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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
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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
– 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
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
– 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
...