{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,15]],"date-time":"2026-07-15T00:43:16Z","timestamp":1784076196066,"version":"3.55.0"},"reference-count":29,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2025,8,19]],"date-time":"2025-08-19T00:00:00Z","timestamp":1755561600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Guangxi Natural Science Foundation","award":["2025GXNSFHA069066"],"award-info":[{"award-number":["2025GXNSFHA069066"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This study examines the issue of wind power smoothing in renewable-energy-grid integration scenarios. Under the \u201cdual-carbon\u201d policy initiative, large-scale renewable energy integration (particularly wind power) has become a global focus. However, the intermittency and uncertainty of wind power output exacerbate grid power fluctuations, posing challenges to power system stability. Consequently, smoothing strategies for wind power energy storage systems are desperately needed to improve operational economics and grid stability. According to current research, single energy storage technologies are unable to satisfy both the system-level economic operating requirements and high-frequency power fluctuation compensation at the same time, resulting in a trade-off between economic efficiency and precision of frequency regulation. Therefore, hybrid energy storage technologies have emerged as a key research focus in wind power energy storage. This study employs the SE-SGMD method, utilizing the distinct characteristics of lithium batteries and supercapacitors to decompose frequency regulation commands into low- and high-frequency components via frequency separation strategies, thereby controlling the output of supercapacitors and lithium batteries, respectively. Additionally, the GA-GWO algorithm is applied to optimize energy-storage-system configuration, with experimental validation conducted. The theoretical contributions of this study include the following: (1) introducing the SE-SGMD frequency separation strategy into hybrid energy storage systems, overcoming the performance limitations of single energy storage devices, and (2) developing a power allocation mechanism on the basis of the inherent properties of energy storage devices. In terms of methodological innovation, the designed hybrid GA-GWO algorithm achieves a balance between optimization accuracy and efficiency. Compared to PSO-DE and GWO-PSO, the GA-GWO energy storage system demonstrates improvements of 21.10% and 17.47% in revenue, along with reductions of 6.26% and 12.57% in costs, respectively.<\/jats:p>","DOI":"10.3390\/sym17081356","type":"journal-article","created":{"date-parts":[[2025,8,19]],"date-time":"2025-08-19T10:59:01Z","timestamp":1755601141000},"page":"1356","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Sim-Geometry Modal Decomposition (SGMD)-Based Optimization Strategy for Hybrid Battery and Supercapacitor Energy Storage Frequency Regulation"],"prefix":"10.3390","volume":"17","author":[{"given":"Yongling","family":"He","sequence":"first","affiliation":[{"name":"School of Mechanical and Naval Architecture & Ocean Engineering, Beibu Gulf University, Qinzhou 535011, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhengquan","family":"Zuo","sequence":"additional","affiliation":[{"name":"School of Mechanical and Naval Architecture & Ocean Engineering, Beibu Gulf University, Qinzhou 535011, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0005-3547-2336","authenticated-orcid":false,"given":"Kang","family":"Shen","sequence":"additional","affiliation":[{"name":"School of Mechanical and Naval Architecture & Ocean Engineering, Beibu Gulf University, Qinzhou 535011, China"},{"name":"School of Electrical Engineering, Guangxi University, Nanning 530004, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jun","family":"Gao","sequence":"additional","affiliation":[{"name":"School of Mechanical and Naval Architecture & Ocean Engineering, Beibu Gulf University, Qinzhou 535011, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Qiuyu","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Mechanical and Naval Architecture & Ocean Engineering, Beibu Gulf University, Qinzhou 535011, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jianqun","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Mechanical and Naval Architecture & Ocean Engineering, Beibu Gulf University, Qinzhou 535011, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Haoyu","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Mechanical and Naval Architecture & Ocean Engineering, Beibu Gulf University, Qinzhou 535011, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2025,8,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"506","DOI":"10.1038\/s41560-021-00796-8","article-title":"The design space for long-duration energy storage in decarbonized power systems","volume":"6","author":"Sepulveda","year":"2021","journal-title":"Nat. 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