Cer Transformatörlerinde Elektriksel Parametrelerin Sonlu Elemanlar Yöntemi ile Analizi
Yıl 2022,
Sayı: 16, 66 - 78, 31.07.2022
Serenay Çürükova
,
Yunus Berat Demirol
,
Oluş Sönmez
,
Mehmet Aytaç Çınar
,
Bora Alboyacı
Öz
Demiryolu sistemlerinde kullanılan elektrikli trenlerin hareket gücünü sağlamak için kullanılan motor sürücülerini cer transformatörleri beslemektedir. Cer transformatörleri lokomotiflerin altında veya üstünde, boyutları sınırlı bir alana yerleştirilmektedir. Bunun yanında tren sistemlerinde kullanılmakta olan ekipmanların güç ihtiyaçlarını karşılayabilmek için farklı gerilim seviyelerinde çok sayıda sargı yapıları cer transformatörlerinde bulunmaktadır. Demiryolu sistemlerinde sürdürülebilirlik, verim ve işletme güvenliğinin yüksek seviyede olması için cer transformatörlerinin tasarım parametrelerinin özel olarak incelenmesi gerekmektedir. Bu kapsamda tasarım aşamasında detaylı analizlerin gerçekleştirilmesi ve standartlar referans alınarak değerlendirilmesi önemli olmaktadır. Cer transformatörlerinde kısa devre empedansı, inrush akımları, kazan kayıpları, çekirdek kayıpları gibi kritik öneme sahip elektriksel parametrelerin doğru bir şekilde hesaplanması teorik yöntemler ile her zaman mümkün olmamakta veya çok zahmetli olmaktadır. Bu durumda sonlu elemanlar analizi yönteminin birçok açıdan avantajı bulunmaktadır. Sonlu elemanlar analizleri ile yüksek doğrulukta ve kısa sürede hesaplamalar yapılabilmektedir. Bu çalışmada örnek bir cer transformatörünün elektriksel parametreleri Ansys Electronics Suite sonlu elemanlar analizi yazılımı ile hesaplanmıştır. Hesaplanan parametreler ile ilgili olarak özet bilgiler verilmiş, analiz adımları açıklanmıştır. Bu kapsamda demiryolu sistemlerinde kullanılan trenlerin kritik elemanlarından biri olan cer transformatörlerinin elektriksel analizi için sonlu elemanlar yönteminin gerekliliği ifade edilmiştir.
Kaynakça
- [1] Z. Ye et al., “A calculation method to adjust the short-circuit impedance of a transformer,” IEEE Access, vol. 8, pp. 223848–223858, 2020, doi: 10.1109/ACCESS.2020.3042983.
- [2] D. Azizian and M. Bigdeli, “Leakage inductance calculations in different geometries of traction transformers,” ECTI Trans. Electr. Eng. Electron. Commun., vol. 12, no. 2, pp. 28–34, 2014.
- [3] B. G. Park, T. S. Kim, K. J. Lee, R. Y. Kim, and D. S. Hyun, “Magnetic-field analysis on winding disposition of transformer for distributed high-speed train applications,” in IEEE Trans. Magn., 2010, vol. 46, no. 6, doi: 10.1109/TMAG.2010.2043646.
- [4] W. H. Ali, M. N. O. Sadiku, S. L. Abood, Fundamentals of Electric Machines: A Primer with MATLAB. Boca Raton, USA: CRC Press, 2019.
- [5] S. V. Kulkarni, S. A. Khaparde. Transformer Engineering: Design, Technology, and Diagnostics. Boca Raton, USA: CRC Press, 2017.
- [6] K. Dawood, B. Alboyaci, M. A. Cinar, O. Sonmez, “A new method for the calculation of leakage reactance in power transformers”, J. Electr. Eng. & Tech., vol. 12, no. 4, pp. 1883-1890, 2017, doi: 10.5370/JEET.2017.12.5.1883.
- [7] I. Sitar, M. Bilo, and D. Vale, “New design of traction transformers for fixed installations,” in International Colloquium Transformer Research and Asset Management, 2009, pp. 1–10.
- [8] I. Sitar and M. Jurković, “Modern design of EMU traction transformers,” in Automation in transportation, 2014, pp. 234–237.
- [9] D. Liu, B. Xiong, Z. Cheng, and F. Liu, “Effects of axial gap length between disc windings on magnetic fields and power losses of evaporative cooling traction transformers,” in Asia-Pacific Power and Energy Engineering Conference, Nanjing, China, 2020, pp.1-7.
