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Perform transformation from three-phase (abc) signal to dq0 rotating reference frame or the inverse

The abc to dq0 block performs a Park transformation in a rotating reference frame.

The dq0 to abc block performs an inverse Park transformation.

The block supports the two conventions used in the literature for Park transformation:

Rotating frame aligned with A axis at t = 0. This type of Park transformation is also known as the cosinus-based Park transformation.

Rotating frame aligned 90 degrees behind A axis. This type of Park transformation is also known as the sinus-based Park transformation. Use it in SimPowerSystems models of three-phase synchronous and asynchronous machines.

Deduce the dq0 components from abc signals by performing an
abc to αβ0 Clarke transformation in a fixed reference
frame. Then perform an αβ0 to dq0 transformation in a
rotating reference frame, that is, −(ω.t) rotation on
the space vector Us = u_{α} + j· u_{β}.

The abc-to-dq0 transformation depends on the dq frame alignment at t = 0. The position of the rotating frame is given by ω.t (where ω represents the dq frame rotation speed).

When the rotating frame is aligned with A axis, the following relations are obtained:

Inverse transformation is given by

When the rotating frame is aligned 90 degrees behind A axis, the following relations are obtained:

Inverse transformation is given by

**Rotating frame alignment (at wt=0)**Select the alignment of rotating frame a t = 0 of the d-q-0 components of a three-phase balanced signal:

(positive-sequence magnitude = 1.0 pu; phase angle = 0 degree)

When you select

`Aligned with phase A axis`, the d-q-0 components are d = 0, q = −1, and zero = 0.When you select

`90 degrees behind phase A axis`, the d-q-0 components are d = 1, q = 0, and zero = 0.

The `power_Transformations``power_Transformations` example
shows various uses of blocks performing Clarke and Park transformations.

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