GE UR Series C70, Instruction Manual

Page: 401 / 614

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