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Equations of magnetic field of transformer steel sheets

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
This study described a method for determining the magnetic field in transformer steel sheets for any magnetisation direction. In the proposed approach, limiting hysteresis loops for the rolling and transverse directions were used. These loops, which were determined separately in both directions, were modified depending on the direction of magnetisation. The assumed area of the magnetic field occurrence was divided into elementary segments, and the appropriate components of field strength and flux density were assigned to the edges and elementary segments of the grid dividing this area. The relationships between the flux density and field strength along both the rolling and transverse directions in the elementary segments were introduced into the equations of the magnetic field distribution, which were based on Maxwell’s equations in the integral form. These equations facilitated the determination of changes in the magnetic field, considering the magnetic hysteresis. The correctness of these equations was validated through comparisons of the results of numerical calculations with the analogous results of measurements performed using a laboratory package of transformer sheets.
Rocznik
Strony
999--1012
Opis fizyczny
Bibliogr. 24 poz., rys., tab., wykr., wz.
Twórcy
  • Department of Electrical Engineering, Cracow University of Technology, Warszawska 24 str., 31-155 Kraków, Poland
  • Department of Electrical Engineering, Cracow University of Technology, Warszawska 24 str., 31-155 Kraków, Poland
Bibliografia
  • [1] Tumański S., Handbook of Magnetic Measurements, CRC Press: Boca Raton (2011).
  • [2] Bozorth R.M., Ferromagnetism, IEEE Press, New York (1978).
  • [3] Iványi A., Hysteresis models in electromagnetic computation, Akadémiai Kiadó, Budapest (1997).
  • [4] Jiles D., Introduction to Magnetism and Magnetic Materials, Chapman & Hall, London (1998).
  • [5] Tumański S., Investigations of the anisotropic behaviour of SiFe Steel, Journal of Magnetism and Magnetic Materials, vol. 254–255, pp. 50–53 (2003), DOI: 10.1016/S0304-8853(02)00745-X.
  • [6] Beckley P., Electrical steels for rotating machines, Bell & Bain Ltd., Glasgow (2002).
  • [7] Mousavi S., Shamei M., Siadatan A., Nabizadeh F., Mirimani S.H., Calculation of Power Transformer Losses by Finite Element Method, IEEE Electrical Power and Energy Conference, EPEC (2018), DOI: 10.1109/EPEC.2018.8598292.
  • [8] Sarac V., FEM 2D and 3D design of transformer for core losses computation, International Scientific Journal – Machines. Technologies. Materials, vol. 2, no. 3, pp. 119–122 (2017).
  • [9] Baron B., Kolańska-Płuska J., Łukaniszyn M., Spałek D., Kraszewski T., Solution of nonlinear stiff differential equations for a three-phase no-load transformer using a Runge–Kutta implicit method, Archives of Electrical Engineering, vol. 71, no. (4), pp. 1081–1106 (2022), DOI: 10.24425/aee.2022.142126.
  • [10] Chen R., Martin F., Li Y., Yue S., Belahcen A., An Energy-based Anisotropic Vector Hysteresis Model for Rotational Electromagnetic Core Loss, IEEE Transactions on Industrial Electronics, vol. 71, no. 6, pp. 6084–6094 (2024), DOI: 10.1109/TIE.2023.3294635.
  • [11] Jabłoński P., Najgebauer M., Bereżnicki M., An Improved Approach to Calculate Eddy Current Loss in Soft Magnetic Materials Based on Measured Hysteresis Loops, Energies, vol. 15, no. 8 (2022), DOI: 10.3390/en15082869.
  • [12] Mikula L., Ramdane B., Blatter Martinho L., Kedous-Lebouc A., Meunier G., Numerical modelling of static hysteresis phenomena using a vector extension of the Loss Surface model, IEEE Conference on Electromagnetic Field Computation, CEFC (2022), DOI: 10.1109/CEFC55061.2022.9940905.
  • [13] Mazgaj W., Sierzega M., Szular Z., Approximation of Hysteresis Changes in Electrical Steel Sheets, Energies, vol. 14, no. 14 (2021), DOI: 10.3390/en14144110.
  • [14] Pfützner H., Rotational Magnetisation and Rotational Losses of Grain Oriented Silicon Steel Sheets – Fundamental Aspects and Theory, IEEE Transactions on Magnetics, vol. 30, no. 5, pp. 2802–2807 (1994), DOI: 10.1109/20.312522.
  • [15] Mao W., Atherton D.L., Magnetisation Vector Directions in a Steel Cube, IEEE Transactions on Magnetics, vol. 36, no. 5, pp. 3084–3086 (2000), DOI: 10.1109/20.908688.
  • [16] Shin S., Schaefer R., DeCooman B.C., Anisotropic magnetic properties and domain structure in Fe-3%Si(110) steel sheet, Journal of Applied Physics, vol. 109, no. 7, 07A307 (2011), DOI: 10.1063/1.3535547.
  • [17] Sudo M., Matsuo T., Magnetisation modeling of silicon steel using a simplified domain structure model, Journal of Applied Physics, vol. 111, no. 7, 07D107 (2012), DOI: 10.1063/1.3672073.
  • [18] Furuya A., Fujisaki J., Uehara Y., Shimizu K., Oshima H., Matsuo., Micromagnetic Hysteresis Model Dealing with Magnetisation Flip Motion for Grain-Oriented Silicon Steel, IEEE Transactions on Magnetics, vol. 50, no. 11 (2014), DOI: 10.1109/TMAG.2014.2329679.
  • [19] Fiorillo L., Dupré R., Appino C., Rietto A.M., Comprehensive model of magnetisation curve, hysteresis loops, and losses in any direction in grain-oriented Fe–Si, IEEE Transactions on Magnetics, vol. 38, no. 3, pp. 1467–1475 (2002), DOI: 10.1109/20.999119.
  • [20] Sierżęga M., Mazgaj W., Modelling of magnetisation processes in transformer steel sheets, Archives of Electrical Engineering, vol. 72, no. 4, pp. 855–870 (2023), DOI: 10.24425/aee.2023.147415.
  • [21] Warzecha A., Mazgaj W., Magnetisation measurements in circle-shaped samples of typical dynamo steel sheets, Przegl ˛ad Elektrotechniczny, no. 6 (2015), DOI: 10.15199/48.2015.06.19.
  • [22] Albanese R., Rubinacci G., Canali M., Stangherlin S., Musolino A., Raugi M., Analysis of a Transient Nonlinear 3-D Eddy Current Problem with Differential and Integral Methods, IEEE Transactions on Magnetics, vol. 32, no. 3, pp. 776–779 (1996), DOI: 10.1109/20.497355.
  • [23] Demenko A., Three Dimensional Eddy Current Calculation Using Reluctance-Conductance Network Formed by Means of FE Method, IEEE Transactions on Magnetics, vol. 36, no. 4, pp. 741–745 (2000), DOI: 10.1109/20.877554.
  • [24] Szular Z., Mazgaj W., Calculations of eddy currents in electrical steel sheets taking into account their magnetic hysteresis, COMPEL, no. 38, pp. 1263–1273 (2019), DOI: 10.1108/COMPEL-10-2018-0424.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-76a4ef81-9b23-4308-8072-0960e85a6225
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