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.

Many works are dedicated to power electronic transformers in order to replace line frequency transformers. These new converters offer many degrees of freedom to the designer (switching frequency, magnetic material, rated voltage for switches. . . ). This paper presents a methodology to optimize the sizing of such power converters in order to compare different topologies for a given application. The proposed procedure maximises the efficiency of the converter under a limited volume. In this paper, the methodology is applied to compare different topologies of power electronic traction transformers (PETT) for railway applications. The considered case is a 2 MW converter supplied by a 25 kV-50 Hz catenary. The procedure is illustrated in simulation on a converter with 3.3 kV SiC switches. The best obtained efficiency is 98.9 % with 23 medium frequency transformers (MFT) of 28.6 L each.

This article presents a nonlinear equivalent circuit model of an isolated dc-dc converter with a 3-phase medium frequency transformer. The model takes into account the magnetic cross saturation of the 3-phase core-type magnetic circuit. The model is suitable in detailed electromagnetic transient simulations of power systems involving isolated dc-dc converters. The model is developed using the Lagrange energy method. It involves a matrix of dynamic inductances containing a nonlinear term resulting from core magnetization and a linear term resulting from leakage flux. The model parameters are determined based on a series of magnetostatic finite element method simulations. This approach is convenient when applied to high power transformers offering a limited characterization effort, or if the transformer prototype does not exist. The experimental validation performed on a novel 3-phase MFT prototype in a 100 kW 1.2 kV 20 kHz dual active bridge converter has proved the validity of the model and model parameters. The no-load steady-state and inrush tests and the full-load test show a very good fit between the simulated and experimentally measured waveforms. The comparison with a classical simplified model neglecting magnetic cross saturation shows a significant difference in the no-load inrush test.

A comprehensive and generic medium frequency transformer (MFT) design methodology is presented in this paper, which can be applied to many transformer structures. Models were found or developed to cover all the necessary calculation, with emphasis on the balance between computation time and accuracy, leading to a fast and efficient design tool. Numerous MFT designs are available at the end with the possibility to choose the best candidate. A multi-megawatt offshore windfarm converter application was chosen to show the optimization procedure of the MFT design inside such a converter. The best potential design was retained and validated by numerous finite element simulations. This procedure was repeated for various MFT structures in order to perform a quantitative comparison of many different combinations of technological choices. This study can give insights on the best technological choices to be used for MFTs, and also shows significant differences in performance between structures.

Power electronic traction transformers (PETT) are multilevel AC/DC on-board converters, studied for railway applications to replace traditional solution with low frequency transformers. This paper focuses on the insulated DC/DC converter in a PETT. Three variants of resonant single active bridges (R-SAB) with 3-level NPC primaries are optimised to maximise the efficiency, under mass and dimension constraints. They are sized and compared for a 2 MW PETT on a 15 kV/16.7 Hz railway infrastructure, using 3.3 kV SiC MOSFETs and nanocrystalline C-core transformers with cast resin insulation and forced air cooling. The highest efficiency at nominal power, 99.17 %, is reached for a configuration with a 3-level full bridge NPC primary, a 2-level full bridge secondary, and a 32.1 L/49.1 kg transformer operating at 6 kHz.