{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,6]],"date-time":"2026-05-06T11:35:02Z","timestamp":1778067302336,"version":"3.51.4"},"reference-count":33,"publisher":"MDPI AG","issue":"19","license":[{"start":{"date-parts":[[2023,9,24]],"date-time":"2023-09-24T00:00:00Z","timestamp":1695513600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China (NSFC)","award":["U21A20146"],"award-info":[{"award-number":["U21A20146"]}]},{"name":"National Natural Science Foundation of China (NSFC)","award":["JCKJ2022A10"],"award-info":[{"award-number":["JCKJ2022A10"]}]},{"name":"National Natural Science Foundation of China (NSFC)","award":["GXXT-2020-070"],"award-info":[{"award-number":["GXXT-2020-070"]}]},{"name":"National Natural Science Foundation of China (NSFC)","award":["DQKJ202103"],"award-info":[{"award-number":["DQKJ202103"]}]},{"name":"Open Research Fund of Anhui Province Key Laboratory of Detection Technology and Energy Saving Devices","award":["U21A20146"],"award-info":[{"award-number":["U21A20146"]}]},{"name":"Open Research Fund of Anhui Province Key Laboratory of Detection Technology and Energy Saving Devices","award":["JCKJ2022A10"],"award-info":[{"award-number":["JCKJ2022A10"]}]},{"name":"Open Research Fund of Anhui Province Key Laboratory of Detection Technology and Energy Saving Devices","award":["GXXT-2020-070"],"award-info":[{"award-number":["GXXT-2020-070"]}]},{"name":"Open Research Fund of Anhui Province Key Laboratory of Detection Technology and Energy Saving Devices","award":["DQKJ202103"],"award-info":[{"award-number":["DQKJ202103"]}]},{"name":"Collaborative Innovation Project of Anhui Universities","award":["U21A20146"],"award-info":[{"award-number":["U21A20146"]}]},{"name":"Collaborative Innovation Project of Anhui Universities","award":["JCKJ2022A10"],"award-info":[{"award-number":["JCKJ2022A10"]}]},{"name":"Collaborative Innovation Project of Anhui Universities","award":["GXXT-2020-070"],"award-info":[{"award-number":["GXXT-2020-070"]}]},{"name":"Collaborative Innovation Project of Anhui Universities","award":["DQKJ202103"],"award-info":[{"award-number":["DQKJ202103"]}]},{"name":"Open Research Fund of Anhui Province Key Laboratory of Electric Drive and Control","award":["U21A20146"],"award-info":[{"award-number":["U21A20146"]}]},{"name":"Open Research Fund of Anhui Province Key Laboratory of Electric Drive and Control","award":["JCKJ2022A10"],"award-info":[{"award-number":["JCKJ2022A10"]}]},{"name":"Open Research Fund of Anhui Province Key Laboratory of Electric Drive and Control","award":["GXXT-2020-070"],"award-info":[{"award-number":["GXXT-2020-070"]}]},{"name":"Open Research Fund of Anhui Province Key Laboratory of Electric Drive and Control","award":["DQKJ202103"],"award-info":[{"award-number":["DQKJ202103"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Outliers can be generated in the power system due to aging system equipment, faulty sensors, incorrect line connections, etc. The existence of these outliers will pose a threat to the safe operation of the power system, reduce the quality of the data, affect the completeness and accuracy of the data, and thus affect the monitoring analysis and control of the power system. Therefore, timely identification and treatment of outliers are essential to ensure stable and reliable operation of the power system. In this paper, we consider the problem of detecting and localizing outliers in power systems. The paper proposes a Minorization\u2013Maximization (MM) algorithm for outlier detection and localization and an estimation of unknown parameters of the Gaussian mixture model (GMM). To verify the performance of the method, we conduct simulation experiments by simulating different test scenarios in the IEEE 14-bus system. Numerical examples show that in the presence of outliers, the MM algorithm can detect outliers better than the traditional algorithm and can accurately locate outliers with a probability of more than 95%. Therefore, the algorithm provides an effective method for the handling of outliers in the power system, which helps to improve the monitoring analyzing and controlling ability of the power system and to ensure the stable and reliable operation of the power system.<\/jats:p>","DOI":"10.3390\/s23198053","type":"journal-article","created":{"date-parts":[[2023,9,24]],"date-time":"2023-09-24T10:48:31Z","timestamp":1695552511000},"page":"8053","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Smart Grid Outlier Detection Based on the Minorization\u2013Maximization Algorithm"],"prefix":"10.3390","volume":"23","author":[{"given":"Lina","family":"Qiao","sequence":"first","affiliation":[{"name":"College of Electrical Engineering, Anhui Polytechnic University, Wuhu 241000, China"},{"name":"Key Laboratory of Advanced Perception and Intelligent Control of High-End Equipment, Chinese Ministry of Education, Wuhu 241000, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2679-4641","authenticated-orcid":false,"given":"Wengen","family":"Gao","sequence":"additional","affiliation":[{"name":"College of Electrical Engineering, Anhui Polytechnic University, Wuhu 241000, China"},{"name":"Key Laboratory of Advanced Perception and Intelligent Control of High-End Equipment, Chinese Ministry of Education, Wuhu 241000, China"}]},{"given":"Yunfei","family":"Li","sequence":"additional","affiliation":[{"name":"College of Electrical Engineering, Anhui Polytechnic University, Wuhu 241000, China"},{"name":"Key Laboratory of Advanced Perception and Intelligent Control of High-End Equipment, Chinese Ministry of Education, Wuhu 241000, China"}]},{"given":"Xinxin","family":"Guo","sequence":"additional","affiliation":[{"name":"College of Electrical Engineering, Anhui Polytechnic University, Wuhu 241000, China"},{"name":"Key Laboratory of Advanced Perception and Intelligent Control of High-End Equipment, Chinese Ministry of Education, Wuhu 241000, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7332-7096","authenticated-orcid":false,"given":"Pengfei","family":"Hu","sequence":"additional","affiliation":[{"name":"College of Electrical Engineering, Anhui Polytechnic University, Wuhu 241000, China"},{"name":"Key Laboratory of Advanced Perception and Intelligent Control of High-End Equipment, Chinese Ministry of Education, Wuhu 241000, China"}]},{"ORCID":"https:\/\/orcid.org\/0009-0008-1353-1579","authenticated-orcid":false,"given":"Feng","family":"Hua","sequence":"additional","affiliation":[{"name":"College of Electrical Engineering, Anhui Polytechnic University, Wuhu 241000, China"},{"name":"Key Laboratory of Advanced Perception and Intelligent Control of High-End Equipment, Chinese Ministry of Education, Wuhu 241000, China"}]}],"member":"1968","published-online":{"date-parts":[[2023,9,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"3188","DOI":"10.1109\/TPWRS.2019.2894769","article-title":"Power system dynamic state estimation: Motivations, definitions, methodologies, and future work","volume":"34","author":"Zhao","year":"2019","journal-title":"IEEE Trans. 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