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 \([y_\mathrm{a}\; y_\mathrm{b}\; y_\mathrm{c}]\). The first input of the block is the vector \([x_\mathrm{d}\; x_\mathrm{q}]\). The second input is the rotation angle \(\varphi\) of the rotating reference frame. \(\varphi\) is given in radians.

\[\begin{split}\left[\!\! \begin{array}{ccc} y_\mathrm{a} \\ [0.2cm] y_\mathrm{b} \\ [0.2cm] y_\mathrm{c} \end{array} \!\!\right] = \left[\!\! \begin{array}{ccc} \cos \varphi & -\sin \varphi \\ [0.2cm] \cos \left(\varphi-120^\circ\right) & -\sin \left(\varphi-120^\circ\right) \\ [0.2cm] \cos \left(\varphi +120^\circ\right) & -\sin \left(\varphi +120^\circ\right) \end{array} \!\!\right] \cdot \left[\!\! \begin{array}{c} x_\mathrm{d} \\ [0.2cm] x_\mathrm{q} \end{array} \!\!\right]\end{split}\]

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