This paper presents a grid-connected seven-level cascaded H-bridge converter operating as photovoltaic inverter. The main issue with this topology are the natural power imbalances between the power cells and the phases of the converter. The control problem is addressed with a Multiobjective Finite Control Set Model Predictive Control, where a dc-link voltage balance among the cells and good tracking of the active and reactive power references injected to the grid are achieved. Furthermore, an average switching frequency control per cell has been included. The proposed control scheme is validated trough simulation results and tested under dynamic conditions.