Modelica.Electrical.Machines.BasicMachines.SynchronousInductionMachines

Models of synchronous induction machines

Information

This package contains models of synchronous induction machines, based on space phasor theory: These models use package SpacePhasors.
Please keep in mind:

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

Package Content

Name Description
Modelica.Electrical.Machines.BasicMachines.SynchronousInductionMachines.SM_PermanentMagnet SM_PermanentMagnet Permanent magnet synchronous induction machine
Modelica.Electrical.Machines.BasicMachines.SynchronousInductionMachines.SM_ElectricalExcited SM_ElectricalExcited Electrical excited synchronous induction machine with damper cage
Modelica.Electrical.Machines.BasicMachines.SynchronousInductionMachines.SM_ReluctanceRotor SM_ReluctanceRotor Synchronous induction machine with reluctance rotor and damper cage

Modelica.Electrical.Machines.BasicMachines.SynchronousInductionMachines.SM_PermanentMagnet Modelica.Electrical.Machines.BasicMachines.SynchronousInductionMachines.SM_PermanentMagnet

Permanent magnet synchronous induction machine

Information

Model of a three phase permanent magnet synchronous induction machine.
Resistance and stray inductance of stator is modeled directly in stator phases, then using space phasor transformation and a rotor-fixed AirGap model. Resistance and stray inductance of rotor's squirrel cage is modeled in two axis of the rotor-fixed coordinate system. Permanent magnet excitation is modelled by a constant equivalent excitation current feeding the d-axis. The machine models take the following loss effects into account:

Whether a damper cage is present or not, can be selected with Boolean parameter useDamperCage (default = true).
Default values for machine's parameters (a realistic example) are:

number of pole pairs p 2
stator's moment of inertia 0.29kg.m2
rotor's moment of inertia 0.29kg.m2
nominal frequency fNominal 50Hz
nominal voltage per phase 100V RMS
no-load voltage per phase 112.3V RMS @ nominal speed
nominal current per phase 100A RMS
nominal torque 181.4Nm
nominal speed 1500rpm
nominal mechanical output 28.5kW
nominal rotor angle 20.75degree
efficiency 95.0%
power factor 0.98
stator resistance 0.03Ohm per phase at reference temperature
reference temperature TsRef 20°C
temperature coefficient alpha20s 01/K
stator reactance Xd 0.4Ohm per phase in d-axis
stator reactance Xq 0.4Ohm per phase in q-axis
stator stray reactance Xss 0.1Ohm per phase
damper resistance in d-axis 0.04Ohm at reference temperature
damper resistance in q-axis same as d-axis
reference temperature TrRef 20°C
temperature coefficient alpha20r 01/K
damper stray reactance in d-axis XDds 0.05Ohm
damper stray reactance in q-axis XDqs same as d-axis
stator operational temperature TsOperational 20°C
damper operational temperature TrOperational 20°C
These values give the following inductances:
main field inductance in d-axis (Xd - Xss)/(2*pi*fNominal)
main field inductance in q-axis (Xq - Xss)/(2*pi*fNominal)
stator stray inductance per phase Xss/(2*pi*fNominal)
damper stray inductance in d-axis XDds/(2*pi*fNominal)
damper stray inductance in q-axis XDqs/(2*pi*fNominal)

Extends from Machines.Interfaces.PartialBasicInductionMachine (Partial model for induction machine).

