A Method for Reconstructing Transient Process Parameters in Critical Infrastructure Security Applications
Keywords:
Keywords: transient process, oscillogram, natural response, forced response, least squares method, critical infrastructures, security, VBA programming, Microsoft Excel, programmable logic controllers.
Abstract
Abstract. This paper addresses the reconstruction of transient process parameters from their oscillograms in the context of critical infrastructure security. It is shown that under real operating conditions the only available information on the dynamic state of electrical systems is often limited to recorded oscillograms, while the parameters of circuit elements may be unknown or vary over time. An engineering-oriented method for determining transient process parameters in first- and second-order circuits is proposed. The method is based on separating the forced and natural responses, forming a time series of the natural response, and subsequently estimating its parameters using logarithmic transformations, the least squares method, and numerical approximation techniques. The method is implemented as specialized software developed in Microsoft Excel using VBA. Numerical testing on a first-order circuit example demonstrated exact parameter recovery for noise-free oscillograms and maintained an accuracy of approximately 1% in the presence of disturbances simulating measurement errors. The obtained results confirm the practical applicability of the proposed approach for non-destructive testing, diagnostics, and improving the security of critical technical systems.
References
1. Hauer, J.F., Demeure, C.J. and Scharf, L.L. (1990). Initial results in Prony analysis of power system response signals’, IEEE Transactions on Power Systems, 5(1), pp. 80–89. doi:https://doi.org/10.1109/59.49090.
2. Darshana Prasad Wadduwage, Annakkage, U.D. and Krish Narendra (2015). Identification of dominant low‐frequency modes in ring‐down oscillations using multiple Prony models. IET generation, transmission & distribution, 9(15), pp.2206–2214. doi:https://doi.org/10.1049/iet-gtd.2014.0947.
3. Almunif, A., Fan, L. and Miao, Z. (2020). A tutorial on data-driven eigenvalue identification: Prony analysis, matrix pencil, and eigensystem realization algorithm, International Transactions on Electrical Energy Systems, 30(4). doi:https://doi.org/10.1002/2050-7038.12283.
4. Wang, H., Liu, R., Sui, Y., Qin, G., Wang, X. and Xing, H. (2025). Effective Time-Domain Reflectometry Measurement and Fault Location for Transmission Cables. 2025 IEEE 3rd International Conference on Sensors, Electronics and Computer Engineering (ICSECE), pp.1019–1023. doi:https://doi.org/10.1109/icsece65727.2025.11257131.
5. Hwang, J.K., Liu, Y. and others (2019). DFT-Based Identification of Oscillation Modes from PMU Transient Data, Energies, 12(22), 4357. doi:https://doi.org/10.3390/en12224357.
6. Shaw, S.R. and Leeb, S.B. (1999). Identification of induction motor parameters from transient stator current measurements. IEEE Transactions on Industrial Electronics, 46(1), pp. 139–149. doi:https://doi.org/10.1109/41.744405.
7. Lindenmeyer, D., Dommel, H.W., Moshref, A. and Kundur, P. (2001). An induction motor parameter estimation method, International Journal of Electrical Power & Energy Systems, [online] 23(4), pp. 251–262. doi:https://doi.org/10.1016/S0142-0615(00)00060-0.
8. Wang, Y. and Xu, W. (2015). Algorithms and field experiences for estimating transmission line parameters based on fault record data. IET Generation, Transmission & Distribution, 9(13), pp.1773–1781. doi:https://doi.org/10.1049/iet-gtd.2014.1092.
9. Bendjabeur, A., Kouadri, A. and Mekhilef, S. (2019). Novel technique for transmission line parameters estimation using synchronised sampled data. IET Generation, Transmission & Distribution, 14(3), pp.506–515. doi:https://doi.org/10.1049/iet-gtd.2019.0702.
10. Sarkar, T.K. and Pereira, O. (1995). Using the matrix pencil method to estimate the parameters of a sum of complex exponentials, IEEE Antennas and Propagation Magazine, 37(1), pp. 48–55. doi:https://doi.org/10.1109/74.370583.
11. ul Hassan, I., Panduru, K. and Walsh, P.J. (2025). Non-destructive testing methods for condition monitoring: A review of techniques and tools. Procedia Computer Science. [online] 257. 420-427. doi:https://doi.org/10.1016/j.procs.2025.03.055.
12. Secue, J.R. and Mombello, E. (2008). Sweep frequency response analysis (SFRA) for the assessment of winding displacements and deformation in power transformers, Electric Power Systems Research, 78(6), pp. 1119–1128. doi:https://doi.org/10.1016/j.epsr.2007.08.005.
13. Wan, Q., Li, Y., Yuan, R., Meng, Q. and Li, X. (2023). Fault Identification and Localization of a Time–Frequency Domain Joint Impedance Spectrum of Cables Based on Deep Belief . Sensors, 23(2), p.684. doi:https://doi.org/10.3390/s23020684.
