Energy storage systems can improve the uncertainty and variability related to renewable energy sources such as wind and solar create in power systems. Aside from applications such as frequency regulation, time-based arbitrage, or the provision of the reserve, where the placement of storage devices is not particularly significant, distributed storage could also be used to improve congestions in the distribution networks. In such cases, the optimal placement of this distributed storage is vital for making a cost-effective investment. Furthermore, the now reached massive spread of distributed renewable energy resources in distribution systems, intrinsically uncertain and non-programmable, together with the new trends in the electric demand, often unpredictable, require a paradigm change in grid planning for properly lead with the uncertainty sources and the distribution system operators (DSO) should learn to support such change. This paper considers the DSO perspective by proposing a methodology for energy storage placement in the distribution networks in which robust optimization accommodates system uncertainty. The proposed method calls for the use of a multi-period convex AC-optimal power flow (AC-OPF), ensuring a reliable planning solution. Wind, photovoltaic (PV), and load uncertainties are modeled as symmetric and bounded variables with the flexibility to modulate the robustness of the model. A case study based on real distribution network information allows the illustration and discussion of the properties of the model. An important observation is that the method enables the system operator to integrate energy storage devices by fine-tuning the level of robustness it willing to consider, and that is incremental with the level of protection. However, the algorithm grows more complex as the system robustness increases and, thus, it requires higher computational effort.