Real solutions number of the switching angles in the selective harmonic eliminated PWM

With the purpose of solving the real solutions number of the nonlinear transcendental equations in the selective harmonic eliminated PWM (SHEPWM) technology, the nonlinear transcendental equations were transformed to a set of polynomial equations with a set of inequality constraints using the multiple-angle formulas, an analytic method based on semi-algebraic systems machine proving algorithm was proposed to classify the real solution number of the switching angles. The complete classifications of the real solution number and the analytic boundary point of the single phase and three phases SHEPWM inverter with switch points of N=3 and the single phase SHEPWM inverter with switch points of N=4 are obtained. The results indicate that the relationship between the modulation ratio and the real solution number can be demonstrated theoretically by this method, which has great implications for the solution procedure of switching angles and the improvement of harmonic elimination effects of the inverter.