GE C70 Instruction Manual page 529

CHAPTER 9: THEORY OF OPERATION
The unbalance ratio k-values that reflect the initial or inherent bank unbalance are chosen as:
Therefore, as seen from the previous two equations, the initial operating signal is zero.
Note that the ratios of the capacitances between phase A and the two other phases are close to unity, and therefore the
correcting factors in equation 9.25 for the B and C-phase voltages are small numbers, while the factor for the V
close to 3. If so, equation 9.25 takes a familiar simplified form:
The V term in the operate equation can be either the neutral component in the bus voltages (one-third of the vectorial
0
sum of the phase voltages calculated by the relay), or directly measured neutral voltage component (open-corner-delta VT
voltage).
9.1.4.3 Sensitivity
Now consider the consequences of a capacitor element failure in one leg, most conveniently leg C, making a small
capacitance change in leg-C capacitance. The effect on the operating signal can be calculated by taking the derivative of
equation 9.25 with respect to C
where the initial value is zero, the derivative of the absolute function is simply the absolute value of the derivative of its
argument. As such, the derivative is:
Recall equation 9.29:
Differentiating this gives:
Substituting for V from equation 9.34 gives:
X
C70 CAPACITOR BANK PROTECTION AND CONTROL SYSTEM – INSTRUCTION MANUAL
. In the general case, the derivative of the absolute value function is messy, but in our case
C
OVERVIEW
Eq. 9-31
voltage is
X
Eq. 9-32
Eq. 9-33
Eq. 9-34
Eq. 9-35
9
Eq. 9-36
9-9