*Result*: Control of the modular multilevel matrix converter based on continuous control set model predictive control
*Further Information*
*The Modular Multilevel Matrix Converter (M3C) is an AC to AC power converter composed of 9 arms that has been proposed for high-power applications such as motor drive and wind energy conversion systems. Due to its complex nature, control of the M3C is usually divided into several sub-goals, and the capacitor voltage regulation varies according to the operating mode, where two classifications are commonly used: Different Frequency Mode (DFM) and Equal Frequency Mode (EFM). EFM is more challenging because of the larger capacitor voltage oscillations that can be produced. In this work, a Continuous-Control-Set Model Predictive Control (CCS-MPC) for energy management and circulating current control of the M3C is proposed. A first MPC stage solves an equality-constrained quadratic programming problem, for which an optimal solution is analytically obtained. The result is a simple control law, which ensures good transient and steady performance in EFM/DFM. The second MPC stage regulates the circulating currents with an inequality-constrained quadratic programming problem. To solve the inherent optimisation problem associated with the second CCS-MPC, an active-set algorithm is implemented. Experimental and simulation results from a 27-cell M3C prototype validate the proposed strategy and show a good overall performance.*