{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,19]],"date-time":"2026-07-19T03:14:45Z","timestamp":1784430885718,"version":"3.55.0"},"reference-count":36,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2023,10,17]],"date-time":"2023-10-17T00:00:00Z","timestamp":1697500800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"China Scholarship Council","award":["201906040194"],"award-info":[{"award-number":["201906040194"]}]},{"name":"China Scholarship Council","award":["22QB1400200"],"award-info":[{"award-number":["22QB1400200"]}]},{"name":"China Scholarship Council","award":["101019718"],"award-info":[{"award-number":["101019718"]}]},{"name":"Shanghai Science and Technology \u201cRising-Star\u201d Program","award":["201906040194"],"award-info":[{"award-number":["201906040194"]}]},{"name":"Shanghai Science and Technology \u201cRising-Star\u201d Program","award":["22QB1400200"],"award-info":[{"award-number":["22QB1400200"]}]},{"name":"Shanghai Science and Technology \u201cRising-Star\u201d Program","award":["101019718"],"award-info":[{"award-number":["101019718"]}]},{"name":"European Union\u2019s Horizon 2020 research and innovation program","award":["201906040194"],"award-info":[{"award-number":["201906040194"]}]},{"name":"European Union\u2019s Horizon 2020 research and innovation program","award":["22QB1400200"],"award-info":[{"award-number":["22QB1400200"]}]},{"name":"European Union\u2019s Horizon 2020 research and innovation program","award":["101019718"],"award-info":[{"award-number":["101019718"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>For this study, we investigated efficient strategies for the recovery of individual links in power grids governed by the direct current (DC) power flow model, under random link failures. Our primary objective was to explore the efficacy of recovering failed links based solely on topological network metrics. In total, we considered 13 recovery strategies, which encompassed 2 strategies based on link centrality values (link betweenness and link flow betweenness), 8 strategies based on the products of node centrality values at link endpoints (degree, eigenvector, weighted eigenvector, closeness, electrical closeness, weighted electrical closeness, zeta vector, and weighted zeta vector), and 2 heuristic strategies (greedy recovery and two-step greedy recovery), in addition to the random recovery strategy. To evaluate the performance of these proposed strategies, we conducted simulations on three distinct power systems: the IEEE 30, IEEE 39, and IEEE 118 systems. Our findings revealed several key insights: Firstly, there were notable variations in the performance of the recovery strategies based on topological network metrics across different power systems. Secondly, all such strategies exhibited inferior performance when compared to the heuristic recovery strategies. Thirdly, the two-step greedy recovery strategy consistently outperformed the others, with the greedy recovery strategy ranking second. Based on our results, we conclude that relying solely on a single metric for the development of a recovery strategy is insufficient when restoring power grids following link failures. By comparison, recovery strategies employing greedy algorithms prove to be more effective choices.<\/jats:p>","DOI":"10.3390\/e25101455","type":"journal-article","created":{"date-parts":[[2023,10,17]],"date-time":"2023-10-17T08:08:33Z","timestamp":1697530113000},"page":"1455","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Recovering Power Grids Using Strategies Based on Network Metrics and Greedy Algorithms"],"prefix":"10.3390","volume":"25","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9848-6886","authenticated-orcid":false,"given":"Fenghua","family":"Wang","sequence":"first","affiliation":[{"name":"Faculty of Electrical Engineering, Mathematics and Computer Science, Delft University of Technology, 2628 CD Delft, The Netherlands"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hale","family":"Cetinay","sequence":"additional","affiliation":[{"name":"Asset Management, System Insights and Advanced Analytics, Stedin, 3011 TA Rotterdam, The Netherlands"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhidong","family":"He","sequence":"additional","affiliation":[{"name":"DS Information Technology Co., Ltd., Shanghai 200032, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Le","family":"Liu","sequence":"additional","affiliation":[{"name":"Faculty of Electrical Engineering, Mathematics and Computer Science, Delft University of Technology, 2628 CD Delft, The Netherlands"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Piet","family":"Van Mieghem","sequence":"additional","affiliation":[{"name":"Faculty of Electrical Engineering, Mathematics and Computer Science, Delft University of Technology, 2628 CD Delft, The Netherlands"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Robert E.","family":"Kooij","sequence":"additional","affiliation":[{"name":"Faculty of Electrical Engineering, Mathematics and Computer Science, Delft University of Technology, 2628 CD Delft, The Netherlands"},{"name":"Unit ICT, Strategy and Policy, Netherlands Organisation for Applied Scientific Research (TNO), 2595 DA Den Haag, The Netherlands"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,10,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"245","DOI":"10.1002\/eqe.622","article-title":"Seismic safety evaluation of electric power supply at urban level","volume":"36","author":"Nuti","year":"2007","journal-title":"Earthq. Eng. Struct. Dyn."