## 1 Introduction  
With the steady growth of peak load demand in recent years and the large-scale deployment of intermittent renewable energy resources, the fluctuation levels and uncertainties of power loads have significantly increased [1, 2]. Moreover, the increasing integration of distributed photovoltaic (PV) systems into distribution networks (DNs) has overwhelmed the power system's accommodation capability, resulting in resource waste such as PV curtailment [3]. Under such circumstances, relying on traditional regulation methods has proven insufficient to ensure the secure, stable, and economical operation of power systems [4]. On the other hand, abundant distributed energy storage (DES) resources within DNs can be utilized to provide flexible regulation services, helping to alleviate the pressure on power grids caused by the integration of renewable energy generation and rapid load growth [5; 6; 7]. Compared with traditional centralized energy storage stations, DES has advantages such as a smaller footprint and lower investment costs, allowing it to be flexibly installed at various locations on the user side [8]. However, the small power and limited capacity of individual DES systems make them unsuitable for direct participation in grid regulation, leading to their regulation potential being underutilized [9]. In contrast, aggregated DES clusters offer greater flexibility and controllable potential for regulation [10]. Therefore, it is necessary to manage DES aggregation, enabling it to participate as a controllable resource in the optimal operation of DNs. The aggregation of feasible regions for DES refers to the process where the wide-area DES resources are aggregated into an overall feasible region, based on the satisfaction of each individual resource's feasible region, through certain aggregation methods. These resources are then managed and scheduled in a unified manner [11]. The feasible region aggregation is mathematically represented as the addition operation in Euclidean space [12], specifically the Minkowski Sum. However, the computation of the Minkowski Sum for two arbitrary polygons is categorized as a nondeterministic polynomial (NP) problem, for which no efficient solution algorithm currently exists [13]. As a result, many studies have focused on developing approximate feasible domain models with specific rules to simplify the aggregation process. In Ref. [14], convex polyhedra were used to describe the feasible regions of resources, and an approximate method was proposed to simplify the feasible region aggregation of energy storage. In Ref. [15], an inner-approximation approach integrating constrained spaces was adopted, where the constraint spaces of all individuals within the cluster were integrated before participating in power system operations. In Ref. [16], a mathematical model of the exact aggregated feasible region for distributed resources was derived, and a \(k\) -order approximation model was used to compute a high-accuracy enclosing model for the feasible region aggregation. In Ref. [17], high-dimensional ellipsoids were employed to approximate the feasible regions of distributed resources, ensuring the aggregation optimality and decomposition feasibility. However, outer-approximation methods among these studies may lead to infeasibility during practical scheduling, while inner-approximation methods often sacrifice significant resource flexibility. In the context of energy storage systems (ESS) participating in the optimal operation of DNs, a resilient microgrid energy management model, which includes diesel generators, energy storage, and load scheduling, is constructed in Ref. [18], and a multi-stage constraint-handling multi-objective optimization method tailored for resilient microgrid energy management is proposed. In Ref. [19], a day-ahead scheduling plan was formulated by integrating the multi-time scale characteristics of ESS and various demand response resources on the load side.