The low-frequency operation of modular multilevel converters, required by variable-speed drives, is generally challenging within the established operation modes. Especially when rated torque beginning from zero speed is required and the rated machine speed is low, the installed module capacitance has to be very high. A possible solution to this problem is quasi-two-level PWM operation, which reduces the capacitance by more than an order of magnitude. Although the multilevel property of the modular multilevel converter has to be sacrificed, all other advantages, i.e. small voltage steps limiting the problems with long machine cables and bearing currents, modularity, scalability to higher voltage levels, and a straight-forward option to add redundancy, are retained from the conventionally operated modular multilevel converters.This thesis presents a derivation of the quasi-two-level PWM operation mode and proposes two suitable control methods. These methods are validated using a downscaled prototype of a modular multilevel converter. Simulations are conducted to evaluate the sensitivity of the proposed control to uncertainities in the knowledge of the converter parameters. Furthermore, the specific effects and properties of the operation mode, such as output voltage errors, reduced overvoltages with long machine cables, and the operation with flat-top modulation, are analyzed.In addition to the presented control methods, the design process is studied. First, the specific design trade-offs between the converter parameters are identified. The evaluation of trade-offs shows that quasi-two-level PWM operation is especially well-suited for modular multilevel converters with a high number of modules per branch. In the next step, the quasi-two-level PWM-operated modular multilevel converters are designed for several study cases of low-frequency medium-voltage drives. The design process utilizes the validated simulation model and derived analytic equations. Additionally, the validated model is also used to simulate a dynamic machine acceleration to confirm the plausibility of the designs.The resulting design indicators of the conducted designs are compared to those of the conventional operation mode of the modular multilevel converter, to the two-level voltage-source inverter based on series-connected IGBTs, and to the modular multilevel matrix converter, which were designed for the same study cases. The comparison to standard operation modes of the modular multilevel converter and to the modular multilevel matrix converter shows design advantages for the quasi-two-level PWM operation of modular multilevel converters. As expected, the output current distortion is significantly increased with the quasi-two-level PWM operation. Nevertheless, the current distortion is likely to be acceptable for medium voltage drives without additional filter requirements. In conclusion, quasi-two-level PWM-operated modular multilevel converters are a favorable alternative for applications in low-speed medium-voltage drives.