14. Bandara, S., Rajeev, P. and Gad, E. (2023). A review on condition assessment technologies for power distribution infrastructure. Structure and Infrastructure Engineering, 20(11), pp.1834–1851. doi:https://doi.org/10.1080/15732479.2023.2177680.
15. Lukens, J.M., Passian, A., Yoginath, S., Law, K.J.H. and Dawson, J.A. (2022). Bayesian Estimation of Oscillator Parameters: Toward Anomaly Detection and Cyber-Physical System Security, Sensors, 22(16), p.6112. doi:https://doi.org/10.3390/s22166112.
16. Vite, O., Uribe, F. and López de Alba, C.A. (2024). Reconstruction of Harmonic and Transient Electrical Signals Through Compressed Sensing Technique. IEEE Access, 12, pp.175328–175337. doi:https://doi.org/10.1109/access.2024.3487933.
17. Jin, M., Li, H. and Liu, S. (2022). Identification and Compensation for D-Dot Measurement System in Transient Electromagnetic Pulse Measurement. Sensors, 22(21), p. 8538. doi:https://doi.org/10.3390/s22218538.
18. Eriksen, T. and Rehman, N. ur (2023). Data-driven nonstationary signal decomposition approaches: a comparative analysis. Scientific Reports, 13(1), 1798. doi:https://doi.org/10.1038/s41598-023-28390-w.
19. Karpilow, A., Derviškadić, A., Frigo, G. and Paolone, M. (2022). Step detection in power system waveforms for improved RoCoF and frequency estimation. Electric Power Systems Research, 212, p.108527. doi:https://doi.org/10.1016/j.epsr.2022.108527.
20. Fasig, J.L., White, C.K., Gilbert, B.K. and Haider, C.R. (2023). Introduction to Non-Invasive Current Estimation (NICE). [online] for Transient EventsarXiv.org. Available at: https://arxiv.org/abs/2301.10237. [Accessed 15 Dec. 2025]
21. Lundvall, A. and Sollie, V. (2021). Quantifying Middle Frequency Transient Currents in Power Consuming Devices. Master’s Programme in Renewable Electricity Production. Available at: https://www.diva-portal.org/smash/get/diva2:1580022/FULLTEXT01.pdf. [Accessed: 15 December 2025].
22. Tektronix (2017). TBS2000B Series Digital Oscilloscopes Programmer Manual. Available at: https://download.tek.com/manual/TBS2000-TBS2000B-Programmer-077114903.pdf. [Accessed: 15 December 2025].
23. User Manual. SDS1000X-E Series Digital oscilloscope UM0101X-E02B. Available at: https://siglent.com.pl/public/assets/SDS1104X-E_User_Manual_UM0101E-E02B.pdf. [Accessed: 15 December 2025].
24. RIGOL User Guide DS1000Z Series Digital Oscilloscope. (2019). Available at: https://cse.sc.edu/~adowney2/resources/data_sheets/Rigol_DS1054z_users_guide.pdf [Accessed: 15 December 2025].
2. Darshana Prasad Wadduwage, Annakkage, U.D. and Krish Narendra (2015). Identification of dominant low‐frequency modes in ring‐down oscillations using multiple Prony models. IET generation, transmission & distribution, 9(15), pp.2206–2214. doi:https://doi.org/10.1049/iet-gtd.2014.0947.
3. Almunif, A., Fan, L. and Miao, Z. (2020). A tutorial on data-driven eigenvalue identification: Prony analysis, matrix pencil, and eigensystem realization algorithm, International Transactions on Electrical Energy Systems, 30(4). doi:https://doi.org/10.1002/2050-7038.12283.
4. Wang, H., Liu, R., Sui, Y., Qin, G., Wang, X. and Xing, H. (2025). Effective Time-Domain Reflectometry Measurement and Fault Location for Transmission Cables. 2025 IEEE 3rd International Conference on Sensors, Electronics and Computer Engineering (ICSECE), pp.1019–1023. doi:https://doi.org/10.1109/icsece65727.2025.11257131.
5. Hwang, J.K., Liu, Y. and others (2019). DFT-Based Identification of Oscillation Modes from PMU Transient Data, Energies, 12(22), 4357. doi:https://doi.org/10.3390/en12224357.
6. Shaw, S.R. and Leeb, S.B. (1999). Identification of induction motor parameters from transient stator current measurements. IEEE Transactions on Industrial Electronics, 46(1), pp. 139–149. doi:https://doi.org/10.1109/41.744405.
7. Lindenmeyer, D., Dommel, H.W., Moshref, A. and Kundur, P. (2001). An induction motor parameter estimation method, International Journal of Electrical Power & Energy Systems, [online] 23(4), pp. 251–262. doi:https://doi.org/10.1016/S0142-0615(00)00060-0.
