Abstract：Modular multilevel matrix converter（M3C）is a multilevel topology that can directly realize ACAC

conversion，which has good application prospects in high-voltage transmission systems and DC distribution

systems，but the existence of bridge-arm circulating channels inside the M3C leads to a very complex control

structure. For this reason，a hierarchical system control strategy was proposed. First，the mathematical model of the

M3C was derived based on the conventional double αβ0 coordinate transformation. Then，a dual-loop control

structure consisting of an outer-loop and an inner-loop controller was employed in the M3C，which is usually

employed in voltage source converters. In addition，in order to suppress the loop current component inside the

system，a bridge arm energy equalization control strategy based on double αβ0 transform decoupling was proposed，through which the capacitive voltage control between the bridge arm and the bridge arm was realized by this control and carrier phase shift modulation. Ultimately，the simulation model and physical prototype were

constructed，and the outcomes validated the viability of the proposed control strategy for the M3C system.

      Key words：modular multilevel matrix converter（M3C）；dual αβ0 coordinate transformation；dual closedloop vector control；bridge arm energy equalisation