Modelica.Magnetic.QuasiStatic.FluxTubes.UsersGuide

The quasi-static flux tubes library is based on the transient library Magnetic.FluxTubes. The main principles of confined flux and flux tubes apply, too. The quasi-static flux tubes library contains components for modelling of electromagnetic devices with lumped magnetic networks based on quasi-static theory. Models based on this library are suited for quasi-static simulation of transformers at component and system level.

The quasi-static components of this library do not consider saturation since linearity is strictly assumed. In case that the permeability of a saturated circuit needs to be considered, a transient permeability estimation sensor is provided do determine the effective permeability from a transient simulation.

A general introduction into quasi-static (quasi-static) phasor can be found in Modelica.Electrical.QuasiStatic.

This user's guide gives a short introduction to the underlying concept of quasi-static magnetic flux tubes, summarizes basic relationships and equations.

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Package Content

Name	Description
FluxTubeConcept	Flux tube concept
Literature	Literature
ReleaseNotes	Release Notes
Contact	Contact

Modelica.Magnetic.QuasiStatic.FluxTubes.UsersGuide.FluxTubeConcept

Overview of the concept of quasi-static magnetic flux tubes

Following below, the concept of magnetic flux tubes is outlined in short. For a detailed description of flux tube elements, please have a look at the listed literature. Magnetic flux tubes enable the modeling of magnetic fields with lumped equivalent circuit networks.

Since quasi-static conditions are assumed, each field quantity can be represented by a complex phasor -- which is indicated by underlining the respective variable:

• Normal component of magnetic flux density,
• Normal component of magnetic field strength,
• Magnetic flux,
• Magnetic potential difference,

The figure below and the following equations illustrate the relationships between

• the normal component of flux density and magnetic flux, and
• the normal component of field strength and magnetic potential difference.

A flux tube confines the magnetic flux. Flied lines, and flux tubes, respectively are always closed. So there is no flux entering or leaving a flux tube. The total flux of a configuration can be represented by parallel flux tubes, representing different flux paths. This is considered by connecting the elements of a lumped circuit model, such that the sum of all fluxes of a connection is equivalent to zero.

For a section of a flux tube with length the magnetic potential difference is determined by the length integral over the magnetic field strength:

The magnetic flux entering, and leaving a flux tube, respectively, is determined by the surface integral of the normal component of the magnetic field strength:

The magnetic potential difference and the magnetic flux have the same angle, so the reluctance a real (non complex) quantity:

For a generic flux tube reluctance with constant area of cross section, , and length, , the magnetic reluctance is:

Assumptions

• Force interaction is not considered
• Reluctance models are linear; so non-linearities can only be taken into account by adapting the constant relative permeability; see example NonLinearInductor

Notes

The parameter and variable names are chosen as close as possible to the transient FluxTubes library, to avoid additional effort when converting transient into quasi-static flux tubes models.

Reference Note

A similar approach on quasi-static flux tube models is published in [Raabe2012].

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Modelica.Magnetic.QuasiStatic.FluxTubes.UsersGuide.Literature

References

Additional References

Additional reference on magnetic flux tubes are listed in Modelica.Magnetic.FluxTubes.

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Modelica.Magnetic.QuasiStatic.FluxTubes.UsersGuide.ReleaseNotes

Version 3.2.3, 2019-01-23

• Included in the MSL 3.2.3
• Added some more examples according to #1515
• Added magnitudes and angles of complex quantities for better result interpretation

Version 1.0.0, 2013-12-18

• Initial version before inclusion in MSL

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Modelica.Magnetic.QuasiStatic.FluxTubes.UsersGuide.Contact

Contact

Dr. Christian Kral
Electric Machines, Drives and Systems
A-1060 Vienna, Austria
email: dr.christian.kral@gmail.com

Anton Haumer
Technical Consulting & Electrical Engineering
D-93049 Regensburg, Germany
email: a.haumer@haumer.at

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