Modelling and analysis of medium frequency transformers for power converters - Publikacja - MOST Wiedzy

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Modelling and analysis of medium frequency transformers for power converters

Abstrakt

The evolutions in power systems and electric vehicles, related to the economic opportunities and the environmental issues, bring the need of high power galvanically isolated DC-DC converter. The medium frequency transformer (MFT) is one of its key components, enabled by the increasing switching frequency of modern power semiconductors like silicon carbide transistors or diodes. The increased operating frequency offers small converter size, leading to the decrease in raw material usage. Most likely this will result in the converter cost reduction what will further increase the demand for solid state transformer solutions. The modelling and analysis are essential in the development of the MFT technology which is attracting lots of research and industrial interest.

In this dissertation the isolated DC-DC converter topologies are introduced with the particular focus on the dual active bridge (DAB). The key components of the isolated DC-DC converters, power semiconductors and medium frequency transformer are reviewed.

A mathematical model of a 3-phase MFT in the isolated DC-DC power converter, suitable in electromagnetic transient and steady state simulation is developed. The transformer modelling methods are reviewed and the Lagrange energy method is used to derive a physically motivated model for circuit analysis. The model involves a matrix of nonlinear magnetizing inductances and a matrix of linear leakage inductances, both including self and mutual values. The macroscopic models of magnetic hysteresis are reviewed and the feedback Preisach model is developed.

The design of a 3-phase 20 kHz transformer for a 100 kW 1.2 kV isolated DC-DC power converter is presented. The particular focus is put on the winding and core design, and power loss and thermal calculations which are the most critical aspects of the high-power density transformer. The design results in two 3-phase MFT prototypes, first of its kind worldwide.

A finite element model of the transformer is developed allowing to determine the magnetic flux characteristic Φ(Θ) and the related inductances required in the circuit model. The finite element model is based on the measured equivalent B(H) and homogenized material properties. Other model parameters are calculated analytically and compared against the measurement on the prototype MFT.

The dissertation is concluded showing the technical feasibility and benefits of the 3-phase MFT. The developed MFT prototype operating at 20 kHz is more than 10 times lighter than the equivalent 50 Hz transformer. The 3-phase 100 kW DC-DC converter efficiency is measured 99.2% what is an impressive result. The efficiency of the 3-phase DC-DC is higher than its equivalent single-phase variant.

A challenge of high power MFT design related to the parasitic air gaps in the core is highlighted. The influence of the air gaps on core power loss is confirmed showing that the increase in the air gap size in a certain range causes a decrease in the core power loss. In the 3‑phase MFT prototype the parasitic air gaps do not cause any measurable effect on winding power loss and temperature. It is shown that the relative magnetic permeability is nonlinearly decreasing with the increase of the number of parasitic air gaps. An exponential interpolation function is proposed allowing to estimate the equivalent magnetic permeability, average air gap length and magnetizing inductance for any high-power ferrite core MFT with a similar core assembly.

The proposed MFT equivalent circuit model is proven accurate in steady state and transient analyses. The no-load inrush test confirms the importance of the magnetic cross saturation involved in the magnetizing inductance model. The influence of the mutual leakage inductance on the operation of the DAB converter is shown. The feedback Preisach model of hysteresis is proven accurate in the modelling of hysteresis loops in the multi air gap ferrite core MFT.

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Kategoria:
Doktoraty, rozprawy habilitacyjne, nostryfikacje
Typ:
Doktoraty, rozprawy habilitacyjne, nostryfikacje
Rok wydania:
2020
Bibliografia: test
  1. ABB, "Why choose HVDC over HVAC." [Online]. otwiera się w nowej karcie
  2. ABB, "MVDC and Grid Interties: enabling new features in distribution, sub-transmission and industrial networks," 2019. [Online].
  3. ABB, "Dry-type low voltage transformers," 2014. [Online]. Available: https://search- ext.abb.com/library/Download.aspx?DocumentID=1LES100025- ZD&LanguageCode=en&DocumentPartId=&Action=Launch. [Accessed: 12-Jan-2020]. otwiera się w nowej karcie
  4. M. Adamowicz, "Power Electronics Building Blocks for implementing Smart MV/LV Distribution Transformers for Smart Grid," Acta Energetica, vol. 4, no. 21, pp. 6-13, 2014. otwiera się w nowej karcie
  5. N. Ahmed, S. Norrga, H.-P. Nee, A. Haider, D. Van Hertem, L. Zhang, and L. Harnefors, "HVDC SuperGrids with modular multilevel converters -The power transmission backbone of the future," in International Multi-Conference on Systems, Signals Devices, 2012, pp. 1-7. otwiera się w nowej karcie
  6. M. Albach and H. Rossmanith, "The influence of air gap size and winding position on the proximity losses in high frequency transformers," in 2001 IEEE 32nd Annual Power Electronics Specialists Conference (IEEE Cat. No.01CH37230), 2001, vol. 3, pp. 1485-1490 vol. 3. otwiera się w nowej karcie
  7. O. Aldosari, L. A. Garcia Rodriguez, J. C. Balda, and S. K. Mazumder, "Design Trade-Offs for Medium-and High-Frequency Transformers for Isolated Power Converters in Distribution System Applications," in 2018 9th IEEE International Symposium on Power Electronics for Distributed Generation Systems (PEDG), 2018, pp. 1-7. otwiera się w nowej karcie
  8. Alstom, "Coradia iLint -the world's 1st hydrogen powered train," Alstom. [Online]. Available: https://www.alstom.com/our-solutions/rolling-stock/coradia-ilint-worlds-1st-hydrogen-powered- train. [Accessed: 30-Dec-2019]. otwiera się w nowej karcie
  9. Ansys, "Help." [Online]. Available: https://ansyshelp.ansys.com/. [Accessed: 06-Mar-2020]. otwiera się w nowej karcie
  10. A. Ayachit and M. K. Kazimierczuk, "Sensitivity of effective relative permeability for gapped magnetic cores with fringing effect," IET Circuits, Devices Systems, vol. 11, no. 3, pp. 209-215, 2017. otwiera się w nowej karcie
  11. A. Ayachit and M. K. Kazimierczuk, "Steinmetz Equation for Gapped Magnetic Cores," IEEE Magnetics Letters, vol. 7, pp. 1-4, 2016. otwiera się w nowej karcie
  12. M. A. Bahmani, "Design considerations of medium-frequency power transformers in HVDC applications," in 2017 Twelfth International Conference on Ecological Vehicles and Renewable Energies (EVER), 2017, pp. 1-6. otwiera się w nowej karcie
  13. M. A. Bahmani, E. Agheb, T. Thiringer, H. K. Høidalen, and Y. Serdyuk, "Core loss behavior in high frequency high power transformers-I: Effect of core topology," Journal of Renewable and Sustainable Energy, vol. 4, no. 3, p. 033112, May 2012. otwiera się w nowej karcie
  14. M. A. Bahmani, T. Thiringer, and M. Kharezy, "Optimization and experimental validation of medium-frequency high power transformers in solid-state transformer applications," in 2016 IEEE Applied Power Electronics Conference and Exposition (APEC), 2016, pp. 3043-3050. otwiera się w nowej karcie
  15. J. P. S. Bala, "DC Connection of Offshore Wind Power Plants without Platform," 2014.
  16. M. Birle and C. Leu, "Breakdown of polymer dielectrics at high direct and alternating voltages superimposed by high frequency high voltages," in 2013 IEEE International Conference on Solid Dielectrics (ICSD), 2013, pp. 656-661. otwiera się w nowej karcie
  17. M. B. Blarke and B. M. Jenkins, "SuperGrid or SmartGrid: Competing strategies for large-scale integration of intermittent renewables?," Energy Policy, vol. 58, pp. 381-390, Jul. 2013. otwiera się w nowej karcie
  18. M. Brokate and E. Della Torre, "The wiping-out property of the moving model (magnetic hysteresis)," IEEE Transactions on Magnetics, vol. 27, no. 5, pp. 3811-3814, Sep. 1991. otwiera się w nowej karcie
  19. A. Cabrera-Tobar, E. Bullich-Massagué, M. Aragüés-Peñalba, and O. Gomis-Bellmunt, "Topologies for large scale photovoltaic power plants," Renewable and Sustainable Energy Reviews, vol. 59, pp. 309-319, Jun. 2016. otwiera się w nowej karcie
  20. S. Calabro, F. Coppadoro, and S. Crepaz, "The Measurement of the Magnetization Characteristics of Large Power Transformers and Reactors through D.C. Excitation," IEEE Transactions on Power Delivery, vol. 1, no. 4, pp. 224-234, Oct. 1986. otwiera się w nowej karcie
  21. L. Chedot and G. Friedrich, "A cross saturation model for interior permanent magnet synchronous machine. Application to a starter-generator," in Conference Record of the 2004 IEEE Industry Applications Conference, 2004. 39th IAS Annual Meeting., 2004, vol. 1, p. 70. otwiera się w nowej karcie
  22. Chroma, "3-Phase Programmable AC Source -61700." [Online]. Available: https://www.chromausa.com/product/3-phase-programmable-ac-source-61700/. [Accessed: 08- Mar-2020].
