One first approach to the concept of severity factor was made by Malewski et al.^[1] Later, Asano et al. applied the Malewski's idea for further analysis but including the concept of Energy Spectral Density (ESD) associated to the transient voltage wave.^[2] A step forward was given by Rocha et al., whom introduced a new coefficient called Frequency Domain Severity Factor (FDSF).^[3][4] For those situations where an internal assessment is necessary a new coefficient named Time Domain Severity Factor (TDSF) was proposed by Casimiro Alvarez-Mariño & Xose M. Lopez-Fernandez.^[4][5][6]

The FDSF is calculated at transformer terminals and it is mathematically defined as

${\displaystyle \mathbf {FDSF(\omega )} ={\frac {\mathbf {{ESD}_{noStd}} (\omega )}{\mathbf {{ESD}_{envol}} (\omega )}}}$ 

where ω is the angular frequency, ESD_noStd(ω) is the maximum energy spectral density of the input no-standard transient voltage applied at transformer terminals and ESD_envol(ω) is the energy spectral density envelope for all standards dielectric tests at terminals.

The TDSF gives further detailed information on the severity supported by the transformer windings due to the transient event coming from the power system, regarding to the internal transient response due to dielectric tests in the time domain. The mathematical expression of this factor is

${\displaystyle \mathbf {TDSF(i)} ={\frac {\mathbf {{\Delta V}_{noStd}} (i)}{\mathbf {{\Delta V}_{envol}} (i)}}}$ 

where ∆V_noStd(i) is the maximum voltage drop along the ith dielectric path due to the no-standard transient events and ∆V_envol(i) is the maximum voltage drop along the same ith dielectric path for all standards dielectric tests.

• Transformer oil testing

Further reading edit

• F. R. Gadotti, S. H. L. Cabral and F. M. Schuartz (2022). Fast Transient Overvoltage Analysis in Current Transformers due to Disconnector Switching Operation. . 2022 7th International Advanced Research Workshop on Transformers (ARWtr). Vol. 1. p. 107458. doi:10.23919/ARWtr54586.2022.9959964.

