Modelica.Magnetic.FundamentalWave.UsersGuide

This library contains components for modelling of electromagnetic fundamental wave models for the application in three phase electric machines. DC machines are (currently) not included in this library. The FundamentalWave library is an alternative approach to the Modelica.Electrical.Machines library. A great advantage of this library is the strict object orientation of the electrical and magnetic components that the electric machines models are composed of. From a didactic point of view this library is very beneficial for students in the field of electrical engineering.

For more details see the concept.

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Package Content

Name Description

Concept Fundamental wave concept

Contact Contact

ReleaseNotes Release Notes

References References

Name	Description
Concept	Fundamental wave concept
Contact	Contact
ReleaseNotes	Release Notes
References	References

Modelica.Magnetic.FundamentalWave.UsersGuide.Concept

Overview of the concept of fundamental waves

The exact magnetic field in the air gap of an electric machine is usually determined by an electro magnetic finite element analysis. The waveform of the magnetic field, e.g., the magnetic potential difference , consists of a spatial fundamental wave - with respect to one pole pair - and additional harmonic waves of different order. The fundamental wave is however dominant in the air gap of an electric machine.

Field lines of a four pole induction machine

In the fundamental wave theory only a pure sinusoidal distribution of magnetic quantities is assumed. It is thus assumed that all other harmonic wave effects are not taken into account.

Magnetic potential difference of a four pole machine, where is the angle of the spatial domain with respect to one pole pair

The waveforms of the magnetic field quantities, e.g., the magnetic potential difference , can be represented by complex phasor, e.g., according to:

Spatial distribution of the magnetic potential difference (red shade = positive sine wave, blue shade = negative sine wave) including complex phasor representing this spatial distribution

The potential and flow quantities of this library are the complex magnetic potential difference and the complex magnetic flux as defined in the basic magnetic port. Due to the sinusoidal distribution of magnetic potential and flux, such a complex phasor representation can be used. This way, the FundamentalWave library can be seen as a spatial extension of the FluxTubes library.

The specific arrangement of windings in electric machines with pole pairs give rise to sinusoidal dominant magnetic potential wave. The spatial period of this wave is determined by one pole pair [Mueller70, Spaeth73].

The main components of an electric machine model based on the FundamentalWave library are multi phase and single phase windings, air gap as well as symmetric or salient cage models. The electric machine models provided in this library are based on symmetrical three phase windings in the stator and equivalent two or three phase windings in the rotor.

Assumptions

The machine models of the FundamentalWave library are currently based on the following assumptions

The number of stator phases is limited to three [Eckhardt82]
The phase windings are assumed to be symmetrical; an extension to this approach can be considererd
Only fundamental wave effects are taken into account
There are no restrictions on the waveforms of voltages and currents
All resistances and inductances are modeled as constant quantities; saturation effects, cross coupling effects [Li07], temperature dependency of resistances and deep bar effects could be considered in an extension to this library
Core losses, i.e., eddy current and hysteresis losses, friction losses and stray load losses are currently not considered [Haumer09]
The only dissipated losses in the electric machine models are currently ohmic heat losses

Note

The term fundamental wave refers to spatial waves of the electro magnetic quantities. This library has no limitations with respect to the waveforms of the time domain signals of any voltages, currents, etc.

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Modelica.Magnetic.FundamentalWave.UsersGuide.Contact

Contact

Christian Kral
Austrian Institute of Technology, AIT
Mobility Department
Giefinggasse 2, 1210 Vienna, Austria
email: christian.kral@ait.ac.at

Anton Haumer
Technical Consulting & Electrical Engineering
3423 St. Andrae-Woerdern, Austria
email: a.haumer@haumer.at

Acknowledgements

Based on an original idea of Michael Beuschel this library was developed [Beuschel00]. The authors of the FundamentalWave library would like to thank Michael Beuschel for contributing his source code to this library.