  23. CIGRE WG C6.31, "Medium voltage direct current (MVDC) grid feasibility study," Feb. 2020.
  24. Dassault Systèmes, "Opera -electromagnetic and electromechanical simulation." [Online]. otwiera się w nowej karcie
  25. R. W. A. A. De Doncker, D. M. Divan, and M. H. Kheraluwala, "A three-phase soft-switched high- power-density DC/DC converter for high-power applications," IEEE Transactions on Industry Applications, vol. 27, no. 1, pp. 63-73, Jan. 1991. otwiera się w nowej karcie
  26. M. De Prada Gil, J. L. Domínguez-García, F. Díaz-González, M. Aragüés-Peñalba, and O. Gomis- Bellmunt, "Feasibility analysis of offshore wind power plants with DC collection grid," Renewable Energy, vol. 78, pp. 467-477, Jun. 2015.
  27. R. W. DeDoncker, M. H. Kheraluwala, and D. M. Divan, "Power conversion apparatus for DC/DC conversion using dual active bridges," US5027264A, 25-Jun-1991.
  28. R. C. Degeneff, "A general method for determining resonances in transformer windings," IEEE Transactions on Power Apparatus and Systems, vol. 96, no. 2, pp. 423-430, Mar. 1977. otwiera się w nowej karcie
  29. R. C. Degeneff, M. R. Gutierrez, and P. J. McKenny, "A method for constructing a reduced order transformer model for system studies from detailed lumped parameter models," in Proceedings of the 1991 IEEE Power Engineering Society Transmission and Distribution Conference, 1991, pp. 532-538. otwiera się w nowej karcie
  30. E. Della Torre and F. Vajda, "Parameter identification of the complete-moving-hysteresis model using major loop data," IEEE Transactions on Magnetics, vol. 30, no. 6, pp. 4987-5000, Nov. 1994.
  31. F. Della Torre, A. P. Morando, and G. Todeschini, "Three-Phase Distributed Model of High-Voltage Windings to Study Internal Steep-Fronted Surge Propagation in a Straightforward Transformer," IEEE Transactions on Power Delivery, vol. 23, no. 4, pp. 2050-2057, Oct. 2008. otwiera się w nowej karcie
  32. A. Demenko, Obwodowe modele układów z polem elektromagnetycznym. Wydaw. Politechniki Poznańskiej, 2004.
  33. A. Demenko, R. M. Wojciechowski, and J. K. Sykulski, "2-D Versus 3-D Electromagnetic Field Modeling in Electromechanical Energy Converters," IEEE Transactions on Magnetics, vol. 50, no. 2, pp. 897-900, Feb. 2014. otwiera się w nowej karcie
  34. C. G. Dincan, P. Kjaer, Y.-H. Chen, E. Sarrá-Macia, S. Munk-Nielsen, C. L. Bak, and S. Vaisambhayana, "Design of a High-Power Resonant Converter for DC Wind Turbines," IEEE Transactions on Power Electronics, vol. 34, no. 7, pp. 6136-6154, Jul. 2019. otwiera się w nowej karcie
  35. D. Dolinar, J. Pihler, and B. Grcar, "Dynamic model of a three-phase power transformer," IEEE Transactions on Power Delivery, vol. 8, no. 4, pp. 1811-1819, Oct. 1993. otwiera się w nowej karcie
  36. M. Dolinar, D. Dolinar, G. Stumberger, B. Polajzer, and J. Ritonja, "A Three-Phase Core-Type Transformer Iron Core Model With Included Magnetic Cross Saturation," IEEE Transactions on Magnetics, vol. 42, no. 10, pp. 2849-2851, Oct. 2006. otwiera się w nowej karcie
  37. P. L. Dowell, "Effects of eddy currents in transformer windings," Proceedings of the Institution of Electrical Engineers, vol. 113, no. 8, pp. 1387-1394, Aug. 1966. otwiera się w nowej karcie
  38. Y. Du, S. Lukic, B. Jacobson, and A. Huang, "Review of high power isolated bi-directional DC-DC converters for PHEV/EV DC charging infrastructure," in 2011 IEEE Energy Conversion Congress and Exposition, 2011, pp. 553-560. otwiera się w nowej karcie
  39. P. Dworakowski, A. Wilk, and B. Lefebvre, "Hysteresis modelling of a medium frequency single- phase transformer," in 2017 19th European Conference on Power Electronics and Applications (EPE'17 ECCE Europe), 2017, p. P.1-P.9. otwiera się w nowej karcie
  40. P. Dworakowski, A. Wilk, M. Michna, A. Fouineau, and M. Guillet, "Lagrangian model of an isolated dc-dc converter with a 3-phase medium frequency transformer accounting magnetic cross saturation," IEEE Transactions on Power Delivery, accepted for publication. otwiera się w nowej karcie
  41. P. Dworakowski, A. Wilk, M. Michna, B. Lefebvre, and T. Lagier, "3-phase medium frequency transformer for a 100kW 1.2kV 20kHz Dual Active Bridge converter," in IECON 2019 -45th otwiera się w nowej karcie
  42. Annual Conference of the IEEE Industrial Electronics Society, 2019, vol. 1, pp. 4071-4076. otwiera się w nowej karcie
  43. P. Dworakowski, A. Wilk, M. Michna, B. Lefebvre, F. Sixdenier, and M. Mermet-Guyennet, "Effective Permeability of Multi Air Gap Ferrite Core 3-Phase Medium Frequency Transformer in Isolated DC-DC Converters," Energies, vol. 13, no. 6, p. 1352, Jan. 2020. [43] ebm-papst, "DC axial compact fan 5214 NHH." [Online]. otwiera się w nowej karcie
  44. A. E. Eiben and J. E. Smith, Introduction to Evolutionary Computing. Berlin Heidelberg: Springer- Verlag, 2003. otwiera się w nowej karcie
  45. J. El Hayek and T. J. Sobczyk, "Equivalent circuit of multi-windings traction transformers including magnetizing currents," in 2005 International Conference on Electrical Machines and Systems, 2005, vol. 3, pp. 1740-1745 Vol. 3.
  46. EMTP Alliance, "EMTP." [Online]. Available: https://www.emtp-software.com/en/products/emtp. [Accessed: 07-Mar-2020]. otwiera się w nowej karcie
  47. P. Fairley, "DC Versus AC: The Second War of Currents Has Already Begun [In My View]," IEEE Power and Energy Magazine, vol. 10, no. 6, pp. 104-103, Nov. 2012. otwiera się w nowej karcie
  48. P. I. Fergestad and T. Henriksen, "Transient Oscillations in Multiwinding Transformers," IEEE Transactions on Power Apparatus and Systems, vol. PAS-93, no. 2, pp. 500-509, Mar. 1974. otwiera się w nowej karcie
  49. Ferroxcube, "Soft ferrites and accessories, data handbook," 2013. [Online]. Available: https://www.ferroxcube.com/en-global/download/download/11. [Accessed: 01-Jan-2020]. otwiera się w nowej karcie
  50. Ferroxcube, "Design of planar power transformers." [Online].
  51. Ferroxcube, "3C90 material specification," 2008. [Online]. otwiera się w nowej karcie
  52. J. M. Filipe, C. L. Moreira, R. J. Bessa, and B. A. Silva, "Optimization of the variable speed pump storage participation in frequency restoration reserve market," in 2016 13th International Conference on the European Energy Market (EEM), 2016, pp. 1-6. otwiera się w nowej karcie
  53. FLIR, "Thermal camera A325sc." [Online]. Available: https://www.flir.com/products/a325sc/. [Accessed: 22-Mar-2020]. otwiera się w nowej karcie
  54. A. Fouineau, "Méthodologies de Conception de Transformateurs Moyenne Fréquence pour application aux réseaux haute tension et réseaux ferroviaires," thesis, Lyon, 2019.
