General formula for SHE problem solution

Abstract

This paper considers cascaded H-bridges multilevel inverters with 2n dc sources, n integer, n >0 and proposes a new general formula to compute those 2n switching angles capable of eliminating n + 1 harmonics and their respective multiples from the output voltage waveform. The proposed procedure uses only scalar products and avoids linear systems, therefore it has a low computational cost. Computed angles do not depend on modulation index, moreover, voltage sources vary linearly. A mathematical proof is given to validate the formula. Three-phase implementations eliminate or mitigate a significant amount of low order harmonics, thus resulting in very low total harmonic distortion. The proposed formula has been experimentally validated using a single-phase nine-level cascaded H-bridge inverter prototype, resulting in a Total Harmonic Distortion (THD) of 5.59%; the first not-mitigated harmonic is the 17th.