The current paper presents an energy storage system that stores the excessive energy, provided by a hybrid system of renewable energy sources, in the form of compressed air and thermal heat. Using energy storage systems together with renewable energy sources represents a major challenge that could ensure the transition to a viable economic future and a decarbonized economy. Thermodynamic calculations are conducted to investigate the performance of such systems by using Matlab simulation tools. The results indicate the values of primary and global efficiencies for various operating scenarios for the energy storage systems which use compressed air as medium storage, and shows that these could be very effective systems, proving the possibility to supply to the final user three types of energy: electricity, heat and cold function of his needs.