Transformation 3ph->RRF

Purpose

Transform 3-phase signal to rotating reference frame

Library

Control / Transformations

Description

This block transforms a three-phase signal \([x_\mathrm{a}\; x_\mathrm{b}\; x_\mathrm{c}]\) into a two-dimensional vector \([x_\mathrm{d}\; x_\mathrm{q}]\) in a rotating reference frame. The first input is the three-phase signal. The second input is the rotation angle \(\theta\) of the rotating reference frame. \(\theta\) is given in radians.

\[\begin{split}\left[\!\! \begin{array}{c} x_\mathrm{d} \\[0.2cm] x_\mathrm{q} \end{array} \! \right] = \frac{2}{3} \left[\!\! \begin{array}{ccc} \cos \theta & \cos \left(\theta-\dfrac{2\pi}{3} \right) & \cos \left(\theta+\dfrac{2\pi}{3} \right) \\[0.2cm] -\sin \theta & -\sin \left(\theta-\dfrac{2\pi}{3} \right) & -\sin \left(\theta+\dfrac{2\pi}{3} \right) \end{array} \! \right]\!\! \cdot \left[\!\! \begin{array}{ccc} x_\mathrm{a} \\[0.2cm] x_\mathrm{b} \\[0.2cm] x_\mathrm{c} \end{array} \! \!\right]\end{split}\]

Any zero-sequence component in the three-phase signals is discarded.

Note

The rotating reference frame transfomation follows the axis alignment and rotation direction conventions presented in Conventions & Definitions.