IEC TR 60909-2:2008

IEC/TR 60909-2
Edition 2.0 2008-11
TECHNICAL
REPORT
Short-circuit currents in three-phase a.c. systems –
Part 2: Data of electrical equipment for short-circuit current calculations

IEC/TR 60909-2:2008(E)
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IEC/TR 60909-2
Edition 2.0 2008-11
TECHNICAL
REPORT
Short-circuit currents in three-phase a.c. systems –
Part 2: Data of electrical equipment for short-circuit current calculations

INTERNATIONAL
ELECTROTECHNICAL
COMMISSION
PRICE CODE
X
ICS 17.220.01; 29.240.20 ISBN 978-2-88910-327-0
– 2 – TR 60909-2 © IEC:2008(E)
CONTENTS
FOREWORD.4
1 General .6
1.1 Scope and object.6
1.2 Normative references .6
2 Data for electrical equipment .6
2.1 General .6
2.2 Data of typical synchronous machines.7
2.3 Data of typical two-winding, three-winding and auto-transformers.10
2.4 Data of typical overhead lines, single and double circuits .14
2.5 Data of typical high-voltage, medium-voltage and low-voltage cables .20
2.6 Data of typical asynchronous motors .35
2.7 Busbars.38
Annex A (informative) Information from National Committees.42
Bibliography.43

Figure 1 – Subtransient reactance of synchronous machines 50 Hz and 60 Hz
(Turbogenerators, salient pole generators, motors SM and condensers SC) .8
Figure 2 – Rated Voltage U and rated power factor cosϕ of synchronous machines
rG rG
(Turbo generators, salient pole generators, motors and condensers 50 Hz and 60 Hz) .9
Figure 3 – Unsaturated and saturated synchronous reactance of two-pole turbo
generators 50 Hz and 60 Hz (relative values).9
Figure 4 – Three-winding transformer (No. 6 of Table 3). .12
Figure 5 – Rated short-circuit voltage u of unit transformers in power stations (ST)
kr
with or without on-load tap-changer .13
Figure 6 – Rated short-circuit voltages u of network transformers .14
kr
' '
Figure 7 – Positive-sequence reactance X = X of low-voltage and medium-voltage
(1) L
overhead lines 50 Hz, Cu or Al, with one circuit according to Equation (15) of
IEC 60909-0 .16
' '
Figure 8 – Positive-sequence reactance X = X of overhead lines 50 Hz (60 Hz-
(1) L
values converted to 50 Hz) .19
Figure 9 – Type of overhead lines.20
Figure 10 – Single-core cable 64 kV / 110 kV with lead sheath [4] .23
Figure 11 – Reduction factor depending on the inducing current for cables with one
lead sheath and two overlapping steel tapes, f = 50 Hz [3].35
Figure 12 – Reduction factor depending on the inducing current for cables with three
lead sheaths and two overlapping steel tapes, f = 50 Hz [3] .35
Figure 13 – Ratio I /I of low-voltage and medium-voltage asynchronous motors,
LR rM
50 Hz and 60 Hz .37
Figure 14 – Product cosϕ xη of low-voltage and medium-voltage motors, 50 Hz
rM rM
and 60 Hz .38
Figure 15 – Geometric mean distance g = g = g of the main conductors .39
L1L1 L2L2 L3L3
'
Figure 16 – Factor α and β for the calculation of X given in Equation (34) .40
(1)
TR 60909-2 © IEC:2008(E) – 3 –
Table 1 – Actual data of typical synchronous generators, motors and condensers .7
Table 2 – Actual data of typical two-winding transformers (NT: network; ST: power
station) .10
Table 3 – Actual data of typical three-winding transformers .11
Table 4 – Actual data of typical autotransformers with and without tertiary winding .12
Table 5 – Actual data of typical overhead lines 50 Hz and 60 Hz .18
Table 6 – Actual data of typical electric cables.21
Table 7 – Equations for the positive-sequence and the zero-sequence impedance of
cables.22
Table 8 – Single-core cables 64/110 kV, 2XK2Y, 3 × 1 × 240 . 1 200 rm, Cu with lead
sheath .24
Table 9 – 10-kV-cables N2XS2Y .25
Table 10 – 20-kV-cables N2XS2Y .26
Table 11 – Positive-sequence and zero-sequence impedance of four low-voltage
single-core cables NYY 4 × 1 × q . (Case No. 2a in Table 7) .27
n
Table 12 – Low-voltage cable NYY .29
Table 13 – Low-voltage cable NYY with three and a half copper conductors .30
Table 14 – Low-voltage cable NYCWY with four copper conductors .32
Table 15 – Low-voltage cable NYCWY.33
Table 16 – Actual data of typical asynchronous motors .36
Table 17 – Actual data of distribution busbars.38
'
Table 18 – Example for the calculation of X for busbars using Figures 15 and 16 .41
(1)
Table A.1 – Information received from National Committees .42

– 4 – TR 60909-2 © IEC:2008(E)
INTERNATIONAL ELECTROTECHNICAL COMMISSION
_____________
SHORT-CIRCUIT CURRENTS IN THREE-PHASE AC SYSTEMS –

