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Fractional-order models of the supercapacitors in the form of RC ladder networks

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Języki publikacji
EN
Abstrakty
EN
In the paper, mathematical models of the supercapacitors are investigated. The models are based on electrical circuits in the form of RC ladder networks. The elementary cell of the network may consist of resistances and capacitances that are connected in series or parallel. The dynamic behavior of the circuit is described using fractional-order differential equations and its properties are analyzed. The identification procedure with quadratic performance index is performed in time domain to identify the parameters of the supercapacitor models. The results of numerical simulations are compared with the results measured experimentally in the physical system. In addition, an example from the automotive industry is used for an experimental evaluation of the theoretical analysis and to present a perspective on the applicability of the approach for other industrial projects.
Rocznik
Strony
581--587
Opis fizyczny
Bibliogr. 32 poz., wykr., tab., rys.
Twórcy
autor
  • Faculty of Electrical Engineering, Automatics, Computer Science and Biomedical Engineering, Department of Automatics and Biomedical Engineering, AGH University of Science and Technology, 30/B1 A. Mickiewicza Ave., 30-059 Cracow, Poland
autor
  • Faculty of Electrical Engineering, Automatics, Computer Science and Biomedical Engineering, Department of Automatics and Biomedical Engineering, AGH University of Science and Technology, 30/B1 A. Mickiewicza Ave., 30-059 Cracow, Poland
Bibliografia
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  • [3] V. Srinivasan and J.W. Weidner, “Mathematical modeling of electrochemical capacitors”, J. Electrochemical Society 146 (5), 1650-1658 (1999).
  • [4] S. Buller, E. Karden, D. Kok, and R.W. De Doncker, “Modeling the dynamic behavior of supercapacitors using impedance spectroscopy”, IEEE Trans. on Industry Applications 38 (6), 1622-1626 (2002).
  • [5] R. Setlak and M. Fice, “Modeling of electric energy storages for electric and hybrid vehicles”, Problem Notebooks - ElectricalMachines 2 (90), 145-150 (2011).
  • [6] L. Shi and M.L. Crow, “Comparison of ultracapacitor electric circuit models”, Proc. IEEE Power and Energy Society GeneralMeeting - Conversion and Delivery of Electrical Energy inthe 21st Century 1, 1-6 (2008).
  • [7] I. Podlubny, Fractional Differential Equations, Holt, Rinehart, and Winston, San Diego, 1999.
  • [8] R. Caponetto, G. Dongola, L. Fortuna, and I. Petras, FractionalOrder Systems: Modeling and Control Applications, World Scientific, New Jersey, 2010.
  • [9] A. Dzielinski, G. Sarwas, and D. Sierociuk, “Comparison and validation of integer and fractional order ultracapacitor models”, Advances in Difference Equations 2011 (1), 11-23 (2011).
  • [10] G. Sarwas, “Modelling and control of systems with ultracapacitors using fractional order calculus”, PhD Thesis, Warsaw University of Technology, Warsaw, 2012.
  • [11] D. Sierociuk, “Control and estimation of the discrete fractional-order models described in state space”, PhD Thesis, Warsaw University of Technology, Warsaw, 2007, (in Polish).
  • [12] A. Dzielinski and D. Sierociuk, “Ultracapacitor modelling and control using discrete fractional order state-space model”, ActaMontanistica Slovaca 113 (1), 136-145 (2008).
  • [13] W. Mitkowski and A. Obraczka, “Simple identyfication of fractional differential equation”, Solid State Phenomena 180, 331-338 (2012).
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  • [15] T. Kaczorek, “Positive fractional linear systems”, Measurements,Automatics, Robotics 15 (2), 91-112 (2011).
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  • [17] M. Weilbeer, “Efficient numerical methods for fractional differential equations and their analytical background”, PhD Thesis, Technical University Braunschweig, Braunschweig 2005.
  • [18] M. Buslowicz, “Stability of state-space models of linear continuous-time fractional order systems”, Acta Mechanica etAutomatica 5 (2), 15-22 (2011).
  • [19] A. Dzielinski and D. Sierociuk, “Stability of discrete fractional order state-space systems”, J. Vibration and Control 14 (9-10), 1543-1556 (2008).
  • [20] T. Kaczorek, “Reachability and controllability to zero of cone fractional linear systems”, Archives of Control Sciences 17 (3), 357-367 (2007).
  • [21] W. Mitkowski, Stabilization of Dynamic Systems, WNT, Warsaw, 1991.
  • [22] W. Mitkowski, “Dynamic feedback in LC ladder network”, Bull. Pol. Ac.: Tech. 51 (2), 173-180 (2003).
  • [23] W. Mitkowski, “Stabilization of LC ladder network”, Bull. Pol.Ac.: Tech. 52 (2), 109-114 (2004).
  • [24] S. Mitkowski, Nonlinear Electric Circuits, AGH, Cracow, 1999.
  • [25] R. Bellman, Introduction to Matrix Analysis, McGraw-Hill, New York, 1960.
  • [26] V.P. Ilin and Yu.I. Kuznyetsow, Tridiagonal Matrices and theirApplications, Science, Moscow, 1985, (in Russian).
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  • [28] W. Mitkowski, “Uniform ladder networks with linear feedback”, Archives of Electrical Engineering 36, 7-18 (1987).
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  • [31] T. Kaczorek, “Reachability of cone fractional continuous-time linear systems”, Int. J. Applied Mathematics and ComputerScience 19 (1), 89-93 (2009).
  • [32] A. Burke, “Ultracapacitor technologies and application in hybrid and electric vehicles”, Int. J. Energy Research 34 (2), 133-151 (2010).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-2ee97182-3a95-4b18-96d2-d82da154ffad
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