The ever-growing diffusion of renewables as electrical generation sources is forcing the electrical power system to face new and challenging regulation problems to preserve grid stability. Among these, the primary control reserve is reckoned to be one of the most important issues, since the introduction of generators based on renewable energies and interconnected through static converters, if relieved from the primary reserve contribution, reduces both the system inertia and the available power reserve in case of network events involving frequency perturbations. In this scenario, renewable plants such as hydroelectric run-of-river generators could be required to provide the primary control reserve ancillary service. In this paper, the integration between a multi-unit run-of-river power plant and a lithium-ion based battery storage system is investigated, suitably accounting for the ancillary service characteristics as required by present grid codes. The storage system is studied in terms of maximum economic profitability, taking into account its operating constraints. Dynamic simulations are carried out within the DIgSILENT PowerFactory 2016 software environment in order to analyse the plant response in case of network frequency contingencies, comparing the pure hydroelectric plant with the hybrid one, in which the primary reserve is partially or completely supplied by the storage system. Results confirm that the battery storage system response to frequency perturbations is clearly faster and more accurate during the transient phase compared to a traditional plant, since time delays due to hydraulic and mechanical regulations are overpassed. A case study, based on data from an existing hydropower plant and referring to the Italian context in terms of operational constraints and ancillary service remuneration, is presented.