The plug setting multiplier (PSM) of an inverse time relay is defined as the ratio of the fault current in the relay to its pick-up current.

In the given scenario, the CT ratio is 500/5, and the relay setting is 50%. Therefore, the pick-up current of the relay is calculated as 5 x (50/100) = 2.5 A.

The fault current given is 2000 A, which is the primary fault current. To calculate the secondary fault current, we use the CT ratio as follows:

Secondary fault current = Primary fault current / CT ratio = 2000 A / (500/5) = 20 A

Using the above values, we can calculate the PSM of the relay as follows:

PSM = Secondary fault current / Pick-up current = 20 A / 2.5 A = 8

Therefore, the plug setting multiplier of the relay is 8.