GATE 2015 EE – Question 51

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

Consider the economic dispatch problem for a power plant having two generating units. The fuel costs in Rs/MWh along with the generation limits for the two units are given below:

$C_1(P_1) = 0.01P_1^2 + 30P_1 + 10$ ; $100\ \text{MW} \leq P_1 \leq 150\ \text{MW}$

$C_2(P_2) = 0.05P_2^2 + 10P_2 + 10$ ; $100\ \text{MW} \leq P_2 \leq 180\ \text{MW}$

The incremental cost (in Rs/MWh) of the power plant when it supplies 200 MW is ________.

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Correct answer: 20

Explanation

The incremental costs are $\lambda_1 = 0.02P_1 + 30$ and $\lambda_2 = 0.1P_2 + 10$. Equal incremental cost with $P_1 + P_2 = 200$ would need $P_1 < 100$, which is outside its limit. So unit 1 is held at its minimum, 100 MW, and unit 2 supplies the other 100 MW. The plant's incremental cost is then $\lambda_2 = 0.1 \times 100 + 10 = 20$ Rs/MWh.