sufficient accuracy on the conservative side. Special methods, adjusted to

particular circumstances, may be used if they give at least the same precision. Short-circuit

currents, resistances and inductances may also be ascertained from system tests or

measurements on model systems. In existing d.c. systems the necessary values can be

ascertained from measurements taken at the assumed short-circuit location. The load current

is not taken into consideration when calculating the short-circuit current. It is necessary to

distinguish between two different values of short-circuit current:

– the maximum short-circuit current which determines the rating of the electrical

equipment;

– the minimum short-circuit current which can be taken as the basis for fuse and protection

ratings and settings.
1.2 Normative references

The following normative documents contain provisions which, through reference in this text,

constitute provisions of this part of IEC 61660. At the time of publication, the edition indicated

was valid. All normative documents are subject to revision, and parties to agreements based

on this part of IEC 61660 are encouraged to investigate the possibility of applying the most

recent editions of the normative documents indicated below. Members of IEC and ISO maintain

registers of currently valid International Standards.
IEC 60038: 1983, IEC standard voltages
---------------------- Page: 10 ----------------------
SIST EN 61660-1:1998
61660-1 © IEC:1997 – 9 –

IEC 60050(151): 1978, International Electrotechnical Vocabulary (IEV) – Chapter 151:

Electrical and magnetic devices

IEC 60050(441): 1984, International Electrotechnical Vocabulary (IEV) – Chapter 441:

Switchgear, controlgear and fuses

IEC 60896-1: 1987, Stationary lead-acid batteries – General requirements and methods of test

– Part 1: Vented types
Amendment 1 (1988)
Amendment 2 (1990)
IEC 60909: 1988, Short-circuit current calculation in three-phase a.c. systems

IEC 61660-2: 1997, Short-circuit currents in d.c. auxiliary installations in power plants and

substations – Part 2: Calculation of effects
1.3 Définitions
For the purpose of this part of IEC 61660, the following definitions apply.

1.3.1 short circuit: The accidental or intentional connection, by a relatively low resistance

or impedance, of two or more points in a circuit which are normally at different voltages.

[IEV 151-03-41]
NOTE – In this standard the connection is assumed to have zero impedance.

1.3.2 short-circuit current: An over-current resulting from a short circuit due to a fault or an

incorrect connection in an electric circuit. [IEV 441-11-07]

NOTE – It is necessary to distinguish between the short-circuit current at the short-circuit location and in the

network branches.

1.3.3 partial short-circuit current: The short-circuit current at the short-circuit location

being fed from one source with all other sources disconnected.

1.3.4 common branch: A network branch with several partial short-circuit currents from

different sources.

1.3.5 initial symmetrical short-circuit current I ′′ : The r.m.s. value of the a.c. symmetrical

component of a prospective short-circuit current applicable at the instant of short circuit if the

impedance remains at zero time value.

1.3.6 peak short-circuit current i : The maximum possible instantaneous value of the

prospective short-circuit current at the d.c. side (figures 1 and 2).

1.3.7 quasi steady-state short-circuit current I : The value of the short-circuit current at

the d.c. side 1 s after the beginning of the short circuit.

1.3.8 time to peak t : The interval between the initiation of the short circuit and the peak

value of the short-circuit current (figures 1 and 2).

1.3.9 short-circuit duration T : The time interval between the initiation of the short circuit

and the breaking of the d.c. short-circuit current.

1.3.10 nominal system voltage U : Voltage (line-to-line) by which a three-phase a.c.

system is designated and to which certain operating characteristics are referred. Values are

given in IEC 60038.
---------------------- Page: 11 ----------------------
SIST EN 61660-1:1998
61660-1 © IEC:1997 – 11 –

1.3.11 nominal voltage U of a lead-acid battery: The nominal voltage of a lead-acid

battery is given by the manufacturer. If the value is unknown, then the nominal voltage of one

cell 2,0 V multiplied by the number of cells in series may be used.

1.3.12 stationary battery: A battery designed for service in a fixed location and which is

permanently connected to the load and to the associated battery charging circuit (see

IEC 60896-1).

