Question

The generator cost curves are:

Unit 1: C₁ (PG₁)=900+45P₁ + 0.01P²₁ s/h
Unit 2: C₂ (PG₂)=2500+43P₂ +0.003P ²₂ s/h
The loss function is:
Pₗ( PG₂) =0.0002 (PG₂−525)² MW
The limits on the generators are:
50 ≤ P₁ ≤ 200 MW
50 ≤ P₂ ≤ 600 MW
​Determine the economic dispatch for a demand of 600MW. Determine the incremental cost.
No losses

Answer 1

To find the economic dispatch and incremental cost for a total demand of 600 MW, we equalize the marginal costs derived from the cost curves of Unit 1 and Unit 2 and solve the system of equations considering their output limits.

Step-by-step explanation:

To determine the economic dispatch when the total demand is 600 MW without considering losses, we minimize the total cost by adjusting the outputs of Unit 1 and Unit 2 within their limits. We start by finding the marginal cost of each generator by taking the derivative of its cost curve with respect to the output power.

For Unit 1:

C₁' = dC₁/dP₁ = 45 + 0.02P₁
For Unit 2:

C₂' = dC₂/dP₂ = 43 + 0.006P₂
We set up the economic dispatch by equating the marginal costs and solving for the unknowns, while the combined output should meet the demanded 600 MW.

Let's label P₁ as the output for Unit 1 and P₂ as the output for Unit 2. The dispatched power equations to meet the demand are:

• P₁ + P₂ = 600

And the equal incremental cost rule for economic dispatch is given by setting the derivatives equal:

• 45 + 0.02P₁ = 43 + 0.006P₂

By solving these two equations, we get the optimal dispatch for Unit 1 and Unit 2 while considering their output limits. The incremental cost at this point of operation is the shared derivative value after plugging in the dispatched powers for each unit.