Park Transformation

The Park transformation used in SimPowerSystems™ 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?