Determination of Coefficients of Decomposition of a Nonlinear Characteristic into a Power Series

The problem of monitoring the parameters of nonlinear elements included in various electrical devices is considered. A new algorithm for reproducing the nonlinear current-voltage characteristic of a device based on the measurement results has been proposed and investigated, which has several advantages over the known ones, allowing, in particular, to obtain an analytical representation of the current-voltage characteristic in real time. The proposed algorithm is based on the direct determination of the coefficients of the polynomial approximation of the current-voltage characteristic. A review of scientific research done to date by other authors dealing with this problem has also been carried out. Formulas for determining the amplitudes of current harmonics through power series coefficients and voltage amplitudes on a nonlinear element are obtained. Binomial coefficients are used to facilitate intermediate calculations. The relations for the zero, odd and even harmonics of the current are obtained, as well as analytical expressions for the coefficients of the polynomial approximation. An experimental study of the proposed method was carried out, according to the results of which an assessment of its accuracy was made. The use of the proposed method significantly simplifies the processing and reduces the measurement time of nonlinear VAC.