Transformation RRF->SRF

Purpose

Transform vector from rotating to stationary reference frame

Library

Control / Transformations

Description

This block transforms a two-dimensional vector \([x_\mathrm{d}\; x_\mathrm{q}]\) from a rotating reference frame into a vector \([x_\alpha\; x_\beta]\) in the stationary reference frame. The first input of the block is the vector \([x_\mathrm{d}\; x_\mathrm{q}]\). The second input is the angle \(\theta\) between the rotating and the stationary frame. \(\theta\) is given in radians.

\[\begin{split}\left[\!\! \begin{array}{c} x_\alpha \\[0.2cm] x_\beta \end{array} \!\!\right] = \left[ \begin{array}{cc} \cos \theta & -\sin \theta\\[0.2cm] \sin \theta & \cos \theta \end{array} \right] \cdot \left[\!\! \begin{array}{c} x_\mathrm{d} \\[0.2cm] x_\mathrm{q} \end{array} \!\!\right]\end{split}\]

Note

This transfomation follows the axis alignment and rotation direction conventions presented in Conventions & Definitions.