Part 2: Data of electrical equipment
for short-circuit current calculations

FOREWORD
1) The International Electrotechnical Commission (IEC) is a worldwide organization for standardization comprising
all national electrotechnical committees (IEC National Committees). The object of IEC is to promote
international co-operation on all questions concerning standardization in the electrical and electronic fields. To
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5) IEC provides no marking procedure to indicate its approval and cannot be rendered responsible for any
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6) All users should ensure that they have the latest edition of this publication.
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Publications.
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.
The main task of IEC technical committees is to prepare International Standards. However, a
technical committee may propose the publication of a technical report when it has collected
data of a different kind from that which is normally published as an International Standard, for
example "state of the art".
IEC 60909-2, which is a technical report, has been prepared by IEC technical committee 73:
Short-circuit currents.
This technical report is to be read in conjunction with IEC 60909-0 and IEC 60909-3.
This second edition cancels and replaces the first edition published in 1992. This edition
constitutes a technical revision.
The significant technical changes with respect to the previous edition are as follows:

TR 60909-2 © IEC:2008(E) – 5 –
– Subclause 2.5 gives equations and examples for the calculation of the positive-, the
negative and the zero-sequence impedances and reduction factors for high-, medium
and low-voltage cables with sheaths and shields earthed at both ends.
– Subclause 2.7 gives equations and figures for the calculation of the positive-sequence
impedances of busbar configurations.
The text of this technical report is based on the following documents:
Enquiry draft Report on voting
73/142/DTR 73/145/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 60909, published under the general title Short-circuit currents in
three-phase a.c. systems, can be found on the IEC website.
The committee has decided that the contents of this publication will remain unchanged until
the maintenance result 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.
A bilingual version of this publication may be issued at a later date.

– 6 – TR 60909-2 © IEC:2008(E)
SHORT-CIRCUIT CURRENTS IN THREE-PHASE AC SYSTEMS –

Part 2: Data of electrical equipment
for short-circuit current calculations

1 General
1.1 Scope and object
This part of IEC 60909 comprises data of electrical equipment collected from different
countries to be used when necessary for the calculation of short-circuit currents in
accordance with IEC 60909-0.
Generally, electrical equipment data are given by the manufacturers on the name plate or by
the electricity supplier.
In some cases, however, the data may not be available. The data in this report may be
applied for calculating short-circuit currents in low-voltage networks if they are in accordance
with typical equipment employed in the user’s country. The collected data and their evaluation
may be used for medium- or high-voltage planning purposes and also for comparison with
data given by manufacturers or electricity suppliers. For overhead lines and cables the
electrical data may in some cases also be calculated from the physical dimensions and the
material following the equations given in this report.
Thus this technical report is an addition to IEC 60909-0. It does not, however, change the
basis for the standardized calculation procedure given in IEC 60909-0 and IEC 60909-3.
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 60909-0:2001, Short-circuit currents in three-phase a.c. systems – Part 0: Calculation of
currents
IEC 60909-3:- , Short-circuit currents in three-phase a.c. systems – Part 3: Currents du-ring
two separate simultaneous line-to-earth short-circuit currents and partial short-circuit currents
flowing through earth
2 Data for electrical equipment
2.1 General
The data presented are necessary for the calculation of short-circuit currents. They are
sometimes presented in the form of curve sheets and sometimes in the form of examples in
tables. In the case of easy equations they are given for the calculations of positive-sequence
and zero-sequence short-circuit impedances for overhead lines and cables.
—————————
To be published.
TR 60909-2 © IEC:2008(E) – 7 –
In all, 15 National Committees provided information in response to a questionnaire sent out
before the first edition of this report. Table 1 of the first edition of this report is given in Annex
A.
In some cases, average values or characteristic trends as function of rated power, rated
voltage, etc. are given.
2.2 Data of typical synchronous machines
Characteristic data of synchronous machines are listed in Table 1. The reactances are given
as relative values related to Z = U / S (see IEC 60909-0). Sometimes they are given in
rG rG
rG
%.
In Figure 1 the sub-transient reactances of synchronous machines (generators, motors and
condensers) in the direct axis of 50 Hz or 60 Hz machines are plotted as a function of the
rated power.
Table 1 – Actual data of typical synchronous generators, motors and condensers
No Type Rated Rated voltage Power Relative values of reactances Note National
a)
appar. and factor and d.c time constant Commit-
b)
power deviation tee
cosϕ "
S U T
± p x x x x
rG rG rG DC
G x (2) (0) d dsat
d
g)
e) f)
c) d)
- MVA kV % - - - - - - s
1 TG2 64 13,8 ± 5 0,85 0,179 0,170 0,104 1,87 1,87 0,220 60 Hz USA

2 TG2 100 10,5 ± 5 0,80 0,134 - - 1,77 1,45 0,246 50 Hz Germany

3 TG2 125 10,5 ± 5 0,80 0,160 0,180 0,08 2,13 1,87 0,460 50 Hz ex-GDR

4 TG2 180 10,5 ± 5 0,90 0,250 0,230 0,14 1,83 1,77 0,480 50 Hz Austria
5 TG2 353 18,0 ± 5 0,85 0,167 0,204 0,089 2,26 2,17 0,194 50 Hz China
6 TG2 388,9 17,5 ± 5 0,90 0,203 0,202 0,099 2,42 2,19 0,250 50 Hz Australia

7 SG14 48 10 ± 5 0,90 0,16 0,17 0,05 0,78 - 0,16 50 Hz Italy

8 SG20 290 18,0 ± 5 0,90 0,22 0,22 0,14 1,03 0,96 0,36 60 Hz Japan
9 SM2 1,45 10 +5 0,90 0,166 0,166 0,046 1,63 - 0,04 50 Hz ex-USSR
–10
10 SM3 3,40 4,0 ± 5 0,80 0,249 0,303 - 2,675 2,675 0,116 60 Hz USA