- [10] C. Yang, Y. Ding, H. Qiu, and B. Xiong, “Analysis of turn-to-turn fault on split-winding transformer using coupled field-circuit approach,” Processes, vol. 9, no. 8, pp. 1–13, 2021, doi: 10.3390/pr9081314.
- [11] D. Azizian, “Nonlinear behavior analysis of split-winding dry-type transformer using a new star model and a coupled field-circuit approach,” Arch. Electr. Eng., vol. 65, no. 4, pp. 773–787, 2016, doi: 10.1515/aee-2016-0054.
- [12] J. Smajic, G. Di Pino, C. Stemmler, W. Mönig, and M. Carlen, “Numerical study of the core saturation influence on the winding losses of traction transformers,” IEEE Trans. Magn., vol. 51, no. 3, pp. 1–4, 2015, doi: 10.1109/TMAG.2014.2360918.
- [13] J. El Hayek, “Influence of harmonics on traction transformers losses,” in ICEMS 2003 – Proc. 6th Int. Conf. on Elect. Mach. and Syst., Beijing, China, 2003, vol. 1, pp. 347–350.
- [14] I. Sitar, Z. Janic, and B. Cucic, “External magnetic field density of main traction transformer for EMU,” COMPEL - Int. J. Comput. Math. Electr. Electron. Eng., vol. 31, no. 2, pp. 716–725, 2012, doi: 10.1108/03321641211200680.
- [15] S. Yuan et al., “Modelling method for thermal field of turbulent cooling dry-type on-board traction transformer in EMUs,” IEEE Trans. Transp. Electrif., vol. 8, no. 1, pp. 298–311, 2021, doi: 10.1109/TTE.2021.3097876.
- [16] A. Palani, S. Santhi, S. Gopalakrishna, V. Jayashankar, “Real-time techniques to measure winding displacement in transformers during short-circuit tests”. IEEE Trans. Power Deliv., vol. 23, no. 2, pp. 726-732, 2007, doi: 10.1109/TPWRD.2007.911110.
- [17] M. Wang, A. J. Vandermaar, K. D. Srivastava, “Review of condition assessment of power transformers in service”. IEEE Electr. Insul. Mag., vol. 18, no. 6, pp. 12-25, 2002, doi: 10.1109/MEI.2002.1161455.
- [18] J. R. Secue, E. Mombello, “Sweep frequency response analysis (SFRA) for the assessment of winding displacements and deformation in power transformers”. Electr. Power Syst. Res., vol. 78, no. 6, pp. 1119-1128, 2008, doi: 10.1016/j.epsr.2007.08.005
- [19] N. Swamy, U. Savadamuthu, “Sweep frequency response based statistical approach for locating faults in transformer windings using sliding window technique”, Electr. Power Syst. Res., vol. 194, no. 1, pp. 1-8, 2021, doi: 10.1016/j.epsr.2021.107061.
- [20] Zhao Z, Tang C, Islam S. Interpretation of transformer winding deformation fault by the spectral clustering of FRA signature. Int. J. Electr. Power & Energy Syst., vol. 130, no. 1, pp. 1-8, 2021, doi: 10.1016/j.ijepes.2021.106933.
- [21] CIGRE, Advances in the interpretation of transformer frequency response analysis (FRA). Technical Note 812, 2020
- [22] L. Zhou, J. Jiang, W. Li, Z. Wu, S. Gao, L. Guo, H. Liu, “FRA modelling for diagnosing axial displacement of windings in traction transformers”, IET Electr. Power Appl., vol. 13, no. 12, pp. 2121-2127, 2019, doi: 10.1049/iet-epa.2019.0362.
- [23] M. F. M. Yousof, C. Ekanayake, T. K. Saha, “Frequency response analysis to investigate deformation of transformer winding”. IEEE Trans. Dielectr. Electr. Insul., vol. 22, no. 4, pp. 2359–2367, 2015, doi: 10.1109/TDEI.2015.004750.
- [24] S. Naiqiu, Z. Can, L. Fang, L. Qisheng, Z. Lingwei, “Study on ultrasonic measurement device for transformer winding deformation”. in IEEE Conference on Power System Technology, Kunming, China, 2002. pp. 1401-1404.
- [25] M. A. Hejazi, G. B. Gharehpetian, G. Moradi, H. A. Alehosseini, M. Mohammad, “On-line monitoring of transformer winding axial displacement and its extent using scattering parameters and k-nearest neighbor method”, IET Gener. Trans. & Distr., vol. 5, pp. 824-832, 2011, doi: 10.1049/iet-gtd.2010.0802.
