Question
The fuel cost functions in rupees/hour for two 600 MW thermal power plants are given by
Plant 1 : C1 = 350 + 6P1 + 0.004P12
Plant 2 : C2 = 450 + aP1 + 0.003P12
where P1 and P2 are power generated by plant 1 and plant 2, respectively, in MW and a is constant. The incremental cost of power ( λ) is 8 rupees per MWh. The two thermal power plants together meet a total power demand of 550 MW. The optimal generation of plant 1 and plant 2 in MW, respectively, are
Options :
200, 350
350, 200
325, 225
250, 300
Answer :
250, 300
Solution :
Given : Fuel cost functions
Plant 1 : C1 = 350 + 6P1 + 0.004P12 Rs/hr
Plant 2 : C2 = 450 + aP1 + 0.003P12 Rs/hr
For optimal generator, to share total load of 550 MW, incremental cost (I.C.) of units in operation must be same.
(IC)1 = dC1/dP1 = 6 + 0.008P1 Rs/MWhr
(IC)2 = dC2/dP2 = a + 0.006P2 Rs/MWhr
For optimal generator, (IC)1= (IC)2=λ
6 + 0.008P1 = a + 0.006P2 = 8 MW
P1 = 8-6/0.008 = 250 MW
P2 = (550-250) MW = 300 MW
P1 = 250 MW and P2 = 300 MW
Hence, the correct option is (D).
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