Energy storage systems are integral to modern power systems for integrating renewable energy sources. This study focuses on a hybrid energy storage system integrated into a hydro power plant. The hybrid system comprises a battery and supercapacitor and cooperates with the hydropower plant in providing primary and secondary frequency control through an ad hoc control system. The control system has two main objectives. On the one hand, it distributes the frequency control effort between the hydropower units, the battery and the supercapacitor, and on the other hand, tries to keep the state of charge (SOC) of the battery and supercapacitors within pre-specified bounds. When the SOC of the energy storage units reaches the predefined upper or lower bounds, the hydro power plant intervenes to restore the SOC to within such bounds. Two symmetrical SOC bands around a central SOC value are defined for each, the battery and supercapacitor, for this purpose. The main goal of this paper is the definition of the SOC control bands and central value to reduce battery aging and wear and tear on different components of the hydro power plant, while providing a quality frequency control action. Specifically, the strategy addresses reducing penstock stress, limiting the distance travelled by the wicket gates, and minimizing the direction changes in the wicket gate movement. Simulation models of the hydro power plant, battery, and supercapacitor were developed to validate the proposed control system. The results highlight the effectiveness of the strategy in achieving acceptable frequency control performance goals while reducing wear and tear on both the energy storage components and the hydro power plant infrastructure.