This article outlines the control implementation for a star-connected Cascaded H-Bridge (CHB) converter, focusing on maintaining balanced capacitor voltages across its submodules in grid-connected high-power configurations like Static Synchronous Compensators (STATCOMs). The architecture utilizes a dual-loop cascaded framework consisting of an outer average voltage regulation loop and an inner vector current control loop operating in the synchronous $dq$ reference frame. To prevent voltage drift, a specialized balancing strategy is decoupled into two primary functions: horizontal balancing, which distributes energy across the three converter phases by applying a grid-frequency common-mode voltage, and vertical balancing, which mitigates variations within individual submodule branches by adjusting local duty cycles via proportional controllers. The complete design is validated through MATLAB/Simulink and PLECS simulation models, alongside experimental testing on Imperix hardware (B-Box RCP and MMC bundle) that demonstrates rapid voltage convergence and precise tracking during reactive power step changes.