ABB RET670 - Page 333

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
62.
( )
A L ph N 0 Nm 0pV p Z1 I K 3I K 3I= × + × + ×
EQUATION1278 V3 EN (Equation 253)
One can also 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 254)
Simplification of equation 63, solving it for 3I0p and substitution of the result into
equation 62 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 255)
If we finally divide equation 64 with equation 59 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 256)
Calculation for a 400 kV line, where we for simplicity have excluded the resistance,
gives with X1L=0.48 Ohm/Mile, X0L=1.4Ohms/Mile, zone 1 reach is set to 90% of
the line reactance p=71% that is, the protection is underreaching with approximately 20%.
1MRK504116-UUS C Section 3
IED application
327
Application manual