Question $2$

For the overcurrent protection scheme shown in Fig. $2,$ the CT ratio is $500/1$ A$.$ The phase overcurrent relays pickup current is $1\mathrm{.}2$ A and that of the earth fault relay is $0\mathrm{.}4$ A $.$ The time dial $T{d}_d$ of all relays is $0\mathrm{.}2.$ Calculate the relays operating time for the following faults:

a$-$ Three$-$phase fault with $I_F=8kA.$

b$-$ Single line to ground fault at phase a with $I_F=7\mathrm{.}5kA.$

c$-$ Double$-$line fault between phases a and $b{I}_F=6kA.$

Use NI curves for all relays and the IEC standard inverse$-$time characteristics in problem $1.$