Z$=4\%13,8$ kVG$20$MVAX,$=15\%$X$,=18\%$Xy$=3\%113,8/138$ kv$20$MVA $|4$X$,=$X$,=$Xo$-8\%6,9$ kVZ$,=6\%$X$=10\%$MX$=10\%138/6,9$ kV$15$ MVAx$=$X$-$X$,=10\%$IZ$,-15\%10$ MVAX,$=16\%$X$=20\%5$X$,-3\%138/13,8$ kv$15$ MVAX,$=$X$=$X$,=9\%13,8$ kvM$,10$ MVA Z$5\%$X$,=15\%$Xy$=18\%$X$,=3\%$

$(1)$ Consider that the impedances in the figure below have their values $$in $$pu$$ at the base of the equipment plate. The impedances of the transmission lines have their mutual impedances as being: j$0\mathrm{.}05$pu$,$ at the respective base of the transmission line. a$)$ Considering all three$-$phase Transformers, draw the zero, positive and negative sequence circuits. b$)$ Calculate the impedances referring to the same base of the entire circuit, considering as reference the $15$kV and $30$MVA base in generator $1.$ c$)$ Calculate the three$-$phase fault current in amperes, for a symmetrical fault at bus $$k$,$ through a fault impedance j$0\mathrm{.}1$ where: k$=1.$ d$)$ Calculate the three$-$phase fault current in amperes, for an asymmetrical single$-$phase fault at bus $$k$,$ through a fault impedance j$0\mathrm{.}1$ where: k$=1.$ e$)$ Calculate the three$-$phase fault current in amperes, for an asymmetrical two$-$phase$-$to$-$ground fault at bus $$k$,$ through a fault impedance j$0\mathrm{.}1$ where: k$=1.$ Also calculate the voltage at a bus where the fault occurs.