Semi-Analytical Methods for Calculation of Leakage
Inductance and Frequency-Dependent Resistance
of Windings in Transformers

Leakage inductance and frequency-dependent resistance of windings are the key parameters for the design of magnetic devices. This paper focuses on analytical or semi-analytical calculation techniques to be integrated into a medium frequency transformer optimization process. To this extend, a review of the currently most used method to calculate the inductance and resistance of windings transformer is established. Based on this review, new calculation methods are developed. Magnetic field cartography is evaluated on the basis of 2-D structures thanks to a combination of Ampère’s law and the image method. From this magnetic field map, leakage inductance can be calculated. The obtained accuracy with this method is equivalent to 3-D finite-element modeling (FEM). For frequency-dependent resistance evaluation, new methods based on 2-D or 1-D approach are compared to FEM and reviewed models. An analysis of the behavior of each model is done, showing that newly developed models are more suitable in the case of a medium frequency transformer design in terms of accuracy, robustness, and calculation time. This paper could be useful to the designers of magnetic devices because newly developed models could easily be adapted to various geometries, such as toroidal structures or even inductors.

Index Terms— Eddy currents, electric resistance, inductance, power transformers.