Refinement of the Steinmetz Coefficient for the Transformer Core Steel
Keywords:
Steinmetz coefficient, hysteresis loss, eddy current loss, magnetic induction, iron loss, no-load experiment
Abstract
The Steinmetz coefficient is the exponent of the power to which the magnetic induction amplitude enters in the expression for hysteresis loss in a ferromagnetic material. In various sources, the value of this coefficient varies from 1 to 3. Information on the exact value of this coefficient will make it possible to predict hysteresis loss more accurately, which in turn makes it possible to efficiently design transformers with low magnetic loss (no-load loss). Assuming that hysteresis loss is proportional to frequency and that eddy current loss is proportional to frequency squared and induction squared, an expression which determines the Steinmetz coefficient for a specific magnetic core is derived. The expression includes the total loss values measured in two no-load experiments, one of which was carried out at an increased magnetization frequency and the other at a reduced voltage. For a single-phase 1600 W transformer, the Steinmetz factor was estimated to be 1.62. A formula for determining the exponent of the power to which the magnetization frequency enters in the expression for the total loss in the magnetic circuit. For the transformer under study, this exponent has been found to be 1.42.
References
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2. Yan Z, Ai-ming S. Simplified Ferrite Core Loss Separation Model for Switched Mode Power Converter. – IET Power Electronics, 2016, vol. 9, iss. 3, pp. 529–535, DOI:10.1049/iet-pel.2015.0146.
3. Sakaki Y., Matsuoka T. Hysteresis Losses in Mn-Zn Ferrite Cores, IEEE Transactions on Magnetics, 1986, vol. 22, No. 5, pp. 623–625, DOI:10.1109/TMAG.1986.1064503.
4. Petrescu L. et al. Steinmetz' Parameters Fitting Procedure for the Power Losses Estimation in Soft Magnetic Materials. – International Conference on Optimization of Electrical and Electronic Equipment (OPTIM), Brasov, 2017, pp. 208–213, DOI:10.1109/OPTIM.2017.7974972.
5. Тихомиров П.М. Расчет трансформаторов. М.: Энергоатомиздат, 1986, 528 с.
6. Дружинин В.В. Магнитные свойства электротехнической стали. М.: Энергия, 1974, 238 с.
7. Васютинский С.В. Вопросы теории и расчета трансформаторов. Л.: Энергия, 1970, 432 с.
8. Bodger P.S., Liew M.C., Johnstone P.T. A Comparison of Conventional and Reverse Transformer Design. – Australasian Universities Power Engineering Conference, 2000, pp. 80–85 [Электрон. ресурс], URL: http://hdl.handle.net/10092/793 (дата обращения 24.10.2022).
9. Reinert J., Brockmeyer A., De Doncker R.W. Calculation of Losses in Ferro- and Ferrimagnetic Materials Based on the Modified Steinmetz Equation. – IEEE Transactions on Industry Applications, 2001, vol. 37(4), pp. 1055–1061, DOI:10.1109/28.936396.
10. Ibrahim М., Pillay P. Advanced Testing and Modeling of Magnetic Materials Including a New Method of Core Loss Separation for Electrical Machines. – IEEE Transactions on Industry Applications, 2012, vol. 48(5), pp.1507–1515, DOI:10.1109/TIA.2012.2210012.
11. Lee P.K. et. al. Prediction of Iron Losses Using the Modified Steinmetz Equation under the Sinusoidal Waveform. – 8th Asian Control Conference (ASCC), Kaohsiung, 2011, pp. 579–584.
12. Saandy T.A. et. al. Analytical Modeling of the Steinmetz Coefficient for Single-Phase Transformer Eddy Current Loss Prediction. – International Journal of Scientific & Technology Research, 2015, vol. 4(12), pp. 270–275.
13. Manyage M.J., Pillay P. New Epstein Frame for Core Loss Measurements at High Frequencies and High Flux Densities. – IEEE Industry Applications Society Annual Meeting, 2008, DOI:10.1109/08IAS.2008.51.
