Documentation

Clarke Transform

Implement abc to αβ0 transform

  • Library:
  • Simscape / Power Systems / Simscape Components / Control / Mathematical Transforms

Description

The Clarke Transform block converts the time-domain components of a three-phase system in an abc reference frame to components in a stationary ɑβ0 reference frame. The block can preserve the active and reactive powers with the powers of the system in the abc reference frame by implementing a power invariant version of the Clarke transform. For a balanced system, the zero component is equal to zero.

The figures show:

  • The direction of the magnetic axes of the stator windings in the abc reference frame and the stationary ɑβ0 reference frame

  • Equivalent ɑ, β, and zero components in the stationary reference frame

  • The time-response of the individual components of equivalent balanced abc and ɑβ0 systems

Equations

The block implements the Clarke transform as

[αβ0]=23[1121203232121212][abc],

where:

  • a, b, and c are the components of the three-phase system in the abc reference frame.

  • α and β are the components of the two-axis system in the stationary reference frame.

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

The block implements the power invariant version of the Clarke transform as

[αβ0]=23[1121203232121212][abc].

Ports

Input

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Components of the three-phase system in the abc reference frame.

Data Types: single | double

Output

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Alpha-axis component,α, beta-axis component β, and zero component in the stationary reference frame.

Data Types: single | double

Parameters

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Preserve the active and reactive power of the system in the abc reference frame.

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.

Introduced in R2017b

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