GATE 2025 EE – Question 64

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

Two units, rated at 100 MW and 150 MW, are enabled for economic load dispatch. When the overall incremental cost is 10,000 Rs./MWh, the units are dispatched to 50 MW and 80 MW respectively. At an overall incremental cost of 10,600 Rs./MWh, the power output of the units are 80 MW and 92 MW, respectively. The total plant MW-output (without overloading any unit) at an overall incremental cost of 11,800 Rs./MWh is ________ (round off to the nearest integer).

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Correct answer: 216

Explanation

Assuming linear incremental cost curves: unit 1 has slope $\dfrac{10600-10000}{80-50}=20$ Rs/MWh per MW, unit 2 has slope $\dfrac{600}{92-80}=50$. At $\lambda=11800$ unit 1 would need $50+\dfrac{1800}{20}=140$ MW, above its 100 MW rating, so it is limited to 100 MW. Unit 2 delivers $80+\dfrac{1800}{50}=116$ MW (within 150 MW). The total is $100+116=216$ MW.