The analysis of the solutions for harmonic elimination PWM bipolar waveform with a specialized differential evolution algorithm

The selective harmonic elimination pulse-width modulation (SHE-PWM) offers multiple solutions depending of the number of switching angles or problem formulation, each one with different harmonic performance. This paper proposes a novel approach to the SHE-PWM problem, using a minimization technique based on a specialized evolutionary algorithm that can find all solutions for a given modulation index. The algorithm, based on the Differential Evolution (DE), is tested on the bipolar waveform with quarter-wave symmetry for three-phase inverters. In order to provide a complete analysis of the solutions, four performance indicators are used: a harmonic distortion factor that takes into account the first two (HDF2) and the first four (HDF4) significant harmonics, the total harmonic distortion (THD) and weighted THD (WTHD) of the output line voltage. The distribution of the switching angles in the first quarter-period is also analyzed and a general formulation that allows the identification of the best solution from the ones found for N switching angles is proposed.