Parameters

NameDescription
pNumber of pole pairs (Integer)
fsNominalNominal frequency [Hz]
JrRotor's moment of inertia [kg.m2]
useSupportEnable / disable (=fixed stator) support
JsStator's moment of inertia [kg.m2]
useThermalPortEnable / disable (=fixed temperatures) thermal port
idq_ss[2]Stator space phasor current / stator fixed frame [A]
idq_sr[2]Stator space phasor current / rotor fixed frame [A]
idq_rs[2]Rotor space phasor current / stator fixed frame [A]
idq_rr[2]Rotor space phasor current / rotor fixed frame [A]
VsOpenCircuitOpen circuit RMS voltage per phase @ fsNominal [V]
Operational temperatures
TsOperationalOperational temperature of stator resistance [K]
TrOperationalOperational temperature of (optional) damper cage [K]
Initialization
phiMechanicalMechanical angle of rotor against stator [rad]
wMechanicalMechanical angular velocity of rotor against stator [rad/s]
ir[2]Damper cage currents [A]
Nominal resistances and inductances
RsStator resistance per phase at TRef [Ohm]
TsRefReference temperature of stator resistance [K]
alpha20sTemperature coefficient of stator resistance at 20 degC [1/K]
LszeroStator zero sequence inductance [H]
LmdStator main field inductance per phase in d-axis [H]
LmqStator main field inductance per phase in q-axis [H]
DamperCage
useDamperCageEnable / disable damper cage
LrsigmadDamper stray inductance in d-axis [H]
LrsigmaqDamper stray inductance in q-axis [H]
RrdDamper resistance in d-axis at TRef [Ohm]
RrqDamper resistance in q-axis at TRef [Ohm]
TrRefReference temperature of damper resistances in d- and q-axis [K]
alpha20rTemperature coefficient of damper resistances in d- and q-axis [1/K]
Losses
frictionParametersFriction loss parameter record
statorCoreParametersStator core loss parameter record; all parameters refer to stator side
strayLoadParametersStray load loss parameter record
permanentMagnetLossParametersPermanent magnet loss parameter record

Connectors

NameDescription
flangeShaft
supportSupport at which the reaction torque is acting
plug_spPositive stator plug
plug_snNegative stator plug
idq_dr[2]Damper space phasor current / rotor fixed frame [A]
Initialization
ir[2]Damper cage currents [A]

Modelica.Electrical.Machines.BasicMachines.SynchronousInductionMachines.SM_ElectricalExcited Modelica.Electrical.Machines.BasicMachines.SynchronousInductionMachines.SM_ElectricalExcited

Electrical excited synchronous induction machine with damper cage

Information

Model of a three phase electrical excited synchronous induction machine with damper cage.
Resistance and stray inductance of stator is modeled directly in stator phases, then using space phasor transformation and a rotor-fixed AirGap model. Resistance and stray inductance of rotor's squirrel cage is modeled in two axis of the rotor-fixed coordinate system. Electrical excitation is modelled by converting excitation current and voltage to d-axis space phasors. The machine models take the following loss effects into account:

Whether a damper cage is present or not, can be selected with Boolean parameter useDamperCage (default = true).
Default values for machine's parameters (a realistic example) are:

number of pole pairs p 2
stator's moment of inertia 0.29kg.m2
rotor's moment of inertia 0.29kg.m2
nominal frequency fNominal 50Hz
nominal voltage per phase 100V RMS
no-load excitation current
@ nominal voltage and frequency
10A DC
warm excitation resistance 2.5Ohm
nominal current per phase 100A RMS
nominal apparent power -30000VA
power factor -1.0ind./cap.
nominal excitation current 19A
efficiency w/o excitation 97.1%
nominal torque -196.7Nm
nominal speed 1500rpm
nominal rotor angle -57.23degree
stator resistance 0.03Ohm per phase at reference temperature
reference temperature TsRef 20°C
temperature coefficient alpha20s 01/K
stator reactance Xd 1.6Ohm per phase in d-axis
giving Kc 0.625
stator reactance Xq 1.6Ohm per phase in q-axis
stator stray reactance Xss 0.1Ohm per phase
damper resistance in d-axis 0.04Ohm at reference temperature
damper resistance in q-axis same as d-axis
reference temperature TrRef 20°C
temperature coefficient alpha20r 01/K
damper stray reactance in d-axis XDds 0.05Ohm
damper stray reactance in q-axis XDqs same as d-axis
excitation resistance 2.5Ohm at reference temperature
reference temperature TeRef 20°C
temperature coefficient alpha20e 01/K
excitation stray inductance 2.5% of total excitation inductance
stator operational temperature TsOperational 20°C
damper operational temperature TrOperational 20°C
excitation operational temperature TeOperational 20°C
These values give the following inductances:
main field inductance in d-axis (Xd - Xss)/(2*pi*fNominal)
main field inductance in q-axis (Xq - Xss)/(2*pi*fNominal)
stator stray inductance per phase Xss/(2*pi*fNominal)
damper stray inductance in d-axis XDds/(2*pi*fNominal)
damper stray inductance in q-axis XDqs/(2*pi*fNominal)

Extends from Machines.Interfaces.PartialBasicInductionMachine (Partial model for induction machine).

