Effect of Material Resistivity and Temperature on Leakage Inductance of Medium Frequency Transformers Made of Al and Cu Foils

Medium-frequency (MF) transformer is employed in several DC-DC converters, where its leakage inductance plays a crucial role in the converter operation, such as creating resonance in soft switching converter, limiting current in dual active bridge converter, etc. Therefore, it is paramount to accurately estimate the leakage inductance during the design stage. In the literature, leakage inductance calculation at medium frequency is analyzed considering the effects of eddy currents, winding arrangement, etc., but the effect of winding material remains unexplored. This is analyzed by calculating the magnetomotive force (MMF) distribution in the winding volume for different conductor materials. This helps deduce the energy stored in the winding and thereby formulate the effective leakage inductance analytically. Moreover, conductor materials with different resistivities exhibit different temperature coefficients. Therefore, this study also investigates the effect of temperature rise in the windings on the effective leakage inductance due to the change in the wire resistivity. Finally, a comparative analysis between Al and Cu foil designs of a 16 kVA, 1.5/20 kV, 20 kHz transformer is presented to summarize the relative benefits of using Al foils for high power MF transformer designs. The analytical model is verified using 2D FEM analysis. This study shows that higher resistivity material leads to higher leakage energy stored in the conductor volume; consequently this helps achieving higher leakage inductance. As the material resistivity increases with temperature, this also leads to higher leakage inductance.