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Sum-Of-Squares Approach For Modeling And Control Of Hail Power System With Time Delay And Conformable Fractional-Order Derivative

Author

Listed:
  • 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)

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.

Suggested Citation

  • Omar Kahouli & Hamdi Gassara & Saleh Albadran & Ahmed El Hajjaji & Abdellatif Ben Makhlouf, 2025. "Sum-Of-Squares Approach For Modeling And Control Of Hail Power System With Time Delay And Conformable Fractional-Order Derivative," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 33(04), pages 1-11.
    • Handle: RePEc:wsi:fracta:v:33:y:2025:i:04:n:s0218348x25400870
    DOI: 10.1142/S0218348X25400870
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