A 30 MVA, 3-phase, 50Hz, 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 __________.

A sustained three phase fault occurs in the power system shown in the figure. The current and voltage phasors during the fault (on a common reference), after the natural transients have died down, are also shown. Where is the fault located?

A three phase, $$100$$ $$MVA,$$ $$25$$ $$kV$$ generator has solidly grounded neutral. The positive, negative, and the zero sequence reactance's of the generator are $$0.2$$ $$pu$$, $$0.2$$ $$pu$$, and 0.05 $$pu,$$ respectively, at the machine base quantities. If a bolted single phase to ground fault occurs at the terminal of the unloaded generator, the fault current in amperes immediately after the fault is __________

In an unbalanced three phase system phase current $${{\rm I}_a} = 1\angle \left( { - {{90}^0}} \right)\,\,pu,\,\,$$ negative sequence current $$\,{{\rm I}_{b2}} = 4\angle \left( { - {{150}^0}} \right)\,\,pu,\,\,$$ zero sequence current $$\,\,{{\rm I}_{c0}} = 3\angle {90^0}\,\,pu.\,\,\,$$ The magnitude of phase current $${{\rm I}_b}$$ in $$pu$ is