For the optimal configuration of storage devices for energy-connected microgrids, this paper constructs a configuration model of a multi-energy storage system considering cross-season gas storage, which proposes a capacity configuration method including electricity storage equipment, heat storage equipment, gas storage equipment and P2G. The wind and photovoltaic output are preprocessed by FCM and divided into multiple probability scenes to reduce the computational complexity. In this paper, the electric-gas-heat-cold balance, unit climbing constraint, energy storage constraint and natural gas supply restriction are comprehensively considered. The annual economic efficiency is the optimization goal, and the cross-season gas storage mode and the non-gas storage mode are compared and analyzed. This paper also discusses the impact of natural gas costs on the optimal configuration of system energy storage. The results show that the multi-energy storage system considering cross-season gas storage is more economical, which can effectively alleviate the supply pressure in winter, and promote non-winter new energy consumption.