Multi-objective framework for a home energy management system with the integration of solar energy and an electric vehicle using an augmented ε-constraint method and lexicographic optimization

Recent innovations in smart grid technology have increased the utilization of advanced techniques and control methods, enabling consumers to purchase and sell electricity more flexibly. Accordingly, the development of a home energy management system (HEMS) is urgently required to support residential consumers in consuming energy efficiently, achieving high satisfaction levels, and meeting grid specifications. Previous studies have only suggested simple HEMS models with one or two optimized objectives. Therefore, we propose a multi-objective mixed-integer linear programming paradigm for a comprehensive HEMS model that fully utilizes the vehicle-to-home and home-to-grid capabilities while optimizing the energy cost, peak-to-average ratio (PAR), and discomfort index (DI). Also, an integration method of the augmented ε-constraint with lexicographic optimization is presented for effectively addressing any multi-objective HEMS problems. The proposed approach is validated across different simulations using both deterministic and stochastic models. The simulation results reveal that the energy costs and PAR can be reduced by 47.96% and 55.24%, respectively, whereas the DI is maintained at a minimum value. Extensive simulations related to the storage capacity, solar photovoltaic sizing, and uncertainty parameters are also analyzed. The proposed HEMS framework is confirmed to be a viable approach for optimally coordinating different home devices.