GATE 2015 EE (EE2) – Question 50

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

Incremental costs in Rs/MWh are dC1/dP1=0.2P1+50 and dC2/dP2=0.24P2+40, with 20≤P1,P2≤150 MW. At the initial dispatch they are 76 and 68.8. Redispatch at unchanged total demand for minimum cost. Find P2 in MW.

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Correct answer: 135 to 137

Explanation

The initial outputs are (76−50)/0.2=130 MW and (68.8−40)/0.24=120 MW, so demand totals 250 MW.

For an interior optimum, marginal costs are equal. Set 0.2(250−P2)+50=0.24P2+40, giving 60=0.44P2.

Thus **P2=136.364 MW** and P1=113.636 MW. Both satisfy 20–150 MW limits, so no bound adjustment is needed.

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