This is the most important transformation in the FOC. In fact, this projection modifies a 2-phase orthogonal system (α, β) in the (d, q) rotating reference frame. Considering the d axis aligned with the rotor flux, Figure 3-5 shows the relationship for the current vector from the two reference frame.

Figure 3-5 Stator Current Space Vector in the d,q Rotating Reference Frame

The flux and torque components of the current vector are determined by Equation 19.

where

• θ is the rotor flux position

These components depend on the current vector (α, β) components and on the rotor flux position; if the right rotor flux position is known then, by this projection, the d,q component becomes a constant. Two phase currents now turn into dc quantity (time-invariant). At this point the torque control becomes easier where constant i_sd (flux component) and i_sq (torque component) current components controlled independently.