A New Model for the Hierarchical Response of Control Devices in the Power Flow Problem

A New Model for the Hierarchical Response of Control Devices in the Power Flow Problem | 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 A New Model for the Hierarchical Response of Control Devices in the Power Flow Problem Paula Oliveira La Gatta, Nicolas Abreu Rocha Leite Netto, Joao Alberto Passos Filho This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4837760/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 25 Nov, 2024 Read the published version in Electrical Engineering → Version 1 posted 11 You are reading this latest preprint version Abstract Various control devices, such as shunt banks, on-load tap changers, and static var compensators, can be connected to a microgrid. Depending on the operating schemes, some of these controls may hierarchically actuate in the system to maintain reactive power reserve. This paper proposes a formulation based on sigmoid functions to perform the hierarchical actuation of control devices in the power flow problem. The methodology was generalized to accommodate N hierarchy levels, where N is the number of control devices. The sigmoid function deals with the operational device, and when it reaches its limits, it activates the performance of the subsequent one. To achieve this, the methodology incorporates equations obtained from combining the steady-state characteristics of the control devices and the sigmoid functions into the power flow formulation. These equations are solved simultaneously with the power flow equations in polar coordinates using the full Newton's method. The methodology is evaluated by applying it to two test systems: 11-bus test system and the well-known Nordic system. The results demonstrate the effectiveness of the proposed approach. Microgrids Power Flow Control Devices Shunt Bank Newton’s Method Hierarchical Controls Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 25 Nov, 2024 Read the published version in Electrical Engineering → Version 1 posted Editorial decision: Revision requested 02 Sep, 2024 Reviews received at journal 24 Aug, 2024 Reviews received at journal 23 Aug, 2024 Reviewers agreed at journal 22 Aug, 2024 Reviews received at journal 20 Aug, 2024 Reviewers agreed at journal 12 Aug, 2024 Reviewers agreed at journal 12 Aug, 2024 Reviewers invited by journal 12 Aug, 2024 Editor assigned by journal 02 Aug, 2024 Submission checks completed at journal 02 Aug, 2024 First submitted to journal 31 Jul, 2024 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. 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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-4837760","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":345749104,"identity":"5058d921-912b-41d5-bb16-9cbf0f60c1ff","order_by":0,"name":"Paula Oliveira La Gatta","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAy0lEQVRIiWNgGAWjYHACxgMMBQxyYOYDhgPE6TnAYMBgDGYlkKIlsYFoLebsZwwO/DCoTe9v7z34IIHhTj5BLZY9OQYHewyO5844cy7ZIIHhmWUDIS0GB3IMDvAYHMvdIJFjJpHAcNiAoC0G598YHPxjcCzdQP6N+Q/itNzIMTjMY1CTYCDBY8ZAlBbLGc8KDssYHDCccSYvWSLB4BlhLeb8yRsfvqmok+dvP3vww4eKO0Q4DEIdBmIeBJcYLXVQLaNgFIyCUTAKsAAAAy5ClLQ6U1sAAAAASUVORK5CYII=","orcid":"","institution":"Brazilian Electric Energy Research Center","correspondingAuthor":true,"prefix":"","firstName":"Paula","middleName":"Oliveira La","lastName":"Gatta","suffix":""},{"id":345749117,"identity":"1be60908-cad2-4e61-b0ab-9b04183aba31","order_by":1,"name":"Nicolas Abreu Rocha Leite Netto","email":"","orcid":"","institution":"Brazilian Electric Energy Research Center","correspondingAuthor":false,"prefix":"","firstName":"Nicolas","middleName":"Abreu Rocha Leite","lastName":"Netto","suffix":""},{"id":345749121,"identity":"ec54f5be-b2c0-42c3-a2e2-a94174d42d8b","order_by":2,"name":"Joao Alberto Passos Filho","email":"","orcid":"","institution":"Universidade Federal de Juiz de Fora","correspondingAuthor":false,"prefix":"","firstName":"Joao","middleName":"Alberto Passos","lastName":"Filho","suffix":""}],"badges":[],"createdAt":"2024-07-31 19:38:24","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4837760/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4837760/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s00202-024-02845-3","type":"published","date":"2024-11-25T15:57:51+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":70388791,"identity":"d58a7d8d-4dc2-42ff-bd18-661762a9ae74","added_by":"auto","created_at":"2024-12-02 17:27:20","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":4915019,"visible":true,"origin":"","legend":"","description":"","filename":"SpringerNatureLaTeXTemplate4.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4837760/v1_covered_4cbc1fa6-c9bd-4c6d-aeb9-4fa1cb457391.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"A New Model for the Hierarchical Response of Control Devices in the Power Flow Problem","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"electrical-engineering","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"elen","sideBox":"Learn more about [Electrical Engineering](http://link.springer.com/journal/202)","snPcode":"202","submissionUrl":"https://submission.nature.com/new-submission/202/3","title":"Electrical Engineering","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Microgrids, Power Flow, Control Devices, Shunt Bank, Newton’s Method, Hierarchical Controls","lastPublishedDoi":"10.21203/rs.3.rs-4837760/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4837760/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Various control devices, such as shunt banks, on-load tap changers, and static var compensators, can be connected to a microgrid. 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