WOLFRAM SYSTEM MODELER
SM_ReluctanceRotorSynchronous machine with reluctance rotor and damper cage |
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Diagram
Wolfram Language
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SystemModel["Modelica.Electrical.Machines.BasicMachines.SynchronousMachines.SM_ReluctanceRotor"]
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Information
This information is part of the Modelica Standard Library maintained by the Modelica Association.
Model of a three-phase synchronous 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:
- heat losses in the temperature dependent stator winding resistances
- optional, when enabled: heat losses in the temperature dependent damper cage resistances
- friction losses
- core losses (only eddy current losses, no hysteresis losses)
- stray load losses
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 | 0.29 | kg.m2 |
| rotor's moment of inertia | 0.29 | kg.m2 |
| nominal frequency fNominal | 50 | Hz |
| nominal voltage per phase | 100 | V RMS |
| nominal current per phase | 50 | A RMS |
| nominal torque | 46 | Nm |
| nominal speed | 1500 | rpm |
| nominal mechanical output | 7.23 | kW |
| efficiency | 96.98 | % |
| power factor | 0.497 | |
| stator resistance | 0.03 | Ohm per phase at reference temperature |
| reference temperature TsRef | 20 | °C |
| temperature coefficient alpha20s | 0 | 1/K |
| rotor resistance in d-axis | 0.04 | Ohm at reference temperature |
| rotor resistance in q-axis | same as d-axis | |
| reference temperature TrRef | 20 | °C |
| temperature coefficient alpha20r | 0 | 1/K |
| stator reactance Xsd in d-axis | 3 | Ohm per phase |
| stator reactance Xsq in q-axis | 1 | Ohm |
| stator stray reactance Xss | 0.1 | Ohm per phase |
| rotor stray reactance in d-axis Xrds | 0.05 | Ohm 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) |
Parameters (26)
| Jr |
Value: Type: Inertia (kg⋅m²) Description: Rotor's moment of inertia |
|---|---|
| useSupport |
Value: false Type: Boolean Description: Enable / disable (=fixed stator) support |
| Js |
Value: Jr Type: Inertia (kg⋅m²) Description: Stator's moment of inertia |
| useThermalPort |
Value: false Type: Boolean Description: Enable / disable (=fixed temperatures) thermal port |
| frictionParameters |
Value: Type: FrictionParameters Description: Friction loss parameter record |
| m |
Value: 3 Type: Integer Description: Number of phases |
| p |
Value: Type: Integer Description: Number of pole pairs (Integer) |
| fsNominal |
Value: Type: Frequency (Hz) Description: Nominal frequency |
| TsOperational |
Value: Type: Temperature (K) Description: Operational temperature of stator resistance |
| Rs |
Value: Type: Resistance (Ω) Description: Stator resistance per phase at TRef |
| TsRef |
Value: Type: Temperature (K) Description: Reference temperature of stator resistance |
| alpha20s |
Value: Type: LinearTemperatureCoefficient20 (1/K) Description: Temperature coefficient of stator resistance at 20 degC |
| Lszero |
Value: Lssigma Type: Inductance (H) Description: Stator zero sequence inductance |
| Lssigma |
Value: Type: Inductance (H) Description: Stator stray inductance per phase |
| statorCoreParameters |
Value: Type: CoreParameters Description: Stator core loss parameter record; all parameters refer to stator side |
| strayLoadParameters |
Value: Type: StrayLoadParameters Description: Stray load loss parameter record |
| TrOperational |
Value: Type: Temperature (K) Description: Operational temperature of (optional) damper cage |
| Lmd |
Value: Type: Inductance (H) Description: Stator main field inductance per phase in d-axis |
| Lmq |
Value: Type: Inductance (H) Description: Stator main field inductance per phase in q-axis |
| useDamperCage |
Value: Type: Boolean Description: Enable / disable damper cage |
| Lrsigmad |
Value: Type: Inductance (H) Description: Damper stray inductance in d-axis |
| Lrsigmaq |
Value: Lrsigmad Type: Inductance (H) Description: Damper stray inductance in q-axis |
| Rrd |
Value: Type: Resistance (Ω) Description: Damper resistance in d-axis at TRef |
| Rrq |
Value: Rrd Type: Resistance (Ω) Description: Damper resistance in q-axis at TRef |
| TrRef |
Value: Type: Temperature (K) Description: Reference temperature of damper resistances in d- and q-axis |
| alpha20r |
Value: Type: LinearTemperatureCoefficient20 (1/K) Description: Temperature coefficient of damper resistances in d- and q-axis |
Inputs (4)
| idq_ss |
Default Value: airGap.i_ss Type: Current[2] (A) Description: Stator space phasor current / stator fixed frame |
|---|---|
| idq_sr |
Default Value: airGap.i_sr Type: Current[2] (A) Description: Stator space phasor current / rotor fixed frame |
| idq_rs |
Default Value: airGap.i_rs Type: Current[2] (A) Description: Rotor space phasor current / stator fixed frame |
| idq_rr |
Default Value: airGap.i_rr Type: Current[2] (A) Description: Rotor space phasor current / rotor fixed frame |
Outputs (8)
| phiMechanical |
Default Value: flange.phi - internalSupport.phi Type: Angle (rad) Description: Mechanical angle of rotor against stator |
