Coordinate transformation from the coordinate system αβ0 to dq0.
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.
Axis and axis are initially aligned.
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.