<p>To cope with complex operating conditions and emergencies efficiently and ensure stable system operation, this paper proposes a distributed compressed air energy storage (D-CAES) primary frequency regulation control strategy based on fuzzy adaptive command decomposition. By integrating dynamic models of the compressor, turbine, heat exchanger, and air storage unit, a comprehensive dynamic model of the D-CAES system is established. A variable-domain adaptive fuzzy PID controller is employed to regulate the air mass flow errors and their rates of change for both the compressor and turbine, as well as the grid frequency deviation. Based on the input variables, the controller generates a frequency regulation command that can flexibly respond to various complex working conditions and emergencies, effectively avoiding intermediate delays and ensuring system stability. The primary frequency modulation command is decomposed into a base control command, a high-frequency component, and a low-frequency component through a fuzzy adaptive adjustment of the filtering time constant. These components are used to adjust the output power of the turbine and compressor, respectively, enabling rapid compensation of instantaneous grid frequency deviations and thereby accomplishing primary frequency regulation of the D-CAES system. Experimental results demonstrate that under different operating conditions, the D-CAES dynamic model established in this study exhibits excellent dynamic response characteristics, effectively achieves primary frequency regulation control, and significantly reduces grid frequency deviation.</p>