The Dyna-C ac-dc converter is a current-source-based topology featuring medium-frequency galvanic isolation. This paper presents the state-space based average and small signal modeling of Dyna-C ac-dc converter. A space vector based modulation strategy is developed, presented and validated by simulation. Based on the proposed small signal model for Dyna-C ac-dc converter, a two stage closed loop control approach is developed. The proposed approach comprises of an outer loop to regulate the transformer magnetizing-current and an inner $\boldsymbol{d}\boldsymbol{q}$ -based vector control strategy for regulating the grid currents. Circuit simulation results are presented to validate the proposed models and the closed loop control scheme for the Dyna-C ac-dc converter.