This paper proposes a model predictive direct power control (MPDPC) approach with reduced switching frequency for grid-connected voltage-sourced converters (VSC). This approach is proposed for both a real/reactive power controller (with a fixed input voltage) and a power port controller (with a variable input voltage). It uses two different cost functions: one for the steady state and one for transients. Utilizing these two cost functions leads to having a low switching frequency in the steady state and a fast response during transients. The proposed MPDPC also provides overcurrent protection of the VSC. In applying the proposed MPDPC to a power port, drawbacks of conventional voltage controllers are addressed by employing power estimation and set point modulation in the controller. Simulation and experimental results validate the proposed MPDPC and the voltage controller.