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This study presents a novel formulation of multilevel selective harmonic elimination pulse width modulation (MSHE-PWM) technique with optimised DC voltage levels suitable for high-power voltage source converter-based applications. The study reformulates the problem in a way in which the levels of the DC voltage sources are made variables within certain constraints. Therefore the degrees of freedom for specifying the cost function are increased when compared to the existing family of selective harmonic elimination-based multilevel control for the same physical structure. Moreover, with the proposed approach, the solution of the switching angles can be sought for the entire range of the modulation index without affecting the number of harmonics being eliminated or the number of the output voltage levels. The effectiveness of the proposed method is investigated with various waveforms. The theoretical and simulation findings are validated through experimental results.