  55. A. Fouineau, M.-A. Raulet, B. Lefebvre, N. Burais, and F. Sixdenier, "Semi-Analytical Methods for Calculation of Leakage Inductance and Frequency-Dependent Resistance of Windings in Transformers," IEEE Transactions on Magnetics, vol. 54, no. 10, pp. 1-10, Oct. 2018. otwiera się w nowej karcie
  56. E. F. Fuchs and Y. You, "Measurement of λ-1 characteristics of asymmetric three-phase transformers and their applications," IEEE Power Engineering Review, vol. 22, no. 8, pp. 69-70, Aug. 2002. otwiera się w nowej karcie
  57. A. Garcia-Bediaga, I. Villar, A. Rujas, I. Etxeberria-Otadui, and A. Rufer, "Analytical Models of Multiphase Isolated Medium-Frequency DC-DC Converters," IEEE Transactions on Power Electronics, vol. 32, no. 4, pp. 2508-2520, Apr. 2017. otwiera się w nowej karcie
  58. A. Garcia-Bediaga, I. Villar, A. Rujas, L. Mir, and A. Rufer, "Multiobjective Optimization of Medium-Frequency Transformers for Isolated Soft-Switching Converters Using a Genetic Algorithm," IEEE Transactions on Power Electronics, vol. 32, no. 4, pp. 2995-3006, Apr. 2017. otwiera się w nowej karcie
  59. GE, "DolWin3 HVDC Voltage Source Converters for Efficient Connection of Renewable Energy." [Online]. Available: http://www.gegridsolutions.com/products/applications/HVDC/HVDC-VSC- Dolwin3-Case-Study-EN-2018-11-Grid-PEA-0578.pdf. [Accessed: 31-Dec-2019]. otwiera się w nowej karcie
  60. H. Geramirad, P. Dworakowski, F. Morel, C. Vollaire, B. Lefebvre, P. Camail, and T. Lagier, "Experimental EMI study of a 3-phase 100kW 1200V Dual Active Bridge converter using SiC MOSFETs," in EPE'20 ECCE Europe 22nd European Conference on Power Electronics and Applications, Lyon, France, 2020, accepted for publication. otwiera się w nowej karcie
  61. H. Geramirad, F. Morel, P. Dworakowski, B. Lefebvre, T. Lagier, P. Camail, C. Vollaire, and A. Breard, "Conducted EMI reduction in a 100kW 1.2kV Dual Active Bridge converter," in PCIM Europe 2020; International Exhibition and Conference for Power Electronics, Intelligent Motion, Renewable Energy and Energy Management, Nuremberg, Germany, 2020, accepted for publication. otwiera się w nowej karcie
  62. A. Globus, "Universal hysteresis loop for soft ferromagnetic materials," in Proc. European Physical Society Conference on Soft Magnetic Materials, 1975. otwiera się w nowej karcie
  63. D. Gómez A., J. D. Páez, M. Cheah-Mane, J. Maneiro, P. Dworakowski, O. Gomis-Bellmunt, and F. Morel, "Requirements for interconnection of HVDC links with DC-DC converters," in IECON 2019 -45th Annual Conference of the IEEE Industrial Electronics Society, 2019, vol. 1, pp. 4854- 4860.
  64. T. Guillod, "Modeling and Design of Medium-Frequency Transformers for Future Medium-Voltage Power Electronics Interfaces," ETH Zurich, 2018. otwiera się w nowej karcie
  65. T. Guillod, J. E. Huber, G. Ortiz, A. De, C. M. Franck, and J. W. Kolar, "Characterization of the voltage and electric field stresses in multi-cell solid-state transformers," in 2014 IEEE Energy Conversion Congress and Exposition (ECCE), 2014, pp. 4726-4734. otwiera się w nowej karcie
  66. J. Gyselinck, P. Dular, N. Sadowski, J. V. Leite, and J. P. A. Bastos, "Incorporation of a Jiles- Atherton vector hysteresis model in 2D FE magnetic field computations: Application of the Newton- Raphson method," COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, vol. 23, pp. 685-693, Sep. 2004. otwiera się w nowej karcie
  67. J. Gyselinck and J. Melkebeek, "Two-dimensional finite element modelling of overlap joints in transformer cores," COMPEL -The international journal for computation and mathematics in electrical and electronic engineering, vol. 20, no. 1, pp. 253-268, Jan. 2001. otwiera się w nowej karcie
  68. A. Hauck, M. Ertl, J. Schöberl, and M. Kaltenbacher, "Accurate magnetostatic simulation of step- lap joints in transformer cores using anisotropic higher order FEM," COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, vol. 32, no. 5, pp. 1581-1595, Jan. 2013. otwiera się w nowej karcie
  69. L. Heinemann, "An actively cooled high power, high frequency transformer with high insulation capability," in APEC. Seventeenth Annual IEEE Applied Power Electronics Conference and Exposition (Cat. No.02CH37335), 2002, vol. 1, pp. 352-357 vol.1. otwiera się w nowej karcie
  70. N. Hihat, E. Napieralska-Juszczak, J.-P. Lecointe, J. K. Sykulski, and K. Komeza, "Equivalent Permeability of Step-Lap Joints of Transformer Cores: Computational and Experimental Considerations," IEEE Transactions on Magnetics, vol. 47, no. 1, pp. 244-251, Jan. 2011. otwiera się w nowej karcie
  71. K. Hollaus and M. Schöbinger, "Multiscale finite element method for perturbation of laminated structures," in 2017 International Conference on Electromagnetics in Advanced Applications (ICEAA), 2017, pp. 1262-1263. otwiera się w nowej karcie
  72. C. Huang, F. Woittennek, and K. Röbenack, "Distributed parameter model of the buck converter with constant inductive load," IFAC-PapersOnLine, vol. 48, no. 1, pp. 691-692, Jan. 2015. otwiera się w nowej karcie
  73. P. Huang, C. Mao, D. Wang, L. Wang, Y. Duan, J. Qiu, G. Xu, and H. Cai, "Optimal Design and Implementation of High-Voltage High-Power Silicon Steel Core Medium-Frequency Transformer," IEEE Transactions on Industrial Electronics, vol. 64, no. 6, pp. 4391-4401, Jun. 2017. otwiera się w nowej karcie
  74. W. G. Hurley, T. Merkin, and M. Duffy, "The Performance Factor for Magnetic Materials Revisited: The Effect of Core Losses on the Selection of Core Size in Transformers," IEEE Power Electronics Magazine, vol. 5, no. 3, pp. 26-34, Sep. 2018. otwiera się w nowej karcie
  75. W. G. Hurley and W. H. Wölfle, Transformers and Inductors for Power Electronics: Theory, Design and Applications. Wiley, 2013. otwiera się w nowej karcie
  76. N. Ida and J. P. A. Bastos, "Electrostatic Fields," in Electromagnetics and Calculation of Fields, N. Ida, J. P. A. Bastos, and R. Mittra, Eds. New York, NY: Springer US, 1992, pp. 47-89. otwiera się w nowej karcie
  77. Infineon, "High Power Thyristors & Diodes Selection Guide 2019/2020," 2019. [Online]. Available: https://www.infineon.com/dgdl?fileId=5546d4625a888733015aad13f7a04835. [Accessed: 01-Jan- 2020].
  78. Infineon, "IGBT Modules." [Online].
  79. A. Ivani, J. Fuzi, and Z. Szabo, "Preisach models of ferromagnetic hysteresis," Przeglad Elektrotechniczny, vol. R. LXXIX 3/2003, pp. 145-150, 2003.
