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

The correct option is offset Mho relay.

An alternator (synchronous generator) requires a continuous direct current (DC) field excitation to generate a magnetic field and remain synchronized with the electrical grid. If the excitation is lost (due to a field winding short circuit, field breaker opening, or exciter failure), the alternator begins to run as an induction generator at a supersynchronous speed, drawing reactive power from the grid rather than supplying it. This can lead to overheating of the rotor and stator windings and system instability.

To protect the alternator against this condition, we monitor the impedance at the generator terminals. When loss of excitation occurs, the equivalent impedance seen at the generator terminals drops and moves into the fourth quadrant of the R-X complex impedance plane. An offset Mho relay (which is a distance relay with its operating characteristic circle shifted or offset on the impedance plane) is specifically designed and commonly used to detect this impedance trajectory. The offset characteristic ensures that it operates reliably for loss of excitation without falsely tripping during normal transient swings or external faults.

Let us briefly look at the other options to understand why they are not correct for this specific purpose:
1. Differential relay: Used primarily for detecting internal phase-to-phase and phase-to-earth faults within the alternator stator windings.
2. Buchholz relay: A gas-actuated relay used for the protection of oil-immersed transformers against internal faults.
3. Overcurrent relay: Used to protect against overloads and external short circuits, but cannot effectively detect the specific reactive power draw and impedance changes associated with a loss of excitation.