# IEC TR 60909-4:2021

(Main)## Short-circuit currents in three-phase AC systems - Part 4: Examples for the calculation of short-circuit currents

## Short-circuit currents in three-phase AC systems - Part 4: Examples for the calculation of short-circuit currents

IEC TR 60909-4:2021 which is a Technical Report, is intended to give help for the application of IEC 60909-0 for the calculation of short-circuit currents in 50 Hz or 60 Hz three-phase AC systems.

This document does not include additional requirements but gives support for the modelling of electrical equipment in the positive-sequence, the negative-sequence and the zero-sequence system (Clause 4), the practical execution of calculations in a low-voltage system (Clause 5), a medium-voltage system with asynchronous motors (Clause 6) and a power station unit with its auxiliary network feeding a large number of medium-voltage asynchronous motors and low-voltage motor groups (Clause 7).

The three examples given in Clauses 5, 6 and 7 are similar to those given in IEC TR 60909-4:2000 but they are revised in accordance with IEC 60909-0, which replaces it. The example given in Clause 8 is new and mirrors the introduction of the new 6.8 of IEC 60909-0:2016.

Clause 9 gives the circuit diagram and the data of a test network and the results for a calculation carried out in accordance with IEC 60909-0, to offer the possibility for a comparison between the results found with a digital program for the calculation of short-circuit currents and the given results for and in a high-voltage network with power station units, generators, asynchronous motors and lines in four different voltage levels 380 kV, 110 kV, 30 kV and 10 kV.

This second edition cancels and replaces the first edition published in 2000. This edition constitutes a technical revision.

This edition includes the following significant technical changes with respect to the previous edition:

a) adaption to IEC 60909-0:2016;

b) addition of an example for the calculation of short-circuit currents of wind power station units;

c) correction of errors.

### General Information

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### Standards Content (Sample)

IEC TR 60909-4

®

Edition 2.0 2021-06

TECHNICAL

REPORT

colour

inside

Short-circuit currents in three-phase AC systems –

Part 4: Examples for the calculation of short-circuit currents

IEC TR 60909-4:2021-06(en)

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

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

IEC TR 60909-4

®

Edition 2.0 2021-06

TECHNICAL

REPORT

colour

inside

Short-circuit currents in three-phase AC systems –

Part 4: Examples for the calculation of short-circuit currents

INTERNATIONAL

ELECTROTECHNICAL

COMMISSION

ICS 17.220.01; 29.240.20 ISBN 978-2-8322-9932-6

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

® Registered trademark of the International Electrotechnical Commission

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

– 2 – IEC TR 60909-4:2021 © IEC 2021

CONTENTS

FOREWORD . 6

1 Scope . 8

2 Normative references . 8

3 Terms and definitions, symbols and indices, and formulae . 8

4 Positive-sequence, negative-sequence and zero-sequence impedances of

electrical equipment . 9

4.1 General . 9

4.2 Overhead lines, cables and short-circuit current-limiting reactors . 9

4.3 Transformers . 10

4.3.1 General . 10

4.3.2 Example . 15

4.4 Generators and power station units . 17

4.4.1 General . 17

4.4.2 Example . 20

5 Calculation of short-circuit currents in a low-voltage system U = 400 V . 22

n

5.1 Problem . 22

5.2 Determination of the positive-sequence impedances . 22

5.2.1 Network feeder . 22

5.2.2 Transformers . 23

5.2.3 Lines (cables and overhead lines) . 24

5.3 Determination of the zero-sequence impedances . 24

5.3.1 Transformers . 24

5.3.2 Lines (cables and overhead lines) . 25

"

5.4 Calculation of I and i for three-phase short circuits . 25

k p

5.4.1 Short-circuit location F1 . 25

5.4.2 Short-circuit location F2 . 27

5.4.3 Short-circuit location F3 . 28

"

