The residential load scheduling problem is concerned with finding an optimal schedule for the operation of residential loads so as to minimize the total cost of energy while aiming to respect a prescribed limit on the power level of the residence. We propose a mixed integer linear programming formulation of this problem that accounts for the consumption of appliances, generation from a photovoltaic system, and the availability of energy storage. A distinctive feature of our model is the use of operational patterns that capture the individual operational characteristics of each load, giving the model the capability to accommodate a wide range of possible operating patterns for the flexible loads. The proposed formulation optimizes the choice of operational pattern for each load over a given planning horizon. In this way, it generates a schedule that is optimal for a given planning horizon, unlike many alternatives based on controllers. The formulation can be incorporated into a variety of demand response systems, in particular because it can account for different aspects of the cost of energy, such as the cost of power capacity violations, to reflect the needs or requirements of the grid. Our computational results show that the proposed formulation is able to achieve electricity costs savings and to reduce peaks in the power consumption, by shifting the demand and by efficiently using a battery.
Technical report, Inria Lille-Nord Europe, Team Inocs, December 2017.