Symmetrical-Components Analysis of the Four-Phase System

Symmetrical-components concepts are developed for the currents, voltages, and impedances of a four-phase system, and formulas are given for various types of short circuits. The idea of symmetry among the members of each set is based on the angular displacement between the members of the set, rather than that of phase rotation which fits the three-phase case very nicely but is inadequate for the four-phase case. Aside from its possible value for four-phase problems, which are rather rare, the paper is presented here in the expectation of an additional benefit, namely, that the parallelisms and contrasts between the four-phase and the three-phase formulas may throw further light on the general theory and applications of symmetrical components.