Engee documentation

Clarke Transform

Coordinate transformation from abc coordinate system to αβ0.

clarke transform

Description

Block Clarke Transform converts components in the time domain of a three-phase system in the reference frame into components in the stationary reference frame .

For a balanced system, the zero component is zero.

Shown below are:

  • Direction of magnetic axes of the stator windings in the coordinate system and coordinate system .

    clarke transform 1

  • Equivalent , and zero components.

    clarke transform 2

Equations

The block implements the Clarke transform as follows:

where

  • , and are the components of the three-phase system in the reference frame ;

  • and are components of the two-coordinate system in the stationary reference frame;

  • - is the zero component of the two-coordinate system in the stationary reference frame.

Ports

Input

abc - a vector that contains values in the abc coordinate system
vector

Components of a three-phase system in the coordinate system .

Data types: Float32, Float64

Output

αβ0 - vector that contains values in the coordinate system αβ0
vector

Components of the three-phase system in the coordinate system .

Data types: Float32, Float64

References

  1. Krause, P., O. Wasynczuk, S. D. Sudhoff, and S. Pekarek. Analysis of Electric Machinery and Drive Systems. Piscatawy, NJ: Wiley-IEEE Press, 2013.