Under the unique climatic conditions of tropical islands, low-carbon parks are characterized by severe fluctuations and high penetrations of renewable energy, limited regulation capacity, and year-round heavy air-conditioning loads. To address the power supply instability caused by source-load mismatches within the parks, most current studies employ energy storage systems to smooth fluctuations and achieve peak shaving and valley filling. However, few studies have investigated the distinct source-load characteristics induced by the tropical island environment. To this end, this paper proposes a multi-time-scale optimal scheduling strategy for generalized energy storage tailored to the specific characteristics of such parks. First, a unique source-load model under tropical island meteorological conditions is constructed and adapted to regional features. Second, a three-tier time-scale coordination framework is established: the long-term scale aims to optimize the economy of the virtual power plant; the medium-term scale corrects prediction deviations based on rolling optimization; and the short-term scale ensures the dynamic response and robustness of the system. Finally, a case study of a user in a park in Hainan Province is presented to verify the proposed method. Simulation results indicate that, compared to traditional bi-level optimization scheduling, the proposed strategy reduces the total daily operating cost by 27.72% (9,649.3 CNY) through optimized peak-valley arbitrage. Consequently, economic and reliable operation is realized with the active participation of user-side energy storage.□