In this work, a method is given to compute the switching angles in a multilevel converter to produce the required fundamental voltage while at the same time cancel out specified higher order harmonics. Specifically, a complete analysis is given for a seven-level converter (three dc sources), where it is shown that for a range of the modulation index , the switching angles can be chosen to produce the desired fundamental 1 = (4 dc) while making the fifth and seventh harmonics identically zero.

The problem of eliminating harmonics in a switching converter is considered. That is, given a desired fundamental output voltage, the problem is to find the switching times (angles) that produce the fundamental while not generating specifically chosen harmonics. In contrast to the well known work of Patel and Hoft and others, here all possible solutions to the problem are found. This is done by first converting the transcendental equations that specify the harmonic elimination problem into an equivalent set of polynomial equations. Then, using the mathematical theory of resultants, all solutions to this equivalent problem can be found. In particular, it is shown that there are new solutions that have not been previously reported in the literature. The complete solutions for both unipolar and bipolar switching patterns to eliminate the fifth and seventh harmonics are given. Finally, the unipolar case is again considered where the fifth, seventh, 11th, and 13th harmonics are eliminated along with corroborative experimental results.

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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 converted to polynomial equations which are then solved using the method of resultants from elimination theory. A di culty with this approach is that when there are several DC sources, the degrees of the polynomials are quite large making the computational burden of their resultant polynomials (as required by elimination theory) quite high. Here, it is shown that the theory of symmetric polynomials can be exploited to reduce the degree of the polynomial equations that must be solved which in turn greatly reduces the computational burden. In contrast to results reported in the literature that use iterative numerical techniques to solve these equations, the approach here produces all possible solutions.