Question $4$

$($a$)$ An $11$ kV generator feeds power to a load of $100$ MW at unity power factor through $3-$phase $11$ kV transmission line is shown in Figure Q$4$ below. The p$.$u$.$ impedance of line based on $100$MVA and $11$ kV is j $0\mathrm{.}2$ pu $.$ The line$-$to$-$line voltage at load terminal is $11$ kV $.$ Calculate the total reactive power to be injected at the terminal of the load to maintain the line voltage at $11$ kV $?($Assume $100$MVA base and $11$ kV base voltage.$)$

$(8$ marks$)$

$($b$)$ A load with three identical coils, each having a resistance of $20$ ohms and a reactance of $15$ ohms $,$ are connected in star to a $\backslash (400\backslash$mathrm$\{$~V$\},3\backslash )-$phase, $50$ Hz supply. Calculate the line current, power supplied and power factor of the load.

$($c$)$ If three identical capacitors are connected in star to the same supply as in part $($b$)$ such that they are in parallel with the load, calculate

i$)$ the capacitance required to give a resultant power factor of $0\mathrm{.}95$ lagging; and

$(4$ marks$)$

ii$)$ the line current taken by the combined circuit.

$(2$ marks$)$

$($d$)$ If the capacitor working voltage in part $($c$)$ is higher than the line voltage $(400$V$),$ from the reactive power compensation point of view, should it be connected in delta? State your choice with calculation on the capacitance difference between star and delta connected capacitor banks.

$(6$ marks$)$

$($Total: $25$ marks$)$