User's Guide


This is the library of quasi static fundamental wave models for multi phase electric machines. This is complementary library with the transient machine models of FundamentalWave.

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Package Content

Name Description
Modelica.Magnetic.QuasiStatic.FundamentalWave.UsersGuide.Concept Concept Fundamental wave concept
Modelica.Magnetic.QuasiStatic.FundamentalWave.UsersGuide.Contact Contact Contact
Modelica.Magnetic.QuasiStatic.FundamentalWave.UsersGuide.ReleaseNotes ReleaseNotes Release Notes
Modelica.Magnetic.QuasiStatic.FundamentalWave.UsersGuide.References References References

Modelica.Magnetic.QuasiStatic.FundamentalWave.UsersGuide.Concept Modelica.Magnetic.QuasiStatic.FundamentalWave.UsersGuide.Concept

Fundamental wave concept


Reference frames

Quasi static magnetic ports contain the complex magnetic flux (flow variable) and the complex magnetic potential difference (potential variable) and a reference angle. The relationship between the different complex phasors with respect to different references will be explained by means of the complex magnetic flux. The same transformation relationships also apply to the complex magnetic potential difference. However, the discussed relationships are important for handling connectors in the air gap model, transform equations into the rotor fixed reference frame, etc.

Let us assume that the air gap model contains stator and rotor magnetic ports which relate to the different sides of the machine. The angle relationship between these ports is


where is the connector reference angle of the stator ports, is the connector reference angle of the rotor ports, and is the difference of the mechanical angles of the flange and the support, respectively, multiplied by the number of pole pairs, . The stator and rotor reference angles are directly related with the electrical frequencies of the electric circuits of the stator, , and rotor, , respectively, by means of:

This is a strict consequence of the electro magnetic coupling between the quasi static electric and the quasi static magnetic domain.

Fig. 1: Reference frames of the quasi static fundamental wave library

The complex magnetic flux with respect a stator and rotor magnetic port are equal,


but the reference phase angles are different according to the relationship explained above. The stator and rotor reference angles refer to quasi static magnetic connectors. The complex magnetic flux of the (stator) port with respect to the stator fixed reference frame is then calculated by


The complex magnetic flux of the (rotor) magnetic port with respect to the rotor fixed reference frame is then calculated by


The two stator and rotor fixed complex fluxes are related by


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Modelica.Magnetic.QuasiStatic.FundamentalWave.UsersGuide.Contact Modelica.Magnetic.QuasiStatic.FundamentalWave.UsersGuide.Contact



Library officers

Dr. Christian Kral
Electric Machines, Drives and Systems
A-1060 Vienna, Austria

Anton Haumer
Technical Consulting & Electrical Engineering
D-93049 Regensburg, Germany

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Modelica.Magnetic.QuasiStatic.FundamentalWave.UsersGuide.ReleaseNotes Modelica.Magnetic.QuasiStatic.FundamentalWave.UsersGuide.ReleaseNotes

Release Notes


Version 3.2.3, 2019-01-23
Version 3.2.2, 2015-02-02
Version 0.4.1, 2013-12-18
Version 0.4.0, 2013-11-13
Version 0.3.0, 2013-11-07
Version 0.2.5, 2013-11-06
Version 0.2.4, 2013-10-02
Version 0.2.3, 2013-09-25
Version 0.2.2, 2013-09-24
Version 0.2.1, 2013-09-23
Version 0.2.0, 2013-09-01
Version 0.1.0, 2013-08-27

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Modelica.Magnetic.QuasiStatic.FundamentalWave.UsersGuide.References Modelica.Magnetic.QuasiStatic.FundamentalWave.UsersGuide.References



[Lang1984] W. Lang, "Über die Bemessung verlustarmer Asynchronmotoren mit Käfigläufer für Pulsumrichterspeisung," Doctoral Thesis, Technical University of Vienna, 1984.

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Automatically generated Thu Jan 24 11:19:52 2019.