9-6 C70 CAPACITOR BANK PROTECTION AND CONTROL SYSTEM – INSTRUCTION MANUALOVERVIEW CHAPTER 9: THEORY OF OPERATION9In this case, we have:Eq. 9-18The derivative is thus:Eq. 9-19Substituting equation 9-17 into equation 9-13, we have:Eq. 9-20Therefore:Eq. 9-21Substituting this value into equation 9-19, we get:Eq. 9-22Or alternately,Eq. 9-23The value can be expressed as:Eq. 9-24In this equation, ΔC A (pu) is the capacitance change as a per-unit of the leg capacitance, VSpg is the system phase-to-ground voltage, and VOP(2A) (pu) is the operating signal resulting from the failure in the lower sub-string. Both voltages are inper-unit of nominal bus phase-to-ground voltage, so V Spg can be taken as 1 when the system is normal (not faulted). Notehowever that under external fault conditions sensitivity can be much different from the non-fault sensitivity.In practice, kA is no less than 2.0 as the tap is no more than half way up the phase string. Comparing equation 9-16 withequation 9-24, it can be seen that VOP(2A) (pu) ≥ VOP(1A) (pu), and thus that an element failure in the lower substring producesa operating signal no smaller than the same failure in the upper sub-string. Thus VOP(1A) (pu) represents the worse casesensitivity. A failure resulting in a 0.01 pu capacitance change in the leg capacitance results in an operating signal of atleast 0.01 pu of bus phase-to-ground voltage.
