A single-phase solid-state transformer (SST) system comprising a cascaded H-bridge (CHB) and dual-active bridge (DAB) converters is a promising solution for a DC fast charger. This work focuses on the control design of a DAB for this system, which has to consider multiple constraints. Some of them are the presence of a double line frequency component on the DC link voltage produced by the inherent operation of a single-phase CHB, load throw-off scenarios, and current sharing among paralleled DABs in a system with multiple SSTs. This work proposes a dual-loop based control design methodology for a DAB while considering these constraints. In this digest, an analytical model is developed to aid the controller design. The analytical model is validated with simulations, and experimental results are also presented for an SST cell.