abc to Alpha-Beta-Zero, Alpha-Beta-Zero to abc

Perform transformation from three-phase (abc) signal to αβ0 stationary reference frame or the inverse

Library

Control and Measurements/Transformations

Description

The abc to Alpha-Beta-Zero block performs a Clarke transform on a three-phase abc signal. The Alpha-Beta-Zero to abc block performs an inverse Clarke transform on the αβ0 components.

[uαuβu0]=[23131301313131313][uaubuc]

The inverse transformation is given by

[uaubuc]=[1011232112321][uαuβu0]

Assume that ua, ub, uc quantities represent three sinusoidal balanced currents:

ia=Isin(ωt)ib=Isin(ωt2π3)ic=Isin(ωt+2π3)

These currents are flowing respectively into windings A, B, C of a three-phase winding, as the figure shows.

In this case, the iα and iβ components represent the coordinates of the rotating space vector Is in a fixed reference frame whose α axis is aligned with phase A axis. Is amplitude is proportional to the rotating magnetomotive force produced by the three currents. It is computed as follows:

Is=ia+jiβ=23(ia+ibej2π3+icej2π3)

Dialog Box and Parameters

The block has no parameters.

Example

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

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