},{"key":"ref_2","unstructured":"Zhou, X., and Yan, C. (2008, January 20\u201324). A blackout in Hainan Island power system: Causes and restoration procedure. Proceedings of the 2008 IEEE Power and Energy Society General Meeting-Conversion and Delivery of Electrical Energy in the 21st Century, Pittsburgh, PA, USA."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"112567","DOI":"10.1016\/j.rser.2022.112567","article-title":"A systematic review on power system resilience from the perspective of generation, network, and load","volume":"167","author":"Wang","year":"2022","journal-title":"Renew. Sustain. Energy Rev."},{"key":"ref_4","unstructured":"Muir, A., and Lopatto, J. (2004). Final Report on the August 14, 2003 Blackout in the United States and Canada: Causes and Recommendations, Technical Report."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"LaCommare, K.H., and Eto, J.H. (2004). Understanding the Cost of Power Interruptions to US Electricity Consumers, Lawrence Berkeley National Lab. (LBNL). Technical Report.","DOI":"10.2172\/834270"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"5249","DOI":"10.1016\/j.enpol.2009.07.049","article-title":"Large blackouts in North America: Historical trends and policy implications","volume":"37","author":"Hines","year":"2009","journal-title":"Energy Policy"},{"key":"ref_7","unstructured":"Van Mieghem, P., Doerr, C., Wang, H., Hernandez, J.M., Hutchison, D., Karaliopoulos, M., and Kooij, R. (2010). A Framework for Computing Topological Network Robustness, Delft University of Technology. Report20101218."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"34","DOI":"10.1007\/s41109-018-0089-9","article-title":"Nodal vulnerability to targeted attacks in power grids","volume":"3","author":"Cetinay","year":"2018","journal-title":"Appl. Netw. Sci."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1975","DOI":"10.1038\/s41467-018-04287-5","article-title":"Dynamically induced cascading failures in power grids","volume":"9","author":"Witthaut","year":"2018","journal-title":"Nat. Commun."},{"key":"ref_10","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. A Stat. Mech. Its Appl."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"112185","DOI":"10.1016\/j.rser.2022.112185","article-title":"Enhancing the resilience of critical infrastructures: Statistical analysis of power grid spectral clustering and post-contingency vulnerability metrics","volume":"159","author":"Rocchetta","year":"2022","journal-title":"Renew. Sustain. Energy Rev."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1591","DOI":"10.1109\/TPWRS.2017.2738326","article-title":"Controlled Islanding Solution for Large-Scale Power Systems","volume":"33","author":"Kyriacou","year":"2018","journal-title":"IEEE Trans. Power Syst."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"112397","DOI":"10.1016\/j.rser.2022.112397","article-title":"Trends in modern power systems resilience: State-of-the-art review","volume":"162","author":"Younesi","year":"2022","journal-title":"Renew. Sustain. Energy Rev."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"332","DOI":"10.1007\/s40565-016-0219-2","article-title":"Power system restoration: A literature review from 2006 to 2016","volume":"4","author":"Liu","year":"2016","journal-title":"J. Mod. Power Syst. Clean Energy"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1357","DOI":"10.1109\/TPWRS.2010.2089646","article-title":"Optimal generator start-up strategy for bulk power system restoration","volume":"26","author":"Sun","year":"2010","journal-title":"IEEE Trans. Power Syst."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"190","DOI":"10.1109\/TSG.2011.2105510","article-title":"A sectionalizing method in power system restoration based on WAMS","volume":"2","author":"Sarmadi","year":"2011","journal-title":"IEEE Trans. Smart Grid"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"122487","DOI":"10.1016\/j.physa.2019.122487","article-title":"Sequential topology recovery of complex power systems based on reinforcement learning","volume":"535","author":"Wu","year":"2019","journal-title":"Phys. A Stat. Mech. Its Appl."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Zhang, Y., Wu, J., Chen, Z., Huang, Y., and Zheng, Z. (2019, January 26\u201329). Sequential Node\/Link Recovery Strategy of Power Grids Based on Q-Learning Approach. Proceedings of the 2019 IEEE International Symposium on Circuits and Systems (ISCAS), Sapporo, Japan.","DOI":"10.1109\/ISCAS.2019.8702107"},{"key":"ref_19","first-page":"1402","article-title":"Integrating Reinforcement Learning and Optimal Power Dispatch to Enhance Power Grid Resilience","volume":"69","author":"Li","year":"2022","journal-title":"IEEE Trans. Circuits Syst. II Express Briefs"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"2997","DOI":"10.1109\/TNSE.2020.3008799","article-title":"Sequential Recovery of Complex Networks Suffering from Cascading Failure Blackouts","volume":"7","author":"Wu","year":"2020","journal-title":"IEEE Trans. Netw. Sci. Eng."