Siemens siprotec 7SA6 User Manual page 200

Functions
Earth Impedance
(Residual)
Compensation with
Magnitude and
Angle (K –Factor)
0
6-18
Resistance ratio:
R R
 
1
E 0
⋅
-- -
------ - = ------ - 1
–
 
R 3 R
L 1
Whereby the following applies
R — Zero sequence resistance of the line
0
X — Zero sequence reactance of the line
0
R — Positive sequence resistance of the line
1
X — Positive sequence reactance of the line
1
These values may either apply to the entire line length or be based on a per unit of line
length, as the quotient is independent of length. Furthermore it makes no difference if
the quotients are calculated with primary or secondary values.
Calculation example:
110 kV overhead line 150 mm
/s = 0.19 Ω/km
R
1
/s = 0.42 Ω/km
X
1
/s = 0.53 Ω/km
R
0
/s = 1.19 Ω/km
X
0
(where s = line length)
The following results are obtained for the earth impedance ratio:
R R
 
1
0
E
⋅
------ - = -- - ------ - 1 =
–
 
3 R
R
1
L
X X
 
1
0
E
⋅
------ - = -- - ------ 1 =
–
 
3 X
X
1
L
The earth impedance (residual) compensation factor setting for the first zone Z1 may
be different from that of the remaining zones of the distance protection. This allows the
setting of the exact values for the protected line, while at the same time the setting for
the back-up zones may be a close approximation even when the following lines have
substantially different earth impedance ratios (e.g. cable after an overhead line).
Accordingly, the settings for the address  5(5/ = and  ;(;/ =
are determined with the data of the protected line while the addresses  5(
5/ =%= and  ;(;/ =%= apply to the remaining zones Z1B
and Z2 up to Z5 (as seen from the relay location).
When the complex earth impedance (residual) compensation factor K
addresses  to  apply.
In this case it is most relevant that the line angle is set correctly (cf Address , see
paragraph "General Line Data", page 6-16) as the device needs the line angle to
calculate the compensation components from the K
with their magnitude and angle which may be calculated with the line data using the
following equation:

Z Z
1
E 0
⋅

-- -
K = ------ - = ----- - 1
0
3
Z  Z
L 1
Whereby the following applies
Z — (complex) zero sequence impedance of the line
0
Z — (complex) positive sequence impedance of the line
1
Reactance ratio:
X
E
------ -
X
L
2
with the following data
Positive sequence impedance
Zero sequence impedance
0.53 Ω /km
 
1
⋅
-- - ---------------------------- - 1 =
–
 
0.19 Ω /km
3
1.19 Ω /km
 
1
⋅
-- - ---------------------------- - 1 =
–
 
0.42 Ω /km
3


–

X
 
1
0
⋅
-- -
= ------ 1
–
 
3 X
1
0.60
0.61
0
–factor. These factors are defined
0
C53000-G1176-C133-1
is set, the
7SA6 Manual