Real solution number of the nonlinear equations in the SHEPWM technology

This paper studied the real solution number of the switch angles for the inverters which are based on the Selective Harmonic Eliminated PWM (SHEPWM) technology. By the method of variable substitution, the nonlinear transcendental equations can be transformed to a Semi-Algebraic system. Then, with the help of the latest progress in the mechanical proving software for the Semi-Algebraic systems, an analytical method to classify the real solution number of the switching angles is proposed. In order to verify the effectiveness of this method, the real solution classifications for the three phase bipolar and unipolar inverters with N = 3 are given. Compared with the exist numerical results, this method can find out the exact boundary points and the final results are analytical.