Modelica.Electrical.Machines.SpacePhasors.Functions

Information

• ToSpacePhasor: transforms a set of threephase values to space phasor and zero sequence system
• FromSpacePhasor: transforms a space phasor and zero sequence system to a set of threephase values
• Rotator: rotates a space phasor (from one coordinate system into another)
• ToPolar: Converts a space phasor from rectangular coordinates to polar coordinates
• FromPolar: Converts a space phasor from polar coordinates to rectangular coordinates

Space phasors are defined as vectors of length = 2, the first element representing the real part and the second element representing the imaginary part of the space phasor.

Extends from Modelica.Icons.Package (Icon for standard packages).

Package Content

Name	Description
ToSpacePhasor	Conversion: three phase -> space phasor
FromSpacePhasor	Conversion: space phasor -> three phase
Rotator	Rotates space phasor
ToPolar	Converts a space phasor to polar coordinates
FromPolar	Converts a space phasor from polar coordinates
quasiRMS	Calculate quasi-RMS value of input
activePower	Calculate active power of voltage and current input

Modelica.Electrical.Machines.SpacePhasors.Functions.ToSpacePhasor

Information

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

Type	Name	Default	Description
Real	x[3]

Outputs

Type	Name	Description
Real	y[2]
Real	y0

Modelica definition

function ToSpacePhasor "Conversion: three phase -> space phasor"
  extends Modelica.Icons.Function;
  constant Integer m=3 "Number of phases";
  constant Real pi=Modelica.Constants.pi;
  input Real x[3];
  output Real y[2];
  output Real y0;
algorithm 
  y := zeros(2);
  for k in 1:m loop
    y := y + 2/m*{+cos((k - 1)/m*2*pi), +sin(+(k - 1)/m*2*pi)}*x[k];
  end for;
  y0 := 1/m*sum(x);
end ToSpacePhasor;

Modelica.Electrical.Machines.SpacePhasors.Functions.FromSpacePhasor

Information

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

Type	Name	Default	Description
Real	x[2]
Real	x0

Outputs

Type	Name	Description
Real	y[3]

Modelica definition

function FromSpacePhasor "Conversion: space phasor -> three phase"
  extends Modelica.Icons.Function;
  constant Integer m=3 "Number of phases";
  constant Real pi=Modelica.Constants.pi;
  input Real x[2];
  input Real x0;
  output Real y[3];
algorithm 
  for k in 1:m loop
    y[k] := x0 + {cos(-(k - 1)/m*2*pi),-sin(-(k - 1)/m*2*pi)}*x;
  end for;
end FromSpacePhasor;

Modelica.Electrical.Machines.SpacePhasors.Functions.Rotator

Information

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

Type	Name	Default	Description
Real	x[2]
Angle	angle		[rad]

Outputs

Type	Name	Description
Real	y[2]

Modelica definition

function Rotator "Rotates space phasor"
  extends Modelica.Icons.Function;
  input Real x[2];
  input Modelica.SIunits.Angle angle;
  output Real y[2];
protected 
  Real RotationMatrix[2,2] = {{+cos(-angle),-sin(-angle)},{+sin(-angle),+cos(-angle)}};
algorithm 
  y := RotationMatrix*x;
end Rotator;

Modelica.Electrical.Machines.SpacePhasors.Functions.ToPolar

Information

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

Type	Name	Default	Description
Real	x[2]

Outputs

Type	Name	Description
Real	absolute
Angle	angle	[rad]

Modelica definition

function ToPolar "Converts a space phasor to polar coordinates"
  extends Modelica.Icons.Function;
  constant Real small=Modelica.Constants.small;
  input Real x[2];
  output Real absolute;
  output Modelica.SIunits.Angle angle;
algorithm 
  absolute := sqrt(x[1]^2 + x[2]^2);
  angle := if absolute <= small then 0 else Modelica.Math.atan2(x[2], x[1]);
/*
  if absolute <= small then
    angle := 0;
  else
    if x[2] >= 0 then
      angle :=  Modelica.Math.acos(x[1]/absolute);
    else
      angle := -Modelica.Math.acos(x[1]/absolute);
    end if;
  end if;
*/
end ToPolar;

Modelica.Electrical.Machines.SpacePhasors.Functions.FromPolar

Information

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

Type	Name	Default	Description
Real	absolute
Angle	angle		[rad]

Outputs

Type	Name	Description
Real	x[2]

Modelica definition

function FromPolar "Converts a space phasor from polar coordinates"
  extends Modelica.Icons.Function;
  constant Real pi=Modelica.Constants.pi;
  constant Real small=Modelica.Constants.small;
  input Real absolute;
  input Modelica.SIunits.Angle angle;
  output Real x[2];
algorithm 
  x := absolute*{cos(angle),sin(angle)};
end FromPolar;

Modelica.Electrical.Machines.SpacePhasors.Functions.quasiRMS

Information

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

Type	Name	Default	Description
Real	x[3]

Outputs

Type	Name	Description
Real	y

Modelica definition

function quasiRMS "Calculate quasi-RMS value of input"
  extends Modelica.Icons.Function;
  constant Integer m=3 "Number of phases";
  constant Real pi=Modelica.Constants.pi;
  input Real x[3];
  output Real y;
protected 
  Real h[2];
algorithm 
  h := zeros(2);
  for k in 1:m loop
    h := h + 2/m*{+cos((k - 1)/m*2*pi), +sin(+(k - 1)/m*2*pi)}*x[k];
  end for;
  y := sqrt(h[1]^2 + h[2]^2)/sqrt(2);
end quasiRMS;

Modelica.Electrical.Machines.SpacePhasors.Functions.activePower

Information

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

Type	Name	Default	Description
Voltage	v[m]		phase voltages [V]
Current	i[m]		phase currents [A]

Outputs

Type	Name	Description
Power	p	Active power [W]

Modelica definition

function activePower 
  "Calculate active power of voltage and current input"
  extends Modelica.Icons.Function;
  constant Integer m=3 "Number of phases";
  import Modelica.Constants.pi;
  input Modelica.SIunits.Voltage v[m] "phase voltages";
  input Modelica.SIunits.Current i[m] "phase currents";
  output Modelica.SIunits.Power p "Active power";
protected 
  Modelica.SIunits.Voltage v_[2] "Voltage space phasor";
  Modelica.SIunits.Current i_[2] "Current space phasor";
algorithm 
  v_ := zeros(2);
  i_ := zeros(2);
  for k in 1:m loop
    v_ := v_ + 2/m*{+cos((k - 1)/m*2*pi), +sin(+(k - 1)/m*2*pi)}*v[k];
    i_ := i_ + 2/m*{+cos((k - 1)/m*2*pi), +sin(+(k - 1)/m*2*pi)}*i[k];
  end for;
  p :=m/2*(+v_[1]*i_[1] + v_[2]*i_[2]);
end activePower;