$[10$ marks$]$ A three$-$phase transmission line is $200$ km long. The series impedance is $z=0\mathrm{.}175+j0\mathrm{.}7$ per phase per $km,$ and the shunt admittance is $y=j4\mathrm{.}22{10}^{-6}$ siemens per phase per $km.$ It delivers $50$ MW at $345$ KV with $0\mathrm{.}8$ lagging pf

a$.$ Choose an appropriate line model and find the voltage and current at the sending end of the line.

b$.$ Calculate the voltage regulation across the line.

c$.$ Draw the equivalent circuit of the line with all voltages, currents, and impedances labeled.

d$.$ Calculate the maximum $($active$)$ power that can be transmitted over the line. Assume VS and VR can not be changed.

e$.$ You wish to install Y$-$connected shunt capacitors at the receiving end of the line that will increase the sending end voltage magnitude to $250kV(L-N).$ Solve the following:

e$\mathrm{.}1)$ Determine the total MVAr per phase of the capacitors.

e$\mathrm{.}2)$ What iss the new voltage regulation across the line?

please solve completely i will upvote and so will others