The Evaluation of Electric Power by Separate Analysis of Fourier Transform Components

Abstract

This paper presents a substantiation of an approach for the evaluation of components of apparent power and intended to simplify the computational procedures which usually should be implemented in order to process the preliminary sampled waveform of instantaneous power. The results of carried out studies have shown that both active and reactive power can be calculated by the analysis of calculated components of sine and cosine Fourier transforms. This paper also presents the discussion of restrictions, which should be imposed on the duration of the analyzed signal and on frequencies of the auxiliary trigonometric functions, which are applied in order to calculate components of Fourier transform which are used for the evaluation of active and reactive power. The compliance with these restrictions allows us to eliminate the undesirable bias of active and reactive power estimation caused by the refusal from the decomposition of the analyzed waveform of the instantaneous power by applying the complete system of orthogonal trigonometric functions, as the evaluation of components of the apparent power is attained based on separate analysis of sine and cosine Fourier transforms calculated for the analyzed signal. The results of carried out simulations illustrate the frequency dependencies of sine Fourier transform calculated for the case of compliance with the restrictions, which allow to attain the highest accuracy of estimation and for the case when the duration of analyzed signal does not fit these restrictions.