Modelica.Electrical.Machines.SpacePhasors.Components

Basic space phasor models

Information


This package contains basic space phasor models.
Real and imaginary part of voltage space phasor are the potentials v_[2] of the space phasor connector; (implicit grounded).
Real and imaginary part of current space phasor are the currents i_[2] at the space phasor connector; a ground has to be used where necessary for currents flowing back.

Extends from Modelica.Icons.Library (Icon for library).

Package Content

NameDescription
Modelica.Electrical.Machines.SpacePhasors.Components.SpacePhasor SpacePhasor Physical transformation: three phase <-> space phasors
Modelica.Electrical.Machines.SpacePhasors.Components.Rotator Rotator Rotates space phasor


Modelica.Electrical.Machines.SpacePhasors.Components.SpacePhasor Modelica.Electrical.Machines.SpacePhasors.Components.SpacePhasor

Physical transformation: three phase <-> space phasors

Modelica.Electrical.Machines.SpacePhasors.Components.SpacePhasor

Information


Physical transformation of voltages and currents: three phases <-> space phasors:
x[k] = X0 + {cos(-(k - 1)/m*2*pi),-sin(-(k - 1)/m*2*pi) * X[Re,Im]
and vice versa:
X0 = sum(x[k])/m
X[Re,Im] = sum(2/m*{cos((k - 1)/m*2*pi),sin((k - 1)/m*2*pi)}*x[k])
were x designates three phase values, X[Re,Im] designates the space phasor and X0 designates the zero sequence system.
Physcial transformation means that both voltages and currents are transformed in both directions.
Zero-sequence voltage and current are present at pin zero. An additional zero-sequence impedance could be connected between pin zero and pin ground.

Parameters

TypeNameDefaultDescription
RealturnsRatio1 

Connectors

TypeNameDescription
PositivePlugplug_p 
NegativePlugplug_n 
PositivePinzero 
NegativePinground 
SpacePhasorspacePhasor 

Modelica definition

model SpacePhasor 
  "Physical transformation: three phase <-> space phasors"
  constant Integer m=3 "number of phases";
  constant Real pi=Modelica.Constants.pi;
  parameter Real turnsRatio=1;
  Modelica.SIunits.Voltage v[m] "instantaneous phase voltages";
  Modelica.SIunits.Current i[m] "instantaneous phase currents";
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.Electrical.MultiPhase.Interfaces.PositivePlug plug_p(final m=m);
  Modelica.Electrical.MultiPhase.Interfaces.NegativePlug plug_n(final m=m);
  Modelica.Electrical.Analog.Interfaces.PositivePin zero;
  Modelica.Electrical.Analog.Interfaces.NegativePin ground;
  Modelica.Electrical.Analog.Basic.Ground gnd;

  Interfaces.SpacePhasor spacePhasor;
equation 
  v/turnsRatio = plug_p.pin.v - plug_n.pin.v;
  i*turnsRatio = +plug_p.pin.i;
  i*turnsRatio = -plug_n.pin.i;
  zero.v = 1/m*sum(v);
  spacePhasor.v_ = TransformationMatrix *v;
//v  = fill(zero.v,m) + InverseTransformation*spacePhasor.v_;
  -zero.i = 1/m*sum(i);
  -spacePhasor.i_ = TransformationMatrix *i;
//-i  = fill(zero.i,m) + InverseTransformation*spacePhasor.i_;
  connect(gnd.p, ground);
end SpacePhasor;

Modelica.Electrical.Machines.SpacePhasors.Components.Rotator Modelica.Electrical.Machines.SpacePhasors.Components.Rotator

Rotates space phasor

Modelica.Electrical.Machines.SpacePhasors.Components.Rotator

Information


Rotates space phasors of left connector to right connector by the angle provided by the input signal "angle" from one coordinate system into another.

Connectors

TypeNameDescription
SpacePhasorspacePhasor_a 
SpacePhasorspacePhasor_b 
input RealInputangle 

Modelica definition

model Rotator "Rotates space phasor"
  constant Real pi=Modelica.Constants.pi;
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 
  Interfaces.SpacePhasor spacePhasor_a;
  Interfaces.SpacePhasor spacePhasor_b;
  Modelica.Blocks.Interfaces.RealInput angle;
equation 
  spacePhasor_b.v_ = RotationMatrix*spacePhasor_a.v_;
//spacePhasor_a.v_ = InverseRotator*spacePhasor_b.v_;
  spacePhasor_b.i_ + RotationMatrix*spacePhasor_a.i_ = zeros(2);
//spacePhasor_a.i_ + InverseRotator*spacePhasor_b.i_ = zeros(2);
end Rotator;

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