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Perform transformation from αβ0 stationary reference frame to dq0 rotating reference frame or the inverse

The Alpha-Beta-Zero to dq0 block performs a transformation of αβ0 Clarke components in a fixed reference frame to dq0 Park components in a rotating reference frame.

The dq0 to Alpha-Beta-Zero block performs a transformation of dq0 Park components in a rotating reference frame to αβ0 Clarke components in a fixed reference frame.

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.

Knowing that the position of the rotating frame is given by
ω.t (where ω represents the frame rotation speed), the
αβ0 to dq0 transformation performs a −(ω.t)
rotation on the space vector U_{s} = u_{α} +
j· u_{β}. The homopolar or zero-sequence
component remains unchanged.

Depending on the frame alignment at t = 0, the dq0 components are deduced from αβ0 components as follows:

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

The inverse transformation is given by

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

The inverse transformation is given by

The abc-to-Alpha-Beta-Zero transformation applied to a set of
balanced three-phase sinusoidal quantities u_{a},
u_{b}, u_{c} produces a space
vector U_{s} whose u_{α} and
u_{β} coordinates in a fixed reference frame
vary sinusoidally with time. In contrast, the abc-to-dq0 transformation
(Park transformation) applied to a set of balanced three-phase sinusoidal
quantities u_{a}, u_{b}, u_{c} produces
a space vector U_{s} whose u_{d} and
u_{q} coordinates in a dq rotating reference frame
stay constant.

**Rotating frame alignment (at wt=0)**Select the alignment of rotating frame, when wt = 0, of the dq0 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 dq0 components are d = 0, q = −1, and zero = 0.When you select

`90 degrees behind phase A axis`, the dq0 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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