Determination of Power Transformer Winding Natural Frequencies and Damping Factors from the Measured Voltage Transfer Functions
Keywords:
power transformers, resonant processes, windings, frequency response, transfer function, natural oscillations, natural frequency, damping factor
Abstract
The problem of damage inflicted to power transformers by high-frequency switching overvoltages occurring in 6–35 kV electric networks is solved by using protective RC circuits and detuning the windings natural frequencies from the frequencies of network voltage transient oscillations. To select the optimal parameters of protective RC circuits, simulation of transients in the cable network together with the transformer primary winding is required. To this end, it is necessary to have a reliable high-frequency model of the transformer. For verifying this model, measured values of natural frequencies and damping factors of free oscillations are required. To detune the transformer winding natural oscillation frequencies, their values have to be measured together with measuring the resonance overvoltage ratios in the transformer windings. Based on this information, the frequency ranges of network voltage transient oscillations that are dangerous for the transformer windings can be estimated. An approach to estimating the natural frequencies and damping factors based on measurements and analysis of voltage transfer functions at accessible intermediate points of power transformers windings is proposed. The article gives a practical example of estimating the natural frequencies and damping factors of free oscillations in the high-voltage winding of a dry transformer using the proposed approach, as well as by approximating transient voltages and analyzing the power transformer primary winding frequency responses.
References
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#
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6. Florkowski M. et al. Overvoltage Impact on Internal Insulation Systems of Transformers in Electrical Networks with Vacuum Circuit Breakers. – Energies, 2020, vol. 13 (23), 6380, DOI: 10.3390/en13236380.
7. Yang Q. et al. Field Experiments on Overvoltage Caused by 12-kV Vacuum Circuit Breakers Switching Shunt Reactors. – IEEE Transactions on Power Delivery, 2016, vol. 31, No. 2, pp. 657–664, DOI: 10.1109/TPWRD.2015.2475397.
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9. Sutherland P.E., Valdes M.E., Fox G.H. Snubber Design for Transformer Protection. – IEEE Transactions on Industry Applications, 2016, vol. 52, No. 1, pp. 692–700, DOI: 10.1109/TIA.2015.2473137.
10. Buehler S.H. et al. Evaluation of a Unique Transient Hardened Transformer Designed to Withstand Primary Switching Transients: Simulation, Lab Tests and Analysis. – IEEE/IAS 55th Industrial and Commercial Power Systems Technical Conference, 2019, DOI: 10.1109/ICPS.2019.8733377.
11. Popov M. et al. Experimental and Theoretical Analysis of Vacuum Circuit Breaker Prestrike Effect on a Transformer. – IEEE Transactions on Power Delivery, 2009, vol. 24, No. 3, pp. 1266–1274, DOI: 10.1109/TPWRD.2009.2013383.
12. Дмитриев М.В. Повреждения силовых трансформаторов при коммутациях кабелей 6–35 кВ. – Электроэнергия. Передача и распределение, 2016, № 2 (35), с. 86–91.
13. Брилинский А.С., Евдокунин Г.А., Пономарёв Т.А. Исследование причин нарушения электрической прочности изоляции устройства РПН трансформатора с сухой изоляцией. – Известия НТЦ Единой энергетической системы, 2018, № 1 (78), c. 130–141.
14. Брилинский А.С. и др. Исследование причин нарушения электрической прочности изоляции трансформатора с сухой изоляцией при замыканиях на землю. – Энергоэксперт, 2019, № 1, с. 28–33.
15. Ларин В.С., Матвеев Д.А., Максимов Б.К. Особенности высокочастотных резонансных перенапряжений в обмотках распределительных трансформаторов 6-35 кВ. – Энергетик, 2019, № 4, с. 12–16.
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17. Larssen J. et al. Experiences from Middelgrunden 40 MW Offshore Wind Farm. – Copenhagen Offshore Wind, 26-28 October 2005, Copenhagen, Denmark.
18. Larsen J., Sagoo R.S. Replacement of Transformers on Middelgrunden Offshore Wind Farm. – European Offshore Wind 2009 Conference & Exhibition, 14-16 September 2009, Stockholm, Sweden.
