For proper working of synchronous motor
(i.e. in order to convert electrical energy into mechanical energy,) it is necessary to create magnetic flux between the air gap of rotor and stator of synchronous motor. Hence magnetizing current is required to set up magnetic flux in the air gap of motor. In case of synchronous motor, magnetic flux is provided by dc excitation. Direct current is fed to the field winding of rotor to produce the required magnetic flux. This magnetizing current lags the supply voltage by
.
Let us consider a synchronous motor having a constant applied voltage V and drives a constant mechanical load. Hence synchronous motor demands a constant air gap flux. The required air gap flux is set up by both of the sources (i.e. AC source of the stator windings and DC source of rotor winding) so that the required flux maintain in a synchronous motor.
One important feature of synchronous motor is that by varying the field current (DC excitation), synchronous motor can be operated at any power factor. When we change the field excitation, power factor of the motor varies. Moreover, armature current also varies when the field current changes. Let consider a few cases of varying field excitation and its effect on the armature current and power factor of synchronous motor.
Effect of Varying Field Excitation on Power Factor :
Normal Excitation:
If the rotor field current (DC excitation) is sufficient to produce the required air gap flux demand by the supply voltage V, the motor is said to be normally excited. In that case, the magnetizing current or lagging reactive power drawn from the AC source is zero and motor operates at unity power factor.
Under Excitation:
The motor is said to be under excited if the rotor field current is not just sufficient to produce the required air gap flux demand by the supply voltage V. In that case, the magnetizing current or lagging reactive power is drawn from the AC source to produce the required flux. Hence motor operates at lagging power factor in under excited condition. This process is called magnetization.
Over Excitation:
When the rotor field current (DC excitation) produces more air gap flux as demand by the supply voltage V, it is said to be over excited synchronous motor. In that case, armature winding draws leading current (leading voltage by 90) from the AC source and neutralize the extra flux by setting flux in the opposite direction. This process is called demagnetization. Since the current drawn leads the supply voltage by, hence power factor of the motor will be leading in over excited condition.
Effect of Varying Field Excitation on the Armature Current:
Let understand the effect of varying field excitation on the armature current by the following given graph. This graph is known as V curve of synchronous motor. The graph is plotted between the armature (stator) current and field current at different constant loads.
Armature Current at Different Constant Loads:
Let analyze the behavior of armature current at different constant loads. When the motor is at no load condition, armature current is minimum (lowest V- Curve). At half load, armature current increases to some extent whereas armature current increases further during full load condition. In simple words, armature current is minimum at no load and it further increases during half load and full load conditions.
Why Armature Current increases during under excited and over excited condition?
From the above V- curve of synchronous motor, we can say that a normally excited synchronous motor operates at unity power factor. During such condition, the armature current is minimum (i.e. at unity Power factor). During under excited and over excited state of motor, the power factor
decreases (either leading or lagging power factor). Since motor drives a constant mechanical load due to which output power 
is also constant. Hence armature current increases in both under excited and over excited conditions (can be seen in the above graph).
Inverted V graph:
Inverted v graph shows us the relation between the field current and power factor in synchronous motor.
It can be seen from the above inverted V-curve graph that power factor of the motor is maximum (unity PF) in normal excited condition. When motor is under excited or over excited, power factor of the motor decreases in both (leading and lagging) condition. This kind of behavior give us inverted V- curve shown above.
Conclusion:
Synchronous motor can be operated at any power factor. When the field current (excitation) of motor varies, power factor and armature current of motor also varies. V- curve is plotted between field current (If) and armature current whereas Inverted V- curve shows the relation of field current and power factor.