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Open AccessArticle

Properties of Fractional-Order Magnetic Coupling

1
Department of Industrial Electrical Engineering and Automatic Control, Kielce University of Technology, Tysiąclecia Państwa Polskiego 7, 25-314 Kielce, Poland
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Department of Power Electronics and Power Engineering, Rzeszow University of Technology, Wincentego Pola 2, 35-959 Rzeszow, Poland
*
Author to whom correspondence should be addressed.
Energies 2020, 13(7), 1539; https://doi.org/10.3390/en13071539
Received: 14 February 2020 / Revised: 14 March 2020 / Accepted: 22 March 2020 / Published: 25 March 2020
This paper presents the properties of fractional-order magnetic coupling. The difficulties connected with the analysis of two coils in dynamic states, resulting from the classical approach, provided motivation for studying the properties of fractional-order magnetic coupling. These difficulties arise from failure to comply with the commutation laws, i.e., a sudden power disappearance in the primary winding caused by a switch-mode power supply. Theoretically, under ideal conditions, a sudden power disappearance in the coil is, according to the classical method, manifested by a sudden voltage surge in the form of the Dirac delta function. As is well-known, it is difficult to obtain such ideal conditions in practice; the time of current disappearance does not equal zero due to the circuit breaker’s imperfection (even when electronic circuit breakers are used, the time equals several hundred nanoseconds). Furthermore, it is necessary to take into account phenomena occurring in real inductances, such as the skin effect, the influence of the ferromagnetic core and many other factors. It would be very difficult to model all these phenomena using classical differential calculus. The application of fractional-order differential calculus makes it possible to model them in a simple way by appropriate selection of coefficients and fractional-order derivatives. It should be mentioned that the analysis could be used, for example, in the case of high-voltage generation systems, including spark ignition systems of internal combustion engines. The use of fractional-order differential calculus will allow for more accurate modeling of phenomena occurring in such systems. View Full-Text
Keywords: high-voltage generation systems; ignition system; fractional-order magnetic coupling; fractional-order calculus; continued fraction expansion (CFE) method high-voltage generation systems; ignition system; fractional-order magnetic coupling; fractional-order calculus; continued fraction expansion (CFE) method
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Różowicz, S.; Zawadzki, A.; Włodarczyk, M.; Wachta, H.; Baran, K. Properties of Fractional-Order Magnetic Coupling. Energies 2020, 13, 1539.

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