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# abc to dq0, dq0 to abc

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

## Library

Control and Measurements/Transformations

## Description

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 = uα + j· uβ.

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

## Dialog Box and Parameters

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.

## Inputs and Outputs

abc

The vectorized abc signal.

dq0

The vectorized dq0 signal.

wt

The angular position of the dq rotating frame, in radians.

## Example

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