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arXiv · 2406.15106

Generalized Vector Locus Transformation for Unbalanced Three-Phase Systems

Maitraya Avadhut Desai·Francisco Escobar·Gabriela Hug
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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.

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BibTeXRIS

Maitraya Avadhut Desai, Francisco Escobar, Gabriela Hug. 2026-07-07. Generalized Vector Locus Transformation for Unbalanced Three-Phase Systems. https://arxiv.org/abs/2406.15106

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