Reactance relay used for the small transmission line. mho relay used in the long transmission line. impedance is non-directional and used in medium transmission lines. reactance relay is non directional and used in short transmission lines.

Relays are protective devices used in power systems to detect abnormal conditions, such as faults, and initiate appropriate actions, such as tripping circuit breakers to isolate the faulty section. There are various types of relays used for different applications based on their operating principles and characteristics.

One type of relay commonly used on short transmission lines is the Reactance relay. Here is a detailed explanation of why Reactance relay is the correct answer:

Explanation:
- Reactance relay is designed to respond to changes in the reactance of the system, which is mainly affected by the distance to the fault location.
- Short transmission lines have relatively low impedance and reactance values compared to long transmission lines. Therefore, reactance relays are suitable for protecting short transmission lines.
- Reactance relays are based on the principle that the impedance of a transmission line varies with the distance from the relay location to the fault location.
- As the fault occurs closer to the relay location, the impedance decreases, and the reactance relay detects this change and initiates the protective action.
- Reactance relays are directional relays, meaning they operate only in one direction (towards the source) to protect the line section between the relay location and the source.
- The reactance relay measures the phasor difference between the voltage and current at the relay location and compares it with a pre-set threshold. If the difference exceeds the threshold, indicating a fault, the relay operates and initiates the tripping action.
- Reactance relays are generally considered reliable and cost-effective for protecting short transmission lines as they are designed to operate based on the reactance rather than the impedance of the system.
- Other types of relays, such as mho relay and impedance relay, are commonly used for longer transmission lines where the reactance component is not dominant.
- Mho relay operates based on the impedance seen by the relay location, which includes both resistance and reactance components. It is suitable for long transmission lines where the reactance component is significant.
- Impedance relay is a combination of both reactance and mho relays, providing a compromise between the two. It is often used for medium-length transmission lines.
- Therefore, for short transmission lines, the correct relay type is the Reactance relay.