19. King R. et al. Switching Transients in Offshore Wind Farms – Impact on the Offshore and Onshore Networks. – International Conference on Power Systems Transients, 2011.
20. Силовые трансформаторы. Справочная книга / Под. ред. С.Д. Лизунова, А.К. Лоханина. М.: Энергоиздат, 2004, 616 с.
21. Gustavsen B., Portillo A. A Damping Factor-Based White-Box Transformer Model for Network Studies. – IEEE Transactions on Power Delivery, 2018, vol. 33, No. 6, pp. 2956–2964. DOI: 10.1109/TPWRD.2018.2847725.
22. 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.
23. Ларин В.С., Матвеев Д.А. Определение коэффициентов затухания по измеренным частотным характеристикам обмоток силовых трансформаторов. Ч. 1. Теоретическое рассмотрение. – Электричество, 2021, № 1, с. 13–22.
24. Ларин В.С., Матвеев Д.А. Определение коэффициентов затухания по измеренным частотным характеристикам обмоток силовых трансформаторов. Ч. 2. Анализ результатов измерений. – Электричество, 2021, № 2, с. 22–28.
25. Ларин В.С. Резонансные перенапряжения в обмотках трансформаторов. Ч.3. Измерение напряжения в обмотках на резонансных частотах. – Электричество, 2016, № 1, с. 20–24.
26. 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, DOI: 10.1109/TDEI.2015.7076828.
27. Soloot A.H. Resonant Overvoltages in Offshore Wind Farms: Analysis, modeling and measurement. – Theses for PhD, Norwegian University of Science and Technology, 2017, DOI:10.13140/RG.2.2.28215.11682.
28. Мандельштам Л.И. Полное собрание трудов: т. 4. Л.: Изд-во АН СССР, 1955, 512 с.
29. Ларин В.С. К развитию теории резонансных процессов в обмотках силовых трансформаторов. Ч. 1. Частотные характеристики схемы с двумя П-звеньями. – Электричество, 2021, № 8, с. 49–55.
30. Зевеке Г.В., Ионкин П.А., Нетушил А.В. Основы теории цепей. М.: Энергия, 1975, 752 с.
31. Бессонов Л.А. Теоретические основы электротехники. Электрические цепи. М.: Высшая школа, 1996, 638 с.
32. Демирчян К.С. и др. Теоретические основы электротехники: т. 1. СПб.: Питер, 2003, 463 с.
33. Бычков Ю.А. и др. Основы теоретической электротехники. СПб.: Лань, 2008, 592 с.
34. Nilsson J.W., Riedel S. Electric Circuits. Pearson, 2019, 816 p.
35. ГОСТ Р 59239–2020 (МЭК 60076-18:2012) Трансформаторы силовые и реакторы. Метод измерения частотных характеристик. М.: Стандартинформ, 2021, 50 с.
36. Ларин В.С., Волков А.Ю. Резонансные перенапряжения в обмотках трансформаторов. Ч.2. Определение резонансных частот обмоток. – Электричество, 2015, № 12, с. 20–25.
#
1. CIGRE Brochure 577A. Electrical Transient Interaction between Transformers and the Power System. Part 1: Expertise. Joint Working Group A2/C4.39, April 2014.
2. CIGRE Brochure 577B. Electrical Transient Interaction between Transformers and the Power System. Part 2: Case Studies. Joint Working Group A2/C4.39, April 2014.
3. IEEE Std C57.142-2010 IEEE Guide to Describe the Occurrence and Mitigation of Switching Transients Induced by Transformers, Switching Device, and System Interaction. 27 April 2011, doi: 10.1109/IEEESTD.2011.5759579. ISBN: 978-0-7381-6519-6.
4. Shipp D.D. et al. Transformer Failure Due to Circuit-Breaker-Induced Switching Transients. – IEEE Transactions on Industry Applications, 2011, vol. 47, No. 2, pp. 707–718, DOI: 10.1109/TIA.2010.2101996.
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2022-11-17
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