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WOLFRAM SYSTEM MODELER

SMPM_MTPA

Test example: PermanentMagnetSynchronousMachine, investigating maximum torque per Amps

Diagram

Wolfram Language

In[1]:=

SystemModel["Modelica.Magnetic.QuasiStatic.FundamentalWave.Examples.BasicMachines.SynchronousMachines.SMPM_MTPA"]

Out[1]:=

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 phasor
phi_i = angle of current phasor
phiphi_v - phi_i = angle between voltage and current phasor
theta = rotor displacement angle
epsilon = phi - theta = current angle

Simulate for 1 second and plot (versus angle epsilon):

smpmQS.tauElectrical: machine torque
smpmQS.abs_vs[1]: machine phase voltage magnitude
phi: 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 (11)

m	Value: 3 Type: Integer Description: Number of phases
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: Synchronous 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)

	smpmData	Type: SM_PermanentMagnetData Description: Synchronous machine data
	smpmQS	Type: SM_PermanentMagnet Description: Permanent magnet synchronous machine with optional damper cage
	quadraticSpeedDependentTorqueQS	Type: ConstantSpeed Description: Constant speed, not dependent on torque
	starMachineQS	Type: Star Description: Star connection
	groundMQS	Type: Ground Description: Electrical ground
	terminalBoxQS	Type: MultiTerminalBox Description: Terminal box Y/D-connection
	currentControllerQS	Type: CurrentController Description: Current controller
	angleSensorQS	Type: AngleSensor Description: Ideal sensor to measure the absolute flange angle
	referenceCurrentSourceQS	Type: ReferenceCurrentSource Description: Variable polyphase AC current with reference angle input
	starQS	Type: Star Description: Star connection
	groundeQS	Type: Ground Description: Electrical ground
	resistorQS	Type: Resistor Description: Polyphase linear resistor
	rotorAngleQS	Type: RotorDisplacementAngle Description: Rotor lagging angle
	currentRMSSensorQS	Type: CurrentQuasiRMSSensor Description: Continuous quasi current RMS sensor for polyphase system
	voltageQuasiRMSSensorQS	Type: VoltageQuasiRMSSensor Description: Continuous quasi voltage RMS sensor for polyphase system
	starMQS	Type: Star Description: Star connection
	rotSource	Type: ComplexRotatingPhasor Description: Generate a phasor with constant magnitude and constant angular velocity of type Complex
	toReal	Type: ComplexToReal Description: Converts complex to Cartesian representation