The most commonly used relay, for the protection of an alternator against loss of excitation, is

The correct answer is offset Mho relay.

An alternator is a synchronous machine, and its excitation (field current) is crucial for maintaining synchronism and generating reactive power. When an alternator loses its excitation (due to a field failure, open circuit, or short circuit in the field winding), it begins to behave as an induction generator. In doing so, it runs at a speed slightly above synchronous speed and draws a large amount of reactive power from the power grid instead of supplying it. This causes high stator currents, overheating, and potential system instability.

Under loss of excitation conditions, the terminal impedance of the alternator (seen from its terminals looking into the machine) decreases and moves into the second or third quadrant of the R-X complex impedance plane. Specifically, the impedance trajectory enters a region that can be accurately enveloped by an offset Mho characteristic.

An offset Mho relay is a distance relay whose operating circular characteristic on the R-X diagram is shifted (offset) from the origin. This offset allows it to cover the specific impedance trajectory that occurs during loss of excitation. Because of this specialized characteristic, the offset Mho relay is the most commonly used and reliable protection scheme against loss of excitation in alternators.

Let's briefly examine why the other options are not appropriate for this specific fault:
- Differential relay: Primarily used to protect against internal phase-to-phase and phase-to-ground stator winding faults, not loss of excitation.
- Buchholz relay: A gas-actuated relay used exclusively for the protection of oil-immersed transformers against internal faults.
- Over current relay: Used for overcurrent and short-circuit protection, but it cannot reliably detect a loss of excitation because the current characteristics during field loss do not always look like a simple overcurrent condition, and it lacks the directional and impedance-based selectivity needed.