11 SC10 40 13,8 ± 5 0 0,119 0,129 - 1,33 1,33 0,1425 60 Hz USA

12 SC6 100 10,5 ± 5 0 0,20 0,25 0,095 1,78 1,60 0,57 50 Hz ex-
Czechos-
lovakia
a) TG2: Two-pole turbo generator c) Negative-sequence reactance
SG: Salient pole generator d) Zero-sequence reactance
SM: Synchronous motor e) Unsaturated synchronous reactance
SC: Salient pole synchronous condenser f) Saturated synchronous reactance
g) DC time constant for a three-phase terminal short circuit
⎛ p ⎞
G
b) U = U ⎜1± ⎟
G rG
⎜ ⎟
100%
⎝ ⎠
– 8 – TR 60909-2 © IEC:2008(E)
Australia Czechoslovakia
ex-Czechoslovakia
Italy
Japan
Austria ex-GDR
Bulgaria
Germany
Norway
USA
China Hungary
%
MVA
x ''d = 0 ,3
SM
x '' = 0,2
d
x ''d = 0,1
x'' 100
d SM
S
rG
SM
x'' = 0,08
d
SM
SM
SM
SM
SM
0,8
0,6
0,4
SC
0,2
0,1
0,08
0,06
0,04
0,02
0,01
0,1 0,2 0,4 0,6 1 2 4 6 10 20 40 60 100 200 MVA 600 1 000 2 000
S
rG
IEC  2028/08
Figure 1 – Subtransient reactance of synchronous machines 50 Hz and 60 Hz
(Turbogenerators, salient pole generators, motors SM and condensers SC)
In Figure 2 the rated voltages and power factors of 50 Hz or 60 Hz synchronous machines
(generators, motors) are plotted as a function of the rated power.
In Figure 3 unsaturated and saturated (x /x ) synchronous reactances for 50 Hz and 60 Hz
dsat d
turbogenerators, used for the calculation of the steady state short-circuit current, are plotted
as a function of the rated power.
Data are also given for the zero-sequence reactance. It is recommended that the relationship
"
X / X = 0,5 is used.
(0) d
TR 60909-2 © IEC:2008(E) – 9 –
kV
U
rG
20 1,0
18 cos ϕ
rG
0,8
0,6
U
rG
0,4
0,2
USA
0,48 kV
0 0
< 1 MVA ≥ 1 MVA > 5 MVA > 10 MVA > 50 MVA > 100 MVA > 500 MVA > 1 000 MVA
≤ 5 MVA ≤ 10 MVA ≤ 50 MVA ≤ 100 MVA ≤ 500 MVA ≤ 1 000 MVA
S
rG
IEC  2029/08
Figure 2 – Rated Voltage U and rated power factor cosϕ of synchronous machines
rG rG
(Turbo generators, salient pole generators, motors and condensers 50 Hz and 60 Hz)
Australia eCxz-ecCzehochsloovsloakviaakia Hungary USA
Austria Denmark Italy
Bulgaria ex-GDR Japan
China Germany Norway
3,0
p.u.
2,8
x
d
2,6
≈ x
d
2,4
2,2
2,0
1,8
1,6
1,4
1,2
These values are excluded from the medium value x /x
dsat d
1,0
x /x
dsat d
0,8
x
dsat
0,6
x
dC
0,4
These values from Norway are excluded from x /x
dsat d
0,2
0 200 400 600 800 1 000 1 200 MVA 1 400
S
rG
IEC  2030/08
Figure 3 – Unsaturated and saturated synchronous reactance of two-pole
turbo generators 50 Hz and 60 Hz (relative values)
cos ϕ
rG
– 10 – TR 60909-2 © IEC:2008(E)
2.3 Data of typical two-winding, three-winding and auto-transformers
In Tables 2, 3 and 4 characteristic data of two-winding, three-winding and auto-trans-formers
are listed.
Table 2 – Actual data of typical two-winding transformers
(NT: network; ST: power station)
No Rated Rated Rated Winding Side of Tap-changer Notes National
X
(0)
appar. voltage short-circuit connec- Earth- Commit-
power voltage tion ing X tee
(1)
symbol
HV   LV
S U
U ± p
u u u u
rT rTLV T
rTHV
kr Rr k + k −
MVA kV kV % % – – % % %
1 0,63 20 0,4 6,0 1,2 Dyn5 LV off-load NT, 50 Hz, ex-GDR
≈ 1 ±5
3 limb
2 24 33 11 24,2 1,12 YNyn0 HV, LV 0,7 24,1 25,3 NT, 50 Hz, UK
±10
3 limb
3 31,5 112 22,2 12,8 0,37 YNd5 HV 13,9 10,5 NT, 50 Hz Germany
±18
≈ 1
4 80 121 6,3 10,5 – YNd5 HV 0,71 – –- NT, 50 Hz, Bulgaria
2× 2,5
3 limb
a)
5 500 400 132 26,1 0,30 YNynd5 HV, LV ≈ 1,6 ±13  NT, 50 Hz Denmark
6 20 138 13,2 10,58 0,49 Dyn1 LV 0,93 +2,5  ST, 60 Hz, USA
– 7,5 3 limb
7 25 132 6,3 10,5 YNd11 HV 1,0  ST, 59 Hz, Hungary
3 limb
8 180 110 10,5 12,0 0,221 Yd11 0,78 ±12  ST, 50 Hz Austria
9 390 350 23,0 15,92 0,554 YNd1 HV 1,0 +10 16,7 15,5 ST, 50 Hz, Australia
– 15 3 limb
10 780 230 21,0 15,3 0,2 YNd5 HV 16,7 14,3 ST, 50 Hz Germany
≈ 0,8 ±15
a)
Two-winding transformer with an auxiliary winding in delta-connection (see Table 3).

