{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,2]],"date-time":"2026-06-02T09:22:14Z","timestamp":1780392134422,"version":"3.54.1"},"reference-count":28,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2026,6,2]],"date-time":"2026-06-02T00:00:00Z","timestamp":1780358400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0"},{"start":{"date-parts":[[2026,6,2]],"date-time":"2026-06-02T00:00:00Z","timestamp":1780358400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Auton. Intell. Syst."],"DOI":"10.1007\/s43684-026-00132-5","type":"journal-article","created":{"date-parts":[[2026,6,2]],"date-time":"2026-06-02T08:55:04Z","timestamp":1780390504000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Cyber-attack-induced equilibria of high-voltage direct-current power transmission systems"],"prefix":"10.1007","volume":"6","author":[{"given":"Haonan","family":"Xu","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Qinyu","family":"Wei","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Kaiyu","family":"Li","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5947-2585","authenticated-orcid":false,"given":"Xiaoqin","family":"Liu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yulong","family":"Ding","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Dongliang","family":"Zheng","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Kairui","family":"Feng","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yue","family":"Song","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jiazuo","family":"Hou","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,6,2]]},"reference":[{"key":"132_CR1","doi-asserted-by":"publisher","first-page":"689","DOI":"10.1146\/annurev-control-042820-011148","volume":"5","author":"T. Liu","year":"2022","unstructured":"T. Liu, Y. Song, L. Zhu, D.J. Hill, Stability and control of power grids. Annu. Rev. Control Robot. Auton. Syst. 5, 689\u2013716 (2022). https:\/\/doi.org\/10.1146\/annurev-control-042820-011148","journal-title":"Annu. Rev. Control Robot. Auton. Syst."},{"key":"132_CR2","doi-asserted-by":"publisher","first-page":"530","DOI":"10.1016\/j.rser.2019.04.062","volume":"112","author":"A. Alassi","year":"2019","unstructured":"A. Alassi, S. Ba\u00f1ales, O. Ellabban, G. Adam, C. MacIver, HVDC transmission: technology review, market trends and future outlook. Renew. Sustain. Energy Rev. 112, 530\u2013554 (2019). https:\/\/doi.org\/10.1016\/j.rser.2019.04.062","journal-title":"Renew. Sustain. Energy Rev."},{"key":"132_CR3","volume-title":"HVDC and FACTS Controllers: Applications of Static Converters in Power Systems. Power Electronics and Power Systems","author":"V.K. Sood","year":"2004","unstructured":"V.K. Sood, HVDC and FACTS Controllers: Applications of Static Converters in Power Systems. Power Electronics and Power Systems (Springer, Boston, 2004). SpringerLink (Online service)"},{"key":"132_CR4","unstructured":"PD IEC TR 62543:2011+a2:2017, High-voltage direct current (HVDC) power transmission using voltage sourced converters (VSC). Technical report, International Electrotechnical Commission (2017)"},{"key":"132_CR5","unstructured":"PD IEC TR 60919-1:2020, Performance of high-voltage direct current (HVDC) systems with line-commutated converters. Steady-state conditions. Technical report, International Electrotechnical Commission (2020)"},{"issue":"2","key":"132_CR6","doi-asserted-by":"publisher","first-page":"717","DOI":"10.1109\/TCSII.2020.3011324","volume":"68","author":"M.R. Habibi","year":"2021","unstructured":"M.R. Habibi, H.R. Baghaee, T. Dragi\u010devi\u0107, F. Blaabjerg, False