Wind and Structures

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Integrating physics-based fragility for hierarchical spectral clustering for resilience assessment of power distribution systems under extreme winds

  • Jintao Zhang (Department of Civil Engineering, University of Connecticut) ;
  • Wei Zhang (Department of Civil Engineering, University of Connecticut) ;
  • William Hughes (Department of Civil Engineering, University of Connecticut) ;
  • Amvrossios C. Bagtzoglou (Department of Civil Engineering, University of Connecticut)
  • Received : 2022.03.23
  • Accepted : 2024.05.23
  • Published : 2024.07.25
⟨ Previous Next ⟩

Abstract

Widespread damages from extreme winds have attracted lots of attentions of the resilience assessment of power distribution systems. With many related environmental parameters as well as numerous power infrastructure components, such as poles and wires, the increased challenge of power asset management before, during and after extreme events have to be addressed to prevent possible cascading failures in the power distribution system. Many extreme winds from weather events, such as hurricanes, generate widespread damages in multiple areas such as the economy, social security, and infrastructure management. The livelihoods of residents in the impaired areas are devastated largely due to the paucity of vital utilities, such as electricity. To address the challenge of power grid asset management, power system clustering is needed to partition a complex power system into several stable clusters to prevent the cascading failure from happening. Traditionally, system clustering uses the Binary Decision Diagram (BDD) to derive the clustering result, which is time-consuming and inefficient. Meanwhile, the previous studies considering the weather hazards did not include any detailed weather-related meteorologic parameters which is not appropriate as the heterogeneity of the parameters could largely affect the system performance. Therefore, a fragility-based network hierarchical spectral clustering method is proposed. In the present paper, the fragility curve and surfaces for a power distribution subsystem are obtained first. The fragility of the subsystem under typical failure mechanisms is calculated as a function of wind speed and pole characteristic dimension (diameter or span length). Secondly, the proposed fragility-based hierarchical spectral clustering method (F-HSC) integrates the physics-based fragility analysis into Hierarchical Spectral Clustering (HSC) technique from graph theory to achieve the clustering result for the power distribution system under extreme weather events. From the results of vulnerability analysis, it could be seen that the system performance after clustering is better than before clustering. With the F-HSC method, the impact of the extreme weather events could be considered with topology to cluster different power distribution systems to prevent the system from experiencing power blackouts.

Keywords

Acknowledgement

The authors gratefully acknowledge the data and support of Eversource Energy, Connecticut, and the Eversource Energy Center at the University of Connecticut. Disclaimer: The views and opinions expressed in this article are those of the authors and do not necessarily reflect the official policy or position of Eversource or any other agency.

