Abstract
The article presents the results of the computations performed for a ferroresonant circuit. Two models for the coil with a ferromagnetic core were used in the simulations. The conventional parallel model and one applying a fractional derivative. Calculations of applied model parameters were obtained through estimations based on measured and recorded steady-state waveforms of currents and voltages of the particular circuit components. The experiment was conducted over a wide range of levels of the supply voltage. During the experiment, the coil worked in the saturation conditions of the magnetic core, but intentionally without reaching the point where ferroresonance occurs. Measurements and recordings were made using the digital interference recorder RZ-1 developed by Kared (Gdansk). Parameter estimations and simulations were performed in Matlab.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Majka, Ć., Paszek, S.: Mathematical model parameter estimation of a generating unit operating in the Polish National Power System. Bull. Pol. Acad. Sci. Tech. Sci. 64(2), 409â416 (2016)
Ferracci, Ph.: Ferroresonance. Schneider-Electric Technical Book, vol. 190. Schneiderâs Group Technical Collection (1998)
IEEE working group on modeling and analysis of systems transients, modeling and analysis guidelines for slow transients â part III: the study of ferroresonance. IEEE Trans. Power Delivery 15(1), 255â265 (2000)
Corea-Araujo, J.A., Gonzalez-Molina, F., Martinez-Velasco, J.A., Barrado-Rodrigo, J.A., Guasch-Pesquer, L.: Tools for characterization and assessment of ferroresonance using 3-D bifurcation diagrams. IEEE Trans. Power Delivery 29(6), 2543â2551 (2014)
Ali Z.: Development of numerical algorithms for ferroresonance monitoring. Doctoral thesis. The University of Manchester, Faculty of Engineering and Physical Science (2015)
Milicevic, K., Lukacevic, I., Flegar, I.: Modeling of nonlinear coil in a ferroresonant circuit. Electr. Eng. (Archiv fur Elektrotechnik) 91, 51â59 (2009)
Schafer I., Kruger K.: Modelling of coils using fractional derivatives. J. Magn. Magn. Mater. 307, 91â98 (2006)
Nana, B., Yamgoue, S.B., Tchitnga, R., Woafo, P.: Simple mathematical model for ferromagnetic core inductance and experimental validation. Am. J. Electric. Electron. Eng. 3(2), 29â36 (2015)
Schafer, I., Kruger, K.: Modelling of lossy coils using fractional derivatives. J. Phys. D: Appl. Phys. 41 (2008). https://doi.org/10.1088/0022-3727/41/4/045001
Lei, Z.-M., Liu, Z.-J., Sun, H.-X., Chang, H.-J.: Research on the control and application of chaos in an electrical system. In: Advances in Machine Learning and Cybernetics. LNAI, vol. 3930, pp. 142â148. Springer, Berlin (2006)
Sowa, P., Ćuszcz, K.: Symulacja chaosu ferrorezonansowego za pomocÄ programu. MicroTran. Electr. Rev. 90(8), 116â121 (2014)
Seker, S., Akinci, T.C., Taskin, S.: Spectral and statistical analysis for ferroresonance phenomenon in electric power systems. Electr. Eng. 94(2), 117â124 (2012)
Milicevic, K., Nyarko, E.K., Biondic, I.: Chuaâs model of nonlinear coil in a ferroresonant circuit obtained using Dommelâs method and grey box modelling approach. Nonlinear Dyn. 86, 51â63 (2016)
KolaĆska-PĆuska, J., Grochowicz, B.: Modelling of a non-linear coil with loss in iron using the Runge-Kutta methods. Arch. Electr. Eng. 65(3), 527â539 (2016)
Amar, F.B., Dhifaoui, R.: Study of the periodic ferroresonance in the electrical power networks by bifurcation diagrams. Int. J. Electr. Power Energy Syst. 33(1), 61â85 (2011)
Moradi, M., Gholami, A.: Harmonic balance based stability domain analysis of period-1 ferroresonance. Electr. Power Compon. Syst. 39(12) (2011)
