A bi-level optimization framework for household distributed energy systems: Integrating multiple flexible loads

This paper presents a bi-level optimization framework for household distributed energy systems (DES), incorporating multiple flexible loads. The upper-level configuration optimization model aims to minimize total system cost, reduce carbon emissions, and maximize renewable energy utilization rate. The lower-level operation optimization model minimizes operational cost while considering multiple flexible loads. This bi-level framework achieves optimal system configuration and efficient operational strategies, enhancing energy efficiency, cost-effectiveness, and environmental performance. This paper also proposes a novel multi-objective optimization method based on Large Language Models (LLM), combined with Mixed Integer Linear Programming (MILP). The impact of flexible loads on DES optimization is evaluated using LLM-MILP and other advanced multi-objective bi-level optimization methods in four scenarios with varying levels of flexible load integration. Furthermore, the performance of these four bi-level optimization methods is assessed based on two metrics: Hypervolume (HV) and running time (RT). The results show that the scenario with fully flexible loads demonstrates notable improvements, with total cost reductions of 20.28%, 16.42%, 13.65%, and 17.43% for MOSFO, MOAHA, NSGA-II, and LLM, respectively. Additionally, carbon emissions decreased by 46.32%, 50.01%, 49.76%, and 49.15%, while renewable energy utilization increased by 1.38%, 22.41%, 25.23%, and 27.56%, compared to the scenario without flexible loads. The proposed LLM-MILP model demonstrates superior computational efficiency, particularly in terms of RT, compared to other bi-level optimization models and can achieve high levels of renewable energy utilization (95.791%), total system cost (933.37 $), and total system carbon emissions (1620.1 t). The seasonal analysis further emphasizes the robustness and adaptability of the optimization framework considering fully flexible loads under varying environmental conditions.