Reduced Reference Frame Transformation Assessment in Unbalanced Three-Phase Four-Wire Systems

Three-phase four-wire systems require a reference frame similar to that used in 3-phase 3-wire system configurations that allow them to be easily analysed, modelled and controlled. A new reference frame called Reduced Reference Frame (RRF) was presented by the authors in a previous work to satisfy these objectives. This is based on the locus of the voltage space vector which is used to perform a transformation applied to 3-phase 4-wire systems. This paper uses the proposed RRF to demonstrate the benefits of this transformation under different conditions of load or voltage imbalance. To this end, the different types of imbalances considered are studied by comparing the results in the classical
$\alpha \beta \gamma $
axes, the so-called
$mno$
-transform specifically developed for 3-phase 4-wire systems and the RRF coordinates. In addition, a theoretical identification of some types of imbalances is done comparing the simulation results and the fundamentals of the RRF.