A Solution for Faults at Two Locations in Three-Phase Power Systems

K N O W L E D G E of the magnitude and phase relation of power system voltages and currents for various types of faults in threephase systems is of importance in the study of various problems, among which are relaying studies, the efficacy of current limiting devices and their reaction on the power network, and estimates of induction in paralleling communication circuits. The method of symmetrical components as developed by Fortescue 1 and others is now extensively used in the solution for currents and voltages in three-phase power systems under fault (short-circuit) conditions. Formulas for special cases of faults, such as single and double line-to-ground faults, can be found in various text books on this subject. The solution for simultaneous faults at two locations has been treated by Miss Clark, 2 in a form particularly adaptable to the use of a calculating board. The present development provides a complete and systematic solution for currents and voltages at times of fault on any number of phases at one or two locations in a three-phase system, in which generators may be assumed in phase and of the same internal voltage, and where load currents can be neglected. These are the usual assumptions made in computing fault currents, except for certain special problems, such as that of power system stability. The methods employed herein could be extended to cases where generators of different phase angles and voltages of more than two points of fault are involved. Formally such cases can be treated in a manner similar to that given in the paper.