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"5453","DOI":"10.1109\/TIA.2023.3287944","article-title":"Service Restoration Using Deep Reinforcement Learning and Dynamic Microgrid Formation in Distribution Networks","volume":"59","author":"Igder","year":"2023","journal-title":"IEEE Trans. Ind. Appl."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"114508","DOI":"10.1016\/j.apenergy.2020.114508","article-title":"New genetic algorithm for economic dispatch of stand-alone three-modular microgrid in DongAo Island","volume":"263","author":"Yeh","year":"2020","journal-title":"Appl. Energy"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"He, Z., Sun, P., and Van Mieghem, P. (2019, January 14\u201316). Topological Approach to Measure Network Recoverability. Proceedings of the 2019 11th International Workshop on Resilient Networks Design and Modeling (RNDM), Nicosia, Cyprus.","DOI":"10.1109\/RNDM48015.2019.8949119"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"44","DOI":"10.1093\/comnet\/cnt004","article-title":"Robustness envelopes of networks","volume":"1","author":"Trajanovski","year":"2013","journal-title":"J. Complex Netw."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"100617","DOI":"10.1016\/j.osn.2021.100617","article-title":"Topological approach to measure the recoverability of optical networks","volume":"41","author":"Sun","year":"2021","journal-title":"Opt. Switch. Netw."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"032311","DOI":"10.1103\/PhysRevE.96.032311","article-title":"Pseudoinverse of the Laplacian and best spreader node in a network","volume":"96","author":"Devriendt","year":"2017","journal-title":"Phys. Rev. E"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Ko\u00e7, Y., Verma, T., Araujo, N.A.M., and Warnier, M. (2013, January 14). MATCASC: A tool to analyse cascading line outages in power grids. Proceedings of the 2013 IEEE International Workshop on Inteligent Energy Systems (IWIES), Vienna, Austria.","DOI":"10.1109\/IWIES.2013.6698576"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"301","DOI":"10.1109\/TNSE.2017.2763746","article-title":"Comparing the effects of failures in power grids under the AC and DC power flow models","volume":"5","author":"Cetinay","year":"2017","journal-title":"IEEE Trans. Netw. Sci. Eng."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"065102","DOI":"10.1103\/PhysRevE.66.065102","article-title":"Cascade-based attacks on complex networks","volume":"66","author":"Motter","year":"2002","journal-title":"Phys. Rev. E"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"016101","DOI":"10.1103\/PhysRevE.84.016101","article-title":"Decreasing the spectral radius of a graph by link removals","volume":"84","author":"Kuipers","year":"2011","journal-title":"Phys. Rev. E"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"026113","DOI":"10.1103\/PhysRevE.69.026113","article-title":"Finding and evaluating community structure in networks","volume":"69","author":"Newman","year":"2004","journal-title":"Phys. Rev. E"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1016\/j.socnet.2004.11.009","article-title":"A measure of betweenness centrality based on random walks","volume":"27","author":"Newman","year":"2005","journal-title":"Soc. Netw."},{"key":"ref_33","first-page":"1","article-title":"The mathematics of networks","volume":"Volume 2","author":"Newman","year":"2008","journal-title":"The New Palgrave Dictionary of Economics"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1016\/0378-8733(78)90021-7","article-title":"Centrality in social networks conceptual clarification","volume":"1","author":"Freeman","year":"1978","journal-title":"Soc. Netw."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"2524","DOI":"10.1109\/JSYST.2016.2573851","article-title":"A topological investigation of power flow","volume":"12","author":"Cetinay","year":"2016","journal-title":"IEEE Syst. J."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"2491","DOI":"10.1016\/j.laa.2011.02.024","article-title":"Effective graph resistance","volume":"435","author":"Ellens","year":"2011","journal-title":"Linear Algebra Its Appl."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/25\/10\/1455\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T21:08:20Z","timestamp":1760130500000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/25\/10\/1455"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,10,17]]},"references-count":36,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2023,10]]}},"alternative-id":["e25101455"],"URL":"https:\/\/doi.org\/10.3390\/e25101455","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,10,17]]}}}