Abstract：The increasing electrification of container ports has strengthened the operational coupling between automated quay cranes (AQCs) and port microgrids, particularly under high penetration of renewable energy. The large and rapidly fluctuating power demands of multiple AQCs, combined with highly variable wind and photovoltaic generation, impose stringent requirements on system flexibility. To address the challenges of instantaneous multi-AQC power aggregation, renewable-generation uncertainty, and lifetime degradation of large-scale energy storage, this paper develops a two-stage flexible energy management strategy for port microgrids. The proposed framework integrates a refined velocity-power coupling model for AQCs and a linearized healthy-operation-region model for energy storage, enabling coordinated logistics execution and energy scheduling, reduced peak load, and enhanced renewable-energy utilization. The methodology begins with the derivation of a physics-based dynamic model for six standard AQC movements: hoisting, trolley travel, and lowering under both loaded and unloaded conditions, each following a trapezoidal velocity profile. Analytical relationships among velocity, acceleration, displacement, and instantaneous power are established, capturing the second-level power variations. Based on this model, controllable operating velocities and adjustable start sequences are formulated to exploit the operational flexibility of individual AQCs. A coordinated de-peaking mechanism is then introduced to prevent simultaneous high-power actions across multiple AQCs. By identifying overlapping movement intervals using binary variables and imposing upper bounds on aggregated crane power, the mechanism effectively mitigates peak-power surges in multi-AQC scenarios. Meanwhile, to ensure the long-term reliability of the storage system under frequent cycling, a linear healthy operational region model is developed. Through hyperspace projection of the nonlinear lifetime surface defined over average state of charge (SoCmean) and maximum depth of discharge (DoDmax), followed by geometric convex approximation, the original nonlinear constraints are transformed into a tractable linear form. This enables the battery system to participate in second-level regulation while remaining within a safe degradation boundary. A two-stage scheduling architecture is built on these components. In the day-ahead stage, hourly decisions on AQC allocation, container-handling quantities, grid purchases, and renewable-energy utilization are optimized under the linearized storage-health constraints. In the intra-day stage, a rolling optimization with a 1-hour window is performed, during which second-level AQC power trajectories are reconstructed from optimized velocity profiles to accommodate deviations in actual renewable generation. The energy storage system and AQC operation are jointly coordinated to absorb forecast errors while ensuring timely completion of logistical tasks. Case studies based on operational data from a U.S. port verify the effectiveness of the proposed framework. Compared with conventional strategies, the method reduces second-level peak load by 33.61%, increases renewable-energy utilization by 15.12%, and extends battery lifetime by 19.88%. The coordinated de-peaking mechanism effectively prevents overlapping high-power stages among cranes, producing a smoother load profile and reducing contracted transformer capacity requirements. The linearized storage-health model constrains deep cycling and maintains SoC trajectories within the safe operating region throughout both scheduling stages. Under conditions with large forecast deviations, dynamically adjusted AQC velocities provide additional demand-side flexibility, enabling full renewable absorption without jeopardizing operational deadlines. Overall, the study establishes an integrated logistics-energy co-optimization framework that combines detailed electromechanical AQC modeling at the second scale, coordinated multi-crane scheduling, and health-aware energy storage operation. The results demonstrate its capability to enhance microgrid flexibility, suppress peak load, and support renewable-rich green port operations.
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2026, Vol. 41 
