Pulsed-Power-Loads (PPLs) are becoming more common in medium-voltage naval DC micro-grids. To reduce their impact on the electrical system, energy storage elements can be installed. For optimal performance the interface converters need to have fast dynamics and excellent disturbance rejection capabilities. Moreover, these converters often need to have a voltage transformation capability and galvanic isolation since common energy storage technologies like batteries and super capacitors typically operate at relatively low voltages. In order to address these issues a Dual-Active-Bridge converter with a Moving Discretized Control Set Model Predictive Control (MDCS-MPC) is proposed in this paper. The controller has a fixed switching frequency, which allows straightforward filter design. The operating principles of the MDCS-MPC are introduced in this paper with the development of a cost function that provides stiff voltage regulation. Resonance damping and sampling noise resistance have been achieved by an adding additional term in the cost function. This paper presents an assessment of the performance of the proposed MDCS-MPC and comparisons with other control methods. Experimental validation from a 300V/300V 20kHz 1kW Dual-Active-Bridge converter are also presented to verify the theoretical claims.