Problem 1:

Consider a Δ-connect, 25 kVA, 480 V, 60 Hz, six pole synchronous generator.  The field current is set such that the line voltage is 504 V when supplying a rated load.  Consider the armature resistance to be negligible.

a. Calculate the speed of the prime mover, in rpm, assuming the prime mover is directly coupled to the generator.

b. When connected to a 0.85 lagging rated load, what is the electrical output power?

c. If the synchronous reactance, X_s, is 80%, calculate the magnitude of the internally generated voltage, E_A, and the torque angle, δ. 

Problem 2:

A 12 HP, 96% efficient, three-phase Wye-connected synchronous motor is connected to a 208 VAC, 60 Hz power supply.  The field excitation is set such that the power factor is unity when the machine draws 7.5 kW from the supply.   The per-phase armature reactance is 110%.

a. Find the internally generated voltage, E_a.

b. Calculate the motor torque angle, δ.

c. Draw the phasor diagram, showing V_φ, E_a, jXsI_A, I_A ,Θ and δ.