Final answer:
The economic dispatch is a method used to determine the optimal allocation of power generation among different generators to meet the demand at the lowest cost. In this case, we have two generators: Unit 1 and Unit 2. To determine the economic dispatch for a demand of 600 MW, we need to minimize the total cost while satisfying the limits on the generators. The incremental cost is the rate of change of the cost with respect to the power output.
Step-by-step explanation:
The economic dispatch is a method used to determine the optimal allocation of power generation among different generators to meet the demand at the lowest cost. In this case, we have two generators: Unit 1 and Unit 2. The cost functions for these units are given as C1(PG1) = 900 + 45P1 + 0.01P2/1 and C2(PG2) = 2500 + 43P2 + 0.003P2/2, where PG1 and PG2 are the power outputs of Unit 1 and Unit 2, respectively, in MW.
To determine the economic dispatch for a demand of 600 MW, we need to minimize the total cost while satisfying the limits on the generators. We can set up the following optimization problem:
- Minimize: Cost = C1(PG1) + C2(PG2)
- Subject to: PG1 + PG2 = 600 MW, 50 ≤ PG1 ≤ 200 MW, and 50 ≤ PG2 ≤ 600 MW
Solving this optimization problem will give us the power outputs of Unit 1 and Unit 2 that minimize the total cost for the given demand.
To determine the incremental cost, we need to calculate the derivative of the cost function with respect to the power output of each generator. The incremental cost is the rate of change of the cost with respect to the power output. For Unit 1, the incremental cost is the derivative of C1(PG1) with respect to PG1, and for Unit 2, the incremental cost is the derivative of C2(PG2) with respect to PG2.