data injection cyber-attacks mitigation in parallel DC\/DC converters based on artificial neural networks. IEEE Trans. Circuits Syst. II, Express Briefs 68(2), 717\u2013721 (2021). https:\/\/doi.org\/10.1109\/TCSII.2020.3011324","journal-title":"IEEE Trans. Circuits Syst. II, Express Briefs"},{"issue":"1","key":"132_CR7","doi-asserted-by":"publisher","first-page":"1258","DOI":"10.1109\/JESTPE.2019.2937800","volume":"10","author":"Y. Chen","year":"2022","unstructured":"Y. Chen, W. Qiu, X. Liu, Y. Kang, A parallel control framework of analog proportional integral and digital model predictive controllers for enhancing power converters cybersecurity. IEEE J. Emerg. Sel. Top. Power Electron. 10(1), 1258\u20131269 (2022). https:\/\/doi.org\/10.1109\/JESTPE.2019.2937800","journal-title":"IEEE J. Emerg. Sel. Top. Power Electron."},{"issue":"3","key":"132_CR8","doi-asserted-by":"publisher","first-page":"38","DOI":"10.1109\/MPE.2019.2897407","volume":"17","author":"D. Roberson","year":"2019","unstructured":"D. Roberson, H.C. Kim, B. Chen, C. Page, R. Nuqui, A. Valdes, R. Macwan, B.K. Johnson, Improving grid resilience using high-voltage DC: strengthening the security of power system stability. IEEE Power Energy Mag. 17(3), 38\u201347 (2019)","journal-title":"IEEE Power Energy Mag."},{"issue":"5","key":"132_CR9","doi-asserted-by":"publisher","first-page":"4915","DOI":"10.1109\/TPEL.2020.3032883","volume":"36","author":"T. Ding","year":"2021","unstructured":"T. Ding, Z. Zeng, B. Qin, J. Zhao, Y. Yang, F. Blaabjerg, Z. Dong, Quantifying cyber attacks on industrial MMC-HVDC control system using structured pseudospectrum. IEEE Trans. Power Electron. 36(5), 4915\u20134920 (2021). https:\/\/doi.org\/10.1109\/TPEL.2020.3032883","journal-title":"IEEE Trans. Power Electron."},{"issue":"3","key":"132_CR10","doi-asserted-by":"publisher","first-page":"2331","DOI":"10.1109\/TSG.2022.3146375","volume":"13","author":"Y. Zhao","year":"2022","unstructured":"Y. Zhao, W. Yao, C.-K. Zhang, X.-C. Shangguan, L. Jiang, J. Wen, Quantifying resilience of wide-area damping control against cyber attack based on switching system theory. IEEE Trans. Smart Grid 13(3), 2331\u20132343 (2022). https:\/\/doi.org\/10.1109\/TSG.2022.3146375","journal-title":"IEEE Trans. Smart Grid"},{"issue":"1","key":"132_CR11","doi-asserted-by":"publisher","first-page":"592","DOI":"10.1109\/TPWRS.2020.3022588","volume":"36","author":"B. Chen","year":"2021","unstructured":"B. Chen, S-i. Yim, H. Kim, A. Kondabathini, R. Nuqui, Cybersecurity of wide area monitoring, protection, and control systems for HVDC applications. IEEE Trans. Power Syst. 36(1), 592\u2013602 (2021). https:\/\/doi.org\/10.1109\/TPWRS.2020.3022588","journal-title":"IEEE Trans. Power Syst."},{"issue":"7","key":"132_CR12","doi-asserted-by":"publisher","first-page":"8488","DOI":"10.1109\/TPEL.2022.3147466","volume":"37","author":"C. Burgos-Mellado","year":"2022","unstructured":"C. Burgos-Mellado, F. Donoso, T. Dragi\u010devi\u0107, R. C\u00e1rdenas-Dobson, P. Wheeler, J. Clare, A. Watson, Cyber-attacks in modular multilevel converters. IEEE Trans. Power Electron. 37(7), 8488\u20138501 (2022). https:\/\/doi.org\/10.1109\/TPEL.2022.3147466","journal-title":"IEEE Trans. Power Electron."},{"issue":"1","key":"132_CR13","doi-asserted-by":"publisher","first-page":"702","DOI":"10.1109\/TPWRS.2022.3168078","volume":"38","author":"K. Sun","year":"2023","unstructured":"K. Sun, W. Qiu, Y. Dong, C. Zhang, H. Yin, W. Yao, Y. Liu, WAMS-based HVDC damping control for cyber attack defense. IEEE Trans. Power Syst. 38(1), 702\u2013713 (2023). https:\/\/doi.org\/10.1109\/TPWRS.2022.3168078","journal-title":"IEEE Trans. Power Syst."