In this gradueate thesis, hydropower plants in general are discussed, and also the basic parts and divisions of hydropower plants. The types and kinds of hydro turbines are described, and in particular the speed of control in hydro power plants and the operation of the hydro power plant in the island mode of operation are described. The main problem that has been processed is the stabilization of the operation of the small hydroelectric power plant Batu Balai in the island mode of operation. In order to ensure stable operation of the hydropower plant in island mode, hybrid energy storage systems with batteries and supercapacitors were used. The basic characteristics and configuration of the battery energy storage system are described. Also, the types and characteristics of batteries and supercapacitors are described. The entire model for the analysis of the operation of the small hydroelectric power plant Batu Balai in the island mode, with all technical parameters, was made and simulated in the Matlab/Simulink software package. In the hydropower model with generator production and consumption curve, a hybrid energy storage system with supercapacitors and batteries is integrated to ensure stable operation of the hydropower plant. Models were made with and without frequency regulation and simulations of operation were processed in order to obtain the optimal amount of batteries, while satisfying that the frequency of the system remained within the limits prescribed for the island mode of operation. The influence of the turbine opening / closing time, and the influence of the moment of inertia of the generator and the turbine on the frequency of the system is also shown. Finally, the results were analyzed and the overall conclusion of the analysis was made.