- [26] S. A. Mousavi, M. Bigdeli, S. M. Mousavi, “A feasibility study on application of positioning sensors to online detect of the transformer winding axial displacement”. in IEEE Symposium on Industrial Electronics & Applications, Kuching, Malaysia, 2013. pp. 1-3.
- [27] X. Li et al., “Partial discharge characteristics of oil-paper insulation for on-board traction transformers under superposed inter-harmonic AC voltages,” IEEE Trans. Dielectr. Electr. Insul., vol. 27, no. 1, pp. 240–248, 2020, doi: 10.1109/TDEI.2019.008404.
- [28] B. Jia, P. Zhang, and Z. Li, “Aging life assessment of oil-paper insulation of traction transformer under shock load,” in Asia Energy and Electrical Engineering Symposium, Chengdu, China, 2020, pp. 1045–1050.
- [29] L. Zhou et al., “Experimental studies on the estimated life of oil-immersed insulation paper in traction transformers,” IEEE Trans. Power Deliv., vol. 36, no. 5, pp. 2646–2657, 2021, doi: 10.1109/TPWRD.2020.3024839.
- [30] A. Ünal, N. Akkuş, and S. Kandil, “Demiryolu aracı disk balatalarının tasarımında yüksek sıcaklığın neden olduğu fren zayıflama probleminin belirlenmesi için sonlu elemanlar yöntemi yaklaşımı,” Demiryolu Mühendisliği, vol. 1, no. 15, pp. 134–144, 2022, doi: 10.47072/demiryolu.1027982.
- [31] F. Çeçen and B. Aktaş, “Lamine CFRP donatılı traverslerin deneysel ve sonlu eleman analizleriyle incelenmesi,” Demiryolu Mühendisliği, vol. 1, no. 14, pp. 26–38, 2021, doi: 10.47072/demiryolu.869946.
- [32] M. E. Arı and İ. Esen, “Design of a metro train and structural analysis of the metro vehicle body by finite element method,” Railway Engineering, vol. 1, no. 15, pp. 30–45, 2022, doi: 10.47072/demiryolu.1018663.
- [33] V. Shrikrishna, S. V. Kulkarni, and S. A. Khaperde, Transformer engineering: design and practice. CRC Press, 2004.
- [34] AkSteel, “AkSteel Product Catalog,” 2022. [Online]. Available: https://www.aksteel.de/files/downloads/AK_CARLITE_GOES_BV_060412.pdf.
- [35] M. A. Cinar, “Evaluation of the technical and economic feasibility of mixed grade cores in transformer design according to EN50588-1,” Teh. Vjesn., vol. 28, no. 4, pp. 1136–1144, 2021, doi: 10.17559/TV-20200402220152.
- [36] T. R. Specht, “Transformer magnetizing inrush currents,” Electr. Eng., vol. 70, no. 4, pp. 324–324, 1951, doi: 10.1109/ee.1951.6437380.
- [37] IEEE Standard for General Requirements for Liquid-Immersed Distribution, Power, and Regulating Transformers, IEEE Std C57.12.00-2015 (Revision of IEEE Std C57.12.00-2010), 2016.
- [38] M. A. Çınar, B. Alboyacı, S. Çürükova, O. Sönmez, and R. Yapıcı, “Calculation of optimum dimensions of magnetic shunt elements to reduce stray losses on transformer tank walls,” J. Fac. Eng. Archit. Gazi Univ., vol. 32, no. 4, pp. 1337–1346, 2017, doi: 10.17341/gazimmfd.369855.
- [39] Y. Li, S. L. Ho, N. Wang, and R. Y. Tang, “Numerical analysis of eddy current field in the ascending flange for the bushings and tank wall of a large transformer”, in Joint Int. Conf. Power Syst. Tech. And IEEE Power India Conference, New Delhi, India, 2008, pp. 1-7.
- [40] C. Guérin and G. Meunier, “Surface impedance for 3D non-linear eddy current problems - application to loss computation in transformers,” IEEE Trans. Magn., vol. 32, no. 3 PART 2, pp. 808–811, 1996, doi: 10.1109/20.497364.
- [41] M. A. S. Masoum, P. S. Moses, and A. S. Masoum, “Derating of asymmetric three-phase transformers serving unbalanced nonlinear loads,” IEEE Trans. Power Deliv., vol. 23, no. 4, pp. 2033–2041, 2008, doi: 10.1109/TPWRD.2008.923057.
