# LEAKAGE INDUCTANCE MODELS

One of the keys to a good engineering design, indistinctly of the technical branch, is a high accuracy in predicting the result of such design. When the design is a transformer, one of the most interesting parameters, due to its positive or negative influence in the power topology, including the risk of several iterations, is the leakage inductance. The objective of this application note is to present two models for calculating the leakage inductance, highlighting when each of them can be used, and to compare them with experimental measurements done in our laboratory.

CASE STUDY

One of the keys to a good engineering design, indistinctly of the technical branch, is a high accuracy in predicting the result of such design. When the design is a transformer, one of the most interesting parameters, due to its positive or negative influence in the power topology, including the risk of several iterations, is the leakage inductance. The objective of this application note is to present two models for calculating the leakage inductance, highlighting when each of them can be used, and to compare them with experimental measurements done in our laboratory.

Classical model

Model works for: Simple winding arrangements

Model does not work for: Layers with different height / Non-uniform magnetomotive force (MMF) distributions / High-frequency effects

As found in the book “Transformer and inductor design handbook”, written by Colonel Wm. T. McLyman.

Stephens-Boyajian (SB) model

This model considers the magnetomotive force distribution and requires detailed knowledge about the winding geometry for calculating the leakage inductance radial and axial components.

Model works for: Complex winding arrangements / Non-uniform MMF distributions

Model does not work for: Layers with different height / High-frequency effects

L. M. R. Oliveira and A. J. M. Cardoso, "Leakage Inductances Calculation for Power Transformers Interturn Fault Studies," in IEEE Transactions on Power Delivery, vol. 30, no. 3, pp. 1213-1220, June 2015.

Results

A total of 5 measurements were done to verify the Classical and SB models, being the winding distribution the variable parameter. The results of the study are  indicated in the table below and, analyzing the data, it can be seen that the Classical model has a 110% average error and the SB model a 51%, and in all the cases the  error using SB is lower, so it can be concluded that this method gives better results due to its higher complexity regarding to the Classical one. At a more detailed level,  and focusing on the SB model, the results using the conventional winding structure (CASES A, B and C) are not correlated at all, but it is shown a high error when there  are a high number of layers, all of them far from the core. When an interleaved structure is used, thanks to consider the MMF distribution, the error is not too high  compared with the Classical model.

Transformer construction:

-Core shape:  PQ40/40
-Core material:  Ferroxcube 3F36
-Number turns:  24 / 24
-Wire:  Round 12AWG / 12AWG
-Gap:  0 mm

In the image below, it  can be  seen the  transformer used for the  CASE C measurement.

Conclusion

A lot of models can be found in literature for trying to calculate the leakage inductance accurately, but in all of them assumptions are  done, so differences between theoretical results and real measurements are almost always found, even in those in which a detailed  study of the winding geometry is done. With all this, if all the parameters of a transformer are wanted to be known before  manufacturing a prototype for checking its performance in the converter in a simulation software, for example, other methods based  on finite element analysis or artificial intelligence are needed.

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