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This paper presents the first systematic study on power control strategies for Modular-Gravity Energy Storage (M-GES), a novel, high-performance, large-scale energy storage technology with significant research and application potential. Addressing the current research gap in M-GES power control technology, we propose two corresponding compensation modes and several power control strategies for Hybrid M-GES and M-GES. The effectiveness of these strategies is validated through simulations on the MATLAB/Simulink platform, including tests using sinusoidal power and feasibility verification based on a natural California load curve. Additionally, we analyze the normal and abnormal operating conditions of M-GES. In conclusion, the characteristics of the proposed control strategies are summarized, providing a guideline for further research. [Display omitted] • Modular-gravity energy storage (M-GES) power control system studied. • Two compensation modes and four control strategies are systematically studied and validated. • The center switching method with hysteresis control (CSM-H) excels in continuous compensation mode. • The center switching method with hysteresis control and dead zone (CSM-HD) excels in overlap compensation mode. • Based on the power control system proposed in this paper, the M-GES plant performs highly in natural power systems. [ABSTRACT FROM AUTHOR]