14. Eldieb А. Evaluation of loss generated by edge- burrs in electrical steel: PhD Thesis, Cardiff University, 2017, 141 p., DOI:orca.cf.ac.uk/id/eprint/105536.
15. Плотников С.М. Определение потерь на вихревые токи и на гистерезис в магнитопроводах электрических машин. – Измерительная техника, 2020, № 6, с. 54–58.
16. Плотников С.М. Оценка погрешностей ваттметрового метода определения магнитных потерь в трансформаторах. – Измерительная техника, 2021, № 3, с. 40–44.
17. Плотников С.М., Колмаков О.В. Решение актуальных вопросов в теории трансформаторов. – Известия вузов. Электромеханика, 2021, т. 64, № 3. с. 5–11.
18. Кацман М.М. Электрические машины. М.: Высшая школа, 1990, 463 с.
19. Иванов-Смоленский А.В. Электрические машины. Т. 1. М.: Изд-во МЭИ, 2004, 656 с.
20. Иванов М.И., Равдоник В.С. Электротехника. М.: Высшая школа, 1984, 375 с.
21. Пат. RU2764780C1. Способ определения показателя магнитной индукции в потерях на гистерезис для стали сердечника трансформатора / С.М. Плотников, 2022.
22. Цицорин А.Н. Моделирование изменения удельных потерь электротехнической стали силовых трансформаторов в течение срока службы. – Электротехника, 2012, № 12, с. 55–58.
#
1. Bertotti G. General Properties of Power Losses in Soft Ferromagnetic Materials. – IEEE Transactions on. Magnetics, 1988, vol.24, pp. 621–630, DOI:10.1109/20.43994.
2. Yan Z, Ai-ming S. Simplified Ferrite Core Loss Separation Model for Switched Mode Power Converter. – IET Power Electronics, 2016, vol. 9, iss. 3, pp. 529–535, DOI:10.1049/iet-pel.2015.0146.
3. Sakaki Y., Matsuoka T. Hysteresis Losses in Mn-Zn Ferrite Cores, IEEE Transactions on Magnetics, 1986, vol. 22, No. 5, pp. 623–625, DOI:10.1109/TMAG.1986.1064503.
4. Petrescu L. et al. Steinmetz' Parameters Fitting Procedure for the Power Losses Estimation in Soft Magnetic Materials. – International Conference on Optimization of Electrical and Electronic Equipment (OPTIM), Brasov, 2017, pp. 208–213, DOI:10.1109/OPTIM.2017.7974972.
5. Tihomirov P.М. Raschet transformatorov (Calculation of the Transformers). М.: Energatomizdat, 1986, 528 p.
6. Druzhinin V.V. Magnitnye svoystva elektrotekhnicheskoy stali (Magnetic Properties of Electrical Steel). М.: Energiya, 1974, 238 p.
7. Vasyutinskiy S.V. Voprosy teorii i rascheta transformatorov (Issue of Theory and Calculation of the Transformers). L.: Energiya, 1970, 432 p.
8. Bodger P.S., Liew M.C., Johnstone P.T. A Comparison of Conventional and Reverse Transformer Design. – Australasian Universities Power Engineering Conference, 2000, pp. 80–85 [Electron. resource], URL: http://hdl.handle.net/10092/793 (Date of appeal 24.10.2022).
9. Reinert J., Brockmeyer A., De Doncker R.W. Calculation of Losses in Ferro- and Ferrimagnetic Materials Based on the Modified Steinmetz Equation. – IEEE Transactions on Industry Applications, 2001, vol. 37(4), pp. 1055–1061, DOI:10.1109/28.936396.
