A $275$kV$,50$ Hz overhead line is rated at $750$MVA and is $25$km long. It has the

following parameters: r$=0\mathrm{.}034/$km$,$ x$=0\mathrm{.}323/$km$,$ y$=3\mathrm{.}610-6$S$/$km$.$ As part of an

urban renewal project, it is intended to replace this overhead line with an

underground cable with the following parameters: r$=0\mathrm{.}025/$km$,$ x$=0\mathrm{.}22/$km$,$

y$=2\mathrm{.}510-4$S$/$km$.$ Assuming that power factor and voltage at the receiving end are

$0\mathrm{.}92$ lagging and $270$kV respectively and that the cable follows the same route as

the overhead line, calculate:

a$)$ The sending end voltage of the overhead line at rated load and at minimum load

of $10\%$ rated load.

b$)$ The expected sending end voltage of the cable under the same loading

conditions.

c$)$ The expected sending end voltage of the cable at minimum load when a

$200$MVAr reactor is added at the receiving end.