This paper proposes a distributed coordinated optimization method for multi?microgrid systems based on the Alternating Direction Method of Multipliers (ADMM). The proposed model comprehensively accounts for generation costs, energy storage operation, and inter?microgrid interactions, while employing second?order cone relaxation techniques to address nonlinear power flow constraints. By optimizing the ADMM iteration process and parameter selection, the method significantly improves computational efficiency while protecting data privacy through its distributed architecture. Case studies demonstrate that the method converges within only five iterations, achieves a 76.7% improvement in computational efficiency compared with centralized optimization, and maintains a solution accuracy within a 0.34% deviation from the global optimum. Compared to linear programming methods, the ADMM enhances voltage regulation performance by 40.0% and reduces line losses by 15.5%. The method exhibits excellent scalability with computational complexity increasing linearly with the number of microgrids, is applicable to various network topologies, and requires sharing only boundary interaction information, thus providing effective technical support for multi?microgrid coordination optimization.