Improved algorithm for periodic steady-state analysis in nonlinear electromagnetic devices

• Autorzy: Sobczyk T. J. , Radzik M.

Identyfikatory

DOI

10.24425/bpasts.2019.130878

• Języki publikacji: EN

Abstrakty

EN

This paper presents the improved methodology for the direct calculation of steady-state periodic solutions for electromagnetic devices, as described by nonlinear differential equations, in the time domain. A novel differential operator is developed for periodic functions and the iterative algorithm determining periodic steady-state solutions in a selected set of time instants is identified. Its application to steady-state analysis is verified by an elementary example. The modified algorithm reduces the complexity of steady-state analysis, particularly for electromagnetic devices described by high-dimensional nonlinear differential equations.

Słowa kluczowe

EN

electromagnetic devices; steady-state analysis; periodic solutions; analysis in time domain; discrete differential operator; iterative algorithms

• Wydawca: Polska Akademia Nauk, Wydział IV Nauk Technicznych
• Czasopismo: Bulletin of the Polish Academy of Sciences. Technical Sciences
• Rocznik: 2019
• Tom: Vol. 67, nr 5
• Strony: 863--869
• Opis fizyczny: Bibliogr. 16 poz., rys.

Twórcy

autor

Sobczyk T. J.

• Cracow University of Technology, Institute on Electromechanical Energy Conversion, 24 Warszawska St, 31-155 Cracow, Poland

autor

Radzik M.

• Technical Institute, State Higher Vocational School in Nowy Sącz, 1A Zamenhofa St., 33-300 Nowy Sącz, Poland

Bibliografia

• [1] T. Hara, T. Naito and J. Umoto, “Time-periodic finite element method for nonlinear diffusions equations”, IEEE Trans. Magn. 21(6), 2261‒2264 (1985).
• [2] O. Biro and K. Preis, “An efficient time domain method for nonlinear periodic eddy current problems”, IEEE Trans. Magn., 42(4), 695‒698 (2006),
• [3] N. Garcia, ”Periodic steady-state solutions of nonlinear circuits based on a differentiation matrix”, Proc. of 2010 IEEE Int.l Symp. Circuits and Systems, 141‒144 (2010).
• [4] T.J. Sobczyk and M. Radzik, “Direct determination of periodic solution in time domain for electromechanical converters, Technical Transactions – Electrical Eng., Cracow Univ. of Tech., 112(2-E), 73‒82 (2015).
• [5] M. Radzik and T.J. Sobczyk, “An algorithm of time domain steady-state analysis for electrical machines accounting for saturation, Proc. of SME 2017, IEEE Explore (978‒1‒5386‒0359‒8/17/$31.00 ©2017 European Union), Paper 13, (2017).
• [6] T.J. Sobczyk and M. Radzik, “A new approach to steady state analysis of nonlinear electrical circuits”, COMPEL, Emerald Pub. Ltd., 36(3), 716‒728 (2017).
• [7] T.J. Sobczyk and M. Radzik, “Application of novel discrete differential operator of periodic function to study electromechanical interaction”, Bull. Pol. Ac.: Tech. (66)5, 645‒653 (2018).
• [8] S. Yamada, K. Besho, and J. Lu, “Harmonic balance finite element method application for nonlinear magnetic analysis”, IEEE Trans. Magn., Vol. 25, 2971‒2973 (1989).
• [9] A. Semlyen, E. Acha, and H.W. Dommel, “Newton-type algorithms for the harmonic phasor analysis of nonlinear power circuits in periodical steady state with special reference to magnetic nonlinearities”, IEEE Trans. Power Delivery, Vol. 6, 1090‒1098 (1991).
• [10] T.J. Sobczyk, “Direct determination of two-periodic solution for nonlinear dynamic systems”, COMPEL, James & James Science Pub. Ltd., Vol. 13, 509‒529 (1994).
• [11] J. Gyselinck, P. Dular, C. Geuzaine, and W. Legros, “Harmonic-balance finite element modeling of electromagnetic devices: a novel approach, IEEE Trans Magnetics. 38(2), 521‒524 (2002).
• [12] O. Deblecker and J. Lobry, “A new efficient technique for harmonic-balance finite element analysis of saturated electromagnetic devices”, IEEE Trans. Magn., Vol. 38, 535‒538, (2006).
• [13] X. Zhao, L. Li, J. Lu, Z. Cheng, and T. Lu, “Analysis of the saturated electromagnetic devices under CD bias condition by the decomposed harmonic balance method”, COMPEL, Vol. 3, 498‒513 (2012).
• [14] E. Lelarasmee, A.E. Ruchli, and A. Sangiovanni-Vincentelli, “The waveform relaxation method for time-domain analysis of large scale integrated circuits”, IEEE Trans. CADIC 1(3), 131‒145 (1982).
• [15] G. Caron, T. Henneron, F. Piriou, and J-C Mipo, “Time-periodic condition of nonlinear magnetostatic problem coupled with electric circuit imposed by waveform relaxation method”, IEEE Trans. Magnetics 52(3) (2016).
• [16] G. Caron, T. Henneron, F. Piriou, and J-C Mipo, “Waveform relaxation-Newton method to determine steady state operation: application to three-phase transformer, COMPEL 36(3), 729‒740 (2017).

Uwagi

PL

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).