With recent technology advances and price drop, battery energy storage systems (BESSs) are considered as a promising storage technology in power systems. In this paper, a stochastic BESS planning model is introduced, which determines optimal capacity and durations of BESSs to co-locate utility-scale solar photovoltaic (PV) systems in a high-voltage power system under the uncertainties of renewable resources and electric load. The optimization model minimizing total costs aims to obtain at least 20% electric energy from renewable sources, while satisfying all the physical constraints. Furthermore, two-stage stochastic programming is applied to formulate mathematical optimization problem to find out optimal durations and capacity of BESSs. In scheduling BESSs, chronology needs to be considered to represent temporal changes of BESS states; therefore, a scenario generation method to generate random sample paths with 1-h time step is adopted to explicitly represent uncertainty and temporal changes. The proposed mathematical model is applied to a modified IEEE 300-bus system that comprises 300 electric buses and 411 transmission lines. Optimal BESS durations and capacity are compared when different numbers of scenarios are employed to see the sensitivity to the number of scenarios in the model, and “value of stochastic solution” (VSS) is calculated to verify the impacts of inclusion of stochastic parameters. The results show that the building costs and capacity of BESSs increase when the number of scenarios increases from 10 to 30. By inspecting VSSs, it is observed that an explicit representation of stochastic parameters affects the optimal value, and the impacts become larger when the larger number of scenarios are applied.