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

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.