Clarke to Park Angle Transform
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:
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The axis and the axis are initially aligned.
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Axis and axis are initially aligned.
In both cases the angle , where
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- the angle between the axes and for alignment with the axis or the angle between the axes and for alignment with the axis ;
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- rotation speed of the coordinate system - ;
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- 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
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and are the components of the two-phase system along the axes and in the stationary coordinate system;
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- zero component;
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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 in the coordinate system to the initially aligned axis of the coordinate system .
Data types: Float32, Float64.