Optimal scheduling of smart home appliances with a stochastic power outage: a two-stage stochastic programming approach

Abstract

This study primarily concentrates on enhancing the scheduling of electric appliances within a smart home equipped with a photovoltaic solar array and a storage battery capable of redistributing excess electricity to the grid. Furthermore, the investigation takes into consideration the unpredictability of a power outage, analyzing the scheduling of these appliances to minimize consumer electricity expenses. To tackle this issue, a two-stage stochastic programming methodology is developed to effectively model the uncertainty surrounding both the onset time and duration of power outages. Additionally, a sample average approximation algorithm (SAA) is devised to efficiently address the problem. Through extensive computational experiments, the outcomes demonstrate that the SAA yields shorter CPU processing times, albeit without guaranteeing optimal solutions. The total average percent deviation of the SAA's upper bound from its lower bound and the optimal solution stands at 4.16% and 4.5%, respectively. Moreover, it is demonstrated that utilizing the stochastic approach, as opposed to the deterministic one, can enhance solution quality by 6.2%. Furthermore, a comprehensive sensitivity analysis is provided, focusing on probability distribution functions of outage start time and duration, alongside an analysis of the solar panel and battery storage capacities. It is revealed that when adopting a Normal distribution instead of a Uniform distribution, the performance of the SAA experiences a slight decline.