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

Name Description

SpacePhasor Physical transformation: three phase <-> space phasors

Rotator Rotates space phasor

Name	Description
SpacePhasor	Physical transformation: three phase <-> space phasors
Rotator	Rotates space phasor

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

Type Name Default Description

Real turnsRatio 1

Type	Name	Default	Description
Real	turnsRatio	1

Connectors

Type Name Description

PositivePlug plug_p

NegativePlug plug_n

PositivePin zero

NegativePin ground

SpacePhasor spacePhasor

Type	Name	Description
PositivePlug	plug_p
NegativePlug	plug_n
PositivePin	zero
NegativePin	ground
SpacePhasor	spacePhasor

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

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

Type Name Description

SpacePhasor spacePhasor_a

SpacePhasor spacePhasor_b

input RealInput angle

Type	Name	Description
SpacePhasor	spacePhasor_a
SpacePhasor	spacePhasor_b
input RealInput	angle

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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