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Selective harmonic elimination pulsewidth modulation techniques are some of the control methods used in voltage/ current source converters. However, challenges such as the task of finding all the multiple sets of solutions of the switching angles for a given problem may be difficult to deal with. In this paper, a direct minimization of the nonlinear transcendental trigonometric Fourier functions in combination with a random search is discussed. The unipolar (three-level) waveform is used to illustrate the proposed method confirming its ability to find multiple sets of solutions, including a case where 51 angles are sought for single- and three-phase applications. A simple harmonic distortion factor is studied for each set of solutions to assess their performance against the noneliminated harmonics. The results presented both at theoretical and experimental level are in close agreement and confirm the robustness of the proposed approach. Index Terms--Function minimization, inverter control, pulsewidth modulation, selective harmonic elimination.

A five-level symmetrically defined multilevel selective harmonic elimination pulsewidth modulation (MSHE-PWM) strategy is reported in this paper. It is mathematically expressed using Fourier-based equations on a line-to-neutral basis. An equal number of switching transitions when compared against the well-known multicarrier phase-shifted sinusoidal PWM (MPS-SPWM) technique is investigated. For this paper, it is assumed that the four triangular carriers of the MPS-SPWM method have nine per unit frequency resulting in seventeen switching transitions for every quarter period. For the proposed MSHE-PWM method, this allows control of sixteen harmonics and the fundamental. It is confirmed that the proposed MSHE-PWM offers significantly higher converter bandwidth in the standard range of the modulation indices. Moreover, when the bandwidth is reduced to be equal with the one offered with the MPS-PWM, the modulation index can be increased resulting in a higher gain and at a reduced switching frequency overall. Selected solutions for the switching transitions are presented and verified experimentally in order to confirm the effectiveness of the proposed technique. Index Terms--Multilevel Converter, optimization, phase-shifted sinusoidal pulsewidth modulation (PS-PWM), pulsewidth modulation (PWM), selective harmonic elimination (SHE).