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9 THEORY OF OPERATION
In the above equation, ΔC
(pu) is the capacitance change as a per-unit of the leg capacitance, V
A
to-ground voltage, and V
OP(1A)
are in per-unit of nominal bus phase-to-ground voltage, so V
Note however that under external fault conditions sensitivity may be much different from the non-fault sensitivity.
Instead of a failure in the upper sub-string, we now suppose a failure in the lower sub-string. The same approach is used,
except to make the algebra easier, the initial operating signal is converted to be in terms of C
In this case, we have:
The derivative is thus:
Substituting equation 8.17 into equation 8.13, we have:
Therefore:
Substituting this value into equation 8.19, we get:
Or alternately,
The value can be expressed as:
In the above equation, ΔC
(pu) is the capacitance change as a per-unit of the leg capacitance, V
A
to-ground voltage, and V
OP(2A)
are in per-unit of nominal bus phase-to-ground voltage, so V
Note however that under external fault conditions sensitivity may be much different from the non-fault sensitivity.
GE Multilin
(pu) is the operating signal resulting from the failure in the upper sub-string. Both voltages
Spg
C
C
1A
2A
C
or C
=
-------------------------- -
A
C
+
C
1A
2A
×
V
=
V
1 k
( )
OP A
Spg
×
V
1 k
=
Spg
d
×
---------- - V
V
---------- - 1 k
=
(
)
OP 2A
Spg
dC
dC
A
×
V
=
--------- -
Spg
C
k
×
--------- -
=
V
Spg
C
C
C
2A
1A
k
=
--------- -
=
----------------------- -
or C
A
C
C
–
C
A
1A
A
k
C
=
-------------- -
1A
k
d
---------- - V
=
(
)
OP 2A
dC
A
=
×
dV
=
V
(
)
OP 2A
Spg
(
)
(
V
pu
=
V
pu
(
)
OP 2A
Spg
(pu) is the operating signal resulting from the failure in the lower sub-string. Both voltages
Spg
C70 Capacitor Bank Protection and Control System
can be taken as 1 when the system is normal (not faulted).
C
C
A
1A
=
----------------------- -
2A
C
–
C
1A
A
C
A
×
--------- -
–
A
C
2A
C
–
C
×
1A
A
----------------------- -
–
A
C
1A
C
C
–
⎛
⎞
d
1A
A
----------------------- -
–
⎝
⎠
A
C
A
1A
k
A
1A
A
1A
=
k
C
–
k
C
1A
A
1A
A
A
C
A
A
1
–
A
k
A
×
V
--------- -
Spg
C
1A
k
1
–
A
×
-------------- -
V
Spg
C
A
dC
A
(
)
×
---------- -
k
–
1
A
C
A
)
×
(
)
×
Δ
(
)
k
–
1
C
pu
A
A
can be taken as 1 when the system is normal (not faulted).
9.1 OVERVIEW
is the system phase-
Spg
using:
1A
(EQ 9.17)
(EQ 9.18)
(EQ 9.19)
(EQ 9.20)
(EQ 9.21)
(EQ 9.22)
(EQ 9.23)
(EQ 9.24)
is the system phase-
Spg
9-5
9
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