Analytical Calculation of Leakage Inductance for Low-Frequency Transformer Modeling

In this paper, a new method for the calculation of leakage inductances between short-circuited windings is proposed. The main objective is to find an analytical alternative to the finite-element method (FEM) for the computation of short-circuit inductances in electromagnetic transients-type (EMT-type) programs. Typical EMT-type tools do not provide complex FEM-based computation engines for this sole purpose. The new approach is derived from the method of images and uses analytical formulations for magnetic vector potential and energy developed in this work. It is shown that the difference between the inductance calculated with the FEM in 2-D and that computed with the method of images decreases as the number of layers of images increases. Also, it is demonstrated that the classical approach, based on an axial flux distribution, can lead to considerable error if the windings have unequal heights and if they are located far from the core yokes.