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Article

Two-Stage Energy Management for Hydrogen-Powered Ships: Integrating Dynamic Empirical Probabilistic Load Forecasting and Model Predictive Control

School of Electrical Engineering, Shandong University, Jinan 250061, China
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Author to whom correspondence should be addressed.
Energies 2026, 19(14), 3310; https://doi.org/10.3390/en19143310
Submission received: 29 May 2026 / Revised: 5 July 2026 / Accepted: 9 July 2026 / Published: 14 July 2026

Abstract

With the advancement of global energy conservation and emission reduction, hydrogen-powered ships (HPSs) have received great attention. However, the current drainage volume of HPSs is generally small, and its operating load fluctuates greatly due to the influence of hydrological and meteorological conditions in the waterway. Therefore, a reasonable energy management strategy (EMS) is needed to allocate the output of hydrogen fuel cells (HFCs) and lithium batteries (LBs). This article proposes a two-stage EMS framework for HPSs based on dynamic empirical modeling and model predictive control (DEM-MPC) to achieve optimal operational energy efficiency of the HFC-LB energy supply system. Firstly, a DEM probabilistic load forecasting (PLF) model was established by combining the operational status data of an HPS system with the meteorological data of waterway water level. The DEM model was constructed using delay coordinate embedding (DCE) and nearest neighbor prediction (NNP) methods to obtain future multi-step PLF sequences as important reference information for the EMS. Subsequently, the PLF sequence is used as input for MPC to optimize the output allocation of the EMS. In the first stage of MPC, the efficiency of HFCs and LBs is optimized, and in the second stage, the comprehensive cost is optimized. Finally, the method was validated using actual data from an HPS in the Yangtze River waterway. The results indicate that the proposed DEM-MPC framework significantly improves the overall operational energy efficiency of HPSs.
Keywords: hydrogen-powered ship energy management; probabilistic load forecasting; dynamic empirical modeling; two-stage model predictive control hydrogen-powered ship energy management; probabilistic load forecasting; dynamic empirical modeling; two-stage model predictive control

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MDPI and ACS Style

Liu, X.; Zou, L.; Han, Z.; Jia, R.; Ma, L. Two-Stage Energy Management for Hydrogen-Powered Ships: Integrating Dynamic Empirical Probabilistic Load Forecasting and Model Predictive Control. Energies 2026, 19, 3310. https://doi.org/10.3390/en19143310

AMA Style

Liu X, Zou L, Han Z, Jia R, Ma L. Two-Stage Energy Management for Hydrogen-Powered Ships: Integrating Dynamic Empirical Probabilistic Load Forecasting and Model Predictive Control. Energies. 2026; 19(14):3310. https://doi.org/10.3390/en19143310

Chicago/Turabian Style

Liu, Xingdou, Liang Zou, Zhiyun Han, Rongzhao Jia, and Liangwang Ma. 2026. "Two-Stage Energy Management for Hydrogen-Powered Ships: Integrating Dynamic Empirical Probabilistic Load Forecasting and Model Predictive Control" Energies 19, no. 14: 3310. https://doi.org/10.3390/en19143310

APA Style

Liu, X., Zou, L., Han, Z., Jia, R., & Ma, L. (2026). Two-Stage Energy Management for Hydrogen-Powered Ships: Integrating Dynamic Empirical Probabilistic Load Forecasting and Model Predictive Control. Energies, 19(14), 3310. https://doi.org/10.3390/en19143310

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