Analytical Solution of Transients in Single-Line-to-Ground Faults in Three-Phase Power Systems

This paper deals with the analytical evaluation of the transient current in single-line-to-ground fault in a three-phase power system. The proposed methodology, in contrast with conventional numerical techniques, is based on the Clarke transformation working in the time domain. Due to the system asymmetry introduced by the single line fault, the modal circuits alpha, beta, and zero, related to the Clarke transformation, result in coupled circuits. A simple circuit representation of such coupling is derived, allowing straightforward evaluation of the fault current in the Laplace domain. Time domain behavior obtained through inverse Laplace transform is validated by means of Simulink time-domain simulation of single line faults.