Analytical Hybrid Quasi-3D Transformer Leakage Inductance Model

Fast and accurate models of the transformer leakage inductance are crucial for optimization-based design of isolated converters. This article proposes an analytical hybrid Quasi-3D (HQ3D) model for E/U/ER/UR-core type transformers that combines the best suited submodels for each winding section of the transformer. A submodel is developed that directly calculates the leakage inductance contribution of curved winding sections based on the integration of the radially weighted magnetic energy density. The HQ3D model can describe arbitrary winding positions and its fully analytical nature guarantees optimal geometrical scalability. The only restriction is that the windings need to be parallel to the core edges. The HQ3D model is in the accuracy range of 3D finite-element method and verified with measurements on nine transformer prototypes with significantly different geometry ranges. The HQ3D model is rapidly executable, and therefore, well suited for optimizations of galvanically isolated converters.