The installation of energy storage systems can mitigate the intensified vulnerability caused by the integration of large-scale distributed photovoltaic (PV) systems into the distribution network. Establishing a comprehensive distribution network vulnerability assessment system can effectively enhance the benefits of energy storage integration. The operational vulnerability of the distribution network is evaluated by considering PV integration and fluctuations in voltage and load, a comprehensive vulnerability index for the distribution network is established. A distribution network energy storage optimal allocation model is developed with vulnerability indicators，economic indicators and active power losses indicators as objective functions. The PV and load uncertainties are addressed using the K-means clustering algorithm, and the model is solved with an improved multiple objective differential evolution algorithm (IMODE). By initializing the population with chaotic sequences, adaptive mutation and crossover factors are introduced, along with optimizations to the mutation operator strategy. Simulation verification is conducted on a distribution network case in a county of Gansu Province. The proposed strategy effectively ensures the safe operation of the distribution network while considering economic factors, reducing network vulnerability by 18.9 % and active power loss by 23.9 %. The proposed vulnerability indexes and model can quantitatively assess distribution network vulnerability and reflect the improvement effects of energy storage integration, providing technical references for the installation and operation of energy storage systems.