A Stochastic Framework for Transmission Line Reliability Assessment Using Poisson Process Modeling
DOI:
https://doi.org/10.68104/ijasit.v1.i3.33Keywords:
transmission line reliability, poisson process, stochastic modeling, power system reliabilityAbstract
Transmission line reliability is essential for secure and continuous power system operation, as outages occur randomly due to aging, environmental stress, and operational conditions. This paper presents a stochastic reliability assessment approach based on Poisson process modeling to represent such random failure and repair behavior. Failure events are modeled using homogeneous and non-homogeneous Poisson processes with a Weibull intensity function, while repair times are described using probabilistic restoration models. Analytical expressions are obtained for key reliability indices, including reliability, mean time to failure, mean time to repair, availability, and loss-of-load probability. Using estimated parameters (β = 1.35, η = 1800 h), the mean time to failure is calculated as 1702 h and the mean time to repair as 12 h, resulting in a steady-state availability of 0.993 for a single transmission line. Results further show that series configurations reduce availability to 0.986, whereas parallel redundancy significantly enhances system performance, achieving availability levels above 0.9999. Statistical validation confirms the suitability of the proposed stochastic model for transmission line reliability evaluation. The framework offers a concise and effective analytical tool for reliability assessment and planning of modern power transmission systems.
Downloads
References
Billinton, R., & Allan, R. N. (1996). Reliability Evaluation of Power Systems (2nd ed.). New York, NY, USA: Plenum Press. doi:10.1007/978-1-4899-1860-4.
Hedman, K. W., O'Neill, R. P., Fisher, E. B., & Oren, S. S. (2009). Optimal transmission switching with contingency analysis. IEEE Transactions on Power Systems, 24(3), 1577–1586. doi:10.1109/TPWRS.2009.2020530.
Barlow, R. E., & Proschan, F. (1975). Statistical Theory of Reliability and Life Testing: Probability Models. New York, NY, USA: Holt, Rinehart and Winston.
Yang, S., Zhou, W., Zhu, S., Ye, L., & Li, H. (2019). Failure probability estimation of overhead transmission lines considering the spatial and temporal variation in severe weather. Journal of Modern Power Systems and Clean Energy, 7, 131–138. doi:10.1007/s40565-017-0370-4.
Zhang, D., Li, G., Bie, Z., & Fan, K. (2024). An analytical method for reliability evaluation of power distribution system with time-varying failure rates. Reliability Engineering & System Safety, 250, 110290. doi:10.1016/j.ress.2024.110290.
Filus, J., & Filus, L. (2014). Parameter dependence in stochastic modeling-Multivariate distributions. Applied Mathematics, 5, 928–940. doi:10.4236/am.2014.56088.
Makvand, S. B., Venkatesh, B., Cheng, D., & Yu, P. (2017). Probabilistic evaluation and planning of power transmission system reliability. IET Generation, Transmission & Distribution, 11(4), 1119–1125. doi:10.1049/iet-gtd.2016.0693.
Sansavini, G., Piccinelli, R., Golea, L. R., & Zio, E. (2014). A stochastic framework for uncertainty analysis in electric power transmission systems with wind generation. Renewable Energy, 64, 71–81. doi:10.1016/j.renene.2013.11.002.
Ovaere, M., Heylen, E., Proost, S., Deconinck, G., & Van Hertem, D. (2019). How detailed value of lost load data impact power system reliability decisions. Energy Policy, 132, 1064–1075. doi:10.1016/j.enpol.2019.06.058.
Billinton, R., & Li, W. (1994). Reliability Assessment of Electric Power Systems Using Monte Carlo Methods. New York, NY, USA: Plenum Press. doi:10.1007/978-1-4899-1346-3.
Billinton, R., & Tang, X. (2004). Selected considerations in utilizing Monte Carlo simulation in quantitative reliability evaluation of composite power systems. Electric Power Systems Research, 69(2–3), 205–211. doi:10.1016/j.epsr.2003.08.012.
Billinton, R., Sankarakrishnan, A., & Balu, N. R. (1995). A comparison of Monte Carlo simulation techniques for composite power system reliability assessment. IEEE Canadian Conference on Electrical and Computer Engineering, 145–150. doi:10.1109/WESCAN.1995.493961.
Billinton, R., & Sankarakrishnan, A. (1994). A system state transition sampling technique for reliability evaluation. Reliability Engineering & System Safety, 44(2), 131–134. doi:10.1016/0951-8320(94)90004-3.
Billinton, R., & Jonnavithula, A. (1997). Application of the state transition sampling technique to system reliability evaluation. Quality and Reliability Engineering International, 13(5), 311–315. doi:10.1002/(SICI)1099-1638
Billinton, R., & Li, W. (1991). Hybrid approach for reliability evaluation of composite generation and transmission systems using Monte-Carlo simulation and enumeration technique. IEE Proceedings C—Generation, Transmission and Distribution, 138(3), 233–241. doi:10.1049/ip-c.1991.0029.
Gbadamosi, S. L., & Nwulu, N. I. (2020). Reliability assessment of composite generation and transmission expansion planning incorporating renewable energy sources. Journal of Renewable and Sustainable Energy, 12(2), 026301. doi:10.1063/1.5119244.
Kumar, S., Saket, R. K., Dheer, D. K., Holm-Nielsen, J. B., & Sanjeevikumar, P. (2020). Reliability enhancement of electrical power system including impacts of renewable energy sources: A comprehensive review. IET Generation, Transmission & Distribution, 14(10), 1799–1815. doi:10.1049/iet-gtd.2019.1402.
Beyza, J., & Yusta, J. M. (2021). The effects of the high penetration of renewable energies on the reliability and vulnerability of interconnected electric power systems. Reliability Engineering & System Safety, 215, 107881. doi:10.1016/j.ress.2021.107881.
Ghazal, H. M., & Khan, U. A. (2026). A comprehensive review of modern transmission expansion planning. Energy Reports, 15, 109313. doi:10.1016/j.egyr.2026.109313.
Gorman, W. (2022). The quest to quantify the value of lost load: A critical review of the economics of power outages. The Electricity Journal, 35(8), 107187. doi:10.1016/j.tej.2022.107187.
Downloads
Published
Issue
Section
License
Copyright (c) 2026 Md.Taukir Ahmed, Mst.Suraiya Sultana
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