Parameters

NameDescription
pNumber of pole pairs (Integer)
fsNominalNominal frequency [Hz]
JrRotor's moment of inertia [kg.m2]
useSupportEnable / disable (=fixed stator) support
JsStator's moment of inertia [kg.m2]
useThermalPortEnable / disable (=fixed temperatures) thermal port
idq_ss[2]Stator space phasor current / stator fixed frame [A]
idq_sr[2]Stator space phasor current / rotor fixed frame [A]
idq_rs[2]Rotor space phasor current / stator fixed frame [A]
idq_rr[2]Rotor space phasor current / rotor fixed frame [A]
Operational temperatures
TsOperationalOperational temperature of stator resistance [K]
TrOperationalOperational temperature of (optional) damper cage [K]
TeOperationalOperational excitation temperature [K]
Initialization
phiMechanicalMechanical angle of rotor against stator [rad]
wMechanicalMechanical angular velocity of rotor against stator [rad/s]
ir[2]Damper cage currents [A]
Nominal resistances and inductances
RsStator resistance per phase at TRef [Ohm]
TsRefReference temperature of stator resistance [K]
alpha20sTemperature coefficient of stator resistance at 20 degC [1/K]
LszeroStator zero sequence inductance [H]
LmdStator main field inductance per phase in d-axis [H]
LmqStator main field inductance per phase in q-axis [H]
DamperCage
useDamperCageEnable / disable damper cage
LrsigmadDamper stray inductance in d-axis [H]
LrsigmaqDamper stray inductance in q-axis [H]
RrdDamper resistance in d-axis at TRef [Ohm]
RrqDamper resistance in q-axis at TRef [Ohm]
TrRefReference temperature of damper resistances in d- and q-axis [K]
alpha20rTemperature coefficient of damper resistances in d- and q-axis [1/K]
Losses
frictionParametersFriction loss parameter record
statorCoreParametersStator core loss parameter record; all parameters refer to stator side
strayLoadParametersStray load loss parameter record
brushParametersBrush loss parameter record
Excitation
VsNominalNominal stator RMS voltage per phase [V]
IeOpenCircuitOpen circuit excitation current @ nominal voltage and frequency [A]
ReExcitation resistance at TRef [Ohm]
TeRefReference temperature of excitation resistance [K]
alpha20eTemperature coefficient of excitation resistance [1/K]
sigmaeStray fraction of total excitation inductance

Connectors

NameDescription
flangeShaft
supportSupport at which the reaction torque is acting
plug_spPositive stator plug
plug_snNegative stator plug
idq_dr[2]Damper space phasor current / rotor fixed frame [A]
pin_epPositive excitation pin
pin_enNegative excitation pin
Initialization
ir[2]Damper cage currents [A]

Modelica.Electrical.Machines.BasicMachines.SynchronousInductionMachines.SM_ReluctanceRotor Modelica.Electrical.Machines.BasicMachines.SynchronousInductionMachines.SM_ReluctanceRotor

Synchronous induction machine with reluctance rotor and damper cage

Information

Model of a three phase synchronous induction machine with reluctance rotor and damper cage.
Resistance and stray inductance of stator is modeled directly in stator phases, then using space phasor transformation. Resistance and stray inductance of rotor's squirrel cage is modeled in two axis of the rotor-fixed coordinate system. Both together connected via a rotor-fixed AirGap model. The machine models take the following loss effects into account:

