GE Multilin C70 Capacitor Bank Protection and Control System 8-58 THEORY OF OPERATION 8.1 OVERVIEW8In the above equation, ΔCA(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, ΔCA(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 AΔ× pu( )=
