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To tackle this challenge, this paper proposes a sequential quadratic programming (SQP) method combined with gradient sampling (GS) in a dual formulation. The highlighted feature is the sample size of the gradient changes dynamically in every iteration, yielding an adaptive gradient sampling (AGS) process. Thus, the computing efficiency is greatly improved owing to the decrease and the parallelization of gradient evaluation, which dominates the computing time of the whole algorithm. Simulations on an IEEE 10-machine 39-bus system and an IEEE 54-machine 118-bus system prove the effectiveness and high efficiency of the proposed method.<\/jats:p>","DOI":"10.1155\/2020\/3912717","type":"journal-article","created":{"date-parts":[[2020,2,11]],"date-time":"2020-02-11T18:31:05Z","timestamp":1581445865000},"page":"1-10","source":"Crossref","is-referenced-by-count":3,"title":["Available Transfer Capability Calculation Constrained with Small-Signal Stability Based on Adaptive Gradient Sampling"],"prefix":"10.1155","volume":"2020","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3203-0904","authenticated-orcid":true,"given":"Peijie","family":"Li","sequence":"first","affiliation":[{"name":"School of Electrical Engineering, Guangxi University, Nanning 530004, China"}]},{"given":"Ling","family":"Zhu","sequence":"additional","affiliation":[{"name":"School of Electrical Engineering, Guangxi University, Nanning 530004, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4383-3892","authenticated-orcid":true,"given":"Xiaoqing","family":"Bai","sequence":"additional","affiliation":[{"name":"School of Electrical Engineering, Guangxi University, Nanning 530004, China"}]},{"given":"Hua","family":"Wei","sequence":"additional","affiliation":[{"name":"School of Electrical Engineering, Guangxi University, Nanning 530004, China"}]}],"member":"311","reference":[{"key":"1","doi-asserted-by":"publisher","DOI":"10.1109\/59.852097"},{"journal-title":"IEEE Transactions on Power Systems","first-page":"347","year":"2009","key":"2"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1109\/tpwrs.2003.820700"},{"issue":"1","key":"4","first-page":"3","volume":"31","year":"2015","journal-title":"IEEE Transactions on Power Systems"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1109\/tpwrs.2016.2598266"},{"year":"2006","key":"6","first-page":"862"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1017\/s0962492900002646"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1137\/090780201"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1080\/10556788.2012.714781"},{"year":"2010","key":"11"}],"container-title":["Complexity"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2020\/3912717.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2020\/3912717.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2020\/3912717.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,2,11]],"date-time":"2020-02-11T18:31:13Z","timestamp":1581445873000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.hindawi.com\/journals\/complexity\/2020\/3912717\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,2,11]]},"references-count":10,"alternative-id":["3912717","3912717"],"URL":"https:\/\/doi.org\/10.1155\/2020\/3912717","relation":{},"ISSN":["1076-2787","1099-0526"],"issn-type":[{"type":"print","value":"1076-2787"},{"type":"electronic","value":"1099-0526"}],"subject":[],"published":{"date-parts":[[2020,2,11]]}}}