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 that operates at very low switching frequency; but, it is still a challenging work to unravel the switching angles from a group of nonlinear transcendental equations, especially for the multilevel converters. Based mostly on the Groebner bases and symmetric polynomial theory, an algebraic technique is proposed for SHE. The SHE equations are reworked to a similar canonical system that consists of a univariate high-order equations and a cluster of univariate linear equations, so the solving procedure is simplified dramatically. In order to solve the ultimate solutions from the definition of the elementary symmetric polynomials, a univariate polynomial equation is built in step with the intermediate solutions and 2 criteria are given to check whether or not the results are true or not. Unlike the commonly used numerical and random searching ways, this method has no demand on selecting initial values and will realize all the solutions. Compared with the prevailing algebraic ways, like the resultant elimination methodology, the calculation potency is improved, and the maximum solvable switching angles is nine. Experiments on 3-part two-level and thirteen-level inverters verify the correctness of the switching angles solved by the proposed technique.

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