|Research Article:||Comparative analysis of suitability of fractional derivatives in modelling the practical capacitor|
|Department/Faculty||Graduate Schools of IT, Siam University, Bangkok 10160|
|Published:||COMPEL – The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, Volume 41, Issue 1, pp. 304-318|
Banchuin, R. (2022). Comparative analysis of suitability of fractional derivatives in modelling the practical capacitor. COMPEL – The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, 41(1), 304-318. https://doi.org/10.1108/COMPEL-08-2021-0293
The purpose of this paper is to compare the suitability of fractional derivatives in the modelling of practical capacitors. Such suitability refers to ability to provide the analytical capacitance function that matches the experimental ones of each fractional derivative.
The analytical capacitance functions based on various fractional derivatives of both local and nonlocal types including the author’s have been derived. The derived capacitance functions have been simulated and compared with the experimental ones of aluminium electrolytic and electrical double layer capacitors (EDLCs).
This paper has found that any local fractional derivative with fractional power law-based relationship with the conventional one is suitable for modelling the aluminium electrolytic capacitor (AEC) by incorporating with the conventional capacitance definition. On the other hand, the author’s nonlocal fractional derivatives have been found to be more suitable than the others for modelling the EDLC by incorporating with the revisited definition of capacitance.
The proposed comparative analysis has been originally presented in this work. The criterion for local fractional derivative, to be suitable for modelling the AEC, has been found. The nonlocal fractional operators which are most suitable for modelling the EDLC have been derived where the unsuitable one has been pointed out.
Keywords: Transient analysis, Time-domain modelling, Aluminium electrolytic capacitor, Capacitance function, Fractional derivative, Electrical double layer capacitors, Local fractional derivative, Nonlocal fractional derivative.
Comparative analysis of suitability of fractional derivatives in modelling the practical capacitor
Graduate Schools, Siam University, Bangkok, Thailand
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