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).
\includegraphics[width=0.5\linewidth]{34.png}
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).
\includegraphics[width=0.5\linewidth]{34.png}
\includegraphics[width=0.5\linewidth]{34.png}
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Incremental cost helps in economic dispatch problems for minimizing generation costs.
Updated On: Jan 23, 2025
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Solution and Explanation
Given:
\[
\lambda = 7400 \, \text{Rs/MWh}
\]
Incremental cost equations:
\begin{align*}
I_{CA}(P_{GA}) = \frac{2000}{100} P_{GA} + 8000
I_{CB}(P_{GB}) &= 40P_{GB} + 6000
\lambda &= I_{CA} = I_{CB} = 7400
2000P_{GA} + 8000 &= 7400
P_{GA} &= -600
P_{GA} &> 0
P_{GB} &= \frac{7400 - 6000}{40} = 35
P_{GA} + P_{GB} &= 35 \text{ MW} \end{align*} Final Answer: The common load is \( 35 \, \text{MW} \). % Quick tip
I_{CB}(P_{GB}) &= 40P_{GB} + 6000
\lambda &= I_{CA} = I_{CB} = 7400
2000P_{GA} + 8000 &= 7400
P_{GA} &= -600
P_{GA} &> 0
P_{GB} &= \frac{7400 - 6000}{40} = 35
P_{GA} + P_{GB} &= 35 \text{ MW} \end{align*} Final Answer: The common load is \( 35 \, \text{MW} \). % Quick tip
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