On Developing the Theory of Resonant Processes in Power Transformer Windings. Part 2. Frequency Responses of a Circuit with Four PI Sections
Keywords:
power transformers, resonant processes, windings, frequency response, natural oscillation frequency
Abstract
In the first part of the article, the results from theoretical studies of frequency responses in a homogeneous chain circuit containing two PI sections were presented, and conclusions about the voltage resonance occurrence conditions were drawn. A circuit with two PI sections has a single independent node and one natural frequency, whereas transformer windings are more complex oscillatory circuits and have a much larger number of natural oscillation frequencies. The second part of the article presents the results from studies of frequency responses in a homogeneous chain circuit containing four PI sections, three independent nodes, and three natural oscillation frequencies. Analytical expressions for the admittances of the equivalent circuit individual parts and the voltages at the intermediate nodes, as well as expressions for the natural frequencies are obtained. Using an analysis of the frequency dependences of the admittances of the equivalent circuit parts, the conditions and frequency ranges under which voltage resonance may occur at the first, second, and third natural frequencies, are shown. It has been demonstrated that for the considered resonant circuits there is a critical frequency above which the conditions for voltage resonance are not satisfied. Formulas for impedances and voltages at intermediate nodes of a chain circuit with an arbitrary number of PI sections are given.
References
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15. Soloot A.H., Høidalen H.K., Gustavsen B. Influence of the Winding Design of Wind Turbine Transformers for Resonant Overvoltage Vulnerability. – IEEE Transactions on Dielectrics and Electrical Insulation, 2015, vol. 22, No. 2, pp. 1250–1257.
16. Soloot A.H. Resonant Overvoltages in Offshore Wind Farms: Analysis, modeling and measurement. Theses for Ph.D, Norwegian University of Science and Technology, 2017, DOI:10.13140/RG.2.2.28215.11682.
#
1. Larin V.S. Elektrichestvo – in Russ. (Electricity), 2021, No. 8, pp. 49–55.
2. Heller B., Veverka A. Impulsnye processi v elektricheskih mashinah (Surge Phenomena in Electrical Machines). M.: Energiya, 1973, 440 p.
3. Beletskiy Z.M., Bunin A.G., Gorbuntsov A.F., Kontorovich L.N. Raschet impul'snyh vozdeystviy v obmotkah transformatorov s primeneniem EVM (Calculation of pulse effects in transformer windings using a computer). М.: Informelektro, 1978, 79 p.
4. Lizunov S.D., Lokhanin А.К. Silovye transformatory. Spravochnaya kniga (Power transformers. Reference book). М.: Energoizdat, 2004, 616 p.
5. Karsai K., Kerényi D., Kiss L. Large power transformers. Amsterdam: Elsevier, 1987, 614 p.
6. Larin V.S., Matveev D.A. Elektrichestvo – in Russ. (Electricity), 2020, No. 12, pp. 44–54.
7. Larin V.S., Matveev D.A. Elektrichestvo – in Russ. (Electricity), 2021, No. 1, pp. 13–22.
8. Del Vecchio R.M., Poulin B., Ahuja R. Calculation and measurement of winding disk capacitances with wound-in-shields. – IEEE Transactions on Power Delivery, 1998, vol. 13, No. 2, pp. 503–509.
9. Del Vecchio R.M., et al. Transformer Design Principles. Boca Raton: CRC Press, 2017, 612 p, DOI: https://doi.org/10.1201/ 9781315155920.
10. Bagheri M., Phung B.T., Naderi M.S. Impulse voltage distribution and frequency response of intershield windings. – IEEE Electrical Insulation Magazine, 2016, vol. 32, No. 5, pp. 32–40, DOI: 10.1109/MEI.2016.7552374.
11. Niasar M.G., Zhao W. Impulse voltage distribution on disk winding: calculation of disk series capacitance using analytical method. – 2020 IEEE International Conference on High Voltage Engineering and Application (ICHVE), 2020, DOI: 10.1109/ICHVE 49031.2020.9279969.
