Compressed air energy storage (CAES) systems have energy interfaces for multiple forms of energy, such as cold, heat, and electricity, and can therefore be combined with combined cooling, heating, and power (CCHP) microgrid applications, thus allowing both systems to fully utilise their respective advantages. However, the principle of multi energy coupling of CAES itself is complex, and the combination with CCHP microgrid makes the system architecture and technical implementation of the new system produce a lot of technical problems. Therefore, this report presents control strategies for CAES connected to the CCHP microgrid. Thus, the stable operation of the system can be achieved, and the supporting theory and practical application guidance can be provided to promote the development of CAES and combined CCHP microgrid. Firstly, the basic structure of CAES and CCHP microgrid is described, and thermodynamic models of key components are established. In the meantime, analyze the operation mechanism of internal combustion engine generator, wind turbine, photovoltaic and other energy supply components in CCHP microgrid system. The mathematical models suitable for optimal control are established. Through the above analysis model, it can provide a strong basis system characteristic analysis and optimal control. Secondly, the efficiency of the CAES system, the state and power of the storage, and the generation efficiency of the internal combustion generator are analysed. Finally, a two-level optimisation model is proposed, where the upper level is used to solve the optimal storage pressure initial value for the CAES system cycle. According to the characteristics of the compressed air energy storage system, NSGA-II is used to solve the output scheduling optimisation problem in the lower level with economy, environmental protection and energy saving as the unobjective under the condition of determining the optimal storage initial value. The simulation results show that the proposed control strategy is reasonable and feasible.