Ellipsoidal Design of Robust Stabilization for Markov Jump Power Systems under Normal and Contingency Conditions

Hisham M. Soliman, Farag A. El-Sheikhi, Ehab H. E. Bayoumi () and Michele De Santis
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Hisham M. Soliman: Department of Electrical Power Engineering, Faculty of Engineering, Cairo University, Giza 12613, Egypt
Farag A. El-Sheikhi: Department of Electrical and Electronics Engineering, Istanbul Esenyurt University, Istanbul 34517, Turkey
Ehab H. E. Bayoumi: Energy and Renewable energy Department, Faculty of Engineering, Egyptian Chinese University, Cairo 11724, Egypt
Michele De Santis: Department of Engineering, Niccolò Cusano University, 00166 Rome, Italy

Energies, 2022, vol. 15, issue 19, 1-16

Abstract: The essential prerequisites for secure customer service are power system stability and reliability. This work shows how to construct a robust switching control for studying power system load changes using an invariant ellipsoid method. Furthermore, the suggested control ensures stability when the system is subjected to random stochastic external disturbances, and functions randomly in two conditions: normal and contingency. The extreme (least) reliability state is chosen as the most severe scenario (corresponding to a transmission line outage). As a two-state Markov random chain, the transition probabilities are utilized to simulate the switching between normal and contingency modes (or processes). To characterize the dynamics of the studied system, a stochastic mathematical model is developed. The effect of stochastic disturbances and random normal/contingency operations is taken into account during the design stage. For a stochastic power system, a novel excitation control is designed. The attractive ellipsoid approach and linear matrix inequalities (LMIs) optimization are used to build the best two-controller gains. Therefore, the proposed modeling/design technique can be employed for the power system under load changes, stochastic topological changes, and random disturbances. Finally, the system’s random dynamics simulation indicates the effectiveness of the designed control law.

Keywords: stochastic stability in power systems; Markov model; switched control; reliability (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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