GATE EE 2023 Set 1 — Question 21
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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 and are given as
Rs/hour
Rs/hour
where is a constant. For a given value of , optimal dispatch requires the total load of 290 MW to be shared as and . With the load remaining unchanged, the value of is increased by 10% and optimal dispatch is carried out. The changes in and the total cost of generation, in Rs/hour will be as follows
Rs/hour
Rs/hour
where is a constant. For a given value of , optimal dispatch requires the total load of 290 MW to be shared as and . With the load remaining unchanged, the value of is increased by 10% and optimal dispatch is carried out. The changes in and the total cost of generation, in Rs/hour will be as follows
Correct answer
(A) P_(G1) will decrease and F will increase
Solution
For optimal dispatch, the incremental costs (IC) of the two units must be equal, and the total generation must meet the total load.Incremental cost functions:
Given initial optimal dispatch:
Total load .At initial optimal dispatch, :
Now, the value of is increased by 10%.
New The total load remains unchanged at .
For the new optimal dispatch, :
Substitute and :
Comparing and :
Since , will decrease.Now, let's calculate the total cost for both scenarios.Initial Total Cost ():
New Total Cost ():
Comparing and :
Since , will increase.Therefore, will decrease and will increase.The final answer is
Given initial optimal dispatch:
Total load .At initial optimal dispatch, :
Now, the value of is increased by 10%.
New The total load remains unchanged at .
For the new optimal dispatch, :
Substitute and :
Comparing and :
Since , will decrease.Now, let's calculate the total cost for both scenarios.Initial Total Cost ():
New Total Cost ():
Comparing and :
Since , will increase.Therefore, will decrease and will increase.The final answer is
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