|---|---|
| wMechanical |
Default Value: der(phiMechanical) Type: AngularVelocity (rad/s) Description: Mechanical angular velocity of rotor against stator |
| tauElectrical |
Default Value: inertiaRotor.flange_a.tau Type: Torque (N⋅m) Description: Electromagnetic torque |
| tauShaft |
Default Value: -flange.tau Type: Torque (N⋅m) Description: Shaft torque |
| powerBalance |
Type: PowerBalanceSMR Description: Power balance |
| vs |
Default Value: plug_sp.pin.v - plug_sn.pin.v Type: Voltage[m] (V) Description: Stator instantaneous voltages |
| is |
Default Value: plug_sp.pin.i Type: Current[m] (A) Description: Stator instantaneous currents |
| i_0_s |
Default Value: spacePhasorS.zero.i Type: Current (A) Description: Stator zero-sequence current |
Connectors (10)
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flange |
Type: Flange_a Description: Shaft |
|---|---|---|
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support |
Type: Flange_a Description: Support at which the reaction torque is acting |
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internalSupport |
Type: Support Description: Support/housing flange of a one-dimensional rotational shaft |
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plug_sp |
Type: PositivePlug Description: Positive stator plug |
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plug_sn |
Type: NegativePlug Description: Negative stator plug |
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thermalPort |
Type: ThermalPortSMR Description: Thermal port of synchronous machine with reluctance rotor |
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internalThermalPort |
Type: ThermalPortSMR Description: Thermal port of synchronous machine with reluctance rotor |
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ir |
Type: RealOutput[2] Description: Damper cage currents |
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idq_dr |
Type: RealOutput[2] Description: Damper space phasor current / rotor fixed frame |
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damperCageLossPower |
Type: RealOutput Description: Damper losses |
Components (17)
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frictionParameters |
Type: FrictionParameters Description: Friction loss parameter record |
|---|---|---|
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inertiaRotor |
Type: Inertia Description: 1D-rotational component with inertia |
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inertiaStator |
Type: Inertia Description: 1D-rotational component with inertia |
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fixed |
Type: Fixed Description: Flange fixed in housing at a given angle |
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friction |
Type: Friction Description: Model of angular velocity dependent friction losses |
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statorCoreParameters |
Type: CoreParameters Description: Stator core loss parameter record; all parameters refer to stator side |
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strayLoadParameters |
Type: StrayLoadParameters Description: Stray load loss parameter record |
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powerBalance |
Type: PowerBalanceSMR Description: Power balance |
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rs |
Type: Resistor Description: Ideal linear electrical resistors |
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lssigma |
Type: Inductor Description: Space phasor inductor |
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lszero |
Type: Inductor Description: Ideal linear electrical inductor |
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statorCore |
Type: Core Description: Model of core losses |
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spacePhasorS |
Type: SpacePhasor Description: Physical transformation: three-phase <-> space phasors |
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strayLoad |
Type: StrayLoad Description: Model of stray load losses dependent on current and speed |
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thermalAmbient |
Type: ThermalAmbientSMR Description: Thermal ambient for synchronous machine with reluctance rotor |
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airGap |
Type: AirGapR Description: Airgap in rotor-fixed coordinate system |
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damperCage |
Type: DamperCage Description: Squirrel Cage |
Used in Examples (3)
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Modelica.Electrical.Machines.Examples.SynchronousMachines Test example: SynchronousMachineReluctanceRotor direct-on-line |
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Modelica.Electrical.Machines.Examples.SynchronousMachines Test example: SynchronousMachineReluctanceRotor with inverter |
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Modelica.Magnetic.FundamentalWave.Examples.BasicMachines.SynchronousMachines Starting of synchronous reluctance machine with inverter |