Re-electrification is an emerging development trend in dealing with environmental pollution and climate change with re-electrification of final energy consumption, such as electrification of oil, coal, transport, etc. This will greatly increase the share of electricity in the final energy consumption, increasing the demand of distribution networks, especially urban networks, and pose great challenges to the reliability and safe operation of the distribution networks. Energy storage is an effective means to deal with these new challenges, ensuring security and reliability of the system. This paper proposes a new model predictive control (MPC) method for cryonic air energy storage (LAES) and compressed air energy storage (CAES) systems. Firstly, a distributed installation framework for LAES and CAES system based on LAES energy hub is proposed, then, a model predictive control method combined with hierarchical optimization that meet the requirements of network security and LAES and CAES system operations. Finally, the method is tested and validated using the modified IEEE 30 test system.