WOLFRAM SYSTEM MODELER
IM_SquirrelCageInduction machine with squirrel cage rotor |
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Diagram
Wolfram Language
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SystemModel["Modelica.Electrical.Machines.BasicMachines.InductionMachines.IM_SquirrelCage"]
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Information
This information is part of the Modelica Standard Library maintained by the Modelica Association.
Model of a three-phase induction machine with squirrel 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 stator-fixed AirGap model. 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
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 | 100 | A RMS |
| nominal torque | 161.4 | Nm |
| nominal speed | 1440.45 | rpm |
| nominal mechanical output | 24.346 | kW |
| efficiency | 92.7 | % |
| power factor | 0.875 | |
| stator resistance | 0.03 | Ohm per phase at reference temperature |
| reference temperature TsRef | 20 | °C |
| temperature coefficient alpha20s | 0 | 1/K |
| rotor resistance | 0.04 | Ohm at reference temperature |
| reference temperature TrRef | 20 | °C |
| temperature coefficient alpha20r | 0 | 1/K |
| stator reactance Xs | 3 | Ohm per phase |
| rotor reactance Xr | 3 | Ohm |
| total stray coefficient sigma | 0.0667 | |
| stator operational temperature TsOperational | 20 | °C |
| rotor operational temperature TrOperational | 20 | °C |
| These values give the following inductances: | ||
| stator stray inductance per phase | Xs * (1 - sqrt(1-sigma))/(2*pi*fNominal) | |
| rotor stray inductance | Xr * (1 - sqrt(1-sigma))/(2*pi*fNominal) | |
| main field inductance per phase | sqrt(Xs*Xr * (1-sigma))/(2*pi*fNominal) |
Parameters (22)
| 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 |
| Lm |
Value: Type: Inductance (H) Description: Stator main field inductance per phase |
| Lrsigma |
Value: Type: Inductance (H) Description: Rotor stray inductance per phase (equivalent three-phase winding) |
| Rr |
Value: Type: Resistance (Ω) Description: Rotor resistance per phase (equivalent three-phase winding) at TRef |
| TrRef |
Value: Type: Temperature (K) Description: Reference temperature of rotor resistance |
| alpha20r |
Value: Type: LinearTemperatureCoefficient20 (1/K) Description: Temperature coefficient of rotor resistance at 20 degC |
| TrOperational |
Value: Type: Temperature (K) Description: Operational temperature of rotor resistance |
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 (9)
| 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: PowerBalanceIMC 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 |
| ir |
Default Value: squirrelCageR.i Type: Current[2] (A) Description: Rotor cage currents |
Connectors (7)
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flange |
Type: Flange_a Description: Shaft |
|---|---|---|
|
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: ThermalPortIMC Description: Thermal port of induction machine with squirrel cage |
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internalThermalPort |
Type: ThermalPortIMC Description: Thermal port of induction machine with squirrel cage |
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: PowerBalanceIMC 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: ThermalAmbientIMC Description: Thermal ambient for induction machine with squirrel cage |
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airGap |
Type: AirGapS Description: Airgap in stator-fixed coordinate system |
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squirrelCageR |
Type: SquirrelCage Description: Squirrel Cage |
Used in Examples (12)
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Modelica.Electrical.Machines.Examples.InductionMachines Test example: InductionMachineSquirrelCage direct-on-line |
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Modelica.Electrical.Machines.Examples.InductionMachines Test example: InductionMachineSquirrelCage Y-D |
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Modelica.Electrical.Machines.Examples.InductionMachines Test example: InductionMachineSquirrelCage Y-D |
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Modelica.Electrical.Machines.Examples.InductionMachines Test example: InductionMachineSquirrelCage transformer starting |
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Modelica.Electrical.Machines.Examples.InductionMachines Test example: InductionMachineSquirrelCage with inverter |
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Modelica.Electrical.Machines.Examples.InductionMachines Test example: InductionMachineSquirrelCage with inverter driving a conveyor |
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Modelica.Electrical.Machines.Examples.InductionMachines Test example: InductionMachineSquirrelCage inverter drive |
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Modelica.Electrical.Machines.Examples.InductionMachines InductionMachineSquirrelCage Steinmetz-connection |
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Modelica.Electrical.Machines.Examples.InductionMachines Test example: InductionMachineSquirrelCage with losses |
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Modelica.Electrical.Machines.Examples.InductionMachines Test example: Steady-State Initialization of InductionMachineSquirrelCage |
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Modelica.Electrical.Machines.Examples.InductionMachines Induction machine with DC current braking |
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Modelica.Magnetic.FundamentalWave.Examples.BasicMachines.InductionMachines Direct on line (DOL) start of induction machine with squirrel cage |