With the rapid development of the digital new infrastructure industry, the energy demand for communication base stations in smart grid systems is escalating daily. The country is vigorously promoting the communication energy storage industry. However, the energy storage capacity of base stations is limited and widely distributed, making it difficult to effectively participate in power grid auxiliary services by only implementing the centralized control of base stations. Aiming at this issue, an interactive hybrid control mode between energy storage and the power system under the base station sleep control strategy is delved into in this paper. Grounded in the spatiotemporal traits of chemical energy storage and thermal energy storage, a virtual battery model for base stations is established and the scheduling potential of battery clusters in multiple scenarios is explored. Then, based on the time of use electricity price and user fitness indicators, with the maximum transmission signal and minimum operating cost as objective functions, a decentralized control device is used to locally and quickly regulate the communication system. Furthermore, a multi-objective joint peak shaving model for base stations is established, centrally controlling the energy storage system of the base station through a virtual battery management system. Finally, a simulation analysis was conducted on data from different types of base stations in the region, designing two distinct scheduling schemes for four regional categories. The analysis results demonstrate that the proposed model can effectively reduce the power consumption of base stations while mitigating the fluctuation of the power grid load.