The problem of locating the distance to a fault can be simply expressed in terms of a single-phase
circuit. This case will be considered first, and the results extended to the case of a phase-toground
fault. The Th´evenin representation of the sources at the two ends of the transmission line is
generators with voltages Er and Es behind impedances Zr and Zs, respectively. Let the phase angles
of Er and Es be δr and δs. The difference between these two angles is primarily responsible for the
prefault load flow in the transmission line. Let Zr represent the impedance of the transmission line
(Figure 13.11). Note that R is the unknown resistance in the fault path. The fractional distance to
the fault is k, which is to be determined as accurately as possible, knowing only the current Ix and
voltage Ex at the relay terminal. If the current in the fault is If = (Is + Ir), the voltage at the relay
location is given by