The modular multilevel converter (MMC) has recently emerged as a promising candidate for medium-voltage megawatt grid emulators (GEs). However, when emulating grid faults, the MMC-based GE may encounter transient overvoltage and voltage imbalance issues in its submodule (SM) capacitors. Following the mechanism analysis of these issues, this article proposes an enhanced SM capacitor energy balancing approach. Differing from conventional methods, this approach effectively mitigates these issues even when emulating faults with residual voltages close to zero, ensuring the reliable operation of SM capacitors within 70%-110% of the rated voltage. Lastly, the effectiveness of the enhanced method is confirmed by the controller hardware-in-the-loop (CHIL) test.