5.5 Calculation of I and i for line-to-earth short circuits . 28

k1 p1

5.5.1 Short-circuit location F1 . 28

5.5.2 Short-circuit location F2 . 29

5.5.3 Short-circuit location F3 . 29

5.6 Collection of results . 30

6 Calculation of three-phase short-circuit currents in a medium-voltage system –

Influence of asynchronous motors . 31

6.1 Problem . 31

6.2 Complex calculation with absolute quantities . 31

6.3 Calculation with per-unit quantities . 35

6.4 Calculation with the superposition method . 37

7 Calculation of three-phase short-circuit currents for a power station unit and the

auxiliary network. 40

7.1 Problem . 40

7.2 Short-circuit impedances of electrical equipment. 43

7.2.1 Network feeder . 43

7.2.2 Power station unit . 43

7.2.3 Auxiliary transformers . 44

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

IEC TR 60909-4:2021 © IEC 2021 – 3 –

7.2.4 Low-voltage transformers 2,5 MVA and 1,6 MVA . 45

7.2.5 Asynchronous motors . 49

7.3 Calculation of short-circuit currents . 49

7.3.1 Short-circuit location F1 . 49

7.3.2 Short-circuit location F2 . 50

7.3.3 Short-circuit location F3 . 51

7.3.4 Short-circuit location F4 . 55

7.3.5 Short-circuit location F5 . 57

8 Calculation of three-phase short-circuit currents in a wind power plant . 59

8.1 General . 59

8.2 Problem . 59

8.3 Data and short-circuit impedances of electrical equipment . 60

8.4 Nodal admittance and nodal impedance matrices . 62

8.5 Short-circuit currents for the wind power plant with ten wind power station

units WD . 63

8.6 Short-circuit currents for the wind power plant with ten wind power station

units WF . 65

8.7 Short-circuit currents for the wind power plant with five wind power station

units WD and five wind power station units WF . 68

9 Test network for the calculation of short-circuit currents with digital programs in

accordance with IEC 60909-0 . 72

9.1 General . 72

9.2 High-voltage test network 380 kV/110 kV/30 kV/10 kV . 73

9.2.1 Network topology and data . 73

9.2.2 Short-circuit impedances of electrical equipment . 76

9.3 Results . 77

9.3.1 General . 77

9.3.2 Three-phase short-circuit currents . 78

9.3.3 Line-to-earth short-circuit currents . 78

Bibliography . 80

Figure 1 – Positive-sequence and zero-sequence impedances of an overhead line

(one circuit) and cable (cross-bonded) . 9

Figure 2 – Positive-sequence and zero-sequence impedance of a short-circuit current-

limiting reactor . 10

Figure 3 – Positive-sequence and zero-sequence system impedances of a two-

winding transformer YNd5 . 11

Figure 4 – Equivalent circuits of a three-winding network transformer . 15

Figure 5 – Short circuit at the high-voltage side of a power station unit with on-load

tap changer . 19

Figure 6 – Low-voltage system Un = 400 V with short-circuit locations F1, F2, F3 . 22

"

Figure 7 – Positive-sequence system (according to Figure 6) for the calculation of I

k

at the short-circuit location F1 . 26

Figure 8 – Positive-sequence, negative-sequence and zero-sequence system with

"

connections at the short-circuit location F1 for the calculation of I . 29

k1

Figure 9 – Medium-voltage network 33 kV/6 kV: data . 32

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– 4 – IEC TR 60909-4:2021 © IEC 2021

"

Figure 10 – Short-circuit current I calculated by the superposition method (S)

k(T1,T2)S

"

compared with I calculated by the IEC method of equivalent voltage source

k(T1,T2)IEC

b b

at the short-circuit location, depending on the load S and the voltage U . 39

"

Figure 11 – Short-circuit current I calculated by the superposition method (S)

kS

"

compared with I calculated by the IEC method of equivalent voltage source at the

kIEC

short-circuit location, depending on the transformation ratio t before the short circuit . 40

Figure 12 – Power station unit (generator and unit transformer with on-load tap-

changer) and auxiliary network with medium- and low-voltage asynchronous

motors: data . 42

Figure 13 – Positive-sequence system for the calculation of the short-circuit currents

at the location F3 (see Figure 12) . 52

Figure 14 – Positive-sequence system for the calculation of the short-circuit currents

at the location F4 (see Figure 12) . 55

Figure 15 – Positive-sequence system for the calculation of the short-circuit currents

at the location F5 (see Figure 12) . 57

Figure 16 – Windfarm with ten wind power station units . 60

Figure 17 – Equivalent circuit diagram for the calculation of the short-circuit current at

the location F1 without the consideration of the internal wind power plant cables

