A small university campus is planning to implement a small$-$scale power system to improve energy efficiency and reliability. As a power systems engineer, you've been tasked with designing and analyzing this network. The system consists of the following components: $1.$ A $1000$kVA, $13\mathrm{.}8$ kV$/480$ V transformer connecting the campus to the main grid $2.$ A $250$ kW solar PV array with a DC$/$DC boost converter $3.$ A $500$ kWh battery energy storage system $($BESS$)$ with a bidirectional DC$/$DC converter $4.$ Three main buildings with the following peak loads: $$ Administration Building: $150$ kW $($load#$1)$ Library: $200$ kW $($load#$2)$ Science Center: $300$ kW $($load#$3)$Develop a single$-$line diagram of the microgrid, treating each building as a load bus, the transformer as the slack bus, and the solar PV$/$BESS as one generation bus. Construct the Y$-$bus matrix for the microgrid. The transformer is connected to load bus#$1,$ bus#$1$ is connected to #$2,$ and #$2$ is connected to load bus#$3$ through lines with the impedance of j$0\mathrm{.}1$X per$-$unit where X is the last digit of your ULID. Also, the BESS$/$PV bus $($generation bus$)$ is connected to load bus#$3$ with the impedance of j$0\mathrm{.}2$X$.$ So$,$ we$$re going to have $4$ lines in our single line diagram.