Siemens siprotec 7SA522 User Manual page 168

Functions
Earth Impedance
(Residual)
Compensation with
Magnitude and
Angle (K –Factor)
0
6-20
When the complex earth impedance (residual) compensation factor K
dresses  to  apply. These factors are defined with their magnitude and
angle which may be calculated with the line data using the following equation:
Whereby the following applies
Z — (complex) zero sequence impedance of the line
0
Z — (complex) positive sequence impedance 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 quotients are independent of length. Furthermore it makes no difference
if the quotients are calculated with primary or secondary values.
For overhead lines it is generally possible to calculate with scalar quantities as the
angle of the zero sequence and positive sequence system only differ by an insignifi-
cant amount. With cables however, significant angle differences may exist as illustrat-
ed by the following example.
Calculation example:
110 kV single conductor oil-filled cable 3×185 mm
j73° Ω/km
Z /s = 0.408·e
1
j18,4°
Z /s = 0.632·e
0
(where s = line length)
The calculation of the earth impedance (residual) compensation factor K
Z
0.632
j(18.4°–73°)
0
⋅
----- - -------------- - e
=
Z 0.408
1

Z
1
0
⋅

K -- - ----- - 1
= –
0
3  Z
1
The magnitude of K0 is therefore
K
Z
1
E ⋅
K -- -
= ------ - =
0
3
Z
L
positive sequence impedance
Ω/km
zero sequence impedance
–j54.6°
1.55 e ⋅
= =
= 0.898 – j1.263

1
⋅ (

-- - 0.898 j1.263
= –
 3
1
2
⋅ ( ) (
-- - 0.102
= – + –
0
3
 
Z
0
 
----- - 1
–
 
Z
1
2
Cu with the following data
⋅ ( )
1.55 0.579 j0.815
–
1
) ⋅ (
1 -- - 0.102
– = – –
3
2
)
1.263 0.42
=
C53000-G1176-C119-2
is set, the ad-
0
results in:
0
)
j1.263
7SA522 Manual