A $14-$pole, Y$-$connected, three$-$phase generator driven by a water turbine has the following ratings: $120$ MVA, $13\mathrm{.}2$ kV$,0\mathrm{.}8$ lagging power factor, and $60$ Hz$.$ Its direct$-$axis reactance is $0\mathrm{.}620$ and its quadrature$-$axis reactance is $0\mathrm{.}400.$ All rotational losses can be neglected.

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

b$)$ What is the voltage regulation of the generator under rated conditions?

c$)$ Draw the power and torque angle curve of the generator.

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

e$)$ How does the maximum power obtained from this generator compare with the maximum power it would provide if it had a cylindrical rotor?