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The Solid-state transformer (SST) has been proposed by researchers to replace the regular distribution transformer in the future smart grid. The SST provides ports for the integration of storage and distributed generation (DG), e.g., photovoltaic (PV), and enables the implementation of power quality features. This paper proposes a SST topology based on a quad-active-bridge (QAB) converter which not only provides isolation for the load, but also for DG and storage. A gyrator-based average model is developed for a general multiactive-bridge (MAB) converter, and expressions to determine the power rating of the MAB ports are derived. These results are then applied to analyze the QAB converter. For the control of the dc-dc stage of the proposed QAB-based SST integrating PV and battery, a technique that accounts for the cross-coupling characteristics of the QAB converter in order to improve the regulation of the high-voltage-dc link is introduced. This is done by transferring the disturbances onto the battery. The control loops are designed using single-input single-output techniques with different bandwidths. The dynamic performance of the control strategy is verified through extensive simulation and experimental results.