CHAPTER 10: THEORY OF OPERATION FAULT LOCATORL30 LINE CURRENT DIFFERENTIAL SYSTEM – INSTRUCTION MANUAL 10-2110Figure 10-9: Equivalent system for fault locationThe following equations hold true for this equivalent system.Eq. 10-37wherem = sought pu distance to faultZ = positive sequence impedance of the lineIF = fault current flowing through the fault pointThe fault network during a fault can be decomposed into a pre-fault and a pure-fault network. Therefore, the fault currentIF is calculated as follows by using the current division rule in the pure-fault network.Eq. 10-38whered is the current distribution factor, which is a complex valueSubstituting the second equation into the first equation and multiplying both sides by the complex conjugate of IAF,Eq. 10-39where* denotes complex conjugateAssuming the system is homogeneous, d is then a real number. The fault resistance does not have any imaginary part. Thepreceding equation solved for the unknown m yields the following fault location algorithm:Eq. 10-40whereIm( ) stands for the imaginary part of a complex numberDepending on the fault type, appropriate voltage and current signals are selected from the phase quantities beforeapplying the preceding equation (the superscripts denote phases, the subscripts denote stations).For AG faults:Eq. 10-41
