$(30$pts$)$ Assume a synchronous generator is delivering power to an infinite bus through a transformer with $x_T=j0\mathrm{.}1$ followed by a transmission line with $x_L=j0\mathrm{.}3.$ The generator is set to operate with an internal voltage of $1\mathrm{.}2$ pu and has $x_d=j0\mathrm{.}2.$ The unit is operating in steadystate, delivering $0\mathrm{.}8$ pu of real power to the infinite bus, when a fault causes both circuit breakers to open. After a while, the fault is cleared, and both circuit breakers are closed.

a$.$ Find the internal operating angle of the machine when in steady$-$state.

b$.$ Calculate the critical clearing angle.