Research on real solutions number of the SHEPWM equations based on the mechanical proving and groebner bases theory

The real solutions number of the switching angles for the SHEPWM inverter has been discussed in this paper. Firstly, the SHEPWM equations were transformed to polynomial equations with inequality constrains by using the multiple-angle formulas and variables substitution, then, the equivalent groebner bases of the polynomial equations were computed, finally, the real solutions number of the SHEPWM equations were discussed with the mechanical proving theory and algorithm of the semi-algebraic systems. The conclusion of there is only one solutions for the single phase SHEPWM inverter with less than 7 switching points in a quarter period and the theoretical maximum modulation ratio were derived for the first time. The experiments and simulations verify the correctness of these conclusions.