A $2300$V$,$ wye connected with $60$ Hz$,1000$ hp$,3-$phase, $20$ pole synchronous motor for

cylindrical rotor theory can be used and all losses can be neglected. It has a synchronous

reactance of $5$ per phase.

a$)$ The motor is operating from an infinite bus supplying rated voltage and rated

frequency, and its field excitation is adjusted so that the power factor is unity, when

the shaft load requiring $750$kW$.$ Compute the maximum torque that the motor can

deliver, given the shaft load is slowly increased with the field excitation held

constant.

b$)$ Instead of infinite bus, the power to the motor is supplied by $1000$kVa, $2300$V wye

connected, $3-$phase, $60$Hz synchronous generator whose synchronous reactance is

$5$ per phase and driven at rated speed. The field excitations of the generator and

motor are adjusted so that the motor absorbs $750$kW at unity power factor and rated

terminal voltage. If the field excitation of both machines are constant and mechanical

load on the synchronous motor is gradually increased, compute the maximum torque

under the conditions. Determine the armature current, terminal voltage and power

factor at the terminals corresponding to this maximum torque.

c$)$ Calculate the maximum torque if instead of remaining constant as in part b$,$ the field

currents of the generator and motor are gradually increased so as to always maintain

rated terminal voltage and unity power factor while the shaft load is increased.