Single-to-three-phase direct AC/AC Modular Multilevel Converters have gained a significant interest in the field of railway interties. The use of such an MMC-based structure implies more advanced control techniques as well as design requirements, especially in the case where the three-phase side experiences grid asymmetries. This paper proposes a global control scheme, which is capable of ensuring high performance in such operating conditions. In addition, the impact of grid unbalances on the MMC capacitive energy storage requirements is evaluated by using different line current control techniques with current amplitude limitation as well as taking into consideration a three-phase reactive power injection. The proposed concepts are validated by means of simulation results. Finally, preliminary experimental results from a down-scaled laboratory prototype are provided.