Power electronics based Medium-Voltage Direct Current (MVDC) Microgrids consist of several interconnected feedback-controlled switching converters. Such systems experience bus voltage stability challenges owing to the negative incremental resistance of Constant Power Loads (CPLs) and converter control loop interactions. To tackle the stability challenges, this paper presents the application of the Interconnection and Damping Assignment Passivity Based Control (IDA-PBC) approach to the Port-Controlled Hamiltonian (PCH) model of Dual Active Bridge (DAB) source-side converters in a MVDC Microgrid. For the DABs, a Fundamental Average Model (FAM) approach considering Phase Shift Modulation (PSM) is provided and used for deriving the corresponding IDA-PBC control law. We analyze the effectiveness of the controller on large signal scenarios considering disturbances such as load step up, and DAB disconnection. Hardware-in-the-Loop (HiL) experiments using Opal-RT and Labview FPGAs, as well as, low power prototype tests are carried out to demonstrate the validity and feasibility of the proposed approach. Port Controlled Hamiltonian Modelling and IDA-PBC Control of Dual Active Bridge Converters for DC Microgrids