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GATE 2022 EE – Question 43

Power Systems · Economic Load Dispatch (with and without considering transmission losses) · 2 marks · Multiple choice

The fuel cost functions in rupees/hour for two 600 MW thermal power plants are given by

Plant 1: $C_1=350+6P_1+0.004P_1^2$

Plant 2: $C_2=450+aP_2+0.003P_2^2$

where $P_1$ and $P_2$ are power generated by plant 1 and plant 2, respectively, in MW and $a$ is constant. The incremental cost of power ($\lambda$) 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

  1. 200, 350
  2. 250, 300
  3. 325, 225
  4. 350, 200

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Correct answer: (B) 250, 300

Explanation

For plant 1, $\frac{dC_1}{dP_1}=6+0.008P_1=8$ gives $P_1=250$ MW. The demand is 550 MW, so $P_2=550-250=300$ MW (which fixes $a=8-0.006\times300=6.2$).