Question

The incremental cost characteristics of two generators delivering a total load of 200 MW are as follows: \[ C_1 = 4.01 + 0.1P_1 \, \text{Rs/MWh} \quad \text{and} \quad C_2 = 1.60 + 0.2P_2 \, \text{Rs/MWh} \] What should be the values of \(P_1\) and \(P_2\) for economic operation?

• A. \( P_1 = P_2 = 100 \, \text{MW} \)
• B. \( P_1 = 80 \, \text{MW}; P_2 = 120 \, \text{MW} \)
• C. \( P_1 = 200 \, \text{MW}; P_2 = 0 \, \text{MW} \)
• D. \( P_1 = 120 \, \text{MW}; P_2 = 80 \, \text{MW} \)

Hint:

For economic operation, the incremental cost for both generators must be equal. This ensures that the total cost of power generation is minimized.

Answer 1

The Correct Option is A

To operate economically, the incremental costs must be equal for both generators. Therefore, we equate the derivatives of the cost functions with respect to \(P_1\) and \(P_2\): \[ \frac{dC_1}{dP_1} = \frac{dC_2}{dP_2} \] This gives: \[ 0.1 = 0.2 \] Solving this equation gives: \[ P_1 = P_2 = 100 \, \text{MW} \] Thus, the economic operation occurs when both generators are producing 100 MW, which corresponds to option (1).