12. Sriyono, U. Khayam and Suwarno. Evaluating the Inter-Resonance Characteristics of Various Power Transformer Winding Designs. – IEEE Access, 2021, vol. 9, pp. 54649–54656, DOI: 10.1109/ACCESS.2021.3070595.
13. Larin V., Matveev D., Maximov B.K. Resonant overvoltages inside power transformer windings and the measures improving their ability to withstand high-frequency stresses. – 48th CIGRE Session, report A2-203, Paris, France, 2020.
14. Soloot A.H., Høidalen H.K., Gustavsen B. Upon the improvement of the winding design of wind turbine transformers for safer performance within resonant overvoltages. – CIGRE SC A2 & C4 JOINT COLLOQUIUM, Zurich, Switzerland, 2013,
15. Soloot A.H., Høidalen H.K., Gustavsen B. Influence of the Winding Design of Wind Turbine Transformers for Resonant Overvoltage Vulnerability. – IEEE Transactions on Dielectrics and Electrical Insulation, 2015, vol. 22, No. 2, pp. 1250–1257.
16. Soloot A.H. Resonant Overvoltages in Offshore Wind Farms: Analysis, modeling and measurement. Theses for Ph.D, Norwegian University of Science and Technology, 2017, DOI:10.13140/RG.2.2.28215.11682.
2. Геллер Б., Веверка А. Импульсные процессы в электрических машинах. М.: Энергия, 1973, 440 с.
3. Белецкий З.М., Бунин А.Г., Горбунцов А.Ф., Конторович Л.Н. Расчет импульсных воздействий в обмотках трансформаторов с применением ЭВМ. М.: Информэлектро, 1978, 79 с.
4. Лизунов С.Д., Лоханин А.К. Силовые трансформаторы. Справочная книга. М.: Энергоиздат, 2004, 616 с.
5. Karsai K., Kerényi D., Kiss L. Large power transformers. Amsterdam: Elsevier, 1987, 614 p.
6. Ларин В.С., Матвеев Д.А. Аппроксимация переходных резонансных напряжений и токов в обмотках силовых трансформаторов для определения собственных частот колебаний и коэффициентов затухания. – Электричество, 2020, №12, с. 44–54.
7. Ларин В.С., Матвеев Д.А. Определение коэффициентов затухания по измеренным частотным характеристикам обмоток силовых трансформаторов. Ч. 1. Теоретическое обоснование. – Электричество, 2021, №1, с. 13–22.
8. Del Vecchio R.M., Poulin B., Ahuja R. Calculation and measurement of winding disk capacitances with wound-in-shields. – IEEE Transactions on Power Delivery, 1998, vol. 13, No. 2, pp. 503–509.
9. Del Vecchio R.M., et al. Transformer Design Principles. Boca Raton: CRC Press, 2017, 612 p, DOI: https://doi.org/10.1201/ 9781315155920.
10. Bagheri M., Phung B.T., Naderi M.S. Impulse voltage distribution and frequency response of intershield windings. – IEEE Electrical Insulation Magazine, 2016, vol. 32, No. 5, pp. 32–40, DOI: 10.1109/MEI.2016.7552374.
11. Niasar M.G., Zhao W. Impulse voltage distribution on disk winding: calculation of disk series capacitance using analytical method. – 2020 IEEE International Conference on High Voltage Engineering and Application (ICHVE), 2020, DOI: 10.1109/ICHVE49031.2020.9279969.
12. Sriyono, U. Khayam and Suwarno. Evaluating the Inter-Resonance Characteristics of Various Power Transformer Winding Designs. – IEEE Access, 2021, vol. 9, pp. 54649–54656, DOI: 10.1109/ACCESS.2021.3070595.
13. Larin V., Matveev D., Maximov B.K. Resonant overvoltages inside power transformer windings and the measures improving their ability to withstand high-frequency stresses. – 48th CIGRE Session, report A2-203, Paris, France, 2020.
