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Perform Park transformation from dq0 reference frame to abc reference frame

Extras/Measurements

A discrete version of this block is available in the Extras/Discrete Measurements library.

The dq0_to_abc Transformation block performs the reverse of the so-called Park transformation, which is commonly used in three-phase electric machine models. 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:

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

The transformation is the same for the case of a three-phase
current; you simply replace the *V _{a}*,

The dq0_to_abc Transformation block is used in the model of
the Synchronous Machine block where the stator quantities are referred
to the rotor. The Park transformation then eliminates time-varying
inductances by referring the stator and rotor quantities to a fixed
or rotating reference frame. The I_{d} and I_{q} currents
represent the two DC currents flowing in the two equivalent rotor
windings (d winding on the same axis as the field winding, and q winding
in quadratic) producing the same flux as the stator I_{a},
I_{b}, and I_{c} currents.

`dq0`Connect to the first input a vectorized signal containing the sequence components [d q 0] to be converted.

`sin_cos`Connect to the second input a vectorized signal containing the [sin(ωt) cos(ωt)] values, where ω is the rotation speed of the reference frame.

`abc`The output is a vectorized signal containing the three-phase sinusoidal quantities [phase A phase B phase C], in the same units as the

`dq0`input signal.

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