This paper proposes a continuous control set model predictive control (CCS-MPC) algorithm of a modular multilevel matrix converter (M3C) for low-frequency AC transmission (LFAC), via which the offshore wind farm (OWF) is integrated. The M3C is operated with a 16.7 Hz frequency at the OWF side and a 50 Hz frequency at the onshore grid side. The balance of the capacitor voltages and the regulation of circulating currents in the M3C are performed using the proposed CCS-MPC algorithm, which is based on the online solution of a cost function with constraints. Simulation and experimental work (with a 5 kW M3C prototype) are provided, showing the performance of the LFAC system to operate with symmetrical and asymmetrical voltage dips, active and reactive power steps, and optimal limitation of currents and voltages using constraints. Unlike previous publications, the predictive control system in this paper allows seamless operation under balanced and unbalanced conditions, for instance, during asymmetrical voltage dips.