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Half-cycle symmetry selective-harmonic-elimination pulsewidth-modulation (SHE-PWM) problems may have a large number of valid solutions, which are beneficial to the optimization design. This paper proposes a novel generalized formulation of half-cycle symmetry SHE-PWM problems for multilevel inverters. The advantages of the proposed formulation include simplicity in format, flexibility in PWM waveforms, and a broad solution space. A method to obtain initial values for the SHE-PWM equations according to the reference modulation index M and the initial phase angle of output fundamental voltage is proposed and investigated thoroughly. Take a five-level inverter with M = 0.75 as an example; six sets of solutions for two typical initial phase angles of 0° and 90° are presented. Simulations and experiments are carried out. It is demonstrated that the experimental results agree well with simulated ones, which proves the validity and practicability of the new method proposed.