SYNCHRONOUS GENERATORS AND MOTORS 633.2.2 Transient state armature reaction
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. Reactances are
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 reactanceX′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 reactanceX′qapproximately
equals the reactanceXq. 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 reactanceX′qis almost
equal toX′d.
3.2.3 Sub-transient state armature reaction
Again assume that the generator is loaded and operating in a steady state. In this situation the
magnitude of the stator current is allowed to change rapidly, as in the case of a short circuit
in the stator circuit. The additional flux produced by the stator winding will try to penetrate the
surface of the rotor poles. Most oil industry generators are provided with damper bars to reduce
the excursions in rotor speed during major disturbances. The bars are made of copper or copper
alloy and placed longitudinally in the face of the rotor poles. They function in a manner similar
to a squirrel cage induction motor when there is a transient change in rotor speed relative to the
synchronous speed. As soon as the additional flux passes through the pole faces it will induce cur-
rents in the damper bars and the solid pole tips, by the process of transformer induction. These
induced currents will set up flux in opposition in order to maintain constant flux linkages with
the stator.
During this transient condition, or more appropriately called a sub-transient condition, the
additional flux is forced to occupy a region consisting of air and the surface of the rotor poles. This
is a high reluctance condition which gives rise to reactances of low values.
Some generators have the damper bars connected to a ring at either end of the pole structure,
which provides some damping action from the quadrature axis. This provides a set of short-circuited
coils in the quadrature axis, which are air cored and able to repel the flux that is attempting to enter
their region.
By the same reasoning as for the ‘transient’ reactances so the ‘sub-transient’ reactances are
derived, and are called the ‘direct axis sub-transient reactanceX′′d’ and the ‘quadrature axis sub-
transient reactanceXq′′’.