SOLUTION

In a synchronous motor, the armature current has large values for both low and high excitation.

The synchronous motor always adjusts its cosφ i.e., power factor nature so that Power component I_a cosφ remains constant when excitation of the motor is changed keeping the load constant. This is the reason why a synchronous motor reacts by changing its power factor to variable excitation conditions.

Under excitation condition: When the excitation is adjusted in such a way that the magnitude of induced emf is less than the applied voltage (E_b < V) the excitation is called under excitation.

Due to this, E_R increases in magnitude. This means for constant Synchronous Impedance (Z_s), the current drawn by the motor increases. But E_R, the phase shift in such a way that, phasor I_a, also shifts (as E_R ^∧ I_a = θ) to keep the Power component of I_a i.e I_a cosφ components constant. So in under excited conditions, the current drawn by the motor increases. The power factor cosφ decreases and becomes more and more lagging in nature.

Over excitation condition: The excitation to the field winding for which the induced emf becomes greater than the applied voltage (E_b > V) is called overexcitation.

Due to the increased magnitude of E_b, E_R also increases in magnitude. But the phase of E_R also changes. Now (as E_R ^∧ I_a = θ) is constant, hence I_a also changes its phase, So φ changes. The I_a increases to keep I_a cosφ constant. The phase of E_R changes so that I_a becomes leading with respect to V_ph in over-excited conditions. So power factor of the motor becomes leading in nature. So overexcited synchronous motor works on leading power factor. So power factor decreases as over excitation increases but it becomes more and more leading in nature.

Two important points stand out clearly from the above discussion :

(i) The magnitude of armature current varies with excitation. The current has a large value both for low and high values of excitation (though it is lagging for low excitation and leading for higher excitation). In between, it has a minimum value corresponding to a certain excitation.

(ii) For the same input, armature current varies over a wide range and so causes the power factor also to vary accordingly. When over-excited, motor runs with leading p.f. and with lagging p.f. when under-excited. In between, the p.f. is unity.

1. When the motor is under excited, the armature current and power factor is lagging. In this case, the motor behaves like an inductive load.
2. When the motor is normally excited, the power factor is unity. In this case, the armature current is minimum and is in phase with the terminal voltage.
3. When the motor is over-excited, the power factor is leading. In this case, the motor behaves like a capacitive load.