TR 60909-2 © IEC:2008(E) – 11 –
Table 3 – Actual data of typical three-winding transformers
No Rated apparent Rated Rated short-circuit Winding Zero-sequence Note National
powers voltages voltages connection reactances related Commit-
symbol to side A tee
U U
S S S U
u u u X X X
rTAB rTAC rTBC rTA rTB rTC
(0)A (0)B (0)C
krAB krAC krBC
HV MV LV
MVA MVA MVA kV kV kV % % %
Ω Ω Ω
1 7,5 7,5 7,5 34,5 13,8 13,8 3,65 3,58 7,96 YN d1 d1 – – – 60 Hz USA
3 limb
2 25 16 16 120 22 11 11,0 14,5 3,5 YN yn0 d11 99,0 – 3,15 50 Hz Hungary
3 limb
3 31,5 31,5 31,5 110 38,5 6,3 10,5 17,5 6,5 YN yn0 d11 6,13 17,23 18,24 “ China
4 94 94 94 239 130 13,8 11,7911,3112,44YN yn0 d1132,3939,23 36,31 “ Italy
5 125 42 42 230 63 20 11,7 10,6 5,9 YN yn0 d11 124,6 - 5,74 50 Hz ex-GDR
5 limb
6 600 150 150 400 230 30 17,5 16,5 11,3 YN yn0 d5 50,5 -3,8 125,3 “ Austria

For the transformer No. 6 in Table 3 the following Figure 4 gives additional information. The
low-voltage winding C (30 kV) is laying near the iron core, the medium-voltage winding B
(230 kV) between the windings A and C. The high-voltage winding A has a main part and an
additional tap winding connected to the on-load tap changer (see b in Figure 4) near the star
point at the high-voltage side of the transformer.
The reactances X , X , X in the positive-sequence system can be calculated from the short-
A B C
circuit voltages given in Table 3. Related to the high-voltage side A (U = 400 kV) the
rTA
results are: X = 51,1 Ω , X = – 4,4 Ω and X = 124,93 Ω without impedance correction
A B C
factors (see IEC 60909-0). The value X has a small negative value similar to X given in
C (0)B
Table 3.
If only the star point at the high-voltage side is earthed then X = X + X shall be
(0)T (0)A (0)C
used. If, on the other side, only the star point at the medium-voltage side is earthed, then
X = X + X is valid related to the high-voltage side or related to the medium-voltage
(0)T (0)B (0)C
2 2
side: X = (X + X ) × (230 kV) /(400 kV) .
(0)Tt (0)B (0)C
– 12 – TR 60909-2 © IEC:2008(E)

IEC  2031/08
Key
a terminals and rated apparent power of the windings A, B and C
b position of the tree windings in relation to the iron core
c positive-sequence reactances
d zero-sequence reactances
A HV-side
B MV-side
C LV-side
SA, SB switches at the HV- and MV-side
Figure 4 – Three-winding transformer (No. 6 of Table 3).
Table 4 – Actual data of typical autotransformers with and without tertiary winding
No. Rated apparent Rated voltages Rated short-circuit Winding Zero-sequence National
powers voltages connection reactances related Commit-
symbol to side A tee
S S S U U U u u u X X X
rTAB rTAC rTBC rTA rTB rTC krAB krAC krBC (0)A (0)B (0)C
HV MV LV
MVA MVA MVA kV kV kV % % % Ω Ω Ω
1 60 60 10 132 66 11 11,0 27,5 79,0 Y yn0 d1 61,6 4,19 1050 Australia
2 200 200 100 230 121 6,6 11,0 32,0 20,0 Y auto d11 30,4 0 54,2 ex-USSR
38,5
3 250 75 75 400 132 18 14,6 12,2 7,1 YN yn0 d1110,11 -7,71 159,1 Hungary
4 250 100 100 400 121 10 12,9 13,1 6,3 YN yn0 d1 95,7 -13,1 113,9 ex-
Czechos
lovakia.
a)
5 660 198 198 400 231 30 10,2 13,5 10,6 III d5 24,35 0,35 84,65 Germany
6 250 250 – 230 130 – 11,6 – – YN yn0 24,55 – – Italy
7 300 300 – 235 165 – 7,0 – – YN yn0 13,0 – – Denmark
a)
Three separate poles.
TR 60909-2 © IEC:2008(E) – 13 –
In Figure 5 the rated short-circuit voltage is plotted as a function of the rated apparent power
of unit transformers (ST) in power stations with or without on-load tap-changer. An average
value for the rated short-circuit voltage is given by:
u S
kr rT
= 8 + 0,92 × ln (1)
% MVA
Australia
Denmark Italy USA
Austria
ex-GDR Japan
China ,
Germany
Norway
Hungary
eCxz-eCczechhoslosloovakvakia ia UK
%
u
kr
u
kr
u
kr
u
kr
0,1 0,2 0,4 0,8 1 2 4 6 8 10 20 40 60 100 200 400 MVA 1 000
S
rT
IEC  2032/08
Figure 5 – Rated short-circuit voltage u of unit transformers
kr
in power stations (ST) with or without on-load tap-changer
From Figure 5 it can be seen that the following average values for u may be used:
kr
S = 1  . . .   10 MVA:  u =  9 %
rT kr
S = 10 . . .  100 MVA:  u = 11 %
rT kr
S = 100 . . . 1000 MVA:  u = 13 %
rT kr
In Figure 6 the rated short-circuit voltage of network transformers (NT) is plotted as a function
of the rated power. For low-voltage transformers u = 4 % and 6 % are commonly used.
kr
In general u values for auto-transformers are lower.
kr
– 14 – TR 60909-2 © IEC:2008(E)
The u values for network transformers in the UK are, on average, twice as high as those
kr
reported from other countries.
The relationship X /X for two and three winding transformers, if only one star point is
(0) (1)
earthed, is as follows:
YNd – transformers: X / X = 0,8 . 1,0
(0) (1)
Yzn – transformers: X / X ≈ 0,1
(0) (1)
Ynyn0d – transformers: X / X = 1,5 . 3,2 (3,7)
(0) (1)
Australia
Denmark Italy USA
Austria
ex-GDR
Japan
China
,
Germany
Norway
ex-Czechoslovakia Hungary
Czechoslovakia UK
%
u
kr
u
kr
u
kr
u
kr
0,1 0,2 0,4 0,8 1 2 4 6 8 10 20 40 60 100 200 400 MVA 1 000
S
rT
IEC  2033/08
Figure 6 – Rated short-circuit voltages u of network transformers
kr
2.4 Data of typical overhead lines, single and double circuits
The positive sequence impedance may be calculated from conductor data such as cross
section and conductor centre-distances (see IEC 60909-0, 3.4, Equations (14) and (15)).
The effective resistance per unit length at a conductor temperature 20 °C is:

