The modular multilevel matrix converter ((MC)-C-3) is a power converter topology for ac to ac conversion that is suitable for high-power applications. The control of this converter is complex, particularly if ac system frequencies are similar. In these cases, the floating capacitors can present large voltage oscillations. Therefore, this study presents a new vector control system to enable the operation of the (MC)-C-3 when the frequencies at the input and output are virtually the same. The effectiveness of the proposed method has been validated using simulations and experimental results from a prototype (MC)-C-3 power converter with 27 cells.