Converters for power grid interface are required to operate under abnormal operating conditions such as unbalanced and non-sinusoidal grid voltage waveforms and hence, the multilevel types of converters offer a good solution to achieve high power and high voltage and that modular control consisting of cascaded structures seems the most appropriate solution towards decentralising the control per individual phases as well. This paper investigates the use of the proposed hybrid repetitive-resonant control in a control scheme for a single phase converter designed to interface with power grids of highly distorted voltage waveforms. The proposed hybrid repetitive-resonant control is employed into two places of the control system to act in one place as a harmonics filter and in the second place as a current controller to provide respectively:- i) high performance extraction of clean and reliable phase angle information and magnitude of the fundamental grid voltage component and ii) control of grid current and the mitigation of harmonics. Grid voltage control is also considered. The Repetitive Controller RPC is known to reject all the harmonics content but with slow dynamics, [25] while the Resonant Controller RSC is faster but rejects only a single frequency component, [16]. Hence, a hybrid RPC/RSC control approach is proposed where the RSC network is tuned at a number of selected low order frequencies and operated in parallel with a full range RPC. The hybrid RPC/RSC control approach is applied to compensate the grid current harmonics and to eliminate the harmonics distortion of the estimated phase angle and magnitude of the fundamental grid voltage component. Detailed modelling and simulation of the proposed control scheme are carried out using PSIM and the results show excellent performance.