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In this paper, a detailed mathematical model of the diabatic compressed air energy storage (CAES) system and a simplified version are proposed, considering independent generators/motors as interfaces with the grid. The models can be used for power system steady-state and dynamic analyses. The models include those of the compressor, synchronous motor, cavern, turbine, synchronous generator, and associated controls. The configuration and parameters of the proposed models are based on the existing bulk CAES facilities of Huntorf, Germany. The models and performance of the CAES system are first evaluated with step responses, and then examined when providing frequency regulation in a test power system with high penetration of wind generation, comparing them with existing models of CAES systems. The simulation results confirm that the dynamic responses of the detailed and simplified CAES models are similar, and demonstrate that the simultaneous charging and discharging can significantly contribute to reduce the frequency deviation of the system from the variability of the wind farm power. [ABSTRACT FROM AUTHOR]