Reluctance machine

Three-phase synchronous reluctance machine.

  • rotational
  • 3-phase
  • Modelica Standard Library
  • 3 ports
  • 4 parameters
BlockReluctance machineKindreluctanceMachineLibraryMachines

Description

A three-phase synchronous reluctance machine with a damper cage. The rotor has no magnets or windings; torque comes from the difference between its d-axis and q-axis inductances.

Inductances are fixed as reactances at fsNominal (d axis 2.9 Ω, q axis 0.9 Ω), so changing fsNominal rescales them.

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 Reluctance machine 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 machinePMSM (MSL)3-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. Sets the inductances from fixed reactances.

  • 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
vs = Rs · is + Lsσ · dis/dt + dψm/dt (stator space phasors)
ψm,d = Lmd · (is,d + ir,d), ψm,q = Lmq · (is,q + ir,q)
τe = (3/2) · p · (Lmd − Lmq) · is,d · is,q in steady state
Lmd = 2.9 Ω / (2π · fsNominal), Lmq = 0.9 Ω / (2π · fsNominal), Lsσ = 0.1 Ω / (2π · fsNominal)

Implementation

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

Assumptions and limitations

  • Linear magnetics: no saturation or cross-coupling between axes.
  • No iron, friction, or stray-load losses. Temperatures are fixed at 20 °C.
  • The damper cage (0.04 Ω per axis) is always present; it lets the machine start on line and pull into step.

See also

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