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Aiming at the solid oxide fuel cell (SOFC) applied to the ship DC microgrid in the face of pulse load disturbance is prone to make the SOFC voltage drop too large leading to the DC grid oscillation problem. In this paper, a stability criterion method for SOFC-Li battery DC system based on hybrid potential function is proposed. Firstly, a mathematical model of shipboard DC microgrid with SOFC-Li battery is established and the accuracy of the model is verified. Then, the stability criterion of the system based on the hybrid potential function under large disturbances is constructed. Subsequently, the effects of system stability under impulse load conditions were analysed under different parameters. Based on the constructed criterion, simulation verification of the stability boundary conditions of the SOFC system operating independently or jointly with a lithium battery system is carried out. The experimental results show that the proposed stability criterion and control strategy are effective in accurately predicting the system stability boundary. The experimental results verify the effectiveness of the proposed method in improving the stability of the system and provide a theoretical basis for further research on the dynamic characteristics of SOFC systems under complex load conditions. [ABSTRACT FROM AUTHOR]