Parallel resultant elimination algorithm to solve the selective harmonic elimination problem

Abstract

Although the resultant elimination method can get all the possible solutions for the selective harmonic elimination (SHE) problem without the selection of initial values, it still has some fatal shortcomings, such as the high computation burden and the huge memory consumption caused by the intermediate expression swell in the procedure of computing the symbolic determinant of the Sylvester matrix. On the basis of the principle of polynomial interpolation, an algorithm framework is proposed to compute the resultant polynomials, which contains the following two major steps: the evaluation of numerical interpolation points and the solution of linear equations. This approach avoids symbolic computing whose computation complexity is usually very high, furthermore, both of these two steps are suitable for parallel implementing which can speed up the computing tremendously. By using the extended n-dimensional Bjorck–Pereyra's algorithm, this algorithm framework is implemented on a parallel computing system, and it has been used to solve the SHE equations for two-level, three-level, and multilevel inverters. As all the possible solutions can be found by this algorithm, the optimal solutions which have the lowest total harmonic distortion can be identified. Experiment results verify the correctness and effectiveness of the proposed method.