GATE 2025 EE Q.64: solution and answer

GATE 2025 · EEQ.64 · 2 marks · NAT

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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Answer and solution

ANSWER

The total plant output at an incremental cost of 11,800 Rs./MWh is 216 MW.

Official answer: 216Source: Official answer key, GATE 2025 EE (IIT Roorkee)

Each unit has a linear incremental cost curve, so its output varies linearly with the system incremental cost $λ$ (while it is within its limits): $P_{i} = P_{i}^{0} + k_{i} (λ - λ_{0})$ , with $λ_{0} = 10000$ and $P_{i}^{0}$ the output at that $λ_{0}$ .
Unit 1 slope from the two given operating points: $k_{1} = \frac{80 - 50}{10600 - 10000} = 0.05 MW per Rs./MWh$ .
Unit 2 slope: $k_{2} = \frac{92 - 80}{10600 - 10000} = 0.02 MW per Rs./MWh$ .
At $λ = 11800$ the increase over the first point is $11800 - 10000 = 1800$ .
Unit 1, unconstrained: $P_{1} = 50 + 0.05 \times 1800 = 140 MW$ . This exceeds its 100 MW rating, and the question says no unit may be overloaded, so $P_{1} = 100 MW$ .
Unit 2: $P_{2} = 80 + 0.02 \times 1800 = 116 MW$ , which is within its 150 MW rating, so it stays as calculated.
Total plant output: $P = 100 + 116 = 216 MW$ .

KEY IDEA

With linear incremental cost curves, each unit's output is a linear function of the common $λ$ . Find each slope from the two given points, extrapolate to the new $λ$ , then clamp any unit that passes its rating at that rating.

WATCH OUT FOR

Adding the unclamped outputs, $140 + 116 = 256$ MW, and so overloading the 100 MW unit. A unit that reaches its limit stays at the limit.

From the GATE 2025 EE paper. Every question of this paper · Download the full paper · All 9 Dispatch & control questions, with notes

GATE 2025 EE Q.64: solution and answer

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