The use of low power PV string inverters, up to a few kW, has been gaining popularity for small scale applications. In this paper a new transformerless PV string inverter is proposed. This inverter makes use of the inversion stage as an unfolding inverter for high output voltages, and a high switching frequency inverter at low voltages and low current, thus achieving a highly efficient operation. The control of the system is performed by a MPC scheme, which allows the use of a reduced dc-link capacitor. Simulations are presented for a 750V(DC) 5.6kW 220V(rms) PV string inverter, showing good results for the proposed inverter and control. Compared with a classical two stage inverter, the proposed PV string inverter presents up to 0.8% higher efficiency for high power operating points, with a maximum simulated efficiency of 96.9%.