Analysis and modeling of time-varying harmonics in frequency domain

Analysing and modeling of time-varying harmonics in the frequency domain are discussed in this paper. In the analysis and modeling, harmonics are considered as complex quantities. For this purpose, a practical definition for the harmonic phase angle is presented. Afterwards, some aspects related to the application of the proposed definition are discussed. Based on the proposed definition, an approach is suggested to take account of the phase shift due to transformer vector groups in harmonic calculations. Furthermore, the modeling of the time variation of harmonics in the frequency domain is addressed. Considering harmonics as random complex quantities, the time variation of the harmonic amplitude and phase angle can be probabilistically modeled. In this regard, two analogous methods are presented to derive the probability distribution function for a given time series of harmonics. In these methods, amplitudes and phase angles are considered as two statistically dependent quantities.