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

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.