GE C70 Instruction Manual page 472

OVERVIEW
Inserting this value into equation 9.43, we have:
The capacitor bank leg-A inherent unbalance factor setting k
As can be seen from the previous two equations, the initial operating signal is zero.
9.1.5.3 Sensitivity
Now consider the consequences of an element failure in a typical string, say string A1, making a small capacitance change
in C capacitance. The effect on the operating signal can be calculated by taking the derivative of equation 9.48 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 I
constant, which investigation has shown results in negligible error. The derivative is thus:
The last step assumes
Alternatively, we can say:
where ΔC(pu) represents the capacitance change as a per-unit of the string capacitance, and I
operating signal resulting from the failure in per-unit of the nominal current of the differential source. I
current on the same base. When the system is normal (no fault), I
phase current I
rated
differential CT primary current rating, or:
Note that under external fault conditions, sensitivity can be much different from the non-fault sensitivity.
9
9.1.5.4 Auto-setting
As a convenient alternative to manually determining inherent unbalance factor settings, the relay can automatically
calculate these settings from its own measurements while the capacitor is in-service, as described in the Commands
chapter. The technique that the relay uses is to set the operate signal variable to zero in equation 9.43 and solve for the
inherent unbalance factor k
9-12
I =
OP A ( )
=
d
---------- -I =
OP A ( )
dC
A1
=
=
≅
and replaces the phase current vector with its magnitude. This can be written as:
C ≅ C
A1 A2
dI
I
OP A ( )
converted to the differential source base. For example, I
I ( pu
OP A ( )
using the average of several successive measurements of the currents. However, the
A
C70 CAPACITOR BANK PROTECTION AND CONTROL SYSTEM – INSTRUCTION MANUAL
I k I
–
DIF A ( ) A A
C C
–
A1 A2
--------------------- -
I × k I
–
A A A
C + C
A1 A2
is chosen to be:
A
C C
–
A1 A2
k = --------------------- -
A
C + C
A1 A2
C C
–
d
 
A1 A2
--------------------- -
---------- - I × k I
–
 
A A A
C + C
dC
A1 A2
A1
( C + C ) ( C C )
– –
A1 A2 A1 A2
× ---------------------------------------------------------- -
I
A
2
( C + C )
A1 A2
2C
A2
× ---------------------------- -
I
A
2
( C + C )
A1 A2
I
1
A
--- × ------- -
2 C
A1
I dC
A A1
= --- × ---------- -
OP A ( )
2 C
A1
I
A
---
( pu ) = × Δ C pu ( )
2
can be taken as the capacitor bank rated primary per-
A
= I
A
I
rated
------------- -
) = × Δ C pu ( )
2I
base
CHAPTER 9: THEORY OF OPERATION
(pu) represents the
OP(A)
is phase A terminal
A
/ I , where I is again the
rated base base
Eq. 9-48
Eq. 9-49
is
A
Eq. 9-50
Eq. 9-51
Eq. 9-52
Eq. 9-53