The 3×2 type modular multilevel matrix converter (M3C) is a topology suitable for three-phase to single phase AC-AC fields. However

as a direct AC/AC converter

the 3×2 type M3C suffers from serious DC capacitor voltage unbalancing when the input frequency of the system is close to or equal to the output frequency

which is an inherent defect in the M3C topology family. In order to solve this problem

a 3×2 type M3C double $\alpha \beta 0$ transformation matrix is constructed for analyzing the branch energy balance mechanism in this paper. Then a hybrid frequency composition circulating current injection in five-component control is proposed to address the DC capacitor voltage unbalancing under equal frequencies mode. This method does not require control switching when the output frequency changes. Experimental results based on the 3×2 type M3C platform verify the effectiveness of the proposed method. Moreover

the dynamic performance is also good with the proposed control strategy under the conditions of output voltage or frequency change

which can recover from the disturbance in only 1 s and 2.9 s

respectively.