Modelica.Magnetic.FundamentalWave.BasicMachines.AsynchronousInductionMachines

Information

This package provides squirrel cage and slip ring induction machine models.

See also

SynchronousInductionMachines

Extends from Modelica.Icons.VariantsPackage (Icon for package containing variants).

Package Content

Name	Description
AIM_SquirrelCage	Asynchronous induction machine with squirrel cage
AIM_SlipRing	Asynchronous induction machine with slip ring rotor

Modelica.Magnetic.FundamentalWave.BasicMachines.AsynchronousInductionMachines.AIM_SquirrelCage

Information

Resistances and stray inductances of the machine refer to the stator phases. The symmetry of the stator and rotor is assumed. The machine models take the following loss effects into account:

• heat losses in the temperature dependent stator winding resistances
• heat losses in the temperature dependent cage resistances
• friction losses
• core losses (only eddy current losses, no hysteresis losses)
• stray load losses

See also

AIM_SlipRing,

Extends from Modelica.Magnetic.FundamentalWave.Interfaces.PartialBasicInductionMachine (Partial model for induction machine).

Parameters

Type	Name	Default	Description
Inertia	Jr		Rotor inertia [kg.m2]
Boolean	useSupport	false	Enable / disable (=fixed stator) support
Inertia	Js		Stator inertia [kg.m2]
Boolean	useThermalPort	false	Enable / disable (=fixed temperatures) thermal port
Integer	p		Number of pole pairs (Integer)
Frequency	fsNominal		Nominal frequency [Hz]
Real	effectiveStatorTurns	1	Effective number of stator turns
Operational temperatures
Temperature	TsOperational		Operational temperature of stator resistance [K]
Temperature	TrOperational		Operational temperature of rotor resistance [K]
Nominal resistances and inductances
Resistance	Rs.start	0.03	Stator resistance per phase at TRef [Ohm]
Temperature	TsRef		Reference temperature of stator resistance [K]
LinearTemperatureCoefficient20	alpha20s		Temperature coefficient of stator resistance at 20 degC [1/K]
Inductance	Lssigma.start	3*(1 - sqrt(1 - 0.0667))/(2*...	Stator stray inductance per phase [H]
Inductance	Lszero	Lssigma	Stator zero inductance per phase [H]
Inductance	Lm		Main field inductance [H]
Inductance	Lrsigma		Rotor leakage inductance w.r.t. stator side [H]
Resistance	Rr		Rotor resistance w.r.t. stator side [Ohm]
Temperature	TrRef		Reference temperature of rotor resistance [K]
LinearTemperatureCoefficient20	alpha20r		Temperature coefficient of rotor resistance at 20 degC [1/K]
Losses
FrictionParameters	frictionParameters		Friction losses
CoreParameters	statorCoreParameters		Stator core losses
StrayLoadParameters	strayLoadParameters		Stray load losses

Connectors

Type	Name	Description
Flange_a	flange	Shaft
Flange_a	support	Support at which the reaction torque is acting
PositivePlug	plug_sp	Positive plug of stator
NegativePlug	plug_sn	Negative plug of stator

Modelica definition

model AIM_SquirrelCage 
  "Asynchronous induction machine with squirrel cage"
  extends Modelica.Magnetic.FundamentalWave.Interfaces.PartialBasicInductionMachine
    (
    is(start=zeros(m)),
    Rs(start=0.03),
    Lssigma(start=3*(1 - sqrt(1 - 0.0667))/(2*pi*fsNominal)),
    final L0(d=2.0*Lm/3.0/effectiveStatorTurns^2, q=2.0*Lm/3.0/effectiveStatorTurns^2),
    redeclare final Modelica.Electrical.Machines.Thermal.AsynchronousInductionMachines.ThermalAmbientAIMC
      thermalAmbient(final Tr=TrOperational),
    redeclare final Modelica.Electrical.Machines.Interfaces.InductionMachines.ThermalPortAIMC
      thermalPort,
    redeclare final Modelica.Electrical.Machines.Interfaces.InductionMachines.ThermalPortAIMC
      internalThermalPort,
    redeclare final Modelica.Electrical.Machines.Interfaces.InductionMachines.PowerBalanceAIMC
      powerBalance(final lossPowerRotorWinding = -rotorCage.heatPortWinding.Q_flow,
                   final lossPowerRotorCore = 0));

  parameter Modelica.SIunits.Inductance Lm(start=3*sqrt(1 - 0.0667)/(2*pi*fsNominal)) 
    "Main field inductance";
  parameter Modelica.SIunits.Inductance Lrsigma(start=3*(1 - sqrt(1 - 0.0667))/(2*pi*fsNominal)) 
    "Rotor leakage inductance w.r.t. stator side";
  parameter Modelica.SIunits.Resistance Rr(start=0.04) 
    "Rotor resistance w.r.t. stator side";
  parameter Modelica.SIunits.Temperature TrRef(start=293.15) 
    "Reference temperature of rotor resistance";
  parameter Modelica.Electrical.Machines.Thermal.LinearTemperatureCoefficient20
    alpha20r(start=0) "Temperature coefficient of rotor resistance at 20 degC";
  parameter Modelica.SIunits.Temperature TrOperational(start=293.15) 
    "Operational temperature of rotor resistance";

