A $275$ kV$,3-$phase, balanced overhead transmission line has an AC resistance at $20$ deg C of $0\mathrm{.}1$ ohms$/$kilometre$,$ an inductive reactance of j$5$ 'ohms$/$kilometre and a shunt conductance of j $\backslash (2\backslash$times $10^\{-6\}\backslash )$ S$/$kilometre$.$

Calculate $-$

a$)$ The "medium length" $"$pi$"$ model equivalent circuit of this line, if the line is $200$ km long. Draw the equivalent circuit $"$pi$"$ model of the line, showing per unit impedances on a power base of $100$ MVA $3-$phase and a voltage base of $330$ kV $.$

b$)$ The 'ABCD' parameters of this line, from the above. Ignore resistance $($i$.$e$.,$ set R$=0)$ in your calculations. Use per unit quantities.

c$)$ The receiving end voltage, when the line is open$-$circuited and the supply voltage at the sending end is $275$ kV $.$ Use the 'ABCD' parameters from the above.

d$)$ The receiving end voltage, when the line is carrying $\text{'}5\text{'}$ MVA at $0\mathrm{.}9$ power factor lagging and the voltage at the sending end is $275$ kV $.$ Use the $\text{'}\backslash ($ A B C D $\backslash )\text{'}$ parameters from the above.

e$)$ The voltage regulation of the line.