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, Razzaqul Ahshan*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Article number414
Issue number1
Publication statusPublished - Dec 29 2022


  • Markov jumps systems
  • attracting ellipsoid method
  • linear matrix inequalities
  • power system stochastic stability

ASJC Scopus subject areas

  • Control and Optimization
  • Energy (miscellaneous)
  • Engineering (miscellaneous)
  • Energy Engineering and Power Technology
  • Electrical and Electronic Engineering
  • Fuel Technology
  • Renewable Energy, Sustainability and the Environment

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