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Modelica.Magnetic.FundamentalWave.UsersGuide.ReleaseNotes

Version 1.7.1, 2010-09-03

Naming and documentation of PartialTwoPort is exchanged by PartialTwoPortElementary to match the naming conventions of Rotational.Interfaces and Translational.Interfaces
Fixed a broken link and updated documentation
Adaptions to Complex SIunits

Version 1.7.0, 2010-05-31

Changed symmetric multi phase winding model
- Added zero sequence inductance based on zero inductor
- Replaced electrical model of stray inductor by stray reluctance model
- Integrated cores losses and heat port
Added rotor core loss parameters in asynchronous induction machine with slip rings
Renamed heat ports of single phase winding and symmetric multi phase winding
Relocated core losses between zero inductor and stray reluctance model in the magntic domain
Renamed instances of stator and rotor (winding) models in each machines
Added magnetic potential sensor
Removed state selections
Updates due to changed loss variable and heat port names in Electrical.Machines
Added machine specific output records to summarize power and loss balance
Updated images of Users Guide
Improved performance due to annotation(Evaluate=true) added to the parameters of the single phase winding
Reduced number of states in symmetric cage model by introducing an additional non-grounded star connection

Version 1.6.0, 2010-05-05

Renamed all parameters windingAngle to orientation. The following classes are affected:
Update due to changed class names in Machines.Icons
Using HeatTransfer.Interfaces.PartialElementaryConditionalHeatPort instead of Analog.Interfaces.ConditionalHeatPort in EddyCurrent
Added modelica:// to all Modelica hyper links
Fixed bug in displayed parameters of EddyCurrent
Updated some images (and renamed image file LossPower.png to lossPower.png)
Exchanged positive and negative stator ports of RotorSaliencyAirGap model, adapted equations accordingly and updated code documentation.

Version 1.5.0, 2010-04-28

Added stator core, friction, stray load and brush losses to all machine types based on loss models of the Machines library.
Changed parameter of EddyCurrent model from R to G
Fixed wrong sign of internal quantity tauElectrical, model behavior does not change
Rewrote equations of electro magnetic coupling to look more elegant

Version 1.4.0, 2010-04-22

Added eddy current model in accordance to FluxTubes library
Added thermal heat port to eddy current model
Minor updates due to dependencies of Machines

Version 1.3.0, 2010-02-26

Changed some icon references
Added state selections for the machine models
Restructured partial machine model
Added copyright information

Version 1.2.0, 2010-02-17

Renamed Machines to BasicMachines
Updated dependencies due to renamed class LinearTemperatureCoefficient20
Added release notes in User's Guide

Version 1.1.0, 2010-02-15

Added thermal connectors and temperature dependent resistances

Version 1.0.0, 2010-02-04

Integrated the libray into the MSL

Version 0.4.0, 2009-10-29

Corrected bug in magnetic potential calculation

Version 0.3.0, 2009-10-28

Renamed number of turns and winding angles

Version 0.2.0, 2009-10-20

Added idle model

Version 0.1.0, 2009-07-22

First version based on the concept of the FluxTubes library and the Magnetics library of Michael Beuschel [Beuschel00]

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Modelica.Magnetic.FundamentalWave.UsersGuide.References

References

[Beuschel00]	M. Beuschel, " A uniform approach for modelling electrical machines," Modelica Workshop, pp. 101-108, October 23-24, 2000.
[Eckhardt82]	H. Eckhardt, Grundzüge der elektrischen Maschinen (in German), B. G. Teubner Verlag, Stuttgart, 1982.
[Haumer09]	A. Haumer, and C. Kral, "The AdvancedMachines Library: Loss Models for Electric Machines," Modelica Conference, 2009.
[Li07]	Y. Li, Z. Q. Zhu, D. Howe, and C. M. Bingham, "Modeling of Cross-Coupling Magnetic Saturation in Signal-Injection-Based Sensorless Control of Permanent-Magnet Brushless AC Motors," IEEE Transactions on Magnetics, vol. 43, no. 6, pp. 2552-2554, June 2007.
[Mueller70]	G, Müller, Elektrische Maschinen -- Grundlagen, Aufbau und Wirkungsweise (in German), VEB Verlag Technik Berlin, 4th edition, 1970.
[Spaeth73]	H. Späth, Elektrische Maschinen -- Eine Einführung in die Theorie des Betriebsverhaltens (in German), Springer-Verlag, Berlin, Heidelberg, New York, 1973.

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