The grid stability threatened by the inherent variability of wind power generation creates a critical need for effective mitigation strategies. To resolve this issue, we aim to develop a battery-supercapacitor hybrid energy storage system (HESS) that integrates an advanced power allocation strategy with a comprehensive techno-economic model to minimize the levelized storage cost. A power-sharing method based on improved complete ensemble empirical mode decomposition with adaptive noise (ICEEMDAN) and Hilbert transform is introduced to optimally decompose fluctuating wind power, allocating high-frequency transients to the supercapacitor and low-frequency components to the battery. The economic model then incorporates the battery capacity status along with battery degradation modelling by reducing battery stress and maintaining the depth of discharge (DOD) primarily within a moderate 0.4–0.6 range. Compared with three existing schemes, i.e., EEMD, CEEMDAN, and ICEEMDAN, the proposed ICEEMDAN-based strategy achieves the most cost-effective configuration with a total annualized cost of 172.25 k CNY. Cost reductions are approximately 9.4% compared with the CEEMDAN-based scheme (190.10 k CNY) and 17.7% compared with the EEMD-based scheme (209.16 k CNY). This verifies that the best techno-economic performance can be achieved by optimally balancing power smoothing efficacy with battery longevity and overall system cost.