14. Soloot A.H., Høidalen H.K., Gustavsen B. Upon the improvement of the winding design of wind turbine transformers for safer performance within resonant overvoltages. – CIGRE SC A2 & C4 JOINT COLLOQUIUM, Zurich, Switzerland, 2013,
15. Soloot A.H., Høidalen H.K., Gustavsen B. Influence of the Winding Design of Wind Turbine Transformers for Resonant Overvoltage Vulnerability. – IEEE Transactions on Dielectrics and Electrical Insulation, 2015, vol. 22, No. 2, pp. 1250–1257.
16. Soloot A.H. Resonant Overvoltages in Offshore Wind Farms: Analysis, modeling and measurement. Theses for Ph.D, Norwegian University of Science and Technology, 2017, DOI:10.13140/RG.2.2.28215.11682.
#
1. Larin V.S. Elektrichestvo – in Russ. (Electricity), 2021, No. 8, pp. 49–55.
2. Heller B., Veverka A. Impulsnye processi v elektricheskih mashinah (Surge Phenomena in Electrical Machines). M.: Energiya, 1973, 440 p.
3. Beletskiy Z.M., Bunin A.G., Gorbuntsov A.F., Kontorovich L.N. Raschet impul'snyh vozdeystviy v obmotkah transformatorov s primeneniem EVM (Calculation of pulse effects in transformer windings using a computer). М.: Informelektro, 1978, 79 p.
4. Lizunov S.D., Lokhanin А.К. Silovye transformatory. Spravochnaya kniga (Power transformers. Reference book). М.: Energoizdat, 2004, 616 p.
5. Karsai K., Kerényi D., Kiss L. Large power transformers. Amsterdam: Elsevier, 1987, 614 p.
6. Larin V.S., Matveev D.A. Elektrichestvo – in Russ. (Electricity), 2020, No. 12, pp. 44–54.
7. Larin V.S., Matveev D.A. Elektrichestvo – in Russ. (Electricity), 2021, No. 1, pp. 13–22.
8. Del Vecchio R.M., Poulin B., Ahuja R. Calculation and measurement of winding disk capacitances with wound-in-shields. – IEEE Transactions on Power Delivery, 1998, vol. 13, No. 2, pp. 503–509.
9. Del Vecchio R.M., et al. Transformer Design Principles. Boca Raton: CRC Press, 2017, 612 p, DOI: https://doi.org/10.1201/ 9781315155920.
10. Bagheri M., Phung B.T., Naderi M.S. Impulse voltage distribution and frequency response of intershield windings. – IEEE Electrical Insulation Magazine, 2016, vol. 32, No. 5, pp. 32–40, DOI: 10.1109/MEI.2016.7552374.
11. Niasar M.G., Zhao W. Impulse voltage distribution on disk winding: calculation of disk series capacitance using analytical method. – 2020 IEEE International Conference on High Voltage Engineering and Application (ICHVE), 2020, DOI: 10.1109/ICHVE 49031.2020.9279969.
12. Sriyono, U. Khayam and Suwarno. Evaluating the Inter-Resonance Characteristics of Various Power Transformer Winding Designs. – IEEE Access, 2021, vol. 9, pp. 54649–54656, DOI: 10.1109/ACCESS.2021.3070595.
13. Larin V., Matveev D., Maximov B.K. Resonant overvoltages inside power transformer windings and the measures improving their ability to withstand high-frequency stresses. – 48th CIGRE Session, report A2-203, Paris, France, 2020.
14. Soloot A.H., Høidalen H.K., Gustavsen B. Upon the improvement of the winding design of wind turbine transformers for safer performance within resonant overvoltages. – CIGRE SC A2 & C4 JOINT COLLOQUIUM, Zurich, Switzerland, 2013,
15. Soloot A.H., Høidalen H.K., Gustavsen B. Influence of the Winding Design of Wind Turbine Transformers for Resonant Overvoltage Vulnerability. – IEEE Transactions on Dielectrics and Electrical Insulation, 2015, vol. 22, No. 2, pp. 1250–1257.
16. Soloot A.H. Resonant Overvoltages in Offshore Wind Farms: Analysis, modeling and measurement. Theses for Ph.D, Norwegian University of Science and Technology, 2017, DOI:10.13140/RG.2.2.28215.11682.
