Documentation

Clarke to Park Angle Transform

Implement αβ0 to dq0 transform

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

Description

The Clarke to Park Angle Transform block converts the alpha, beta, and zero components in a stationary reference frame to direct, quadrature, and zero components in a rotating reference frame. For balanced three-phase systems, the zero components are equal to zero.

You can configure the block to align the phase a-axis of the three-phase system to either the q- or d-axis of the rotating reference frame at time, t = 0. The figures show the direction of the magnetic axes of the stator windings in the three-phase system, a stationary αβ0 reference frame, and a rotating dq0 reference frame where:

  • The a-axis and the q-axis are initially aligned.

  • The a-axis and the d-axis are initially aligned.

In both cases, the angle θ = ωt, where

  • θ is the angle between the a and q axes for the q-axis alignment or the angle between the a and d axes for the d-axis alignment.

  • ω is the rotational speed of the d-q reference frame.

  • t is the time, in s, from the initial alignment.

The figures show the time-response of the individual components of equivalent balanced αβ0 and dq0 for an:

  • Alignment of the a-phase vector to the q-axis

  • Alignment of the a-phase vector to the d-axis

Equations

The Clarke to Park Angle Transform block implements the transform for an a-phase to q-axis alignment as

[dq0]=[sin(θ)cos(θ)0cos(θ)sin(θ)0001][αβ0]

where:

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

  • 0 is the zero component.

  • d and q are the direct-axis and quadrature-axis components of the two-axis system in the rotating reference frame.

For an a-phase to d-axis alignment, the block implements the transform using this equation:

[dq0]=[cos(θ)sin(θ)0sin(θ)cos(θ)0001][αβ0]

Ports

Input

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Alpha-axis, α, beta-axis, β, and zero components of the two-phase system in the stationary reference frame.

Data Types: single | double

Angular position of the rotating reference frame. The value of this parameter is equal to the polar distance from the vector of the a-phase in the abc reference frame to the initially aligned axis of the dq0 reference frame.

Data Types: single | double

Output

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Direct-axis and quadrature-axis components and the zero component of the system in the rotating reference frame.

Data Types: single | double

Parameters

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Align the a-phase vector of the abc reference frame to the d- or q-axis of the rotating 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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