Leakage Inductance Modelling of Transformers: Accurate and Fast Models to Scale the Leakage Inductance Per Unit Length

Abstract

Fast and accurate transformer leakage inductance models are crucial for optimisation-based design of galvanically isolated converters. Analytical models are rapidly executable and therefore specially suitable for such optimisations. These analytical leakage inductance models typically consist of two steps: First, acquire the leakage inductance per unit length and second, scale this value with a suitable length. In this paper, the term leakage length is introduced for the scaling length. It is shown that the leakage length depends on the magnetic energy distribution and the most influential factors are determined. Furthermore, two accurate and fast leakage length models for E-core and U-core transformers with concentric windings are proposed: The Empirically Corrected Axial Flux (ECAF) model is based on a compact modification of the known axial flux formula. The cut line (CL) model pursues a semi-analytical approach and achieves high accuracy at the cost of higher computational effort. The models are verified with more than 6000 FEM simulations and the error of both models is significantly lower than the error of the known axial flux formula.