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 voltagewaveforminduced 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).
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
where ω is the angular frequency, ESDnoStd(ω) is the maximum energyspectral density of the input no-standard transient voltage applied at transformer terminals and ESDenvol(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
where ∆VnoStd(i) is the maximum voltage drop along the ith dielectric path due to the no-standard transient events and ∆Venvol(i) is the maximum voltage drop along the same ith dielectric path for all standards dielectric tests.
^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.
^Asano, R., Rocha, A., Bastos, G. M., “Electrical Transient Interaction Between Transformers and the Power System”, CIGRÉ A2-D1 Colloquium, Brugge, Belgium, October 2007.
^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.
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.