Visintin, A.: Differential Models of Hysteresis. Applied Mathematical Science. Springer, New York (1994)
Biondic, I., Topalovic, R., Milicevic, K.: Comparison of basic ferromagnetic coil hysteresis models. In: Papers of 33rd International Scientific Conference: Science in Practice
Cundeva, S.: A transformer model based on the jiles-atherton theory of ferromagnetic hysteresis. Serb. J. Electr. Eng. 5(1), 21â30 (2008)
Chwastek, K., SzczygĆowski, J.: Estimation methods for the Jiles-Atherton model parameters - a review. Electr. Rev. 84(12), 145â148 (2008)
Benabou, A., Clenet, S., Piriou, F.: Comparison of Preisach and Jiles-Atherton models to take into account hysteresis phenomenon for finite element analysis. J. Magn. Magn. Mater. 261(1â2), 139â160 (2003)
Carnevale, D., Nicosia, S., Zaccarian, L.: Generalized constructive model of hysteresis. IEEE Trans. Magn. 42(12), 3809â3817 (2006)
Voros, J.: Modeling and identification of hysteresis using special forms of the Coleman-Hodgdon model. J. Electr. Eng. 60(2), 100â105 (2009)
Noel, J.P., Esfahani, A.F., Kerschen, G., Schoukens, J.: A nonlinear state-space approach to hysteresis identification. Mech. Syst. Signal Process. 84, 171â184 (2017)
Bastos, J.P.A., Sadowski, N., Leite, J.V., Jhoe Batistela, N.J., Hoffmann, K., Meunier, G., Chadebec, O.: A differential permeability 3-D formulation for anisotropic vector hysteresis analysis. IEEE Trans. Magn. 50(2), 341â344 (2014)
Milicevic, K., Vinko, D., Emin, Z.: Identifying ferroresonance initiation for a range of initial conditions and parameters. Nonlinear Dyn. 66, 755â762 (2011)
Majka, Ć.: Measurement based inductor modeling for the purpose of ferroresonance analyses. In: Proceedings of International Conference on AMTEE, Trebic, Czech Republic, pp. Vâ3 (2015)
Majka, Ć.: Measurement verification of the nonlinear coil models. In: Proceedings of the 39th International Conference on IC-SPETO, UstroĆ, pp. 89â90 (2016)
Majka, Ć.: Measurements and simulation for a ferroresonance circuit. In: Proceedings of the 40th International Conference on IC-SPETO, UstroĆ, pp. 47â48 (2017)
Caputo, M.: Linear models of dissipation whose Q is almost frequency independent-ii. Geophys. J. Roy. Astron. Soc. 13(5), 529â539 (1967)
http://www.kared.com.pl/Products/11/48/Cyfrowy-rejestrator-zaklocen-RZ-1.html
Powell, M.J.D.: A fortran subroutine for solving systems of nonlinear algebraic equations. In: Numerical Methods for Nonlinear Algebraic Equations, Chap. 7 (1970)
Sowa, M.: A subinterval-based method for circuits with fractional order elements. Bull. Pol. Acad. Sci., Tech. Sci. 62(3), 449â454 (2014)
Sowa M.: Application of SubIval, a method for fractional-order derivative computations in IVPs. In: Babiarz, A., Czornik, A., Klamka, J., Niezabitowski, M. (eds.) 8th Conference on Non-integer Order Calculus and Its Applications. Theory and Applications of Non-Integer Order Systems, Zakopane, Poland, pp. 489â499. Springer, Berlin (2017)
Sowa, M.: Application of SubIval in solving initial value problems with fractional derivatives. Appl. Math. Comput. 319, 86â103 (2018)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer International Publishing AG, part of Springer Nature
About this paper
Cite this paper
Majka, Ć. (2019). Fractional Derivative Approach in Modeling of a Nonlinear Coil for Ferroresonance Analyses. In: Ostalczyk, P., Sankowski, D., Nowakowski, J. (eds) Non-Integer Order Calculus and its Applications. RRNR 2017. Lecture Notes in Electrical Engineering, vol 496. Springer, Cham. https://doi.org/10.1007/978-3-319-78458-8_13
Download citation
DOI: https://doi.org/10.1007/978-3-319-78458-8_13
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-78457-1
Online ISBN: 978-3-319-78458-8
eBook Packages: EngineeringEngineering (R0)