Analysis of unbalanced polyphase networks by the method of phase co-ordinates. Part 1: System representation in phase frame of reference

The analysis of unbalanced-power-system problems depends usually on transformation methods by which the primary or phase quantities are substituted by, for example, symmetrical-component quantities. These transformations have had computational advantages in the past, but with the use of the digital computer, they no longer appear to be necessary. Investigations into system-unbalance problems and their solution using only the actual system phase voltages, currents and impedances show that a major difficulty concerns the representation of transformers. In this paper the principles of transformer models in phase co-ordinates are derived and applied to the development of the phase equivalent circuits of a number of balanced and unbalanced polyphase multiwinding transformers. The basic element of these equivalent circuits is shown to be a symmetrical lattice network that is bilinear in all cases except for quadrature boosting transformers. With these equivalent circuits and with the phase representations of the transmission lines, generators and other system components it is then possible to solve unbalanced polyphase network problems entirely in phase co-ordinates, retaining symmetrical components only as measures of system unbalance.