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[Objective] Distributed energy storages are widely applied in microgrid due to its capability to effectively suppress fluctuations in wind and solar power outputs and improve the consumption rates of renewable energies. A consensus-based vector control method is usually adopted by the distributed energy storage grid-connected system， which has limited stability. The system is prone to instability when a significant uncertainty disturbance or communication failure occur in the microgrid. To address this issue and aiming at the nonlinear and strong coupling characteristics of distributed energy storage， the global energy function is constructed from the perspective of energy. [Methods] A port-controlled Hamiltonian model of energy storage grid-connected converter is established to accurately capture the nonlinear relationship between state and control variables and avoid deviations caused by local linearization. A hierarchical control approach is designed. In the second lever， a passivity-based controller is proposed and the trajectory tracking consensus errors are embed into the control law. The fast synchronized tracking of the desired trajectories of voltage and frequency are obtained with minimal communication. It leads to achieve global asymptotic stability by minimizing the global energy function at the equilibrium point. In the primary level， a state of charge （SOC） balance control method for distributed energy storages based on dynamic event triggering mechanism is applied. The damping injection demand of the passivity-consensus-based control is adjusted by energy storage SoC errors of adjacent nodes in real time. The tracking speed of the grid-connected voltage amplitude and frequency desired trajectory is improved. [Results] It is shown by the experimental results based on dSPACE that when load mutation， parameter perturbation and communication failure occur in microgrid， the proposed method achieves a short settling time of approximately 3 seconds. In both discharging and charging modes， the overshoot and steady-state error remain below 1% and 1 W， respectively. [Conclusions] The method enables stable coordinated control of distributed energy storage， accurate power sharing， and dynamic SoC balancing. The proposed method exhibits superior dynamic performance， excellent synchronization， and a wide stability margin.