The integration of large-scale wind power into modern grids gives rise to a complicated issue due to meteorological variability, threatening power stability and security. Although these adverse effects can be somehow mitigated by leveraging the geo-spatiotemporal distribution through the rapid response of energy storage devices, the wind power fluctuations are being increasingly taken up in public debate, even influencing energy prices and leading to acceptance problems. For this reason, in this work, we aim to minimize wind power fluctuations using improved complete ensemble empirical mode decomposition with adaptive noise (ICEEMDAN) and Hilbert spectral analysis in a hybrid energy storage system (HESS). Initially, K-means clustering is used to find cluster center positions. Each cluster, median fluctuations, and noise levels are then analyzed from typical daily data. Statistical analysis to smooth wind output power is conducted, incorporating a weighted combination of moving average filtering (MAF) and anti-pulse interference average filtering (AIAF) algorithms. The HESS reference power is decomposed into various intrinsic mode functions (IMFs) spanning high- to low-frequency bands using ICEEMDAN methods. The time–frequency characteristics of each IMF are derived using Hilbert transform (HT) analysis. High-frequency power fluctuations are managed by a supercapacitor, whereas the battery handles low-frequency components. The effectiveness of the proposed strategy is validated using actual sampling data, demonstrating that the impact of wind power fluctuations on grid stability can be significantly reduced.