CHAPTER 9: THEORY OF OPERATION OVERVIEWC70 CAPACITOR BANK PROTECTION AND CONTROL SYSTEM – INSTRUCTION MANUAL 9-119Figure 9-5: Phase current unbalance applicationThe protection operates when the operate signal is greater than the set pickup level for the set pickup delay. Identicalrelations apply to phases B and C.Sensitivity is the key performance parameter. The applied comparator uses a simple integration method in addition to thestandard hysteresis approach, to deal with chattering of the operating signal at the boundary of operation.9.1.5.2 Balanced caseTo understand phase current unbalance protection, first note that the currents are driven by the individual admittances ineach string:Eq. 9-44In these equations, Ibase represents the differential CT primary current rating. This places the string currents on the sameper-unit base used by the C70. Voltages are expressed in primary volts, capacitances in Farads, and frequency in radiansper second.The differential current is the vector difference between the two currents:Eq. 9-45The total phase current is the vector sum of the two currents:Eq. 9-46Inserting equation 9.46 into equation 9.45, to eliminate the voltages, we get:Eq. 9-47834747A1.CDRI B1IAI DIF(A)window CTgrounded orungroundedC B1IA2C A2IA1CA1I C2C C2I C1CC1IB2C B2IB I CI DIF(B)window CTI DIF(C)window CTVXVAI A1jωC A1 V A V X–( )I base-----------------------------------; I A2jωC A2 V A V X–( )I base-----------------------------------= =I DIF A( ) I A1 I A2–=jω V A V X–( ) C A1 C A2–( )I base-----------------------------------------------------=I A I A1 I A2+=jω V A V X–( ) C A1 C A2+( )I base------------------------------------------------------=I DIF A( ) I AC A1 C A2–C A1 C A2+----------------------×=
