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I.L. 41-496.52D
1.1.
Fundamentals of Distance Measurement
On Ground Faults
The SDG-T type distance relay operates on both sin-
gle and double line-to-ground faults. In either case,
neglecting fault resistance, the faulted phase-to-
ground voltages at the relay consists of the line drop:
V LG
=
Faulted phase-to-ground relay voltage
= K 1 I 1 nZ 1 L
I OE nZ OM
Where K
, K
, K
are current distribution factors for
1
2
0
the pos., neg., and zero sequence networks, respec-
tively.
I
, I
, I
are the pos., neg., and zero sequence cur-
1
2
0
rents in the fault .
nZ
, nZ
are the pos. and zero sequence line
1L
0L
impedances to the fault .
I
is the adjacent line zero sequence current.
0E
Z
zero sequence mutual impedance.
0M
See Figure 16 for further definition of terms. For an A
to ground fault Eq. ( 1 ) would be written in terms of
the phase A quantities (ignoring mutual effect).
V AG
=
K 1 I A 1 nZ 1 L
Eq. ( 2 ) also applies for an AB to ground fault or any
other fault. Additional expressions apply for the
phase B and C quantities.
A distance ground relay made to respond to single
phase-to-ground faults will also respond in the same
way to double line-to-ground faults. This is true
except for the effect of ground resistance, R
different nature of these effects can be sensed from
Figure 17. In Figure 17 the ground current 3I
through R
is essentially in phase with the total
G
faulted phase current. This is so, since I
This is not true for a 2L-G fault. The current 3I
of phase with K
IA
and K
1
1
with K
I
and K
I
). As a result the drop across R
1
B1
2
B2
produces an apparent reactance term to the distance
relay, causing it to underreach on one phase and
2
+
K 2 I 2 nZ 1 L
+
K 0 I 0 nZ 0 L +
Eq. (1)
+
K 2 I A 2 nZ 1 L + K 0 I 0 nZ 0 L
Eq. (2)
G
flowing
0
= I
A1
A2
0
IA
(also out of phase
2
2
overreach on the other faulted phase. The SDG-1T
and SDG-2T relays contain a desensitizer circuit to
prevent overreach on 2L-G faults, by reducing the
reach of the relay.
The restraint voltages V
the use of compensators with an impedance Z
to match the desired positive sequence line imped-
ance reach. Only positive and negative sequence
voltages appear in Eq. ( 3 ) to ( 5 ).
(
V XN
=
V A 1
(
V YN
=
V B 1
(
V ZN
=
V C 1
The zero sequence voltage is filtered out by not
grounding the neutral of the set of Y-connected auxil-
iary transformers (T
to feed the restraint portion of the magnitude com-
parison circuit. These same connections render the
zero sequence current flowing in the phase compen-
sators ineffective. So the restraint voltages duplicate
the delta voltage conditions at the fault when the fault
is Z
ohms from the relay (i.e., at the balance point).
C
Zero sequence quantities are not required to dupli-
cate the system voltage triangle at the balance point
since zero sequence voltages cancels out of the line
to line voltages.
The operating voltage is:
V WO
=
V 0
. The
Here V
is the relay zero sequence voltage: it is
0
= I
.
0
compensated by using a compensator impedance
is out
(Z
/Z
) Z
0L
1L
C
impedance to the desired balance point. For mutual
coupled lines this compensator can be fed with not
G
only the protected line current but also with a portion
of the mutual current I
, V
, V
XN
YN
ZN
) Z C K A I A 1
(
+
V A 2
–
) Z C K 1 I B 1
(
+
V B 2
–
) Z C K L I C 1
(
+
V C 2
–
, T
and T
) which are used
A2
B2
C2
Z 0 L
---------- -
¥
Z C
K 0 I 0
+
I 0E
–
Z 1 L
representing the zero sequence line
(See Figure 16). The operat-
0E
are obtained by
, set
C
)
+
K 2 I A 2
Eq. (3)
)
+
K 2 I B 2
Eq. (4)
)
+
K 2 I C 2
Eq. (5)
Z 0 M
-------------
Z 0 L
Eq. (6)
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