A universal formulation for selective harmonic elimination PWM with half-wave symmetry for multilevel voltage source converters

Selective harmonic elimination (SHE) - pulse with modulation (PWM), when applied to multilevel converters (MCs), can be optimized in case a half-wave (HW) symmetry is implemented. This kind of symmetry is able to provide a wide variety of solutions. This paper proposes a novel method, based on optimization algorithms, which provides a universal formulation of the SHE-PWM problem with HW symmetry, in such a way that different equation systems are not required to find a solution when different switching patterns are considered. In this way, the proposed technique is able to search simultaneously both the switching patterns and their associated firing angles that solve the SHE-PWM problem, without using predefined waveforms. Therefore, the search process is significantly simplified and the flexibility to find solutions with different waveforms, throughout the reference modulation index, ma, range, is increased. Different sets of solutions provided by this method have been presented and simulation results, obtained from a five-level modular multilevel converter (MMC), have proved the validity of the new proposed technique.