$2)$ Consider a $6-$pulse $(\backslash (\backslash$Delta $\backslash )-$connected$)$ TCR connected to a transmission line by means of a $\backslash (500\backslash$mathrm$\{$kV$\}\backslash$mathrm$\{$V$\}\_\{\backslash$mathrm$\{$LL$\}\}/18\backslash$mathrm$\{$kV$\}\backslash$mathrm$\{$VLL$\}\backslash )$ coupling transformer. A$)$ What should be the value of the required inductances so that the three$-$phase TCR can absorb a maximum of $60$ MVAr $?$ B$)$ How much reactive power would it absorb when the firing angle of the thyristors is $\backslash (150^\{\backslash$circ$\}\backslash )?$ C$)$ Draw the following waveforms for $\backslash (\backslash$alpha$=120^\{\backslash$circ$\}\backslash )$ : $($i$)$ line voltage in the output of the transformer, $($ii$)$ voltage across one inductor, $($iii$)$ voltage across the antiparallel thyristors and $($iv$)$ current through the inductor. Hint: consider the KVL for one "phase of the three$-$phase TCR$."$ Now assume that $2$ threephase Y$-$connected TSCs$,$ rated at $30$ MVA each, are placed in parallel with the TCR$,$ in the secondary of the coupling transformer. D$)$ What should be the value of the capacitances of each element of the TSCs$?$ E$)$ Assuming that the TSC was previously in service $($Vcap not zero$),$ draw the following waveforms when the thyristors of the TSC are not being fired: $($i$)$ voltage across one phase of the TSC $($input voltage$),($ii$)$ voltage across one capacitor, $($iii$)$ voltage across the antiparallel thyristors. Identify the maximum voltage across the thyristors. Recall that the thyristors should be rated to withstand this voltage level. Hint: consider the KVL for one "phase of the three$-$phase TSC$."$