The large amount of renewable energy sources (RESs) recently integrated within the electric power systems across the world poses new challenges for their operation. Among several viable solutions, energy storage systems are the most promising to increase reliability and flexibility. This paper proposes a novel topological and probabilistic approach to find the optimal capacity and siting of energy storage devices, in order to increase the system reliability and the hosting capacity of renewables. Wind and solar productions, generators availability, and real-time demand are modeled with proper distribution functions, and the yearly expected energy not supplied is estimated using a sequential Monte Carlo technique. Four siting policies are applied and compared to place the optimal storage capacity on eight grids with different topological characteristics. Power flows are linearized and the optimization of resources is formulated as a linear programming problem. The results show that large-scale batteries operated by the Transmission System Operator can significantly improve system reliability and exploitation of RESs. The presence of energy-hubs and small-world properties strongly increase the transmission effectiveness of weakly- and well-meshed grids. A siting policy based on the Power Transfer Distribution Factors matrix of the grid turns out to be particularly successful.