TR 60909-2 © IEC:2008(E) – 15 –
ρ
'
R = (2)
L
q
n
At a conductor temperature of 20 °C for the calculation of the maximum short-circuit current,
the following values may be used:
2 2 2
1 Ω mm 1 Ω mm 1 Ω mm
Copper: ρ = ;  Aluminium: ρ = ;  Aluminium alloy: ρ = ;
54 m
34 m 31 m
In case of aluminium/steel conductors only the aluminium cross-section shall be used for q .
n
The following equations can be used for the calculation of the short-circuit impedances in the
positive-sequence and the zero-sequence system of overhead lines with single conductors or
bundled conductors with one or two three-phase a.c. circuits without or with earth wires.
Single circuit line (I)
Positive-sequence system impedance:

'
⎛ ⎞ Example for a bundle
R μ 1 d
' 'I
L 0
⎜ ⎟
Z = Z = + jω + ln                                       (3)
conductor with two
⎜ ⎟
(1) (1)
n 2π 4n r
B
⎝ ⎠
subconductors
n is the number of subconductors (n =1, 2, 3, 4, 6), in case of n = 1 there is only one con-
ductor, r is the radius of the subconductor, d = d d d is the geometric mean
L1L2 L1L3 L2L3
n
n−1
distance between the conductors, r = nrR is the effective bundle radius with R as the
B
radius of the circle on which the subconductors are placed according to the figure above.
Zero-sequence system impedance without earth wire:
⎛ ⎞
'
R μ μ ⎜ 1 δ ⎟
'I 0 0
L
Z = + 3ω + jω + 3ln (4)
⎜ ⎟
(0)
n 8 2π 4n 2
⎜ ⎟
r d
B
⎝ ⎠
The zero-sequence system impedances in Figures 7 and 8 and in Table 5 are referred to an
earth resistivity of ρ = 100Ωm and therefore to an equivalent depth of current return of
δ = 930m (50 Hz) or δ = 850 m (60 Hz). For the calculation of δ see IEC 60909-3, Equation
(36).
Zero-sequence impedance with one earth wire Q:
'2
Z
'IQ 'I QLE
Z = Z − 3 (5)
(0) (0)
'
Z
QQE
with
⎛ μ ⎞
μ μ δ
'
' 0 0 rQ
⎜ ⎟
Z = R + ω + jω + ln ,
Q
QQE ⎜ ⎟
8 2π 4 r
Q
⎝ ⎠
– 16 – TR 60909-2 © IEC:2008(E)
μ μ δ
'
0 0
Z = + j ln ,  and  d = d d d
ω ω
QL QL1 QL2 QL3
QLE
8 2π d
QL
μ depends on the material and structure of the earth wire.
rQ
Zero-sequence impedance with two earth wires Q1 and Q2:
'2
Z
'IQ1Q2 'I
Q1Q2LE
Z = Z − 3 (6)
(0) (0) '
Z
Q1Q2E
with
'
⎛ ⎞
R μ μ μ δ
' Q rQ
0 0⎜ ⎟
Z = + + j + ln ,
ω ω
Q1Q2E
⎜ ⎟
2 8 2π 8
r d
Q Q1Q2
⎝ ⎠
μ μ δ
' 0 0
Z = ω + jω ln ,
Q1Q2LE
8 2π
d d d d d d
Q1L1 Q1L2 Q1L3 Q2L1 Q2L2 Q2L3
IEC  2034/08
NOTE In case of 60 Hz, the values shall be multiplied by 1,2.
' '
Figure 7 – Positive-sequence reactance X = X of low-voltage and medium-voltage
(1) L
overhead lines 50 Hz, Cu or Al, with one circuit according to Equation (15) of
IEC 60909-0
TR 60909-2 © IEC:2008(E) – 17 –
μ 1 d
⎛ ⎞
'
Calculated values X = ω ⎜ + ln ⎟
(1)
2π 4 r
⎝ ⎠
with
d = d d d
L1L2 L1L3 L2L3
Double circuit line (II)
Positive-sequence impedance per circuit:
'
R μ ⎛ 1 d × d ⎞
'II 0
L mL1M2
⎜ ⎟
Z = + jω + ln (7)
⎜ ⎟
(1)
n 2π 4n r d
B mL1M1
⎝ ⎠
with
3 3
d = d d d  and  d = d d d ,
mL1M1 L1M1 L2M2 L3M3 mL1M2 L1M2 L1M3 L2M3
if the line conductors of both circuits are symmetrical to the tower, otherwise use:
d = d d d d d d
mL1M2 L1M2 L1M3 L2M3 L2M1 L3M1 L3M2
In many cases the quotient, d / d , has results in the neighbourhood of one and
mL1M2 mL1M1
'II 'I
then the positive sequence impedance per circuit is Z ≈ Z .
(1) (1)
– 18 – TR 60909-2 © IEC:2008(E)
Table 5 – Actual data of typical overhead lines 50 Hz and 60 Hz
