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Leakage Inductance with AI

The leakage inductance is a measure of how many magnetic flux lines are not coupled due to the imperfect coupling existing between two windings. It appears as an inductance in series with the magnetizing inductance, and it is proportional to the total inductance and inversely to the square of the coupling factor between the coupled windings, which depends uniquely on geometric factors (e.g., the level of interleaving or the isolation between the windings). 

As generally it is difficult to calculate the coupling between two given windings, the classical methods for calculating the leakage inductance rely on calculating the energy stored in the virtual series inductance and equating it to the energy stored due to the present H field in the interstices between the wires. 

In order to obtain this energy, the H field is calculated horizontally along the concentric layers [1, 2], and vertically between different windows (in the case of top-down designs) of a winding window [2]. This H field distribution generates a storage of energy that depends on the relative permeability of the interstitial material, which usually is air or insulation. 

A special case is considered regarding the Litz wires, which in reality is comprised of tens, hundreds or thousands of individual strands, isolated between them, so there is a large quantity of energy stored in this insulation. Additionally, not all strands have the same coupling factor from a given source. These two effects must be taken into account in order to properly obtain the leakage inductance for a Litz wire. 

A proprietary model for leakage inductance has been derived from the aforementioned principles. This implementation alone can provide leakage inductance values that are on par with those calculated with 3D Finite Elements Analysis, in a thousandth of the time. 

To be able to improve these results, an AI-based data architecture was developed. From the introduced model we sampled values varying all the affecting geometrical parameters (number of turns, number of parallels, core shapes, wires, etc.) and created a dataset of analytical values. This dataset is them mixed together with another dataset of measurements taken in our Laboratory in Madrid (Spain), sampling the same input parameters and obtaining its measured leakage inductance. 

The mixed dataset is given different weights, depending on the provenance (measured data is much more important than calculated data) and a Machine Learning model is trained, which is able to incorporate the principles and tendencies of the analytical data and correct the model’s shortcoming with real measured data.  

This full data architecture is completely parameter-agnostic (it can be used for calculating other parameters, like the core or winding losses) and it will be presented in "Improved Prediction of a Transformer Design using Machine Learning alongside Analytical Methods" in EPE'22. 

Additionally, the leakage inductance measurements are done following a new holistic method that will also be presented in Epe’22, as "Transformer inductances: rationale and experimental determination"

[1] Z. Ouyang, J. Zhang and W. G. Hurley, "Calculation of Leakage Inductance for High-Frequency Transformers," in IEEE Transactions on Power Electronics, vol. 30, no. 10, pp. 5769-5775, Oct. 2015, doi: 10.1109/TPEL.2014.2382175. 

[2] M. S. Sanjari Nia, P. Shamsi and M. Ferdowsi, "Investigation of Various Transformer Topologies for HF Isolation Applications," in IEEE Transactions on Plasma Science, vol. 48, no. 2, pp. 512-521, Feb. 2020, doi: 10.1109/TPS.2020.2967412.