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This is a simple Linear Programming LP Example with a generic power system, constraints, and determines optimal solution
Completion of LP Formulation
Variables:
There are 8 variables in my generator model problem: x1, x2, x3, x4, x5, x6, x7, x8. They are defined as given below:
Variable Definition
x1 G1 Bidding Quantity 20 MW Step
x2 G1 Bidding Quantity 30 MW Step
x3 G1 Bidding Quantity 15 MW Step
x4 G1 = x1 + x2 + x3 or total MW to be bid by G1
x5 G2 Bidding Quantity 18 MW Step
x6 G2 Bidding Quantity 26 MW Step
x7 G2 Bidding Quantity 32 MW Step
x8 G2 = x5 + x6 + x7 or total MW to be bid by G2
Objective Function:
The objective of the problem is to minimize cost of combined bids of both generators.
The objective function is the sum of the unit price of the MW multiplied by the quantity to be bid added to the other bid ranges and their respective products.
Note: In the MATLAB portion of the model, the x4 and x8 variables are set equal to 0 since it is not in the problem definition to minimize these.
Constraints
Optimal Solution
Accepted Quantity
The accepted quantity from each generator range is shown below and in the MATLAB results (attached):
Cost to Supply Load
The minimized cost under the optimal model to supply 100 MW load is $2,330.00. The cost to supply load by generator G1 will be $1150 from G2, $1180.