Large-scale grid-connection of distributed power helps to achieve the goal of "dual carbon", but also exacerbates the vulnerability of active distribution network. The access of energy storage device can effectively support the vulnerable link of power grid. Based on the Gini coefficient and Theil entropy theory, the uniformity of power transmission in the topology of active distribution network and the equilibrium degree of voltage shock distribution in the operation state were evaluated respectively. The comprehensive vulnerability index of each node was constructed from the structure and state, and the installation scope of distributed energy storage was defined. In this paper, a double-layer optimization scheme of distributed energy storage with constant volume is proposed. In the outer layer, the optimal economic benefit is taken as the objective, the improvement degree of energy storage to the vulnerability of distribution network is considered in the constraint conditions, and the energy storage capacity is solved by particle swarm optimization algorithm. The inner layer aims at the optimal effect of peak shaving and valley filling. Based on the constant power charge and discharge strategy of energy storage, the optimal charge and discharge strategy is formulated for different capacities to realize the optimization of energy storage charge and discharge. The calculation results of IEEE 33-node system show that the proposed energy storage configuration method can effectively improve the vulnerability of active distribution network and has economic advantages.