Litz Wire Homogenization with COMSOL and MATLAB

This COMSOL and MATLAB tool extracts homogenized material parameters for a litz wire. This means that a complex litz wire, which is composed of many strands, can be replaced with a homogeneous material. This virtual material parameters are defined such that the energy and losses matches the stranded litz wire. More concretely, a virtual complex permeability and complex conductivity are extracted.

The method features several advantages:

• A reduced computational cost, since the discrete strands are not modeled
• The mesh can be coarse, independent of the skin depth
• Method valid up to several megahertz
• The litz wire can feature an arbitrary shape
• The impact of the eddy current on the magnetic field is considered

The following limitations exist:

• The litz wire is composed of round strands
• The litz wire is ideal (insulated and perfectly twisted strands)
• The litz wire is defined with a fill factor, the exact position of the strands is not considered

This tool is developed by the Power Electronic Systems Laboratory at ETH Zurich and is available under the BSD License. The code is also available on the ETH Data Archive.

Example

A simple circular air coil realized with litz wire is considered:

• run_1_homogenization.m - Extract the winding geometry, energy and field patterns from FEM
• run_2_packing.m - Compute the geometry of a round litz wire
• run_3_simulation.m - Simulate with FEM a circulate litz wire coil (with and without homogenization)
• run_4_plot.m - Plot the result (homogenization, geometry, and simulation)

This example compare two different methods:

• Simulation with the homogenized material parameters (fast)
• Simulation of all the discrete strands (slow)

The following parameters are extracted and compared:

• Energy
• Losses
• Induced voltage

The following conclusion are made:

• Both methods are equivalent (less than 2% deviation)
• The computation with homogenized parameters is much faster

Homogenized Parameters and Wire Geometry

Energy, Losses, And Induced Voltage

Current Density: 10kHz and 10MHz

Magnetic Field: 10kHz and 10MHz

Compatibility

The tool is tested with the following MATLAB setup:

• Tested with MATLAB R2018b or 2019a
• No toolboxes are required.
• Compatibility with GNU Octave not tested but probably problematic.

The tool is tested with the following COMSOL setup:

• COMSOL Multiphysics 5.4 or 5.5
• AC/DC Module (for the magnetic simulation)
• MATLAB Livelink (for communication with MATLAB)

References

References for the litz wire losses:

• Guillod, T. / Litz Wire Losses: Effects of Twisting Imperfections / 2017
• Meeker, D. / An Improved Continuum Skin and Proximity Effect Model for Hexagonally Packed Wires / 2012
• Xi, N. / An Equivalent Complex Permeability Model for Litz-Wire Windings / 2009

Author

• Thomas Guillod, ETH Zurich, Power Electronic Systems Laboratory - GitHub Profile

License

• This project is licensed under the BSD License, see LICENSE.md.
• This project is copyrighted by: (c) 2016-2020, ETH Zurich, Power Electronic Systems Laboratory, T. Guillod.