Fractional-order models: The case study of the supercapacitor capacitance measurement

• Autorzy: Lewandowski M. , Orzyłowski M.

Identyfikatory

DOI

10.1515/bpasts-2017-0050

• Języki publikacji: EN

Abstrakty

EN

At the beginning of the paper, the fractional calculus is briefly presented. Then, the models of dielectric relaxation in supercapacitors are described. On the basis of the Cole-Cole model, a fractional-order model of supercapacitor impedance is formulated. The frequency characteristics of selected supercapacitors and their voltage response to a current step are assumed as a basis for the analysis of their dynamics. An example of the fractional dynamic model application was used for the critical assessment of the IEC standard recommendation on the conditions of supercapacitor capacitance measurements. The presented study shows some imperfections of the IEC standard recommendations, which probably result from the use of an inaccurate dynamics model. At the end of the paper, the authors propose a solution to this problem by changing the measurement conditions and introducing a concept of dynamic capacitance. The conclusions of the paper indicate that the models of fractional-order dynamics may be useful not only for the control purposes but also in other domains.

Słowa kluczowe

EN

fractional calculus; supercapacitor model; capacitance measurement; IEC standard

PL

rachunek różniczkowy; model superkondensatora; pomiar pojemności; norma IEC

• Wydawca: Polska Akademia Nauk, Wydział IV Nauk Technicznych
• Czasopismo: Bulletin of the Polish Academy of Sciences. Technical Sciences
• Rocznik: 2017
• Tom: Vol. 65, nr 4
• Strony: 449--457
• Opis fizyczny: Bibliogr. 22 poz., rys., wykr., tab.

Twórcy

autor

Lewandowski M.

• Warsaw University of Technology, Faculty of Electrical Engineering, 1 Politechniki Sq., 00-661 Warszawa, Poland

autor

Orzyłowski M.

• University of Social Sciences, Information Technology Institute, 9 Sienkiewicza St., 90-113 Łódź, Poland

Bibliografia

• [1] C.A. Monje, Y. Chen, B.M. Vinagre, D. Xue, and V. Feliu-Batlle, Fractional-Order Systems and Controls: Fundamentals and Applications, Springer-Verlag, London, 2010.
• [2] S. Guermah, S. Djnnoune, and M. Bettayeb, Advances in Discrete-Time Systems. Chapter 8: Discrete-Time Fractional-Order Systems: Modelling and Stability, Intech, 2012.
• [3] I. Petras, B.M. Vinagre, L. Dorcak, and V. Feliu, “Fractional digital control of a heat solid: Experimental results”, Proceedings of the International Carpathian Control Conference, 365–370 (2002).
• [4] C.M.A. Brett and A.M. Oliveira-Brett, Electrochemistry. Principles, Methods, and Applications, Oxford University Press, Oxford, 1993.
• [5] Y.Q. Chen, I. Petras, and D. Xue, “Fractional order control – A tutorial”, 2009 American Control Conference, ACC ‘09, (2009).
• [6] L. Shi, M.L. Crow, “Comparison of ultracapacitor electric circuit models”, 2008 IEEE Power and Energy Society General Meeting – Conversion and Delivery of Electrical Energy in the 21st Century, (2008).
• [7] G.A. Badea, “Supercapacitors – the batteries of future”, Bulletin Scientifique en Langues Étrangères Appliquées 3, http://revues-eco.refer.org/BSLEA/index.php?id=491, (2015).
• [8] R. Martin, J.J. Quintana, A. Ramos, and I. de la Nuez, “Modeling electrochemical double layer capacitor, from classical to fractional impedance”, Journal of Computational and Nonlinear Dynamics 3 (2), 61–66 (2008).
• [9] H. Göhr, “Impedance modelling of porous electrode”, Electrochemical Applications 1, 2–3 (1997).
• [10] X. Yang, C. Cheng, Y. Wang, L. Qiu, and D. Li, “Liquid-mediated dense integration of graphene materials for compact capacitive energy storage”, Science 341 (6145), 534–537 (2013).
• [11] R. Farma, M. Deraman, A. Awitdrus, I.A. Talib, R. Omar, J.G. Manjunatha, M.M. Ishak, N.H. Basri, and B.N.M. Dola, “Physical and electrochemical properties of supercapacitor electrodes derived from carbon nanotube and biomass carbon”, International Journal of Electrochemical Science 8, 257–273 (2013).
• [12] N. Bertrand, J. Sabatier, O. Briat, and J.-M. Vinassa, “Fractional non-linear modeling of ultracapacitors”, Communications Nonlinear Science and Numerical Simulation 15 (5), 1327–1337 (2010).
• [13] J.-L. Déjardin and J. Jadzyn, “Determination of the nonlinear dielectric increment in the Cole-Davidson model”, The Journal of Chemical Physics 125 (11), 114503 (2006).
• [14] A. Dzieliński, G. Sarwas, and D. Sierociuk, “Comparison and validation of integer and fractional order ultracapacitor models”, Advances in Difference Equations 2011:11, (2011)
• [15] T.J. Freeborn, B. Moundy, and A.S. Elwakil, “Measurement of supercapacitor fractional-order model parameters from voltage-excited step response”, IEEE Journal on Emerging and Selected Topics in Circuits and Systems 3 (3), 367–376 (2013).
• [16] N. Maim, D. Isa, and R. Arelhi, “Modelling of ultracapacitor using a fractional–order equivalent circuit”, International Journal of Renewable Energy Technology 6 (2), 142–163 (2015).
• [17] M. Orzyłowski and M. Lewandowski, “Computer modeling of supercapacitor with Cole-Cole relaxation model”, Journal of Applied Computer Science Methods 5 (2), 105–121 (2013).
• [18] M. Lewandowski and M. Orzyłowski, “The application of fractional calculus for supercapacitor dynamics modeling”, Przegląd Elektrotechniczny 90 (8), 13–17 (2014), [in Polish].
• [19] A. Szeląg and T. Maciołek, “A 3 kV DC electric traction system modernisation for increased speed and trains power demand – problems of analysis and synthesis”, Przegląd Elektrotechniczny 89 (3a), 21–28 (2013).
• [20] M. Wieczorek and M. Lewandowski, “Mathematical representation of an energy management strategy for hybrid energy storage system in electric vehicle and real time optimization using a genetic algorithm”, Applied Energy 192, 222–233 (2017).
• [21] International Standard IEC 62391‒1:2006. Fixed Electric Double- Layer Capacitors for Use in Electronic Equipment. Part 1: Generic Application, IEC, 2006.
• [22] GS130/GS230 Supercapacitor Datasheet V4.1, CAP-XX, 2015.

Uwagi

PL

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).