This paper proposes a mixed linear control and model predictive control (MPC) scheme with extended horizon for a neutral point inverter topology (NPC) for photovoltaic applications connected to the AC network. The strategy is able to minimize the unbalance of the voltages of the capacitors in the DC link and to draw a sinusoidal current on the network with a unity displacement power factor. Unlike other MPCs, the resulting algorithm is easy to implement, the weighing factors of the cost function are not needed, and the computational cost is reduced. These advantages are added to the ability to operate the photovoltaic module at the point of maximum power (MPP).