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Fixed some minor wrong html-tags.
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git-svn-id: https://svn.modelica.org/projects/Modelica/trunk@6392 7ce873d0-865f-4ce7-a662-4bb36ea78beb
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142 changes: 113 additions & 29 deletions Modelica/Magnetic/FundamentalWave.mo
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Expand Up @@ -108,43 +108,120 @@ The term <b>fundamental wave</b> refers to spatial waves of the electro magnetic
extends Modelica.Icons.Information;
annotation (Documentation(info="<html>
<p><b>Symmetrical three phase system</b> </p>
<p>Symmetrical three phases systems of currents (or voltages) consists of three sinusoidal sine waves with with an angular displacement of <img src=\"modelica://Modelica/Resources/Images/Magnetic/FundamentalWave/UsersGuide/MultiPhase/2pi_3.png\"/>. </p>
<p><img src=\"modelica://Modelica/Resources/Images/Magnetic/FundamentalWave/UsersGuide/MultiPhase/i123.png\"/>, </p>
<p>Electrical three phase machines have (usually) symmetrical three phase windings which excite spatial magnetic potential with a spacial displacement of <img src=\"modelica://Modelica/Resources/Images/Magnetic/FundamentalWave/UsersGuide/MultiPhase/2pi_3.png\"/> -- with respect to the fundamental wave, see [<a href=\"modelica://Modelica.Magnetic.FundamentalWave.UsersGuide.References\">Laughton02</a>]. Such a symmetrical three phase system of currents (or voltages) can be represented by <a href=\"http://en.wikipedia.org/wiki/Phasor\">phasors</a>, as depicted in Fig. 1(a). The associated three phase winding is depicted in Fig. 2(a). The winding axis are displaced by <img src=\"modelica://Modelica/Resources/Images/Magnetic/FundamentalWave/UsersGuide/MultiPhase/2pi_3.png\"/>: </p>
<p><img src=\"modelica://Modelica/Resources/Images/Magnetic/FundamentalWave/UsersGuide/MultiPhase/orientationk_3.png\"/> </p>
<p>So there is is a strong coherence between angular displacement in the time and spatial domain which also applies to multi phase systems. </p>
<p><b>Fig. 1:</b> Symmetrical (a) three phase and (b) five phase current system </p>
<table cellspacing=\"0\" cellpadding=\"2\" border=\"0\"><tr>
<td><p><img src=\"modelica://Modelica/Resources/Images/Magnetic/FundamentalWave/UsersGuide/MultiPhase/phase35.png\"/> </p></td>
<p>
Symmetrical three phases systems of currents (or voltages) consists of three sinusoidal
sine waves with with an angular displacement of
<img src=\"modelica://Modelica/Resources/Images/Magnetic/FundamentalWave/UsersGuide/MultiPhase/2pi_3.png\"/>.
</p>

<p>
<img src=\"modelica://Modelica/Resources/Images/Magnetic/FundamentalWave/UsersGuide/MultiPhase/i123.png\"/>,
</p>

<p>
Electrical three phase machines have (usually) symmetrical three phase windings which
excite spatial magnetic potential with a spacial displacement of
<img src=\"modelica://Modelica/Resources/Images/Magnetic/FundamentalWave/UsersGuide/MultiPhase/2pi_3.png\"/>
- with respect to the fundamental wave,
see [<a href=\"modelica://Modelica.Magnetic.FundamentalWave.UsersGuide.References\">Laughton02</a>].
Such a symmetrical three phase system of currents (or voltages) can be represented by
<a href=\"http://en.wikipedia.org/wiki/Phasor\">phasors</a>, as depicted in Fig. 1(a).
The associated three phase winding is depicted in Fig. 2(a). The winding axis are displaced by
<img src=\"modelica://Modelica/Resources/Images/Magnetic/FundamentalWave/UsersGuide/MultiPhase/2pi_3.png\"/>:
</p>

<p>
<img src=\"modelica://Modelica/Resources/Images/Magnetic/FundamentalWave/UsersGuide/MultiPhase/orientationk_3.png\"/>
</p>

<p>
So there is is a strong coherence between angular displacement in the time and
spatial domain which also applies to multi phase systems.
</p>

<p>
<b>Fig. 1:</b> Symmetrical (a) three phase and (b) five phase current system
</p>

