A $14-$pole, Y$-$connected, three$-$phase generator driven by a hydraulic turbine has the following ratings: $150$ MVA, $13\mathrm{.}8$ kV$,0\mathrm{.}8$ lagging power factor, and $60$ Hz$.$ Its direct axis reactance is $0\mathrm{.}62$ p$\mathrm{.}0$ and its quadrature axis reactance is $0\mathrm{.}40$ p$\mathrm{.}0.$ All rotational losses can be neglected.

a$)$ What internal voltage does this generator require to operate under nominal conditions?

b$)$ At what angle delta will the generator reach its maximum power?

c$)$ How does the maximum power obtained from this generator compare to the maximum power it would provide if it had a cylindrical rotor? Determine the percentage.

NOTE: Work in p$.$u$.$