Abstract: Multiple integrated energy microgrids configured with shared storage can significantly improve system energy utilization and storage utilization efficiency. However, the system faces many challenges in actual operation, such as collaborative management of subjects, stochasticity of new energy output, power uncertainty of multiple energy loads, and privacy protection of each subject. To address the above problems, this paper proposes a two-stage robust multi-integrated energy microgrid-shared energy storage plant cooperative optimization operation strategy. First, the min-max-min two-stage robust optimization model is constructed; the first stage decides the amount of electrical energy interaction between each IEM and SES, and the second stage decides the scheduling plan within each IEM in the worst case and for the problem of the second stage which contains 0-1 integer variables that cannot be solved by KKT condition to turn the dyadic solution, according to which the solution method of the reconfiguration and decomposition-column constraints generation algorithm is proposed. Secondly, based on the Nash negotiation theory, the problem of maximizing the operational efficiency of the multi-IEM-SES system and the problem of maximizing the payment of electricity transactions are established. Finally, to protect the privacy of each IEM, the alternating direction multiplier method is used to solve the two problems in a distributed manner. Through simulation verification, the proposed strategy balances the system's robustness and economy and effectively protects each subject's privacy.