Transformation RRF->3ph

Purpose

Transform vector in rotating reference frame into 3-phase signal

Library

Control / Transformations

Description

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

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

The resulting three-phase signal does not have any zero-sequence component.

Note

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