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GATE EE 2026 Set 1 — Question 58

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NAT+2 / -0HardEconomic Load DispatchEconomic Operation & CompensationPower SystemsPenalty Factor & Incremental Cost

Power Systems → Economic Operation & Compensation → Economic Load Dispatch

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Question

A system with two generators G1 and G2 (without generator limits) is shown.
Two-bus single-line diagram: generator G1 on the left bus and generator G2 on the right bus, joined by one transmission line. Arrow PG1 shows G1 power injected into the left bus and arrow PG2 shows G2 power injected into the right bus. A load of 1000 MW is drawn from the G1 bus and a load of 184 MW is drawn from the G2 bus.
The total load on the system is 1184 MW. The expressions for the cost of generation (C1C_1 and C2C_2) and real power loss (PLossP_{Loss}) are as follows:C1(PG1)=1000+50PG1+0.01(PG1)2C_1(P_{G1}) = 1000 + 50P_{G1} + 0.01(P_{G1})^2 Rs/MWh
C2(PG2)=2000+50PG2+0.001(PG2)2C_2(P_{G2}) = 2000 + 50P_{G2} + 0.001(P_{G2})^2 Rs/MWh
PLoss=0.001(PG2−50)2P_{Loss} = 0.001(P_{G2} - 50)^2 MW
When the generators are operating at their optimal generation, meeting the total load requirement, the real power loss in the system is ________ MW (Round off to one decimal place)
Consider the Lagrange multiplier λ=70.25\lambda = 70.25 for optimal generation.

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