{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,1]],"date-time":"2026-06-01T16:07:52Z","timestamp":1780330072978,"version":"3.54.1"},"reference-count":33,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2022,10,11]],"date-time":"2022-10-11T00:00:00Z","timestamp":1665446400000},"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":["11702195"],"award-info":[{"award-number":["11702195"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Vulnerability is a major concern for power networks. Malicious attacks have the potential to trigger cascading failures and large blackouts. The robustness of power networks against line failure has been of interest in the past several years. However, this scenario cannot cover weighted situations in the real world. This paper investigates the vulnerability of weighted power networks. Firstly, we propose a more practical capacity model to investigate the cascading failure of weighted power networks under different attack strategies. Results show that the smaller threshold of the capacity parameter can enhance the vulnerability of weighted power networks. Furthermore, a weighted electrical cyber-physical interdependent network is developed to study the vulnerability and failure dynamics of the entire power network. We perform simulations in the IEEE 118 Bus case to evaluate the vulnerability under various coupling schemes and different attack strategies. Simulation results show that heavier loads increase the likelihood of blackouts and that different coupling strategies play a crucial role in the cascading failure performance.<\/jats:p>","DOI":"10.3390\/e24101449","type":"journal-article","created":{"date-parts":[[2022,10,11]],"date-time":"2022-10-11T22:18:13Z","timestamp":1665526693000},"page":"1449","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Analysis of Vulnerability on Weighted Power Networks under Line Breakdowns"],"prefix":"10.3390","volume":"24","author":[{"given":"Lixin","family":"Yang","sequence":"first","affiliation":[{"name":"School of Mathematics & Data Science, Shaanxi University of Science and Technology, Xi\u2019an 710021, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ziyu","family":"Gu","sequence":"additional","affiliation":[{"name":"School of Mathematics & Data Science, Shaanxi University of Science and Technology, Xi\u2019an 710021, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yuanchen","family":"Dang","sequence":"additional","affiliation":[{"name":"School of Mathematics & Data Science, Shaanxi University of Science and Technology, Xi\u2019an 710021, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Peiyan","family":"He","sequence":"additional","affiliation":[{"name":"School of Mathematics & Data Science, Shaanxi University of Science and Technology, Xi\u2019an 710021, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2022,10,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2688","DOI":"10.1016\/j.physa.2013.01.023","article-title":"The Power Grid as a complex network: A survey","volume":"392","author":"Pagani","year":"2013","journal-title":"Phys. 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