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A novel simplex homotopic fixed-point algorithm for computation of optimal PWM patterns

A novel simplex homotopic fixed-point algorithm to solve the optimal PWM problem is introduced in this paper. The goal of optimal PWM is to select the switching instants (angles) in such a way that a waveform with a particular characteristic is obtained and a certain criterion is minimized. The algorithms, which have been given so far in the literature to address this problem, use off-line precalculations and look-up tables. The proposed algorithm transforms the nonlinear equations to a polynomial set, uses the simplex homotopic fixed-point approach to find the initial values of the roots, and then uses cubic iteration to refine the roots. The salient features of the algorithm presented in this paper are: high accuracy, fast speed (low computational cost), and robustness even when facing ill-conditioned cases. With typical contemporary DSP, this algorithm can be used to set amplitudes of several tens of harmonics within one cycle of the AC power waveform. Since the switching angles are calculated independently from each other, the algorithm can be easily implemented for parallel processing. This would enable its use in demanding waveform processing applications.