Frequency converters are required to supply power from the public three-phase network to railways using 16.7 Hz single-phase in their rolling stock. The emerging Modular Multilevel Converter (M2C) technology offers the possibility to make such power conversion in one step using Modular Multilevel Frequency Converters (MMFC) with full-bridge sub-modules. A detailed study of the modulation and control of such converters is presented in this paper. The voltage inserted by each arm of the MMFC is a mixture of the three-phase 50 Hz voltage and the single phase 16.7 Hz voltage. It is important that the voltage reference given to the modulator will be carefully reproduced by the converter because any deviation can introduce undesired frequency components from the single-phase side to the three-phase side and vice versa. The fact that the low frequency, single-phase load causes low-frequency ripple in the total capacitor voltage complicates the problem to generate the correct modulation pattern. In this paper it is proposed to solve that difficulty by estimating the instaneous total capacitor voltages in each arm and provide that information to the modulator. It is shown that such estimations can be performed using measured currents on the single- and three-phase sides. Stable single-phase voltage, symmetrical undistorted three-phase currents and stable converter capacitor voltages are achieved under varying loading conditions. Models in Matlab/Simulink (continuous) and EMTDC/PSCAD (discrete sub-modules) have been developed in this study.