Generalized Vector Locus Transformation for Unbalanced Three-Phase Systems
This work addresses the problem of simplifying computations in unbalanced three-phase power systems, which is important for power system analysis and control.
The paper proposes a Generalized Vector Locus (GVL) transformation for unbalanced three-phase systems that ensures both a null zero-coordinate and constant-valued signals, overcoming limitations of existing transformations. The GVL transformation generalizes the classical Clarke transformation, which is recovered in the balanced case.
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.