  80. J. Jacobs, M. Thommes, and R. De Doncker, "A transformer comparison for three-phase single active bridges," in 2005 European Conference on Power Electronics and Applications, 2005, pp. 10 pp.-P.10. otwiera się w nowej karcie
  81. C. Jedryczka, P. Sujka, and W. Szelag, "The influence of magnetic hysteresis on magnetorheological fluid clutch operation," COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, vol. 28, pp. 711-721, May 2009. otwiera się w nowej karcie
  82. M. Jesenik, M. Beković, A. Hamler, and M. Trlep, "Analytical modelling of a magnetization curve obtained by the measurements of magnetic materials' properties using evolutionary algorithms," Applied Soft Computing, vol. 52, pp. 387-408, Mar. 2017. otwiera się w nowej karcie
  83. E. Jezierski, Transformatory. Warszawa: WNT, 1983.
  84. D. Jiles and D. Atherton, "Ferromagnetic hysteresis," IEEE Transactions on Magnetics, vol. 19, no. 5, pp. 2183-2185, Sep. 1983. otwiera się w nowej karcie
  85. M. Kabalo, B. Blunier, D. Bouquain, and A. Miraoui, "State-of-the-art of DC-DC converters for fuel cell vehicles," in 2010 IEEE Vehicle Power and Propulsion Conference, 2010, pp. 1-6. otwiera się w nowej karcie
  86. M. Kachniarz, J. Salach, R. Szewczyk, and A. Bieńkowski, "Temperature Influence on the Magnetic Characteristics of Mn-Zn Ferrite Materials," in Progress in Automation, Robotics and Measuring Techniques, Cham, 2015, pp. 121-127. otwiera się w nowej karcie
  87. G. Kadar and E. Torre, "Hysteresis modeling: I. Non-congruency," IEEE Transactions on Magnetics, vol. 23, no. 5, pp. 2820-2822, Sep. 1987. otwiera się w nowej karcie
  88. A. Kazerooni, G. De Carne, M. Andersen, M. Liserre, M. Eves, and J. Yu, "Technical requirements of Smart Transformer for Deployment in Grid Application," in CIRED 2019 Conference, Madrid, Spain, 2019.
  89. A. Keyhani, S. W. Chua, and S. A. Sebo, "Maximum likelihood estimation of transformer high frequency parameters from test data," IEEE Transactions on Power Delivery, vol. 6, no. 2, pp. 858- 865, Apr. 1991. otwiera się w nowej karcie
  90. M. H. Kheraluwala, D. W. Novotny, and D. M. Divan, "Coaxially wound transformers for high- power high-frequency applications," IEEE Transactions on Power Electronics, vol. 7, no. 1, pp. 54- 62, Jan. 1992. otwiera się w nowej karcie
  91. L. Knypinski, L. Nowak, P. Sujka, and K. Radziuk, "Application of a PSO algorithm for identification of the parameters of Jiles-Atherton hysteresis model," Archives of Electrical Engineering, vol. 61, pp. 1-2, Jan. 2011. otwiera się w nowej karcie
  92. M. A. Krasnosel'skii and A. V. Pokrovskii, Systems with Hysteresis. Berlin Heidelberg: Springer- Verlag, 1989.
  93. P. A. Kyaw, J. Qiu, and C. R. Sullivan, "Analytical Thermal Model for Inductor and Transformer Windings and Litz Wire," in 2018 IEEE 19th Workshop on Control and Modeling for Power Electronics (COMPEL), 2018, pp. 1-9. otwiera się w nowej karcie
  94. T. Lagier, "Convertisseurs continu-continu pour les réseaux d'électricité à courant continu," thesis, Toulouse, INPT, 2016. otwiera się w nowej karcie
  95. T. Lagier, L. Chédot, L. Ghossein, F. Wallart, B. Lefebvre, P. Dworakowski, M. Mermet-Guyennet, and C. Buttay, "A 100 kW 1.2 kV 20 kHz DC-DC converter prototype based on the Dual Active Bridge topology," in 2018 IEEE International Conference on Industrial Technology (ICIT), 2018, pp. 559-564. otwiera się w nowej karcie
  96. T. Lagier, P. Dworakowski, C. Buttay, P. Ladoux, A. Wilk, P. Camail, and E. Anak, "Experimental validation and comparison of a SiC MOSFET based 100 kW 1.2 kV 20 kHz three-phase dual active bridge converter using two vector groups," in EPE'20 ECCE Europe 22nd European Conference on Power Electronics and Applications, Lyon, France, 2020, accepted for publication. otwiera się w nowej karcie
  97. T. Lagier and P. Ladoux, "Method of Controlling a Dual-Bridge Dc/Dc Converter," EP3449555 (A1). otwiera się w nowej karcie
  98. T. Lagier and P. Ladoux, "Theoretical and experimental analysis of the soft switching process for SiC MOSFETs based Dual Active Bridge converters," in 2018 International Symposium on Power Electronics, Electrical Drives, Automation and Motion (SPEEDAM), 2018, pp. 262-267. otwiera się w nowej karcie
  99. T. Lagier, P. Ladoux, and P. Dworakowski, "Potential of silicon carbide MOSFETs in the DC/DC converters for future HVDC offshore wind farms," High Voltage, vol. 2, no. 4, pp. 233-243, 2017. otwiera się w nowej karcie
  100. J. F. Lazar and R. Martinelli, "Steady-state analysis of the LLC series resonant converter," in APEC 2001. Sixteenth Annual IEEE Applied Power Electronics Conference and Exposition (Cat. No.01CH37181), 2001, vol. 2, pp. 728-735 vol.2. otwiera się w nowej karcie
  101. Y. Lee, G. Vakil, Alan. J. Watson, and P. W. Wheeler, "Geometry optimization and characterization of three-phase medium frequency transformer for 10kVA Isolated DC-DC converter," in 2017 IEEE Energy Conversion Congress and Exposition (ECCE), 2017, pp. 511-518. otwiera się w nowej karcie
  102. M. Leibl, G. Ortiz, and J. W. Kolar, "Design and Experimental Analysis of a Medium-Frequency Transformer for Solid-State Transformer Applications," IEEE Journal of Emerging and Selected Topics in Power Electronics, vol. 5, no. 1, pp. 110-123, Mar. 2017. otwiera się w nowej karcie
  103. F. de Leon and A. Semlyen, "Reduced order model for transformer transients," IEEE Transactions on Power Delivery, vol. 7, no. 1, pp. 361-369, Jan. 1992. otwiera się w nowej karcie
  104. A. Lesnicar and R. Marquardt, "An innovative modular multilevel converter topology suitable for a wide power range," in 2003 IEEE Bologna Power Tech Conference Proceedings, 2003, vol. 3, pp. 6 pp. Vol.3-. otwiera się w nowej karcie
  105. T. J. Lewis, "The transient behaviour of ladder networks of the type representing transformer and machine windings," Journal of the Institution of Electrical Engineers, vol. 1954, no. 10, pp. 278- 280, Oct. 1954. otwiera się w nowej karcie
  106. D. Lin, P. Zhou, and A. Bergqvist, "Improved Vector Play Model and Parameter Identification for Magnetic Hysteresis Materials," IEEE Transactions on Magnetics, vol. 50, no. 2, pp. 357-360, Feb. 2014. otwiera się w nowej karcie
  107. F. Liorzou, B. Phelps, and D. L. Atherton, "Macroscopic models of magnetization," IEEE Transactions on Magnetics, vol. 36, no. 2, pp. 418-428, Mar. 2000. otwiera się w nowej karcie
  108. C. Liu, L. Qi, X. Cui, and X. Wei, "Experimental Extraction of Parasitic Capacitances for High- Frequency Transformers," IEEE Transactions on Power Electronics, vol. 32, no. 6, pp. 4157-4167, Jun. 2017. otwiera się w nowej karcie
  109. H. Y. Lu, J. G. Zhu, and S. Y. R. Hui, "Measurement and Modeling of Thermal Effects on Magnetic Hysteresis of Soft Ferrites," IEEE Transactions on Magnetics, vol. 43, no. 11, pp. 3952-3960, Nov. 2007. otwiera się w nowej karcie
  110. M. Luo, D. Dujic, and J. Allmeling, "Modeling Frequency Independent Hysteresis Effects of Ferrite Core Materials Using Permeance-Capacitance Analogy for System-Level Circuit Simulations," IEEE Transactions on Power Electronics, vol. 33, no. 12, pp. 10055-10070, Dec. 2018. otwiera się w nowej karcie
  111. M. V. F. da Luz, P. Dular, J. V. Leite, and P. Kuo-Peng, "Modeling of Transformer Core Joints via a Subproblem FEM and a Homogenization Technique," IEEE Transactions on Magnetics, vol. 50, no. 2, pp. 1009-1012, Feb. 2014. otwiera się w nowej karcie
  112. W. Lyskawinski, P. Sujka, W. Szelag, and M. Baranski, "Numerical analysis of hysteresis loss in pulse transformer," Archives of Electrical Engineering, vol. 60, Jun. 2011. otwiera się w nowej karcie
