Space-vector state-equation analysis of three-phase transients

Abstract

This paper investigates the analysis of transients in three-phase systems by means of the Clarke transformation. Under the commonly accepted assumption of phase symmetry (i.e., three-phase basic elements with symmetrical parameters), the alpha and beta dynamic circuits are independent and characterized by the same circuit parameters. Thus, since the space vector is defined as the combination of alpha and beta variables, the state equation approach based on space vector variables results in an effective tool for three-phase transient analysis. In fact, the space vector approach presented in this work exploits the system symmetry providing state equations with reduced dynamic order. Moreover, it is shown that the space vector shape on the complex plane provides a concise and rich representation of the transients of the three phase variables. Indeed, despite the assumption of system symmetry, it is shown that the transient behavior of the three phase variables is not symmetrical. In particular, maximum over voltages and over currents can be easily detected from the space vector shape. Numerical examples are presented in order to show the effectiveness and adequacy of the general methodology presented in this work for the analysis of three-phase dynamic circuits.