Mixed-integer bilinear and piecewise-linear models for designing switching strategies of multilevel power converters

With the adoption of multilevel converters in the industry, the importance of their optimal operation has increased. Able to operate with more than three voltage levels, multilevel converters are often modulated by vectors defined in time, which can be optimized to reduce the number of commutations or total harmonic distortion. This papers presents two formulations that do not use trigonometric functions for selecting optimal switching angles, focusing on the minimization of the current weighted total harmonic distortion. The first relies on bilinear terms to yield a mixed-integer nonlinear programming (MINLP) formulation that can be tackled with MINLP algorithms. The second uses piecewise-linear approximation to enable the application of mixed-integer quadratic programming. Computational results from the application of these formulations are reported, in conjunction with a simulation of the optimal angles that were computed for a 5-level Neutral-Point Clamped converter.