  Modelica.Magnetic.FundamentalWave.BasicMachines.Components.SymmetricMultiPhaseCageWinding
    rotorCage(
    final Lsigma=Lrsigma,
    final m=m,
    final effectiveTurns=effectiveStatorTurns,
    final useHeatPort=true,
    final RRef=Rr,
    final TRef=TrRef,
    final TOperational=TrRef,
    final alpha20=alpha20r) 
    "Symmetric rotor cage winding including resistances and stray inductances";

equation 
  connect(airGap.port_rn, rotorCage.port_n);
  connect(airGap.port_rp, rotorCage.port_p);
  connect(rotorCage.heatPortWinding, internalThermalPort.heatPortRotorWinding);
end AIM_SquirrelCage;

Modelica.Magnetic.FundamentalWave.BasicMachines.AsynchronousInductionMachines.AIM_SlipRing

Information

Resistances and stray inductances of the machine always refer to either stator or rotor phases. The symmetry of the stator and rotor is assumed. The machine models take the following loss effects into account:

• heat losses in the temperature dependent stator winding resistances
• heat losses in the temperature dependent rotor winding resistances
• friction losses
• core losses (only eddy current losses, no hysteresis losses)
• stray load losses

See also

AIM_SquirrelCage,

Extends from Modelica.Magnetic.FundamentalWave.Interfaces.PartialBasicInductionMachine (Partial model for induction machine).

Parameters

Type	Name	Default	Description
Inertia	Jr		Rotor inertia [kg.m2]
Boolean	useSupport	false	Enable / disable (=fixed stator) support
Inertia	Js		Stator inertia [kg.m2]
Boolean	useThermalPort	false	Enable / disable (=fixed temperatures) thermal port
Integer	p		Number of pole pairs (Integer)
Frequency	fsNominal		Nominal frequency [Hz]
Real	effectiveStatorTurns	1	Effective number of stator turns
Boolean	useTurnsRatio		Use TurnsRatio or calculate from locked-rotor voltage?
Real	TurnsRatio		Effective number of stator turns / effective number of rotor turns
Voltage	VsNominal		Nominal stator voltage per phase [V]
Voltage	VrLockedRotor		Locked rotor voltage per phase [V]
Operational temperatures
Temperature	TsOperational		Operational temperature of stator resistance [K]
Temperature	TrOperational		Operational temperature of rotor resistance [K]
Nominal resistances and inductances
Resistance	Rs.start	0.03	Stator resistance per phase at TRef [Ohm]
Temperature	TsRef		Reference temperature of stator resistance [K]
LinearTemperatureCoefficient20	alpha20s		Temperature coefficient of stator resistance at 20 degC [1/K]
Inductance	Lssigma.start	3*(1 - sqrt(1 - 0.0667))/(2*...	Stator stray inductance per phase [H]
Inductance	Lszero	Lssigma	Stator zero inductance per phase [H]
Inductance	Lm		Main field inductance [H]
Inductance	Lrsigma		Rotor leakage inductance w.r.t. stator side [H]
Inductance	Lrzero	Lrsigma	Rotor zero inductance w.r.t. stator side [H]
Resistance	Rr		Rotor resistance w.r.t. stator side [Ohm]
Temperature	TrRef		Reference temperature of rotor resistance [K]
LinearTemperatureCoefficient20	alpha20r		Temperature coefficient of rotor resistance at 20 degC [1/K]
Losses
FrictionParameters	frictionParameters		Friction losses
CoreParameters	statorCoreParameters		Stator core losses
StrayLoadParameters	strayLoadParameters		Stray load losses
CoreParameters	rotorCoreParameters		Rotor core losses

Connectors

Type	Name	Description
Flange_a	flange	Shaft
Flange_a	support	Support at which the reaction torque is acting
PositivePlug	plug_sp	Positive plug of stator
NegativePlug	plug_sn	Negative plug of stator
NegativePlug	plug_rn	Negative plug of rotor
PositivePlug	plug_rp	Positive plug of rotor