10. Ibrahim М., Pillay P. Advanced Testing and Modeling of Magnetic Materials Including a New Method of Core Loss Separation for Electrical Machines. – IEEE Transactions on Industry Applications, 2012, vol. 48(5), pp.1507–1515, DOI:10.1109/TIA.2012.2210012.
11. Lee P.K. et.al. Prediction of Iron Losses Using the Modified Steinmetz Equation under the Sinusoidal Waveform. – 8th Asian Control Conference (ASCC), Kaohsiung, 2011, pp. 579–584.
12. Saandy T.A. et. al. Analytical Modeling of the Steinmetz Coefficient for Single-Phase Transformer Eddy Current Loss Prediction. – International Journal of Scientific & Technology Research, 2015, vol. 4(12), pp. 270–275.
13. Manyage M.J., Pillay P. New Epstein Frame for Core Loss Measurements at High Frequencies and High Flux Densities. – IEEE Industry Applications Society Annual Meeting, 2008, DOI:10.1109/08IAS.2008.51.
14. Eldieb А. Evaluation of loss generated by edge- burrs in electrical steel: PhD Thesis, Cardiff University, 2017, 141 p., DOI:orca.cf.ac.uk/id/eprint/105536.
15. Plotnikov S.M. Izmeritel'naya tekhnika – in Russ. (Measuring Equipment), 2020, No. 6, pp. 54–58.
16. Plotnikov S.M. Izmeritel'naya tekhnika – in Russ. (Measuring Equipment), 2021, No. 3, pp. 40–44.
17. Plotnikov S.M., Kolmakov O.V. Izvestiya vuzov. Elektromekhanika – in Russ. (News of Universities. Electromechanics), 2021, vol. 64, No. 3. pp. 5–11.
18. Katsman М.М. Elektricheskie mashiny (Electric Machines). М.: Vysshaya shkola, 1990, 463 p.
19. Ivanov-Smolenskiy A.V. Elektricheskie mashiny (Electric Machines). Vol. 1. М.: Izd-vo MEI, 2004, 656 p.
20. Ivanov M.I., Ravdonik V.S. Elektrotekhnika (Electrical Engineering). М.: Vysshaya shkola, 1984, 375 p.
21. Pаt. RU2764780C1. Sposob opredeleniya pokazatelya magnitnoy induktsii v poteryah na gisterezis dlya stali serdechnika transformatora (Method for Determining the Magnetic Induction Index in Hysteresis Losses for Transformer Core Steel) / S.М. Plotnikov, 2022.
22. Tsitsorin A.N. Elektrotekhnika – in Russ. (Electrical Engineering), 2012, No. 12, pp. 55–58.
2. Yan Z, Ai-ming S. Simplified Ferrite Core Loss Separation Model for Switched Mode Power Converter. – IET Power Electronics, 2016, vol. 9, iss. 3, pp. 529–535, DOI:10.1049/iet-pel.2015.0146.
3. Sakaki Y., Matsuoka T. Hysteresis Losses in Mn-Zn Ferrite Cores, IEEE Transactions on Magnetics, 1986, vol. 22, No. 5, pp. 623–625, DOI:10.1109/TMAG.1986.1064503.
4. Petrescu L. et al. Steinmetz' Parameters Fitting Procedure for the Power Losses Estimation in Soft Magnetic Materials. – International Conference on Optimization of Electrical and Electronic Equipment (OPTIM), Brasov, 2017, pp. 208–213, DOI:10.1109/OPTIM.2017.7974972.
5. Тихомиров П.М. Расчет трансформаторов. М.: Энергоатомиздат, 1986, 528 с.
6. Дружинин В.В. Магнитные свойства электротехнической стали. М.: Энергия, 1974, 238 с.
7. Васютинский С.В. Вопросы теории и расчета трансформаторов. Л.: Энергия, 1970, 432 с.
8. Bodger P.S., Liew M.C., Johnstone P.T. A Comparison of Conventional and Reverse Transformer Design. – Australasian Universities Power Engineering Conference, 2000, pp. 80–85 [Электрон. ресурс], URL: http://hdl.handle.net/10092/793 (дата обращения 24.10.2022).
