Induction machine

Three-phase squirrel-cage induction machine (star-connected stator terminals).

  • rotational
  • 3-phase
  • Modelica Standard Library
  • 3 ports
  • 5 parameters
BlockInduction machineKindinductionMachineLibraryMachines

Description

A three-phase squirrel-cage induction machine, modeled with space phasors: stator resistance and leakage, a main-field inductance, and a rotor cage referred to the stator. It develops torque from slip, the difference between the field speed 2π · f / p and the rotor speed.

Only resistances and inertia are exposed. The inductances are fixed as reactances at fsNominal, 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 Induction 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)PMSM (MSL)Reluctance 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, or through Delta.

  • 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 · fsNominal / p.

  • Nominal frequencyfsNominal50 Hz

    ≥ 0

    Nominal supply frequency, in hertz. Sets the inductances from fixed reactances.

  • Stator resistanceRs0.03 Ω

    ≥ 0

    Stator resistance per phase, in ohms.

  • Rotor resistanceRr0.04 Ω

    ≥ 0

    Rotor resistance per phase, referred to the stator, in ohms. Sets the slip at a given torque.

  • 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)
0 = Rr · ir + Lrσ · dir/dt + dψm/dt (rotor, in rotor coordinates)
ψm = Lm · (is + ir)
τe = (3/2) · p · (ψm,α · is,β − ψm,β · is,α)
Lm = 2.898 Ω / (2π · fsNominal), Lsσ = Lrσ = 0.102 Ω / (2π · fsNominal)

Implementation

Modelica Standard Library 4.1.0Modelica.Electrical.Machines.BasicMachines.InductionMachines.IM_SquirrelCage
MSL documentation

Assumptions and limitations

  • Linear magnetics: no saturation of the main or leakage paths.
  • No iron, friction, or stray-load losses. Temperatures are fixed at 20 °C.
  • Single cage: no deep-bar or double-cage effects.

Tips

  • The fixed reactances correspond to the library’s 100 V, 100 A per-phase reference machine. Supply about 100 V RMS per phase at fsNominal for sensible currents.
  • Started direct on line from a Three-phase source, the machine draws a large inrush current before it reaches its slip speed.

See also

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