Solid-State Transformers (SSTs) enable significant improvements in size and functionality compared to conventional power transformers. However, one of the key challenges in Solid-State Transformer design is achieving reliable insulation between the high-voltage and low-voltage sections. This proposal presents the design and optimization of a high-insulation Medium-Frequency Transformer (MFT) for 66 kV grids operating at 50 kHz and delivering up to 75 kW for SST applications using Inductive Power Transfer (IPT) technology. A fixed 50 mm gap between the primary and secondary windings is filled with dielectric oil to enhance insulation. The proposed IPT system employs a double-D coil design developed through iterative 2D and 3D finite element method simulations to optimize the magnetic circuit, thereby significantly reducing stray flux and losses. Notably, the double-D configuration reduces enclosure losses from 269.6 W, observed in a rectangular coil design, to 4.38 W, resulting in an overall system loss reduction of 42.4% while maintaining the electrical parameters required for zero-voltage switching operation. These advancements address the critical limitations in conventional Medium-Frequency Transformers by providing enhanced insulation and improved thermal management. The proposed IPT-based design offers a low-loss solution with easy thermal management for solid-state transformer applications in high-voltage grids.