Reverse power flow into a generator can occur during synchronization if the generator is spinning too slowly, or the voltage phase angle is lagging relative to the power system. If the generator is spinning too slowly, power from the system is used by the generator to increase its' speed. If the phase angle is lagging, an initial spike of power will flow into the generator to force it into sync with the system.
Typically generator's will match system frequency very closesly, and force the phase angle to leading slightly between the generator and the system. When synchronized, an extra bump of power will flow out while the generator is torqued into phase with the system. This will avoid tripping any reverse power devices.
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Reverse power relays are often used in generator protection to trip breakers if generators are "sucking in" power (since this shouldn't occur, it is a BAD thing when it does). I'm not sure there is a use for reverse power relays beyond this; directional relays looking in a reverse direction are often used in pilotting schemes, though (not "reverse power").
Not necessarily. Reverse power simply means that the load is providing power to the generator, instead of the reverse. Its not a good place to be, because you waste the power needed to turn the generator, and you could damage it as well.
the power leads were wired wrong
by reverse breakdown voltage & forward current capacity
A reverse current relay senses Power in (uses both voltage and current, and looks at the phase angle between these), and operates if power is flowing in the reverse direction, and the current is above a set point. An overcurrent relay looks at only current, and operates if it is above a set point regardless of power flow direction. Reverse current relays are often referred to as reverse power relays.