8-2 C60 BREAKER PROTECTION SYSTEM – INSTRUCTION MANUALFAULT LOCATOR CHAPTER 8: THEORY OF OPERATION8m = sought pu distance to faultZ = positive sequence impedance of the lineThe currents from the local and remote systems can be parted between their fault (F) and pre-fault load (pre) components:Eq. 8-2and neglecting shunt parameters of the line:Eq. 8-3Inserting the IA and IB equations into the VA equation and solving for the fault resistance yields:Eq. 8-4Assuming the fault components of the currents, IAF and I BF are in phase, and observing that the fault resistance, asimpedance, does not have any imaginary part gives:Eq. 8-5where Im() represents the imaginary part of a complex number. Solving this equation for the unknown m creates thefollowing fault location algorithm:Eq. 8-6where * denotes the complex conjugate and .Depending on the fault type, appropriate voltage and current signals are selected from the phase quantities beforeapplying the preceding two equations (the superscripts denote phases, the subscripts denote stations).For AG faults:Eq. 8-7For BG faults:Eq. 8-8For CG faults:Eq. 8-9For AB and ABG faults:Eq. 8-10For BC and BCG faults:Eq. 8-11For CA and CAG faults:Eq. 8-12where K 0 is the zero sequence compensation factor (for the first six equations).For ABC faults, all three AB, BC, and CA loops are analyzed and the final result is selected based upon consistency of theresults.The element calculates the distance to the fault (with m in miles or kilometers) and the phases involved in the fault.I A I AF I Apre+=I B I BF I Apre–=R FV A m Z I A –I AF 1 I BFI AF------+ -------------------------------=Im V A m Z I A –I AF------------------------------- 0=m Im V A I AF Im Z I A I AF -----------------------------------=I AF I A I Apre–=V A V AA= , I A I AA K 0 I 0A+=V A V AB= , I A I AB K 0 I 0A+=V A V AC= , I A I ABC K 0 I 0A+=V A V AA V AB–= , I A I AA I AB–=V A V AB V AC–= , I A I AB I AC–=V A V AC V AA–= , I A I AC I AA–=
