Time-frequency single-phase power components measurements for harmonics and inter-harmonics distortion based on Wavelet Packet transform; Part I: Mathematical formulation

This paper represents the first part of a two-part study focusing on power components measurement in the time-frequency domain using Wavelet Packet Transform (WPT). The recommended power components that are contained in the IEEE Standard 1459-2010 [I] are derived based on the Fourier transform approach, which produces inaccurate results in the case of interharmonic distortion. On the other hand, the "in-phase quadrature" approach that is defined in the time-domain can provide accurate values only for the total active power, total nonactive power and total apparent power, while the remaining power components in this standard cannot be evaluated using this approach. This paper proposes redefining the recommended power components in [I] using the "in-phase quadrature" approach in the time-frequency domain using WPT. This allows the evaluation of the all the recommended power components in both time and frequency domains while providing more accurate results than Fourier transform based approach, especially in case of inter-harmonic distortion. Moreover, defining those power components in the time-frequency domain provides a complete time-frequency picture for these components. This can be useful for many power system applications such unreal-time monitoring of active and residual currents at each frequency, selective switching of harmonic, inter-harmonic elimination, instantaneous non-active power compensation and power quality evaluation.