Q:

A three-phase ( m = 3), four-pole ( p = 4) nonsalientpole (round-rotor) synchronous machine has the parameters X _S = 2 pu and R _a = 0.05 pu. It is operated at (the phase voltage) V _a = 1 pu at an overexcited (lagging current based on the generator reference system, where the current flows out of the machine) displacement power factor of cos ? = 0.8 lagging, and per-phase current ? _a = 1 pu. The base (rated phase) values are A, and the base impedance is Z _base = V _base/ I _base = 17.14 ?.

1. Draw the per-phase equivalent circuit of this machine.

2. What is the total rated apparent input power S (expressed in MVA)?

3. What is the total rated real input power P (expressed in MW)?

4. Draw a per-phase phasor diagram with the voltage scale of 1.0 pu ? 3 inches, and the current scale of 1.0 pu ? 2.5 inches.

5. From this phasor diagram determine the perphase induced voltage ? _a and the torque angle ?.

6. Calculate the rated speed (in rpm) of this machine at f = 60 Hz.

7. Calculate the angular velocity ? _S (in rad/s).

8. Calculate the total (approximate) shaft power P _shaft ?