For integrating large batteries in the medium voltage grid, current fed solid-state transformers offer galvanic isolation and a significant weight and size reduction. While the power losses increase with frequency and flux density, the core volume is contrariwise. Therefore, a design optimisation to achieve minimum losses and/or a minimum volume is essential. An optimisation strategy is proposed in this paper to find the optimum operating frequency and core flux density under certain practical constraints such as winding voltage per turn, clearance between transformer windings, saturation flux density and minimum efficiency. Differently from previous works, the proposed strategy provides a holistic approach for the design considering all main power losses from all main components using nonsinusoidal voltage waveforms and different operating conditions. Analytical equations for the power losses calculation and the cores design are derived and validated using ANSYS and MATLAB Simulink software packages. Simulation results of the power loss calculation under different operating frequencies and duty cycles are presented and compared with the analytical results. A case study for designing a 1.0 MW, 0.6/18 kV current fed solid-state transformer is presented. The results of two optimisation objectives, minimum power losses or minimum total cores housing volume are also shown.