Symmetrical components in the time domain and their application to power network calculations

Although the symmetrical component transformation has existed for 80 years, its application in the time-dependent form is practically restricted to the electric-machine theory. In the power systems field one uses the transformation applied to steady-state sinusoidal phasors in a nonunitary form for fault calculations. For time-domain calculations the real equivalent, 0, α, β, is preferred, usually extended to 0, d, q-components. In network calculations, however, the application of time-dependent symmetrical components makes sense, since many net-component parameters are already available in this form. In this paper a short historical overview of the symmetrical-component transformation and the application of unitary and orthogonal transformations are presented. From these general transformations logic choices for base quantities necessary in per unit calculations are derived. The relations between real and complex transformations, steady-state phasors and well-known sequence networks are given and illustrated through the use of some examples with asymmetrical faults