Ferromagnetic core coil hysteresis modeling using fractional derivatives
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ORIGINAL PAPER
Ferromagnetic core coil hysteresis modeling using fractional derivatives Marcin Sowa
· Łukasz Majka
Received: 19 March 2020 / Accepted: 6 July 2020 © The Author(s) 2020
Abstract The modeling of a ferromagnetic core coil magnetic hysteresis has been considered. The measurement basis consisted of waveforms that have been recorded for various levels of the iron core saturation levels. The investigated models included classical cases as well as models including a nonlinear fractional coil. The possibilities of solutions for transient problems including such models have been recalled. The details of the estimation process have been described next, where each model evaluation made use of an original methodology dealing with periodic steady states. The influence of the model response on parameter changes has also been studied. Further on the parameter estimation procedure has been described, and the results for the various models have been presented. Keywords Ferromagnetic coil · Fractional derivative · Numerical method · Hysteresis · Measurements · Nonlinear
M. Sowa (B) · Ł. Majka Faculty of Electrical Engineering, Silesian University of Technology, Akademicka Street 2A, 44-100 Gliwice, Poland e-mail: [email protected] Ł. Majka e-mail: [email protected]
1 Introduction 1.1 Ferromagnetic core coil modeling The modeling of distinct circuit elements is important due to the need for simulations of real phenomena of electrical engineering in power systems and electronic circuits. This, in no small part, is due to the need of foresight of the events that can occur in a studied system. An element category, which is challenging when it comes to modeling, comprises of iron-core coils and transformers. This is largely caused by the need to reflect magnetic hystereses, which is especially difficult during transient states or nonsinusoidal responses with a significant contribution of higher harmonics. The subject of accurate modeling of the more difficult cases of attempts to resemble magnetic hystereses is still an open topic [1,2]. Some of the most popular models are: the Jiles–Atherton model [3], the Preisach model [4] and the Chua model [5]. Over the years, there have been many propositions to modify these models in order to reflect the results of measurements made on iron-core coils more accurately [6,7]. Unfortunately, the application of a significant number of models yields at least one of the following problems:
– a complex description, which leads to difficulties in implementations [8]; also—adaptability becomes a problem, e.g., when one wants to include the model
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in computations in a selected computational environment (e.g., in Matlab [9], Octave [10]), – a large number of equations, which directly leads to longer computation times [11], – the involvement of sophisticated functions, e.g., in models supporting anisotropy [12], – problems in numerical stability, due to some nonlinearities difficult to handle for typical algorithms [13]. The paper is focused on the introdu
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