modelica · AHaumer · Feb 20, 2022 · Mar 25, 2022 · Apr 19, 2022 · May 13, 2022
diff --git a/Modelica/Magnetic/FundamentalWave/UsersGuide/PermanentMagnets.mo b/Modelica/Magnetic/FundamentalWave/UsersGuide/PermanentMagnets.mo
@@ -0,0 +1,65 @@
+within Modelica.Magnetic.FundamentalWave.UsersGuide;
+class PermanentMagnets "Concept of permanent magnet modeling"
+  extends Modelica.Icons.Information;
+  annotation (Documentation(info="<html>
+
+<h4>Concept of permanent magnet modeling</h4>
+
+<p>
+High performance permanent magnets (e.g. NdFeB) operate on their largest hysteresis loop. 
+This characteristic is nearly linear in the second quadrant between remnant flux density B<sub>r</sub> and coercive field strength H<sub>c</sub>. 
+As an example, typical values are B<sub>r</sub> = 1.3 T and H<sub>c</sub> = 1000 kA/m. 
+This proves that the slope of the hysteresis loop is nearly fully saturated with a relative permeability &mu;<sub>r</sub> = B<sub>r</sub> / H<sub>c</sub> / &mu;<sub>0</sub> = 1.
+</p>
+
+<p>
+At normal operational temperatures, the bend below that demagnetization could occur is left from coercive field strength at negative flux density. 
+The permanent magnet's energy density is the maximum of the product B x H along this characteristic. 
+It can be calculated as B<sub>r</sub> x H<sub>c</sub> / 4 = 325 kJ/m<sup>3</sup> for the above mentioned example.
+</p>
+
+<p>
+Using geometry, flux density is proportional to magnetic flux and magnetic field strength is proportional to magnetomotive force. 
+The point of operation can be found at the intersection (1) between the magnet's hysteresis loop and the characteristic of the rest of the machine's magnetic circuit in d-axis. 
+The magnet can be represented as a linear source with open-circuit magnetomotive force mmf<sub>0</sub> resulting from H<sub>c</sub>, 
+short-circuit flux &psi;<sub>sc</sub> resulting from B<sub>r</sub> and an inner magnetic resistance R<sub>i</sub> = &psi;<sub>sc</sub> / mmf<sub>0</sub> equivalent to that of air. 
+If this inner magnetic resistance R<sub>i</sub> is added to the nonlinear characteristic of the rest of the machine's magnetic circuit R<sub>m</sub>, 
+the permanent magnet can be characterized by its open-circuit mmf<sub>0</sub> (2).
+</p>
+
+<table border=\"0\" cellspacing=\"0\" cellpadding=\"2\">
+  <caption><strong>Fig. 1:</strong> Magnetic characteristic and </caption>
+  <tr>
+    <td>
+      <img src=\"modelica://Modelica/Resources/Images/Magnetic/FundamentalWave/UsersGuide/PermanentMagnets/PM.png\">
+    </td>
+  </tr>
+</table>
+
+<p>
+In <a href=\"modelica://Modelica.Electrical.Machines\">Modelica.Electrical.Machines</a> this open-circuit mmf<sub>0</sub> is modeled as a constant equivalent excitation current source, 
+in <a href=\"modelica://Modelica.Magnetic.FundamentalWave\">Modelica.Magnetic.FundamentalWave</a> as a constant magnetic potential difference. 
+In both models, the permanent magnet's inner magnetic resistance R<sub>i</sub> is assumed to be comprised in the d-axis inductance L<sub>d</sub>.
+</p>
+
+<p>
+The remnant flux density B<sub>r</sub> and coercive field strength H<sub>c</sub> are known to be dependent on temperature, 
+with a relative temperature coefficient of approximately &alpha;<sub>B</sub> = - 0.1 &#37;/K for B<sub>r</sub> and &alpha;<sub>H</sub> = - 0.5 &#37;/K for H<sub>c</sub>. 
+This results in a temperature dependency of the inner magnetic resistance R<sub>i</sub> = &psi;<sub>sc</sub> / mmf<sub>0</sub> 
+and therefore a temperature dependency of d-axis inductance L<sub>d</sub>. 
+</p>
+
+<p>
+Assuming the same temperature coefficient for B<sub>r</sub> and H<sub>c</sub>, the inner magnetic resistance R<sub>i</sub> 
+and furthermore the d-axis inductance L<sub>d</sub> would be invariant with respect to temperature.
+However, this temperature effects are not taken into account in the Modelica Standard Library.
+</p>
+
+<h4>Further reading</h4>
+
+<p>
+[VAC] Vacuumschmelze, <a href=\"https://vacuumschmelze.de/03_Documents/Brochures/VACODYM-VACOMAX%20en.pdf\"><em>Rare Earth Permanent Magnets</em></a>.
+</p>
+
+</html>"));
+end PermanentMagnets;
diff --git a/Modelica/Magnetic/FundamentalWave/UsersGuide/References.mo b/Modelica/Magnetic/FundamentalWave/UsersGuide/References.mo
@@ -67,6 +67,13 @@ class References "References"
         Springer-Verlag, Berlin, Heidelberg, New York, 1973.</td>
     </tr>
 
+    <tr>
+      <td>[VAC]</td>
+      <td>Vacuumschmelze,
+        <a href=\"https://vacuumschmelze.de/03_Documents/Brochures/VACODYM-VACOMAX%20en.pdf\"><em>Rare Earth Permanent Magnets</em></a>
+        </td>
+    </tr>
+
 </table>
 </html>"));
 end References;
diff --git a/Modelica/Magnetic/FundamentalWave/UsersGuide/package.order b/Modelica/Magnetic/FundamentalWave/UsersGuide/package.order
@@ -2,6 +2,7 @@ Concept
 Polyphase
 WindingModel
 Parameters
+PermanentMagnets
 Contact
 ReleaseNotes
 References
diff --git a/...ca/Resources/Images/Magnetic/FundamentalWave/UsersGuide/PermanentMagnets/PM.png b/...ca/Resources/Images/Magnetic/FundamentalWave/UsersGuide/PermanentMagnets/PM.png