class Concept "Fundamental wave concept"
extends Modelica.Icons.Information;
annotation (Documentation(info = "<html>\n\n<h4>Overview of the concept of fundamental waves</h4>\n\n<p>\nThe 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 <img src=\"modelica://Modelica/Resources/Images/Magnetic/FundamentalWave/V_m_phi.png\">, consists of a spatial fundamental wave - with respect to an equivalent two pole machine - and additional harmonic waves of different order. The fundamental wave is however dominant in the air gap of an electric machine.\n</p>\n\n<table border=\"0\" cellspacing=\"0\" cellpadding=\"2\">\n <caption align=\"bottom\"><strong>Fig. 1:</strong> Field lines of a four pole induction machine</caption>\n <tr>\n <td>\n <img src=\"modelica://Modelica/Resources/Images/Magnetic/FundamentalWave/UsersGuide/Concept/aimc_fem.png\">\n </td>\n </tr>\n</table>\n\n<p>\nIn 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.</p>\n\n<table border=\"0\" cellspacing=\"0\" cellpadding=\"2\">\n <caption align=\"bottom\"><strong>Fig. 2:</strong> Magnetic potential difference of a four pole machine, where <img src=\"modelica://Modelica/Resources/Images/Magnetic/FundamentalWave/varphi.png\"> is the angle of the spatial domain with respect to one pole pair</caption>\n <tr>\n <td>\n <img src=\"modelica://Modelica/Resources/Images/Magnetic/FundamentalWave/UsersGuide/Concept/four_pole_V_m.png\">\n </td>\n </tr>\n</table>\n\n<p>\nThe waveforms of the magnetic field quantities, e.g., the magnetic potential difference <img src=\"modelica://Modelica/Resources/Images/Magnetic/FundamentalWave/V_m_phi.png\">, can be represented by complex phasor, e.g., <img src=\"modelica://Modelica/Resources/Images/Magnetic/FundamentalWave/V_m.png\"> according to:\n</p>\n\n<p>\n <img src=\"modelica://Modelica/Resources/Images/Magnetic/FundamentalWave/V_m_real_complex.png\">\n</p>\n\n<p>It is important to note that the magnetic potential used in this library <strong>always</strong> refers to an equivalent two pole machine.</p>\n\n<table border=\"0\" cellspacing=\"0\" cellpadding=\"2\">\n <caption align=\"bottom\"><strong>Fig. 3:</strong> Spatial distribution of the magnetic potential difference (red shade = positive sine wave, blue shade = negative sine wave) including complex phasor representing this spatial distribution</caption>\n <tr>\n <td>\n <img src=\"modelica://Modelica/Resources/Images/Magnetic/FundamentalWave/UsersGuide/Concept/electrical_reference_V_m.png\">\n </td>\n </tr>\n</table>\n\n<p>\nThe potential and flow quantities of this library are the complex magnetic potential difference and the complex magnetic flux as defined in the basic <a href=\"modelica://Modelica.Magnetic.FundamentalWave.Interfaces.MagneticPort\">magnetic port</a>. 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 <a href=\"modelica://Modelica.Magnetic.FluxTubes\">FluxTubes</a> library.\n</p>\n\n<p>\nThe specific arrangement of windings in electric machines with <img src=\"modelica://Modelica/Resources/Images/Magnetic/FundamentalWave/p.png\"> pole pairs give rise to sinusoidal dominant magnetic potential wave. The spatial period of this wave is determined by one pole pair\n[<a href=\"modelica://Modelica.Magnetic.FundamentalWave.UsersGuide.References\">Mueller70</a>,\n <a href=\"modelica://Modelica.Magnetic.FundamentalWave.UsersGuide.References\">Spaeth73</a>].\n</p>\n\n<p>\nThe main components of an electric machine model based on the FundamentalWave library are <a href=\"modelica://Modelica.Magnetic.FundamentalWave.BasicMachines.Components.SymmetricMultiPhaseWinding\">multi phase</a> and <a href=\"modelica://Modelica.Magnetic.FundamentalWave.BasicMachines.Components.SinglePhaseWinding\">single phase windings</a>, <a href=\"modelica://Modelica.Magnetic.FundamentalWave.BasicMachines.Components.RotorSaliencyAirGap\">air gap</a> as well as <a href=\"modelica://Modelica.Magnetic.FundamentalWave.BasicMachines.Components.SymmetricMultiPhaseWinding\">symmetric</a> or <a href=\"modelica://Modelica.Magnetic.FundamentalWave.BasicMachines.Components.SaliencyCageWinding\">salient cage</a> models.\nThe electric machine models provided in this library are based on symmetrical windings in the stator and equivalent two or three phase windings in squirrel cage rotors. Slip ring induction machines may have different phase numbers in the stator and rotor.\n</p>\n\n<h4>Assumptions</h4>\n\n<p>\nThe machine models of the FundamentalWave library are currently based on the following assumptions\n</p>\n\n<ul>\n<li>The number of stator phases is greater or equal to three\n [<a href=\"modelica://Modelica.Magnetic.FundamentalWave.UsersGuide.References\">Eckhardt82</a>]\n </li>\n<li>The phase windings are assumed to be symmetrical; an extension to this approach can be considered</li>\n<li>Only fundamental wave effects are taken into account</li>\n<li>The magnetic potential difference refers to an equivalent two pole machine</li>\n<li>There are no restrictions on the waveforms of voltages and currents</li>\n<li>All resistances and inductances are modeled as constant quantities; saturation effects, cross coupling effects\n [<a href=\"modelica://Modelica.Magnetic.FundamentalWave.UsersGuide.References\">Li07</a>], temperature dependency of resistances and deep bar effects could be considered in an extension to this library</li>\n<li>Hysteresis losses are currently not considered [<a href=\"modelica://Modelica.Magnetic.FundamentalWave.UsersGuide.References\">Haumer09</a>]</li>\n<li>The losses dissipated in the electric machine models are\n <ul>\n <li>ohmic heat losses,</li>\n <li>eddy current losses in the stator core,</li>\n <li>stray load losses,</li>\n <li>friction losses.</li>\n </ul>\n</li>\n</ul>\n\n<h4>Note</h4>\n\n<p>\nThe term <strong>fundamental wave</strong> 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.\n</p>\n</html>"));
end Concept;