For a Vehicle to Grid (V2G) interfacing an integrated AC/DC-DC/AC bi-directional converter is presented in this paper. It is realised as a combination of 2.5 kW DC-AC grid inverter and bidirectional Dual Active Bridge (DAB) dc-dc converter for battery charging and for feeding the electric energy stored the battery back into the grid. For the target micro-sized electrical cars, the main challenge is the realization of a light-weight power converter. Particularly the high frequency power transformer design optimization and high frequency effects like skin and proximity losses in the transformer windings are analysed in details. Based on finite element method (FEM) numerical simulation as well as on analytical approach the stranding level proximity losses in a Litzwire are estimated and an optimal number of the Litzwire strands as well as their diameter are determined for minimum losses in a given transformer. The resulting high efficiency bi-directional DAB converter with optimised transformer for Electrical Vehicle battery charging and grid interfacing system is implemented in a prototype design.