Conditional Value-at-Risk Model for Smart Home Energy Management Systems

This paper presents a self-scheduling framework, using a risk-constrained optimization model for the home energy management system (HEMS), considering fixed, controllable, and interruptible loads, as a new contribution to earlier studies. The objectives are reducing the electricity bill and managing the risk of purchasing energy over on-peak hours and prosumer's discomfort index (DI) due to shifting load to undesired hours. In this regard, the problem formulation is represented as a mixed-integer linear programming (MILP) model. Afterward, the proposed HEMS is promoted to a conditional value-at-risk (CVaR) model. The prosumer is equipped with an energy storage system and a solar photovoltaic (PV) panel. A substantial fraction of the load demand is controllable, and there is an inverter-based heating, ventilation, and air conditioning (HVAC), where HVAC is modeled as a variable-capacity interruptible load. The optimal scheduling of the loads is supposed to be done by the proposed HEMS, and the time-of-use (TOU) mechanism is utilized, including three price steps over the day. The results, obtained from thoroughly simulating the problem using household data, validate the performance of the presented HEMS in mitigating the amount of the electricity bill, while keeping the discomfort index of the prosumer at a desired level.