- [42] D. Pejovski, K. Najdenkoski, and M. Digalovski, “Impact of different harmonic loads on distribution transformers,” in Procedia Engineering, 2017, vol. 202, pp. 76–87, doi: 10.1016/j.proeng.2017.09.696.
- [43] J. E. Holcomb, “Distribution transformer magnetizing inrush current,” Trans. Am. Inst. Electr. Eng. Part III Power Appar. Syst., vol. 80, no. 3, 1961, doi: 10.1109/AIEEPAS.1961.4501117.
Analysis of Electrical Parameters in Traction Transformers by Finite Element Method
Yıl 2022,
Sayı: 16, 66 - 78, 31.07.2022
Serenay Çürükova
,
Yunus Berat Demirol
,
Oluş Sönmez
,
Mehmet Aytaç Çınar
,
Bora Alboyacı
Öz
Traction transformers feed the motor drivers used in electric locomotives in railway systems. Traction transformers are placed in a limited area above or below the locomotives. Due to the power needs of the equipment used in train systems, there are many winding structures at different voltage levels in traction transformers. Therefore, the design parameters of traction transformers should be specifically evaluated for providing a high level of sustainability, efficiency, and operational safety in railway systems. It is crucial to carry out detailed analyses during the design phase and evaluate them according to standards. Accurate calculation of critical electrical parameters such as short circuit impedance, inrush currents, tank losses and core losses in traction transformers is not always possible or very laborious with theoretical methods. In this case, the finite element analysis method has many advantages. With finite element analysis, calculations can be made with high accuracy and in a short time. This study calculated the electrical parameters of a sample traction transformer with Ansys Electronics Suite finite element analysis software. Summary information about the calculated parameters is given, and the analysis steps are explained. In this context, the necessity of the finite element method for the electrical analysis of traction transformers, which is one of the most critical components in railway systems, has been expressed.
Kaynakça
- [1] Z. Ye et al., “A calculation method to adjust the short-circuit impedance of a transformer,” IEEE Access, vol. 8, pp. 223848–223858, 2020, doi: 10.1109/ACCESS.2020.3042983.
- [2] D. Azizian and M. Bigdeli, “Leakage inductance calculations in different geometries of traction transformers,” ECTI Trans. Electr. Eng. Electron. Commun., vol. 12, no. 2, pp. 28–34, 2014.
- [3] B. G. Park, T. S. Kim, K. J. Lee, R. Y. Kim, and D. S. Hyun, “Magnetic-field analysis on winding disposition of transformer for distributed high-speed train applications,” in IEEE Trans. Magn., 2010, vol. 46, no. 6, doi: 10.1109/TMAG.2010.2043646.
- [4] W. H. Ali, M. N. O. Sadiku, S. L. Abood, Fundamentals of Electric Machines: A Primer with MATLAB. Boca Raton, USA: CRC Press, 2019.
- [5] S. V. Kulkarni, S. A. Khaparde. Transformer Engineering: Design, Technology, and Diagnostics. Boca Raton, USA: CRC Press, 2017.
- [6] K. Dawood, B. Alboyaci, M. A. Cinar, O. Sonmez, “A new method for the calculation of leakage reactance in power transformers”, J. Electr. Eng. & Tech., vol. 12, no. 4, pp. 1883-1890, 2017, doi: 10.5370/JEET.2017.12.5.1883.
- [7] I. Sitar, M. Bilo, and D. Vale, “New design of traction transformers for fixed installations,” in International Colloquium Transformer Research and Asset Management, 2009, pp. 1–10.
- [8] I. Sitar and M. Jurković, “Modern design of EMU traction transformers,” in Automation in transportation, 2014, pp. 234–237.
- [9] D. Liu, B. Xiong, Z. Cheng, and F. Liu, “Effects of axial gap length between disc windings on magnetic fields and power losses of evaporative cooling traction transformers,” in Asia-Pacific Power and Energy Engineering Conference, Nanjing, China, 2020, pp.1-7.
- [10] C. Yang, Y. Ding, H. Qiu, and B. Xiong, “Analysis of turn-to-turn fault on split-winding transformer using coupled field-circuit approach,” Processes, vol. 9, no. 8, pp. 1–13, 2021, doi: 10.3390/pr9081314.
- [11] D. Azizian, “Nonlinear behavior analysis of split-winding dry-type transformer using a new star model and a coupled field-circuit approach,” Arch. Electr. Eng., vol. 65, no. 4, pp. 773–787, 2016, doi: 10.1515/aee-2016-0054.
