Park transform

Rotate stationary-frame currents into the rotor d/q frame.

  • signal
  • Gradara equations
  • 5 ports
BlockPark transformKindparkLibraryControl

Description

Rotates stationary-frame (α, β) quantities into the rotor d/q frame at the electrical angle theta. With theta aligned to the rotor flux, id is the flux-producing current and iq the torque-producing current.

Uses the d-axis-aligned convention: at theta = 0, the d axis coincides with α.

Example

PMSM · Field-oriented control 1500 rpm speed command with cascaded d/q current control. A 48 V averaged inverter drives a surface PMSM and a mechanical load that increases at 0.45 s. Ideal current and rotor-position feedback; continuous controllers; no PWM ripple or sensor noise.

Speed commandrpm → rad/sSpeed errorKp · speedKi · speedIntegralPI sumCurrent limitq-axis errorq-axis PIid* = 0 Ad-axis errord-axis PIInverse Park / ClarkeAveraged inverterPMSMMechanical loadClarkePark
In Gradara, select a Park transform block and press F1, then choose Open example. It opens as a new model in My models, ready to run.

Also in this example:SumSubtractConstantLimited integratorCurrent PIClarke transformInverse transformsThree-phase inverterPMSMMechanical loadStepGainSaturation

Ports

Inputs 3

  • αalphasignal · A

    α-axis current, in amperes, typically from Clarke transform.

  • βbetasignal · A

    β-axis current, in amperes.

  • θethetasignal · rad

    Electrical rotor angle θe, in radians (mechanical angle times pole pairs).

Outputs 2

  • didsignal · A

    d-axis current, in amperes.

  • qiqsignal · A

    q-axis current, in amperes.

Equations

Modelica
id = alpha · cos(theta) + beta · sin(theta)
iq = −alpha · sin(theta) + beta · cos(theta)

Implementation

The block’s Modelica model
id = alpha*cos(theta) + beta*sin(theta);
iq = -alpha*sin(theta) + beta*cos(theta);

Assumptions and limitations

  • Uses theta as given: no angle estimation, filtering, or sensor delay.

Tips

  • Feed theta from the PMSM’s θe output. A mechanical angle gives wrong d/q currents unless the motor has one pole pair.

Used in

These larger examples use it too. Open them from Examples in the app.

  • PMSM · Field-oriented control

See also

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