  113. Manitoba Hydro International, "PSCAD." [Online].
  114. Mathworks, "Simulink Real-Time." [Online]. otwiera się w nowej karcie
  115. Mathworks, "Simscape saturable transformer with hysteresis." [Online]. Available: https://fr.mathworks.com/help/physmod/sps/powersys/ref/saturabletransformer.html. [Accessed: 06-Mar-2020]. otwiera się w nowej karcie
  116. S. F. Mauser and T. E. McDermott, "Electromagnetic Transients Program (EMTP): Application guide: Final report," Westinghouse Electric Corp., Pittsburgh, PA (USA). Power System Engineering Dept.; Electric Power Research Inst., Palo Alto, CA (USA), EPRI-EL-4650, Nov. 1986. otwiera się w nowej karcie
  117. I. Mayergoyz, "Mathematical models of hysteresis," IEEE Transactions on Magnetics, vol. 22, no. 5, pp. 603-608, Sep. 1986. otwiera się w nowej karcie
  118. I. D. Mayergoyz and A. A. Adly, "Numerical implementation of the feedback Preisach model," IEEE Transactions on Magnetics, vol. 28, no. 5, pp. 2605-2607, Sep. 1992. otwiera się w nowej karcie
  119. K. Meah and S. Ula, "Comparative Evaluation of HVDC and HVAC Transmission Systems," in 2007 IEEE Power Engineering Society General Meeting, 2007, pp. 1-5. otwiera się w nowej karcie
  120. J. Meisel, Principles of electromechanical-energy conversion. McGraw-Hill, 1966.
  121. M. Michna, P. Dworakowski, A. Wilk, F. Kutt, and M. Mermet-Guyennet, "Modified Preisach model of hysteresis in multi air gap ferrite core medium frequency transformer," Energies, submitted for publication. otwiera się w nowej karcie
  122. M. Michna, A. Wilk, P. Dworakowski, and B. Lefebvre, "Determination of Mathematical Model Parameters of a Medium Frequency Transformer," in 2018 International Symposium on Electrical Machines (SME), 2018, pp. 1-5. otwiera się w nowej karcie
  123. J. Millán, P. Godignon, X. Perpiñà, A. Pérez-Tomás, and J. Rebollo, "A Survey of Wide Bandgap Power Semiconductor Devices," IEEE Transactions on Power Electronics, vol. 29, no. 5, pp. 2155- 2163, May 2014. otwiera się w nowej karcie
  124. M. Mogorovic and D. Dujic, "100 kW, 10 kHz Medium-Frequency Transformer Design Optimization and Experimental Verification," IEEE Transactions on Power Electronics, vol. 34, no. 2, pp. 1696-1708, Feb. 2019. otwiera się w nowej karcie
  125. A. Morched, L. Marti, and J. Ottevangers, "A high frequency transformer model for the EMTP," IEEE Transactions on Power Delivery, vol. 8, no. 3, pp. 1615-1626, Jul. 1993. otwiera się w nowej karcie
  126. J. J. Moré, "The Levenberg-Marquardt algorithm: Implementation and theory," in Numerical Analysis, Berlin, Heidelberg, 1978, pp. 105-116. otwiera się w nowej karcie
  127. B. A. Mork, F. Gonzalez, D. Ishchenko, D. L. Stuehm, and J. Mitra, "Hybrid Transformer Model for Transient Simulation-Part I: Development and Parameters," IEEE Transactions on Power Delivery, vol. 22, no. 1, pp. 248-255, Jan. 2007. otwiera się w nowej karcie
  128. B. A. Mork, F. Gonzalez, D. Ishchenko, D. L. Stuehm, and J. Mitra, "Hybrid Transformer Model for Transient Simulation-Part II: Laboratory Measurements and Benchmarking," IEEE Transactions on Power Delivery, vol. 22, no. 1, pp. 256-262, Jan. 2007. otwiera się w nowej karcie
  129. L. H. Mweene, C. A. Wright, and M. F. Schlecht, "A 1 kW 500 kHz front-end converter for a distributed power supply system," IEEE Transactions on Power Electronics, vol. 6, no. 3, pp. 398- 407, Jul. 1991. otwiera się w nowej karcie
  130. A. Nabae, I. Takahashi, and H. Akagi, "A New Neutral-Point-Clamped PWM Inverter," IEEE Transactions on Industry Applications, vol. IA-17, no. 5, pp. 518-523, Sep. 1981. otwiera się w nowej karcie
  131. T. Nakata, N. Takahashi, and Y. Kawase, "Magnetic performance of step-lap joints in distribution transformer cores," IEEE Transactions on Magnetics, vol. 18, no. 6, pp. 1055-1057, Nov. 1982. otwiera się w nowej karcie
  132. M. Noah, S. Kimura, S. Endo, M. Yamamoto, J. Imaoka, K. Umetani, and W. Martinez, "A novel three-phase LLC resonant converter with integrated magnetics for lower turn-off losses and higher power density," in 2017 IEEE Applied Power Electronics Conference and Exposition (APEC), 2017, pp. 322-329. otwiera się w nowej karcie
  133. M. Noah, K. Umetani, J. Imaoka, and M. Yamamoto, "Lagrangian dynamics model and practical implementation of an integrated transformer in multi-phase LLC resonant converter," IET Power Electronics, vol. 11, no. 2, pp. 339-347, 2018. otwiera się w nowej karcie
  134. S. Okabe, M. Koto, G. Ueta, T. Saida, and S. Yamada, "Development of high frequency circuit model for oil-immersed power transformers and its application for lightning surge analysis," IEEE Transactions on Dielectrics and Electrical Insulation, vol. 18, no. 2, pp. 541-552, Apr. 2011. otwiera się w nowej karcie
  135. G. Ortiz, J. Biela, D. Bortis, and J. W. Kolar, "1 Megawatt, 20 kHz, isolated, bidirectional 12kV to 1.2kV DC-DC converter for renewable energy applications," in The 2010 International Power Electronics Conference -ECCE ASIA -, 2010, pp. 3212-3219. otwiera się w nowej karcie
  136. G. Ortiz, J. Biela, and J. W. Kolar, "Optimized design of medium frequency transformers with high isolation requirements," in IECON 2010 -36th Annual Conference on IEEE Industrial Electronics Society, 2010, pp. 631-638. otwiera się w nowej karcie
  137. J. D. Páez, D. Frey, J. Maneiro, S. Bacha, and P. Dworakowski, "Overview of DC-DC Converters Dedicated to HVdc Grids," IEEE Transactions on Power Delivery, vol. 34, no. 1, pp. 119-128, Feb. 2019.
  138. Pan-Seok Shin and Jinhee Lee, "Magnetic field analysis of amorphous core transformer using homogenization technique," IEEE Transactions on Magnetics, vol. 33, no. 2, pp. 1808-1811, Mar. 1997.
  139. A. M. Pereira, "Conception de Transformateurs Moyennes Fréquences : application aux convertisseurs DC-DC haute tension et forte puissance," thesis, Lyon, 2016.
  140. A. Pereira, F. Sixdenier, M. A. Raulet, B. Lefebvre, and N. Burais, "Comparison Between Numerical and Analytical Methods of AC Resistance Evaluation for Medium-Frequency Transformers: Validation on a Prototype and Thermal Impact Analysis," Canadian Journal of Electrical and Computer Engineering, vol. 40, no. 2, pp. 101-109, Spring 2017. otwiera się w nowej karcie
  141. M. Pietruszka and E. Napieralska-Juszczak, "Lamination of T-joints in the transformer core," IEEE Transactions on Magnetics, vol. 32, no. 3, pp. 1180-1183, May 1996. otwiera się w nowej karcie
