Solving the I11-conditioned polynomial for the optimal PWM

The selective harmonic elimination (SHE) pulse-width modulation (PWM) inverter eliminates low-order harmonics by optimizing the switching angles distribution and can generate high quality output waveforms. The switching angles can be obtained through solving a set of transcendental equations with the coefficients from the inverter output waveform Fourier series. The conventional algorithm for resolving SHE-PWM problem is Newton-Raphson algorithm. The main shortcoming in applying Newton-type algorithms is that the results deeply depend on the selection of initial values. In this paper, a new algorithm is proposed to solve the nonlinear system in the SHE-PWM problem without suffering from above shortcoming. The algorithm first transforms the nonlinear equations into a polynomial problem. An important observation is that the original system and thus the polynomial are highly illconditioned, so the conventional algorithms can seldom accurately computing roots for the polynomial. A novel Eigensolve algorithm is introduced since the algorithm is especially good for solving the highly illconditioned polynomial. The simulation results indicate the robustness of the method.