1.3.13 final voltage of a battery (end-of-discharge voltage): The minimum permissible

voltage after a specified discharge time.
1.4 Symbols and subscripts

All equations are written without specifying units. The symbols represent quantities possessing

both numerical values and dimensions that are independent of units, provided a coherent unit

system is chosen, for example the International System of Units (SI).
1.4.1 Symbols
A Conductor cross-section
a Centre-line distance between conductors
d Thickness of rectangular conductor
C Capacitance
c Voltage factor according to IEC 60909
cU / 3 Equivalent voltage source according to IEC 60909
E Open-circuit voltage of a battery
f System frequency
b Height of rectangular conductor
I Three-phase initial symmetrical short-circuit current
I Quasi steady-state short-circuit current
I Rated current
i Instantaneous value of current
i ,i Sections of the standard approximation function
1 2
i Short-circuit current in a branch
i Peak short-circuit current
i Corrected current
cor
J Moment of inertia of the whole rotating part

k ,k Factors for calculating the rise-time and decay-time constant of the capacitor

1C 2C
current
k Factor for calculating the time to peak of the motor current
k ,k Factors for calculating the rise-time constant of the motor current
2M 3M
k Factor for calculating the decay-time constant of the motor current
L,L′ Inductance, inductance per unit length
L Equivalent saturated inductance of the field circuit at short circuit
---------------------- Page: 12 ----------------------
SIST EN 61660-1:1998
61660-1 © IEC:1997 – 13 –
L Equivalent unsaturated inductance of the field circuit at no-load
l Length
M Rated torque of the motor
n,n ,n Motor speed, no-load motor speed, nominal motor speed
o n
p Ratio I /i
k p
R,R ′ Resistance, resistance per unit length
R Joint resistance
joint
r Radius of the conductor
T Short-circuit duration
t Time
t Time to peak
U Voltage at the short-circuit location before short circuit
U Nominal system voltage of the three-phase a.c. system, line-to-line (r.m.s.)
U Nominal voltage of a battery
X Reactance
Z Impedance of the three-phase a.c. network
δ Decay coefficient
κ Factor for calculating the peak short-circuit current

λ Factor for calculating the quasi steady-state short-circuit current of the rectifier

μ Absolute permeability of vacuum, μ = 4 π ⋅ 10 H/m
o o
ρ Resistivity
σ Correction factor for the partial short-circuit current
τ Armature time constant of the motor
τ Field circuit time constant of the motor
τ Mechanical time constant of the motor
mec
τ , τ Rise-time, decay-time constants of the standard approximation function
1 2
ω ,ω Undamped, damped natural angular frequency
o d
1.4.2 Subscripts
a.c. Alternating current
B Battery
Br Branch on the d.c. side
C Capacitor
cor Corrected
D Rectifier
d.c. Direct current
F Short-circuit location
F Field circuit of the motor
---------------------- Page: 13 ----------------------
SIST EN 61660-1:1998
61660-1 © IEC:1997 – 15 –
HV, LV High voltage, low voltage
i Internal
j,m Numeral/number of the voltage source
k Short circuit
LLine
M Motor
max, min Maximum, minimum
mec Mechanical
N Three-phase a.c. network
n Nominal
p Peak
P Power cable
Q Feeder connection point according to IEC 60909
R Commutation reactor
r Rated
res Residual
S Smoothing reactor
T Transformer
Y Common branch
O No load/undamped
2 Calculation of short-circuit currents
2.1 General

A complete calculation of the short-circuit currents provides details of the time variation of the

currents at the short-circuit location, from the initiation of the short circuit to its end. Due to

many variations of current and the non-linearity of equipment, such calculations can only be

performed by numerical means. The expense is very high, especially since there are no

universal methods of calculation. For this reason only calculation of characteristic quantities is

dealt with.

Figure 1 shows the typical short-circuit currents of various sources. The total short-circuit

current at the short-circuit location may be produced by the action of several different sources.

