A generating plant consists of four 200 MVA, 13.8 kV, 0.9 PF (-) synchronous generators. The governors are set to produce a 3 Hz drop from no load to full load. Three of these generators each supply a constant load of 120 MW at a frequency of 60 Hz, while the fourth generator, called a compensator, supplies the load increases in the system while maintaining the frequency of the system at 60 Hz.

a) At a given instant, the total system load is 540 MW at a frequency of 60 Hz. What is the no-load frequency of each of the generators?

b) If the load on the system is raised to 700 MW and the governor settings do not change, what will be the new system frequency?

c) At what no-load frequency should the compensating generator governor be set to restore the system frequency to 60 Hz?

d) If the system is operating under the conditions described in part "c," what would happen if the compensating generator were disconnected from the line?

At a given instant, the total system load is 540 MW at a frequency of 60 Hz. To find the no-load frequency of each generator, we can use the formula:

No-load frequency = Full load frequency + Frequency drop from no load to full load. No-load frequency = 60 + 3No-load frequency = 63 Hz

Therefore, the no-load frequency of each generator is 63 Hz.

b) If the load on the system is raised to 700 MW and the governor settings do not change, we can use the frequency-power equation to find the new system frequency.

f = (P1/P2)f = (360 MW/700 MW) x 60 Hz f = 30.86 Hz

The new system frequency would be 30.86 Hz.

c) To find the no-load frequency at which the compensating generator governor should be set to restore the system frequency to 60 Hz, we can use the following formula:

f = (P1 + P2 + P3)/(P1/Pf1 + P2/Pf2 + P3/Pf3 + Pc/Pfc)f = (360 MW + 120 MW + 120 MW + 120 MW)/(360 MW/60 Hz + 120 MW/63 Hz + 120 MW/63 Hz + Pc/Pfc)60 Hz = (720 MW)/(6 + Pc/Pfc)6 + Pc/Pfc = 720/60 = 12Pc/Pfc = 12 - 6 = 6Pc/Pfc = 6/63 = 0.0952

Therefore, the no-load frequency at which the compensating generator governor should be set to restore the system frequency to 60 Hz is 63 - 0.0952 x 3 = 62.7144 Hz

d) If the compensating generator were disconnected from the line, the system frequency would decrease since the compensator maintains the frequency of the system.

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