In the case of the unloaded generator, the air gap flux is equal to the rotor flux. On a loaded generator, the air gap flux is equal to the vector sum of the rotor and armature reaction flux. When the generator is supplying lagging current, the armature reaction flux detracts from the rotor flux, reducing the voltage induced in the stator windings and hence the terminal voltage. Leading current produces an armature reaction flux that is additive to the rotor flux, boosting the induced stator voltage and the generator terminal voltage.
When the generator is under load, the stator current will lead or lag Eq by angle B, depending on whether the load is capacitive or inductive, as shown in Figure below. Note that angle B is not the power factor angle. The power factor angle is measured between the current and the generator terminal voltage; under load, Eq is an internal generator voltage.
Load current produces a second flux within the generator. This flux, sometimes referred to as the armature reaction flux, is formed in the air gap by the vector summation of the alternating flux in each stator phase winding. The intuitive conclusion would be that the summation of the phase flux would be zero, because the balanced load currents that produce the individual phase flux sum to zero. This conclusion would be correct if the phase windings were physically aligned with each other. The individual phase flux would then be displaced by 120° and sum to zero just as the currents do. However, since the stator windings are physically displaced by 120° around the stator, the individual phase flux are shifted and produce a resultant flux that is in phase with the “A” phase stator current and lags the rotor flux by 90° + B, as shown in Figure.
The air gap flux can be represented by flux components projected on the d- and q-axes, as shown in Figure below. These components are aligned with the machine’s two magnetic circuits to facilitate analysis. Because the two axes are at right angles to one another, there is no magnetic interaction between them and the analysis of each axis can be carried out independently of the other.
Generator behavior is predicted by determining the response of each axis individually, then combining the d and q components to define the air gap response. The variations of the air gap flux determine the transient characteristic of the short-circuit current. Generator loading determines magnitude of the air gap flux and angle Ø in Figure below; hence, it determines the initial magnitude of the flux component in each axis.
Because of flux inherent characteristics (e=-dØ/dt) the flux linkages between the various windings cannot change instantaneously. When a fault occurs, the initial current is determined by the flux linkages “stamped” into each axis by the prefault load condition.