{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,18]],"date-time":"2026-06-18T18:31:25Z","timestamp":1781807485628,"version":"3.54.5"},"reference-count":40,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2024,9,17]],"date-time":"2024-09-17T00:00:00Z","timestamp":1726531200000},"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":["61971033"],"award-info":[{"award-number":["61971033"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["2021YJ0313"],"award-info":[{"award-number":["2021YJ0313"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Sichuan Application and Basic Research Funds","award":["61971033"],"award-info":[{"award-number":["61971033"]}]},{"name":"Sichuan Application and Basic Research Funds","award":["2021YJ0313"],"award-info":[{"award-number":["2021YJ0313"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>To mitigate the impact of wind power uncertainty and power\u2013communication coupling on the robustness of a new power system, a bi-level mixed-integer robust optimization strategy is proposed. Firstly, a coupled network model is constructed based on complex network theory, taking into account the coupled relationship of energy supply and control dependencies between the power and communication networks. Next, a bi-level mixed-integer robust optimization model is developed to improve power system resilience, incorporating constraints related to the coupling strength, electrical characteristics, and traffic characteristics of the information network. The upper-level model seeks to minimize load shedding by optimizing DC power flow using fuzzy chance constraints, thereby reducing the risk of power imbalances caused by random fluctuations in wind power generation. Furthermore, the deterministic power balance constraints are relaxed into inequality constraints that account for wind power forecasting errors through fuzzy variables. The lower-level model focuses on minimizing traffic load shedding by establishing a topology\u2013function-constrained information network traffic model based on the maximum flow principle in graph theory, thereby improving the efficiency of network flow transmission. Finally, a modified IEEE 39-bus test system with intermittent wind power is used as a case study. Random attack simulations demonstrate that, under the highest link failure rate and wind power penetration, Model 2 outperforms Model 1 by reducing the load loss ratio by 23.6% and improving the node survival ratio by 5.3%.<\/jats:p>","DOI":"10.3390\/e26090795","type":"journal-article","created":{"date-parts":[[2024,9,18]],"date-time":"2024-09-18T01:16:10Z","timestamp":1726622170000},"page":"795","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Robust Optimization Research of Cyber\u2013Physical Power System Considering Wind Power Uncertainty and Coupled Relationship"],"prefix":"10.3390","volume":"26","author":[{"given":"Jiuling","family":"Dong","sequence":"first","affiliation":[{"name":"School of Computer and Communication Engineering, University of Science and Technology Beijing, Beijing 100083, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zilong","family":"Song","sequence":"additional","affiliation":[{"name":"School of Computer and Communication Engineering, University of Science and Technology Beijing, Beijing 100083, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yuanshuo","family":"Zheng","sequence":"additional","affiliation":[{"name":"School of Information Science and Technology, Hainan Normal University, Haikou 571158, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8486-222X","authenticated-orcid":false,"given":"Jingtang","family":"Luo","sequence":"additional","affiliation":[{"name":"State Grid Sichuan Economic Research Institute, Chengdu 610041, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3293-6121","authenticated-orcid":false,"given":"Min","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Computer and Communication Engineering, University of Science and Technology Beijing, Beijing 100083, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5102-6962","authenticated-orcid":false,"given":"Xiaolong","family":"Yang","sequence":"additional","affiliation":[{"name":"School of Computer and Communication Engineering, University of Science and Technology Beijing, Beijing 100083, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1785-4024","authenticated-orcid":false,"given":"Hongbing","family":"Ma","sequence":"additional","affiliation":[{"name":"Department of Electronic Engineering, Tsinghua University, Beijing 100084, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2024,9,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"5620","DOI":"10.1109\/TSG.2018.2888629","article-title":"Robust Routing Optimization for Smart Grids Considering Cyber-Physical Interdependence","volume":"10","author":"Xu","year":"2019","journal-title":"IEEE Trans. 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