4-11. A paper mill has installed three steam generators (boilers) to provide process steam...

4-11. A paper mill has installed three steam generators (boilers) to provide process steam and also to use some its waste products as an energy source. Since there is extra capacity, the mill has installed three 10-MW turbine generators to take advantage of the situation. Each generator is a 4160-V, 12.5 MVA, 60 Hz, 0.8-PF-lagging, two-pole, Y-connected synchronous generator with a synchronous reactance of 1.10 and an armature resistance of 0.03 Generators 1 and 2 have a characteristic power-frequency slope sP of 5 MW/Hz, and generator 3 has a slope of 6 MW/Hz.

(a) If the no-load frequency of each of the three generators is adjusted to 61 Hz, how much power will the three machines be supplying when actual system frequency is 60 Hz?

(b) What is the maximum power the three generators can supply in this condition without the ratings of one of them being exceeded? At what frequency does this limit occur? How much power does each generator supply at that point?

(c) What would have to be done to get all three generators to supply their rated real and reactive powers at an overall operating frequency of 60 Hz?

(d) What would the internal generated voltages of the three generators be under this condition?