A Complete Solution to the Harmonic Elimination Problem

TLDR

The harmonic elimination problem in switching converters is addressed. The goal is to determine switching angles that achieve a desired fundamental voltage while suppressing selected harmonics. The authors transform the transcendental equations into polynomial form and use resultant theory to enumerate all solutions. They find all possible solutions—including previously unknown ones—and present complete solutions for unipolar and bipolar patterns eliminating fifth and seventh harmonics, with experimental confirmation for the unipolar case eliminating fifth, seventh, 11th, and 13th harmonics.

Abstract

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.