CHAPTER 9: THEORY OF OPERATION OVERVIEW
C70 CAPACITOR BANK PROTECTION AND CONTROL SYSTEM – INSTRUCTION MANUAL 9-9
9
The unbalance ratio k-values that reflect the initial or inherent bank unbalance are chosen as:
Eq. 9-31
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
X
voltage is
close to 3. If so, equation 9.25 takes a familiar simplified form:
Eq. 9-32
The V
0
term in the operate equation can be either the neutral component in the bus voltages (one-third of the vectorial
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
C
. 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. As such, the derivative is:
Eq. 9-33
Recall equation 9.29:
Eq. 9-34
Differentiating this gives:
Eq. 9-35
Substituting for V
X
from equation 9.34 gives:
Eq. 9-36
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