Generalization of selective harmonic control/elimination

Previous work on selective harmonic elimination/control has made fundamental assumptions that enforce output waveform quarter- or half- wave symmetry, presumably in order to reduce the complexity of the resulting equations. However, the quarter- or half-wave symmetric assumption is not required and it restricts the solution space, which can result in sub-optimal solutions with regard to the uncontrolled harmonic distribution. More general formulations can be proposed which have varying degrees of additional complexity. In order to understand how these more general formulations can be obtained, a qualitative description of the waveform construction process for the two-level waveform case will be discussed followed by presentation of the resulting system of equations. This two-level case is then generalized to the m-level, n-harmonic control problem. Finally, this generalization is used to analyze three-level waveforms. All solutions presented in this paper are unattainable utilizing previous techniques.