  142. A. M. Plamitzer, Maszyny elektryczne. Wydawnictwa Naukowo-Techniczne, 1972.
  143. F. Preisach, "Über die magnetische Nachwirkung," Z. Physik, vol. 94, no. 5, pp. 277-302, May 1935. otwiera się w nowej karcie
  144. C. Ragusa, "An analytical method for the identification of the Preisach distribution function," Journal of Magnetism and Magnetic Materials, vol. 254-255, pp. 259-261, Jan. 2003. otwiera się w nowej karcie
  145. W. A. Roshen, "Fringing Field Formulas and Winding Loss Due to an Air Gap," IEEE Transactions on Magnetics, vol. 43, no. 8, pp. 3387-3394, Aug. 2007. otwiera się w nowej karcie
  146. D. Rothmund, T. Guillod, D. Bortis, and J. W. Kolar, "99% Efficient 10 kV SiC-Based 7 kV/400 V DC Transformer for Future Data Centers," IEEE Journal of Emerging and Selected Topics in Power Electronics, vol. 7, no. 2, pp. 753-767, Jun. 2019. otwiera się w nowej karcie
  147. R. Rudenberg, "Performance of traveling waves in coils and windings," Electrical Engineering, vol. 59, no. 12, pp. 1031-1040, Dec. 1940. otwiera się w nowej karcie
  148. R. Ryndzionek and Ł. Sienkiewicz, "Evolution of the HVDC Link Connecting Offshore Wind Farms to Onshore Power Systems," Energies, vol. 13, no. 8, p. 1914, Jan. 2020. otwiera się w nowej karcie
  149. A. Schoppa, J. Schneider, C.-D. Wuppermann, and T. Bakon, "Influence of welding and sticking of laminations on the magnetic properties of non-oriented electrical steels," Journal of Magnetism and Magnetic Materials, vol. 254-255, pp. 367-369, Jan. 2003. otwiera się w nowej karcie
  150. F. C. Schwarz and J. B. Klaassens, "A Controllable 45-kW Current Source for DC Machines," IEEE Transactions on Industry Applications, vol. IA-15, no. 4, pp. 437-444, Jul. 1979. otwiera się w nowej karcie
  151. R. Sellick, M. Agamy, L. Hao, and K. Weeber, "A high-speed HVDC breaker topology with integral voltage-changing capability," in 2015 IEEE Electrical Insulation Conference (EIC), 2015, pp. 123- 126. otwiera się w nowej karcie
  152. X. She, A. Q. Huang, and R. Burgos, "Review of Solid-State Transformer Technologies and Their Application in Power Distribution Systems," IEEE Journal of Emerging and Selected Topics in Power Electronics, vol. 1, no. 3, pp. 186-198, Sep. 2013.
  153. Y. Shibuya and S. Fujita, "High frequency model and transient response of transformer windings," in IEEE/PES Transmission and Distribution Conference and Exhibition, 2002, vol. 3, pp. 1839- 1844 vol.3. otwiera się w nowej karcie
  154. A. Shintemirov, W. H. Tang, and Q. H. Wu, "A Hybrid Winding Model of Disc-Type Power Transformers for Frequency Response Analysis," IEEE Transactions on Power Delivery, vol. 24, no. 2, pp. 730-739, Apr. 2009. otwiera się w nowej karcie
  155. P. Shuai and J. Biela, "Design and optimization of medium frequency, medium voltage transformers," in 2013 15th European Conference on Power Electronics and Applications (EPE), 2013, pp. 1-10. otwiera się w nowej karcie
  156. Siemens, "MVDC PLUS® -the grid connector," siemens.com Global Website. [Online]. Available: https://new.siemens.com/global/en/products/energy/medium-voltage/solutions/mvdc.html. [Accessed: 30-Dec-2019].
  157. G. R. Slemon, "Equivalent circuits for transformers and machines including non-linear effects," Proceedings of the IEE -Part IV: Institution Monographs, vol. 100, no. 5, pp. 129-143, Oct. 1953. otwiera się w nowej karcie
  158. N. Soltau, H. Stagge, R. W. De Doncker, and O. Apeldoorn, "Development and demonstration of a medium-voltage high-power DC-DC converter for DC distribution systems," in 2014 IEEE 5th International Symposium on Power Electronics for Distributed Generation Systems (PEDG), 2014, pp. 1-8. otwiera się w nowej karcie
  159. SP Energy Networks, "LV Engine -a smarter electricity network," 2018. [Online]. Available: https://www.spenergynetworks.co.uk/userfiles/file/LV_Engine_Smarter_Network.pdf. [Accessed: 28-Feb-2020]. otwiera się w nowej karcie
  160. Speedgoat, "Simulink real-time-target performance computer." [Online]. Available: https://www.speedgoat.com/products-services/real-time-target-machines/performance. [Accessed: 06-Mar-2020].
  161. C. Stackler, F. Morel, P. Ladoux, and P. Dworakowski, "25 kV-50 Hz railway supply modelling for medium frequencies (0-5 kHz)," in 2016 International Conference on Electrical Systems for Aircraft, Railway, Ship Propulsion and Road Vehicles International Transportation Electrification Conference (ESARS-ITEC), 2016, pp. 1-6. otwiera się w nowej karcie
  162. C. Stackler, F. Morel, P. Ladoux, A. Fouineau, F. Wallart, and N. Evans, "Optimal sizing of a power electronic traction transformer for railway applications," in IECON 2018 -44th Annual Conference of the IEEE Industrial Electronics Society, 2018, pp. 1380-1387. otwiera się w nowej karcie
  163. Chas. P. Steinmetz, "On the Law of Hysteresis," Transactions of the American Institute of Electrical Engineers, vol. IX, no. 1, pp. 1-64, Jan. 1892. otwiera się w nowej karcie
  164. M. Stojadinović and J. Biela, "Modelling and Design of a Medium Frequency Transformer for High Power DC-DC Converters," in 2018 International Power Electronics Conference (IPEC-Niigata 2018 -ECCE Asia), 2018, pp. 1103-1110. otwiera się w nowej karcie
  165. E. C. Stoner and E. P. Wohlfarth, "A mechanism of magnetic hysteresis in heterogeneous alloys," Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, vol. 240, no. 826, pp. 599-642, May 1948. otwiera się w nowej karcie
  166. G. Stumberger, B. Polajzer, B. Stumberger, M. Toman, and D. Dolinar, "Evaluation of experimental methods for determining the magnetically nonlinear characteristics of electromagnetic devices," IEEE Transactions on Magnetics, vol. 41, no. 10, pp. 4030-4032, Oct. 2005. otwiera się w nowej karcie
  167. Q. Su, R. E. James, and D. Sutanto, "A Z-transform model of transformers for the study of electromagnetic transients in power systems," IEEE Transactions on Power Systems, vol. 5, no. 1, pp. 27-33, Feb. 1990. otwiera się w nowej karcie
  168. Tektronix, "5 Series MSO Mixed Signal Oscilloscope." [Online]. Available: https://www.tek.com/oscilloscope/5-series-mso-mixed-signal-oscilloscope. [Accessed: 15-Mar- 2020].
