Multilevel synchronous optimal pulsewidth modulation generalized formulation

With the growing interest of the industry in high power medium voltage multilevel inverters and the technological limitation in high voltage power semiconductors switches, the synchronous optimal pulsewidth modulation technique, originally developed for two/three-level inverters, became once again a topic of interest, now to optimize multilevel waveforms. This work proposes a new formulation for the problem of optimizing the modulation pattern of multilevel converters, including in a single optimization problem the decision of the directions for each step transition in addition to the switching angles and, thus, completely defining the optimized multilevel waveform for a given modulation index.