{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,20]],"date-time":"2026-06-20T06:30:20Z","timestamp":1781937020388,"version":"3.54.5"},"reference-count":33,"publisher":"The Royal Society","issue":"2210","license":[{"start":{"date-parts":[[2018,2,1]],"date-time":"2018-02-01T00:00:00Z","timestamp":1517443200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/royalsociety.org\/journals\/ethics-policies\/data-sharing-mining\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Nature Science Foundation of China","doi-asserted-by":"crossref","award":["11475253"],"award-info":[{"award-number":["11475253"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"name":"National Key R&D Program of China"}],"content-domain":{"domain":["royalsocietypublishing.org"],"crossmark-restriction":true},"short-container-title":["Proc. R. Soc. A."],"published-print":{"date-parts":[[2018,2]]},"abstract":"<jats:p>The classic equal-area criterion (EAC) is of key importance in power system analysis, and provides a powerful, pictorial and quantitative means of analysing transient stability (i.e. the system's ability to maintain stable operation when subjected to a large disturbance). Based on the traditional EAC, it is common sense in engineering that there is a critical cleaning time (CCT); namely, a power system is stable (unstable) if a fault is cleared before (after) this CCT. We regard this form of CCT as bipartite. In this paper, we revisit the EAC theory and, surprisingly, find different kinds of transient stability behaviour. Based on these analyses, we discover that the bipartite CCT is only one type among four major types, and, actually, the forms of CCT can be diversified. In particular, under some circumstances, a system may have no CCT or show a periodic CCT. Our theoretical analysis is verified by numerical simulations in a single-machine-infinite-bus system and also in multi-machine systems. Thus, our study provides a panoramic framework for diverse transient stability behaviour in power systems and also may have a significant impact on applications of multi-stability in various other systems, such as neuroscience, climatology or photonics.<\/jats:p>","DOI":"10.1098\/rspa.2017.0733","type":"journal-article","created":{"date-parts":[[2018,2,8]],"date-time":"2018-02-08T05:00:02Z","timestamp":1518066002000},"page":"20170733","update-policy":"https:\/\/doi.org\/10.1098\/crossmark-policy","source":"Crossref","is-referenced-by-count":14,"title":["Equal-area criterion in power systems revisited"],"prefix":"10.1098","volume":"474","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8847-8337","authenticated-orcid":false,"given":"Yong","family":"Sun","sequence":"first","affiliation":[{"name":"Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, People's Republic of China"},{"name":"University of the Chinese Academy of Sciences, Beijing 100049, People's Republic of China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jinpeng","family":"Ma","sequence":"additional","affiliation":[{"name":"Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, People's Republic of China"},{"name":"University of the Chinese Academy of Sciences, Beijing 100049, People's Republic of China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"J\u00fcrgen","family":"Kurths","sequence":"additional","affiliation":[{"name":"Potsdam Institute for Climate Impact Research (PIK), 14473 Potsdam, Germany"},{"name":"Department of Physics, Humboldt University, 12489 Berlin, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Meng","family":"Zhan","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Advanced Electromagnetic Engineering and Technology, Hubei Electric Power Security and High Efficiency Key Laboratory, School of Electrical and Electronic Engineering, Huazhong University of Science and Technology, Wuhan 430074, People's Republic of China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"175","published-online":{"date-parts":[[2018,2,7]]},"reference":[{"key":"e_1_3_6_2_2","volume-title":"Power systems analysis","author":"Bergen AR","year":"1986"},{"key":"e_1_3_6_3_2","volume-title":"Power system stability and control","author":"Kundur P","year":"1994"},{"key":"e_1_3_6_4_2","doi-asserted-by":"publisher","DOI":"10.1109\/9780470545577"},{"key":"e_1_3_6_5_2","first-page":"170","article-title":"System stability as a design problem","volume":"28","author":"Park RH","year":"1929","journal-title":"AIEE Trans."},{"key":"e_1_3_6_6_2","first-page":"185","article-title":"Stability of the general 2-machine system","volume":"54","author":"Dahl OGC","year":"1935","journal-title":"AIEE Trans."},{"key":"e_1_3_6_7_2","doi-asserted-by":"publisher","DOI":"10.1109\/EE.1940.6435162"},{"key":"e_1_3_6_8_2","first-page":"367","article-title":"The transient stability of alternators: a graphical solution of the two-machine case","volume":"99","author":"Prescott JC","year":"1952","journal-title":"Proc. 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