Improving Power Grid Network Robustness by Optimized Switch Allocation: A Large-Scale Case Study in Brazil

Improving Power Grid Network Robustness by Optimized Switch Allocation: A Large-Scale Case Study in Brazil | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Improving Power Grid Network Robustness by Optimized Switch Allocation: A Large-Scale Case Study in Brazil Fabio Guerra, João Jacobsen, Ana Caroline Bonafin, Kallil Zielinski, and 10 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9438133/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 4 You are reading this latest preprint version Abstract Radial distribution networks are inherently vulnerable to cascading outages: a single fault on an unprotected lateral can trip the feeder breaker and de-energize thousands of consumers. Optimally placing protective switches to segment these networks is an NP-hard combinatorial problem whose exact formulation scales at $O(2^N)$, making it intractable for real utility-scale grids. We propose a scalable graph-theoretic heuristic based on a Cumulative Downstream Load (CDL) metric that identifies the electrical backbone of each feeder through a two-pass tree traversal in $O(N)$ time. The method exploits a formal isomorphism between radial power flow and hydrological stream ordering (Horton-Strahler), treating the feeder as a ''reverse river'' where load accumulates from consumers to the substation. Applied to the full distribution network of COPEL, a major Brazilian utility encompassing approximately 3.8 million nodes and 2,415 feeders, the algorithm proposed 6,979 switch locations across 1,757 feeders in under five minutes on commodity hardware. Of these, 92.6% correspond to genuinely unprotected locations, while the remaining 7.4% independently confirm devices already placed by utility engineers. In aggregate, the proposed allocation would protect over 349,000 backbone consumer units from unnecessary cascading outages while isolating over one million lateral consumer units into properly segmented fault zones, with a highly skewed per-switch impact distribution that enables priority-based phased deployment. The results demonstrate that linear-time network science heuristics can deliver actionable infrastructure recommendations at scales where conventional optimization methods fail to converge. Power distribution network Switch allocation Network robustness Graph theory Cumulative downstream load Stream ordering Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Reviewers invited by journal 11 May, 2026 Editor assigned by journal 17 Apr, 2026 Submission checks completed at journal 17 Apr, 2026 First submitted to journal 16 Apr, 2026 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-9438133","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":624302561,"identity":"5003bf18-f082-4ad3-b917-43aa4e9e15d8","order_by":0,"name":"Fabio Guerra","email":"data:image/png;base64,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","orcid":"","institution":"Tech2Think - 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Optimally placing protective switches to segment these networks is an NP-hard combinatorial problem whose exact formulation scales at $O(2^N)$, making it intractable for real utility-scale grids. We propose a scalable graph-theoretic heuristic based on a Cumulative Downstream Load (CDL) metric that identifies the electrical backbone of each feeder through a two-pass tree traversal in $O(N)$ time. The method exploits a formal isomorphism between radial power flow and hydrological stream ordering (Horton-Strahler), treating the feeder as a ''reverse river'' where load accumulates from consumers to the substation. Applied to the full distribution network of COPEL, a major Brazilian utility encompassing approximately 3.8 million nodes and 2,415 feeders, the algorithm proposed 6,979 switch locations across 1,757 feeders in under five minutes on commodity hardware. Of these, 92.6\\% correspond to genuinely unprotected locations, while the remaining 7.4\\% independently confirm devices already placed by utility engineers. In aggregate, the proposed allocation would protect over 349,000 backbone consumer units from unnecessary cascading outages while isolating over one million lateral consumer units into properly segmented fault zones, with a highly skewed per-switch impact distribution that enables priority-based phased deployment. 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