Generalized Vector Locus Transformation for Unbalanced Three-Phase Systems

Abstract

Coordinate transformations significantly simplify power systems computations. Most notably, the classical Clarke and $dq0$ transformations are widely used in three-phase systems, as together they transform balanced $abc$ quantities into constant-valued signals. However, during unbalanced operation, the utility of these transformations diminishes, since a null $0$-coordinate cannot be ensured and oscillating signals emerge. While recently proposed transformations ensure a null $0$-coordinate, they either do not lead to constant-valued signals in the $dq0$ domain or fail under various unbalanced scenarios. In this paper, we propose a Generalized Vector Locus (GVL) transformation that ensures both a null $0$-coordinate and constant-valued signals. Moreover, we show that, in the balanced case, the classical amplitude-invariant Clarke transformation is an instance of the proposed GVL transformation.