9. Reinert J., Brockmeyer A., De Doncker R.W. Calculation of Losses in Ferro- and Ferrimagnetic Materials Based on the Modified Steinmetz Equation. – IEEE Transactions on Industry Applications, 2001, vol. 37(4), pp. 1055–1061, DOI:10.1109/28.936396.
10. Ibrahim М., Pillay P. Advanced Testing and Modeling of Magnetic Materials Including a New Method of Core Loss Separation for Electrical Machines. – IEEE Transactions on Industry Applications, 2012, vol. 48(5), pp.1507–1515, DOI:10.1109/TIA.2012.2210012.
11. Lee P.K. et. al. Prediction of Iron Losses Using the Modified Steinmetz Equation under the Sinusoidal Waveform. – 8th Asian Control Conference (ASCC), Kaohsiung, 2011, pp. 579–584.
12. Saandy T.A. et. al. Analytical Modeling of the Steinmetz Coefficient for Single-Phase Transformer Eddy Current Loss Prediction. – International Journal of Scientific & Technology Research, 2015, vol. 4(12), pp. 270–275.
13. Manyage M.J., Pillay P. New Epstein Frame for Core Loss Measurements at High Frequencies and High Flux Densities. – IEEE Industry Applications Society Annual Meeting, 2008, DOI:10.1109/08IAS.2008.51.
14. Eldieb А. Evaluation of loss generated by edge- burrs in electrical steel: PhD Thesis, Cardiff University, 2017, 141 p., DOI:orca.cf.ac.uk/id/eprint/105536.
15. Плотников С.М. Определение потерь на вихревые токи и на гистерезис в магнитопроводах электрических машин. – Измерительная техника, 2020, № 6, с. 54–58.
16. Плотников С.М. Оценка погрешностей ваттметрового метода определения магнитных потерь в трансформаторах. – Измерительная техника, 2021, № 3, с. 40–44.
17. Плотников С.М., Колмаков О.В. Решение актуальных вопросов в теории трансформаторов. – Известия вузов. Электромеханика, 2021, т. 64, № 3. с. 5–11.
18. Кацман М.М. Электрические машины. М.: Высшая школа, 1990, 463 с.
19. Иванов-Смоленский А.В. Электрические машины. Т. 1. М.: Изд-во МЭИ, 2004, 656 с.
20. Иванов М.И., Равдоник В.С. Электротехника. М.: Высшая школа, 1984, 375 с.
21. Пат. RU2764780C1. Способ определения показателя магнитной индукции в потерях на гистерезис для стали сердечника трансформатора / С.М. Плотников, 2022.
22. Цицорин А.Н. Моделирование изменения удельных потерь электротехнической стали силовых трансформаторов в течение срока службы. – Электротехника, 2012, № 12, с. 55–58.
#
1. Bertotti G. General Properties of Power Losses in Soft Ferromagnetic Materials. – IEEE Transactions on. Magnetics, 1988, vol.24, pp. 621–630, DOI:10.1109/20.43994.
2. Yan Z, Ai-ming S. Simplified Ferrite Core Loss Separation Model for Switched Mode Power Converter. – IET Power Electronics, 2016, vol. 9, iss. 3, pp. 529–535, DOI:10.1049/iet-pel.2015.0146.
3. Sakaki Y., Matsuoka T. Hysteresis Losses in Mn-Zn Ferrite Cores, IEEE Transactions on Magnetics, 1986, vol. 22, No. 5, pp. 623–625, DOI:10.1109/TMAG.1986.1064503.
4. Petrescu L. et al. Steinmetz' Parameters Fitting Procedure for the Power Losses Estimation in Soft Magnetic Materials. – International Conference on Optimization of Electrical and Electronic Equipment (OPTIM), Brasov, 2017, pp. 208–213, DOI:10.1109/OPTIM.2017.7974972.
