Recently, Modular Multilevel Converter (MMC) is becoming one of the most preferred multilevel converter topology for high power medium voltage applications. However, the widespread of MMC in Variable Speed Drive (VSD) applications is still limited. This can be attributed to the fact that the submodule (SM) capacitor voltage ripples increase during low-speed constant torque operation. This paper proposes a modified Carrier Phase Shift Pulse Width Modulation (CPS-PWM) that can reduce the average voltage of the SM at low speed constant torque operation. By using this method, larger capacitor voltage ripples can be tolerated without exceeding the maximum capacitor voltage limits while maintaining speed stability of the Induction Motor. Therefore, MMC can be used without the requirement of oversizing the rated value of these capacitors. Simulation has been conducted to verify the effectiveness of this proposed method. © 2020 IEEE.