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Qhat is the reason for reduction in speed with increase in alternator terminal load? If that alternator is in parallel with some other alternators, what is the reason for this?

You haven't provided enough details about the event for us to comment on what happened specifically.

Suffice it to say that a single synchronous generator, more properly called an alternator as you have noted, when being operated in parallel with other synchronous generators (alternators) cannot have a speed/frequency different from the other alternators. (As has been noted before on control.com, they don't call it "synchronism" for nothing.) The prime mover of an alternator being operated in parallel with other alternators, depending on the type and "coupling" between the prime mover and alternator, might have it's speed vary as load changes but the alternator speed should not. We're talking now about frequency/speed differences which exist for appreciable periods of time, seconds or even minutes, not "instantaneous" changes which might exist for a few cycles.

It's the nature of synchronous machines that when operated in parallel with other synchronous machines that the frequency of all the machines will be the same. (It's that synchronism thing!)

But we don't have remotely enough information to make a proper response to a particular event.