Question

A synchronous  generator  is  driven  by  a  diesel engine  to  provide  electricity to a remote  mining  operation. The  generator  is three-phase, Y-connected, 60 Hz, 900 rpm, 600 V, 3300 kW, 4125 kVA, and it has a synchronous reactance of 0.120 Ω per phase.  Ignore all losses, and assume the machine iron is not saturated.

(a)  The generator is set to deliver its rated active power at unity power factorand rated terminal voltage.  Determine:

i.  The speed of the diesel engine driving the generator;

ii.  The rotor electrical angle, δ;

iii.  The rotor mechanical angle;

iv.  The excitation voltage in volts (line voltage).

(b)  While keeping all controls constant, determine the terminal voltage of thegenerator if it delivers its rated active power, but now at 0.92 power factorlagging.  Provide a quantitative answer.  Draw an approximate phasor diagram depicting the relationship between the terminal voltage, excitation voltage, stator current and the back EMF of the generator.

(c)  What needs to be done to bring back the terminal voltage to its rated value?Provide a quantitative answer.

(d)  While keeping the excitation settings found in (c),  determine the steady-state mechanical power and mechanical torque provided by the diesel engineif now the generator delivers 3000 kW. What is the terminal voltage nowand the reactive power output?

(e)  Had this generator been fitted with a rotor with permanent magnets only(i.e.,  without  a  rotor  winding),  how  would  your  answers  to  (c)  and  (d) change?  Explain briefly.