9-4 C70 CAPACITOR BANK PROTECTION AND CONTROL SYSTEM – INSTRUCTION MANUALOVERVIEW CHAPTER 9: THEORY OF OPERATION9Figure 9-2: Voltage differential application to grounded and ungrounded banksThe voltage differential protection uses the following operating signal for grounded banks:Eq. 9-7The voltage differential protection uses the following operating signal for ungrounded banks:Eq. 9-8In these equations, kA is a match factor setting for the A-leg of the bank. The voltages are as defined in the precedingfigure and are in per-unit values on the nominal bus phase-to-ground voltage base. The first equation is implementedusing primary voltage magnitudes, while the second equation is implemented using primary voltage phasors. Theprotection operates when the operate signal is greater than the set pickup level for the set pickup delay.Identical relations 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.9.1.3.2 Balanced caseTo understand how the voltage differential protection works, consider for simplicity the following grounded bank operatingequation:Eq. 9-9The ungrounded case is similar except that all voltages have VX subtracted. If the initial factory balanced A-leg string hasan initial capacitance of CA , divided into sub-strings with initial capacitances of C1A and C 2A , and the bank is energizedwith system phase-to-ground voltage V Spg , then the string forms a voltage divider and the initial measured voltages are:Eq. 9-10Eq. 9-11834750A1.CDRGrounded bank Ungrounded bankV2AV1AABCC1AC2AC AVXV2AV1AABCC1AC2AC AV OP A( ) V 1A k A V 2A–=V OP A( ) V 1A V X–( ) k A V 2A V X–( )–=V OP A( ) V 1A k A V 2A–=V 1A V Spg=V 2A V SpgC AC 2A--------×=
