1. bookVolume 23 (2012): Issue 1 (September 2012)
Journal Details
License
Format
Journal
eISSN
2083-4608
ISSN
1895-8281
First Published
26 Feb 2008
Publication timeframe
4 times per year
Languages
English
access type Open Access

Global Sensitivity Analysis of Multi-State Markov Reliability Models of Power Equipment Approximated by Polynomial Chaos Expansion / Analiza Globalnej Wrażliwości Wielostanowych Modeli Niezawodności Markowa Dla Urządzeń Energetycznych Aproksymowanych Za Pomocą Rozwinięcia W Chaos Wielomianowy

Published Online: 15 Nov 2013
Volume & Issue: Volume 23 (2012) - Issue 1 (September 2012)
Page range: 59 - 70
Journal Details
License
Format
Journal
eISSN
2083-4608
ISSN
1895-8281
First Published
26 Feb 2008
Publication timeframe
4 times per year
Languages
English
Abstract

Reliability and availability of electric power system equipment (e.g., generator units, transformers) are often evaluated by defining and solving Markov models. Transition rates among the identified equipment states are estimated from experimental and field data, or expert judgment, with inevitable uncertainty. For model understanding and to guide validation and confidence building, it is of interest to investigate the effects of the uncertainty in the input transition rates on the output reliability and availability. To this aim, Global Sensitivity Analysis (GSA) can be used for defining importance (sensitivity) indexes that allow a ranking of the transition rates with respect to their influence on the uncertainty in the output. In general, GSA requires a large number of model evaluations. In this paper, a metamodel is defined to estimate the performance index of interest (e.g. reliability or availability). The metamodel is built based on polynomial chaos expansion (PCE), a multidimensional polynomial model approximation whose coefficients are determined by evaluating the model in a reduced set of predetermined values of the input. The proposed approach is illustrated on a power generating unit.

Keywords

Słowa kluczowe

[1] Billinton R., Allan R.: "Reliability Evaluation of Engineering Systems", Second Edition, Plenum Press 199210.1007/978-1-4899-0685-4Search in Google Scholar

[2] Lisnianski A., Elmakias D., Laredo D., BenHaim H.: A multi-state Markov model for a short-term reliability analysis of a power generating unit, Reliability Engineering and System Safety, 2012, 98, ,1-610.1016/j.ress.2011.10.008Search in Google Scholar

[3] Billinton R, Fotuhi-Firuzabad M, Sidhu TS.: Determination of the optimum routine test and self checking intervals in protective relaying using a reliability model. IEEE Trans Power Syst 2002; 17(3).10.1109/TPWRS.2002.800871Search in Google Scholar

[4] Seyedi H, Fotuhi M, Sanaye-Pasand M.: An extended Markov model to determine the reliability of protective system. In: Power India conference, IEEE; April 1, 2006. p. 10-12.10.1109/POWERI.2006.1632549Search in Google Scholar

[5] Aminifar F, Firuzabad MF, Billinton R.: Extended reliability model of a unified power flow controller. Gener Transm Distrib IET 2007;1(6):896-903.10.1049/iet-gtd:20070089Search in Google Scholar

[6] Sefidgaran M., Mirzaie M., Ebrahimzadeh A.: Reliability model of the power transformer with ONAF cooling, Electrical Power and Energy Systems 35 (2012) 97-104Search in Google Scholar

[7] Do Van P., Barros A., Bérenguer C.: Reliability importance analysis of Markovian systems at steady state using perturbation analysis, Reliability Engineering and System Safety, 2008, 93, 1605-1615.10.1016/j.ress.2008.02.020Search in Google Scholar

[8] Do Van P., Barros A., Bérenguer C.: From differential to difference importance measures for Markov reliability models, European Journal of Operational Research, 2010, 513-52110.1016/j.ejor.2009.11.025Search in Google Scholar

[9] Zio E.: Computational Methods For Reliability And Risk Analysis, Series on Quality, Reliability & Engineering Statistics Vol 14, World Scientific Publishing Company, 200910.1142/7190Search in Google Scholar

[10] Marseguerra M., Padovani E., Zio E., Tarantola S., Saltelli A.: Sensitivity Analysis of a non-linear reliability model. Proceeding of the European Conference on Safety and Reliability ESREL 1998, Norway, 1998, pp. 1395-1401.Search in Google Scholar

