Solve the Selective Harmonic Elimination Problem with Groebner Bases Theory

In this paper, an algebraic method which is based on the groebner bases theory is proposed to solve the selective harmonic elimination PWM(SHEPWM) problem. Firstly, the SHEPWM equations are transformed to polynomial equations by using the multiple-angle formulas and variables substitution, then, the polynomial equations are converted to an equivalent triangular form by computing the reduced groebner bases under the pure lexicographic monomial order, finally, the triangular equations can be solved by a successive back-substitution manner just like the Gaussian elimination which is used to solve the linear equations. A software package is developed under the symbolic computing software Maple, and it can solve the SHEPWM equations with no more than 8 switching angles for the single-phase inverters and 5 switching angles for the three-phase inverters. In contrast with the common used numerical and intelligent methods, the advantages of this method are there is no need to choose the initial values and all the real solutions can be found. Experimental results verify the correctness of the switching angles computed by the proposed method.