GE C70 Instruction Manual page 533

CHAPTER 9: THEORY OF OPERATION
Inserting equation 9.46 into equation 9.45, to eliminate the voltages, we get:
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 C ≅ C
A1
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 converted to the differential source base. For example, I
rated
differential CT primary current rating, or:
C70 CAPACITOR BANK PROTECTION AND CONTROL SYSTEM – INSTRUCTION MANUAL
and replaces the phase current vector with its magnitude. This can be written as:
A2
is chosen to be:
A
can be taken as the capacitor bank rated primary per-
A
= I / I
A rated base
OVERVIEW
Eq. 9-47
Eq. 9-48
Eq. 9-49
A
Eq. 9-50
Eq. 9-51
Eq. 9-52
(pu) represents the
OP(A)
is phase A terminal
A
, where I is again the
base
Eq. 9-53
9-13
is
9