GATE EE 2025 Set 1 — Question 64
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Power Systems → Economic Operation & Compensation → Economic Load Dispatch
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Question
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).
Correct answer
216 to 216
Solution
Assume linear incremental cost curves for both units: .For Unit 1:
Using the given data points and :
Subtracting the first from the second: Rs/MW h.
Rs/MWh.
So, .For Unit 2:
Using the given data points and :
Subtracting the first from the second: Rs/MW h.
Rs/MWh.
So, .At overall incremental cost Rs/MWh:
For Unit 1: MW.
For Unit 2: MW.Check against ratings:
Unit 1 is rated at 100 MW. Since the calculated MW exceeds its rating, it must be limited to MW to avoid overloading.
Unit 2 is rated at 150 MW. The calculated MW is within its rating.Total plant output = MW.
Using the given data points and :
Subtracting the first from the second: Rs/MW h.
Rs/MWh.
So, .For Unit 2:
Using the given data points and :
Subtracting the first from the second: Rs/MW h.
Rs/MWh.
So, .At overall incremental cost Rs/MWh:
For Unit 1: MW.
For Unit 2: MW.Check against ratings:
Unit 1 is rated at 100 MW. Since the calculated MW exceeds its rating, it must be limited to MW to avoid overloading.
Unit 2 is rated at 150 MW. The calculated MW is within its rating.Total plant output = MW.
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