Generalized Vector Locus Transformation for Unbalanced Three-Phase Systems

TL;DR

This paper introduces a generalized vector locus transformation for unbalanced three-phase systems that guarantees a null zero-sequence component and constant signals, improving upon classical transformations especially in unbalanced conditions.

Contribution

The paper proposes a novel generalized transformation that ensures both null zero-sequence and constant signals, unifying and extending classical methods for unbalanced systems.

Findings

Ensures null zero-sequence component in unbalanced systems

Produces constant-valued signals in the dq0 domain

Recovers classical Clarke transformation in balanced cases

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 still do not lead to constant-valued signals in the dq0 domain. In this letter, we propose a generalized vector locus 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 transformation.