PMSM (MSL)

Three-phase permanent-magnet synchronous machine with damper cage.

  • rotational
  • 3-phase
  • Modelica Standard Library
  • 3 ports
  • 4 parameters
BlockPMSM (MSL)KindpmSyncMachineLibraryMachines

Description

A three-phase permanent-magnet synchronous machine with a damper cage on the rotor, from the Modelica library. The magnets give a fixed rotor flux; torque comes from the stator current in quadrature with it.

The back EMF is fixed at 112.3 V RMS per phase at fsNominal. Inductances are fixed as reactances at fsNominal, so changing fsNominal rescales them and the magnet flux.

Example

AC machines on the mains Induction, permanent-magnet, and reluctance machines started straight from a 50 Hz supply.

100 V rms IMStar IM supplyGround IM supplyStar IMGround IMInductionSpeed IM112.3 V rms PMSMStar PMSM supplyGround PMSM supplyStar PMSMGround PMSMPM synchronousSpeed PMSM100 V rms SynRMStar SynRM supplyGround SynRM supplyStar SynRMGround SynRMReluctanceSpeed SynRM
In Gradara, select a PMSM (MSL) block and press F1, then choose Open example. It opens as a new model in My models, ready to run.

Also in this example:GroundSpeed sensor (ideal)Induction machineReluctance machine3-phase AC sourceStar point

Ports

Conserving terminals 3

  • abcplug_sp3-phase

    Stator phase terminals a, b, c. Current into plug_sp is counted as positive.

  • nplug_sn3-phase

    Stator winding ends. Connect them to a Star point for a star connection.

  • shaftflangerotational

    Shaft, rotational, carrying the rotor inertia Jr. The stator is fixed to ground internally.

Parameters

  • Pole pairsp2

    ≥ 1

    Number of pole pairs, an integer ≥ 1. Synchronous speed is 2π · f / p.

  • Nominal frequencyfsNominal50 Hz

    ≥ 0

    Nominal frequency, in hertz. The open-circuit voltage 112.3 V RMS is reached at this frequency.

  • Stator resistanceRs0.03 Ω

    ≥ 0

    Stator resistance per phase, in ohms.

  • Rotor inertiaJr0.29 kg·m²

    ≥ 0

    Rotor moment of inertia, in kg·m².

Equations

Modelica
ψPM = √2 · 112.3 V / (2π · fsNominal) (peak, rotor d axis)
vs = Rs · is + Lsσ · dis/dt + dψm/dt (stator space phasors)
ψm,d = Lmd · (is,d + ir,d) + ψPM, ψm,q = Lmq · (is,q + ir,q)
τe = (3/2) · p · (ψm,α · is,β − ψm,β · is,α) = (3/2) · p · ψPM · is,q in steady state
Lmd = Lmq = 0.3 Ω / (2π · fsNominal), Lsσ = 0.1 Ω / (2π · fsNominal)

Implementation

Modelica Standard Library 4.1.0Modelica.Electrical.Machines.BasicMachines.SynchronousMachines.SM_PermanentMagnet
MSL documentation

Assumptions and limitations

  • Surface-magnet rotor (Lmd = Lmq), so there is no reluctance torque.
  • Linear magnetics: no saturation, no demagnetization, no cogging.
  • No iron, magnet, friction, or stray-load losses. Temperatures are fixed at 20 °C.
  • The damper cage (0.04 Ω per axis) is always present. It damps transients but is not found in most inverter-fed PM machines.

Tips

  • Drive it from an inverter with field-oriented control, taking the rotor angle from Electrical angle sensor or Resolver.
  • For a simpler PMSM with directly entered dq parameters, see PMSM.

See also

Select a block in Gradara and press F1 to open its page offline.