{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,24]],"date-time":"2026-09-24T16:10:31Z","timestamp":1790266231817,"version":"4.1.0"},"reference-count":32,"publisher":"Public Library of Science (PLoS)","issue":"1","license":[{"start":{"date-parts":[[2026,1,7]],"date-time":"2026-01-07T00:00:00Z","timestamp":1767744000000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["www.plosone.org"],"crossmark-restriction":false},"short-container-title":["PLoS One"],"abstract":"<jats:p>As grid-forming converters (GFM) and grid-following converters (GFL) continue to be integrated into low-inertia power systems in place of traditional synchronous generators, the characteristics and forms of system inertia have undergone significant transformation. This evolution poses significant challenges to conventional inertia response mechanisms and analytical methodologies. To address these challenges, this study proposes a novel grid index frequency stability margin (FSM) from the perspective of frequency stability, encompassing its definition, quantitative evaluation, and practical applications. This paper first introduces the mathematical foundations and operational definitions of the FSM. It then systematically investigates the factors influencing FSM and presents a comprehensive mathematical model specifically developed for low-inertia power systems. The FSM calculation method based on aggregated system modelling was developed, followed by the derivation of a simplified estimation approach suitable for practical engineering applications. The effectiveness of the FSM in analyzing the frequency stability of low-inertia grids was validated through case studies based on provincial-level power grid data from China and a modified IEEE 39-bus system. The findings establish a theoretical framework for optimizing the planning and development of new energy power plants, as well as for formulating grid operation control strategies. This framework offers essential guidance to ensure the secure and stable operation of low-inertia power systems.<\/jats:p>","DOI":"10.1371\/journal.pone.0340648","type":"journal-article","created":{"date-parts":[[2026,1,7]],"date-time":"2026-01-07T19:08:55Z","timestamp":1767812935000},"page":"e0340648","update-policy":"https:\/\/doi.org\/10.1371\/journal.pone.corrections_policy","source":"Crossref","is-referenced-by-count":3,"title":["A new index for frequency stability assessment in Low-Inertia Power Systems"],"prefix":"10.1371","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0009-0003-5295-5351","authenticated-orcid":true,"given":"Sishi","family":"Qin","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Sim Sy","family":"Yi","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Chao","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Huaying","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"340","published-online":{"date-parts":[[2026,1,7]]},"reference":[{"issue":"7","key":"pone.0340648.ref001","doi-asserted-by":"crossref","first-page":"9153","DOI":"10.1109\/TPEL.2025.3547018","article-title":"Preset Power Based Droop Control for Improving Primary Frequency Regulation of Inverters Under Large Disturbances","volume":"40","author":"L Liu","year":"2025","journal-title":"IEEE Trans Power Electron"},{"issue":"6","key":"pone.0340648.ref002","doi-asserted-by":"crossref","first-page":"4920","DOI":"10.1109\/TPWRS.2020.3020725","article-title":"PLL and Additional Frequency Control Constituting an Adaptive Synchronization Mechanism for VSCs","volume":"35","author":"M Zhang","year":"2020","journal-title":"IEEE Trans Power Syst"},{"issue":"4","key":"pone.0340648.ref003","doi-asserted-by":"crossref","first-page":"1553","DOI":"10.1109\/JESTPE.2017.2703814","article-title":"Modeling and Design of $df\/dt$ -Based Inertia Control for Power Converters","volume":"5","author":"D Duckwitz","year":"2017","journal-title":"IEEE J Emerg Sel Topics Power Electron"},{"issue":"6","key":"pone.0340648.ref004","doi-asserted-by":"crossref","first-page":"7249","DOI":"10.1109\/TPWRS.2018.2843381","article-title":"Estimation of Power System Inertia From Ambient Wide Area Measurements","volume":"33","author":"K Tuttelberg","year":"2018","journal-title":"IEEE Trans Power Syst"},{"issue":"3","key":"pone.0340648.ref005","doi-asserted-by":"crossref","first-page":"2748","DOI":"10.1109\/TPWRS.2022.3186525","article-title":"Impedance-Based Online Estimation of Nodal Inertia and Primary Frequency Regulation Capability","volume":"38","author":"W Zhang","year":"2023","journal-title":"IEEE Trans Power Syst"},{"issue":"5","key":"pone.0340648.ref006","doi-asserted-by":"crossref","first-page":"3747","DOI":"10.1109\/TPWRS.2021.3134818","article-title":"Estimation of Inertia for Synchronous and Non-Synchronous Generators Based on Ambient Measurements","volume":"37","author":"J Guo","year":"2022","journal-title":"IEEE Trans Power Syst"},{"issue":"1","key":"pone.0340648.ref007","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1109\/TPWRS.2019.2925127","article-title":"Estimation of Parameters of a Dynamic Generator Model From Modal PMU Measurements","volume":"35","author":"A Gorbunov","year":"2020","journal-title":"IEEE Trans Power Syst"},{"key":"pone.0340648.ref008","doi-asserted-by":"crossref","unstructured":"Zhai B, Li X, Yang Q, Li W, Sun R, Gao B. Penetration rate-equivalent inertia time constant function identification method of renewable energy power system. In: 2021 IEEE Sustainable Power and Energy Conference (iSPEC). 2021. p. 1\u20136. doi: 10.1109\/ispec53008.2021.9770420","DOI":"10.1109\/iSPEC53008.2021.9770420"},{"issue":"16","key":"pone.0340648.ref009","first-page":"5179","article-title":"Research on inertia system of frequency response for power system with high penetration electronics","volume":"40","author":"H Sun","year":"2020","journal-title":"Proc CSEE"},{"key":"pone.0340648.ref010","unstructured":"AEMO. Notice of South Australia inertia requirements and shortfall. 2020. [Online]. Available from: https:\/\/aemo.com.au\/-\/media\/files\/electricity\/nem\/security_and_reliability\/system-security-market-frameworks-review\/2020\/2020-notice-of-south-australia-inertia-requirements-and-shortfall.pdf?la=en"},{"key":"pone.0340648.ref011","unstructured":"National Grid. System operability framework. 2016. [Online]. Available from: https:\/\/www.nationalgrid.com\/sites\/default\/files\/documents\/8589937803-SOF%202016%20-%20Full%20Interactive%20Document.pdf"},{"key":"pone.0340648.ref012","doi-asserted-by":"crossref","unstructured":"Garcia-Ruiz M, Cantos-Alcantara GJ, Martinez-Ramos JL, Marano-Marcolini A. Minimum Required Inertia for a Fully Renewable AC Interconnected System. 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Foundations and Challenges of Low-Inertia Systems (Invited Paper). In: 2018 Power Systems Computation Conference (PSCC). 2018. p. 1\u201325. doi: 10.23919\/pscc.2018.8450880","DOI":"10.23919\/PSCC.2018.8450880"},{"key":"pone.0340648.ref017","unstructured":"Technical specifications for grid-connected operation and control of electrochemical energy storage station\u2014 Part 7: Inertia support and damping control, DL\/T 2246.7-2021. 2021."},{"key":"pone.0340648.ref018","unstructured":"National Grid. Distribution Code: DC0079 frequency changes during large disturbances and their impact on the total system (Phase 4). 2019. [Online]. Available from: https:\/\/www.ofgem.gov.uk\/sites\/default\/files\/docs\/2019\/08\/dc0079_d.pdf"},{"key":"pone.0340648.ref019","unstructured":"EirGrid and SONI. Mitigating technical challenges arising from high RES-E penetration on the island of Ireland. 2021. [Online]. 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Reactive power control for load sharing with virtual synchronous generator control. 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