References

  1. ANSI-O5.1. (2002), Wood Poles Specifications and Dimensions, Alliance for Telecommunications Industry Solutions, Washington, DC, USA.
  2. ASCE (2013), Minimum Design Loads for Buildings and Other Structures. ASCE/SEI 7-16, Reston, VA, USA.
  3. Brandi, G. and Di Matteo, T. (2021), "Higher-order hierarchical spectral clustering for multidimensional data", Int. Conference Comput. Sci., 12746, 387-400. https://doi.org/10.1007/978-3-030-77977-1_31. 
  4. Bruffaerts, R., Gors, D., Barcenas Gallardo, A., Vandenbulcke, M., Van Damme, P., Suetens, P., Van Swieten, J.C., Borroni, B., Sanchez-Valle, R., Moreno, F. and Laforce Jr, R. (2022), "Hierarchical spectral clustering reveals brain size and shape changes in asymptomatic carriers of C9orf72", Brain Commun., 4(4), https://doi.org/10.1093/braincomms/fcac182. 
  5. Bryant, R.E. (1986), "Graph-based algorithms for boolean function manipulation", IEEE Transact. Comput., C-35(8), 677-691. https://doi.org/10.1109/TC.1986.1676819. 
  6. Davidson, R., Liu, H., Sarpong, I., Sparks, P. and Rosowsky, D. (2003), "Electric power distribution system performance in Carolina Hurricanes", Nat. Haz. Rev., 4(1), 36-45. https://doi.org/10.1061/(ASCE)1527-6988(2003)4:1(36). 
  7. Davodi, M., Reihani, E. and Davodi, M. (2010), "Application of hierarchical clustering method for separation of power system". Int. J. Power Energy Conversion, 2(3), 279-288. https://doi.org/10.1504/IJPEC.2010.037632. 
  8. Der Kiureghian, A., Lin, H. and Hwang, S. (2008), "Second-order reliability approximations", J. Eng. Mech., 113(8), 1208-1225. https://doi.org/10.1007/s00158-021-03013-y. 
  9. Dey, P., Mehra, R., Kazi, F., Wagh, S. and Singh, N.M. (2016), "Impact of topology on the propagation of cascading failure in power grid", IEEE Transact. Smart Grid, 7(4), 1970-1978. https://doi.org/10.1109/TSG.2016.2558465. 
  10. Ding, L., Gonzalez-Longatt, F.M., Wall, P. and Terzija, V. (2013), "Two-step spectral clustering controlled islanding algorithm", IEEE Transact. Power Syst., IEEE, 28(1), 75-84. https://doi.org/10.1109/PESMG.2013.6672655. 
  11. Everitt, B.S., Landau, S., Leese, M. and Stahl, D. (2011), Cluster Analysis. Wiley Series in Probability and Statistics, John Wiley & Sons, Ltd, Chichester, UK. 
  12. Faza, A.Z., Sedigh, S. and McMillin, B.M. (2009), "Reliability analysis for the advanced electric power grid: From cyber control and communication to physical manifestations of failure", In Computer Safety, Reliability, and Security: 28th International Conference, 5775 LNCS, 257-269. https://doi.org/10.1007/978-3-642-04468-7_21. 
  13. Galili, T. (2015), "Dendextend: An R package for visualizing, adjusting and comparing trees of hierarchical clustering", Bioinformatics, 31(22), 3718-3720. https://doi.org/10.1093/bioinformatics/btv428. 
  14. Gonen, T. (2008), Electric Power Distribution System Engineering, Taylor & Francis Group, Boca Raton, FL, USA.
  15. Gors, D., Suetens, P., Vandenberghe, R. and Claes, P. (2017), "Hierarchical spectral clustering of MRI for global-to-local shape analysis: Applied to brain variations in Alzheimer's disease", Proceedings - International Symposium on Biomedical Imaging, 787-791. https://doi.org/10.1109/ISBI.2017.7950636. 
  16. Han, S., Rosowsky, D. and Guikema, S. (2014), "Integrating models and data to estimate the structural reliability of utility poles during hurricanes", Risk Analysis, 34(6), 1079-1094. https://doi.org/10.1111/risa.12102. 
  17. He, X., Cai, D., Shao, Y., Bao, H. and Han, J. (2011), "Laplacian regularized Gaussian mixture model for data clustering", IEEE Transact. Knowledge Data Eng., 23(9), 1406-1418. https://doi.org/10.1109/TKDE.2010.259. 
  18. Hines, P., Cotilla-Sanchez, E. and Blumsack, S. (2010), "Do topological models provide good information about electricity infrastructure vulnerability?", Chaos, 20(3). https://doi.org/10.1063/1.3489887. 