[11] Aperjis, D., White D.C., Schweppe F.C., Mettler M., Merrill H.M.: Energy Strategy Planning for Electric Utilities Part II, Smarte Methodology Case Study. IEEE Transactions on Power Apparatus and Systems 1982, PAS-101(2): 347-355.10.1109/TPAS.1982.317113Search in Google Scholar

[12] Merrill, H.M. and Schweppe F.C.: Energy Strategy Planning for Electric Utilities Part II, Smarte Methodology. IEEE Transactions on Power Apparatus and Systems, 1982, PAS-101(2): 340-346.10.1109/TPAS.1982.317112Search in Google Scholar

[13] Rocco C.M.: Effects of transition-rate uncertainty on steady-state probabilities of Markov models using Interval Arithmetic, Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability April 2012 vol. 226 no. 2 234-24510.1177/1748006X11422624Search in Google Scholar

[14] Rocco C.M.: “Affine Arithmetic for assessing the uncertainty propagation on steady-state probabilities of Markov models due to uncertainties in transition rates”, submitted to Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability, 201210.1177/1748006X13485189Search in Google Scholar

[15] Saltelli A., Chan K., Scott E.M.: “Sensitivity Analysis”, John Wiley & Sons, Probability and Statistics series, 2000Search in Google Scholar

[16] Saltelli, A., Tarantola, S., Campolongo, F., Ratto, M.: “Sensitivity Analysis in Practice. A Guide to Assessing Scientific Models”, John Wiley & Sons, Probability and Statistics series, 2004Search in Google Scholar

[17] Campolongo F., Saltelli A., Cariboni J.: From screening to quantitative sensitivity analysis. A unified approach Computer Physics Communications 182 (2011) 978-988Search in Google Scholar

[18] Haro E., Anstett-Collin F., Basset M., Sensitivity study of dynamic systems using polynomial Chaos, Reliability Engineering and System Safety, 2012, 104 , pp. 15-2610.1016/j.ress.2012.04.001Search in Google Scholar

[19] Ghanem R., Spanos P. D., Polynomial chaos in stochastic finite elements, Journal of Applied Mechanics 57 (1990) 197-202.10.1115/1.2888303Search in Google Scholar

[20] Sudret B., Global sensitivity analysis using polynomial chaos expansions, Reliability Engineering and System Safety 93 (7) (2008) 964-979.10.1016/j.ress.2007.04.002Search in Google Scholar

[21] Crestaux T., Maitre O. L, Martinez J., Polynomial chaos expansion for sensitivity analysis, Reliability Engineering & System Safety 94 (2009) 1161-1172.10.1016/j.ress.2008.10.008Search in Google Scholar

[22] Oladyshkin S., Class H., Helmig R., Nowak W., A concept for data-driven uncertainty quantification and its application to carbon dioxide storage in geological formations, Advances in Water Resources 34 (2011) 1508-1518. doi:10.1016/j.advwatres.2011.08.005.10.1016/j.advwatres.2011.08.005Search in Google Scholar

[23] Saltelli, A., Ratto, M., Andres, T., Campolongo, F., Cariboni, J., Gatelli, D. Saisana, M., Tarantola, S.: “Global Sensitivity Analysis: The Primer”, John Wiley & Sons, 200810.1002/9780470725184Search in Google Scholar

[24] Wiener N., The homogeneous chaos, American Journal of Mathematics 60 (4) (1938) 897-936. 10.2307/2371268Search in Google Scholar

[25] Xiu D., Karniadakis G., The Wiener-Askey polynomials chaos for stochastic Differential equations, Journal of Scientific Computing 26 Volume 24 Issue 2, 2002, 619 - 644.10.1137/S1064827501387826Search in Google Scholar

[26] Petras K., Smolyak cubature of given polynomial degree with few nodes for increasing dimension, Numerische Mathematik, 2002, Volume 93, Number 4, Pages 729-75310.1007/s002110200401Search in Google Scholar

[27] Baudin M., Martinez J., Polynômes de chaos sous Scilab via librairie NISP, in: 42 emes Journees de Statistique, 2010.Search in Google Scholar

[28] Heiss F., Winschel V., Likelihood approximation by numerical integration on sparse grids, Journal of Econometrics, Volume 144, Issue 1, May 2008, Pages 62-80 10.1016/j.jeconom.2007.12.004Search in Google Scholar

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