Modelica definition

model AIM_SlipRing 
  "Asynchronous induction machine with slip ring rotor"
  extends Modelica.Magnetic.FundamentalWave.Interfaces.PartialBasicInductionMachine
    (
    is(start=zeros(m)),
    Rs(start=0.03),
    Lssigma(start=3*(1 - sqrt(1 - 0.0667))/(2*pi*fsNominal)),
    final L0(d=2.0*Lm/3.0/effectiveStatorTurns^2, q=2.0*Lm/3.0/effectiveStatorTurns^2),
    redeclare final Modelica.Electrical.Machines.Thermal.AsynchronousInductionMachines.ThermalAmbientAIMS
      thermalAmbient(final Tr=TrOperational),
    redeclare final Modelica.Electrical.Machines.Interfaces.InductionMachines.ThermalPortAIMS
      thermalPort,
    redeclare final Modelica.Electrical.Machines.Interfaces.InductionMachines.ThermalPortAIMS
      internalThermalPort,
    redeclare final Modelica.Electrical.Machines.Interfaces.InductionMachines.PowerBalanceAIMS
      powerBalance(final lossPowerRotorWinding = -sum(rotor.heatPortWinding.Q_flow),
                   final lossPowerRotorCore = -rotor.heatPortCore.Q_flow,
                   final lossPowerBrush = 0,
                   final powerRotor = Modelica.Electrical.Machines.SpacePhasors.Functions.activePower(vr, ir)));
  Modelica.Electrical.MultiPhase.Interfaces.NegativePlug plug_rn(final m=m) 
    "Negative plug of rotor";
  Modelica.Electrical.MultiPhase.Interfaces.PositivePlug plug_rp(final m=m) 
    "Positive plug of rotor";

  parameter Modelica.SIunits.Inductance Lm(start=3*sqrt(1 - 0.0667)/(2*pi*fsNominal)) 
    "Main field inductance";
  parameter Modelica.SIunits.Inductance Lrsigma(start = 3*(1 - sqrt(1 - 0.0667))/(2*pi*fsNominal)) 
    "Rotor leakage inductance w.r.t. stator side";
  parameter Modelica.SIunits.Inductance Lrzero=Lrsigma 
    "Rotor zero inductance w.r.t. stator side";
  parameter Modelica.SIunits.Resistance Rr(start = 0.04) 
    "Rotor resistance w.r.t. stator side";
  parameter Modelica.SIunits.Temperature TrRef(start=293.15) 
    "Reference temperature of rotor resistance";
  parameter Modelica.Electrical.Machines.Thermal.LinearTemperatureCoefficient20
    alpha20r(start=0) "Temperature coefficient of rotor resistance at 20 degC";
  parameter Modelica.SIunits.Temperature TrOperational(start=293.15) 
    "Operational temperature of rotor resistance";

  parameter Boolean useTurnsRatio(start=true) 
    "Use TurnsRatio or calculate from locked-rotor voltage?";
  parameter Real TurnsRatio(final min=Modelica.Constants.small, start=1) 
    "Effective number of stator turns / effective number of rotor turns";
  parameter Modelica.SIunits.Voltage VsNominal(start=100) 
    "Nominal stator voltage per phase";
  parameter Modelica.SIunits.Voltage VrLockedRotor(
    start=100*(2*pi*fsNominal*Lm)/sqrt(Rs^2+(2*pi*fsNominal*(Lm+Lssigma))^2)) 
    "Locked rotor voltage per phase";

  parameter Modelica.Electrical.Machines.Losses.CoreParameters
    rotorCoreParameters(
    final m=3,
    PRef=0,
    VRef(start=1)=1,
    wRef(start=1)=1) "Rotor core losses";

  output Modelica.SIunits.Voltage vr[m] = plug_rp.pin.v - plug_rn.pin.v 
    "Rotor instantaneous voltages";
  output Modelica.SIunits.Current ir[m] = plug_rp.pin.i 
    "Rotor instantaneous currents";

protected 
  final parameter Real internalTurnsRatio=if useTurnsRatio then TurnsRatio else 
    VsNominal/VrLockedRotor*(2*pi*fsNominal*Lm)/sqrt(Rs^2+(2*pi*fsNominal*(Lm+Lssigma))^2);
public 
  Components.SymmetricMultiPhaseWinding rotor(
    final m=m,
    final Lsigma=Lrsigma,
    final effectiveTurns=effectiveStatorTurns/internalTurnsRatio,
    final useHeatPort=true,
    final RRef=Rr,
    final TRef=TrRef,
    final TOperational=TrOperational,
    final Lzero=Lrsigma,
    final alpha20=alpha20r,
    final GcRef=rotorCoreParameters.GcRef) 
    "Symmetric rotor winding including resistances, zero and stray inductances and zero core losses";
    
  /* previously used: state selection, now commented
  FundamentalWave.Interfaces.StateSelector stateSelectorR(
    final m=m,
    final xi=ir,
    final gamma=0) "State selection of rotor currents"
    annotation (Placement(transformation(extent={{-10,-10},{10,10}},
        rotation=90,
        origin={-90,0})));
  */
equation 

  connect(rotor.plug_n, plug_rn);
  connect(airGap.port_rn, rotor.port_n);
  connect(airGap.port_rp, rotor.port_p);
  connect(rotor.heatPortCore, internalThermalPort.heatPortRotorCore);
  connect(rotor.heatPortWinding, internalThermalPort.heatPortRotorWinding);
  connect(plug_rp, rotor.plug_p);
end AIM_SlipRing;