A subinterval-based method for circuits with fractional order elements

Sowa, Marcin

doi:10.2478/bpasts-2014-0047

Cited by 16 publications

(14 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The first criterion by which the accuracy of the solution is determined is comparison with results obtained through the SubIval solver, which can obtain highly accurate solutions for linear transient problems and AC problems [46,51,52]. The most important parameters for the SubIval solver are given in Table 2.…”

Section: Comparison With the Numerical Resultsmentioning

confidence: 99%

See 1 more Smart Citation

A Harmonic Balance Methodology for Circuits with Fractional and Nonlinear Elements

Sowa

2018

Circuits Syst Signal Process

View full text Add to dashboard Cite

This paper discusses the ability to obtain periodic steady-state solutions for fractional nonlinear circuit problems. For a class of nonlinear problems with fractional derivatives (based on the Caputo or Riemann-Liouville definitions), a methodology is proposed to derive equations representing the dependencies between the harmonics of the sought variables. Two approaches are considered for how to address the apparent nonlinear dependencies: one based on symbolic computation and the other a numerical approach based on the analysis of time functions. An example problem with fractional and nonlinear elements is presented to illustrate the usefulness of the proposed methodology. Two error criteria are introduced to verify the accuracy of the obtained results. The methodology is mainly designed to provide referential solutions in analyses of the numerical method called SubIval (the subinterval-based method for computation of the fractional derivative in initial value problems).

show abstract

Section: Comparison With the Numerical Resultsmentioning

confidence: 99%

“…The steady-state solutions have been compared with results obtained through a selected numerical method-an adaptive time step size solver applying SubIval [46,51,52].…”

Section: Discussionmentioning

confidence: 99%

A Harmonic Balance Methodology for Circuits with Fractional and Nonlinear Elements

Sowa

2018

Circuits Syst Signal Process

View full text Add to dashboard Cite

show abstract

“…-the application of the FeD system and its algorithms for investigation of different types of ferroresonance modes, e.g., subharmonic and quasi-periodic modes; in this study, intentionally-only the fundamental mode was taken into account because of its predictability and deterministic behavior, -with an increase of the ferromagnetic core saturation level, the resistance decreases (what has been proven in Sect. 5.6); the obtained resistance data will be used for study of various ferromagnetic core coil models so that an optimal one can be selected (reflecting this behavior), -incorporation of simulations of dynamic behaviors of ferroresonant circuits (including cases where ferromagnetic core coils are modeled with the usage of fractional derivatives); this requires the implementation of specific solvers (e.g., there are ones basing on various numerical methods for fractional differential equations like the SubIval numerical method [80][81][82] and others [83,84].…”

Section: Discussionmentioning

confidence: 99%

“…23 Intersection points from Fig. 22 shown on a phase plane with the steady state for two analyzed saturation conditions of the coil core complexity of such problems (fractional differential equation and nonlinear function), this requires numerical methods (e.g., as given in [81][82][83]).…”

Section: Simulation Modulementioning

confidence: 99%

Diagnostic approach in assessment of a ferroresonant circuit

Majka

Klimas

2019

Electr Eng

View full text Add to dashboard Cite

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.

show abstract

“…This method has found an application for solving many problems formulated with the aid of ordinary and partial differential equations [24][25][26][27], including the heat conduction problems [28][29][30][31], fractional differential equations [32,33] (for some other applications of the fractional calculus see for example [34][35][36]), integral equations [37][38][39], integro-differential equations [40,41] and others. A particular case of the homotopy analysis method is the homotopy perturbation method [16,17,42].…”

Section: Introductionmentioning

confidence: 99%

An analytical method for solving the two-phase inverse Stefan problem

Hetmaniok¹,

Słota²,

Wituła³

et al. 2015

Bulletin of the Polish Academy of Sciences Technical Sciences

View full text Add to dashboard Cite

Abstract. In the paper we present an application of the homotopy analysis method for solving the two-phase inverse Stefan problem. In the proposed approach a series is created, having elements which satisfy some differential equation following from the investigated problem. We reveal, in the paper, that if this series is convergent then its sum determines the solution of the original equation. A sufficient condition for this convergence is formulated. Moreover, the estimation of the error of the approximate solution, obtained by taking the partial sum of the considered series, is given. Additionally, we present an example illustrating an application of the described method.

show abstract

A subinterval-based method for circuits with fractional order elements

Cited by 16 publications

References 13 publications

A Harmonic Balance Methodology for Circuits with Fractional and Nonlinear Elements

A Harmonic Balance Methodology for Circuits with Fractional and Nonlinear Elements

Diagnostic approach in assessment of a ferroresonant circuit

An analytical method for solving the two-phase inverse Stefan problem

Contact Info

Product

Resources

About