(values are related to the 20 kV voltage level), variant 1 . 64

Figure 18 – Equivalent circuit diagram for the calculation of the short-circuit current at

the location F1 without the consideration of the internal wind power plant cables

(values are related to the 20 kV voltage level), variant 2 . 67

Figure 19 – Equivalent circuit diagram for the calculation of the short-circuit current at

the location F1 without the consideration of the internal wind power plant cables

(values are related to the 20 kV voltage level), variant 3 . 70

Figure 20 – High-voltage AC test network 380 kV/110 kV/30 kV/10 kV . 74

Table 1 – Examples for equivalent circuit-diagrams of transformers in the positive-

sequence and the zero-sequence system . 12

Table 2 – Approximations for the ratios X /X of two- and three-winding

(0)T T

transformers . 15

Table 3 – Data of electrical equipment for the example in Figure 6 – Positive-

sequence and zero-sequence impedances (Z = Z ) . 23

(2) (1)

Table 4 – Short-circuit impedances and short-circuit currents . 30

Table 5 – Joule integral depending on T at the short-circuit location F2 and F3 . 30

k

Table 6 – Calculation of the short-circuit impedances of electrical equipment and

Z at the short-circuit location F, without motors (circuit-breakers CB1 and CB2

k T1,T2

( )

are open) . 33

Table 7 – Calculation of the per-unit short-circuit reactances of electrical equipment

and *X at the short-circuit location F . 36

k(T1,T2)

Table 8 – Data of transformers 10 kV/0,73 kV and 10 kV/0,42 kV, data of low-voltage

motor groups and partial short-circuit currents of these motor groups on busbars B

and C respectively . 47

Table 9 – Data of medium-voltage asynchronous motors and their partial short-circuit

currents at short-circuit locations on busbars B and C respectively . 48

Table 10 – Data and impedances of the electrical equipment (see Figure 16) referred

to the 20 kV side . 61

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IEC TR 60909-4:2021 © IEC 2021 – 5 –

Table 11 – The diagonal elements of the nodal admittance matrices for the three

variants in 1/Ω . 62

Table 12 – Short-circuit impedances and short-circuit currents at F1 to F14 for wind

power stations units with doubly fed asynchronous generators WD . 63

Table 13 – Short-circuit impedances and short-circuit currents at F1 to F3 for wind

power stations units with doubly fed asynchronous generators WD neglecting the

internal wind power plant cables . 64

Table 14 – Quotients Z /Z for i = 1 to 14 and j = 3…6, 8…10, 12…14 and the sum

ij kFi

of the columns . 66

Table 15 – Short-circuit impedances and short-circuit currents at F1 to F14 for wind

power stations units with full size converters WF . 66

Table 16 – Short-circuit impedances and short-circuit currents at F1 to F3 for wind

power stations units with full size converters WF neglecting the internal wind power

plant cables . 68

Table 17 – Quotients Z /Z for i = 1 to 14 and j = 3, 10, 12, 13, 14 and the sum of the

ij kFi

columns . 69

Table 18 –Short-circuit impedances and short-circuit currents at F1 to F14 for five

wind power stations units with doubly fed asynchronous generators WD and five wind

power station units with full size converters WF . 69

Table 19 – Short-circuit impedances and short-circuit currents at F1 to F3 for five wind

power stations units with doubly fed asynchronous generators WD and five wind power

station units with full size converters WF neglecting the internal wind power plant

cables . 71

Table 20 – Overhead lines and cables . 76

Table 21 – Impedances (corrected if necessary) of the electrical equipment (see

Figure 20) referred to the 110 kV side with Z = Z . 77

(2) (1)

"

Table 22 – Results I , i , I and I . 78

k p b k

"

I

Table 23 – Results and i . 79

k p1

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– 6 – IEC TR 60909-4:2021 © IEC 2021

INTERNATIONAL ELECTROTECHNICAL COMMISSION

____________

SHORT-CIRCUIT CURRENTS IN THREE-PHASE AC SYSTEMS –

Part 4: Examples for the calculation of short-circuit currents

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.

