The Modular multilevel matrix converter (M3C) is a promising topology for medium-voltage, high-power applications. Due to the modular structure, it is scalable, produces high quality output waveforms and can be fault tolerant. However, the M3C suffers from capacitor-voltage fluctuation if the output frequency is similar to the input frequency. This problem could limit the circuit's application in the adjustable speed drives (ASD). This paper introduces a theoretical analysis in the phasor-domain to find the branch energy equilibrium point of the M3C when operating with equal input and output frequencies. On the basis of this equilibrium point, a branch current reallocation based energy balancing control method is proposed to equalize the energy stored in the nine converter branches. With this novel control method, the M3C can effectively overcome the capacitor voltage fluctuation without using balancing techniques based on common mode voltage or applying reactive power at the input side.