No Type of Voltage Conductors/ Earth Geometric data Positive- Zero- National
line/ subcon- wire (see 2.4 and Figure 8) sequence sequence Commit-
a)
number ductors number Impedance
impedance tee
a
)
of number material
'
circuits material q q
Z =
n n r d d
()1
d
mL1M2 d '
Q1Q2
(Fig. 9)
QL Z =
()0
d d
r ' '
B LM mL1M1
R + jX
(1) (1)
' '
R + jX
(0) (0)
2 2
kV mm mm mm m m m m
Ω/ km Ω/ km
1 A/1 0,40 1 ×Al 95 (PEN) 6,25 0,6 - - - 0,31+j0,302 0,63+j0,941Austria
2 B/1 20 1 ×Cu 25 - 3,15 1,23 - - - 0,746+j0,396 0,854+j1,643Italy
3 D/1 66 1 × Al/St Al/St 25 13,86 3,77 - 3,0 4,9 0,072+j0,365 0,410+j0,882 Norway
Condor
4 F/1 110 1 × Al/St 1 ×St 50 10,95 4,06 - - 10,8 0,119+j0,387 0,309+j1,382Germany
240/40
5 C/1 110 1 × Al/St 1 ×St 50 9,2 4,61 - - 4,33 0,156+j0,395 0,370+j1,34Bulgaria
185/25
6 C/1 132 1 × Al/St 1 × Al/St 15,8 5,81 - - 12 0,061+j0,387 0,202+j0,931Denmark
525/68 138/68
7 E/1 220 1 × Al/St 2 × St 50 11,75 6,39 - 5,8 6,99 0,108+j0,411 0,352+j1,242 China
291/37,2
b)
8 220 1 × Al/St 1 × St 70 13,75 8,0 - - 11,6 0,075+j0,420 0,250+j1,340 ex-USSR
C/
400/51
9 G/2 220 2 × Al/St 1 × Al/St 10,95 6,24 15,8 - 16,3 0,06+j0,299 0,273+j1,479Germany
240/40 240/40
66,2 15,3 14,4
10 K/2 275 4 × Al/St 1 × AS 160 17,1 9,85 16,39 13,0 16,84 0,015+j0,239 0,111+j1,708 Japan
(50 Hz)
610/79,4 304 13,74 12,60
11 K/2 380 2 × Al/St 1 × Al/St 18,0 11,5 19,2 - 21,6 0,0215+j0,303 0,243+j1,400Austria
c)
240/40 48,9 19,1 23,2
680/85
12 D/1 500 4 × Al/St 2 × Al/St 11,75 17,64 - 24,0 18,08 0,031+j0,286 0,233+j0,715Australia
291/37,2 120/22
197,3
13 K/2 500 4 × Al/St 2 × Al/St 38,4 15,13 25,23 20,4 26,92 0,009+j0,304 0,356+j1,224 Japan
(60 Hz)
814 / 56 150 / 87 287,3 19,38
a)
Impedances per circuit and resistances at a temperature of 20 °C.
b)
Special design. Two separate lines in one single right-of-way.
c)
Since 2006, a new configuration of conductors is typical: 3 × Al/St 635/117.

Zero-sequence impedance with one earth wire Q per circuit:
'2
Z
'IIQ 'I ' QLE
Z = Z + 3Z − 6 (8)
(0) (0) LME
'
Z
QQE
with
μ μ d
'
0 0
Z = ω + jω ln
LME
8 2π d
LM
3 2
3 3
d = d d ; d = d d d ; d = d d d ,
LM mL1M1 mL1M2 mL1M1 L1M1 L2M2 L3M3 mL1M2 L1M2 L1M3 L2M3
if the line conductors of both circuits are symmetrical to the tower.

TR 60909-2 © IEC:2008(E) – 19 –
' '
Z and Z see the information following Equation (5).
For
QQE
QLE
Australia Japan
Denmark
Austria ex-G D R Norway
Bulgaria Germany
China Ita ly
n = 1
N um ber of sub-conductors
n = 2
n = 4
0,46
132 220 220
110 n = 1
Ω
n = 2
20 220
km
n = 4
0,42
132 20
X X 20
' = '
(1) 1L
0,40
0,38
380 132
220 330
0,36 220
0,38 220
0,34
220 110
2 50
0,32
0,30 380
Voltage in kV
No. of sub-conductors
275 380
4 2
0,28 380
4 220 2
0,26
0,24
500 750
4 4
0,22
23 456789 23 456789
10 100 1 0 00
d /r ; d /r
B
C alculated values:
n
= 1 X ' = ω μ /2 π (1 /4 n + ln d /r )
(1)L 0 B
n = 2 d = √ d d d
L1L2 L1L3 L2L3
n
n -1
r =  √ nrR
n = 4
B IEC  2035/08
' '
Figure 8 – Positive-sequence reactance X = X of overhead lines 50 Hz
(1) L
(60 Hz-values converted to 50 Hz)
Zero-sequence impedance with two earth wires Q1 and Q2:
'
Z
'IIQ1Q2 'I '
Q1Q2LE
Z = Z + 3Z − 6 (9)
(0)
(0) LME
'
Z
Q1Q2E
' ' '
For Z , see the information following Equation (8) respectively for Z and Z ,
LME Q1Q2E Q1Q2LE
see the information following Equation (6).

