Reduced Reference Frame Transform: Deconstructing Three-Phase Four-Wire Systems

Abstract

This paper proposes a new reference frame, namely Reduced Reference Frame (RRF), specially suited for unbalanced three-phase four-wire systems which improves the performance of the classical Fortescue, Clarke and Park transformations. The RRF transfomation allows to represent any unbalanced three-phase sinusoidal magnitude with just two components even if the zero-sequence component is present. For doing so, the RRF transformation takes into account that the abc space-vector trajectory of the transformed three-phase sinusoidal magnitude is always within a plane. The geometric properties of this trajectory are considered for outlining a general classification of the transformation depending on the input voltages and an adequate reference frame within the plane. Then, a step-by-step procedure for computing the transformation matrix is detailed. Once the voltages and currents are transformed into the RRF, it is proposed a power theory which allows to compute the instantaneous active and reactive powers. The paper includes two simulations and an experimental validation through a real-time application to highlight the benefits of the proposal. The paper closes with the main conclusions and some future research lines where this transformation can be applied.