This work proposes an model-predictive-control (MPC) strategy applied to Modular Multilevel Matrix Converter (M3C) for Low-Frequency AC (LFAC) transmission systems. The novelty of the proposal is the use of a current and local-cluster balancing (LCB) control based on MPC for a LFAC transmission system which is composed by at least one grid-forming and grid-following control for M3Cs. As a results, the MPC-based strategy allows to control cluster currents and to regulate the local and cluster energies with low capacitor voltage ripple and operate at low frequency while generating a low-frequency grid and extracting/injecting power from the LFAC system. Simulations are presented to validate the proposed strategy for both M3Cs. The first M3C generates the low-frequency voltage grid and the second M3C transfers power from one side to the other.