  169. J. Tellinen, "A simple scalar model for magnetic hysteresis," IEEE Transactions on Magnetics, vol. 34, no. 4, pp. 2200-2206, Jul. 1998. otwiera się w nowej karcie
  170. B. Tellini, R. Giannetti, G. Robles, and S. Lizon-Martinez, "New method to characterize magnetic hysteresis in soft ferrites up to high frequencies," IEEE Transactions on Instrumentation and Measurement, vol. 55, no. 1, pp. 311-315, Feb. 2006. otwiera się w nowej karcie
  171. G. J. Thaler and M. L. Wilcox, Electric machines: dynamics and steady state. Wiley, 1966. otwiera się w nowej karcie
  172. B. Z. Tomczuk, D. Koteras, and A. Waindok, "Electromagnetic and Temperature 3-D Fields for the Modular Transformers Heating Under High-Frequency Operation," IEEE Transactions on Magnetics, vol. 50, no. 2, pp. 317-320, Feb. 2014. otwiera się w nowej karcie
  173. F. Tourkhani and P. Viarouge, "Accurate analytical model of winding losses in round Litz wire windings," IEEE Transactions on Magnetics, vol. 37, no. 1, pp. 538-543, Jan. 2001. otwiera się w nowej karcie
  174. J. Turowski, M. Turowski, and M. Kopec, "Method of three-dimensional network solution of leakage field of three-phase transformers," IEEE Transactions on Magnetics, vol. 26, no. 5, pp. 2911-2919, Sep. 1990. otwiera się w nowej karcie
  175. K. Umetani, "A generalized method for Lagrangian modeling of power conversion circuit with integrated magnetic components," IEEJ Transactions on Electrical and Electronic Engineering, vol. 7, no. S1, pp. S146-S152, 2012. otwiera się w nowej karcie
  176. P. T. M. Vaessen, "Transformer model for high frequencies," IEEE Transactions on Power Delivery, vol. 3, no. 4, pp. 1761-1768, Oct. 1988. otwiera się w nowej karcie
  177. P. Vas, K. E. Hallenius, and J. E. Brown, "Cross-Saturation in Smooth-Air-Gap Electrical Machines," IEEE Transactions on Energy Conversion, vol. EC-1, no. 1, pp. 103-112, Mar. 1986. otwiera się w nowej karcie
  178. K. Venkatachalam, C. R. Sullivan, T. Abdallah, and H. Tacca, "Accurate prediction of ferrite core loss with nonsinusoidal waveforms using only Steinmetz parameters," in 2002 IEEE Workshop on Computers in Power Electronics, 2002. Proceedings., 2002, pp. 36-41. otwiera się w nowej karcie
  179. I. Villar, A. Garcia-Bediaga, U. Viscarret, I. Etxeberria-Otadui, and A. Rufer, "Proposal and validation of medium-frequency power transformer design methodology," in 2011 IEEE Energy Conversion Congress and Exposition, 2011, pp. 3792-3799. otwiera się w nowej karcie
  180. I. Villar, L. Mir, I. Etxeberria-Otadui, J. Colmenero, X. Agirre, and T. Nieva, "Optimal design and experimental validation of a Medium-Frequency 400kVA power transformer for railway traction applications," in 2012 IEEE Energy Conversion Congress and Exposition (ECCE), 2012, pp. 684- 690. otwiera się w nowej karcie
  181. G. R. Walker and P. C. Sernia, "Cascaded DC-DC converter connection of photovoltaic modules," IEEE Transactions on Power Electronics, vol. 19, no. 4, pp. 1130-1139, Jul. 2004. otwiera się w nowej karcie
  182. M. Wattenberg, U. Schwalbe, and M. Pfost, "Impact of DC-Bias on Dual Active Bridge Control and How to Avoid it," in 2019 21st European Conference on Power Electronics and Applications (EPE '19 ECCE Europe), 2019, p. P.1-P.8. otwiera się w nowej karcie
  183. Wayne Kerr Electronics, "6500B Series Impedance Analyzer." [Online]. Available: http://www.waynekerrtest.com/products_detail.php?indexs=4. [Accessed: 06-Mar-2020].
  184. D. C. White and H. H. Woodson, Electromechanical Energy Conversion. Wiley, 1959. otwiera się w nowej karcie
  185. A. Wilk, "Representation of magnetic hysteresis in a circuit model of a single-phase transformer," COMPEL -The international journal for computation and mathematics in electrical and electronic engineering, vol. 34, pp. 778-791, May 2015. otwiera się w nowej karcie
  186. A. Wilk, Modelowanie obwodowo-polowe transformatorów trakcyjnych w aspekcie diagnostyki opartej na modelu referencyjnym. Politechnika Gdańska, 2012.
  187. A. Wilk, M. Michna, P. Dworakowski, and B. Lefebvre, "Influence of air gap size on magnetizing current and power losses in ferrite core transformers -experimental investigations," in EPNC 2018 Twenty-fifth Symposium on Electromagnetic Phenomena in Nonlinear Circuits, Arras, France, 2018.
  188. A. Wilk, J. Nieznanski, I. Moson, P. Dobrowolski, and G. Kostro, "Nonlinear equivalent circuit model of a traction transformer for winding internal fault diagnostic purposes," in 2008 18th International Conference on Electrical Machines, 2008, pp. 1-5. otwiera się w nowej karcie
  189. R. M. Wojciechowski, A. Demenko, and J. K. Sykulski, "Inducted currents analysis in multiply connected conductors using reluctance-resistance networks," COMPEL -The international journal for computation and mathematics in electrical and electronic engineering, vol. 29, no. 4, pp. 908- 918, Jan. 2010. otwiera się w nowej karcie
  190. Wolfspeed, "CAS300M17BM2 1700V 225A 8.0mΩ SiC Half-Bridge." [Online]. Available: https://www.wolfspeed.com/power/products/sic-power-modules/cas300m17bm2. [Accessed: 01- Jan-2020].
  191. Wolfspeed, "SiC Custom Power Services," 2017. [Online].
  192. Q. Wu, T. Hong, S. Jazebi, and F. de León, "Experimentally Validated Method to Measure the lambda-i Characteristics of Asymmetric Three-Phase Transformers," IEEE Transactions on Magnetics, vol. 55, no. 4, pp. 1-9, Apr. 2019. otwiera się w nowej karcie
  193. Q. Wu, S. Jazebi, and F. de Leon, "Parameter Estimation of Three-Phase Transformer Models for Low-Frequency Transient Studies From Terminal Measurements," IEEE Transactions on Magnetics, vol. 53, no. 7, pp. 1-8, Jul. 2017. otwiera się w nowej karcie
  194. G. Xue, P. Zhang, Z. He, D. Li, Z. Yang, and Z. Zhao, "Modification and Numerical Method for the Jiles-Atherton Hysteresis Model," Communications in Computational Physics, vol. 21, no. 3, pp. 763-781, Mar. 2017. otwiera się w nowej karcie
  195. J. Xue, F. Wang, D. Boroyevich, and Z. Shen, "Single-phase vs. three-phase high density power transformers," in 2010 IEEE Energy Conversion Congress and Exposition, 2010, pp. 4368-4375. otwiera się w nowej karcie
  196. M. Yilmaz and P. T. Krein, "Review of benefits and challenges of vehicle-to-grid technology," in 2012 IEEE Energy Conversion Congress and Exposition (ECCE), 2012, pp. 3082-3089. otwiera się w nowej karcie
  197. Yokogawa, "WT1800E High-Performance Power Analyzer." [Online]. Available: https://tmi.yokogawa.com/fr/solutions/products/power-analyzers/wt1800e-high-performance- power-analyzer/. [Accessed: 08-Mar-2020].
  198. J. Yu, K. Smith, M. Urizarbarrena, N. MacLeod, R. Bryans, and A. Moon, "Initial designs for the ANGLE DC project; converting existing AC cable and overhead line into DC operation," in 13th IET International Conference on AC and DC Power Transmission (ACDC 2017), 2017, pp. 1-6. otwiera się w nowej karcie
  199. K. Zakrzewski and M. Lukaniszyn, "Three-dimensional model of one-and three-phase transformer for leakage field calculation," IEEE Transactions on Magnetics, vol. 28, no. 2, pp. 1344-1347, Mar. 1992. otwiera się w nowej karcie
  200. K. Zakrzewski, B. Tomczuk, and D. Koteras, "Simulation of forces and 3-D field arising during power autotransformer fault due to electric arc in HV winding," IEEE Transactions on Magnetics, vol. 38, no. 2, pp. 1153-1156, Mar. 2002. otwiera się w nowej karcie
  201. ZES Zimmer, "LMG670 -1 to 7 Channel Power Analyzer." [Online]. Available: https://www.zes.com/en/Products/Discontinued-Products/Energy-and-Power-Meters/LMG670. [Accessed: 06-Mar-2020].
  202. C. Zhao, M. Weiss, A. Mester, S. Lewdeni-Schmid, D. Dujic, J. K. Steinke, and T. Chaudhuri, "Power electronic transformer (PET) converter: Design of a 1.2MW demonstrator for traction applications," in Automation and Motion International Symposium on Power Electronics Power Electronics, Electrical Drives, 2012, pp. 855-860. otwiera się w nowej karcie
  203. Z. Zhao, F. Liu, Z. Cheng, W. Yan, L. Liu, J. Zhang, and Y. Fan, "Measurements and Calculation of Core-Based $B-H$ Curve and Magnetizing Current in DC-Biased Transformers," IEEE Transactions on Applied Superconductivity, vol. 20, no. 3, pp. 1131-1134, Jun. 2010.
  204. "ELIPTIC project." [Online]. Available: https://www.eliptic-project.eu/. [Accessed: 10-Mar-2020].
