WOLFRAM SYSTEM MODELER

# SMPM_MTPA

Test example: PermanentMagnetSynchronousMachine, investigating maximum torque per Amps

# 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 Value: 100 Type: Voltage (V) Description: Nominal RMS voltage per phase Value: 50 Type: Frequency (Hz) Description: Nominal frequency Value: 50 Type: Frequency (Hz) Description: Actual frequency Value: 1 Type: Time (s) Description: Frequency ramp Value: 181.4 Type: Torque (N⋅m) Description: Nominal load torque Value: 1.2 Type: Time (s) Description: Time of load torque step Value: 0.29 Type: Inertia (kg⋅m²) Description: Load's moment of inertia Value: 2 * pi * fNominal / smpmData.p Type: AngularVelocity (rad/s) Description: Nominal angular velocity Value: false Type: Boolean Description: Use positive range of angles, if true Value: Description: Synchronous machine data

# Outputs (5)

theta Default Value: rotorAngleQS.rotorDisplacementAngle Type: Angle (rad) Description: Rotor displacement angle, quasi-static Default Value: Modelica.Math.wrapAngle(smpmQS.arg_is[1], positiveRange) Type: Angle (rad) Description: Angle of current Default Value: Modelica.Math.wrapAngle(smpmQS.arg_vs[1], positiveRange) Type: Angle (rad) Description: Angle of voltage Default Value: Modelica.Math.wrapAngle(phi_v - phi_i, positiveRange) Type: Angle (rad) Description: Angle between voltage and current Default Value: Modelica.Math.wrapAngle(phi - theta, positiveRange) Type: Angle (rad) Description: Current angle

# Components (18)

smpmData Description: Synchronous machine data Type: SM_PermanentMagnet Description: Permanent magnet synchronous machine with optional damper cage Type: ConstantSpeed Description: Constant speed, not dependent on torque Type: Star Description: Star connection Type: Ground Description: Electrical ground Type: MultiTerminalBox Description: Terminal box Y/D-connection Type: CurrentController Description: Current controller Type: AngleSensor Description: Ideal sensor to measure the absolute flange angle Description: Variable polyphase AC current with reference angle input Type: Star Description: Star connection Type: Ground Description: Electrical ground Type: Resistor Description: Polyphase linear resistor Description: Rotor lagging angle Description: Continuous quasi current RMS sensor for polyphase system Description: Continuous quasi voltage RMS sensor for polyphase system Type: Star Description: Star connection Description: Generate a phasor with constant magnitude and constant angular velocity of type Complex Type: ComplexToReal Description: Converts complex to Cartesian representation