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Correlation between the bifurcation diagram structure and the predominant harmonics of an electrical power network response

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  • Zarouan, Mohamed
  • Allali, Sofiène
  • Benrejeb, Mohamed

Abstract

After localization of initial starting bifurcation points from the fixed points diagram, in our work, the fold diagrams, the pitchfork diagram, and the Hopfs diagram were traced, in order to put forward a new structure of bifurcation diagram of a faulted mono-phase electrical power network. Then, the correlation between the predominant harmonic map and the bifurcation diagram is highlighted in this article. In fact, we deduced that the fold diagram existence implies the odd predominant harmonic existence, and the existence of pitchfork diagram implies, this way and that, the even predominant harmonic existence.

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  • Zarouan, Mohamed & Allali, Sofiène & Benrejeb, Mohamed, 2009. "Correlation between the bifurcation diagram structure and the predominant harmonics of an electrical power network response," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 483-491.
    • Handle: RePEc:eee:chsofr:v:42:y:2009:i:1:p:483-491
    DOI: 10.1016/j.chaos.2009.01.016
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    References listed on IDEAS

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    1. Hammami, S. & Ben Saad, K. & Benrejeb, M., 2009. "On the synchronization of identical and non-identical 4-D chaotic systems using arrow form matrix," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 101-112.
    2. Barrio, Roberto, 2005. "Sensitivity tools vs. Poincaré sections," Chaos, Solitons & Fractals, Elsevier, vol. 25(3), pages 711-726.
    3. Yang, Jianping & Jing, Zhujun, 2009. "Control of chaos in a three-well duffing system," Chaos, Solitons & Fractals, Elsevier, vol. 41(3), pages 1311-1328.
    4. Xu, Jianxue, 2009. "Some advances on global analysis of nonlinear systems," Chaos, Solitons & Fractals, Elsevier, vol. 39(4), pages 1839-1848.
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