A Bi-level Model for the Resilient Operation of Distribution Systems using a Matheuristic Nested Decomposition

Matheuristic is a hybrid method that combines metaheuristics with classical mathematical methods to benefit from their respective features. This paper presents a novel bi-level matheuristic nested decomposition approach for the resilience optimization of distribution systems. The proposed methodology uses a dedicated bioinspired technique based on artificial immune systems and a classical deterministic optimization method combined in a matheuristic nested decomposition approach. The model is cast as a mixed-integer nonlinear programming problem, aiming to maximize the load supplied through optimal feeder reconfiguration and optimal power flow, for example, after a lack of generation event caused by an extreme event. One of the main features of the proposed technique is that the metaheuristic parameters are not user-defined; instead, they are set automatically based on the system's characteristics. Results obtained from three different strategies are assessed, highlighting the potential of the proposed methodology as the size of the problem increases compared to a metaheuristic algorithm and classical mathematical programming.