Harmonic elimination for multilevel converter with Groebner bases and symmetric polynomials

Abstract

Selective harmonic elimination technology has been widely used in many medium and high power converters which operating at very low switching frequency, however, it is still a challenging work to solve the switching angles from a group of nonlinear transcendental equations, especially for the multilevel converters. In this paper, an algebraic method is proposed for selective harmonic elimination. First, the order of the SHE equations is reduced by using the symmetric polynomials theory, and then, its Groebner bases is computed. After this two conversions, the solving of multivariable high order SHE equations is converted to solve two univariate equations and a set of univariate linear equations which simplifies the solving procedure dramatically and abandon the requirement on initial values and can find all the solutions. Compared with the existing algebraic method, such as the resultant elimination method, the calculation efficiency is improved. Experimental verification is also shown in this paper.