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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.