Haar wavelet-based decomposition of nonactive power for nonsinusoidal waveforms

This paper deals with some key properties of the nonactive power resulting from non-sinusoidal periodical voltage and current waveforms represented by using discrete samples. The Haar wavelet-based decomposition of the waveforms, written in a form consistent with a multi-resolution approach, provides the transformed voltage and current vectors. These vectors are used to build a suitable antisymmetrical matrix, from whose off-diagonal elements, containing information on both phasor displacement and waveform distortion aspects, it is possible to obtain the nonactive power of the circuit. In particular, the elements of this matrix can provide a detailed view on the nonactive power components by conserving the same total nonactive power computed from voltages and currents in the time domain. The paper discusses the effects of the decomposition of the nonactive power into several components associated to the wavelet multi-resolution approach. Illustrative examples are provided to show the properties of the Haar transformation-based representation applied to calculating the nonactive power components in the presence of distorted voltage and current waveforms with different amplitudes and phase angles of the harmonics.