This paper presents a combined framework for power distribution network expansion planning (DNEP) and energy storage systems (ESSs) allocation in active distribution networks (ADNs) hosting large amount of photovoltaic (PV) generations and loads. The proposed DNEP ensures the reliable operation of the targeted ADN with the objective of achieving its dispatchability while minimizing grid losses by determining the optimal grid expansion to connect new nodes, the reinforcement of existing lines, and the ESS allocation. The allocated ESSs compensate for the stochastic power flows caused by the stochastic loads and generation, allowing ADNs to follow a pre-defined power schedule at the grid connection point. The grid constraints are modeled by using a modified augmented relaxed optimal power flow (AR-OPF) model that convexifies the classical AC-OPF providing the global optimal and the exact solution of the OPF problem for radial networks. The DNEP problem’s complexity is handled by employing a sequential algorithm where new nodes are added one by one, following the priorities determined by the user. In each stage of the sequential planning, the Benders decomposition algorithm determines the optimal solution for investments and ADN operation iteratively. Moreover, the siting and sizing problems associated with the ESSs and line investment are solved separately to enhance the convergence speed. Simulations are conducted on a real 55-node Swiss ADN hosting sizeable stochastic photovoltaic generation.