A $2000$hp$,4160$V$,$ three phase, cylindrical rotor, synchronous machine has a saturated reactance of $10.$

a$)$ What value of generated voltage, Eaf, is required when the motor delivers half of the rated real

power at unity power factor? Express your answer in volts line$-$line. $[2]$

b$)$ What is the motor torque angle for the condition in a$)[2]$

c$)$ If the field excitation is held constant and the motor output is increased to rated value, determine

the armature current and power factor. $[2]$

d$)$ What is the new torque angle for the condition in c$)[2]$

e$)$ For the condition in c$)$ if the field current is increased, how will the reactive power change and

why?