Inverse Park Transform
Coordinate transformation from the dq0 coordinate system to abc.
Description
The Inverse Park Transform unit converts longitudinal, transverse and zero components in a rotating coordinate system in the time domain into three-phase system components in the coordinate system . The block can store active and reactive powers in the rotating coordinate system, realising an invariant version of the Park Transform. For a balanced system, the zero component is zero.
The unit can be configured to align the axis of the three-phase system with the or axes of the rotating coordinate system at time . The figures show the direction of the magnetic axes of the stator windings in the 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 Inverse Park Transform block implements a transformation to align the phase of to the axis as
where
-
, and are components of the three-phase system in the coordinate system ;
-
and - components of the two-coordinate system in the rotating coordinate system;
-
- zero component of the two-axis system in the stationary coordinate system.
For invariant power equalisation of the phase and along the axis, the unit implements the transformation using the following equation:
To align the phase of to the axis, the block implements a transformation using the following equation:
For invariant power equalisation of the phase and along the axis, the block implements the transformation using the following equation:
Ports
Input
dq0 - a vector that contains values in the dq0 coordinate system
vector
Longitudinal, transverse and zero components in a rotating 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.
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 .
Power Invariant - power invariant transformation
off (by default) | on
Option to save active and reactive power in the coordinate system .