2.1.4 Inverse Clarke Transformation

The Inverse Clarke Transformation transforms electrical signals from the stationary two axis orthogonal reference frame (αβ) to the three axis reference frame (abc) as shown in the following figure.

The transform is expressed by the following equations:

${\displaystyle U_a=U_{\alpha }}$

${\displaystyle U_b=-\frac{1}{2}{U}_{\alpha }+\frac{\sqrt{3}}{2}{U}_{\beta }}$

${\displaystyle U_c=-\frac{1}{2}{U}_{\alpha }-\frac{\sqrt{3}}{2}{U}_{\beta }}$

Where:

U_α and U_β are the two-phase orthogonal voltages in the αβ reference frame, U_a, U_b, and U_c are the three-phase voltages in the abc reference frame.