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A $30 MVA$, $3$-phase, $50 Hz$, $13.8 kV$, star-connected synchronous generator has positive, negative and zero sequence reactances, $15$%, $15$% and $5$% respectively. A reactance $(X_{n})$ is connected between the neutral of the generator and ground. A double line to ground fault takes place involving phases $‘b’$ and $‘c’$, with a fault impedance of $j0.1 p.u$. The value of $X_{n}$ (in p.u.) that will limit the positive sequence generator current to $4270$ A is ________.
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