Inverse Clarke Transform

Implement αβ to abc transformation

  • Library:
  • Motor Control Blockset / Controls / Math Transforms

Description

The Inverse Clarke Transform block computes the Inverse Clarke transformation of balanced, two-phase orthogonal components in the stationary αβ reference frame. It outputs the balanced, three-phase components in the stationary abc reference frame.

The block accepts the α-β axis components as inputs and outputs the corresponding three-phase signals, where the phase-a axis aligns with the α-axis.

  • The α and β input components in the αβ reference frame.

  • The direction of the equivalent a, b, and c output components in the abc reference frame and the αβ reference frame.

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

Equations

The following equation describes the Inverse Clarke transform computation:

[fafbfc]=[1011232112321][fαfβf0]

For balanced systems like motors, the zero sequence component calculation is always zero:

ia+ib+ic=0

Therefore, you can use only two current sensors in three-phase motor drives, where you can calculate the third phase as,

ic=(ia+ib)

By using these equations, the block implements the Inverse Clarke transform as,

[fa fb fc ]= [1012321232][fαfβ] 

where:

  • fα and fβ are the balanced two-phase orthogonal components in the stationary αβ reference frame.

  • f0 is the zero component in the stationary αβ reference frame.

  • fa, fb, and fc are the balanced three-phase components in the abc reference frame.

Ports

Input

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Alpha-axis component, α, in the stationary αβ reference frame.

Data Types: single | double | fixed point

Beta-axis component, β, in the stationary αβ reference frame.

Data Types: single | double | fixed point

Output

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

Data Types: single | double | fixed point

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

Data Types: single | double | fixed point

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

Data Types: single | double | fixed point

Introduced in R2020a