2.1.1 Clarke Transformation

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

The transform is expressed by the following equations:

${\displaystyle i_a+i_b+i_c=0}$

${\displaystyle i_{\alpha }=i_a}$

${\displaystyle i_{\beta }=\frac{1}{\sqrt{3}}(i_b-i_c)}$

Where:

i_α, i_b and i_c are the three-phase currents in abc reference frame, i_α and i_β are the two-phase orthogonal currents in the αβ reference frame.