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2 Functions
pedance compensation factors are defined with their magnitude and angle which may
be calculated with the line data using the following equation:
Where
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
The calculation of the earth impedance (residual) compensation factor K
The magnitude of K
When determining the angle, the quadrant of the result must be considered. The fol-
lowing table indicates the quadrant and range of the angle which is determined by the
signs of the calculated real and imaginary part of K
Table 2-2
In this example the following result is obtained:
62
Z
= (complex) zero sequence impedance of the line
0
Z
= (complex) positive sequence impedance of the line
1
Z
/s
= 0.408 · e
1
Z
/s
= 0.632 · e
0
(where s
= line length)
is therefore
0
Quadrants and ranges of the angle K
tan ϕ(K0)
Real part Imaginary
part
+
+
+
–
–
–
–
+
2
j73°
Ω/km positive sequence impedance
j18.4°
Ω/km zero sequence impedance
0
0
Quadrant/range
+
I
0° ... +90°
–
IV
–90° ... 0°
+
III
–90° ... –180°
–
II
+90° ... +180°
Cu with the following data
results in:
0
.
Calculation
arc tan (|Im| / |Re|)
–arc tan (|Im| / |Re|)
arc tan (|Im| / |Re|) –180°
–arc tan (|Im| / |Re|) +180°
7SD5 Manual
C53000-G1176-C169-1
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