  19. Hohenbichler, M. and Rackwitz, R. (1982), "First-order concepts in system reliability", Struct. Safety, 1(3), 177-188. https://doi.org/10.1016/0167-4730(82)90024-8. 
  20. Hohenbichler, M. and Rackwitz, R. (2008), "Improvement of second-order reliability estimates by importance sampling", J. Eng. Mech., 114(12), 2195-2199. https://doi.org/10.1061/(ASCE)0733-9399(1988)114:12(2195). 
  21. Karamlou, A. and Bocchini, P. (2017), "Functionality-fragility surfaces", Earthq. Eng. Struct. Dyn., 46(10), 1687-1709. https://doi.org/10.1002/eqe.2878. 
  22. Koc, Y., Warnier, M., Van Mieghem, P., Kooij, R.E. and Brazier, F. M.T. (2014), "A topological investigation of phase transitions of cascading failures in power grids", Physica A: Statistic. Mech. Appl., 415, 273-284. https://doi.org/10.1016/j.physa.2014.07.083. 
  23. Koutsourelakis, P.S. (2010), "Assessing structural vulnerability against earthquakes using multi-dimensional fragility surfaces: A Bayesian framework", Probab. Eng. Mech., 25(1), 49-60. https://doi.org/10.1016/j.probengmech.2009.05.005. 
  24. Li, G., Zhang, P., Luh, P.B., Li, W., Bie, Z., Serna, C. and Zhao, Z. (2014), "Risk analysis for distribution systems in the northeast U.S. under wind storms", IEEE Transact. Power Syst., IEEE, 29(2), 889-898. https://doi.org/10.1109/PESGM.2014.6939519. 
  25. Liu, H., Davidson, R.A., Rosowsky, D.V. and Stedinger, J.R. (2005), "Negative binomial regression of electric power outages in hurricanes", J. Infrastruct. Syst., 11(4), 258-267. https://doi.org/10.1061/(ASCE)1076-0342(2005)11:4(258). 
  26. Liu, L., Liu, W., Cartes, D.A. and Chung, I.Y. (2009), "Slow coherency and Angle Modulated Particle Swarm Optimization based islanding of large-scale power systems", Adv. Eng. Inform., 23(1), 45-56. https://doi.org/10.1109/IJCNN.2007.4371280. 
  27. Lloyd, S.P. (1982), "Least squares quantization in PCM", IEEE Transact. Inform. Theory, 28(2), 129-137. https://doi.org/10.1109/TIT.1982.1056489. 
  28. Maier, H.R., Lence, B.J., Tolson, B.A. and Foschi, R.O. (2001), "First-order reliability method for estimating reliability, vulnerability, and resilience", Water Resources Res., 37(3), 779-790. https://doi.org/10.1029/2000WR900329. 
  29. Mall, R., Langone, R. and Suykens, J.A.K. (2014), "Multilevel hierarchical kernel spectral clustering for real-life large scale complex networks", PLoS ONE, 9(6). https://doi.org/10.1371/journal.pone.0099966. 
  30. Maurizio, F., Francesco, C., Francesco, M. and Stefano, R. (2008), "A survey of kernel and spectral methods for clustering", Pattern Recognition, 41(1), 176-190. https://doi.org/10.1016/j.patcog.2007.05.018. 
  31. Mohammadi Darestani, Y. and Shafieezadeh, A. (2019), "Multi-dimensional wind fragility functions for wood utility poles", Eng. Struct., 183(January), 937-948. https://doi.org/10.1016/j.engstruct.2019.01.048. 
  32. NESC (2015), National Electrical Safety Code. Scientific American, New York, NY, USA. 
  33. Ng, A.Y., Jordan, M.I. and Weiss, Y. (2002), "On spectral clustering: Analysis and an algorithm", Adv. Neural Inform. Processing Syst., 1017-1024. 
  34. Ortega, F. and Taspinar, S. (2018), "Rising sea levels and sinking property values: Hurricane Sandy and New York's housing market", J. Urban Economics, 106, 81-100. https://doi.org/10.1016/j.jue.2018.06.005. 
  35. Peng, R., Sun, H. and Zanetti, L. (2015), "Partitioning well-clustered graphs: Spectral clustering works!", J. Machine Learning Res., 40(2015), https://doi.org/10.1137/15M1047209. 
  36. Rocchetta, R. and Patelli, E. (2018), "Assessment of power grid vulnerabilities accounting for stochastic loads and model imprecision", Int. J. Electrical Power Energy Systems, 98(May 2017), 219-232. https://doi.org/10.1016/j.ijepes.2017.11.047. 
  37. Rokach, L. and Maimon, O. (2010), Chapter 15- Clustering methods. The Data Mining and Knowledge Discovery Handbook. Springer, Boston, MA, USA. 
  38. Rosato, V., Bologna, S. and Tiriticco, F. (2007), "Topological properties of high-voltage electrical transmission networks", Electric Power Syst. Res., 77(2), 99-105. https://doi.org/10.1016/j.epsr.2005.05.013. 
