Unified Selective Harmonic Elimination for Multilevel Converters

For multilevel converters, as their selective harmonic elimination (SHE) equations are highly related to the switching patterns, it is almost impossible to give a complete study for all the switching patterns under the traditional SHE framework. In this paper, a unified SHE approach is proposed, in which the various SHE equations for different switching patterns are merged into one group of unified SHE equations and the inequality constraints on the switching angles are eliminated at all. This unified SHE equations can be solved by any methods, which have been used in solving the traditional SHE problems. By using the theory of Groebner bases and symmetric polynomials, all the possible switching patterns and the corresponding switching angles can be solved simultaneously. The study on the case for four switching angles discovers some unusual switching patterns that have the lowest total harmonic distortion for low-modulation indices. Also, the case for nine switching angles with modulation index m=0.72 is studied; in total, there exist 43 groups of switching angles, which belong to 33 different switching patterns. Experiments on a 13-level cascaded-H bridge converter verify the correctness of this unified multilevel SHE approach.