Abstract: Traditional distribution networks are gradually evolving into flexible interconnected distribution networks, and intelligent soft open point (SOP) and energy storage, as representative devices in the flexible distribution network, can improve the consumption capacity of distributed photovoltaic (PV) generation. Therefore, this study proposes a distributed PV hosting capacity interval evaluation method that takes into account the uncertainty of energy storage and SOP operation as well as unplanned islanding operation. Firstly, for the SOP integrated with energy storage (E-SOP) structure, an E-SOP model is established and the uncertainty of its unplanned islanding is described. Subsequently, the deterministic model and the double-layer robust optimization model are employed to describe the most optimistic and pessimistic absorption capacities, respectively, and the distributed PV absorption capacity interval evaluation model is constructed. Deterministic models constitute linear programming problems that can be solved directly using solvers. The two-layer robust optimization model is transformed into a mixed-integer linear programming problem using the Karush-Kuhn-Tucker (KKT) optimality condition. Finally, the simulation results obtained from the IEEE 123-bus system verify the effectiveness of the proposed method.