GE Multilin C70 Capacitor Bank Protection and Control System 8-58 THEORY OF OPERATION 8.1 OVERVIEW8In the above equation, CA(pu) is the capacitance change as a per-unit of the leg capacitance, VSpg is the system phase-to-ground voltage, and VOP(1A) (pu) is the operating signal resulting from the failure in the upper sub-string. Both voltagesare in per-unit of nominal bus phase-to-ground voltage, so VSpg can be taken as 1 when the system is normal (not faulted).Note however that under external fault conditions sensitivity may be much different from the non-fault sensitivity.Instead of a failure in the upper sub-string, we 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 C1A using:(EQ 8.17)In this case, we have:(EQ 8.18)The derivative is thus:(EQ 8.19)Substituting equation 8.17 into equation 8.13, we have:(EQ 8.20)Therefore:(EQ 8.21)Substituting this value into equation 8.19, we get:(EQ 8.22)Or alternately,(EQ 8.23)The value can be expressed as:(EQ 8.24)In the above equation, CA(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 voltagesare in per-unit of nominal bus phase-to-ground voltage, so VSpg can be taken as 1 when the system is normal (not faulted).Note however that under external fault conditions sensitivity may be much different from the non-fault sensitivity.C AC1A C2AC1A C2A+---------------------------= or C2AC A C1AC1A C A–------------------------=V OP A V Spg 1 k AC AC2A----------–=V Spg 1 k AC1A C A–C1A------------------------–=ddC A-----------V OP 2A V SpgddC A----------- 1 k AC1A C A–C1A------------------------– =V Spgk AC1A----------=V Spgk AC1A----------=k AC2AC A---------- C1AC1A C A–------------------------= = or C 1A k A C1A k A C A–=C1Ak A C Ak A 1–---------------=ddC A-----------V OP 2A V Spgk AC1A----------=V Spgk A 1–C A---------------=dV OP 2A V Spg= k A 1– dC AC A-----------V OP 2A pu V Spg pu k A 1– C A pu =
