Modular multilevel converters (MMCs) can be configured to perform ac/ac conversion, which makes them suitable as railway power supplies. In this paper, a hierarchical control scheme for ac/ac MMCs for railway power supplies is devised and evaluated, considering the requirements and the operating conditions specific to this application. Furthermore, admittance models of the ac/ac MMC are developed, showing how the suggested hierarchical control scheme affects the three-phase and the single-phase side admittances of the converter. These models allow for analyzing the stability of the interconnected system using the impedance-based stability criterion and the passivity-based stability assessment. Finally, the findings presented in this paper are validated experimentally, using a down-scaled MMC.