  39. Sanchez-Garcia, R.J., Fennelly, M., Norris, S., Wright, N., Niblo, G., Brodzki, J. and Bialek, J.W. (2014), "Hierarchical spectral clustering of power grids", IEEE Transact. Power Syst., 29(5), 2229-2237. https://doi.org/10.1109/TPWRS.2014.2306756. 
  40. Shafieezadeh, A., Onyewuchi, U.P., Begovic, M.M. and Desroches, R. (2014), "Age-dependent fragility models of utility wood poles in power distribution networks against extreme wind hazards", IEEE Transact. Power Delivery, 29(1), 131-139. https://doi.org/10.1109/TPWRD.2013.2281265. 
  41. Shi, J. and Malik, J. (2000), "Normalized cuts and image segmentation", IEEE Transact. Pattern Anal. Machine Intell., 22(8), 888-905. https://doi.org/10.1109/34.868688. 
  42. Short, J.R. (2016), "A perfect storm: Climate change, the power grid, and regulatory regime change after network failure", Environ. Planning C: Govern. Policy, 34(2), 244-261. https://doi.org/10.1177/0263774X15614185. 
  43. Skamarock, W.C., Klemp, J.B., Dudhia, J., Gill, D.O., Barker, D. M., Duda, M.G. and Powers, J.G. (2008), A Description of the Advanced Research WRF Version 3. NCAR Technical Note, 475(125), 10-5065. 
  44. Spemannstr, B.C. (2007), "A tutorial on spectral clustering", Statistic. Comput., 1-32. https://doi.org/10.1007/s11222-007-9033-z. 
  45. Spencer, N.H. (2013), Essentials of Multivariate Data Analysis. Essentials of Multivariate Data Analysis, Chapman and Hall/CRC, Boca Raton, FL, USA. 
  46. Sun, K., Zheng, D.Z. and Lu, Q. (2003), "Splitting strategies for islanding operation of large-scale power systems using OBDD-based methods", IEEE Transact. Power Syst., 18(2), 912-923. https://doi.org/10.1109/TPWRS.2003.810995. 
  47. Tiryaki, S. and Hamzacebi, C. (2014), "Predicting modulus of rupture (MOR) and modulus of elasticity (MOE) of heat treated woods by artificial neural networks", Measure. J. Int. Measure. Confederation, 49(1), 266-274. https://doi.org/10.1016/j.measurement.2013.12.004. 
  48. Vickery, P.J., Twisdale, L.A., Montpellier, P. and Steckley, A.C. (1996), Hurricane Vulnerability and Risk Analysis of the VINLEC Transmission and Distribution System. 
  49. Von Luxburg, U. (2007), "A tutorial on spectral clustering", Statistics Comput., 17(4), 395-416. https://doi.org/10.1007/s11222-007-9033-z. 
  50. Wang, F., Chen, P., Zhen, Z., Yin, R., Cao, C., Zhang, Y. and Duic, N. (2022), ""Dynamic spatio-temporal correlation and hierarchical directed graph structure based ultra-short-term wind farm cluster power forecasting method", Appl. Energy, 323. https://doi.org/10.1016/j.apenergy.2022.119579. 
  51. Wei, N., La, J. De, Lopez, R. and Centeno, V.A. (2016), "A line outage study for prediction of static power flow redistribution by", Ph.D. Dissertation, Virginia Polytechnic Institute and State University, Blacksburg. 
  52. Wolfe, R. and Moody, R. (1997), "Standard specifications for wood poles", 1997 Utility Pole Structures Conference and Trade Show, 1924. 
  53. Yang, X., Yu, W., Wang, R., Zhang, G. and Nie, F. (2020), "Fast spectral clustering learning with hierarchical bipartite graph for large-scale data", Pattern Recognition Lett., 130, 345-352. https://doi.org/10.1016/j.patrec.2018.06.024. 
  54. Yuan, H., Zhang, W., Zhu, J. and Bagtzoglou, A.C. (2018), "Resilience assessment of overhead power distribution system under strong winds for hardening prioritization", ASCE-ASME J. Risk Uncertainty Eng. Syst., Part A: Civil Eng., 4(Dagher 2006), 1-10. https://doi.org/10.1061/AJRUA6.0000988. 
  55. Zha, H., Ding, C., Gu, M., He, X. and Simon, H. (2001), "Spectral relaxation for k-means clustering", Adv. Neural Inform. Processing Syst., 14, 1057-1064. 
  56. Zhao, Q., Sun, K., Zheng, D.Z., Ma, J. and Lu, Q. (2003), "A study of system splitting strategies for island operation of power system: A two-phase method based on OBDDs", IEEE Transact. Power Syst., 18(4), 1556-1565. https://doi.org/10.1109/TPWRS.2003.818747.