Vulnerability-Driven Multi-Objective Energy Storage Planning Using Enhanced Beluga Whale Optimization for Resilient Distribution Networks

The large-scale integration of distributed photovoltaics (DPV) and their inherent uncertainties have significantly increased the operational risks of distribution networks. Moreover, frequent outages caused by extreme events further impose substantial losses on these networks, highlighting the urgent need to enhance their disaster resilience and load-supply capabilities. To address these challenges, this paper proposes an energy storage allocation method that simultaneously considers economic performance and comprehensive vulnerability. First, a vulnerability assessment framework for distribution networks is established from both pre-disaster and post-disaster perspectives. In the pre-disaster stage, an improved electrical betweenness index, voltage deviation index, and network-balance index are employed to identify weak lines and nodes. In the post-disaster stage, based on the identified weak components, two types of scenarios, namely random line failures and worst-case failures, are constructed to emulate extreme events, and an enhanced network supply efficiency index is developed to quantitatively evaluate the network’s recovery capability. Subsequently, a multi-objective optimal allocation model for energy storage is formulated with economic cost and comprehensive vulnerability as objective functions, and an Enhanced Beluga Whale Optimization algorithm is adopted to obtain the optimal siting and sizing of energy storage systems. Case studies on an improved IEEE 33-bus distribution system show that, compared with the no-ESS scheme, the proposed plan yields about a 66.4% reduction in network loss cost, around 22% improvement in average voltage deviation, and a roughly 10% reduction in the comprehensive vulnerability index under normal operation. Under random and targeted line outage scenarios, the proposed scheme also achieves the highest area under curve and average network effectiveness indices and the lowest performance volatility among the benchmark strategies. These results demonstrate that, for the tested IEEE 33-bus system, the vulnerability-driven ESS planning framework can markedly enhance both economic efficiency and resilience to extreme events.