A converter system includes a rectifier, a DC link stage and an inverter connected in series. A control unit includes a slow reference frame angle determination unit that generates a slow reference frame angle θr,slow representing an angle that is slowly following a grid phase deviation, and a fast Phase Locked Loop generating a fast reference frame angle θr,fast representing an angle that is fast following a grid phase deviation. The control unit uses the slow reference frame angle θr,slow and the fast reference frame angle θr,fast to control the rectifier output current, and the fast reference frame angle θr,fast to control the inverter output voltage and to synchronize the inverter output voltage with the grid voltage.