Current and voltage loci in 3-phase Y-Y circuits

Engineers often find it convenient to be able to determine the various currents and voltages in an electrical system not merely for one fixed condition, but for any value of any impedance element from zero to infinity. In an effort to facilitate such computations, the method presented in this paper has been developed. Although the method as presented is applied specifically to the star-star (Y-Y) circuit, the treatment is said to be applicable also to other circuits. All voltages and currents in this circuit are shown to follow circular loci when any self-impedance is varied; these loci are determined by the use of a circle in the form of a linear fractional transformation. The practical application of the method is illustrated by numerical examples.