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Ellipsoidal Design of Robust Stabilization of Power Systems Exposed to a Cycle of Lightning Surges Modeled by Continuous-Time Markov Jumps

Author

Listed:
  • Alexander Poznyak

    (Departamento de Control Automatico, CINVESTAV, Mexico City 07360, Mexico)

  • Hussain Alazki

    (Department of Mechatronics, Faculty of Engineering, Autonomous University Carmen, C. 56 4, Benito Juárez, Cd del Carmen 24180, Mexico)

  • Hisham M. Soliman

    (Department of Electrical Power Engineering, Faculty of Engineering, Cairo University, Cairo 3725121, Egypt)

  • Razzaqul Ahshan

    (Department of Electrical and Computer Engineering, College of Engineering, Sultan Qaboos University, Muscat 123, Oman)

Abstract

Power system stability is greatly affected by two types of stochastic or random disturbances: (1) topological and (2) parametric. The topological stochastic disturbances due to line faults caused by a series of lightning strikes (associated with circuit breaker, C.B., opening, and auto-reclosing) are modeled in this paper as continuous-time Markov jumps. Additionally, the stochastic parameter changes e.g., the line reactance, are influenced by the phase separation, which in turn depends on the stochastic wind speed. This is modeled as a stochastic disturbance. In this manuscript, the impact of the above stochastic disturbance on power system small-disturbance stability is studied based on stochastic differential equations (SDEs). The mean-square stabilization of such a system is conducted through a novel excitation control. The invariant ellipsoid and linear matrix inequality (LMI) optimization are used to construct the control system. The numerical simulations are presented on a multi-machine test system.

Suggested Citation

  • Alexander Poznyak & Hussain Alazki & Hisham M. Soliman & Razzaqul Ahshan, 2022. "Ellipsoidal Design of Robust Stabilization of Power Systems Exposed to a Cycle of Lightning Surges Modeled by Continuous-Time Markov Jumps," Energies, MDPI, vol. 16(1), pages 1-16, December.
    • Handle: RePEc:gam:jeners:v:16:y:2022:i:1:p:414-:d:1019380
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    References listed on IDEAS

    as
    1. Zhen Zhang & Yanhong Liu, 2018. "Stochastic Small Signal Interval Stability of Power Systems with Asynchronous Wind Turbine Generators," Mathematical Problems in Engineering, Hindawi, vol. 2018, pages 1-13, January.
    2. Farag Ali El-Sheikhi & Hisham M. Soliman & Razzaqul Ahshan & Eklas Hossain, 2021. "Regional Pole Placers of Power Systems under Random Failures/Repair Markov Jumps," Energies, MDPI, vol. 14(7), pages 1-14, April.
    Full references (including those not matched with items on IDEAS)

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