Effective energy storage technologies represent one of the key elements to solving the growing challenges of electrical energy supply of the 21st century. Several energy storage systems are available, from ones that are technologically mature to others still at a research stage. Each technology has its inherent limitations that make its use economically or practically feasible only for specific applications. The present paper aims at integrating hydrogen generation into compressed air energy storage systems to avoid natural gas combustion or thermal energy storage. A proper design of such a hybrid storage system could provide high roundtrip efficiencies together with enhanced flexibility thanks to the possibility of providing additional energy outputs (heat, cooling, and hydrogen as a fuel), in a distributed energy storage framework. Such a system could be directly connected to the power grid at the distribution level to reduce power and energy intermittence problems related to renewable energy generation. Similarly, it could be located close to the user (e.g., office buildings, commercial centers, industrial plants, hospitals, etc.). Finally, it could be integrated in decentralized energy generation systems to reduce the peak electricity demand charges and energy costs, to increase power generation efficiency, to enhance the security of electrical energy supply, and to facilitate the market penetration of small renewable energy systems. Different configurations have been investigated (simple hybrid storage system, regenerate system, multistage system) demonstrating the compressed air and hydrogen storage systems effectiveness in improving energy source flexibility and efficiency, and possibly in reducing the costs of energy supply. Round-trip efficiency up to 65% can be easily reached. The analysis is conducted through a mixed theoretical-numerical approach, which allows the definition of the most relevant physical parameters affecting the system performance.