The criterion for determining number of harmonics of finite Fourier series approximating voltages and currents of transformer

Abstract

The results of measurements of the transformer voltages and currents are often approximated by Fourier series. The accuracy of the approximation depends on the number of retained harmonics. The criterion for determining the number of harmonics of a finite Fourier series is proposed in the article. The correlation coefficient between measurements (in the form of digital data arrays) and their approximation by a finite Fourier series is equal to one. The resulting approximation relative error estimation does not exceed 0,31 %. The working capacity of the criterion in the ranges of variation of the Total Harmonic Distortion for current (3,27…70,97) % and the voltage (0,19 ... 9,29) % is shown. It is established that a decrease in the current correlation coefficient to 0,996...0,947 (with a decrease in the number of harmonics in comparison with the calculated one) leads to an increase in the estimation of the relative error of approximation to (8,27...29,65) %. The proposed criterion
can be used: a) in the study of periodic steady-state processes in the transformer both in idling mode and under load; b) to determine the dynamic magnetic properties of soft magnetic materials.