– 20 – TR 60909-2 © IEC:2008(E)

IEC  2036/08
Key
A to F: Single-circuit lines
G to K: Double-circuit lines
Figure 9 – Type of overhead lines
2.5 Data of typical high-voltage, medium-voltage and low-voltage cables
The impedances of high-, medium and low-voltage cables depend on national techniques and
standards and may be taken from textbooks or the manufacturers’ data. In Table 6 collected
characteristic data of 50-Hz cables are given.

TR 60909-2 © IEC:2008(E) – 21 –
Table 6 – Actual data of typical electric cables
No Rated Conductors Cross Type No. Sheath Positive- Current Zero- Country
voltage section c) of (shield) sequence return sequence
and type cores impedance g) impedance
U
r
Num- Mate- b) d) Type Mate-
Z′ =
a) ′ (0)
Z =
ber rial e) rial (1)
′ ′
R + jX
(0) (0)
R′ + jX ′
(1) (1)
f)
f)
kV - - mm - - - - -
Ω/km Ω/km
th
1 0,6/1 4 Al 240/120 NR 3½ - - 0,129+j0,04 4 +E ex-
′ ′
4,2R + j4,6X
(1) (1)
rST Czechosl.
h)
2 6/10 Cu 120 rST R SC W+T Cu 0,16+j0,116 S+E - Hungary
3×1
3 10 3 Cu 240 rST NR TC M Pb 0,088+j0,069 S+E +j0,242 China
i)
4 22 3 Cu 120 rST NR TC FW Cu 0,153+j0,104 S+E - Norway
5 50 Al 500r R SC W Cu 0,084+j0,11 S+E 0,456+j0,156 Denmark
3×1
j)
6 110 3×1 Cu 240 HO R SC M Pb/Al0,079+j0,12 S+E 0,51+j0,30 Germany
7 132 Cu 220r HO R SC M Pb 0,084+j0,12 S 0,58+j0,061 Italy
3×1
8 275 3×1 Cu 1400sST R SC M Al 0,0131+j0,14 S+E 0,047+j0,047 Japan
9 330 Cu 1200s R SC M Al 0,0205+j0,18 S+E 0,0719+j0,0566 Australia
3×1
HO
10 380 Cu 1200sST R SC M Al 0,018+j0,188 S 0,047+j0,070 Austria
3×1
a) Line-to-line voltage. f) AC resistance at 20°C.
th
b) r = round, HO = hollow, s = sector form, ST = stranded. g) S in the sheath (shield), E in earth, 4 in the fourth
conductor.
c) R = radial field, NR = non-radial field.
h) N2YSY.
d) SC = single core, TC three-core cable.
i) DKAB.
e) T = tapes; W = wires; M = metallic sheath.
j) Oil pressure.
Table 7 gives the equations for the calculation of the positive-sequence and the zero-
sequence impedance of single-core cables without and with metallic sheath or shield earthed
at both ends. Case No. 2 is valid for low-voltage systems with four equal cores (N = PEN).

– 22 – TR 60909-2 © IEC:2008(E)
Table 7 – Equations for the positive-sequence
and the zero-sequence impedance of cables
Ca Cable configuration Positive-sequence and zero-sequence impedance
se
No
Cable without metallic
μ ⎛ 1 d ⎞
' '
Z = R + j ⎜ + ln ⎟                        (10)
ω
sheath or shield
L
(1) ⎜ ⎟
2π 4 r
⎝ L⎠
⎛ ⎞
μ μ 1 δ
⎜ ⎟
' ' 0 0
1a Z = R + 3ω + jω + 3ln              (11)
(0) L
⎜ ⎟
8 2π 4 2
⎜ ⎟
r d
L
⎝ ⎠
with
1b
d = d d d and δ from Equation (36) of IEC 60909-3
L1L2 L1L3 L2L3
Cable without metallic Four equal single-core cables (low voltage)

sheath or shield
⎛ ⎞
μ 1 d
' '
' 0
⎜ ⎟
Z = Z = R + jω + ln                   (12)
L
⎜ ⎟
(1)N (1)
2π 4 r
L
⎝ ⎠
Current return through the fourth conductor N
2a
⎛ ⎞
d
μ 1
⎜ ⎟
' ' LN
Z = 4R + j4ω + ln                   (13)
L
⎜ ⎟
(0)N
2π 4
⎜ r d ⎟
L
⎝ ⎠
2b
Current return through the fourth conductor N and the earth E

⎛ ⎞
μ μ δ
0 0
⎜ ⎟
ω + jω ln
⎜ ⎟
8 2π d
' ' ⎝ LN⎠
Z = Z − 3           (14)