5. Tihomirov P.М. Raschet transformatorov (Calculation of the Transformers). М.: Energatomizdat, 1986, 528 p.
6. Druzhinin V.V. Magnitnye svoystva elektrotekhnicheskoy stali (Magnetic Properties of Electrical Steel). М.: Energiya, 1974, 238 p.
7. Vasyutinskiy S.V. Voprosy teorii i rascheta transformatorov (Issue of Theory and Calculation of the Transformers). L.: Energiya, 1970, 432 p.
8. Bodger P.S., Liew M.C., Johnstone P.T. A Comparison of Conventional and Reverse Transformer Design. – Australasian Universities Power Engineering Conference, 2000, pp. 80–85 [Electron. resource], URL: http://hdl.handle.net/10092/793 (Date of appeal 24.10.2022).
9. Reinert J., Brockmeyer A., De Doncker R.W. Calculation of Losses in Ferro- and Ferrimagnetic Materials Based on the Modified Steinmetz Equation. – IEEE Transactions on Industry Applications, 2001, vol. 37(4), pp. 1055–1061, DOI:10.1109/28.936396.
10. Ibrahim М., Pillay P. Advanced Testing and Modeling of Magnetic Materials Including a New Method of Core Loss Separation for Electrical Machines. – IEEE Transactions on Industry Applications, 2012, vol. 48(5), pp.1507–1515, DOI:10.1109/TIA.2012.2210012.
11. Lee P.K. et.al. Prediction of Iron Losses Using the Modified Steinmetz Equation under the Sinusoidal Waveform. – 8th Asian Control Conference (ASCC), Kaohsiung, 2011, pp. 579–584.
12. Saandy T.A. et. al. Analytical Modeling of the Steinmetz Coefficient for Single-Phase Transformer Eddy Current Loss Prediction. – International Journal of Scientific & Technology Research, 2015, vol. 4(12), pp. 270–275.
13. Manyage M.J., Pillay P. New Epstein Frame for Core Loss Measurements at High Frequencies and High Flux Densities. – IEEE Industry Applications Society Annual Meeting, 2008, DOI:10.1109/08IAS.2008.51.
14. Eldieb А. Evaluation of loss generated by edge- burrs in electrical steel: PhD Thesis, Cardiff University, 2017, 141 p., DOI:orca.cf.ac.uk/id/eprint/105536.
15. Plotnikov S.M. Izmeritel'naya tekhnika – in Russ. (Measuring Equipment), 2020, No. 6, pp. 54–58.
16. Plotnikov S.M. Izmeritel'naya tekhnika – in Russ. (Measuring Equipment), 2021, No. 3, pp. 40–44.
17. Plotnikov S.M., Kolmakov O.V. Izvestiya vuzov. Elektromekhanika – in Russ. (News of Universities. Electromechanics), 2021, vol. 64, No. 3. pp. 5–11.
18. Katsman М.М. Elektricheskie mashiny (Electric Machines). М.: Vysshaya shkola, 1990, 463 p.
19. Ivanov-Smolenskiy A.V. Elektricheskie mashiny (Electric Machines). Vol. 1. М.: Izd-vo MEI, 2004, 656 p.
20. Ivanov M.I., Ravdonik V.S. Elektrotekhnika (Electrical Engineering). М.: Vysshaya shkola, 1984, 375 p.
21. Pаt. RU2764780C1. Sposob opredeleniya pokazatelya magnitnoy induktsii v poteryah na gisterezis dlya stali serdechnika transformatora (Method for Determining the Magnetic Induction Index in Hysteresis Losses for Transformer Core Steel) / S.М. Plotnikov, 2022.
22. Tsitsorin A.N. Elektrotekhnika – in Russ. (Electrical Engineering), 2012, No. 12, pp. 55–58.
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2023-02-20
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