Incremental fuel costs (in some appropriate unit) for a

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Incremental fuel costs (in some appropriate unit) for a power plant consisting of three generating units are IC₁ = 20 + 0.3 P₁, IC₂ = 32 + 0.4 P₂, IC₃ = 30where P₁ is the power in MW generated by unit i, for i = 1, 2 and 3. Assume that all the three units are operating all the time. Minimum and maximum loads on each unit are 50 MW and 300 MW repectively. If the plant is operating on economic load dispatch to supply the total power generated by each unit is

1. P₁ = 242.86 MW; P₂ = 157.14 MW; and P₃ = 300 MW
2. P₁ = 157.14 MW; P₂ = 242.86 MW; and P₃ = 300 MW
3. P₁ = 300.0 MW; P₂ = 300.0 MW; and P₃ = 100 MW
4. P₁ = 233.3 MW; P₂ = 233.3 MW; and P₃ = 233.4 MW

Correct Option: A

For optimal generation,
P₃ = 300 (maximum load)
and IC₁ = IC₂
or 20 + 0.3P₁ – 30 + 0.4P₂ ..........(i)
Now, as P₁ + P₂ + P₃ = 700
or P₁ + P₂ = 400 MW .........(ii)
Then, from equation (i),
20 + 0.3 P₁ = 30 + 0.4 (400 – P₁)
or 0.7 P₁ = 170 MW
or P₁ = 242.8 MW
and P₂ = (400 – 242.8) MW
= 157.14 MW