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Potential saturation in the benefits, and competition between the two services, are explored as the battery maximum power output increases.<\/jats:p>\n          <jats:p>This article is part of the theme issue \u2018The mathematics of energy systems\u2019.<\/jats:p>","DOI":"10.1098\/rsta.2019.0433","type":"journal-article","created":{"date-parts":[[2021,6,7]],"date-time":"2021-06-07T07:14:56Z","timestamp":1623050096000},"page":"20190433","update-policy":"https:\/\/doi.org\/10.1098\/crossmark-policy","source":"Crossref","is-referenced-by-count":3,"title":["A rare-event study of frequency regulation and contingency services from grid-scale batteries"],"prefix":"10.1098","volume":"379","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1249-9238","authenticated-orcid":true,"given":"Maldon","family":"Patrice Goodridge","sequence":"first","affiliation":[{"name":"School of Mathematics, Queen Mary University of London, London, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"John","family":"Moriarty","sequence":"additional","affiliation":[{"name":"School of Mathematics, Queen Mary University of London, London, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7334-0685","authenticated-orcid":true,"given":"Andrea","family":"Pizzoferrato","sequence":"additional","affiliation":[{"name":"University of Bath, Bath, UK"},{"name":"The Alan Turing Institute, London, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"175","published-online":{"date-parts":[[2021,6,7]]},"reference":[{"key":"e_1_3_7_2_2","unstructured":"International Renewable Energy Agency. 2018 Global energy transformation: a roadmap to 2050 . 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