P$11\mathrm{.}1$ Consider the small system shown in Figure P$11\mathrm{.}1.$ Each of the lines is modeled as an inductive reactance of $0\mathrm{.}75$ pu $.$ If the generator at Bus $\backslash ($ A $\backslash )$ maintains a constant voltage magnitude of $1\mathrm{.}05$ pu at its terminals, calculate the maximum active power that this system can supply if the load has a unity power factor, a $0\mathrm{.}95$ pf lag, and a $0\mathrm{.}95$ pf lead. What is the voltage at these critical loads?

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Figure P$11\mathrm{.}1$System of Problems P$11\mathrm{.}1-$P$11\mathrm{.}13.$

P$11\mathrm{.}2$ Repeat Problem P$11\mathrm{.}1$ for the case when only two lines are in service.

P$11\mathrm{.}3$ The system of Problem P$11\mathrm{.}1$ serves an active load of $1\mathrm{.}5$ pu $.$ What is the lowest value of a lagging power factor that would make this load critical?