Question $(2)$: $[18$ Marks$]$

A three$-$phase, $\backslash (60\backslash$mathrm$\{$HZ$\},200\backslash$mathrm$\{$~km$\}\backslash )$ overhead transmission line has a flat horizontal spacing $($D$)$ of $12$ m measured from the centers of the adjacent phases as in Figure $(1).$ Each phase includes four sub$-$conductors arranged on the corners of a square whose side length $($ S $)$ is $45$ cm and the resistance of each sub conductor is $0\mathrm{.}04$ Ohm$/$km$.$ The line has a load absorbing $350$ MW at $500$ KV and $0\mathrm{.}85$ lagging power factor. Given that the resistivity of the conductor material is $\backslash (1\mathrm{.}72\backslash$times $10^\{-6\}\backslash$mathrm$\{$Ohm$\}.\backslash$mathrm$\{$cm$\}\backslash )$ at ambient temperature, calculate the following:

a$.$ The total line series impedance in Ohm per phase.

b$.$ The capacitance$-$to$-$neutral in $\backslash (\backslash$mathrm$\{$F$\}/\backslash$mathrm$\{$m$\}\backslash )$ and the admittance$-$to$-$neutral in $\backslash (\backslash$mathrm$\{$S$\}/\backslash$mathrm$\{$km$\}\backslash ).$

c$.$ The total charging current if line operates at $500$ kV $.$

d$.$ The complex ABCD constants of transmission line assuming a medium PI$-$model.

e$.$ The sending end current, voltage, and power angle $($Phase angle of the sending end voltage$).$

f$.$ The percentage voltage regulation and comment on the result obtained.

Figure $(1)$