Berth allocation and energy scheduling for all-electric ships in seaport microgrid: A Stackelberg game approach

The rapid development of all-electric ships (AESs) poses significant challenges to the coordinated optimization of port berth allocation and seaport microgrid (SMG) energy dispatch. This paper proposes a two-stage collaborative decision-making framework to enhance port operational efficiency while balancing the interests of the seaport microgrid operator (SMGO) and the electric ships operating company (ESOC). In the first stage, the SMGO formulates the optimal berth allocation strategy by considering AESs' berthing schedules, energy demands, and berth-specific energy transmission constraints, with the objective of minimizing waiting times and departure delays. In the second stage, we develop a two-layer energy scheduling model based on a Stackelberg game, where the SMGO acts as the leader to optimize local energy resources and set energy and compensation prices, while the ESOC, as the follower, determines AESs’ charging/discharging strategies and adjusts flexible load demands. By integrating the Karush-Kuhn-Tucker (KKT) conditions, strong duality theory, and the Big-M method, the original two-layer model is reformulated into a single-layer mixed-integer linear programming (MILP) problem. Numerical case studies demonstrate that the proposed joint optimization model achieves a balanced trade-off between the SMGO and ESOC interests while improving port operational efficiency. The framework serves as a valuable reference for designing future port management strategies and dynamic pricing mechanisms.