Design of Polynomial Observer-Based Control of Fractional-Order Power Systems

Gassara, Hamdi; Iben Ammar, Imen; Ben Makhlouf, Abdellatif; Mchiri, Lassaad; Rhaima, Mohamed

doi:10.3390/math11214450

Cited by 2 publications

(1 citation statement)

References 34 publications

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“…Historically, ever since Christiaan Huygens initiated the use of the scientific paradigm to study simple pendulums [2], the only tool available for theoretical analysis has been the law of conservation of energy, a status quo that persists to this day. Similarly, various analytical energy function methods have been proposed under the law of conservation of energy and Lyapunov's second method [3,4] over the past years in the field of power system stability analysis. However, the systematic construction of an energy function with minimal model dependencies for stability analysis remains an open question [5] in the power system community.…”

Section: Introductionmentioning

confidence: 99%

Estimation of the Region of Attraction of Polynomial Swing Equation Using Sum of Squares Theory

Li,

Wu,

Zhan

et al. 2024

Energies

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Estimation of the region of attraction of the power system using sum of squares (SOS) programming theory is investigated in this paper. Firstly, the Taylor expansion formula is applied to explore the inherent polynomial structure of the swing equation. The single machine projection equation for a multi-machine system is proposed based on the amplitude characteristic of the rotor angle response in decoupled space. Secondly, the theory of SOS programming originating from the polynomial system is derived, and the theory about estimation of the region of attraction for the differential algebraic system is summarized. Thirdly, the method for estimating the region of attraction for the polynomial swing equation based on a V-S two-stage iterative procedure is proposed. Finally, a single machine infinite bus power system, an IEEE 3-machine power system, and an IEEE 4-machine power system are employed to validate the effectiveness and accuracy of the proposed method and analysis.

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Section: Introductionmentioning

confidence: 99%

Estimation of the Region of Attraction of Polynomial Swing Equation Using Sum of Squares Theory

Li,

Wu,

Zhan

et al. 2024

Energies

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Practical Stability of Observer-Based Control for Nonlinear Caputo–Hadamard Fractional-Order Systems

Issaoui,

Naifar,

Tlija

et al. 2024

Fractal Fract

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This paper investigates the problem of observer-based control for a class of nonlinear systems described by the Caputo–Hadamard fractional-order derivative. Given the growing interest in fractional-order systems for their ability to capture complex dynamics, ensuring their practical stability remains a significant challenge. We propose a novel concept of practical stability tailored to nonlinear Hadamard fractional-order systems, which guarantees that the system solutions converge to a small ball containing the origin, thereby enhancing their robustness against perturbations. Furthermore, we introduce a practical observer design that extends the classical observer framework to fractional-order systems under an enhanced One-Sided Lipschitz (OSL) condition. This extended OSL condition ensures the convergence of the proposed practical observer, even in the presence of significant nonlinearities and disturbances. Notably, the novelty of our approach lies in the extension of both the practical observer and the stability criteria, which are innovative even in the integer-order case. Theoretical results are substantiated through numerical examples, demonstrating the feasibility of the proposed method in real-world control applications. Our contributions pave the way for the development of robust observers in fractional-order systems, with potential applications across various engineering domains.

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Design of Polynomial Observer-Based Control of Fractional-Order Power Systems

Cited by 2 publications

References 34 publications

Estimation of the Region of Attraction of Polynomial Swing Equation Using Sum of Squares Theory

Estimation of the Region of Attraction of Polynomial Swing Equation Using Sum of Squares Theory

Practical Stability of Observer-Based Control for Nonlinear Caputo–Hadamard Fractional-Order Systems

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