This work investigates the application of an ac-ac dual active bridge converter for solid state transformer. The proposed converter topology consists of two active H-bridges and one high frequency transformer. Four-quadrant switch cells are used to ensure bi-directional power flow. The advantages of direct ac-ac conversion include fewer power conversion stages and minimized passive components. The ac-ac dual active bridge converter is controlled with phase shift modulation. Operating modes for both power flow directions are described and zero-voltage switching criteria are analyzed. One design example is presented. Simulation results verify the theoretical analysis.