<table cellspacing=\"0\" cellpadding=\"2\" border=\"0\">
<tr><td><p><img src=\"modelica://Modelica/Resources/Images/Magnetic/FundamentalWave/UsersGuide/MultiPhase/phase35.png\"/> </p></td>
</tr>
</table>
<p><br/><b>Fig. 2:</b> Symmetrical (a) three phase and (b) five phase winding </p>
<table cellspacing=\"0\" cellpadding=\"2\" border=\"0\"><tr>
<td><p><img src=\"modelica://Modelica/Resources/Images/Magnetic/FundamentalWave/UsersGuide/MultiPhase/winding35.png\"/> </p></td>

<p>
<br/><b>Fig. 2:</b> Symmetrical (a) three phase and (b) five phase winding
</p>

<table cellspacing=\"0\" cellpadding=\"2\" border=\"0\">
<tr><td><p><img src=\"modelica://Modelica/Resources/Images/Magnetic/FundamentalWave/UsersGuide/MultiPhase/winding35.png\"/> </p></td>
</tr>
</table>
<p><br/><b>Symmetrical multi phase system</b> </p>
<p>In symmetrical multi phase systems odd and even phase numbers have to be distinguished. </p>
<p><b><font style=\"font-size: 7pt; \">Odd number of phases</b> </p>
<p>For a symmetrical multi phase system with <img src=\"modelica://Modelica/Resources/Images/Magnetic/FundamentalWave/UsersGuide/MultiPhase/m.png\"/> phases the displacement in the time and spatial domain is <img src=\"modelica://Modelica/Resources/Images/Magnetic/FundamentalWave/UsersGuide/MultiPhase/2pi_m.png\"/>, as depicted in Fig. 1 and 2. </p>
<p>Mathematically, this symmetry is expressd in terms of phase currents by: </p>

<p>
<br/><b>Symmetrical multi phase system</b> </p>

<p>
In symmetrical multi phase systems odd and even phase numbers have to be distinguished.
</p>

<h5>Odd number of phases</h5>

<p>
For a symmetrical multi phase system with <img src=\"modelica://Modelica/Resources/Images/Magnetic/FundamentalWave/UsersGuide/MultiPhase/m.png\"/>
phases the displacement in the time and spatial domain is
<img src=\"modelica://Modelica/Resources/Images/Magnetic/FundamentalWave/UsersGuide/MultiPhase/2pi_m.png\"/>,
as depicted in Fig. 1 and 2.
</p>

<p>
Mathematically, this symmetry is expressd in terms of phase currents by:
</p>

<p><img src=\"modelica://Modelica/Resources/Images/Magnetic/FundamentalWave/UsersGuide/MultiPhase/ik_odd.png\"/> </p>
<p>The orientation of the winding axis of such winding is given by: </p>

<p>
The orientation of the winding axis of such winding is given by:
</p>

<p><img src=\"modelica://Modelica/Resources/Images/Magnetic/FundamentalWave/UsersGuide/MultiPhase/orientationk_m.png\"/> </p>
<p><b>Even number of phases</b> </p>
<p>In the current implementation of the FundamentalWave library, phase numbers equal to the power of two are not supported. However, any other multi phase system with even an phase number, <img src=\"modelica://Modelica/Resources/Images/Magnetic/FundamentalWave/UsersGuide/MultiPhase/m.png\"/>, can be recursively split into various symmetrical systems with odd phase numbers, as depicted in Fig. 3 and 4. The displacement between the two symmetrical systems is <img src=\"modelica://Modelica/Resources/Images/Magnetic/FundamentalWave/UsersGuide/MultiPhase/pi_m.png\"/>. A function for calculating the <a href=\"Modelica.Electrical.MultiPhase.Functions.symmetricOrientation\">symmetricOrientation</a> is available. </p>

<h5>Even number of phases</h5>

<p>
In the current implementation of the FundamentalWave library, phase numbers equal
to the power of two are not supported. However, any other multi phase system with even
an phase number, <img src=\"modelica://Modelica/Resources/Images/Magnetic/FundamentalWave/UsersGuide/MultiPhase/m.png\"/>,
can be recursively split into various symmetrical systems with odd phase numbers, as depicted in Fig. 3 and 4.
The displacement between the two symmetrical systems is
<img src=\"modelica://Modelica/Resources/Images/Magnetic/FundamentalWave/UsersGuide/MultiPhase/pi_m.png\"/>.
A function for calculating the <a href=\"Modelica.Electrical.MultiPhase.Functions.symmetricOrientation\">symmetricOrientation</a> is available.
</p>

