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Frequency Method for Determining the Equivalent Parameters of Fractional-Order Elements L\(_{\beta }\)C\(_{\alpha }\)

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Book cover Advances in Non-Integer Order Calculus and Its Applications (RRNR 2018)

Part of the book series: Lecture Notes in Electrical Engineering ((LNEE,volume 559))

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Abstract

The paper proposes a method for the determination of parameters of the fractional-order elements, i.e. the supercapacitor and the fractional-order coil. The method is based on the phase resonance phenomenon in a series circuit containing the fractional-order element L\(_{\beta }, \)(C\(_{\alpha }\)) and the classic reactance element - capacitor C, or induction coil L. In the case of determining the parameters of the fractional-order coil L\(_{\beta }\), the two resonance frequencies have to be measured, in the circuit containing this coil and two switchable classic capacitors C\(_{1}\), C\(_{2}\). Similarly, when calculating the supercapacitor parameters, two resonance frequencies also need to be measured in a circuit containing a supercapacitor and two switchable reference inductances L\(_{1}\), L\(_{2}\). The developed method allows the determination of the lossy parameters of the fractional-order elements too. The paper presents a detailed description of the developed method, its physical basis, simulation and experimental verification.

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Authors and Affiliations

  1. Faculty of Electrical Engineering, Silesian University of Technology, Gliwice, Poland

    Agnieszka Jakubowska-Ciszek & Janusz Walczak

Authors
  1. Agnieszka Jakubowska-Ciszek
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  2. Janusz Walczak
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Corresponding author

Correspondence to Agnieszka Jakubowska-Ciszek .

Editor information

Editors and Affiliations

  1. Faculty of Computer Science, Bialystok University of Technology, Białystok, Poland

    Agnieszka B. Malinowska

  2. Faculty of Computer Science, Bialystok University of Technology, Białystok, Poland

    Dorota Mozyrska

  3. Faculty of Electrical Engineering, Bialystok University of Technology, Białystok, Poland

    Łukasz Sajewski

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Jakubowska-Ciszek, A., Walczak, J. (2020). Frequency Method for Determining the Equivalent Parameters of Fractional-Order Elements L\(_{\beta }\)C\(_{\alpha }\). In: Malinowska, A., Mozyrska, D., Sajewski, Ł. (eds) Advances in Non-Integer Order Calculus and Its Applications. RRNR 2018. Lecture Notes in Electrical Engineering, vol 559. Springer, Cham. https://doi.org/10.1007/978-3-030-17344-9_19

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