This paper presents the design and optimization of a Medium Frequency Transformer (MFT) for use in Solid State Transformer (SST) systems supporting green hydrogen production. Operating at 1 kHz and integrated within an LLC resonant converter, the transformer is optimized for minimal weight and high efficiency while ensuring adequate leakage inductance and insulation performance. A core-type configuration with cylindrical windings was selected based on FEM simulations and mass-efficiency trade-offs. The final prototype, using copper conductors, achieves 97.8% efficiency with a mass below 50 kg and meets the required 7 mH leakage inductance. High-voltage testing, including partial discharge and breakdown tests, confirmed the insulation coordination of the design. The results demonstrate a practical and scalable approach for high-performance SST integration in renewable energy applications.