Stochastic Time-of-Use-Type Constraints for Uninterruptible Services

In this paper, a mixed integer linear formulation for problems considering time-of-use-type constraints for uninterruptible services is presented. This paper is motivated by demand response (DR) problems in power systems, in which certain devices must remain online once they are switched on, along with a certain number of periods. Classically, this kind of constraints are modeled as a summation over a rolling time windows. This makes it difficult to consider this time-of-use parameter as uncertain. We propose an alternative formulation in which the time of use is on the right-hand side of a constraint instead on the limit of a summation. This allows applying existing stochastic optimization methodologies easily. An illustrative model for the optimal allocation of an uninterruptible load for the DR problem supports the proposed formulation.