A two-stage energy management strategy for hybrid ship power systems considering the dynamic output characteristics of batteries

To address the issues of multi-energy coordination and optimal allocation in hybrid ships, a two-stage energy management algorithm that considers the dynamic output characteristics of batteries is proposed. First, an electro-thermal coupled model of a lithium-ion battery was constructed based on a combined data- and model-driven approach. This model could describe the battery's dynamic output characteristics, including voltage, temperature, and state of power, and its accuracy was validated through experiments. A two-stage energy management strategy combining mixed-integer nonlinear programming (MINLP) and model predictive control (MPC) was then developed. To minimise equivalent fuel consumption, an MINLP model was established considering the dynamic output characteristics of batteries, an adjustable battery equivalent fuel factor and a series of constraints. By solving the global optimal problem within the prediction horizon, the optimal solution was obtained and subsequently used as a reference trajectory for MPC, thereby achieving optimised real-time power allocation. Finally, a case study of a hybrid diesel–electric tugboat was conducted to verify the feasibility and effectiveness of the proposed strategy, and a robustness analysis was performed. The simulation results show that the two-stage energy management strategy can achieve optimisation outcomes similar to those of offline global optimisation, with a deviation of no more than 0.456 %. Additionally, the proposed strategy demonstrates good performance in balancing the battery output and smoothing power fluctuations of the generator set. Moreover, under uncertain load conditions, the strategy maintains its adaptability and optimisation effectiveness.