Proceedings of the PowerUp Conference

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.