consider the following problem there are two

Question

Consider the following problem: There are two generators in this system and there is a load of 1,000MW. There is only one node in this network.

Variables:

P1 : Real power generated by generator 1

P2 : Real power generated by generator 2

U1: Unit commitment (binary) variable representing the status of generator 1 (U = 1: On, U = 0: off)  U2 : Unit commitment (binary) variable representing the status of generator 1 (U = 1: On, U = 0: off)

Costs:
The total cost of Generator 1 is: 20P1 + 8000U1

The total cost of Generator 2 is: 35P2 + 2000U2

a. Determine the values of P1, P2, U1, and U2.

min : 20P1 + 35P2 + 8000U1 + 2000U2

s.t: 600∗U1 ≤P1 ≤900∗U1

300∗U2 ≤P2 ≤1200∗U2
P1 + P2 = 1000
U1 ∈{0,1}
U2 ∈{0,1}

Hint: you don't need to program this. Solution is trivial.

Fill the following table

P1
P2
U1
U2

b. What is the market clearing price (locational marginal price)?