d and q axis concept and need of dq0

d-axis and q-axis

In a synchronous machine two axes are fixed on the rotor and rotate with it:

• Direct axis (d-axis): along the centre line of the rotor field poles (the axis of the field mmf). The air gap is smallest here, so reluctance is low and reactance $X_d$ is high.
• Quadrature axis (q-axis): 90° electrical ahead of the d-axis, i.e. midway between the poles. The air gap is large in a salient-pole machine, so $X_q < X_d$.

             q-axis
               ^
               |
     S ---- [ rotor ] ---- N  ---> d-axis
               |        (field axis)

The armature current and mmf are resolved into $I_d$ along the d-axis and $I_q$ along the q-axis (Blondel's two-reaction theory), each acting on its own reactance.

Need for the dq0 frame

1. In the phase (abc) frame, the self and mutual inductances of the stator windings vary with rotor position $\theta$ (especially in salient-pole machines), giving differential equations with time-varying coefficients.
2. Park's (dq0) transformation refers stator quantities to the rotor axes; the inductances become constant ($L_d$, $L_q$, $L_0$).
3. In steady state, sinusoidal ac quantities become dc quantities, which makes analysis, simulation and control (e.g. vector control, AVR, stability studies) much simpler.
4. The zero-sequence component (0) handles unbalanced conditions; it is zero for balanced operation.