SMPM_MTPATest example: PermanentMagnetSynchronousMachine, investigating maximum torque per Amps |
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Diagram
Information
This information is part of the Modelica Standard Library maintained by the Modelica Association.
This example investigates the maximum torque per amps (MTPA) of a quasi static permanent magnet synchronous machine. The machines is operated at constant speed. The current magnitude is kept constant and the current angle is rotated from 0 to 360 degrees with the simulation period of one second.
In this simulation the angle is the following angles are calculated:
phi_v= angle of voltage phasorphi_i= angle of current phasorphiphi_v - phi_i= angle between voltage and current phasortheta= rotor displacement angleepsilon = phi - theta= current angle
Simulate for 1 second and plot (versus angle epsilon):
smpmQS.tauElectrical: machine torquesmpmQS.abs_vs[1]: machine phase voltage magnitudephi: phase angle between voltage and current phasor
Note
The resistors connected to the terminals of the windings of the quasi static machine model are necessary to numerically stabilize the simulation.
Parameters (10)
| VNominal |
Value: 100 Type: Voltage (V) Description: Nominal RMS voltage per phase |
|---|---|
| fNominal |
Value: 50 Type: Frequency (Hz) Description: Nominal frequency |
| f |
Value: 50 Type: Frequency (Hz) Description: Actual frequency |
| tRamp |
Value: 1 Type: Time (s) Description: Frequency ramp |
| TLoad |
Value: 181.4 Type: Torque (N·m) Description: Nominal load torque |
| tStep |
Value: 1.2 Type: Time (s) Description: Time of load torque step |
| JLoad |
Value: 0.29 Type: Inertia (kg·m²) Description: Load's moment of inertia |
| wNominal |
Value: 2 * pi * fNominal / smpmData.p Type: AngularVelocity (rad/s) Description: Nominal angular velocity |
| positiveRange |
Value: false Type: Boolean Description: Use positive range of angles, if true |
| smpmData |
Value: Type: SM_PermanentMagnetData Description: Machine data |
Outputs (5)
| theta |
Default Value: rotorAngleQS.rotorDisplacementAngle Type: Angle (rad) Description: Rotor displacement angle, quasi static |
|---|---|
| phi_i |
Default Value: Modelica.Math.wrapAngle(smpmQS.arg_is[1], positiveRange) Type: Angle (rad) Description: Angle of current |
| phi_v |
Default Value: Modelica.Math.wrapAngle(smpmQS.arg_vs[1], positiveRange) Type: Angle (rad) Description: Angle of voltage |
| phi |
Default Value: Modelica.Math.wrapAngle(phi_v - phi_i, positiveRange) Type: Angle (rad) Description: Angle between voltage and current |
| epsilon |
Default Value: Modelica.Math.wrapAngle(phi - theta, positiveRange) Type: Angle (rad) Description: Current angle |
Components (18)
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smpmData |
Type: SM_PermanentMagnetData Description: Machine data |
|---|---|---|
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smpmQS |
Type: SM_PermanentMagnet |
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quadraticSpeedDependentTorqueQS |
Type: ConstantSpeed |
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starMachineQS |
Type: Star |
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groundMQS |
Type: Ground |
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terminalBoxQS |
Type: MultiTerminalBox |
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currentControllerQS |
Type: CurrentController |
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angleSensorQS |
Type: AngleSensor |
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referenceCurrentSourceQS |
Type: ReferenceCurrentSource |
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starQS |
Type: Star |
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groundeQS |
Type: Ground |
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resistorQS |
Type: Resistor |
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rotorAngleQS |
Type: RotorDisplacementAngle |
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currentRMSSensorQS |
Type: CurrentQuasiRMSSensor |
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voltageQuasiRMSSensorQS |
Type: VoltageQuasiRMSSensor |
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starMQS |
Type: Star |
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rotSource |
Type: ComplexRotatingPhasor |
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toReal |
Type: ComplexToReal |