},{"issue":"4","key":"132_CR14","doi-asserted-by":"publisher","first-page":"3227","DOI":"10.1109\/TSG.2022.3156796","volume":"13","author":"J. Hou","year":"2022","unstructured":"J. Hou, S. Lei, W. Yin, W. Sun, Y. Hou, Cybersecurity enhancement for multi-infeed high-voltage DC systems. IEEE Trans. Smart Grid 13(4), 3227\u20133240 (2022). https:\/\/doi.org\/10.1109\/TSG.2022.3156796","journal-title":"IEEE Trans. Smart Grid"},{"key":"132_CR15","doi-asserted-by":"publisher","unstructured":"R. Nuqui, Cyber attack resilient HVDC system (CARDS) (final scientific\/technical report). Technical report, ABB Inc. (2019). https:\/\/doi.org\/10.2172\/1810571. https:\/\/www.osti.gov\/biblio\/1810571","DOI":"10.2172\/1810571"},{"key":"132_CR16","unstructured":"Cyber security for HVDC & FACTS - cyber security services. Technical report, Siemens Energy (2021). https:\/\/assets.siemens-energy.com\/siemens\/assets\/api\/uuid:2ec35f7e-6264-4c33-a857-08cfddb53d08\/se-ff-en-cyber-security.pdf"},{"issue":"2","key":"132_CR17","doi-asserted-by":"publisher","first-page":"1719","DOI":"10.1109\/TSG.2024.3492956","volume":"16","author":"H. Faraji","year":"2025","unstructured":"H. Faraji, A. Khorsandi, S. Hossein Hosseinian, Multi-level frequency control, resilience enhancement and cyber-attack identification in multi-area LCC-HVDC interconnected networks. IEEE Trans. Smart Grid 16(2), 1719\u20131731 (2025). https:\/\/doi.org\/10.1109\/TSG.2024.3492956","journal-title":"IEEE Trans. Smart Grid"},{"issue":"4","key":"132_CR18","doi-asserted-by":"publisher","first-page":"3220","DOI":"10.1109\/TSG.2023.3266780","volume":"14","author":"Q. Jiang","year":"2023","unstructured":"Q. Jiang, B. Li, T. Liu, F. Blaabjerg, P. Wang, Study of cyber attack\u2019s impact on LCC-HVDC system with false data injection. IEEE Trans. Smart Grid 14(4), 3220\u20133231 (2023). https:\/\/doi.org\/10.1109\/TSG.2023.3266780","journal-title":"IEEE Trans. Smart Grid"},{"issue":"6","key":"132_CR19","doi-asserted-by":"publisher","first-page":"5305","DOI":"10.1109\/TPWRS.2021.3078770","volume":"36","author":"K. Sun","year":"2021","unstructured":"K. Sun, W. Qiu, W. Yao, S. You, H. Yin, Y. Liu, Frequency injection based HVDC attack-defense control via squeeze-excitation double CNN. IEEE Trans. Power Syst. 36(6), 5305\u20135316 (2021). https:\/\/doi.org\/10.1109\/TPWRS.2021.3078770","journal-title":"IEEE Trans. Power Syst."},{"key":"132_CR20","volume":"4","author":"R. Guo","year":"2025","unstructured":"R. Guo, M. Liu, R. Deng, Vulnerability assessment of high-voltage direct current transmission systems to cyberattacks. Secur. Saf. 4, 2025008 (2025)","journal-title":"Secur. Saf."},{"issue":"6","key":"132_CR21","doi-asserted-by":"publisher","first-page":"5992","DOI":"10.1109\/TSG.2024.3409704","volume":"15","author":"J. Hou","year":"2024","unstructured":"J. Hou, H. Deng, J.C.-H. Peng, A butterfly effect: attack-induced heterogeneous equilibrium points of high-voltage DC systems. IEEE Trans. Smart Grid 15(6), 5992\u20136004 (2024). https:\/\/doi.org\/10.1109\/TSG.2024.3409704","journal-title":"IEEE Trans. Smart Grid"},{"key":"132_CR22","doi-asserted-by":"publisher","DOI":"10.1002\/9781119566632","volume-title":"High Voltage Direct Current Transmission: Converters, Systems and DC Grids","author":"D. Jovcic","year":"2019","unstructured":"D. Jovcic, High Voltage Direct Current Transmission: Converters, Systems and DC Grids (Wiley, 2019)"},{"key":"132_CR23","volume-title":"Power System Stability and Control","author":"P. Kundur","year":"1994","unstructured":"P. Kundur, Power System Stability and Control (McGraw-Hill, New York, 1994)"},{"issue":"2","key":"132_CR24","doi-asserted-by":"publisher","first-page":"1775","DOI":"10.1109\/TSG.2024.3508732","volume":"16","author":"J. Hou","year":"2025","unstructured":"J. Hou, H. Deng, X. Gong, J.C.