When mutual coupling is introduced, the voltage at the relay point A will be changed
according to equation 118.
0 0
0
0 1
1 3 3
3 1 3 1
m
L L
ph p
ph L
L L
Z
Z Z
V Z I I I
Z Z
æ ö
-
= × + × +
ç ÷
× ×
è ø
EQUATION1276 V4 EN-US (Equation 118)
By dividing equation 118 by equation 117 and after some simplification we can write
the impedance present to the relay at A side as:
3 0
1 1
3 0
æ ö
×
= +
ç ÷
+ ×
è ø
L
I KNm
Z Z
I ph I KN
EQUATION1277 V3 EN-US (Equation 119)
Where:
KNm = Z0m/(3 · Z1L)
The second part in the parentheses is the error introduced to the measurement of the
line impedance.
If the current on the parallel line has negative sign compared to the current on the
protected line, that is, the current on the parallel line has an opposite direction
compared to the current on the protected line, the distance function will overreach. If
the currents have the same direction, the distance protection will underreach.
Maximum overreach will occur if the fault current infeed from remote line end is
weak. If considering a single phase-to-
ground fault at 'p' unit of the line length from A
to B on the parallel line for the case when the fault current infeed from remote line end
is zero, the voltage
V
A
in the faulty phase at A side as in equation
120.
( )
0 0
p 3 3= 1 +
A L ph N Nm p
V Z I K I K I× × + ×
EQUATION1278 V4 EN-US (Equation 120)
One can also notice that the following relationship exists between the zero sequence
currents:
3 0 3 0 0 2
0
I Z I Z p
L p L
⋅ = ⋅ −
( )
EQUATION1279 V3 EN-US (Equation 121)
Section 8 1MRK 504 163-UUS A
Impedance protection
268 Transformer protection RET670 2.2 ANSI
Application manual
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