Harmonic elimination for constrained optimal PWM

The Selected Harmonic Elimination (SHE) Pulse-Width Modulation (PWM) inverter eliminates low-order harmonics by optimizing the distribution of switching angles and can generate high quality output waveforms. The goal of optimal SHE-PWM is to select the switching instances (angles) in such a way that a waveform with a particular characteristic is obtained and a certain criterion is minimized. To keep the results realizable in hardware, it is required that the computed consecutive switching angles are sufficiently distant from each other. This well-separation feature is not controlled by classical SHE-PWM algorithms. In this paper, a new algorithm is proposed to solve the SHE-PWM problem with a constraint that any two consecutive solutions are well separated. The algorithm first transforms the problem into a constrained optimization problem, then uses the Differential Evolution (DE) algorithm to find the roots with the necessary distance of separation. Since the obtained switching angles are reasonably distant from each other, the inverter switches have enough time to operate and can properly finish the switching transitions. Essentially, the proposed method computes the best possible tradeoff between the maximum error for system performance and the minimum distance between consecutive switching angles under certain constraints and it is robust.