With the increasing integration of multi-energy microgrid (MEM) and shared energy storage station (SESS), the coordinated operation between MEM and energy storage systems becomes critical. To solve the problems of high operating costs in independent configuration of microgrid and high influence of renewable energy output uncertainty. This paper takes the SESS connecting multiple microgrids as the research object, and proposes a robust optimal scheduling method considering double uncertainty, so as to better achieve efficient energy utilization and promote sustainable development. First, in order to cope with the uncertainty challenge, a min-max-maxmin four-layer robust optimization model based on the worst-case scenario probability of multi-scenario data is formulated for the MEM system, considering the uncertainties of renewable energy generation (wind and photovoltaic) and scenario probability uncertainty on the basis of traditional two-stage robust optimization. The outer model solves the SESS capacity configuration problem, the middle layer finds the worst probability distribution value, and the inner model solves the problem of optimal operation of the MEM system. Second, a column and constraint generation algorithm with an alternating iteration strategy (C&CG-AIS) is intended to reduce the solution time by decoupling the subproblems. Finally, the rationality and validity of the proposed model are verified by analyzing an example. The results show that compared with personal energy storage station(PESS), constructed SESS improves energy storage utilization by 46.17 % and reduces demand response load by 42.31 %. Compared with the single uncertainty, the operating cost of the MEM system with double uncertainty was reduced by 19.72 %, while the SESS revenue was increased by 33.15 %. In addition, the operation optimization of the MEM system and the optimal capacity configuration of the SESS are realized. The results demonstrate that the proposed method can balance the robustness and economy of the system, SESS can effectively reduce user costs, save energy storage resources, and realize the mutual benefits of the microgrid side and the energy storage side.