Modelica.Electrical.Machines.SpacePhasors.Blocks

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

Modelica.Electrical.Machines.SpacePhasors.Blocks.ToSpacePhasor

Information

Extends from Modelica.Blocks.Interfaces.MIMO (Multiple Input Multiple Output continuous control block).

Parameters

Type	Name	Default	Description
Integer	nin	m	Number of inputs
Integer	nout	2	Number of outputs

Connectors

Type	Name	Description
input RealInput	u[nin]	Connector of Real input signals
output RealOutput	y[nout]	Connector of Real output signals
output RealOutput	zero

Modelica definition

block ToSpacePhasor "Conversion: three phase -> space phasor"
  extends Modelica.Blocks.Interfaces.MIMO(final nin=m, final nout=2);
  constant Integer m=3 "Number of phases";
  constant Real pi=Modelica.Constants.pi;
protected 
  parameter Real TransformationMatrix[ 2, m]=2/m*
    {{cos(+(k - 1)/m*2*pi) for k in 1:m}, {+sin(+(k - 1)/m*2*pi) for k in 1:m}};
  parameter Real InverseTransformation[m, 2]=
    {{cos(-(k - 1)/m*2*pi), -sin(-(k - 1)/m*2*pi)} for k in 1:m};
public 
  Modelica.Blocks.Interfaces.RealOutput zero;

equation 
  m*zero = sum(u);
  y = TransformationMatrix *u;
//u = fill(zero,m) + InverseTransformation*y;
end ToSpacePhasor;

Modelica.Electrical.Machines.SpacePhasors.Blocks.FromSpacePhasor

Information

Extends from Modelica.Blocks.Interfaces.MIMO (Multiple Input Multiple Output continuous control block).

Parameters

Type	Name	Default	Description
Integer	nin	2	Number of inputs
Integer	nout	m	Number of outputs

Connectors

Type	Name	Description
input RealInput	u[nin]	Connector of Real input signals
output RealOutput	y[nout]	Connector of Real output signals
input RealInput	zero

Modelica definition

block FromSpacePhasor "Conversion: space phasor -> three phase"
  extends Modelica.Blocks.Interfaces.MIMO(final nin=2, final nout=m);
  constant Integer m=3 "Number of phases";
  constant Real pi=Modelica.Constants.pi;
protected 
  parameter Real TransformationMatrix[ 2, m]=2/m*
    {{cos(+(k - 1)/m*2*pi) for k in 1:m}, {+sin(+(k - 1)/m*2*pi) for k in 1:m}};
  parameter Real InverseTransformation[m, 2]=
    {{cos(-(k - 1)/m*2*pi), -sin(-(k - 1)/m*2*pi)} for k in 1:m};
public 
  Modelica.Blocks.Interfaces.RealInput zero;
equation 
  y = fill(zero,m) + InverseTransformation*u;
//m*zero = sum(y);
//u = TransformationMatrix *y;
end FromSpacePhasor;

Modelica.Electrical.Machines.SpacePhasors.Blocks.Rotator

Information

Extends from Modelica.Blocks.Interfaces.MIMOs (Multiple Input Multiple Output continuous control block with same number of inputs and outputs).

Parameters

Type	Name	Default	Description
Integer	n	2	Number of inputs (= number of outputs)

Connectors

Type	Name	Description
input RealInput	u[n]	Connector of Real input signals
output RealOutput	y[n]	Connector of Real output signals
input RealInput	angle

Modelica definition

block Rotator "Rotates space phasor"
  extends Modelica.Blocks.Interfaces.MIMOs(final n=2);
protected 
  Real RotationMatrix[2,2] = {{+cos(-angle),-sin(-angle)},{+sin(-angle),+cos(-angle)}};
//Real InverseRotator[2,2] = {{+cos(+angle),-sin(+angle)},{+sin(+angle),+cos(+angle)}};
public 
  Modelica.Blocks.Interfaces.RealInput angle;
equation 
  y = RotationMatrix*u;
//u = InverseRotator*y;
end Rotator;

Modelica.Electrical.Machines.SpacePhasors.Blocks.ToPolar

Information

Extends from Modelica.Blocks.Interfaces.MIMOs (Multiple Input Multiple Output continuous control block with same number of inputs and outputs).

Parameters

Type	Name	Default	Description
Integer	n	2	Number of inputs (= number of outputs)

Connectors

Type	Name	Description
input RealInput	u[n]	Connector of Real input signals
output RealOutput	y[n]	Connector of Real output signals

Modelica definition

block ToPolar "Converts a space phasor to polar coordinates"
  extends Modelica.Blocks.Interfaces.MIMOs(final n=2);
  constant Real small=Modelica.Constants.small;
equation 
  y[1] = sqrt(u[1]^2 + u[2]^2);
  y[2] = if noEvent(y[1] <= small) then 0 else Modelica.Math.atan2(u[2], u[1]);
/*
  if y[1] <= small then
    y[2] = 0;
  else
    if u[2] >= 0 then
      y[2] =  Modelica.Math.acos(u[1]/y[1]);
    else
      y[2] = -Modelica.Math.acos(u[1]/y[1]);
    end if;
  end if;
*/
end ToPolar;

Modelica.Electrical.Machines.SpacePhasors.Blocks.FromPolar

Information

Extends from Modelica.Blocks.Interfaces.MIMOs (Multiple Input Multiple Output continuous control block with same number of inputs and outputs).

Parameters

Type	Name	Default	Description
Integer	n	2	Number of inputs (= number of outputs)

Connectors

Type	Name	Description
input RealInput	u[n]	Connector of Real input signals
output RealOutput	y[n]	Connector of Real output signals

Modelica definition

block FromPolar "Converts a space phasor from polar coordinates"
  extends Modelica.Blocks.Interfaces.MIMOs(final n=2);
equation 
  y = u[1]*{cos(u[2]),sin(u[2])};
end FromPolar;