## 3-2 *dq* Winding Representation

We studied in the previous chapter that the stator and the rotor flux linkages and depend on the rotor angle *θ*_{m} because the mutual inductances between the stator and the rotor windings are position dependent. The main reason for the *d*- and *q*-axis analysis in machines like the induction machines is to control them properly, for example, using vector control principles. In most textbooks, this analysis is discussed as a mathematical transformation called the Park's transformation. In this chapter, we will take a physical approach to this transformation, which is much easier to visualize and arrive at identical results.

### 3-2-1 Stator *dq* Winding Representation

In Fig. 3-1a at time *t*, phase currents *i*_{a} (*t*), *i*_{b} (*t*), and *i*_{c} (*t*) are represented by a stator current space vector