General Mathematical Solution for Selective Harmonic Elimination

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 (MI!) inverter configurations with a wide range of modulation indexes (mi). The proposed procedure eliminates the targeted number of harmonics “l” for switching angles 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. !n this proposed algorithm, the nonlinear transcendental harmonic equations were transformed into a linear system of equations (AX = 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. !t 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 α
₁
, α
₂
, . . . ,α
_k
based on a preset objective functions. The simulation and experimental results in some selected cases are provided to validate the proposed algorithms.