Perform Park transformation from dq0 reference frame to abc reference frame

powerlib_extras/Measurements, powerlib_extras/Discrete Measurements

The Transformations section of the Control and Measurements library contains the dq0 to abc to block. This is an improved version of the dq0_to_abc Transformation block. The new block features a mechanism that eliminates duplicate continuous and discrete versions of the same block by basing the block configuration on the simulation mode. If your legacy models contain the dq0_to_abc Transformation block, they continue to work. However, for best performance, use the dq0 to abc block in your new models.

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:

$$\begin{array}{c}{V}_{a}={V}_{d}\mathrm{sin}(\omega t)+{V}_{q}\mathrm{cos}(\omega t)+{V}_{0}\\ {V}_{b}={V}_{d}\mathrm{sin}(\omega t-2\pi /3)+{V}_{q}\mathrm{cos}(\omega t-2\pi /3)+{V}_{0}\\ {V}_{c}={V}_{d}\mathrm{sin}(\omega t+2\pi /3)+{V}_{q}\mathrm{cos}(\omega t+2\pi /3)+{V}_{0},\end{array}$$

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.

See the example of the abc_to_dq0 Transformation block for an example using the dq0 to abc block (the improved version of the dq0_to_abc Transformation block).

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

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