Implementing minimum downtime for a three-state process
AnsweredI am trying to model something similar to the minimum downtime in unit commitment problems, but for a three-state process. In unit commitment, the generators have only two states - ON or OFF. I have tried to illustrate the three-state process in the figure below:
Is there a way to enforce the minimum downtime T1 between two mode changes (i.e. only if the state changes from charging to discharging or vice versa) and a different downtime T2 when there is no mode change involved? I have no restriction on the binary variables that must be defined to achieve this.
-
Official comment
-
Gurobi Staff
Hi Joel,
Thank you for reaching out!
I have a question. Is there any restriction on the minimum time for the charging or discharging modes? I assume not.
One way to achieve what you propose is to assign a binary variable to each of the 3 states for each time interval: Vc(t), Vd(t), Vo(t) (charge, discharge, offline). Then, you can use additional binary variables to model de transition between the states that make sense here. For instance, a transition variable Tco(t) will be 1 if the battery goes from charging to offline mode on time interval t. You can construct your variables according to the transitions that make sense (i.e., you don't need to consider the case of going from charging to discharging mode in one interval). For the T1 and T2 times, you could use constraints like:
T1*Tco(t) <= Vo(t+1) + Vo(t+2) + Vo(t+T1)
T1*Tdo(t) <= Vo(t+1) + Vo(t+2) + Vo(t+T1)
Does this help? Please try to derive the formulation.
Thanks,
Rodrigo
-
-
Hi Rodrigo,
Yes! That is an interesting way to model this. I will try to derive the formulation using this approach.
Note: Your assumption is correct - there is no minimum (up) time for the states.
Thank you,
Joel
0 -
Please sign in to leave a comment.
Comments
2 comments