Robust Stability Region for Load Frequency Control with Inverter Air Conditioner using Kharitonov’s Theorem

Robust Stability Region for Load Frequency Control with Inverter Air Conditioner using Kharitonov’s Theorem | 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 Robust Stability Region for Load Frequency Control with Inverter Air Conditioner using Kharitonov’s Theorem Muhanned Al-Shalah, Azhar Jabbar Abdulridha, Saffet Ayasun This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7364331/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 02 Apr, 2026 Read the published version in Electrical Engineering → Version 1 posted 14 You are reading this latest preprint version Abstract The widespread use of inverter based air conditioners (IACs) as a controllable load makes them a promising tool in the frequency regulation of power systems. However, utilization an open communication network in the aggregation and control of several IACs introduces time delays which adversely affect the frequency stability. Moreover, uncertainties in system parameters makes the stability issue as challenging problem together with time delays. Time delays and uncertainties degrade the controller performance cause undesirable fluctuation in system frequency and may even lead to instability. Therefore, a robust controller design is essential to maintain stability under disturbances considering both delays and parametric uncertainties. This work proposes a novel utilization of Kharitonov’s Theorem with stability boundary locus approach—to determine robust all stabilizing controller gains constituting a stable region. The influences of parametric uncertainties, the number of IACs and time delays on stability regions are comprehensively analyzed. Results clearly show that increase in time delay and uncertainty reduces the size of the robust stability, indicating diminished stability robustness. Finally, the accuracy of theoretical results is verified by using MATLAB Simulink and quasi-polynomial mapping-based root finder algorithm. Communication time delays Inverter air conditioners Kharitonov Theorem Load frequency control Robust stability region Stability boundary locus Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 02 Apr, 2026 Read the published version in Electrical Engineering → Version 1 posted Editorial decision: Revision requested 07 Dec, 2025 Reviewers agreed at journal 18 Oct, 2025 Reviews received at journal 16 Oct, 2025 Reviews received at journal 14 Oct, 2025 Reviewers agreed at journal 14 Oct, 2025 Reviewers agreed at journal 10 Oct, 2025 Reviews received at journal 02 Oct, 2025 Reviews received at journal 30 Sep, 2025 Reviewers agreed at journal 23 Sep, 2025 Reviewers agreed at journal 22 Sep, 2025 Reviewers invited by journal 22 Sep, 2025 Editor assigned by journal 14 Aug, 2025 Submission checks completed at journal 14 Aug, 2025 First submitted to journal 13 Aug, 2025 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-7364331","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":523918479,"identity":"9d429cd5-f721-4f9b-8f5c-fda1298315a8","order_by":0,"name":"Muhanned Al-Shalah","email":"","orcid":"","institution":"Gazi University","correspondingAuthor":false,"prefix":"","firstName":"Muhanned","middleName":"","lastName":"Al-Shalah","suffix":""},{"id":523918480,"identity":"4c9b48b3-f298-4bf9-aa85-ad9cf69089f9","order_by":1,"name":"Azhar Jabbar Abdulridha","email":"","orcid":"","institution":"Gazi 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However, utilization an open communication network in the aggregation and control of several IACs introduces time delays which adversely affect the frequency stability. Moreover, uncertainties in system parameters makes the stability issue as challenging problem together with time delays. Time delays and uncertainties degrade the controller performance cause undesirable fluctuation in system frequency and may even lead to instability. Therefore, a robust controller design is essential to maintain stability under disturbances considering both delays and parametric uncertainties. This work proposes a novel utilization of Kharitonov\u0026rsquo;s Theorem with stability boundary locus approach\u0026mdash;to determine robust all stabilizing controller gains constituting a stable region. The influences of parametric uncertainties, the number of IACs and time delays on stability regions are comprehensively analyzed. Results clearly show that increase in time delay and uncertainty reduces the size of the robust stability, indicating diminished stability robustness. 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