IEC TR 60909-4 has been prepared by IEC technical committee 73: Short-circuit currents. It is

a Technical Report.

This second edition cancels and replaces the first edition published in 2000. This edition

constitutes a technical revision.

This edition includes the following significant technical changes with respect to the previous

edition:

a) adaption to IEC 60909-0:2016;

b) addition of an example for the calculation of short-circuit currents of wind power station

units;

c) correction of errors.

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

IEC TR 60909-4:2021 © IEC 2021 – 7 –

The text of this Technical Report is based on the following documents:

Draft Report on voting

73/187/DTR 73/193/RVDTR

Full information on the voting for its approval can be found in the report on voting indicated in

the above table.

The language used for the development of this Technical Report is English.

This document was drafted in accordance with ISO/IEC Directives, Part 2, and developed in

accordance with ISO/IEC Directives, Part 1 and ISO/IEC Directives, IEC Supplement, available

at www.iec.ch/members_experts/refdocs. The main document types developed by IEC are

described in greater detail at www.iec.ch/standardsdev/publications.

A list of all parts in the IEC 60909 series, published under the general title Short-circuit currents

in three-phase AC systems, can be found on the IEC website.

The committee has decided that the contents of this document will remain unchanged until the

stability date indicated on the IEC website under webstore.iec.ch in the data related to the

specific document. At this date, the document will be

• reconfirmed,

• withdrawn,

• replaced by a revised edition, or

• amended.

IMPORTANT – The 'colour inside' logo on the cover page of this publication indicates that it

contains colours which are considered to be useful for the correct understanding of its

contents. Users should therefore print this document using a colour printer.

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– 8 – IEC TR 60909-4:2021 © IEC 2021

SHORT-CIRCUIT CURRENTS IN THREE-PHASE AC SYSTEMS –

Part 4: Examples for the calculation of short-circuit currents

1 Scope

This part of IEC 60909, which is a Technical Report, is intended to give help for the application

of IEC 60909-0 for the calculation of short-circuit currents in 50 Hz or 60 Hz three-phase AC

systems.

This document does not include additional requirements but gives support for the modelling of

electrical equipment in the positive-sequence, the negative-sequence and the zero-sequence

system (Clause 4), the practical execution of calculations in a low-voltage system (Clause 5),

a medium-voltage system with asynchronous motors (Clause 6) and a power station unit with

its auxiliary network feeding a large number of medium-voltage asynchronous motors and low-

voltage motor groups (Clause 7).

The three examples given in Clauses 5, 6 and 7 are similar to those given in IEC TR 60909-

4:2000 but they are revised in accordance with IEC 60909-0, which replaces it. The example

given in Clause 8 is new and mirrors the introduction of the new 6.8 of IEC 60909-0:2016.

Clause 9 gives the circuit diagram and the data of a test network and the results for a calculation

carried out in accordance with IEC 60909-0, to offer the possibility for a comparison between

the results found with a digital program for the calculation of short-circuit currents and the given

""

results for and i in a high-voltage network with power station units,

I ,,iI , I , I

k p k k1 p1

b

generators, asynchronous motors and lines in four different voltage levels 380 kV, 110 kV,

30 kV and 10 kV.

2 Normative references

IEC 60038:2009, IEC standard voltages

IEC 60909-0:2016, Short-circuit currents in three-phase a.c. systems – Part 0: Calculation of

currents

3 Terms and definitions, symbols and indices, and formulae

For the purposes of this document, the terms and definitions, symbols and indices, and formulae

given in IEC 60909-0 apply.

ISO and IEC maintain terminological databases for use in standardization at the following

addresses:

• IEC Electropedia: available at http://www.electropedia.org/

• ISO Online browsing platform: available at http://www.iso.org/obp

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

IEC TR 60909-4:2021 © IEC 2021 – 9 –

4 Positive-sequence, negative-sequence and zero-sequence impedances of

electrical equipment

4.1 General

In addition to Clause 6 of IEC 60909-0:2016, modelling and calculation of the positive-sequence

and the zero-sequence impedances of electrical equipment is given. In most cases, the

negative-sequence impedances are equal to the positive-sequence impedances when

calculating the initial symmetrical short-circuit currents, but see 6.6.1 of IEC 60909-

**...**

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