Application of clarke's transformation to the modal analysis of asymmetrical single‐circuit three‐phase line configurations

Abstract

AbstractThis paper addresses three interrelated topics concerning the modal analysis of asymmetrical single‐circuit three‐phase transmission lines. The subject of the study is a three‐phase overhead line whose set of conductors lie on a plane arbitrarily tilted with respect to the ground surface. Varying the angle of tilt from zero to ninety degrees transforms a flat line into a vertical line configuration. The first topic discussed is the dependence of the exact modal parameters (attenuation, phase velocity, eigenvectors) on the tilt angle measuring the line asymmetry degree. The second topic deals with the well‐known Clarke transformation which can be used to successfully diagonalize ZY matrices other than those describing balanced lines. The third topic refers to the computation of approximate modal parameters for the asymmetrical tilted line, using a very simple perturbation theory approach based on the Clarke transformation. Illustrative computation results reveal that the exact and the approximate modal parameters match well, although errors tend to increase with increasing line asymmetry.