Transformation SRF->RRF

Purpose

Transform vector from stationary to rotating reference frame

Library

Control / Transformations

Description

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

\[\begin{split}\begin{bmatrix} x_\mathrm{d} \\ x_\mathrm{q} \end{bmatrix} = \begin{bmatrix} \cos \theta & \sin \theta\\ -\sin \theta & \cos \theta \end{bmatrix} \cdot \begin{bmatrix} x_\alpha \\ x_\beta \end{bmatrix}\end{split}\]

Note

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