A Multi-Period MILP Framework for Home Energy Management with Battery Storage and Electric Vehicle Charging Under Uncertainty

The residential home energy management system (HEMS) needs to manage the interplay among photovoltaic (PV) generation, battery storage, electric vehicle (EV) charging and/or other loads, as well as exchanging electricity with the grid under uncertain PV outputs, load demands, and electricity prices. A multi-period mixed-integer linear programming (MILP) model has been developed to provide a joint resource scheduling solution. To handle forecast uncertainty in PV output/or load demand and electricity prices, this problem has been solved using a distributionally robust optimization (DRO) method based on Wasserstein metrics. The DRO formulation is implemented over a 24 h moving horizon of 96 periods, each period being 15 min long. The optimized dispatch provided $0.3019 in net revenue when the amount of supply equaled the amount of demand at 2.762 kW, and there was a power balance residual of less than or equal to 1.0 × 10−6 kW. During the 24 h horizon, the framework delivered 70.00 kWh of EV charging energy at an aggregate operating cost of USD 1.4931. Based on the total end-use energy of 82.49 kWh, this corresponds to a cost intensity of USD 0.0181 per end-use kWh. There were no constraint violations across any of the 96 time periods; i.e., the battery state of charge (SOC) ranged from 0.500 to 3.000 kWh (5–30%) with the goal of reaching 3.000 kWh SOC during the last time period. Simultaneously, charging and discharging were also prohibited. When 30 percent forecast uncertainty existed, the DRO-MILP reduced the operating costs to about $1.75 for an adverse scenario, whereas the deterministic MILP produced costs of about $2.90, resulting in an approximate 40 percent reduction in adverse scenario costs. Compared to base case conditions, operating costs due to DRO were greater by about 17 percent, whereas operating costs due to the deterministic formulation were greater by about 104 percent. Thus, it appears that the proposed HEMS framework can achieve cost-effective scheduling solutions with exact physical feasibility and resilience against forecast errors.