Reconstruction of spectrum of the nonlinearly distorted periodic signals sampled non-coherently

Factors characterizing the electrical energy quality (e.g. THD) are determined on the basis of voltage and current signals spectrum. The spectrum estimation errors come from the spectrum leakage caused by the non-coherent sampling and distortions appearing in the input circuits of the measuring system. This paper concerns the problem of accurate reconstruction of the nonlinearly distorted signal spectrum. The proposed method of the periodic input signal reconstruction (e.g. the CT primary current) is based on the modeling of the nonlinear system in a periodic steady state by a set of circular parametric operators (CPOs). This method requires coherent sampling of the measured signal that is inconvenient because of the electro-energetic system natural frequency changes. To avoid this limitation the reconstruction calculations are transferred to the spectral domain. The spectrum of the reconstructed signal is determined by means of the spectral version of the CPO (i.e. the SCPO) on the basis of the spectrum of the distorted signal. A modified discrete Fourier transform (MDFT) is used to determine the distorted signal spectrum. The MDFT is designed for the non-coherently sampled signal high accuracy spectrum analysis. The DFT modification idea consists in the adjustment of base function frequencies of the Fourier series to the analyzed signal harmonics frequencies. Some results of experiments are included.