This paper proposes a two-stage planning model for soft open point (SOP) and energy storage system (ESS) that considers the cost of faults in response to the current issue of SOP and ESS systems not considering the impact of SOP access on load transfer in the event of a fault in the distribution network. Firstly, considering the uncertainty of “PV-load”, typical scenarios of PV and load are constructed based on the clustering algorithm. Secondly, aiming at the economic performance of the distribution network and the capacity of PV access, a two-stage optimization model is established for the joint integration of SOP and ESS into the distribution network (normal and fault operation) under typical scenarios. The model is solved by using the second-order cone programming algorithm and steady-state genetic algorithm (SOCP-SSGA). Stage one involves planning for the integration capacity and location of SOP and ESS into the distribution network under each scenario within a period based on SOCP with the goal of minimizing economic costs. In stage two, the PV access capacity of the distribution network is optimized using SSGA with the goal of enhancing the PV accommodation capability. Finally, verification and analysis are conducted on an improved IEEE33 node system. The results show that when the system optimizes access to a group of SOP and ESS, the total economic cost is reduced by RMB 61,729 compared to random access, and the accessible PV capacity is increased by 0.5278 MW. Moreover, optimizing access to two sets of SOP and ESS can further reduce the total economic cost by RMB 107,048 compared to the optimized access group and increase accessible PV capacity by 1.5751 MW. Therefore, the proposed plan for SOP and ESS planning in this paper can significantly reduce the economic cost of distribution networks, enhance the absorption capacity of distributed photovoltaics, improve the voltage level of power grid operation, and, thereby, improve the economic and reliability of distribution network operation.