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Power and energy analysis of fractional-order electrical energy storage devices

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  • Fouda, M.E.
  • Elwakil, A.S.
  • Radwan, A.G.
  • Allagui, A.

Abstract

Characterizing and modeling electrical energy storage devices is essential for their proper integration in larger systems. However, basic circuit elements, i.e. resistors, inductors, and capacitors, are not well-suited to explain their complex frequency-dependent behaviors. Instead, fractional-order models, which are based on non-integer-order differential equations in the time-domain and include for instance the constant phase element (CPE), are mathematically more fit to this end. Here, the electrical power and energy of fractional-order capacitance and inductance are derived in both steady-state and transient conditions, and verified using a number of commercial supercapacitors and fractional-order coils. A generalized expression for the energy stored in a supercapacitor/fractional-order inductor is derived and found to depend on the capacitance/inductance and the dispersion coefficient of the device, as well as on the properties of the applied voltage waveform.

Suggested Citation

  • Fouda, M.E. & Elwakil, A.S. & Radwan, A.G. & Allagui, A., 2016. "Power and energy analysis of fractional-order electrical energy storage devices," Energy, Elsevier, vol. 111(C), pages 785-792.
    • Handle: RePEc:eee:energy:v:111:y:2016:i:c:p:785-792
    DOI: 10.1016/j.energy.2016.05.104
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    References listed on IDEAS

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    3. Jakubowska-Ciszek, A. & Walczak, J., 2018. "Analysis of the transient state in a parallel circuit of the class RLβCα," Applied Mathematics and Computation, Elsevier, vol. 319(C), pages 287-300.
    4. Xu, Ying & Ren, Li & Zhang, Zhongping & Tang, Yuejin & Shi, Jing & Xu, Chen & Li, Jingdong & Pu, Dongsheng & Wang, Zhuang & Liu, Huajun & Chen, Lei, 2018. "Analysis of the loss and thermal characteristics of a SMES (Superconducting Magnetic Energy Storage) magnet with three practical operating conditions," Energy, Elsevier, vol. 143(C), pages 372-384.
    5. Capasso, Clemente & Lauria, Davide & Veneri, Ottorino, 2018. "Experimental evaluation of model-based control strategies of sodium-nickel chloride battery plus supercapacitor hybrid storage systems for urban electric vehicles," Applied Energy, Elsevier, vol. 228(C), pages 2478-2489.
    6. Allagui, Anis & Benaoum, Hachemi & Olendski, Oleg, 2021. "On the Gouy–Chapman–Stern model of the electrical double-layer structure with a generalized Boltzmann factor," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 582(C).
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    8. Hernández-Balaguera, Enrique, 2023. "Fractional model of the chemical inductor," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).

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