• Chang-Hung Hsu (2022). Experimental results of electromechanical structure properties of noise and vibration on power transformers after lightning impulse test. . International Journal of Electrical Power & Energy Systems. Vol. 134. p. 58-63. doi:10.1016/j.ijepes.2021.107458.
• Yong Wang; Zhong Xu; Kai Zhou; Junxiang Liu; Qianwen Guo (2021). "On the Correlation Model between Extreme Disaster Weather and Distribution Transformer Fault Types". 2021 IEEE 10th Data Driven Control and Learning Systems Conference (DDCLS). . pp. 935–940. doi:10.1109/DDCLS52934.2021.9455668. ISBN 978-1-6654-2423-3.
• S.V. Kuzmin; E.V. Umetskaia; A.A. Zavalov (2020). Influence of Power Quality on Value of Switching Overvoltages in Networks 6-10kV. . pp. 1–4. doi:10.1109/FarEastCon50210.2020.9271527. ISBN 978-1-7281-6951-4.
• Marek Florkowski; Jakub Furgał; Maciej Kuniewski; Piotr Pająk (2020). Overvoltage Impact on Internal Insulation Systems of Transformers in Electrical Networks with Vacuum Circuit Breakers. Energies, vol. 13, pp. 6380, 2020. Energies. Vol. 13, no. 23. p. 6380. doi:10.3390/en13236380.
• Yaxun Guo; Xiaofeng Jiang; Yun Chen; Ming Zheng; Gang Liu; Xiaohua Li; Wenhu Tang (November 2020). Reignition overvoltages induced by vacuum circuit breakers and its suppression in offshore wind farms. International Journal of Electrical Power & Energy Systems, Vol. 122, 106227, 7 pages, November 2020. ISBN 0 471 05014 8). International Journal of Electrical Power & Energy Systems. Vol. 122. p. 106227. doi:10.1016/j.ijepes.2020.106227.
• J. McBride; T. Melle; X. M. Lopez-Fernandez; L. Coffeen; R. Degeneff; P. Hopkinson; B. Poulin; P. Riffon; A. Rocha; M. Spurlock; L. Wagenaar (2021). Investigation of the Interaction between Substation Transients and Transformers in HV and EHV Applications. . IEEE Transactions on Power Delivery. Vol. 36, no. 3. pp. 1768–1774. doi:10.1109/TPWRD.2020.3014595.
• Jakub Furgal; Maciej Kuniewski; Piotr Pajak (January 2020). Analysis of Internal Overvoltages in Transformer Windings during Transients in Electrical Networks. Energies Journal 13(10):2644, March 2020. (ISSN 1996-1073). Energies. Vol. 13, no. 10. p. 2644. doi:10.3390/en13102644.
• Marek Florkowski; Jakub Furgał; Maciej Kuniewski (January 2020). Propagation of Overvoltages in the Form of Impulse, Chopped and Oscillating Waveforms in Transformer Windings—Time and Frequency Domain Approach. Energies Journal 13(2):304, January 2020. (ISSN 1996-1073). Energies. Vol. 13, no. 2. p. 304. doi:10.3390/en13020304.
• Jim McBride; Xose M. Lopez-Fernandez; Casimiro Alvarez-Mariño. Integration of TDSF Analysis into TECAM Transformer on Line Monitoring System. ARWtr 2019 - 6th International Advanced Research Workshop on Transformers, pp. 54-58, Cordoba-Spain, Oct 2019.(ISBN 978-84-09-11168-8).
• M. Popov (August 2018). General approach for accurate resonance analysis in transformer windings. Electric Power Systems Research, Volume 161, August 2018, Pages 45-51. Electric Power Systems Research. Vol. 161. pp. 45–51. doi:10.1016/j.epsr.2018.04.002.
• Xose M. Lopez-Fernandez; Luis Rouco; Casimiro Alvarez-Mariño; Hugo Gago; Carlos Vila. A High Frequency Power Transformers Model for Network Studies and TDSF Monitoring (PDF). I47 CIGRE Session - CIGRE 2018, 10-pages París, France, Aug 2018.
• R. Oliveirs; P. Bokoro; W. Doorsamy. Investigation of Very Fast-Front Transient Overvoltages for Selection and Placement of Surge Arresters. 2018 Power Systems Computation Conference (PSCC).
• Marek Florkowsk; Jakub Furgał; Maciej Kuniewski; Piotr Pająk (2018). Comparison of transformer winding responses to standard lightning impulses and operational overvoltages. IEEE Transactions on Dielectrics and Electrical Insulation, Volume: 25, Issue: 3, June 2018. IEEE Transactions on Dielectrics and Electrical Insulation. Vol. 25, no. 3. pp. 965–974. doi:10.1109/TDEI.2018.007001.
• Haifeng Ye; Xiang Tian; Hao Wu; Yabo Li; Zhen Wu; Guoming MA. Research on Evaluation Method of Transient Overvoltage Hazard Based on S-Transform (PDF). 2nd International Symposium on Advances in Electrical, Electronics and Computer Engineering (ISAEECE 2017). Advances in Engineering Research (AER), volume 124.
• Luis Rouco; Xose M. Lopez-Fernandez; Casimiro Alvarez-Mariño; Hugo Gago. Fast Front Transients in Transformer Connected to Gas Insulated Substations: (White+Black) Box Models and TDSF Monitoring (PDF). ARWtr 2016 - 5th International Advanced Research Workshop on Transformers, pp. 175-183, Spain, Oct 2016. e-ARWtr2016 transformers book (ISBN 978-84-617-9183-5).
• Banda, Cedric Amittai. Electrical transient interaction between transformers and the power system: case study of an onshore wind farm (PDF). Ph.D Report 2016.
• Marek FLORKOWSKI; Jakub FURGAŁ; Maciej KUNIEWSKI; Piotr PAJĄK. Exposure Surge transformer insulation systems the impulse voltage test and operating conditions (in Polish) (PDF). PRZEGLĄD ELEKTROTECHNICZNY, ISSN 0033-2097, R. 92 NR 10/2016.
• S. M. Ghafourian; I. Arana; J. Holbøll; T. Sørensen; M. Popov; V. Terzija. General Analysis of Vacuum Circuit Breaker Switching Overvoltages in Offshore Wind Farms. IEEE Transactions on Power Delivery 2016.
• A Holdyk; B Gustavsen. External and Internal Overvoltages in a 100 MVA Transformer During High-Frequency Transients. International Conference on Power Systems Transients (IPST2015) in June 15–18, 2015. Cavtat, Croatia.
• Giuseppe Simioli. Transformers and electric grid transient interactions – The phenomena and some topics to consider in insulation design. Transformer Life Management Conference (TLM2014).