GE C70 Instruction Manual page 591

CHAPTER 9: THEORY OF OPERATION
Substituting these results into the first equation, the initial operating signal is:
The match factor setting k is chosen as:
A
Therefore, as can be seen from the previous two equations, the initial operating signal is zero.
9.1.3.3 Sensitivity
Now consider the consequences of an element failure in the upper sub-string of leg A, making a small capacitance change
in C . The effect on the operating signal can be calculated by taking the derivative of equation 9-12 with respect to C
1A
holding C constant. In the general case, the derivative of the absolute value function is messy, but in our case where the
2A
initial value is zero, the derivative of the absolute function is simply the absolute value of the derivative of its argument. The
derivative is thus:
Substituting equation 9-13, we have:
This can be written as:
In this equation, ΔC
(pu) is the capacitance change as a per-unit of the leg capacitance, V
A
ground voltage, and V (pu) is the operating signal resulting from the failure in the upper sub-string. Both voltages are
OP(1A)
in per-unit of nominal bus phase-to-ground voltage, so V
Note however that under external fault conditions, sensitivity can be much different from the non-fault sensitivity.
Instead of a failure in the upper sub-string, 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
C70 CAPACITOR BANK PROTECTION AND CONTROL SYSTEM – INSTRUCTION MANUAL
can be taken as 1 when the system is normal (not faulted).
Spg
OVERVIEW
Eq. 9-12
Eq. 9-13
A
Eq. 9-14
Eq. 9-15
Eq. 9-16
is the system phase-to-
Spg
using:
1A
Eq. 9-17
,
9
9-5