Why alternator works only in lagging power factor? not leading powerfactor?



Answer:
When the load is inductive, e.g., an induction motor, the current lags the applied voltage, and the power factor is said to be a lagging power factor. When the load is capacitive, e.g., a synchronous motor or a capacitive network, the current leads the applied voltage, and the power factor is said to be a leading power factor. Therefore, since alterantor is an inducion motor it works in lagging power factor.
See Power Factor, etc. in the link for a clue to your question. It is a complex issue depending on the specific motor/generator and excitation.
Alternator is a inductive motor.
v(t) = -Ldi/dt

for AC current
i(t) = Ipsin(2pift)
di/dt = 2pif*Ip*cos(2pift)
v(t) = 2pifLIpcos(2pift)

where Ip is the amplitude of the current

The power factor is real power / apparent power = P/S
The apparent power S is made up of the reactive power Q and the real power P
S^2 = P^2 + Q^2
If phi is the phase angle between the current and voltage, then the power factor is magnitude(cos(phi))

and
P = S*magnitude(cos(phi))

Thus if the current lags the voltage the sign of phi is negative and we say the power factor is lagging.

The power factor can be corrected by adding a capacitive bank.

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