In the operation of battery energy storage systems based on the cascaded H-bridge converter, it is beneficial to balance the state of charge of batteries in different submodules within the converter phase-arm. This is achieved by distributing the active power among the submodules. Although multiple methods have been proposed for this purpose, they face the challenge of rendering optimal active power distributions that maximize balancing speed while meeting power constraints in the battery energy storage system. To overcome this challenge, a model predictive control scheme is developed in this article. The proposed method is remarkably robust against parametric uncertainties (battery voltage, capacity, etc.), as evidenced by its ability to tolerate a substantial 50% uncertainty in the parameters, resulting in a mere 0.05% steady-state error. Furthermore, because the predictive control can be executed at a low frequency, the computational burden is comparable to other existing methods.