Hi,

I am working on the Unit Commitment Problem. I have a GAMS code with different constraints added, but now I want to represent the start-up cost as a function of the number of periods (intervals) the unit has been shut down. What I thought was to follow the idea presented in the literature that represents this cost, for any unit, as a set of constraints:

C(i) >= Kt*(u(i) – SUM (n=1 to t, u(i-n)))

Where i is the time interval in the planning horizon, C(i) is a continuous variable that will be the start-up cost in interval i, Kt is the cost of start-up the unit after it has been shut down for t intervals, u(i) is the binary variable to represent if the unit is on (1) in the interval i.

In my case t can take three values (first is the hot start-up, the second is the warm one, and the third is the cold done).

My problem, and it is warned, is how to manage the operational history of the unit, it is when the index (i-n) is less than zero in the SUM. I do know the status of the unit at its initial condition (i=0), and I know how many periods the unit has been in that condition.

Any comment, help or suggestion will be very appreciated.

Best regards.