The emergence of medium-voltage silicon carbide (SiC) power semiconductor devices, in ranges of 10–15 kV, has led to the development of simple two-level converter systems for medium-voltage applications. A medium-voltage mobile utility support equipment-based three-phase solid state transformer (MUSE-SST) system, based on Gen3 10 kV SiC MOSFETs, is developed to interconnect a three-phase 4160 V/60 Hz grid to a three-phase 480 V/60 Hz grid to provide a shore-to-ship power interface for naval vessels. The MUSE-SST system consists of three power conversion stages, namely, MVac/MVdc stage (MV: active front-end converter), MVdc/LVdc stage (dual active bridge converter), and LVdc/LVac stage (LV: active front-end converter). The galvanic isolation is introduced in the MVdc/LVdc stage using MV/LV high-frequency transformers (HFTs). This article demonstrates the operation of the three-phase Y–<inline-formula> <tex-math notation="LaTeX">$\Delta $ </tex-math></inline-formula> connected dual active bridge converter used in the MVdc/LVdc stage of the MUSE-SST system. Equations for phase currents, power flow, and zero-voltage switching (ZVS) boundaries are derived for all possible modes for the three-phase Y–<inline-formula> <tex-math notation="LaTeX">$\Delta $ </tex-math></inline-formula> configuration. A detailed parasitic simulation model is derived by measuring and experimentally verifying the parasitic elements of the HFT. A brief discussion regarding the design considerations required for the hardware development of the medium- and low-voltage sides of the three-phase dual active bridge converter is also provided. Successful tests demonstrating the operation and feasibility of the medium-voltage dual active bridge converter, at medium-voltage levels (7.2 kV dc-link voltage), are shown. The results indicate that these devices can accelerate the growth and deployment of the medium-voltage SiC-based converter for isolated and bidirectional medium- to low-voltage dc systems.