$(20$ Points$)$ A single$-$line diagram of a power system is shown. The reactance of the transmission line is $x=30$ Ohms. The generators and transformers are rated as follows:

$G1$: $20$MVA,$12kV,x=1\mathrm{.}2pu,G2$:

$G3$: $20$MVA,$13\mathrm{.}2MV,$MVA$=13\mathrm{.}2$pukV,$x=1\mathrm{.}4pu$

$T2$: $60$MVA,$\frac{69}{13\mathrm{.}8}kV,x=0\mathrm{.}14pu,T1$:

$25$MVA,$\frac{12}{69}kV,x=0\mathrm{.}08pu$

$,75$MVA,$\frac{13\mathrm{.}2}{69}kV,x=0\mathrm{.}16pu$

Choose a base of $50$ MVA and a base of $12$ kV in the circuit of generator $1.$ Draw an equivalent reactance diagram showing all values in pu and form the bus admittance matrix.