This work addresses problems that arise with the application of Model Predictive Control (MPC) to Modular Multilevel Converters (MMCs), by aiming to reduce the complexity of the optimization problem associated with the controller while properly tracking the converter states. Due to the complexity of the MMC, principally attributed to the high dimension of its state space model along with the high number of discontinuous switching variables available, solving the optimization problem associated with the MPC can be challenging. This becomes more significant when long prediction horizons are required. In order to address this problem, this work presents a reduced order model that aims to reduce the complexity of the state space model of the MMC and to eliminate the discontinuities associated with the converter switches. In order to validate this approach, the accuracy and limitations of this model are analyzed and identified in detail. Moreover, with the help of the reduced order model, detailed references for the MMC are carefully designed and, for the case presented in this work, reference parameters are selected optimally in order to reduce the voltage ripple in the converter modules.The complexity of the optimization problem associated with the MPC is also reduced with the help of the reduced order model by considering just one continuous control signal per converter arm. To further aid the optimization, a method to derive conditions that guarantee its convexity is presented. By guaranteeing convexity, it is possible to use very well studied and efficient optimization algorithms, easing the application of MPC on MMC, especially in the case where long prediction horizons are required. In order to illustrate the proposed procedure, numerical examples are presented in a simulation environment.