Mathematical proof of a harmonic elimination procedure for multilevel inverters

In this paper, a single phase cascaded H-bridge inverter with s variable dc sources (s≥2), l=2s+1 levels has been considered. A mathematical proof is presented to demonstrate that, under a particular choice of the switching angles, which number corresponds to the number of dc sources i.e. s, and of the dc voltages, all harmonics are eliminated from the output voltage waveform, except those of order n=4p⋅s±1, p=1,2,…. With this method, the dc voltage sources vary linearly according to the modulation index m, while the switching angles do not depend on m. The resulting output voltage has low total harmonic distortion, that remains independent on m. Compared to a conventional selective harmonic elimination procedure and to a pulse amplitude method, the proposed procedure reduces distortion in a wide range of modulation index.