As a power converter of battery energy storage, the multi-level converter and its battery balancing control have received much attention from scholars. This paper focuses on the modular multi-level half-bridge energy storage converter (MMH-ESC), including its topology, working principle, and pulse width modulation (PWM) methods. Under the battery balancing control strategy based on level-shifted carrier PWM (LS-PWM), formulas are derived and calculations are performed to get the charge or discharge of each submodule (SM), thereby obtaining the tolerance for capacity differences among these batteries. A range of battery capacity values that can maintain a balanced state is provided to enhance flexibility in battery configuration and utilization, avoiding the limitation of all batteries to the same capacity. Finally, a new bridge arm modulation wave allocation method is proposed. This method significantly expands the range of SM battery capacity selection and provides a high-tolerance modulation method for the converter under extreme or even fault conditions.