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This paper proposes a generalized formulation for selective harmonic elimination pulse-width modulation (SHE-PWM) control suitable for high-voltage high-power cascaded multilevel voltage source converters (VSC) with both equal and nonequal dc sources used in constant frequency utility applications. This formulation offers more degrees of freedom for specifying the cost function without any physical changes to the converter circuit, as compared to conventional stepped waveform technique, and hence the performance of the converter is greatly enhanced. The paper utilizes the merits of the hybrid real coded genetic algorithm (HRCGA) in finding the optimal solution to the nonlinear equation system with fast and guaranteed convergence. It is confirmed that multiple independent sets of solutions exist. Different operating points for both five-and seven-level converters including singleand three-phase patterns are documented. Selected experimental results are reported to verify and validate the theoretical and simulation findings.Index Terms-Cascaded multilevel converter, hybrid genetic algorithm, pulse-width modulation (PWM), 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).

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