{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,16]],"date-time":"2026-07-16T10:42:31Z","timestamp":1784198551000,"version":"3.55.0"},"reference-count":20,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2021,5,25]],"date-time":"2021-05-25T00:00:00Z","timestamp":1621900800000},"content-version":"vor","delay-in-days":144,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51967001"],"award-info":[{"award-number":["51967001"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004607","name":"Natural Science Foundation of Guangxi Province","doi-asserted-by":"publisher","award":["2018JJA160164"],"award-info":[{"award-number":["2018JJA160164"]}],"id":[{"id":"10.13039\/501100004607","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Complexity"],"published-print":{"date-parts":[[2021,1]]},"abstract":"<jats:p>For enhancing the stability of the microgrid operation, this paper proposes an optimization model considering the small\u2010signal stability constraint. Due to the nonsmooth property of the spectral abscissa function, the droop controller parameters\u2019 optimization is a nonsmooth optimization problem. The Sequential Quadratic Programming with Gradient Sampling (SQP\u2010GS) is implemented to optimize the droop controller parameters for solving the nonsmooth problem. The SQP\u2010GS method can guarantee the solution of the optimization problem globally and efficiently converges to stationary points with probability of one. In the current iteration, the gradient of the nonsmooth function can be evaluated on a set of randomly generated nearby points by computing closed\u2010form sensitivities. A test on the microgrid system shows that the optimality and the efficiency of the SQP\u2010GS are better than those of the heuristic algorithms.<\/jats:p>","DOI":"10.1155\/2021\/5634274","type":"journal-article","created":{"date-parts":[[2021,5,25]],"date-time":"2021-05-25T18:50:07Z","timestamp":1621968607000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Parameter Optimization of Droop Controllers for Microgrids in Islanded Mode by the SQP Method with Gradient Sampling"],"prefix":"10.1155","volume":"2021","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3203-0904","authenticated-orcid":false,"given":"Peijie","family":"Li","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ziyi","family":"Yang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Shuchen","family":"Huang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jun","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2021,5,25]]},"reference":[{"key":"e_1_2_10_1_2","doi-asserted-by":"publisher","DOI":"10.1109\/tsg.2013.2295514"},{"key":"e_1_2_10_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.apenergy.2021.117024"},{"key":"e_1_2_10_3_2","doi-asserted-by":"publisher","DOI":"10.1109\/tsg.2017.2788042"},{"key":"e_1_2_10_4_2","doi-asserted-by":"publisher","DOI":"10.1007\/s12555-018-0506-y"},{"key":"e_1_2_10_5_2","doi-asserted-by":"publisher","DOI":"10.1109\/tie.2016.2607681"},{"key":"e_1_2_10_6_2","doi-asserted-by":"publisher","DOI":"10.1109\/tpel.2010.2100101"},{"key":"e_1_2_10_7_2","doi-asserted-by":"publisher","DOI":"10.1049\/iet-rpg.2019.0428"},{"key":"e_1_2_10_8_2","doi-asserted-by":"publisher","DOI":"10.1109\/TIA.2010.2044970"},{"key":"e_1_2_10_9_2","doi-asserted-by":"publisher","DOI":"10.1109\/access.2019.2931151"},{"key":"e_1_2_10_10_2","doi-asserted-by":"publisher","DOI":"10.1109\/TSG.2015.2501316"},{"key":"e_1_2_10_11_2","doi-asserted-by":"publisher","DOI":"10.1145\/937503.937505"},{"key":"e_1_2_10_12_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.sorms.2010.07.001"},{"key":"e_1_2_10_13_2","doi-asserted-by":"publisher","DOI":"10.1137\/090780201"},{"key":"e_1_2_10_14_2","doi-asserted-by":"crossref","unstructured":"LiP. HuangS. QiJ. WeiH. andBaiX. Optimal coordination of PSSs and pods by sequential quadratic programming with gradient sampling Proceedings of the 2020 IEEE\/IAS Industrial and Commercial Power System Asia (I & CPS Asia) July 2020 Weihai China 604\u2013610 https:\/\/doi.org\/10.1109\/ICPSAsia48933.2020.9208363.","DOI":"10.1109\/ICPSAsia48933.2020.9208363"},{"key":"e_1_2_10_15_2","doi-asserted-by":"publisher","DOI":"10.1109\/tpel.2006.890003"},{"key":"e_1_2_10_16_2","doi-asserted-by":"publisher","DOI":"10.1007\/s102080010008"},{"key":"e_1_2_10_17_2","doi-asserted-by":"publisher","DOI":"10.1017\/s0962492900002646"},{"key":"e_1_2_10_18_2","doi-asserted-by":"publisher","DOI":"10.1137\/030601296"},{"key":"e_1_2_10_19_2","doi-asserted-by":"publisher","DOI":"10.35833\/MPCE.2019.000225"},{"key":"e_1_2_10_20_2","doi-asserted-by":"publisher","DOI":"10.1090\/s0025-5718-1980-0572855-7"}],"container-title":["Complexity"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2021\/5634274.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2021\/5634274.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/2021\/5634274","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,9]],"date-time":"2024-08-09T22:48:27Z","timestamp":1723243707000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/2021\/5634274"}},"subtitle":[],"editor":[{"given":"Chun","family":"Wei","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"editor"}]}],"short-title":[],"issued":{"date-parts":[[2021,1]]},"references-count":20,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2021,1]]}},"alternative-id":["10.1155\/2021\/5634274"],"URL":"https:\/\/doi.org\/10.1155\/2021\/5634274","archive":["Portico"],"relation":{},"ISSN":["1076-2787","1099-0526"],"issn-type":[{"value":"1076-2787","type":"print"},{"value":"1099-0526","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,1]]},"assertion":[{"value":"2021-04-08","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2021-05-14","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2021-05-25","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"5634274"}}