Question

The incremental cost curves of two generators (\( \text{Gen A} \) and \( \text{Gen B} \)) in a plant supplying a common load are shown. If the incremental cost of supplying the common load is \( \lambda = 7400 \, \text{Rs/MWh} \), the common load in MW is ________________ (rounded to the nearest integer).

 

Hint:

Incremental cost helps in economic dispatch problems for minimizing generation costs.

Answer 1

Correct Answer: 35

Given:

\( \lambda = 7400 \; \text{Rs/MWh} \)

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Incremental cost equations:

For generator A:

\( I_{CA}(P_{GA}) = \dfrac{2000}{100} P_{GA} + 8000 = 20P_{GA} + 8000 \)

For generator B:

\( I_{CB}(P_{GB}) = 40P_{GB} + 6000 \)

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Apply equal incremental cost criterion

\( \lambda = I_{CA} = I_{CB} = 7400 \)

For generator A:

\( 20P_{GA} + 8000 = 7400 \)

\( P_{GA} = -30 \;\text{MW} \)

Since generation cannot be negative:

\( P_{GA} = 0 \)

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For generator B:

\( 40P_{GB} + 6000 = 7400 \)

\( P_{GB} = \dfrac{7400 - 6000}{40} = 35 \;\text{MW} \)

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Total load supplied:

\( P_{GA} + P_{GB} = 0 + 35 = \mathbf{35 \; MW} \)

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Final Answer:

The common load is 35 MW.