Equivalent circuit and phasor of synchronous generator

The equivalent circuit of synchronous generator in show in fig.(a) .it is redrawn in fig (b) by taking Xs = XAR + Xa

Lagging Power Factor cos Φ :

Fig shows the phasor diagram for lagging load. the power factor is cosΦ lagging. In this diagram the terminal voltage V is taken as reference phasor along OA such that OA = V. For lagging  power factor cos Φ the direction of the armature current Ia lags behind V by angle f along OB , where OB = Ia. the voltage drop in the armature resistance is Ia Ra .  It is represented by phasor AC . 

The voltage drop in synchronous reactance is Ia Xs . ti is represented by CD. it leads the current Ia by  90 and , therefore CD drawn in a direction perpendicular to OB the total voltage drop in the synchronous impedance is the phasor sum Ia Ra and Ia Xs . ti is represented by AD. the phasor OD represents Ea.  

Unity Power Factor :

The phasor diagram for unity power factor is shown in figure.

Leading Power Factor cos Φ :

The phasor diagram for leading power factor is shown in figure.

the angle between Ea and V is called the power angle or torque angle of the machine.It varies with load and is a measure of air gap power developed in the machine.