Optimal basis number in S1.

Integrated Community Energy Systems (ICES) aim to optimize energy efficiency through the integration of diverse energy resources, encompassing electricity, heating systems, and natural gas. However, the rapid integration of renewable energy sources and the rising energy demands pose significant challenges in evaluating the reliability of ICES. This difficulty arises from the need to evaluate numerous system states to determine the minimal load curtailment. To address this issue, we propose a method based on optimal bases to enhance computational efficiency in the reliability assessments of ICES. The optimal load curtailment model is developed to facilitate system state evaluation, accounting for variations in load levels and renewable generation. Subsequently, the optimal basis is employed to accelerate this evaluation process. By matching most system states with their corresponding optimal basis based on the optimality criterion, efficient computation of optimal load curtailment is achieved through matrix multiplications, eliminating the need for time-consuming optimization algorithms. The efficacy of the optimal basis-based method is validated through comprehensive case studies.