Selective Harmonic Elimination With Groebner Bases and Symmetric Polynomials

Selective harmonic elimination (SHE) technology has been widely used in many medium- and high-power converters which operates 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. Based on the Groebner bases and symmetric polynomial theory, an algebraic method is proposed for SHE. The SHE equations are transformed to an equivalent canonical system which consists of a univariate high-order equations and a group of univariate linear equations, thus the solving procedure is simplified dramatically. In order to solve the final solutions from the definition of the elementary symmetric polynomials, a univariate polynomial equation is constructed according to the intermediate solutions and two criteria are given to check whether the results are true or not. Unlike the commonly used numerical and random searching methods, this method has no requirement on choosing initial values and can find all the solutions. Compared with the existing algebraic methods, such as the resultant elimination method, the calculation efficiency is improved, and the maximum solvable switching angles is nine. Experiments on three-phase two-level and 13-level inverters verify the correctness of the switching angles solved by the proposed method.