Symmetrical Components Using Matrix Methods

The method of symmetrical components has been an important tool for the study of unbalanced three‐phase systems, unsymmetrical short‐circuit currents, models of rotating machines and transmission lines, etc. This chapter studies three‐phase balanced systems, by considering these as single‐phase system. The simplicity of representing a three‐phase as a single phase system is lost for unbalanced systems. There have been two approaches for the study of symmetrical components: A physical description, without going into much mathematical matrix algebra equations. The mathematical approach is adopted in this chapter. Symmetrical component method is a transform. There are three steps that are applicable in any transform for the solution of a problem. The matrix theory can be applied to understand some fundamental aspects of symmetrical components. The chapter also discusses the similarity transformation, symmetrical component transformation, and Clarke component transformation. The significance of symmetrical components is illustrated with an example.