Question $3$:

A single$-$phase transformer is rated at $\frac{69}{110}kV,20$MVA. It is to be protected by a differential relay, with input taps of $3\mathrm{.}0,4\mathrm{.}0,4\mathrm{.}5,4\mathrm{.}8,4\mathrm{.}9,5\mathrm{.}0,5\mathrm{.}1,5\mathrm{.}2,5\mathrm{.}5$ A secondary$.$ The transformer has an under load tap changer $($ULTC$)$ with a turns ratio of $+-7\mathrm{.}5\%.$ The CTs are of the class $15$ C$400.$

a$)$ Specify the CTs ratio and the ratio mismatch.

b$)$ Set the pickup setting and percentage differential slope for the relay. The available slopes are $10,20$ and $40\%.$

c$)$ What is the level of fault current, for an unloaded transformer, for which the differential relay will not operate?