GE C70 Instruction Manual page 425

8 THEORY OF OPERATION
In the above equation, C
(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, C
(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 ---------- - 1 k
V
=
 
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
       
k 1 C pu
–
A A
can be taken as 1 when the system is normal (not faulted).
8.1 OVERVIEW
is the system phase-
Spg
using:
1A
(EQ 8.17)
(EQ 8.18)
(EQ 8.19)
(EQ 8.20)
(EQ 8.21)
(EQ 8.22)
(EQ 8.23)
(EQ 8.24)
is the system phase-
Spg
8-5
8