General Mathematical Solution for Selective Harmonic Elimination

Abstract

This article proposes a general mathematical solution for a selective harmonic elimination (SHE) technique. The proposed procedure is valid for both symmetrical and unsymmetrical multilevel inverter (MLI) inverter configurations with a wide range of modulation indexes (mi). The proposed procedure eliminates the targeted number of harmonics “ $l$ ” for switching angles $\text {NS}= 2^{l}$ regardless to the MLI output waveform levels. The proposed procedure receives the values and ratios of the dc sources, and then, it calculates the NS values to generate a suitable set of harmonic equations. In this proposed algorithm, the nonlinear transcendental harmonic equations were transformed into a linear system of equations ( $A X=B$ ); the resulting equations can be solved online easily by formulating matrix A and matrix B and then multiplying the inversion of matrix A by matrix B. It has been found that only the last element in matrix B needs to be updated for each change in the modulation index or in the ac output fundamental component, resulting in reduced computation time. The proposed technique generates the switching angles $\alpha _{1}, \alpha _{2}, \ldots, \alpha _{k}$ based on a preset objective functions. The simulation and experimental results in some selected cases are provided to validate the proposed algorithms.