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Robust Fuzzy Control for Uncertain Nonlinear Power Systems

Author

Listed:
  • Tawfik Guesmi

    (Department of Electrical Engineering, College of Engineering, University of Ha’il, Ha’il 81481, Saudi Arabia)

  • Badr M. Alshammari

    (Department of Electrical Engineering, College of Engineering, University of Ha’il, Ha’il 81481, Saudi Arabia)

  • Yosra Welhazi

    (Department of Electrical Engineering, National Engineering School of Sfax, University of Sfax, Sfax 3038, Tunisia)

  • Hsan Hadj Abdallah

    (Department of Electrical Engineering, National Engineering School of Sfax, University of Sfax, Sfax 3038, Tunisia)

  • Ahmed Toumi

    (Department of Electrical Engineering, National Engineering School of Sfax, University of Sfax, Sfax 3038, Tunisia)

Abstract

This paper presents a new control technique based on uncertain fuzzy models for handling uncertainties in nonlinear dynamic systems. This approach is applied for the stabilization of a multimachine power system subject to disturbances. In this case, a state-feedback controller based on parallel distributed compensation (PDC) is applied for the stabilization of the fuzzy system, where the design of control laws is based on the Lyapunov function method and the stability conditions are solved using a linear matrix inequalities (LMI)-based framework. Due to the high number of system nonlinearities, two steps are followed to reduce the number of fuzzy rules. Firstly, the power network is subdivided into sub-systems using Thevenin’s theorem. Actually, each sub-system corresponds to a generator which is in series with the Thevenin equivalent as seen from this generator. This means that the number of sub-systems is equal to the number of system generators. Secondly, the significances of the nonlinearities of the sub-systems are ranked based on their limits and range of variation. Then, nonlinearities with non-significant variations are assumed to be uncertainties. The proposed strategy is tested on the Western systems coordinating council (WSCC) integrated with a wind turbine. The disturbances are assumed to be sudden variations in wind power output. The effectiveness of the suggested fuzzy controller is compared with conventional regulators, such as an automatic voltage regulator (AVR) and power system stabilizers (PSS).

Suggested Citation

  • Tawfik Guesmi & Badr M. Alshammari & Yosra Welhazi & Hsan Hadj Abdallah & Ahmed Toumi, 2022. "Robust Fuzzy Control for Uncertain Nonlinear Power Systems," Mathematics, MDPI, vol. 10(9), pages 1-26, April.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:9:p:1463-:d:803431
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    References listed on IDEAS

    as
    1. Mahdi Saadatmand & Gevork B. Gharehpetian & Innocent Kamwa & Pierluigi Siano & Josep M. Guerrero & Hassan Haes Alhelou, 2021. "A Survey on FOPID Controllers for LFO Damping in Power Systems Using Synchronous Generators, FACTS Devices and Inverter-Based Power Plants," Energies, MDPI, vol. 14(18), pages 1-26, September.
    2. Benjamin C. Gruenwald & Tansel Yucelen & Gerardo De La Torre & Jonathan A. Muse, 2020. "Adaptive control for uncertain dynamical systems with nonlinear reference systems," International Journal of Systems Science, Taylor & Francis Journals, vol. 51(4), pages 687-703, March.
    3. Hamid Ghadiri & Hamed Khodadadi & Saleh Mobayen & Jihad H. Asad & Thaned Rojsiraphisal & Arthur Chang, 2021. "Observer-Based Robust Control Method for Switched Neutral Systems in the Presence of Interval Time-Varying Delays," Mathematics, MDPI, vol. 9(19), pages 1-20, October.
    4. T. H. Yan & B. Wu & B. He & W. H. Li & R. B. Wang, 2016. "A Novel Fuzzy Sliding-Mode Control for Discrete-Time Uncertain System," Mathematical Problems in Engineering, Hindawi, vol. 2016, pages 1-9, August.
    5. Qiang Zhang & Hongliang Yu & Xiaohong Wang, 2013. "Integral Terminal Sliding Mode Control for a Class of Nonaffine Nonlinear Systems with Uncertainty," Mathematical Problems in Engineering, Hindawi, vol. 2013, pages 1-11, December.
    6. Yonghui Liu & Tinggang Jia & Yugang Niu & Yuanyuan Zou, 2015. "Design of sliding mode control for a class of uncertain switched systems," International Journal of Systems Science, Taylor & Francis Journals, vol. 46(6), pages 993-1002, April.
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    Cited by:

    1. Chan Gu & Encheng Chi & Chujia Guo & Mostafa M. Salah & Ahmed Shaker, 2023. "A New Self-Tuning Deep Neuro-Sliding Mode Control for Multi-Machine Power System Stabilizer," Mathematics, MDPI, vol. 11(7), pages 1-18, March.

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