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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.

The cascaded H-bridge (CHB) low-capacitance static compensator (LC-StatCom) has a limited negative-sequence current injection capability compared to a conventional CHB StatCom, due to the comparatively larger oscillations on the capacitor voltages. Placing limits on the ability to provide negative-sequence current to the grid for a given capacitor size is required to prevent overmodulation. This article shows that these limits can be maximized by injecting an optimal third-harmonic circulating current. The effects of injecting the third-harmonic current on the capacitor voltages, both in balanced and unbalanced grid voltage conditions, are analyzed. Specifically, the procedure allows the knowledge of the potential capability of the LC-StatCom when injecting negative-sequence currents. The procedure is based on a linear programming approach. Although the procedure is applicable to any CHB StatCom, regardless of the submodule capacitor size, it is particularly important in LC-StatComs. To corroborate the proposed analysis, simulation and experimental results under balanced and unbalanced grid voltage conditions are presented.