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

Alexander Poznyak, Hussain Alazki (), Hisham M. Soliman and Razzaqul Ahshan ()
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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

Energies, 2022, vol. 16, issue 1, 1-16

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.

Keywords: power system stochastic stability; attracting ellipsoid method; linear matrix inequalities; Markov jumps systems (search for similar items in EconPapers)
JEL-codes: Q Q0 Q4 Q40 Q41 Q42 Q43 Q47 Q48 Q49 (search for similar items in EconPapers)
Date: 2022
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