Figure 2 shows the standard approximation function which covers the different current

variations. The function is described by equations (1) to (3).
−tτ
1e−
it =i 0 ≤ t ≤ t (1)
1p p
−t τ
1e−
 
−−tt τ
it=−i()1ep +p t ≤ t (2)
2p p
 
---------------------- Page: 14 ----------------------
SIST EN 61660-1:1998
61660-1 © IEC:1997 – 17 –
p = (3)
where
i is the peak short-circuit current;
I is the quasi steady-state short-circuit current;
t is the time to peak;
τ is the rise-time constant;
τ is the decay-time constant.

If there is no defined maximum current present, then i = I and t = T ; equation (1) then

p k p k
describes the whole time variation of the short-circuit current.

By calculation of the characteristic quantities for the time variation of the short-circuit current

according to figure 2, the mechanical and thermal short-circuit stresses can be ascertained. If

only the quasi steady-state short-circuit currents are required, the equations (13), (22), (36)

and (37) should be used.

The assumptions that the impedance is zero between points of different potential at the

short-circuit location and that the load resistances (shunt resistors) can be ignored, are valid

for calculation of both the maximum and minimum short-circuit currents.

When calculating the maximum short-circuit currents the following switching and operating

conditions shall be taken into account so that the maximum short-circuit current is flowing:

– the conductor resistances are referred to a temperature of 20 °C;
– the joint resistances of the busbars are neglected;
– the control for limiting the rectifier current is not effective;
– any diodes for decoupling parts of the system are neglected;
– the battery is charged to full capacity;

– the current-limiting effect of fuses or other protective devices shall be taken into account.

When calculating the minimum short-circuit currents the following switching and operating

conditions shall be taken into account so that the minimum short-circuit current is flowing:

– the conductor resistances are referred to the maximum operating temperature;
– the joint resistances shall be taken into account (see 2.3.1);
– the contribution of the rectifier is the rated short-circuit current;
– the battery is at the final voltage as specified by the manufacturer;
– any diodes for decoupling parts of the system are taken into account;

– the current-limiting effect of fuses or other protective devices shall be taken into account.

---------------------- Page: 15 ----------------------
SIST EN 61660-1:1998
61660-1 © IEC:1997 – 19 –
D i
i i
pD pB
I I
kD kB
t t
t t
IEC 679/97
IEC 680/97
Figure 1a – Rectifier without and with
Figure 1b – Battery
smoothing reactor
i i
C M
t t
IEC 681/97 IEC 682/97
Figure 1c – Capacitor Figure 1d
___
Motor without additional inertia mass
..... Motor with additional inertia mass
Figure 1 – Diagrams of typical short-circuit currents
(t)
(t)
I Quasi steady-state short-circuit
current
i Peak short-circuit current
T Short-circuit duration
t Time to peak
τ Rise-time constant
τ Decay-time constant
t T t
p k
IEC 683/97
Figure 2 – Standard approximation function
---------------------- Page: 16 ----------------------
SIST EN 61660-1:1998
61660-1 © IEC:1997 – 21 –
2.2 Calculating methods

Figure 3 shows the equivalent circuit diagram of a system containing four sources: a rectifier in

three-phase a.c. bridge connection, a battery, a capacitor, and a motor. For the characteristic

quantities of the equivalent circuit diagrams of these sources, see 2.4, 2.5, 2.6 and 2.7.

If the equivalent circuit diagram of the system contains only one source, the short-circuit

current at the short-circuit location is calculated allowing for the series resistances and

inductances only.

If the equivalent circuit diagram contains several sources, the short-circuit current, in case of a

short-circuit location F1, is found by adding the short-circuit currents of the different sources.

If the equivalent circuit diagram contains several sources and a common branch, the short-

circuit current, in case of a short-circuit location F2, is found in the following way:

– calculate the short-circuit currents for the diffferent sources as in the case of short-circuit

location F1 but add R and L of the common branch;
Y Y

– correct the short-circuit currents calculated in this way with the correction factor

according to 3.1;

– insert the calculated values for the different sources to equations (1) to (3);

– add the different time functions to the time function of the total short-circuit current in F2.

