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This paper presents a new variation of selective harmonic elimination (SHE) technique for cascaded multilevel converter with variant DC voltage sources. The paper formulates the problem in a way which the levels of the DC sources are made variables within certain constraints. Therefore, the degrees of freedom for specifying the cost function are doubled when compared to existing family of techniques and for the same physical structure. Moreover, the proposed formulation provides an output with wider range of modulation indices without affecting the number of harmonics being eliminated. The theoretical findings are validated through extensive simulation studies.