Severity factor

A severity factor is established as a coefficient to assess the dielectric severity supported by a transformer winding considering the incoming transient overvoltage (voltage spike). It determines the safety margin regarding to the standard acceptance tests either in the frequency or time domain.

Severity factors are a newly concept for analyzing the dielectric severity supported along transformer windings when a transformer is submitted to a non-standardized transient voltage waveform induced from the power system.

Two are the new factors considered for evaluating the severity supported by the insulation windings both in factory and in service. One factor is called Time Domain Severity Factor (TDSF) and another one is the Frequency Domain Severity Factor (FDSF).

Background

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]

Frequency Domain Severity Factor (FDSF)

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.

Time Domain Severity Factor (TDSF)

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.

See also

• Transformer oil testing

References

1. R. Malewski, J. Douville, L. Lavallee, "Measurement of Switching Transients in 735 kV Substations and Assessment of their Severity for Transformer Insulation," IEEE Transactions on Power Delivery, vol.3, no.4, pp.1380-1390, Oct. 1988.
2. Asano, R., Rocha, A., Bastos, G. M., “Electrical Transient Interaction Between Transformers and the Power System”, CIGRÉ A2-D1 Colloquium, Brugge, Belgium, October 2007.
3. A. C. O. Rocha, “Electrical Transient Interaction Between Transformers and the Power Systems”, CIGRÉ Session 2008, pp. 1-10, Paris France, August 2008.
4. Joint Working Group SC A2 CIGRÉ, "Electrical Transient Interaction between Transformers and Power Systems Archived 2014-11-29 at the Wayback Machine", Technical Brochure JWGA2/C439, Part-1 Expertise&Part-2 Case Studies, April 2014
5. Álvarez‐Mariño, Casimiro; Lopez‐Fernandez, Xose M.; Jacomo Ramos, Antonio J.M.; Castro Lopes, Ricardo A.F.; Miguel Duarte Couto, José (2012). "Time domain severity factor (TDSF)". Compel - the International Journal for Computation and Mathematics in Electrical and Electronic Engineering. 31 (2): 670–681. doi:10.1108/03321641211200644.
6. Xose m. Lopez-Fernandez and Casimiro Alvarez-Mariño, "Induced Transient Voltage Performance Between Transformers and VCB. Severity Factors and Case Studies,"IEEE Transactions on Power Delivery, Issue 99., April 2015.

Further reading

• S.V. Kuzmin; E.V. Umetskaia; A.A. Zavalov. Influence of Power Quality on Value of Switching Overvoltages in Networks 6-10kV. 2020 International Multi-Conference on Industrial Engineering and Modern Technologies (FarEastCon). 4 pages , October 2020. (ISSN 978-1-7281-6951).
• Yaxun Guo; Xiaofeng Jiang; Yun Chen; Ming Zheng; Gang Liu; Xiaohua Li; Wenhu Tang. 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).
• J. McBride; T. Melle; X. M. Lopez-Fernandez; L. Coffeen; R. Degeneff; P. Hopkinson; B. Poulin; P. Riffon; A. Rocha; M. Spurlock; L. Wagenaar. Investigation of the Interaction between Substation Transients and Transformers in HV and EHV Applications. IEEE Transactions on Power Delivery ( Early Access ), 06 August 2020, DOI: 10.1109/TPWRD.2020.3014595.
• Jakub Furgal; Maciej Kuniewski; Piotr Pajak. Analysis of Internal Overvoltages in Transformer Windings during Transients in Electrical Networks. Energies Journal 13(10):2644, March 2020. (ISSN 1996-1073).
• Marek Florkowski; Jakub Furgał; Maciej Kuniewski. 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).
• 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. General approach for accurate resonance analysis in transformer windings. Electric Power Systems Research, Volume 161, August 2018, Pages 45-51.
• 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).
• 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).