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 \([y_\mathrm{d}\; y_\mathrm{q}]\) in a rotating reference frame. The first input is the three-phase signal. The second input is the rotation angle \(\varphi\) of the rotating reference frame. \(\varphi\) is given in radians.

\[\begin{split}\left[\!\! \begin{array}{c} y_\mathrm{d} \\ [0.2cm] y_\mathrm{q} \end{array} \! \right] = \frac{2}{3} \left[\!\! \begin{array}{ccc} \cos \varphi & -\sin \varphi \\ [0.2cm] \cos \left(\varphi-120^\circ\right) & -\sin \left(\varphi-120^\circ\right) \\ [0.2cm] \cos \left(\varphi +120^\circ\right) & -\sin \left(\varphi +120^\circ\right) \end{array} \! \right]^\mathrm{T}\!\! \cdot \left[\!\! \begin{array}{ccc} x_\mathrm{a} \\ [0.2cm] x_\mathrm{b} \\ [0.2cm] x_\mathrm{c} \end{array} \! \!\right]\end{split}\]

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