Current decomposition in asymmetrical, unbalanced three-phase systems under nonsinusoidal conditions

The most attractive theories found in the literature for the representation of the electrical systems under nonsinusoidal conditions can be divided to a great extent into those operating in the time domain and those operating in the frequency domain. When three-phase systems are concerned, the time-domain approach is mainly due to Akagi and Nabae under the name of “instantaneous power theory” or “p-q theory” and is based on the Park transformation. The frequency-domain approach is mainly due to Czarnecki. At a first reading, these two theories seem to be quite different. This paper shows how the application of some interesting properties of the Park transformation leads to a unified approach to the harmonic and sequence components and hence allows derivation of the frequency-domain current decomposition proposed by Czarnecki in a more straightforward way. Moreover, an extension of this decomposition to the case of asymmetrical supply voltages is considered