SUM-OF-SQUARES APPROACH FOR MODELING AND CONTROL OF HAIL POWER SYSTEM WITH TIME DELAY AND CONFORMABLE FRACTIONAL-ORDER DERIVATIVE

Omar Kahouli, Hamdi Gassara (), Saleh Albadran (), Ahmed El Hajjaji () and Abdellatif Ben Makhlouf ()
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Omar Kahouli: Department of Electronics Engineering, Community College, University of Ha’il, 2440 Ha’il, Saudi Arabia2Scientific and Engineering Research Center, University of Ha’il, 2440 Ha’il, Saudi Arabia
Hamdi Gassara: Laboratory of Sciences and Techniques of Automatic Control and Computer Engineering, National School of Engineering of Sfax, University of Sfax, PB 1173, 3038 Sfax, Tunisia
Saleh Albadran: Department of Electrical Engineering, College of Engineering, University of Ha’il, 2440 Ha’il, Saudi Arabia
Ahmed El Hajjaji: Modeling, Information, and Systems Laboratory, University of Picardie Jules Verne, UFR of Sciences, 33 Rue St Leu, 80000 Amiens, France
Abdellatif Ben Makhlouf: Department of Mathematics, Faculty of Sciences of Sfax, University of Sfax, BP 1171, Sfax, Tunisia

FRACTALS (fractals), 2025, vol. 33, issue 04, 1-11

Abstract: This research focuses on stabilization challenges of a Power System (PS) described by a delayed conformable fractional-order nonlinear model. We adopt the Polynomial Fitting Approximation Algorithm (PFAA) to approximate the cardinal sine function by a Square Of Polynomial (SOP). A polynomial representation is made for PS with different behaviors by dividing the operating range into r regions and then calculating an SOP approximation for each region. Thus, the PS is characterized by r distinct models, each applicable within its respective region. An Observer Based Control (OBC) is designed to stabilize the considered PS. The proposed result ensures the stabilization of the different r models by satisfying sufficient conditions based on the sum-of-squares (SOS) approach.

Keywords: Power System; Polynomial Model; SOS Approach; Time Delay (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1142/S0218348X25400870

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