<p><b>Fig. 3:</b> Symmetrical (a) six and (b) ten phase current system </p>
<table cellspacing=\"0\" cellpadding=\"2\" border=\"0\"><tr>
<td><p><img src=\"modelica://Modelica/Resources/Images/Magnetic/FundamentalWave/UsersGuide/MultiPhase/phase610.png\"/> </p></td>

<table cellspacing=\"0\" cellpadding=\"2\" border=\"0\">
<tr><td><p><img src=\"modelica://Modelica/Resources/Images/Magnetic/FundamentalWave/UsersGuide/MultiPhase/phase610.png\"/> </p></td>
</tr>
</table>
<p><br/><b>Fig. 4:</b> Symmetrical (a) six and (b) ten phase winding </p>

<p>
<br/><b>Fig. 4:</b> Symmetrical (a) six and (b) ten phase winding
</p>

<table cellspacing=\"0\" cellpadding=\"2\" border=\"0\"><tr>
<td><p><img src=\"modelica://Modelica/Resources/Images/Magnetic/FundamentalWave/UsersGuide/MultiPhase/winding610.png\"/> </p></td>
</tr>
</table>
<p><br/><h4>Note</h4></p>
<p>In a fully symmetrical machine, the orientation of the winding axes and the symmetrical currents (or voltages) <a href=\"http://en.wikipedia.org/wiki/Phasor\">phasors</a> have different signs; see Fig. 1 and 2 for odd phase numbers and Fig. 3 and 4 for even phase numbes. </p>

<p>
<br/><h4>Note</h4>
</p>

<p>
In a fully symmetrical machine, the orientation of the winding axes and the symmetrical currents (or voltages)
<a href=\"http://en.wikipedia.org/wiki/Phasor\">phasors</a> have different signs; see Fig. 1 and 2 for odd phase numbers
and Fig. 3 and 4 for even phase numbes.
</p>
</html>"));
end MultiPhase;

Expand Down Expand Up @@ -269,7 +346,7 @@ no. 829420.
<h5>Version 3.2.1, 2013-05-12</h5>

<ul>
<li>Added voltages, currents, complex flux and magnetic potential difference as global variables in
<li>Added voltages, currents, complex flux and magnetic potential difference as global variables in
<a href=\"modelica://Modelica.Magnetic.FundamentalWave.Components.MultiPhaseElectroMagneticConverter\">multi phase converter</a></li>
<li>Added two more component examples, showing the equivalent nature of electrical and magnetic domain</li>
</ul>
Expand Down Expand Up @@ -512,8 +589,16 @@ model from R to G</li>
end References;
annotation (Documentation(info="<html>
<p>
This library contains components for modelling of electromagnetic fundamental wave models for the application in multi phase phase
<a href=\"modelica://Modelica.Magnetic.FundamentalWave.BasicMachines\">electric machines</a>. The number of phases is not restricted to three. DC machines are (currently) not included in this library. The FundamentalWave library is an alternative approach to the <a href=\"modelica://Modelica.Electrical.Machines\">Modelica.Electrical.Machines</a> 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.
This library contains components for modelling of electromagnetic fundamental wave
models for the application in multi phase phase
<a href=\"modelica://Modelica.Magnetic.FundamentalWave.BasicMachines\">electric machines</a>.
The number of phases is not restricted to three. DC machines are (currently) not included
in this library. The FundamentalWave library is an alternative approach to the
<a href=\"modelica://Modelica.Electrical.Machines\">Modelica.Electrical.Machines</a> 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.
</p>

<p>
Expand All @@ -522,13 +607,12 @@ For more details see the <a href=\"modelica://Modelica.Magnetic.FundamentalWave.

<h5>Note</h5>

<p>
<ul>
<li>All the machine models provided in this library are equivalent two pole machines.
The magnetic potential difference of the connector therefore also refers to an equivalent two pole machine</li>
<li>In machines with <strong>more than three phases</strong> only effects of currents and voltages on the magnetic <strong>fundamental waves</strong> are considered. Other magnetic effects due to higher harmonic are not taken into account.</li>
</ul>
</p>


</html>"));
end UsersGuide;
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