{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,24]],"date-time":"2026-06-24T17:26:15Z","timestamp":1782321975287,"version":"3.54.5"},"reference-count":12,"publisher":"Association for Computing Machinery (ACM)","issue":"3","license":[{"start":{"date-parts":[[2020,9,1]],"date-time":"2020-09-01T00:00:00Z","timestamp":1598918400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Commun. Comput. Algebra"],"published-print":{"date-parts":[[2020,9]]},"abstract":"<jats:p>We propose solving the power flow equations using monodromy. We prove the variety under consideration decomposes into trivial and nontrivial subvarieties and that the nontrivial subvariety is irreducible. We also show various symmetries in the solutions. We finish by giving numerical results comparing monodromy against polyhedral and total degree homotopy methods and giving an example of a network where we can find all solutions to the power flow equation using monodromy where other homotopy techniques fail. This work gives hope that finding all solutions to the power flow equations for networks of realistic size is possible.<\/jats:p>","DOI":"10.1145\/3457341.3457346","type":"journal-article","created":{"date-parts":[[2021,3,15]],"date-time":"2021-03-15T22:07:02Z","timestamp":1615846022000},"page":"100-104","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":4,"title":["Exploiting symmetry in the power flow equations using monodromy"],"prefix":"10.1145","volume":"54","author":[{"given":"Julia","family":"Lindberg","sequence":"first","affiliation":[{"name":"University of Wisconsin-Madison"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Nigel","family":"Boston","sequence":"additional","affiliation":[{"name":"University of Wisconsin-Madison"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Bernard C.","family":"Lesieutre","sequence":"additional","affiliation":[{"name":"University of Wisconsin-Madison"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[2021,3,15]]},"reference":[{"issue":"12","key":"e_1_2_1_1_1","first-page":"2972","article-title":"Numerical polynomial homotopy continuation method to locate all the power flow solutions","volume":"10","author":"Mehta D.","year":"2016","unstructured":"D. Mehta , H. D. Nguyen , and K. Turitsyn . Numerical polynomial homotopy continuation method to locate all the power flow solutions . IEEE Transactions on Power Systems , 10 ( 12 ): 2972 -- 2980 , 2016 . D. Mehta, H. D. Nguyen, and K. Turitsyn. Numerical polynomial homotopy continuation method to locate all the power flow solutions. IEEE Transactions on Power Systems, 10(12):2972--2980, 2016.","journal-title":"IEEE Transactions on Power Systems"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1109\/ALLERTON.2017.8262861"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1109\/TPWRS.2017.2724030"},{"key":"e_1_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.1109\/ALLERTON.2018.8635895"},{"key":"e_1_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.1109\/ALLERTON.2019.8919943"},{"key":"e_1_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.1109\/ISCAS.2018.8351675"},{"key":"e_1_2_1_7_1","doi-asserted-by":"publisher","DOI":"10.1093\/imanum\/dry017"},{"key":"e_1_2_1_8_1","volume-title":"Solving parameterized polynomial systems with decomposable projections. arXiv preprint arXiv:1612.08807","author":"Am\u00e9ndola Carlos","year":"2016","unstructured":"Carlos Am\u00e9ndola and Jose Israel Rodriguez . Solving parameterized polynomial systems with decomposable projections. arXiv preprint arXiv:1612.08807 , 2016 . Carlos Am\u00e9ndola and Jose Israel Rodriguez. Solving parameterized polynomial systems with decomposable projections. arXiv preprint arXiv:1612.08807, 2016."},{"key":"e_1_2_1_9_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jsc.2016.07.019"},{"key":"e_1_2_1_10_1","doi-asserted-by":"publisher","DOI":"10.1137\/17M1145665"},{"key":"e_1_2_1_11_1","first-page":"458","volume-title":"International Congress on Mathematical Software","author":"Breiding Paul","year":"2018","unstructured":"Paul Breiding and Sascha Timme . Homotopycontinuation.jl : A package for homotopy continuation in Julia . In International Congress on Mathematical Software , pages 458 -- 465 . Springer , 2018 . Paul Breiding and Sascha Timme. Homotopycontinuation.jl: A package for homotopy continuation in Julia. In International Congress on Mathematical Software, pages 458--465. Springer, 2018."},{"key":"e_1_2_1_12_1","doi-asserted-by":"publisher","DOI":"10.1137\/17M1128198"}],"container-title":["ACM Communications in Computer Algebra"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3457341.3457346","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3457341.3457346","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,17]],"date-time":"2025-06-17T20:17:19Z","timestamp":1750191439000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3457341.3457346"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,9]]},"references-count":12,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2020,9]]}},"alternative-id":["10.1145\/3457341.3457346"],"URL":"https:\/\/doi.org\/10.1145\/3457341.3457346","relation":{},"ISSN":["1932-2240"],"issn-type":[{"value":"1932-2240","type":"print"}],"subject":[],"published":{"date-parts":[[2020,9]]},"assertion":[{"value":"2021-03-15","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}