Three Dimensional Space Vector Modulation Theory: Practices without Proofs

Abstract

In three dimensional (3D) space vector modulation (SVM) theory with α-β-γ frame there are some issues which are well known and are widely practiced being quite obvious but without any proof so far. In this paper necessary scientific foundations to those issues have been provided. The foremost of these issues has been with the frame of reference to be considered in 3D SVM applications for unbalanced three phase systems. Although for balanced three phase systems there has been no controversy with α-β frame as the frame of reference but in 3D it has not yet been established which one, α-β-γ frame or the a-b-c frame, is mathematically correct. Another significant issue addressed in this work has been to ascertain the exact reason when a three phase system has to be represented in 2D or 3D space to apply SVM. It has been presented for the first time in this work that the key factor that determines whether 3D or 2D SVM has to be applied depends on the presence of time independent symmetrical components in a three phase ac system. Also it has been proved that the third axis, the Y–axis, represents the time independent quantity and that it must be directed perpendicular to the α-β plane passing through the origin.