Fractional Derivative Approach in Modeling of a Nonlinear Coil for Ferroresonance Analyses

Majka, Łukasz

doi:10.1007/978-3-319-78458-8_13

Cited by 8 publications

(10 citation statements)

References 17 publications

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“…The studies in this paper make use of the results of measurements that have been accumulated throughout the last three years [48,50,55,56]. The measurements have been performed initially with a digital interference and event recorder RZ1 (manufactured by the Kared Company [57]).…”

Section: Measurementsmentioning

confidence: 99%

Ferromagnetic core coil hysteresis modeling using fractional derivatives

Sowa

Majka

2020

Nonlinear Dyn

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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.

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Section: Measurementsmentioning

confidence: 99%

Ferromagnetic core coil hysteresis modeling using fractional derivatives

Sowa

Majka

2020

Nonlinear Dyn

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“…The FeD diagnostic system has been equipped with a simulation module used to model the nonlinear core coil. After a literature survey of many possible alternatives (as given in [66][67][68]) and basing on authors' personal experiences (various studies [9,10,17,18]), a fractional calculus model of the ferromagnetic coil has been chosen. From the field of fractional calculus, the Caputo fractional derivative is applied [69,70]:…”

Section: Simulation Modulementioning

confidence: 99%

“…where only the range of α ∈ [0, 1] is considered. Fractional derivatives have been applied with success in circuit analyses in modeling supercapacitors [71][72][73][74] and (important for this study) ferromagnetic core coils [9,[75][76][77]. Model containing a nonlinear fractional coil and a resistance connected in parallel (Fig.…”

Section: Simulation Modulementioning

confidence: 99%

“…The nature of a phenomenon described above and referred to in many research papers [4,[8][9][10][11][12][13][14][15][16] leaves no doubt as to the constant need of studying low-loss circuits containing capacitors and saturable inductors. Taking into account their tendency to become prone to ferroresonance condition, a new and interesting approach to the problem focuses on developing of new detection, diagnostic and monitoring procedures.…”

Section: Introductionmentioning

confidence: 99%

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Diagnostic approach in assessment of a ferroresonant circuit

Majka

Klimas

2019

Electr Eng

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This paper presents possibilities offered by a diagnostic system called FeD. The system is completely original; it has been developed by the authors on the basis of Arduino platform. The system has been designed to perform and record measurements and to carry out different numerical operations. The real-time function for several operations is incorporated in this system. The necessary input data for the system consist of the electrical voltage waveforms only. Rescaled voltage quantities can be displayed, measured, recorded or computed in any chosen way. The system has been developed particularly for measurements and computations in the ferroresonant circuits. The strongest part of the system is its versatility. It works with a standard PC and supports a universal connection (USB standard). This is undeniably a cost-wise solution. Driving and control of the system functions are carried out using the authors' original software implemented in SciLab environment. This is free software, similar to and compatible with other existing CAD programs such as Octave and MATLAB. The obtained data, scripts and results can be freely transferred between them. The program is equipped with a transparent GUI. The need of constructing a special system to diagnose the ferroresonant circuit has emerged during earlier ferroresonance analyses and computations. Every ferroresonant circuit requires specific kind of diagnostics to estimate and display its base features in order to determine the best scientific approach to the problem. The ferroresonance phenomenon belongs to the domain of nonlinear problems. Its analysis requires excellent skills in mathematics and physics as well as computer science. Moreover, this subject also requires specialized engineering knowledge, particularly in the field of power engineering and power system equipment. Modern mathematical models and analyses used in ferroresonant computations are quite accurate; however, in case of a common user, they are often difficult to understand or implement. This paper provides full description of construction, features and test results of the developed hardware/software system designed for diagnostics of ferroresonant circuits. The test circuit case study has been performed in the entire power supply range. Results of measurements and computations as well as screenshots captured from authors' original software are shown in different figures. The developed software and recorded data have been finally used in modeling and further simulations. During this, the application of the fractional derivative iron core coil model to ferroresonance analysis has been shown. The waveforms obtained from computer simulations have been compared with those obtained from measurements performed in the test circuit.

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“…In the articles [7,8] the heat conduction process was considered in composites and porous aluminum. More about the applications of the fractional derivatives can be found in [9][10][11][12].…”

Section: Introductionmentioning

confidence: 99%

Parameter Identification in the Two-Dimensional Riesz Space Fractional Diffusion Equation

2020

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This paper presents the application of the swarm intelligence algorithm for solving the inverse problem concerning the parameter identification. The paper examines the two-dimensional Riesz space fractional diffusion equation. Based on the values of the function (for the fixed points of the domain) which is the solution of the described differential equation, the order of the Riesz derivative and the diffusion coefficient are identified. The paper includes numerical examples illustrating the algorithm’s accuracy.

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Fractional Derivative Approach in Modeling of a Nonlinear Coil for Ferroresonance Analyses

Cited by 8 publications

References 17 publications

Ferromagnetic core coil hysteresis modeling using fractional derivatives

Ferromagnetic core coil hysteresis modeling using fractional derivatives

Diagnostic approach in assessment of a ferroresonant circuit

Parameter Identification in the Two-Dimensional Riesz Space Fractional Diffusion Equation

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