Waveform Quality Evaluation Method of Variable-Frequency Current Based on Curve Fitting

Since total harmonic distortion (THD) is mainly used as the evaluation index for the waveform quality of periodic signals, it cannot be applied to variable-frequency signals. However, there is scarce research on the evaluation methods and indicators of variable-frequency signals in the literature. In this paper, an evaluation method of the waveform distortion (WD) of variable-frequency signals based on curve fitting is proposed. First, the variable-frequency current expression of the coefficients to be optimized is obtained through theoretical derivation. Second, the coefficients are optimized by curve fitting in the time domain through the nonlinear least-squares method. Then, the waveform distortion of the variable-frequency current (I-WDVF) is calculated. In order to validate the proposed evaluation method, the simulation model of a synchronous motor driven by a cascaded H-bridge five-level inverter is built. The simulation results show that, for the same constant-frequency current, the current THD (I-THD) obtained by the FFT method is the same as the current WD (I-WD) obtained by the curve fitting method, which verifies the equivalence of the two methods. The influence of different sampling frequencies on the I-WD and I-THD is compared. The higher the sampling frequency, the more sampling points, and the more accurate the results. For the linear variable-frequency current, the I-WDVF obtained by the curve fitting method is close to the average value of the I-THD obtained by FFT, which indicates that the time-domain curve fitting method is reasonable to solve the I-WDVF. For nonlinear variable-frequency current waveforms, the curve fitting method can also reasonably calculate the I-WDVF. The curve fitting method can solve the evaluation problem of the variable-frequency current, and provide an evaluation means for the optimal design of a modulation strategy aiming at the optimal waveform quality of the variable- frequency current.