Bender's decomposition algorithm for model predictive control of a modular multi-level converter

In this paper, we consider an optimization problem solving for model predictive control (MPC) of a modular multilevel converter (MMC). An MMC consists of a large number of submodules. The objective of the MPC is to determine the best switching sequences for the submodules in the MMC to track the phase current references for T time horizons. The MPC is formulated as a nonlinear mixed-integer programming (MIP) problem with the on/off status of submodules as binary decision variables and MMC dynamic states such as phase currents, circulating currents and submodule capacitor voltages as continuous decision variables. With a large number of submodules and a large number of time horizons, the dimension of the nonlinear MIP problem becomes difficult to handle. Our contribution is to formulate this problem and solve this problem using Bender's decomposition. An example 5-level single-phase MMC is demonstrated for the proposed algorithm.