If the short-circuit forces have to be calculated according to IEC 61660-2, then it is necessary

to find the standard approximation function of figure 2 according to 3.3.
---------------------- Page: 17 ----------------------
SIST EN 61660-1:1998
61660-1 © IEC:1997 – 23 –
Feeder
Commu- Three-
connection
tation phase
Power Trans- Smoothing
point
reactor bridge
cable reactor
former
Feeder
Line
R L R L
S S DL DL
R , X
R , X Q R , X R , X R R
Q Q P P T T
Z = R + jX
N N N
Rectifier branch
Line
Common
branch
R L R L
B B BL BL
R L
Y Y
Lead-acid battery B
F F
1 2
Line
R R L
C CL CL
Capacitor
Moment of
inertia Line
Field Armature
R L R L R L
F F M M ML ML
Motor E E
IEC 684/97
Short-circuit locations:
F1 Short circuit without common branch
F2 Short circuit with common branch

Figure 3 – Equivalent circuit diagram for calculating the partial short-circuit currents

---------------------- Page: 18 ----------------------
SIST EN 61660-1:1998
61660-1 © IEC:1997 – 25 –
2.3 Resistance and inductance of conductor

The values of resistance and inductance are obtained by multiplying the respective values of

loop resistance and loop inductance per unit length R′ and L′ by the one-way length of

conductor.
2.3.1 Resistance per unit length and joint resistance

The loop resistance per unit length can be calculated from the nominal cross-section A and the

resistivity ρ:
R′ = 2 (4a)
NOTE –The resistance at 20 °C may be calculated with:
1 Ωmm
ρ= for copper
54 m
1 Ωmm
ρ= for aluminium
34 m

The resistance at other temperatures θ can be calculated from the resistance at 20 °C, R ,

using the following equation:
RR=+1 0,004 K θ− 20°C (4b)
[]()

When determining the maximum short-circuit current the joint resistances are neglected. When

determining the minimum short-circuit current the joint resistance of the bolted joints shall be

assessed using equation (5) and figure 4.
14ρ⋅d
R = (5)
joint
IEC 685/97
Figure 4 – Bolted joint
---------------------- Page: 19 ----------------------
SIST EN 61660-1:1998
61660-1 © IEC:1997 – 27 –
2.3.2 Loop inductance per unit length
IEC 686/97
IEC 687/97
Figure 5a – Cable arrangement
Figure 5b – Busbar arrangement
Figure 5 – Loop inductance per unit length

The loop inductance per unit length of single core cables according to figure 5a is given by:

 
o1 a
′  
L=+ ln (6)
 
π4 r
where:
μ = 4 π ⋅ 10 H/m, is the absolute permeability of vacuum;
a is the centre-line distance between conductors;
r is the conductor radius.

The loop inductance per unit length of conductors of rectangular cross-section according to

figure 5b is given by:
 
o 3 a
L=+ln when a > b (7)
 
π 2 ()
d+ b
 

The loop inductance of several parallel cables or bars is found using the method of geometric

mean distance.
2.4 Rectifier
2.4.1 Equivalent circuit diagram and short-circuit parameters
R L R i F
N N DBr DBr D
AC side DC side
IEC 688/97
NOTE – cU / 3 is the equivalent voltage source according to IEC 60909.
Figure 6 – Equivalent circuit diagram of the rectifier
for the calculation of short-circuit currents
---------------------- Page: 20 ----------------------
SIST EN 61660-1:1998
61660-1 © IEC:1997 – 29 –

R and X in figure 6 are abbreviations for the resistances and reactances of the a.c. side of

N N
the rectifier branch in figure 3.
RR=+RR+ +R (8)
NQ P T R
XX=+XX+ +X (9)
NQP T R
were

R , X is the short-circuit resistance and reactance of the a.c. feeder according to

Q Q
IEC 60909 referred to the secondary side of the transformer;

R , X is the short-circuit resistance and reactance of the power supply cable referred

P P
to the secondary side of the transformer;

R , X is the short-circuit resistance and reactance of the transformer referred to the

T T
secondary side, determined according to IEC 60909;

R , X is the short-circuit resistance and reactance of the commutating reactor, if it

R R
exists.

