Clarke transform

Amplitude-invariant three-phase to stationary-frame current transform.

  • signal
  • Gradara equations
  • 5 ports
BlockClarke transformKindclarkeLibraryControl

Description

Converts three phase currents into the two-axis stationary frame (α, β), using the amplitude-invariant form: a balanced set of phase currents with peak Î gives α and β with the same peak Î.

Use it with Park transform to turn measured motor currents into d/q currents.

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 Clarke 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 PIPark transformInverse transformsThree-phase inverterPMSMMechanical loadStepGainSaturation

Ports

Inputs 3

  • aiasignal · A

    Phase a current, in amperes.

  • bibsignal · A

    Phase b current, in amperes.

  • cicsignal · A

    Phase c current, in amperes.

Outputs 2

  • αalphasignal · A

    α-axis current, in amperes, aligned with phase a.

  • βbetasignal · A

    β-axis current, in amperes, 90° ahead of α.

Equations

Modelica
alpha = (2 · ia − ib − ic)/3
beta = (ib − ic)/√3

Implementation

The block’s Modelica model
alpha = (2*ia-ib-ic)/3;
beta = (ib-ic)/sqrt(3);

Assumptions and limitations

  • Any zero-sequence (common-mode) component ia + ib + ic is discarded; it does not appear in either output.

Tips

  • All three currents are used. Connect ic even when the phases sum to zero; it is not reconstructed from ia and ib.

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.