A design methodology of a dual active bridge (DAB) converter for solid state transformer applications is proposed using an elaborate mathematical model of the converter. The DAB converter is popular in bi-directional power conversion applications because of soft switching capability and seamless control in bi-directional power flows. However, several design considerations should be considered to overcome its demerits such as high RMS current at heavy load condition and limited soft switching capability at light load condition. Design methodology of the power stage will be discussed to minimize the conduction loss and to enlarge the soft switching region. In addition, the algorithm for soft start will be discussed to reduce overcurrent stress of the power switches during a start-up sequence. Experimental results of a 3.3 kW prototype DAB converter demonstrate the validity and effectiveness of the proposed methods.