-H. Peng, Infinitesimal-attack-high-impact phenomena: cyber-attack bifurcation in two-terminal HVDC power delivery systems. IEEE Trans. Smart Grid 16(2), 1775\u20131789 (2025). https:\/\/doi.org\/10.1109\/TSG.2024.3508732","journal-title":"IEEE Trans. Smart Grid"},{"issue":"1","key":"132_CR25","doi-asserted-by":"publisher","first-page":"34","DOI":"10.1109\/TPWRS.2013.2279268","volume":"29","author":"J. Beerten","year":"2014","unstructured":"J. Beerten, S. Cole, R. Belmans, Modeling of multi-terminal VSC HVDC systems with distributed DC voltage control. IEEE Trans. Power Syst. 29(1), 34\u201342 (2014). https:\/\/doi.org\/10.1109\/TPWRS.2013.2279268","journal-title":"IEEE Trans. Power Syst."},{"issue":"10","key":"132_CR26","doi-asserted-by":"publisher","first-page":"9707","DOI":"10.1109\/TIE.2020.3020033","volume":"68","author":"Y. Wang","year":"2021","unstructured":"Y. Wang, S. Mondal, C. Deng, K. Satpathi, Y. Xu, S. Dasgupta, Cyber-resilient cooperative control of bidirectional interlinking converters in networked AC\/DC microgrids. IEEE Trans. Ind. Electron. 68(10), 9707\u20139718 (2021). https:\/\/doi.org\/10.1109\/TIE.2020.3020033","journal-title":"IEEE Trans. Ind. Electron."},{"issue":"6","key":"132_CR27","doi-asserted-by":"publisher","first-page":"6298","DOI":"10.1109\/TSG.2017.2708114","volume":"9","author":"W.-L. Chin","year":"2018","unstructured":"W.-L. Chin, C.-H. Lee, T. Jiang, Blind false data attacks against ac state estimation based on geometric approach in smart grid communications. IEEE Trans. Smart Grid 9(6), 6298\u20136306 (2018). https:\/\/doi.org\/10.1109\/TSG.2017.2708114","journal-title":"IEEE Trans. Smart Grid"},{"key":"132_CR28","volume-title":"IEE International Conference on AC and DC Power Transmission","author":"H. Maddox","year":"1985","unstructured":"H. Maddox, G. Nail, W. K\u00fchn, K. Sadek, The Blackwater HVDC back-to-back tie. In: IEE International Conference on AC and DC Power Transmission (1985)"}],"container-title":["Autonomous Intelligent Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s43684-026-00132-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s43684-026-00132-5","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s43684-026-00132-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,6,2]],"date-time":"2026-06-02T08:55:13Z","timestamp":1780390513000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s43684-026-00132-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,6,2]]},"references-count":28,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2026,12]]}},"alternative-id":["132"],"URL":"https:\/\/doi.org\/10.1007\/s43684-026-00132-5","relation":{},"ISSN":["2730-616X"],"issn-type":[{"value":"2730-616X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,6,2]]},"assertion":[{"value":"7 December 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"14 March 2026","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"26 April 2026","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"2 June 2026","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare no competing interests.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}}],"article-number":"12"}}