Whether a damper cage is present or not, can be selected with Boolean parameter useDamperCage (default = true).
Default values for machine's parameters (a realistic example) are:

number of pole pairs p 2
stator's moment of inertia 0.29kg.m2
rotor's moment of inertia 0.29kg.m2
nominal frequency fNominal 50Hz
nominal voltage per phase 100V RMS
nominal current per phase 50A RMS
nominal torque 46Nm
nominal speed 1500rpm
nominal mechanical output 7.23kW
efficiency 96.98%
power factor 0.497
stator resistance 0.03Ohm per phase at reference temperature
reference temperature TsRef 20°C
temperature coefficient alpha20s 01/K
rotor resistance in d-axis 0.04Ohm at reference temperature
rotor resistance in q-axis same as d-axis
reference temperature TrRef 20°C
temperature coefficient alpha20r 01/K
stator reactance Xsd in d-axis 3Ohm per phase
stator reactance Xsq in q-axis 1Ohm
stator stray reactance Xss 0.1Ohm per phase
rotor stray reactance in d-axis Xrds 0.05Ohm per phase
rotor stray reactance in q-axis Xrqs same as d-axis
stator operational temperature TsOperational 20°C
damper operational temperature TrOperational 20°C
These values give the following inductances:
stator stray inductance per phase Xss/(2*pi*fNominal)
rotor stray inductance in d-axis Xrds/(2*pi*fNominal)
rotor stray inductance in q-axis Xrqs/(2*pi*fNominal)
main field inductance per phase in d-axis (Xsd-Xss)/(2*pi*fNominal)
main field inductance per phase in q-axis (Xsq-Xss)/(2*pi*fNominal)

Extends from Machines.Interfaces.PartialBasicInductionMachine (Partial model for induction machine).

Parameters

NameDescription
pNumber of pole pairs (Integer)
fsNominalNominal frequency [Hz]
JrRotor's moment of inertia [kg.m2]
useSupportEnable / disable (=fixed stator) support
JsStator's moment of inertia [kg.m2]
useThermalPortEnable / disable (=fixed temperatures) thermal port
idq_ss[2]Stator space phasor current / stator fixed frame [A]
idq_sr[2]Stator space phasor current / rotor fixed frame [A]
idq_rs[2]Rotor space phasor current / stator fixed frame [A]
idq_rr[2]Rotor space phasor current / rotor fixed frame [A]
Operational temperatures
TsOperationalOperational temperature of stator resistance [K]
TrOperationalOperational temperature of (optional) damper cage [K]
Initialization
phiMechanicalMechanical angle of rotor against stator [rad]
wMechanicalMechanical angular velocity of rotor against stator [rad/s]
ir[2]Damper cage currents [A]
Nominal resistances and inductances
RsStator resistance per phase at TRef [Ohm]
TsRefReference temperature of stator resistance [K]
alpha20sTemperature coefficient of stator resistance at 20 degC [1/K]
LszeroStator zero sequence inductance [H]
LmdStator main field inductance per phase in d-axis [H]
LmqStator main field inductance per phase in q-axis [H]
DamperCage
useDamperCageEnable / disable damper cage
LrsigmadDamper stray inductance in d-axis [H]
LrsigmaqDamper stray inductance in q-axis [H]
RrdDamper resistance in d-axis at TRef [Ohm]
RrqDamper resistance in q-axis at TRef [Ohm]
TrRefReference temperature of damper resistances in d- and q-axis [K]
alpha20rTemperature coefficient of damper resistances in d- and q-axis [1/K]
Losses
frictionParametersFriction loss parameter record
statorCoreParametersStator core loss parameter record; all parameters refer to stator side
strayLoadParametersStray load loss parameter record

Connectors

NameDescription
flangeShaft
supportSupport at which the reaction torque is acting
plug_spPositive stator plug
plug_snNegative stator plug
idq_dr[2]Damper space phasor current / rotor fixed frame [A]
Initialization
ir[2]Damper cage currents [A]
Automatically generated Tue Apr 05 09:36:19 2016.