Compressed air energy storage (CAES) system is one of the highly efficient and low capital cost energy storage technologies, which is used on a large scale. However, due to multiple operational and technical limitations, the CAES operation should be incorporated with thermodynamic characteristics. Therefore, in this paper, novel thermodynamic modeling of CAES facility integrated with the hybrid thermal, wind, and photovoltaic (PV) farms to participate in energy and reserve markets is investigated. Considering the thermodynamic characteristics makes the proposed scheduling more realistic, while imposes multiple constraints on the optimal operation of the hybrid system. The operation of the CAES facility during charging and discharging modes, considering thermodynamic characteristics are analyzed simultaneously, and the state of charge of the cavern is calculated for both modes. In addition to taking into account the thermodynamic characteristics, the recovery cycle capability is embedded for the CAES facility to recover heat from the turbine in the preheater results in increased turbine efficiency. The proposed scheduling of the hybrid system is exposed by high-level uncertainty caused by energy and reserve market prices, as well as wind and PV farms power fluctuation. Hence, the scenario-based stochastic approach is applied based on real historical data of the KHAF station in IRAN to handle existing uncertainties. Numerical results are provided for different cases. The major conclusions of the numerical results show the effectiveness of the recovery cycle from profit improvement and burned fuel reduction up to 11.36% and 11.33%, respectively, while the thermodynamical constraints in the CAES performance make the realistic model, compared with the conventional CAES.