{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,31]],"date-time":"2025-10-31T08:06:39Z","timestamp":1761897999936,"version":"build-2065373602"},"reference-count":46,"publisher":"MDPI AG","issue":"21","license":[{"start":{"date-parts":[[2024,10,27]],"date-time":"2024-10-27T00:00:00Z","timestamp":1729987200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["62303121","62473100","62303125","62373111","U23A20341","U21A20522","2023M740750","2022A1515110949"],"award-info":[{"award-number":["62303121","62473100","62303125","62373111","U23A20341","U21A20522","2023M740750","2022A1515110949"]}]},{"name":"China Postdoctoral Science Foundation","award":["62303121","62473100","62303125","62373111","U23A20341","U21A20522","2023M740750","2022A1515110949"],"award-info":[{"award-number":["62303121","62473100","62303125","62373111","U23A20341","U21A20522","2023M740750","2022A1515110949"]}]},{"name":"Guangdong Basic and Applied Basic Research Foundation","award":["62303121","62473100","62303125","62373111","U23A20341","U21A20522","2023M740750","2022A1515110949"],"award-info":[{"award-number":["62303121","62473100","62303125","62373111","U23A20341","U21A20522","2023M740750","2022A1515110949"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Due to its vulnerability to a variety of cyber attacks, research on cyber security for power systems has become especially crucial. In order to maintain the safe and stable operation of power systems, it is worthwhile to gain insight into the complex characteristics and behaviors of cyber attacks from the attacker\u2019s perspective. The consensus-based distributed state estimation problem is investigated for power systems subject to collaborative attacks. In order to describe such attack behaviors, the denial of service (DoS) attack model for hybrid remote terminal unit (RTU) and phasor measurement unit (PMU) measurements, and the false data injection (FDI) attack model for neighboring estimation information, are constructed. By integrating these two types of attack models, a different consensus-based distributed estimator is designed to accurately estimate the state of the power system under collaborative attacks. Then, through Lyapunov stability analysis theory, a sufficient condition is provided to ensure that the proposed distributed estimator is stable, and a suitable consensus gain matrix is devised. Finally, to confirm the viability and efficacy of the suggested algorithm, a simulation experiment on an IEEE benchmark 14-bus power system is carried out.<\/jats:p>","DOI":"10.3390\/s24216886","type":"journal-article","created":{"date-parts":[[2024,10,28]],"date-time":"2024-10-28T08:39:07Z","timestamp":1730104747000},"page":"6886","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Consensus-Based Power System State Estimation Algorithm Under Collaborative Attack"],"prefix":"10.3390","volume":"24","author":[{"given":"Zhijian","family":"Cheng","sequence":"first","affiliation":[{"name":"School of Automation, Guangdong-Hong Kong Joint Laboratory for Intelligent Decision and Cooperative Control, and Guangdong Provincial Key Laboratory for Intelligent Decision and Cooperative Control, Guangdong University of Technology, Guangzhou 510006, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7860-4475","authenticated-orcid":false,"given":"Guanjun","family":"Chen","sequence":"additional","affiliation":[{"name":"CSSC Systems Engineering Research Institute, China State Shipbuilding Corporation Limited, Beijing 100094, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiao-Meng","family":"Li","sequence":"additional","affiliation":[{"name":"School of Mechanical and Electrical Engineering, Guangzhou University, Guangzhou 510006, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hongru","family":"Ren","sequence":"additional","affiliation":[{"name":"School of Automation, Guangdong-Hong Kong Joint Laboratory for Intelligent Decision and Cooperative Control, and Guangdong Provincial Key Laboratory for Intelligent Decision and Cooperative Control, Guangdong University of Technology, Guangzhou 510006, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,10,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"3221","DOI":"10.1049\/iet-cta.2017.0629","article-title":"Recent advances on state estimation for power grids with unconventional measurements","volume":"11","author":"Hu","year":"2017","journal-title":"IET Control Theory Appl."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1784","DOI":"10.1109\/TAC.2018.2852774","article-title":"Power grid AC-based state estimation: Vulnerability analysis against cyber attacks","volume":"64","author":"Jin","year":"2019","journal-title":"IEEE Trans. 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