The M2DC exploits the interleaving between the three legs of an MMC to realize a promising uninsulated DC/DC converter to interconnect HVDC grids. This paper details a current and energies decoupled model of the M2DC. The major idea proposed in this paper is focused on the full energy control generating optimal current references to minimize the internal currents magnitude. The energy sum and difference models are fully detailled. Both current and energy control loops are based on the model inversion principle in order to control all the state variables. The proposed control is based a dynamic control developed with the model inversion principle associated on an optimization of the current magnitude deduced from a quasi static analysis. All dynamics of the system are then explicitly controlled, which guarantee a good dynamic behavior during the transient. Therefore, current and energy controls are presented in details. Simulation results show the dynamic behavior of the converter for various operating points.