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Solid-state transformers (SSTs) are emerging as pivotal power conversion systems, providing compact, efficient, and flexible interfaces between the medium-voltage (MV) grid and low-voltage (LV) DC loads. The modularized Bridge Rectifier (mBR) topology represents a promising single-stage SST implementation, utilizing only one diode and isolated DC/DC converter per submodule to achieve superior power density and simplicity. This paper presents a comprehensive modeling framework for the mBR SST, upon which a hierarchical control architecture, comprising grid current regulation, branch current distribution, branch current control, and DC-link voltage regulation, is developed. A novel branch current distribution method is proposed to narrow the operating voltage range of branch DC/DC converters across various grid power factor requirements. Furthermore, a modeling approach based on the dq0−ΔΣ transformation is introduced, enabling the full decoupling of branch current control into four independent regulation loops. As an extension, this paper provides the first in-depth exploration of the mBR's multi-port functionality for MVAC/MVDC/LVDC power conversion, integrating this capability into the proposed control strategies. Finally, a large-scale real-time hardware-in-the-loop (RT-HIL) system, incorporating seven distributed real-time simulators and twenty-five real-time controllers, is developed for the validation of a 250 kW mBR SST. RT-HIL results under various operating conditions demonstrate the excellent and robust performance of mBR SST under the proposed control schemes.