Harmonic

```block Harmonic "Calculate harmonic over period 1/f"
extends Modelica.Blocks.Icons.Block;

parameter Modelica.SIunits.Frequency f(start = 50) "Base frequency";
parameter Integer k(start = 1) "Order of harmonic";
parameter Boolean useConjugateComplex = false "Gives conjugate complex result if true"
annotation (
Evaluate = true,
HideResult = true,
choices(checkBox = true));
parameter Real x0Cos = 0 "Start value of cos integrator state";
parameter Real x0Sin = 0 "Start value of sin integrator state";
Sources.Cosine sin1(final amplitude = sqrt(2), final freqHz = k * f, final phase = 0) annotation (Placement(transformation(
extent = {
{-10, -10},
{10, 10}},
rotation = 270,
origin = {-80, 70})));
Blocks.Sources.Sine sin2(final amplitude = sqrt(2), final phase = 0, final freqHz = k * f) annotation (Placement(transformation(
extent = {
{-10, -10},
{10, 10}},
rotation = 90,
origin = {-80, -70})));
MultiProduct product1(nu = 2) annotation (Placement(transformation(extent = {
{-60, 30},
{-40, 50}})));
MultiProduct product2(nu = 2) annotation (Placement(transformation(extent = {
{-60, -50},
{-40, -30}})));
Mean mean1(final f = f, final x0 = x0Cos) annotation (Placement(transformation(extent = {
{-20, 30},
{0, 50}})));
Mean mean2(final f = f, final x0 = x0Sin) annotation (Placement(transformation(extent = {
{-20, -50},
{0, -30}})));
Blocks.Interfaces.RealInput u annotation (Placement(transformation(extent = {
{-140, -20},
{-100, 20}})));
Blocks.Interfaces.RealOutput y_rms "Root mean square of polar representation"
annotation (Placement(transformation(extent = {
{100, 50},
{120, 70}})));
Blocks.Interfaces.RealOutput y_arg(unit = "rad") "Angle of polar representation"
annotation (Placement(transformation(extent = {
{100, -70},
{120, -50}})));
Blocks.Math.RectangularToPolar rectangularToPolar annotation (Placement(transformation(extent = {
{40, -12},
{60, 8}})));
Gain gain(final k = if useConjugateComplex then -1 else 1) annotation (Placement(transformation(
extent = {
{-10, -10},
{10, 10}},
rotation = 270,
origin = {80, -30})));
equation
connect(u,product1.u[2]) annotation (Line(
points = {
{-120, 0},
{-80, 0},
{-80, 36.5},
{-60, 36.5}},
color = {0, 0, 127}));
connect(u,product2.u[1]) annotation (Line(
points = {
{-120, 0},
{-80, 0},
{-80, -36.5},
{-60, -36.5}},
color = {0, 0, 127}));
connect(gain.y,y_arg) annotation (Line(
points = {
{80, -41},
{80, -60},
{110, -60}},
color = {0, 0, 127}));
connect(mean1.y,rectangularToPolar.u_re) annotation (Line(
points = {
{1, 40},
{20, 40},
{20, 4},
{38, 4}},
color = {0, 0, 127}));
connect(mean2.y,rectangularToPolar.u_im) annotation (Line(
points = {
{1, -40},
{20, -40},
{20, -8},
{38, -8}},
color = {0, 0, 127}));
connect(product1.y,mean1.u) annotation (Line(
points = {
{-38.3, 40},
{-22, 40}},
color = {0, 0, 127}));
connect(product2.y,mean2.u) annotation (Line(
points = {
{-38.3, -40},
{-22, -40}},
color = {0, 0, 127}));
connect(sin1.y,product1.u[1]) annotation (Line(
points = {
{-80, 59},
{-80, 59},
{-80, 43.5},
{-60, 43.5}},
color = {0, 0, 127}));
connect(sin2.y,product2.u[2]) annotation (Line(
points = {
{-80, -59},
{-80, -43.5},
{-60, -43.5}},
color = {0, 0, 127}));
connect(rectangularToPolar.y_abs,y_rms) annotation (Line(
points = {
{61, 4},
{80, 4},
{80, 60},
{110, 60}},
color = {0, 0, 127}));
connect(rectangularToPolar.y_arg,gain.u) annotation (Line(
points = {
{61, -8},
{80, -8},
{80, -18}},
color = {0, 0, 127}));

annotation (
Documentation(info = "<html>\n<p>\nThis block calculates the root mean square and the phase angle of a single harmonic <em>k</em> of the input signal u over the given period 1/f, using the\n<a href=\"modelica://Modelica.Blocks.Math.Mean\">mean block</a>.\n</p>\n<p>\nNote: The output is updated after each period defined by 1/f.\n</p>\n<p>\nNote:<br>\nThe harmonic is defined by <code>&radic;2 rms cos(k 2 &pi; f t - arg)</code> if useConjugateComplex=false (default)<br>\nThe harmonic is defined by <code>&radic;2 rms cos(k 2 &pi; f t + arg)</code> if useConjugateComplex=true\n</p>\n</html>"),
Icon(graphics = {
Text(
extent = {
{-80, 60},
{80, 20}},
textString = "H%k"),
Text(
extent = {
{-80, -20},
{80, -60}},
textString = "f=%f"),
Text(
extent = {
{20, 100},
{100, 60}},
textString = "rms"),
Text(
extent = {
{20, -60},
{100, -100}},
textString = "arg")}));
end Harmonic;

```