To determine the maximum d.c. short-circuit current, the mimimum impedance Z is calcu-

Qmin

lated using the maximum short-circuit current I′′ of the system at the feeder connection

kQmax
point Q:
Z = (10a)
Qmin
3 I ′′
kQmax

To determine the minimum d.c. short-circuit current, the maximum impedance Z is calcu-

Qmax

lated using the minimum a.c. short-circuit current I ′′ of the system at the feeder connection

Qkmin
point Q:
Z = (10b)
Qmax
3 I
kQmin

R and L in figure 6 are abbreviations for the resistances and inductances of the d.c. side

DBr DBr
of the rectifier and the d.c. system, according to figure 3:
R = R + R + R (11)
DBr S DL Y
L = L + L + L (12)
DBr S DL Y
where
R , L is the resistance and inductance of the d.c. saturated smoothing reactor;
S S
R , L is the resistance and inductance of the conductor in the rectifier branch;
DL DL
R , L is the resistance and inductance of the common branch, if it exists.
Y Y
2.4.2 Partial short-circuit current

The method is used for determining the characteristic quantities of the standard approximation

function according to figure 2. The parameters defined in 2.4.1 are used.
---------------------- Page: 21 ----------------------
SIST EN 61660-1:1998
61660-1 © IEC:1997 – 31 –
2.4.2.1 Quasi steady-state short-circuit current I
The quasi steady-state short-circuit current is:
3 2 cU U
n rTLV
I = λ ⋅ ⋅ (13)
kD D
π U
3 Z
rTHV
The factor λ depends on R /X and R /R and can be taken from figure 7.
D N N DBr N
2.4.2.2 Peak short-circuit current i
The peak short-circuit current is:
i = κ I (14)
pD D kD
The factor κ , dependent on:
 
R 2 R L
N DBr DBr
 
1+ and
 
X 3 R L
 
N N N
is taken from figure 8.
2.4.2.3 Time to peak t
When κ ≥ 1,05, the time to peak is:
DBr
t = (3 κ + 6) ms when ≤ 1 (15)
pD D
 
 
L L
DBr DBr
 
 
t=+36κ +4 −1 ms when > 1 (16)
pD D
 
 L  L
 
 N  N

NOTE – If κ < 1,05, the maximum current, compared with the quasi steady-state short-circuit current is

neglected and t = T is used.
pD k
2.4.2.4 Rise-time constant τ
When f = 50 Hz, the rise-time constant is:
 
 
DBr
 
 
τκ=+2 − 0,9 2,5+ 9 ms when κ ≥ 1,05 (17)
1D D D
 
 L 
 
 N 
 
 
   
R L L
N DBr DBr
 
 
   
τ =+0,7 7− 1+ 0,1+ 0,2 ms when κ < 1,05 (18)
1D D
   
 
 X 3L  L
   
 N N N
 
For simplification τ = t may be used on the conservative side.
1D pD
---------------------- Page: 22 ----------------------
SIST EN 61660-1:1998
61660-1 © IEC:1997 – 33 –
2.4.2.5 Decay-time constant τ
When f = 50 Hz, the decay-time constant is:
2ms
τ = (19)
R R
N DBr
 
0,6 + 0,9
 
X R
 
N N
DBr
1,0
0,01
0,1
0,2
0,4
0,5
0,8
0,6
0,8
1,0
0,6
1,5
2,0
2,5
3,0
0,4
3,5
4,0
5,0
0,2
0,0
0 0,2 0,4 0,6 0,8 1,0 1,2
IEC 689/97
Figure 7 – Factor λ for determining the quasi steady-state short-circuit current
I (equation in annex A)
---------------------- Page: 23 ----------------------
SIST EN 61660-1:1998
61660-1 © IEC:1997 – 35 –
2,0
LDBr
1,8
0,1
0,2
0,3
1,6
0,5
0,7
1,0
1,4
1,5
2,0
3,0
...

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