Abstract: The selective harmonic elimination(SHE) based staircase modulation is a commonly used fundamental frequency modulation strategy for multilevel converters.However,the solutions to the staircase SHE equations cannot cover the full range of modulation index,which limits the applications of this modulation method.In order to solve this problem,this paper extends the staircase switching pattern to the general switching patterns,in which,the Groebner bases method is used to solve the SHE equations,and the achievable range of modulation index and the complete solutions for each switching patterns are obtained.By evaluating the total harmonic distortion,the optimal switching pattern and the corresponding optimal switching angles can be identified for the modulation indices in full range.Experiment results verify the correctness of the proposed method.