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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


Simscape / Electrical / Specialized Power Systems / Control

  • abc to Alpha-Beta-Zero, Alpha-Beta-Zero to abc block


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.


The inverse transformation is given by


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


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:



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

Version History

Introduced in R2013a