A unified approach to solving the harmonic elimination equations in multilevel converters

A method is presented to compute the switching angles in a multilevel converter so as to produce the required fundamental voltage while at the same time not generate higher order harmonics. Using a staircase fundamental switching scheme, previous work has shown that this is possible only for specific ranges of the modulation index. Here it is shown that, by considering all possible switching schemes, one can extend the lower range of modulation indices for which such switching angles exist. A unified approach is presented to solve the harmonic elimination equations for all of the various switching schemes. In particular, it is shown that all such schemes require solving the same set of equations where each scheme is distinguished by the location of the roots of the harmonic elimination equations. In contrast to iterative numerical techniques, the approach here produces all possible solutions.