Frequency scan on a phase-coordinates frame for unbalanced systems

Abstract

The unbalanced electric networks analysis has upgraded from the sequence components frame models to the phase-coordinates frame models. The electric power distribution systems for industrial plants, commercial buildings or residential costumers can contain several network unbalances that can be easily represented by phase-coordinates models. The phase-coordinates models can be used for the analysis of distribution systems at fundamental frequency as well as for other frequencies and are well suited for the harmonic analysis of unbalanced networks. The formulation of the frequency scan method in a phase-coordinates frame, besides allowing for a more accurate modeling of unbalanced networks, allows the specification of harmonic injections of any type: single-phase or three-phase of the desired sequence. Therefore, it is possible to study the effect of the non-linear loads according to its features and connection to the circuit. This paper develops the phase-coordinates model of an unbalanced distribution power system, considering the representation of three-phase transformer banks of three or two single-phase transformers, as well as other asymmetries that can be found in the electrical systems of industrial plants, commercial or service facilities. The present model improves the representation of the single-phase transformer with mid-tap on the secondary side. The frequency scan based on the present model is tested with a simple example of a four-wire delta system that highlights the possibilities of the model in phase-coordinates.