Question $2$

A three$-$phase, $50km,50Hz$ transmission line with a resistance and inductance of $0\mathrm{.}25$ and $2$ mH per km respectively is shown in Figure Q$2.$ Voltage at the receiving end is $132$ kV and the power delivered is $80$ MVA at $0\mathrm{.}8$ power factor lagging. Voltage at the sending end is maintained at $140$ kV by a reactive power compensator at the receiving end.

$($a$)$ Determine the output and nature of the reactive power before connection of the load at the receiving end.

$(12$ marks$)$

$($b$)$ Determine the output and nature of the reactive power after connection of the load at the receiving end.

$(10$ marks$)$

$($c$)$ What is the equivalent power factor as seen at the transmission line infeed to the receiving end busbar after connection of the load?

$(3$ marks$)$

The following equations may be used:

$P_R=\frac{|V_S||V_R|}{|Z_L|}cos(-)-\frac{|V_R{|}^2}{|Z_L|}cos$

$Q_R=\frac{|V_S||V_R|}{|Z_L|}sin(-)-\frac{|V_R{|}^2}{|Z_L|}sin$

where $Z_L=$ transmission line impedance, $=$ angle of $Z_L,$ and $=$ angle of $V_s$ with respect to $V_R.$