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small fix
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ceraolo committed Jul 1, 2023
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59 changes: 9 additions & 50 deletions Modelica/Electrical/Analog/Lines/Functions/LineCmatrix.mo
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Expand Up @@ -4,8 +4,6 @@ function lineCmatrix
extends Modelica.Icons.Function;
import Modelica.Constants.epsilon_0;
import Modelica.Constants.pi;
import Modelica.ComplexMath;
import Modelica.Utilities.Streams;
input Integer n "Number of conductors";
input Modelica.Units.SI.Length x[n] "Horizontal abscissas of conductors";
input Modelica.Units.SI.Length y[n] "Vertical abscissas of conductors";
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end for;
annotation (
Documentation(info="<html>
<p>
This function computes Capacitances of multi-conductor transmission lines, according to
the formulas as reported in
[<a href=\"modelica://Modelica.Electrical.Analog.UsersGuide.References\">Cerolo2018</a>, Appendix].
The results obtained with this function have been checked with Fig. 4.1 of
[<a href=\"modelica://Modelica.Electrical.Analog.UsersGuide.References\">EmtpTheoryBook</a>],
with good compliance.
</p>
<p>
Internally, it computes the <strong>C</strong> matrix, which corresponds to the formulas
<strong>V</strong>&nbsp;=&nbsp;<strong>Y</strong><strong>I</strong>,
<strong>Y</strong>&nbsp;=&nbsp;&omega;<strong>C</strong>
where
</p>
<p>This function computes Capacitances of multi-conductor transmission lines, according to the formulas as reported in [<a href=\"modelica://Modelica.Electrical.Analog.UsersGuide.References\">Cerolo2018</a>, Appendix]. The results obtained with this function have been checked with Fig. 4.1 of [<a href=\"modelica://Modelica.Electrical.Analog.UsersGuide.References\">EmtpTheoryBook</a>], with good compliance. </p>
<p>Internally, it computes the <b>C</b> matrix, which corresponds to the formulas <b>V</b>&nbsp;=&nbsp;<b>YI</b>, <b>Y</b>&nbsp;=&nbsp;&omega;<b>C</b> where </p>
<ul>
<li>
<strong>V</strong> is the vector of voltages between conductors and the reference
(the return conductor, usually ground),
</li>
<li>
<strong>I</strong>&nbsp;is the vector of transverse currents (between conductors and the
return conductor, usually ground) due to the capacitive coupling between the conductors,
</li>
<li>
<strong>Y</strong> is the matrix of transverse admittances of the multiconductor line (S/m),
</li>
<li>
&omega; is the angular frequency when constant-frequency steady-state operation of the
line is considered
</li>
<li><b>V</b> is the vector of voltages between conductors and the reference (the return conductor, usually ground), </li>
<li><b>I</b>&nbsp;is the vector of transverse currents (between conductors and the return conductor, usually ground) due to the capacitive coupling between the conductors, </li>
<li><b>Y</b> is the matrix of transverse admittances of the multiconductor line (S/m), </li>
<li>&omega; is the angular frequency when constant-frequency steady-state operation of the line is considered </li>
</ul>
<p>
This matrix&nbsp;<strong>C</strong>, has always negative off-diagonal values, and positive
diagonal values.
</p>
<p>
From <strong>C</strong> matrix, the internal <strong>Cflat</strong> matrix is computed,
containing physical capacitors that can be imagined between conductors to model capacitive
effects. For instance C12 is the capacitance (per unit length) to be put between
conducturors 1 and 2. The output array <strong>Ccompact</strong> contains the elements of
the <strong>Cflat</strong> matrix ordered as described in the
<a href=\"modelica://Modelica.Electrical.Analog.Lines.M_OLine\">M_OLine</a> model, and is
used in example
<a href=\"modelica://Modelica.Electrical.Analog.Examples.Lines.PowerLineWithFence\">Examples.Lines.PowerLineWithFence</a>
in conjunction with M_OLine.
</p>
<p>
For an example on how to use this function, consider model
Electrical.Analog.Examples.Lines.TestCmatrix.
</p>
<p>This matrix&nbsp;<b>C</b>, has always negative off-diagonal values, and positive diagonal values. </p>
<p>From <b>C</b> matrix, the internal <b>Cflat</b> matrix is computed, containing physical capacitors that can be imagined between conductors to model capacitive effects. For instance C12 is the capacitance (per unit length) to be put between conducturors 1 and 2. The output array <b>Ccompact</b> contains the elements of the <b>Cflat</b> matrix ordered as described in the <a href=\"modelica://Modelica.Electrical.Analog.Lines.M_OLine\">M_OLine</a> model, and is used in example <a href=\"modelica://Modelica.Electrical.Analog.Examples.Lines.PowerLineWithFence\">Examples.Lines.PowerLineWithFence</a> in conjunction with M_OLine. </p>
<p>For an example on how to use this function, consider model Electrical.Analog.Examples.Lines.CompareCmatrix. </p>
</html>", revisions="<html>
<p><i>July, 2023</i> </p>
<p>Original implementation by Massimo Ceraolo of the University of Pisa </p>
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