A simple high$-$voltage DC transmission system is shown in the figure below. The operating line to line voltage input to the rectifier circuit in $\text{'}$AC System $1\text{'}$ is $490$ kV rms$.$ The input real power to the $"$AC system $1"$ is $1000$ MW $.$ The thyristor firing angle of the $\text{'}$AC System $\backslash (1^\{\backslash$prime$\}\backslash )$ is set to $\backslash (45^\{\backslash$circ$\}\backslash ).$ The dc link resistance $\backslash (($R$)\backslash )$ is $\backslash (10\backslash$Omega $\backslash ),$ and the inductance is large enough to consider the DC current to be ripple free. The output $($system $2)$ AC line to line voltage is $520$ kV rms$.$ Assuming three phase rectifier circuit is used, Determine: $($i$)$ DC voltage of the AC System $1$; $($ii$)$ the power loss in the DC link; $($iii$)$ DC voltage of the AC System $2$ ; $($iv$)$ the firing angle of AC system $2$