Hello! Please solve this step by step. Thank you! a single$-$ phase power system consists of a $\frac{480}{{?}_{}}V,60Hz,$ generator supplying two loads connected in parallel, with $Z_{L1}=4+j3$ and $Z_{L2}=5+j2$ through a transmission line of impedance $Z_{\text{L}\text{i}\text{n}\text{e}}=0\mathrm{.}18+j0\mathrm{.}24.$ Suppose a step up transformer with ratio $a_1=\frac{N_1}{N_2}$ at the generator end of the transmission line and step down transformer with ration $a_2=\frac{N_1}{N_2}$ is placed at the load end of the transmission line.

Draw the power system configuration and find the load voltage and transmission line losses as function in $,a_1$ and $a_2.$

Using MATLAB or Excel to plot the relation between load voltage and $$ at $a_1=20,$ and $a_2=\frac{1}{20},$ and explain what is the best value of $$ that gives the desired load voltage.

Using MATLAB or Excel to plot the relation between load voltage and $a_1$ at $=0$ and $a_2=\frac{1}{20}.$ It is required to discuss that what is the best value of $a_1$ to give a good voltage regulation.

Using MATLAB or Excel to plot the relation between load voltage and $a_2$ at $=0$ and $a_1=20.$ It is required to explain what is the best value of $a_2$ to give the maximum efficiency.

A according to the above simulation, you need to select the optimum values of $,a_1$ and $a_2$ to design a power system to supply the mentioned load.

Notes: Assumed that $$ changed from $0$ to $180$;$a_1$ and $a_2$ changed from $0$ to $30$ for part $2,3$ and $4.$