Analytical expression for voltage drops on return paths of ground-fault current when faults occur in transmission line

The paper presents an original analytical expression for the estimation of the voltage drops on the return paths of the ground fault current when the fault occurs at any point of an arbitrarily long overhead line. The expression includes all paths (ground wire(s), towers and stations grounding electrodes) used by the ground fault current to return to its sources. The derivation of the expression is based on the equations for solving uniform lumped parameter ladder circuits of any size and under any terminal conditions. As a general illustration, an analysis of a faulted, double-fed, three-phase line is provided. As a rule, modern digital fault location algorithms are based on the assumption that the ground fault return paths are purely resistive. A more realistic representation of the influence of the ground fault current return paths certainly leads to an increased accuracy of the fault locator.