| Summary: | 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>I<sub>WDVF</sub></i>) 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>I<sub>THD</sub></i>) obtained by the FFT method is the same as the current WD (<i>I<sub>WD</sub></i>) obtained by the curve fitting method, which verifies the equivalence of the two methods. The influence of different sampling frequencies on the <i>I<sub>WD</sub></i> and <i>I<sub>THD</sub></i> 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>I<sub>WDVF</sub></i> obtained by the curve fitting method is close to the average value of the <i>I<sub>THD</sub></i> obtained by FFT, which indicates that the time-domain curve fitting method is reasonable to solve the <i>I<sub>WDVF</sub></i>. For nonlinear variable-frequency current waveforms, the curve fitting method can also reasonably calculate the <i>I<sub>WDVF</sub></i>. 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.
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