The modular multilevel converter is the state-of-the-art topology for voltage source converter HVDC. Despite its advantages, this converter handles large internal low-frequency energy ripples, and the capacitance that supports these dynamics is a key design parameter that affects the operating region of the converter. Different strategies can be found in the literature to increase the feasible region of operation of the converter. Nevertheless, they are typically open loop in nature and use precalculated control references. This paper presents an alternative based on model predictive control that steers the system through optimal control trajectories that are calculated online. This provides feedback and corrective control action in real time. The predictive controller used for this purpose is presented and a linear time-varying approximation is used to reduce the computational burden of the algorithm. The feasible boundaries of the converter are sought and the final performance of the control algorithm is evaluated through detailed simulations using a switching model of the converter.