Documentation

This is machine translation

Translated by Microsoft
Mouseover text to see original. Click the button below to return to the English verison of the page.

Note: This page has been translated by MathWorks. Please click here
To view all translated materals including this page, select Japan from the country navigator on the bottom of this page.

Park Transformation

The Park transformation used in Simscape™ Power Systems™ models and functions corresponds to the definition provided in [1].

It transforms three quantities (direct axis, quadratic axis, and zero-sequence components) expressed in a two-axis reference frame back to phase quantities.

The following transformation is used:

Va=Vdsin(ωt)+Vqcos(ωt)+V0Vb=Vdsin(ωt2π/3)+Vqcos(ωt2π/3)+V0Vc=Vdsin(ωt+2π/3)+Vqcos(ωt+2π/3)+V0,

where ω = rotation speed (rad/s) of the rotating frame.

The following reverse transformation is used:

Vd=23(Vasin(ωt)+Vbsin(ωt2π/3)+Vcsin(ωt+2π/3))Vq=23(Vacos(ωt)+Vbcos(ωt2π/3)+Vccos(ωt+2π/3))V0=13(Va+Vb+Vc),

where ω = rotation speed (rad/s) of the rotating frame.

The transformations are the same for the case of a three-phase current; you simply replace the Va, Vb, Vc, Vd, Vq, and V0 variables with the Ia, Ib, Ic, Id, Iq, and I0 variables.

References

[1] Krause, P. C. Analysis of Electric Machinery. New York: McGraw-Hill, 1994, p.135.

Was this topic helpful?