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 overreaches. If the
currents have the same direction, the distance protection underreaches.
Maximum overreach occurs if the fault infeed from remote end is weak. If we consider
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 infeed from remote end is zero, we can draw the
voltage V in the faulty phase at A side as in equation
107.
( )
A L ph N 0 Nm 0pV p Z1 I K 3I K 3I= × + × + ×
EQUATION1278 V3 EN (Equation 107)
Notice that the following relationship exists between the zero sequence currents:
( )
0
3 0 3 0 0 2
L L
I Z I p Z p× = × -
EQUATION1279 V2 EN (Equation 108)
Simplification of equation 108, solving it for 3I0p and substitution of the result into
equation 107 gives that the voltage can be drawn as:
3 0
1 3 0
2
A L N m
I p
V p Z Iph K I KN
p
æ ö
×
= × + × + ×
ç ÷
-
è ø
EQUATION1280 V1 EN
(Equation 109)
If we finally divide equation 109 with equation 104 we can draw the impedance
present to the IED as
0
0
3
3 0
2
1
3
m
L
I p
Iph KN I KN
p
Z p Z
Iph I KN
é ù
æ ö
×
+ × + ×
ê ú
ç ÷
-
è ø
ê ú
= ×
ê ú
+ ×
ê ú
ë û
EQUATION1379 V2 EN (Equation 110)
Section 3 1MRK504116-UUS C
IED application
198
Application manual
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