Assume the generator is loaded and operating in a steady state. If the peak-to-peak or rms value of the stator current changes in magnitude then its corresponding change in magneto-motive force (mmf) will try to change the air-gap flux by armature reaction. Relatively slow changes will allow the change in flux to penetrate into the rotor. When this occurs an emf is induced in the field winding. This emf drives a transient current around a circuit consisting of the field winding itself and the exciter that is supplying the winding. The induction of current is by transformer action. An increase in stator current will be matched by an increase in field current during the transient state. A voltage drop will occur in the machine due to the armature reaction and the reduction in air-gap flux. Reactance is associated with this type of armature reaction.
When the rotor poles are coincident with the stator coils axis the armature reaction is a maximum and the reactance is called the direct axis transient reactance X’d .
When the rotor poles are coincident with the stator coils axis the armature reaction is a maximum and the reactance is called the direct axis transient reactance X’d .
The situation is different when the rotor poles are at right angles to the stator coils. There is no induction in the field circuit and the reluctance is high, being almost the same as for the steady state condition. In this situation the corresponding quadrature axis transient reactance X’q approximately equals the reactance Xq . Cylindrical rotors of two-pole high speed generators have a nearly uniform rotor diameter and almost constant air gap all around the periphery. Hence the reactance X’q is almost equal to X’d .