Class Project about Bus Protection

$10\mathrm{.}25$ Consider a protected bus that terminates four lines, as shown in Figure $10\mathrm{.}51.$ Assume that the linear couplers have the standard $x_m=5m$ and a three$-$phase fault externally located on line $3$ causes the fault currents shown in Figure $10\mathrm{.}51.$ Note that the infeed current on line $3$ to the fault is $-$j $10$ kA $.($a$)$ Determine $V_o.($b$)$ Let the fault be moved to an internal location on the protected bus between lines $3$ and $4.$ Find $V_o$ and discuss what happens. $($c$)$ By moving the external fault from line $3$ to a corresponding point on $($i$)$ line $2$ and $($ii$)$ line $4,$ determine $V_o$ in each case.

FIGURE $10\mathrm{.}5$ I

Problem $10\mathrm{.}25-$Bus differential protection using linear couplers