Topological considerations on the symmetrical components transformation

This paper presents the well-known symmetrical components transformation (SCT) by means of a different approach from the traditional matrix analysis: a topological lecture provides, in fact, the results obtained by the existing analysis in a more suitable form for network applications. This approach leaves more space to the intuitive analysis, simplifying the application of such a method for teaching purposes, and completing the traditional mathematical view. Moreover, the use of graph concept allows the unified analysis of unbalanced faults leading the matter to the general theory of balanced three-phase systems. Typical for the physical balanced networks, the real convenience of SCT is also confirmed from the topological point of view, even for the fault analysis.