Recently, there have been numerous DC microgrids coming up in every sector. Some of these microgrids operate as independent entities with their own renewable energy sources, active loads, distribution networks and energy storage units. However, they are not highly reliable as the renewable energy sources are location and climate dependent. Having a large energy storage unit can be one possible solution, but that involves high expenditure and occupies a large amount of space. Thus, an alternative is to connect the independent DC microgrid to an established AC grid. With the advancements in power electronic technologies, such a connection can be established by a multi-stage converter known as Solid state transformer (SST). Numerous studies have been conducted on SSTs for low-voltage levels, and there is a wide scope for research in the area of medium and high-voltage converters. Also, the scope of using Planar transformer (PT) as high-frequency transformers in DC-DC converters for medium and high-voltage applications is yet to be extensively explored. Hence, the main focus of this thesis would be to develop an isolated bidirectional DC-DC converter with a planar transformer that can be used in an SST which can potentially connect a low-voltage DC microgrid comprising a solar-based car parking system, to a medium-voltage AC grid. Firstly, various DC-DC converter topologies have been investigated, and the single phase Dual active full bridge (DAFB) is chosen as the best suitable topology for this application. Secondly, various control strategies have been investigated, and single-phase shift control has been implemented due to its simple control techniques and low data transfer requirement across high isolation. Thereafter, a script is developed to identify the optimal parameters for the Dual active bridge (DAB) and PT design. Further, the planar transformer with high isolation is realized by considering various factors like shielding and termination into account. Finally, a single-cell prototype is developed and tested for DAB operation and isolation requirement of the designed planar transformer. The result of the presented work is a single-cell isolated bidirectional DC-DC converter rated for 12 kW designed and developed with a PT rated for 16.3 kV isolation.