- [12] J. Smajic, G. Di Pino, C. Stemmler, W. Mönig, and M. Carlen, “Numerical study of the core saturation influence on the winding losses of traction transformers,” IEEE Trans. Magn., vol. 51, no. 3, pp. 1–4, 2015, doi: 10.1109/TMAG.2014.2360918.
- [13] J. El Hayek, “Influence of harmonics on traction transformers losses,” in ICEMS 2003 – Proc. 6th Int. Conf. on Elect. Mach. and Syst., Beijing, China, 2003, vol. 1, pp. 347–350.
- [14] I. Sitar, Z. Janic, and B. Cucic, “External magnetic field density of main traction transformer for EMU,” COMPEL - Int. J. Comput. Math. Electr. Electron. Eng., vol. 31, no. 2, pp. 716–725, 2012, doi: 10.1108/03321641211200680.
- [15] S. Yuan et al., “Modelling method for thermal field of turbulent cooling dry-type on-board traction transformer in EMUs,” IEEE Trans. Transp. Electrif., vol. 8, no. 1, pp. 298–311, 2021, doi: 10.1109/TTE.2021.3097876.
- [16] A. Palani, S. Santhi, S. Gopalakrishna, V. Jayashankar, “Real-time techniques to measure winding displacement in transformers during short-circuit tests”. IEEE Trans. Power Deliv., vol. 23, no. 2, pp. 726-732, 2007, doi: 10.1109/TPWRD.2007.911110.
- [17] M. Wang, A. J. Vandermaar, K. D. Srivastava, “Review of condition assessment of power transformers in service”. IEEE Electr. Insul. Mag., vol. 18, no. 6, pp. 12-25, 2002, doi: 10.1109/MEI.2002.1161455.
- [18] J. R. Secue, E. Mombello, “Sweep frequency response analysis (SFRA) for the assessment of winding displacements and deformation in power transformers”. Electr. Power Syst. Res., vol. 78, no. 6, pp. 1119-1128, 2008, doi: 10.1016/j.epsr.2007.08.005
- [19] N. Swamy, U. Savadamuthu, “Sweep frequency response based statistical approach for locating faults in transformer windings using sliding window technique”, Electr. Power Syst. Res., vol. 194, no. 1, pp. 1-8, 2021, doi: 10.1016/j.epsr.2021.107061.
- [20] Zhao Z, Tang C, Islam S. Interpretation of transformer winding deformation fault by the spectral clustering of FRA signature. Int. J. Electr. Power & Energy Syst., vol. 130, no. 1, pp. 1-8, 2021, doi: 10.1016/j.ijepes.2021.106933.
- [21] CIGRE, Advances in the interpretation of transformer frequency response analysis (FRA). Technical Note 812, 2020
- [22] L. Zhou, J. Jiang, W. Li, Z. Wu, S. Gao, L. Guo, H. Liu, “FRA modelling for diagnosing axial displacement of windings in traction transformers”, IET Electr. Power Appl., vol. 13, no. 12, pp. 2121-2127, 2019, doi: 10.1049/iet-epa.2019.0362.
- [23] M. F. M. Yousof, C. Ekanayake, T. K. Saha, “Frequency response analysis to investigate deformation of transformer winding”. IEEE Trans. Dielectr. Electr. Insul., vol. 22, no. 4, pp. 2359–2367, 2015, doi: 10.1109/TDEI.2015.004750.
- [24] S. Naiqiu, Z. Can, L. Fang, L. Qisheng, Z. Lingwei, “Study on ultrasonic measurement device for transformer winding deformation”. in IEEE Conference on Power System Technology, Kunming, China, 2002. pp. 1401-1404.
- [25] M. A. Hejazi, G. B. Gharehpetian, G. Moradi, H. A. Alehosseini, M. Mohammad, “On-line monitoring of transformer winding axial displacement and its extent using scattering parameters and k-nearest neighbor method”, IET Gener. Trans. & Distr., vol. 5, pp. 824-832, 2011, doi: 10.1049/iet-gtd.2010.0802.
- [26] S. A. Mousavi, M. Bigdeli, S. M. Mousavi, “A feasibility study on application of positioning sensors to online detect of the transformer winding axial displacement”. in IEEE Symposium on Industrial Electronics & Applications, Kuching, Malaysia, 2013. pp. 1-3.
- [27] X. Li et al., “Partial discharge characteristics of oil-paper insulation for on-board traction transformers under superposed inter-harmonic AC voltages,” IEEE Trans. Dielectr. Electr. Insul., vol. 27, no. 1, pp. 240–248, 2020, doi: 10.1109/TDEI.2019.008404.