  205. "393-1991 -IEEE Standard for Test Procedures for Magnetic Cores." IEEE SA, 1992. otwiera się w nowej karcie
  206. "IEC 60404-2:1996 Magnetic materials -Part 2: Methods of measurement of the magnetic properties of electrical steel sheet and strip by means of an Epstein frame." 1996. otwiera się w nowej karcie
  207. "IEC 60404-3:1992 Magnetic materials -Part 3: Methods of measurement of the magnetic properties of magnetic sheet and strip by means of a single sheet tester." 1992. otwiera się w nowej karcie
  208. "IEC 60404-10:2016 Magnetic materials -Part 10: Methods of measurement of magnetic properties of electrical steel strip and sheet at medium frequencies." 2016. otwiera się w nowej karcie
  209. "IEC 60404-6:2003 Magnetic materials -Part 6: Methods of measurement of the magnetic properties of magnetically soft metallic and powder materials at frequencies in the range 20 Hz to 200 kHz by the use of ring specimens." 2003. otwiera się w nowej karcie
  210. "IEC 62044 Cores made of soft magnetic materials -Measuring methods." 2002. otwiera się w nowej karcie
  211. LmNL*ThetaCom(1) * LmM, LmNL*ThetaCom(2));
  212. dPhiC1dTheta2 = dPhiC1dTheta2 * LmM; otwiera się w nowej karcie
  213. dPhiC3dTheta1 = dPhiC3dTheta1 * LmM; otwiera się w nowej karcie
  214. %% Magnetizing inductance Mc(1,1) = Np*dPhiC1dTheta1*Np -Np*dPhiC2dTheta1*Np; otwiera się w nowej karcie
  215. Mc(2,1) = -Np*dPhiC2dTheta1*Np + Np*dPhiC3dTheta1*Np; otwiera się w nowej karcie
  216. Mc(3,1) = Ns*dPhiC1dTheta1*Np -Ns*dPhiC2dTheta1*Np;
  217. Mc(4,1) = -Ns*dPhiC2dTheta1*Np + Ns*dPhiC3dTheta1*Np;
  218. Mc(5,1) = Ne*dPhiC1dTheta1*Np -Ne*dPhiC2dTheta1*Np;
  219. Mc(6,1) = -Ne*dPhiC2dTheta1*Np + Ne*dPhiC3dTheta1*Np;
  220. Mc(1,2) = Np*dPhiC1dTheta2*Np -Np*dPhiC2dTheta2*Np; otwiera się w nowej karcie
  221. Mc(2,2) = -Np*dPhiC2dTheta2*Np + Np*dPhiC3dTheta2*Np; otwiera się w nowej karcie
  222. Mc(3,2) = Ns*dPhiC1dTheta2*Np -Ns*dPhiC2dTheta2*Np;
  223. Mc(4,2) = -Ns*dPhiC2dTheta2*Np + Ns*dPhiC3dTheta2*Np;
  224. Mc(5,2) = Ne*dPhiC1dTheta2*Np -Ne*dPhiC2dTheta2*Np;
  225. Mc(6,2) = -Ne*dPhiC2dTheta2*Np + Ne*dPhiC3dTheta2*Np;
  226. Mc(1,3) = Np*dPhiC1dTheta1*Ns -Np*dPhiC2dTheta1*Ns;
  227. Mc(2,3) = -Np*dPhiC2dTheta1*Ns + Np*dPhiC3dTheta1*Ns;
  228. Mc(3,3) = Ns*dPhiC1dTheta1*Ns -Ns*dPhiC2dTheta1*Ns; otwiera się w nowej karcie
  229. Mc(4,3) = -Ns*dPhiC2dTheta1*Ns + Ns*dPhiC3dTheta1*Ns; otwiera się w nowej karcie
  230. Mc(5,3) = Ne*dPhiC1dTheta1*Ns -Ne*dPhiC2dTheta1*Ns; otwiera się w nowej karcie
  231. Mc(6,3) = -Ne*dPhiC2dTheta1*Ns + Ne*dPhiC3dTheta1*Ns; otwiera się w nowej karcie
  232. Mc(1,4) = Np*dPhiC1dTheta2*Ns -Np*dPhiC2dTheta2*Ns; otwiera się w nowej karcie
  233. Mc(2,4) = -Np*dPhiC2dTheta2*Ns + Np*dPhiC3dTheta2*Ns;
  234. Mc(3,4) = Ns*dPhiC1dTheta2*Ns -Ns*dPhiC2dTheta2*Ns; otwiera się w nowej karcie
  235. Mc(4,4) = -Ns*dPhiC2dTheta2*Ns + Ns*dPhiC3dTheta2*Ns; otwiera się w nowej karcie
  236. Mc(5,4) = Ne*dPhiC1dTheta2*Ns -Ne*dPhiC2dTheta2*Ns; otwiera się w nowej karcie
  237. Mc(6,4) = -Ne*dPhiC2dTheta2*Ns + Ne*dPhiC3dTheta2*Ns; otwiera się w nowej karcie
  238. Mc(1,5) = Np*dPhiC1dTheta1*Ne -Np*dPhiC2dTheta1*Ne; otwiera się w nowej karcie
  239. Mc(2,5) = -Np*dPhiC2dTheta1*Ne + Np*dPhiC3dTheta1*Ne;
  240. Mc(3,5) = Ns*dPhiC1dTheta1*Ne -Ns*dPhiC2dTheta1*Ne; otwiera się w nowej karcie
  241. Mc(4,5) = -Ns*dPhiC2dTheta1*Ne + Ns*dPhiC3dTheta1*Ne; otwiera się w nowej karcie
  242. Mc(5,5) = Ne*dPhiC1dTheta1*Ne -Ne*dPhiC2dTheta1*Ne;
  243. Mc(6,5) = -Ne*dPhiC2dTheta1*Ne + Ne*dPhiC3dTheta1*Ne;
  244. Mc(1,6) = Np*dPhiC1dTheta2*Ne -Np*dPhiC2dTheta2*Ne; otwiera się w nowej karcie
  245. Mc(2,6) = -Np*dPhiC2dTheta2*Ne + Np*dPhiC3dTheta2*Ne;
  246. Mc(3,6) = Ns*dPhiC1dTheta2*Ne -Ns*dPhiC2dTheta2*Ne; otwiera się w nowej karcie
  247. Mc(4,6) = -Ns*dPhiC2dTheta2*Ne + Ns*dPhiC3dTheta2*Ne; otwiera się w nowej karcie
  248. Mc(5,6) = Ne*dPhiC1dTheta2*Ne -Ne*dPhiC2dTheta2*Ne;
  249. Mc(6,6) = -Ne*dPhiC2dTheta2*Ne + Ne*dPhiC3dTheta2*Ne;
  250. %% Leakage inductance Ml(1,1) = Lfg(1,1) -Lfg(2,1); otwiera się w nowej karcie
  251. Ml(2,1) = -Lfg(2,1) + Lfg(3,1); otwiera się w nowej karcie
  252. Ml(3,1) = Lfg(4,1) -Lfg(5,1); otwiera się w nowej karcie
  253. Ml(4,1) = -Lfg(5,1) + Lfg(6,1); otwiera się w nowej karcie
  254. Ml(1,2) = Lfg(1,2) -Lfg(2,2); otwiera się w nowej karcie
  255. Ml(2,2) = -Lfg(2,2) + Lfg(3,2); otwiera się w nowej karcie
  256. Ml(3,2) = Lfg(4,2) -Lfg(5,2); otwiera się w nowej karcie
  257. Ml(4,2) = -Lfg(5,2) + Lfg(6,2); otwiera się w nowej karcie
  258. Ml(2,3) = -Lfg(2,3) + Lfg(3,3); otwiera się w nowej karcie
  259. Ml(3,3) = Lfg(4,3) -Lfg(5,3); otwiera się w nowej karcie
  260. Ml(4,3) = -Lfg(5,3) + Lfg(6,3); otwiera się w nowej karcie
  261. Ml(5,5) = Leh;
  262. Ml(6,6) = Leh;
  263. %% Inductance matrix Mx = Mc + Ml; end Listing A5. DAB3_model_Fsys.m function Fx = DAB3_model_Fsys(t,y) DAB3_param;
  264. Rx(1,1) = R1+R2; otwiera się w nowej karcie
  265. Rx(2,1) = R2;
  266. Rx(1,2) = R2; otwiera się w nowej karcie
  267. Rx(2,2) = R2+R3; otwiera się w nowej karcie
  268. Rx(3,3) = R4+R5;
  269. Rx(4,3) = R5; otwiera się w nowej karcie
  270. Rx(3,4) = R5; otwiera się w nowej karcie
  271. Rx(5,5) = R7+R8; otwiera się w nowej karcie
  272. Rx(6,5) = R8; otwiera się w nowej karcie
  273. Rx(5,6) = R8; otwiera się w nowej karcie
  274. Rx(6,6) = R8+R9 otwiera się w nowej karcie
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