The contribution of the renewable energy sources in the electricity generation mix is greatly increasing. Nonetheless, the intermittence of these sources breaks the balance between supply and demand for electricity. Thus, the integration of the energy storage technologies with the electrical grid is becoming crucial to restore this balance. Hence, this paper discusses the modeling of a novel isobaric adiabatic compressed air energy storage (IA-CAES) system. This system is characterized by the recovery of the compression heat and the storage of the compressed air under fixed pressure in hydro-pneumatic tanks. This allows the improvement of the efficiency of the storage system. A steady state model is then developed to perform energy and exergy analyses of the IA-CAES system. An exergoeconomic model is also carried out in order to optimize the cost-effectiveness of the storage system by using a genetic algorithm. The system efficiency is 55.1% in the base case, it is improved to 56.6% after optimization with a decrease in the capital investment by 5.6%. Global sensitivity analyses are finally carried out to estimate the effects of some key parameters on the system's cost-effectiveness. They show that the system is mostly influenced by the isentropic efficiency of the air turbines.