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GATE EE 2023 Set 1 — Question 21

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MCQ+1 / -0.33MediumEconomic Load DispatchEconomic Operation & CompensationPower Systems

Power Systems → Economic Operation & Compensation → Economic Load Dispatch

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Question

The expressions of fuel cost of two thermal generating units as a function of the respective power generation PG1P_{G1} and PG2P_{G2} are given as
F1(PG1)=0.1aPG12+40PG1+120F_1(P_{G1}) = 0.1aP_{G1}^2 + 40 P_{G1} + 120 Rs/hour
F2(PG2)=0.2PG22+30PG2+100F_2(P_{G2}) = 0.2P_{G2}^2 + 30 P_{G2} + 100 Rs/hour
0 MW≤PG1≤350 MW0 \text{ MW} \leq P_{G1} \leq 350 \text{ MW}
0 MW≤PG2≤300 MW0 \text{ MW} \leq P_{G2} \leq 300 \text{ MW}
where aa is a constant. For a given value of aa, optimal dispatch requires the total load of 290 MW to be shared as PG1=175 MWP_{G1} = 175 \text{ MW} and PG2=115 MWP_{G2} = 115 \text{ MW}. With the load remaining unchanged, the value of aa is increased by 10% and optimal dispatch is carried out. The changes in PG1P_{G1} and the total cost of generation, F(=F1+F2)F (= F_1 + F_2) in Rs/hour will be as follows
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