Spectral Analysis of Multilevel PWM Strategies Using a One-Dimensional Fourier Series

Abstract

This paper presents a novel spectral analysis technique for multilevel modulation. Conventionally, such analyses use a double Fourier series technique, but this approach can become intractable when complex reference waveforms (e.g., multilevel space vector offsets) and regular sampling processes are considered. In contrast, the strategy proposed in this paper separates the multilevel pulse width modulation (PWM) waveform into a spectral image of the reference, and sideband basis functions which are then expanded using a one-dimensional Fourier series. The coefficients of this Fourier series are defined by a one-dimensional Fourier integral that is simpler in form compared to the corresponding double integral associated with the double Fourier series. This analysis technique naturally incorporates regular sampling, and a discrete formulation is developed that enables complex PWM reference waveforms, including centered space vector offsets, to be solved. Results of this analysis are validated against previously published multilevel inverter double Fourier series results and matching switched simulations.