- [28] B. Jia, P. Zhang, and Z. Li, “Aging life assessment of oil-paper insulation of traction transformer under shock load,” in Asia Energy and Electrical Engineering Symposium, Chengdu, China, 2020, pp. 1045–1050.
- [29] L. Zhou et al., “Experimental studies on the estimated life of oil-immersed insulation paper in traction transformers,” IEEE Trans. Power Deliv., vol. 36, no. 5, pp. 2646–2657, 2021, doi: 10.1109/TPWRD.2020.3024839.
- [30] A. Ünal, N. Akkuş, and S. Kandil, “Demiryolu aracı disk balatalarının tasarımında yüksek sıcaklığın neden olduğu fren zayıflama probleminin belirlenmesi için sonlu elemanlar yöntemi yaklaşımı,” Demiryolu Mühendisliği, vol. 1, no. 15, pp. 134–144, 2022, doi: 10.47072/demiryolu.1027982.
- [31] F. Çeçen and B. Aktaş, “Lamine CFRP donatılı traverslerin deneysel ve sonlu eleman analizleriyle incelenmesi,” Demiryolu Mühendisliği, vol. 1, no. 14, pp. 26–38, 2021, doi: 10.47072/demiryolu.869946.
- [32] M. E. Arı and İ. Esen, “Design of a metro train and structural analysis of the metro vehicle body by finite element method,” Railway Engineering, vol. 1, no. 15, pp. 30–45, 2022, doi: 10.47072/demiryolu.1018663.
- [33] V. Shrikrishna, S. V. Kulkarni, and S. A. Khaperde, Transformer engineering: design and practice. CRC Press, 2004.
- [34] AkSteel, “AkSteel Product Catalog,” 2022. [Online]. Available: https://www.aksteel.de/files/downloads/AK_CARLITE_GOES_BV_060412.pdf.
- [35] M. A. Cinar, “Evaluation of the technical and economic feasibility of mixed grade cores in transformer design according to EN50588-1,” Teh. Vjesn., vol. 28, no. 4, pp. 1136–1144, 2021, doi: 10.17559/TV-20200402220152.
- [36] T. R. Specht, “Transformer magnetizing inrush currents,” Electr. Eng., vol. 70, no. 4, pp. 324–324, 1951, doi: 10.1109/ee.1951.6437380.
- [37] IEEE Standard for General Requirements for Liquid-Immersed Distribution, Power, and Regulating Transformers, IEEE Std C57.12.00-2015 (Revision of IEEE Std C57.12.00-2010), 2016.
- [38] M. A. Çınar, B. Alboyacı, S. Çürükova, O. Sönmez, and R. Yapıcı, “Calculation of optimum dimensions of magnetic shunt elements to reduce stray losses on transformer tank walls,” J. Fac. Eng. Archit. Gazi Univ., vol. 32, no. 4, pp. 1337–1346, 2017, doi: 10.17341/gazimmfd.369855.
- [39] Y. Li, S. L. Ho, N. Wang, and R. Y. Tang, “Numerical analysis of eddy current field in the ascending flange for the bushings and tank wall of a large transformer”, in Joint Int. Conf. Power Syst. Tech. And IEEE Power India Conference, New Delhi, India, 2008, pp. 1-7.
- [40] C. Guérin and G. Meunier, “Surface impedance for 3D non-linear eddy current problems - application to loss computation in transformers,” IEEE Trans. Magn., vol. 32, no. 3 PART 2, pp. 808–811, 1996, doi: 10.1109/20.497364.
- [41] M. A. S. Masoum, P. S. Moses, and A. S. Masoum, “Derating of asymmetric three-phase transformers serving unbalanced nonlinear loads,” IEEE Trans. Power Deliv., vol. 23, no. 4, pp. 2033–2041, 2008, doi: 10.1109/TPWRD.2008.923057.
- [42] D. Pejovski, K. Najdenkoski, and M. Digalovski, “Impact of different harmonic loads on distribution transformers,” in Procedia Engineering, 2017, vol. 202, pp. 76–87, doi: 10.1016/j.proeng.2017.09.696.
- [43] J. E. Holcomb, “Distribution transformer magnetizing inrush current,” Trans. Am. Inst. Electr. Eng. Part III Power Appar. Syst., vol. 80, no. 3, 1961, doi: 10.1109/AIEEPAS.1961.4501117.