Let the reginal power system with 2 generating station, A and B. This station serve customers in region X and Y. Customers in region X have the total demand of 35MW(megawatts), where as customers in region Y have total demand of 50MW. Generating station A has the production capacity of 105MW, with operating cost $119 per MW. Generating station B has the production capacity of 120MW, with the operating cost of $120 per MW. Power can be transmitted directly from the generaing station to customer region, but there is 15% loss in power. Power can also be trasmitted from one generating station to other. In this case there is 10% loss in power. Every transmission line has maximum capacity (in units of MW), as given in following table (where "-" indicates that no power can be transmitted):
|
|
To |
|
|
| From |
A |
B |
X |
Y |
| A |
- |
65 |
45 |
50 |
| B |
95 |
- |
40 |
55 |
The goal is to determine the optimal plan for power distribution, including quality of power generated at each statation.
i) State decision variable required to solve problem.
ii) Prepare linear program (LP) associated with this problem.
iii) Solve proble using Gurobi.
iv) Use the table to provide the summary of solution.