model EddyCurrent "Constant loss model under sinusoidal magnetic conditions"
import Modelica.Constants.pi;
extends Modelica.Magnetic.FundamentalWave.Interfaces.PartialTwoPortElementary;
parameter Modelica.SIunits.Conductance G(min = 0) "Equivalent symmetric loss conductance";
extends Modelica.Thermal.HeatTransfer.Interfaces.PartialElementaryConditionalHeatPort(final T = 273.15);
equation
if 0 < G then
0.5 * pi * V_m.re = G * der(Phi.re);
0.5 * pi * V_m.im = G * der(Phi.im);
else
V_m.re = 0;
V_m.im = 0;
end if;
lossPower = 0.5 * pi * (V_m.re * der(Phi.re) + V_m.im * der(Phi.im));
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Documentation(info = "<html>\n<p>\nThe eddy current loss model with respect to fundamental wave effects is designed in accordance to\n<a href=\"modelica://Modelica.Magnetic.FluxTubes.Basic.EddyCurrent\">FluxTubes.Basic.EddyCurrent</a>.\n</p>\n\n<blockquote>\n<img src=\"modelica://Modelica/Resources/Images/Magnetic/FundamentalWave/Components/eddycurrent.png\"\n alt=\"eddycurrent.png\">\n</blockquote>\n\n<table border=\"0\" cellspacing=\"0\" cellpadding=\"2\">\n <caption align=\"bottom\">Fig. 1: equivalent models of eddy current losses</caption>\n <tr>\n <td>\n <img src=\"modelica://Modelica/Resources/Images/Magnetic/FundamentalWave/Components/eddycurrent_electric.png\"\n alt=\"eddycurrent_electric.png\">\n </td>\n </tr>\n</table>\n\n<p>Due to the nature of eddy current losses, which can be represented by symmetric\nconductors in an equivalent electric circuit (Fig. 1), the respective\nnumber of phases <img src=\"modelica://Modelica/Resources/Images/Magnetic/FundamentalWave/m.png\" alt=\"m\"> has to be taken into account.\nAssume that the <img src=\"modelica://Modelica/Resources/Images/Magnetic/FundamentalWave/m.png\" alt=\"m\"> conductances\nof the equivalent circuit are <img src=\"modelica://Modelica/Resources/Images/Magnetic/FundamentalWave/Components/Gc.png\" alt=\"G_c\">,\nthe conductance for the eddy current loss model is determined by</p>\n\n<blockquote>\n<img src=\"modelica://Modelica/Resources/Images/Magnetic/FundamentalWave/Components/GGc.png\"\n alt=\"GGc\">\n</blockquote>\n\n<p>\nwhere <img src=\"modelica://Modelica/Resources/Images/Magnetic/FundamentalWave/N.png\" alt=\"N\"> is the number of turns of the symmetric electro magnetic coupling.\n</p>\n\n<p>For such an <img src=\"modelica://Modelica/Resources/Images/Magnetic/FundamentalWave/m.png\" alt=\"m\"> phase system\nthe relationship between the voltage and current <a href=\"https://www.haumer.at/refimg/SpacePhasors.pdf\">space phasors</a>\nand the magnetic flux and magnetic potential difference phasor is\n</p>\n\n<blockquote>\n<img src=\"modelica://Modelica/Resources/Images/Magnetic/FundamentalWave/Components/vPhi.png\" alt=\"vPhi\">,<br>\n<img src=\"modelica://Modelica/Resources/Images/Magnetic/FundamentalWave/Components/iV_m.png\" alt=\"iV_m\">,\n</blockquote>\n\n<p>\nwhere <img src=\"modelica://Modelica/Resources/Images/Magnetic/FundamentalWave/v_k.png\" alt=\"v_k\">\nand <img src=\"modelica://Modelica/Resources/Images/Magnetic/FundamentalWave/i_k.png\" alt=\"i_k\">\nare the phase voltages and currents, respectively.\n</p>\n\n<p>\nThe dissipated loss power\n</p>\n<blockquote>\n<img src=\"modelica://Modelica/Resources/Images/Magnetic/FundamentalWave/Components/lossPower.png\" alt=\"lossPower\">\n</blockquote>\n<p>\ncan be determined for the <a href=\"https://www.haumer.at/refimg/SpacePhasors.pdf\">space phasor</a>\nrelationship of the voltage and current space phasor.\n</p>\n<h4>See also</h4>\n\n<p><a href=\"modelica://Modelica.Magnetic.FluxTubes.Basic.EddyCurrent\">FluxTubes.Basic.EddyCurrent</a></p>\n\n</html>"));
end EddyCurrent;