class Power "Real and reactive power"
extends Modelica.Icons.Information;
annotation (Documentation(info = "<html>\n\n<p>For periodic waveforms, the average value of the instantaneous power is <strong>real power</strong> <em>P</em>.\n<strong>Reactive power</strong> <em>Q</em> is a term\nassociated with inductors and capacitors. For pure inductors and capacitors, real power is equal to zero.\nYet, there is instantaneous power exchanged with connecting network.\n</p>\n\nThe\n<a href=\"modelica://Modelica.Electrical.QuasiStationary.SinglePhase.Examples.SeriesResonance\">\n series resonance circuit</a> which was also addressed in the\n<a href=\"modelica://Modelica.Electrical.QuasiStationary.UsersGuide.Overview.ACCircuit\">\n AC circuit</a>\nwill be investigated.\n\n<h5>Power of a resistor</h5>\n\n<p>\nThe instantaneous voltage and current are in phase:\n</p>\n<p>\n<img border=\"0\" src=\"modelica://Modelica/Resources/Images/Electrical/QuasiStationary/UsersGuide/Overview/Power/v_r.png\"\n alt=\"v_r.png\"><br>\n<img border=\"0\" src=\"modelica://Modelica/Resources/Images/Electrical/QuasiStationary/UsersGuide/Overview/Power/i_r.png\"\n alt=\"i_r.png\">\n</p>\n\n<p>\nTherefore, the instantaneous power is\n</p>\n<p>\n<img border=\"0\" src=\"modelica://Modelica/Resources/Images/Electrical/QuasiStationary/UsersGuide/Overview/Power/power_r.png\"\n alt=\"power_r.png\">\n</p>\n\n<p>A graphical representation of these equations is depicted in Fig. 1</p>\n\n<table border=\"0\" cellspacing=\"0\" cellpadding=\"2\">\n <tr>\n <td>\n <img src=\"modelica://Modelica/Resources/Images/Electrical/QuasiStationary/UsersGuide/Overview/Power/power_resistor.png\"\n alt=\"power_resistor.png\">\n </td>\n </tr>\n <caption align=\"bottom\">Fig. 1: Instantaneous voltage, current of power of a resistor</caption>\n</table>\n\n<p>Real power of the resistor is the average of instantaneous power:</p>\n<p>\n<img border=\"0\" src=\"modelica://Modelica/Resources/Images/Electrical/QuasiStationary/UsersGuide/Overview/Power/p_r.png\"\n alt=\"p_r.png\">\n</p>\n\n<h5>Power of an inductor</h5>\n\n<p>\nThe instantaneous voltage leads the current by a quarter of the period:\n</p>\n<p>\n<img border=\"0\" src=\"modelica://Modelica/Resources/Images/Electrical/QuasiStationary/UsersGuide/Overview/Power/v_l.png\"\n alt=\"v_l.png\"><br>\n<img border=\"0\" src=\"modelica://Modelica/Resources/Images/Electrical/QuasiStationary/UsersGuide/Overview/Power/i_l.png\"\n alt=\"i_l.png\">\n</p>\n\n<p>\nTherefore, the instantaneous power is\n</p>\n<p>\n<img border=\"0\" src=\"modelica://Modelica/Resources/Images/Electrical/QuasiStationary/UsersGuide/Overview/Power/power_l.png\"\n alt=\"power_l.png\">\n</p>\n\n<p>A graphical representation of these equations is depicted in Fig. 2</p>\n\n<table border=\"0\" cellspacing=\"0\" cellpadding=\"2\">\n <tr>\n <td>\n <img src=\"modelica://Modelica/Resources/Images/Electrical/QuasiStationary/UsersGuide/Overview/Power/power_inductor.png\"\n alt=\"power_inductor.png\">\n </td>\n </tr>\n <caption align=\"bottom\">Fig. 2: Instantaneous voltage, current of power of an inductor</caption>\n</table>\n\n<p>Reactive power of the inductor is:</p>\n<p>\n<img border=\"0\" src=\"modelica://Modelica/Resources/Images/Electrical/QuasiStationary/UsersGuide/Overview/Power/q_l.png\"\n alt=\"q_l.png\">\n</p>\n\n<h5>Power of a capacitor</h5>\n\n<p>\nThe instantaneous voltage lags the current by a quarter of the period:\n</p>\n<p>\n<img border=\"0\" src=\"modelica://Modelica/Resources/Images/Electrical/QuasiStationary/UsersGuide/Overview/Power/v_c.png\"\n alt=\"v_c.png\"><br>\n<img border=\"0\" src=\"modelica://Modelica/Resources/Images/Electrical/QuasiStationary/UsersGuide/Overview/Power/i_c.png\"\n alt=\"i_c.png\">\n</p>\n\n<p>\nTherefore, the instantaneous power is\n</p>\n<p>\n<img border=\"0\" src=\"modelica://Modelica/Resources/Images/Electrical/QuasiStationary/UsersGuide/Overview/Power/power_c.png\"\n alt=\"power_c.png\">\n</p>\n\n<p>A graphical representation of these equations is depicted in Fig. 3</p>\n\n<table border=\"0\" cellspacing=\"0\" cellpadding=\"2\">\n <tr>\n <td>\n <img src=\"modelica://Modelica/Resources/Images/Electrical/QuasiStationary/UsersGuide/Overview/Power/power_capacitor.png\"\n alt=\"power_capacitor.png\">\n </td>\n </tr>\n <caption align=\"bottom\">Fig. 3: Instantaneous voltage, current of power of a capacitor</caption>\n</table>\n\n<p>Reactive power of the capacitor is:</p>\n<p>\n<img border=\"0\" src=\"modelica://Modelica/Resources/Images/Electrical/QuasiStationary/UsersGuide/Overview/Power/q_c.png\"\n alt=\"q_c.png\">\n</p>\n\n<h5>Complex apparent power</h5>\n\n<p>For an arbitrary component with two pins, real and reactive power can be determined by the complex phasors:</p>\n<p>\n<img border=\"0\" src=\"modelica://Modelica/Resources/Images/Electrical/QuasiStationary/UsersGuide/Overview/Power/s.png\"\n alt=\"s.png\">\n</p>\n\n<p>\nIn this equation <sup>*</sup> represents the conjugate complex operator\n</p>\n\n<h4>See also</h4>\n<a href=\"modelica://Modelica.Electrical.QuasiStationary.UsersGuide.Overview.Introduction\">\n Introduction</a>,\n<a href=\"modelica://Modelica.Electrical.QuasiStationary.UsersGuide.Overview.ACCircuit\">\n AC circuit</a>,\n<a href=\"modelica://Modelica.Electrical.QuasiStationary.UsersGuide.Overview.ReferenceSystem\">\n Reference system</a>\n</html>"));
end Power;