8. Wang, Y. and Xu, W. (2015). Algorithms and field experiences for estimating transmission line parameters based on fault record data. IET Generation, Transmission & Distribution, 9(13), pp.1773–1781. doi:https://doi.org/10.1049/iet-gtd.2014.1092.
9. Bendjabeur, A., Kouadri, A. and Mekhilef, S. (2019). Novel technique for transmission line parameters estimation using synchronised sampled data. IET Generation, Transmission & Distribution, 14(3), pp.506–515. doi:https://doi.org/10.1049/iet-gtd.2019.0702.
10. Sarkar, T.K. and Pereira, O. (1995). Using the matrix pencil method to estimate the parameters of a sum of complex exponentials, IEEE Antennas and Propagation Magazine, 37(1), pp. 48–55. doi:https://doi.org/10.1109/74.370583.
11. ul Hassan, I., Panduru, K. and Walsh, P.J. (2025). Non-destructive testing methods for condition monitoring: A review of techniques and tools. Procedia Computer Science. [online] 257. 420-427. doi:https://doi.org/10.1016/j.procs.2025.03.055.
12. Secue, J.R. and Mombello, E. (2008). Sweep frequency response analysis (SFRA) for the assessment of winding displacements and deformation in power transformers, Electric Power Systems Research, 78(6), pp. 1119–1128. doi:https://doi.org/10.1016/j.epsr.2007.08.005.
13. Wan, Q., Li, Y., Yuan, R., Meng, Q. and Li, X. (2023). Fault Identification and Localization of a Time–Frequency Domain Joint Impedance Spectrum of Cables Based on Deep Belief . Sensors, 23(2), p.684. doi:https://doi.org/10.3390/s23020684.
14. Bandara, S., Rajeev, P. and Gad, E. (2023). A review on condition assessment technologies for power distribution infrastructure. Structure and Infrastructure Engineering, 20(11), pp.1834–1851. doi:https://doi.org/10.1080/15732479.2023.2177680.
15. Lukens, J.M., Passian, A., Yoginath, S., Law, K.J.H. and Dawson, J.A. (2022). Bayesian Estimation of Oscillator Parameters: Toward Anomaly Detection and Cyber-Physical System Security, Sensors, 22(16), p.6112. doi:https://doi.org/10.3390/s22166112.
16. Vite, O., Uribe, F. and López de Alba, C.A. (2024). Reconstruction of Harmonic and Transient Electrical Signals Through Compressed Sensing Technique. IEEE Access, 12, pp.175328–175337. doi:https://doi.org/10.1109/access.2024.3487933.
17. Jin, M., Li, H. and Liu, S. (2022). Identification and Compensation for D-Dot Measurement System in Transient Electromagnetic Pulse Measurement. Sensors, 22(21), p. 8538. doi:https://doi.org/10.3390/s22218538.
18. Eriksen, T. and Rehman, N. ur (2023). Data-driven nonstationary signal decomposition approaches: a comparative analysis. Scientific Reports, 13(1), 1798. doi:https://doi.org/10.1038/s41598-023-28390-w.
19. Karpilow, A., Derviškadić, A., Frigo, G. and Paolone, M. (2022). Step detection in power system waveforms for improved RoCoF and frequency estimation. Electric Power Systems Research, 212, p.108527. doi:https://doi.org/10.1016/j.epsr.2022.108527.
20. Fasig, J.L., White, C.K., Gilbert, B.K. and Haider, C.R. (2023). Introduction to Non-Invasive Current Estimation (NICE). [online] for Transient EventsarXiv.org. Available at: https://arxiv.org/abs/2301.10237. [Accessed 15 Dec. 2025]
21. Lundvall, A. and Sollie, V. (2021). Quantifying Middle Frequency Transient Currents in Power Consuming Devices. Master’s Programme in Renewable Electricity Production. Available at: https://www.diva-portal.org/smash/get/diva2:1580022/FULLTEXT01.pdf. [Accessed: 15 December 2025].
22. Tektronix (2017). TBS2000B Series Digital Oscilloscopes Programmer Manual. Available at: https://download.tek.com/manual/TBS2000-TBS2000B-Programmer-077114903.pdf. [Accessed: 15 December 2025].
23. User Manual. SDS1000X-E Series Digital oscilloscope UM0101X-E02B. Available at: https://siglent.com.pl/public/assets/SDS1104X-E_User_Manual_UM0101E-E02B.pdf. [Accessed: 15 December 2025].
24. RIGOL User Guide DS1000Z Series Digital Oscilloscope. (2019). Available at: https://cse.sc.edu/~adowney2/resources/data_sheets/Rigol_DS1054z_users_guide.pdf [Accessed: 15 December 2025].
Published
2026-04-23
Section
Theoretical Electrical Engineering
This work is licensed under a Creative Commons Attribution 4.0 International License.
