Engee documentation

Clarke Transform

Transformation of coordinates from the coordinate system abc to αß0.

blockType: SubSystem

clarke transform

Path in the library:

/Physical Modeling/Electrical/Control/Mathematical Transforms/Clarke Transform

Description

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

For a balanced system, the zero component is zero.

Below are shown:

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

    clarke transform 1

  • Equivalent , and zero components.

    clarke transform 2

Equations

The block implements the Clark transformation as follows:

Where

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

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

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

Ports

Input

abc is a vector that contains values in the abc pass coordinate sy\$
\$ vector

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

Data types: Float32, Float64

Output

αß0 is a vector that contains values in the αß0 pass coordinate sy\$
\$ vector

Components of a 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.