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

Alexis Fouineau (1, 2) , Marie-Ange Raulet (2) , Bruno Lefebvre (1) , Noël Burais (3) , Fabien Sixdenier (2)

1 SuperGrid Institute SAS
2 EE - Ampère, Département Energie Electrique
3 BioIng - Ampère, Département Bioingénierie

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

Mots clés: Electric resistance; Power transformers; Inductance; Index Terms— Eddy currents

Domaines: Electromagnétisme

Alexis Fouineau, Marie-Ange Raulet, Bruno Lefebvre, Noël Burais, Fabien Sixdenier. Semi-Analytical Methods for Calculation of Leakage Inductance and Frequency-Dependent Resistance of Windings in Transformers. IEEE Transactions on Magnetics, 2018, 54 (10), pp.8400510. ⟨10.1109/TMAG.2018.2858743⟩. ⟨hal-01859899⟩