The use of power sums to solve the harmonic elimination equations for 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. Previous work has shown that the transcendental equations characterizing the harmonic content can be convened to polynomial equations which are then solved using the method of resultants from elimination theory. However, when there are several DC sources, the degree of the polynomials are quite large making the computational burden of their resultant polynomials via elimination theory quite high. Here, it is shown that by reformulating the problem in terms of power sums, the degree of the polynomial equations that must be solved are reduced significantly which in turn reduces the computational burden. In contrast to numerical techniques, the approach here produces all possible solutions.