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Abstract

In this paper,we start by the research of the existence of Lyapunov homogeneous function for a class of homogeneous fractional Systems, then we shall prove that local and global behaviors are the same. The uniform Mittag-Leffler stability of homogeneous fractional time-varying systems is studied. A numerical example is given to illustrate the efficiency of the obtained results.
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Bibliography

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[4] M.A. Duarte-Mermoud, N. Aguila-Camacho, J.A. Gallegos, and R. Castro-Linares: Using general quadratic Lyapunov functions to prove Lyapunov uniform stability for fractional order systems. Commun. Nonlinear Sci. Numer. Simul., 22(1-3) (2015), 650–659, DOI: 10.1016/j.cnsns. 2014.10.008.
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[7] Y. Li, Y. Chen, and I. Podlubny: Stability of fractional-order nonlinear dynamic system: Lyapunov direct method and generalized Mittag- Leffler stability. Comput. Math. Appl, 59(5) (2010), 1810–1821, DOI: 10.1016/j.camwa.2009.08.019.
[8] Y. Li, Y. Chen, and I. Podlubny: Mittag-Leffler stability of fractional order nonlinear dynamic systems. Automatica, 45 (2009), 1965–1969, DOI: 10.1140/epjst/e2011-01379-1.
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Authors and Affiliations

Tarek Fajraoui
1
Boulbaba Ghanmi
1
ORCID: ORCID
Fehmi Mabrouk
1
Faouzi Omri
1

  1. University of Gafsa, Tunisia, Faculty of Sciences of Gafsa, Department of Mathematics, University campus Sidi Ahmed Zarroug 2112 Gafsa, Tunisia
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Abstract

Long transmission lines have to be compensated to enhance the transport of active power. But a wrong design of the compensation may lead to subsynchronous resonances (SSR). For studies often park equivalent circuits are used. The parameters of the models are often determined analytically or by a three-phase short-circuit test. Models with this parameters give good results for frequencies of 50 Hz and 100 Hz resp. 60 Hz and 120 Hz. But SSR occurs at lower frequencies what arises the question of the reliability of the used models. Therefore in this publication a novel method for the determination of Park equivalent circuit parameters is presented. Herein the parameters are determined form time functions of the currents and the electromagnetic moment of the machine calculated by transient finite-element simulations. This parameters are used for network simulations and compared with the finite-element calculations. Compared to the parameters derived by a three-phase short-circuit a significant better accuracy of simulation results can be achieved by the presented method.

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Authors and Affiliations

Christian Kreischer
Stefan Kulig
Carsten Göbel

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