Question $2$

$1-$phase Transformer Differential protection

A $1ph1\mathrm{.}2$MVA,$40kV-8kV$ transformer is equipped with a differential protection scheme. The differential relay is sourced from $25$:$5$A CT on the HV side and a $100$:$5$A CT on the LV side. The relay taps are set at $2$ A for the HV CT and $2\mathrm{.}5$ A for the LV CT$.$ The relay slope is $40\%,$ with a minimum pickup current of $0\mathrm{.}3$ A $.$

Draw a SLD diagram showing the differential protection scheme, relay elements and currents.

$2$

$($a$)$ If the transformer magnetization current is $6\%$FLA at $0\mathrm{.}5$ pf $,$ calculate the relay currents at no$-$load. Plot this operating point on the relay characteristic graph. What is the $\%$ slope for this condition? Will the relay trip?

$($a$)$ If the transformer magnetization current is $6\%$ FLA at $0\mathrm{.}5$ pf $,$ calculate the relay currents at no$-$load. Plot this operating point on the relay characteristic graph. What is the $\%$ slope for this condition? Will the relay trip?

$($b$)$ Calculate the relay currents when the transformer is supplying full$-$load at upf. Show the operating point on the graph of part $($a$).$ What is the $\%$slope for this condition? Will the relay trip?

$($c$)$ Calculate the relay currents for an external fault of $400$ A on the LV side. Ignore magnetizing current. Show the operating point on the graph of part $($a$).$ What is the $\%$slope for this condition? Will the relay trip?

$($d$)$ Calculate the relay currents for an internal fault that results in $\frac{20}{{?}_{-}}45A$ on the HV side and $\frac{40}{{?}_0}A$ on the LV side. Ignore magnetizing current. Show the operating point on the graph of part $($a$).$ What is the $\%$slope for this condition? Will the relay trip?