GE C70 Instruction Manual page 435

8 THEORY OF OPERATION
I I
=
OP DIF

I
=
1

I
=
1

I
=
1
The capacitor bank positive sequence inherent unbalance factor setting k
This allows the first and second terms in the I
numbers, virtually vanishes as well. Under normal system conditions (non-fault), the zero-sequence voltage and thus the
zero-sequence current is small. The k
matched, and so are also small. In addition, it is very likely that they will be of varying signs, and thus their sum will be dou-
bly small. Thus the initial operating signal under normal operating conditions is seen to be virtually zero.
c) SENSITIVITY
Now consider the consequences of an element failure in a typical string, say string A1, making a small capacitance change
in the C capacitance. The effect on the operating signal can be calculated by taking the derivative of equation 8.63 with
A1
respect to C .
A1
In the general case, the derivative of the absolute value function is messy, but in our case where the initial value is zero, the
derivative of the absolute function is simply the absolute value of the derivative of its argument. We assume here that the
currents remain constant, which investigation has shown results in negligible error. The derivative is thus:
d
------------- - I ------------- - I
=
OP
dC dC
A1
dk
------------- - I
=
dC
dk
------------- - I
=
dC

C
--------------------------------------------------------------------- I
=
----------------------------------
=

C
I
A
 ---- 
2

The final step assumes C
A1
Alternately, we can say:
where C(pu) represents the capacitance change as a per-unit value of the string capacitance, and I
operating signal resulting from the failure in per-unit of the nominal current of the differential source. I
phase A terminal current on the same base. When the system is normal (no fault), I
rated primary per-phase current I
is again the differential CT primary current rating, or with system normal:
GE Multilin
*
 
k I k I
– –
1 1 1 2
2
a ˆ a ˆ k a ˆ k
 
k k I k
+ + + +
A B C 2 A
2
a ˆ a ˆ k
 
k k k I k
+ + – +
A B C 1 2 A
2
a ˆ a ˆ k
 
k k k I k
+ + – +
A B C 1 2 A
2
a ˆ a ˆ k
k k k
= + +
1 A B C
C C C
–
2
A1 A2 a ˆ
-------------------------- - -------------------------- -
= +
C C C
+
A1 A2
equation above to vanish. The last term, being the product of two small
OP
, k , and k value involve the difference between two capacitances that are factory
A B C
d
2
a ˆ a ˆ k
  
k k k
+ + – +
1 A B C 1
A1
dk dk
A A A
------------- - I ------------- - I
+ +
1 2 0
dC dC
A1 A1 A1
A
A
A1
  
C C C
+ – –
A1 A2 A1 A2
A
2
 
C C
+
A1 A2
2C I
A2 A
2

C
+
A1 A2
1
--------- -
C
A1
C , and replaces the phase current vector with its magnitude. This can be written as:
A2
I
----
dI
=
OP
 
I pu
=
OP
converted to the differential source base. For example, I
rated
C70 Capacitor Bank Protection and Control System
2
a ˆ
   k
k I k k k
+ + + + –
B C 0 A B C
2 *
a ˆ k a ˆ
 
k k I k k
+ + – + +
B C 1 0 A
*
2
a ˆ a ˆ k
 
k k I k k
+ + – + +
B C 1 0 A
is chosen to be:
1
C C C
– –
B1 B2 a ˆ C1 C2
-------------------------- -
+
C C C
+ +
B1 B2 C1 C2
*
2
a ˆ a ˆ k
 
I k k k I
+ + – +
2 A B C 1 0
dC
A A1

------------- -
2 C
A1
I
A
   
----
C pu
2
may be taken as the capacitor bank's
A
8.1 OVERVIEW
*
I k I
–
1 1 1 2
(EQ 8.63)

k
+
B C

k
+
B C
(EQ 8.64)
  
k k k
+ +
A B C
(EQ 8.65)
(EQ 8.66)
(EQ 8.67)
(pu) represents the
OP
represents the
A
= I / I , where I
A rated base
8
base
8-15