Question $1$

Three overcurrent relays R$1,$ R$2$ and R$3$ are connected as shown in Fig. $1.$

$R1$:$CTR=\frac{500}{5}A,I\frac{p}{u}=550A,Td=0\mathrm{.}1.$

R$2$: $CTR=\frac{800}{5}A,I\frac{p}{u}=900A.$

R$3$: $CTR=\frac{800}{5}A,I\frac{p}{u}=900A.$

A fault at F results in a fault current of $5000$ A $.$

a$-$ Find the Td of R$2$ and R$3$ to give time margin of $0\mathrm{.}3$ s between relays. Use VI curves for both relays.

b$-$ Find the operating time of relay R$3$ with a fault current of $10$ kA $.$

$0$ A

IEC standard inverse$-$time characteristics are depicted by:

$t=\frac{**T_d}{(\frac{I_f}{I_{\frac{P}{U}}}{)}^{-1}}$

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