(0)NE (0)
⎛ ⎞
μ μ 1 δ
' 0 0
⎜ ⎟
R + ω + jω + ln
L
⎜ ⎟
8 2π 4 r
L
⎝ ⎠
'
with Z from Equation (11) and d = d d d
LN L1N L2N L3N
(0)
Cable with metallic
⎛ ⎞
μ d
sheath (shield) S ⎜ ⎟
ω ln
⎜ ⎟
2π r
Sm
earthed at both ends ' ' ⎝ ⎠
Z = Z +                     (15)
(1)S (1)
μ d
'
R + jω ln
S
2π r
Sm
Current return through sheath (shield) and earth
3a
⎛ ⎞
⎜ μ μ δ ⎟
0 0
3ω + j3ω ln
⎜ ⎟
8 2π 2
⎜ ⎟
r d
Sm
' ' ⎝ ⎠
Z = Z −          (16)
(0)SE (0)
μ μ δ
' 0 0
R + 3ω + j3ω ln
S
8 2π 2
r d
3b
Sm
' '
with Z from Equation (10), Z from Equation (11) and the
(1) (0)
medium radius r = 0,5(r + r ) of the sheath or the shield.
Sm Si Sa
'
R
S
r =                 (17)
μ μ δ
' 0 0
R + 3ω + j3ω ln
S
8 2π 2
r d
Sm
TR 60909-2 © IEC:2008(E) – 23 –
High-voltage cables
Case No. 3 in Table 7, with Equations (15) and (16), is valid for three single-core high-voltage
cables, for instance 64 kV/110 kV (Figure 10), with a metallic sheath or shield connected and
earthed at both ends. As well in the case of a positive-sequence current system as in the case
of a zero-sequence current system, currents are flowing through the sheaths or shields of the
three cables. In this case therefore the calculation of the reduction factor (see IEC 60909-3)
has to take care of the three sheaths (or shields), too.

IEC  2037/08
Key
1  al-conductor, stranded
2  conductor screen: semi-conducting XLPE
3  insulation: XLPE, 18 mm
4  insulation screen: extruded semi-conducting XLPE
5  bedding: semi-conducting tape
6  metallic sheath: lead alloy
7  outer sheath: PE black
Figure 10 – Single-core cable 64 kV / 110 kV with lead sheath [4]
The following Table 8a gives the data and the results calculated with Equations (15) and (16)
of Table 7 (Case No.3a: triangular configuration) for three high-voltage single-core cables
with lead sheath for 64/110 kV (U = 123 kV) 2XK2Y. Data are given from the
m
manufacturer [4]. Table 8b deals with the flat configuration of the cables. In this case it is
necessary to calculate arithmetic medium values.
—————————
Figures in square brackets refer to the Bibliography.

– 24 – TR 60909-2 © IEC:2008(E)
Table 8 – Single-core cables 64/110 kV, 2XK2Y,
3 × 1 × 240 . 1 200 rm, Cu with lead sheath
a) in triangular configuration
' ''
Zero-sequence impedance ZR== jX in case of current return through the
(0)SE (0)SE (0)SE
sheath and the earth, f = 50 Hz, ρ = 100 Ωm,

' '
R X
' '
(0)SE (0)SE
q r q r D d   Equation (15) r
n L S Sm a 3
R R
L S
' '
'
' '
R X
Z = R + jX
(1)S (1)S
a) a) b)
(1)S (1)S d)
(1)S
c) c)
2 2
Ω/km Ω/km Ω/km
mm mm mm mm mm mm - - -
240 9,3 440 33,3 72 76,3 0,0754 0,473 0,0811+j 0,1473 6,30 1,40 0,245
300 10,3 460 34,9 74 78,4 0,0601 0,453 0,0657+j 0,1426 7,29 1,36 0,236
400 11,9 480 36,4 77 81,6 0,0470 0,434 0,0528+j 0,1360 8,53 1,33 0,228
500 13,8 520 37,6 80 84,8 0,0366 0,401 0,0430+j 0,1290 9,60 1,24 0,213
630 15,6 550 39,8 85 90,1 0,0283 0,379 0,0351+j 0,1250 10,98 1,19 0,203
800 17,35 580 42,0 88 93.3 0,0221 0,359 0,0290+j 0,1204 12,50 1,15 0,193
1000 19,40 640 44,3 93 98,6 0,0176 0,326 0,0252+j 0,1167 13,06 1,06 0,177
1200 21,7 670 46,4 98 104 0,0151 0,311 0,0232+j 0,1128 13,52 1,02 0,170
a) q = 2πr d with d thickness of the lead sheath.
S Sm S S
b) d ≈ 1,06D in case of a triangle configuration.
a
'
c) Z according to Equation (16).
(0)SE
d) Reduction factor of the three sheaths of the single-core cables, see Equation (17).

b) in flat configuration
' '
R X
' '
(0)SE (0)SE
d
q r q r D r
L S Sm a R R  Equ. (15) 3
n
L S
' '
' ''
R X
(1)S (1)S
b) ZR=+ jX
a) a)
d)
(1)S ((1)S 1)S
c) c)
2 2
mm mm mm mm mm mm Ω/km Ω/km Ω/km
- - -
240 9,3 440 33,3 72 178,9 0,0754 0,473 0,0990+j 0,2015 5,12 1,047 0,259
300 10,3 460 34,9 74 181,4 0,0601 0,453 0,0838+j 0,1959 5,68 1,016 0,249
400 11,9 480 36,4 77 185,2 0,0470 0,434 0,0711+j 0,1882 6,29 0,982 0,240
500 13,8 520 37,6 80 189,0 0,0366 0,401 0,0623+j 0,1801 6,59 0,911 0,224
630 15,6 550 39,8 85 195,3 0,0283 0,379 0,0547+j 0,1745 7,01 0,870 0,213
800 17,35 580 42,0 88 199,1 0,0221 0,359 0,0487+j 0,1690 7,39 0,836 0,203
...