$2.)$ Given the power system shown below, with reactance in positive values. Utility and transformer modeling have the same sequence modeling, $\frac{?}{xI}=x2=x0,$ otherwise stated. The autotransformer windings are assumed to have reactance values. Determine the following using an MVAb$=80$ and the utility is connected as wye ground.

a$.)$ The sequence networks of the power system $(20$ pts $)$

b$.)$ If the fault point occurs at the LOAD, determine Zth$1,$ Zth$2$ and Zth$0.(20$ pts$)$

c$.)$ The fault current and dead short circuit MVA if the fault point occurs at the UTILITY side $(20$ pts$).$

T$1$ specs:

H: $100$MVA $1$

X: $50$ MVA $6$

Y: $30$ MVA $3.$

$Z_{Hx}=60$ ohr

$Z_{HY}=100$ohr

$Z_{xy}=5$ ohms

$Zn=j0\mathrm{.}1$ohn

Bus$2=69KV$

M$2$

$10$ MVA

$xl=0\mathrm{.}2pu$

$x2=0\mathrm{.}9$ of XI

$x0=$ value of $x1$

less than $10\%$

$Zn=j0\mathrm{.}05pu$