A Stackelberg game-based multi-time scale optimization for hybrid power ship and port

Multi-energy ships are considered as a promising alternative for addressing marine pollution issues. However, the effects of source-load prediction errors on ship energy systems under multi-time scale have been rarely studied. To address this, a hybrid power ship that integrates a diesel generator, photovoltaic cells, hydrogen fuel cell and energy storage is established to meet the electrical, thermal, and cooling demands. Furthermore, to enhance energy efficiency and multi-energy interaction, equipment for electrical-to-thermal, electrical-to-cooling, and thermal-to-cooling conversions is integrated into the hybrid power ship. Then, a multi-time scale optimization model considering multi-energy complementary plan is proposed. In the day-ahead scheduling, a Stackelberg game model, in which the leader is responsible for setting electricity prices for cold-ironing and the energy management of the ship is determined by the follower, is established. Theoretical analysis regarding the existence and uniqueness of the Stackelberg equilibrium point is provided. Accordingly, a distributed iterative algorithm with faster convergence speed is proposed to achieve Stackelberg equilibrium. Subsequently, according to the response time of energy adjustment, the results of thermal/cooling and electricity energies are refined by rolling optimization in intra-day and real-time stages, respectively, to reduce the prediction errors from photovoltaic cells and loads. Comparison results with an existing distributed iterative algorithm demonstrate that the proposed method achieves faster convergence. In addition, the multi-time scale optimization model is conducive to enhance the reliability of ship operations, mitigating the effects of prediction errors in supply and demand.