Optimization

The fuel costs of three units at a station supplying a total load of 1200 MW are:

Unit 1:

$/hour

Unit 2:

$/hour

Unit 3:

$/hour

(a) Calculate the cost of generation when the three generators share the load equally.

= 12220 $/hour

(b) Assuming that the three units have no lower and upper limits, calculate the optimum generation allocation. What is the corresponding cost of generation? What is the incremental cost?

Use Lagrange formulation:

(c) Assuming that Unit–1 has a maximum capacity of 300 MW, obtain the optimum generation allocation. What is the corresponding cost of generation? What are the incremental costs?

Set:

Therefore:

= 12,245 $/hour

Incremental Costs: