Variable-Order interval Type-II Fuzzy Fractional PID Controller for Load Frequency Control Optimized via Hybrid Optimization

Variable-Order interval Type-II Fuzzy Fractional PID Controller for Load Frequency Control Optimized via Hybrid Optimization | 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 Variable-Order interval Type-II Fuzzy Fractional PID Controller for Load Frequency Control Optimized via Hybrid Optimization Mohammad Ali Labbaf Khaniki, Mahsan Tavakoli-Kakhki, Mohammad Teshnehlab This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3914154/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract The main goal of the Load Frequency Control (LFC) system is to reduce the deviation of frequency and stabilize the power system against disturbances. In this paper, a Variable-Order interval type-II Fuzzy Fractional PID (VOFFPID) controller with hybrid optimization is proposed for frequency control of multi-source two-area interconnected power system. Interval type-II Fuzzy Inference System (FIS) determines the coefficients of the Fractional Order PID (FOPID) controller and the derivative and integral order online, to give a higher degree of freedom to the controller. This model includes hydro, thermal and gas generation in each area. To improve the performance of the system, the initial control parameters of the FOPID controller have been obtained using Whale Optimization Algorithm (WOA). Moreover, Stochastic Gradient Descent (SGD) is used to optimize the consequent part of the fuzzy controller during control procedure. To verify the robustness of the proposed control system, the designed controller is applied in the presence of a wide range of disturbances, uncertainties and nonlinearity. The controller is capable of guaranteeing the integrity since when the controller of one area is dropped, the other controller can control the whole system. Load Frequency Control Fractional-Order PID Controller Whale Optimization Algorithm Stochastic Gradient Descent Interval Type-II Fuzzy Inference System. Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted 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. 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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-3914154","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":271286889,"identity":"1a8f596b-f392-4e43-8574-c1491a74bc55","order_by":0,"name":"Mohammad Ali Labbaf Khaniki","email":"data:image/png;base64,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","orcid":"","institution":"K.N. 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