Engee documentation

Clarke to Park Angle Transform

Coordinate transformation from the coordinate system αβ0 to dq0.

clarke to park angle transform

Description

The Clarke to Park Angle Transform unit converts , and zero components in a stationary coordinate system to longitudinal, transverse and zero components in a rotating coordinate system. For balanced three-phase systems, the zero components are zero.

You can set the unit to align the axis of the three-phase system with the axes or of the rotating coordinate system at time . The figures show the direction of the magnetic axes of the stator windings in the three-phase coordinate system , the stationary coordinate system and in the rotating coordinate system , where:

  • The axis and the axis are initially aligned.

park to clarke angle transform 1

  • Axis and axis are initially aligned.

park to clarke angle transform 2

In both cases the angle , where

  • - the angle between the axes and for alignment with the axis or the angle between the axes and for alignment with the axis ;

  • - rotation speed of the coordinate system - ;

  • - time in seconds since the initial alignment.

Equations

The Clarke to Park Angle Transform block implements a transformation to align the phase of to the axis as

where

  • and are the components of the two-phase system along the axes and in the stationary coordinate system;

  • - zero component;

  • and - longitudinal and transverse components of the two-coordinate system in the rotating coordinate system.

To align the phase to the axis, the unit implements the transformation using the following equation:

Ports

Input

αβ0 is a vector that contains values in the αβ0 coordinate system
vector

Axis component , axis component and zero component of a two-phase system in a stationary coordinate system.

Data types: Float32, Float64.

θabc - rotation angle, rad
scalar

Angular position of the rotating coordinate system. The value of this parameter is equal to the polar distance from the phase vector а in the coordinate system to the initially aligned axis of the coordinate system .

Data types: Float32, Float64.

Output

dq0 - vector, which contains values in dq0 coordinate system
vector

Longitudinal, transverse and zero components in a rotating coordinate system .

Data types: Float32, Float64.

Parameters

Phase-a axis alignment - axis along which the dq0 coordinate system will be aligned
Q-axis (by default) | D-axis

Align the phase of the coordinate system to the axis or to the axis of the rotating coordinate system .

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.

Additional options

C code generation: Yes