# Stochastic Time-of-use-type Constraints for Uninterruptible Services

## TL;DR

This paper introduces a new stochastic optimization formulation for modeling uninterruptible services with time-of-use constraints, improving flexibility in demand response power systems.

## Contribution

It proposes an alternative MILP formulation that treats time-of-use as a parameter on the right-hand side, enabling easier application of stochastic methods.

## Key findings

- New MILP formulation for uninterruptible load constraints
- Enhanced modeling flexibility with stochastic parameters
- Demonstrated effectiveness in demand response scenarios

## Abstract

In this paper, a mixed integer linear formulation for problems considering time-of-use-type constraints for uninterruptible services is presented. Our work is motivated by demand response 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 window. 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 demand response problem supports the proposed formulation.