{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,8]],"date-time":"2026-05-08T09:54:24Z","timestamp":1778234064430,"version":"3.51.4"},"reference-count":27,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2016,6,1]],"date-time":"2016-06-01T00:00:00Z","timestamp":1464739200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51407150"],"award-info":[{"award-number":["51407150"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100013286","name":"Specialized Research Fund for the Doctoral Program of Higher Education of China","doi-asserted-by":"publisher","award":["20130184110002"],"award-info":[{"award-number":["20130184110002"]}],"id":[{"id":"10.13039\/501100013286","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Based on the fast kernel entropy optimization independent component analysis and the minimum conditional entropy, this paper proposes a harmonic source localization method which aims at accurately estimating harmonic currents and identifying harmonic sources. The injected harmonic currents are estimated by the fast kernel entropy optimization independent component analysis (FKEO-ICA) in the absence of prior knowledge of harmonic impedances. Then, the minimum conditional entropy is applied to locate the harmonic sources based on the estimated harmonic currents. The proposed harmonic source localization method is validated on the IEEE 34-bus system. By applying the correlation coefficient and three error evaluation indicators, comparison has been made among the performances of the FKEO-ICA and three other ICA algorithms. The results show that the FKEO-ICA algorithm could achieve a significantly better accuracy of harmonic current estimation, while the minimum conditional entropy could determine the locations of harmonic sources precisely.<\/jats:p>","DOI":"10.3390\/e18060214","type":"journal-article","created":{"date-parts":[[2016,6,1]],"date-time":"2016-06-01T19:22:34Z","timestamp":1464808954000},"page":"214","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Harmonic Source Localization Approach Based on Fast Kernel Entropy Optimization ICA and Minimum Conditional Entropy"],"prefix":"10.3390","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5995-3442","authenticated-orcid":false,"given":"Tianlei","family":"Zang","sequence":"first","affiliation":[{"name":"School of Electrical Engineering, Southwest Jiaotong University, Chengdu 610031, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhengyou","family":"He","sequence":"additional","affiliation":[{"name":"School of Electrical Engineering, Southwest Jiaotong University, Chengdu 610031, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ling","family":"Fu","sequence":"additional","affiliation":[{"name":"School of Electrical Engineering, Southwest Jiaotong University, Chengdu 610031, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jing","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Electrical Engineering, Southwest Jiaotong University, Chengdu 610031, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qingquan","family":"Qian","sequence":"additional","affiliation":[{"name":"School of Electrical Engineering, Southwest Jiaotong University, Chengdu 610031, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2016,6,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"569","DOI":"10.1109\/61.19248","article-title":"Identification of harmonic sources by a state estimation technique","volume":"4","author":"Heydt","year":"1989","journal-title":"IEEE Trans. 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