Skip to main content
SpringerLink
Log in

MSS Models of Smart Grids with Multi-level Degradation and Recovery

  • Chapter
  • First Online:
Green IT Engineering: Concepts, Models, Complex Systems Architectures

Part of the book series: Studies in Systems, Decision and Control ((SSDC,volume 74))

Abstract

Digital substations (DS) of smart grid are complex multi-component maintained systems, consisting of a lot of hardware and software components. Failures of the components cause functional and parametrical degradation of the substations. According with systems (DS) structure the reliability-block diagram (RBD), the structure function and the structure function and the Direct Partial Logical Derivatives (DPLDs) for RMSS “electronic transformers—merging unit” are considered. The mathematical tool of logical differential calculus and DPLD in particular are used in many application problems. One of them is reliability engineering. The principal condition of the DPLD application in reliability analysis is the representation of system under investigation by the structure function. We consider the calculation some of these measures as structural, Birnbaum’s, and criticality for the analysis of the electronic transformers—merging unit. The structure function of this unit based on the operation conditions of this system (unit). The construction of this function allows estimating the most important components of this system in stationary state through structural, Birnbaum’s, and criticality importance measures. According with developed technique an example of DS availability model is presented and discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Levitin, G., Lisnianski, A., Haim, H.: Redundancy optimization for series-parallel multi-state systems. IEEE Trans. Reliab. 47(2), 165–172 (1998)

    Article  Google Scholar 

  2. Gurler, U., Kaya, A.: A maintenance policy for a system with multi-state components: an approximate solution. Reliab. Eng. Syst. Saf. 76, 117–127 (2002)

    Article  Google Scholar 

  3. Huang, C., Yuan, J.: A two-stage preventive maintenance policy for a multi-state deterioration system. Reliab. Eng. Syst. Saf. 95(11), 1255–1260 (2010)

    Article  Google Scholar 

  4. Isaac, W., Nourelfath, M., Daoud, A.: Performance evaluation of multi-state degraded systems with minimal repairs and imperfect preventive maintenance. Reliab. Eng. Syst. Saf. 95(2), 65–69 (2010)

    Article  Google Scholar 

  5. Nahas, N., Khatab, A., Daoud, A.: Extended great deluge algorithm for the imperfect preventive maintenance optimization of multi-state systems. Reliab. Eng. Syst. Saf. 93(11), 1658–1672 (2008)

    Article  Google Scholar 

  6. Tan, C., Raghavan, N.: A framework to practical predictive maintenance modeling for multi-state systems. Reliab. Eng. Syst. Saf. 93(8), 1138–1150 (2008)

    Article  Google Scholar 

  7. Nourelfath, M., Dutuit, Y.: A combined approach to solve the redundancy optimization problem for multi-state systems under repair policies. Reliab. Eng. Syst. Saf. 86(3), 205–213 (2004)

    Article  Google Scholar 

  8. Yingkui, G., Jing, L.: Multi-state system reliability: a new and systematic Review. Procedia. Eng. 29, 531–536 (2012)

    Article  Google Scholar 

  9. Albasrawi, M., Jarus, N., Joshi, K., Sarvestani, S.: Analysis of Reliability and Resilience for Smart Grids. In: Proceedings of IEEE 38th Annual on Computer Software and Applications Conference (COMPSAC), pp. 529–534 (2014)

    Google Scholar 

  10. Zio, E.: Reliability Engineering: Old Problems and New Challenges. Reliab. Eng. Syst. Saf. 94, 125–141 (2009)

    Article  Google Scholar 

  11. Praks, P., Kopustinskas, V.: Monte-Carlo based Reliability Modelling of a Gas Network using Graph Theory Approach. In: 2014 Ninth International Conference on Availability, Reliability and Security. IEEE, pp. 380–386 (2014)

    Google Scholar 

  12. Zaitseva, E., Levashenko, V., Rusin, M.: Reliability Analysis of Healthcare System. In: 2011 Federated Conference on Computer Science and Information Systems FedCSIS 2011. IEEE, pp. 169–175 (2011)

    Google Scholar 

  13. Rausand, M., Høyland, A.: System Reliability Theory. John Wiley and Sons Inc, Haboken, NJ (2004)

    MATH  Google Scholar 

  14. Murchland, J.D.: Fundamental Concepts and Relations for Reliability Analysis of Multistate System. In: Reliability and Fault Tree Analysis, Theoretical and Applied Aspects of System Reliability. SIAM, pp. 581–618 (1975)

    Google Scholar 

  15. Barlow, R.E., Wu, A.S.: Coherent Systems with Multi-State Components. Math. Oper. Res. 3, 275–281 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  16. Hudson, J.C., Kapur, K.C.: Modules in Coherent Multistate Systems. IEEE Trans. Reliab. 32, 183–185 (1983)

    Article  MATH  Google Scholar 

  17. Lisnianski, A., Levitin, G.: Multi-state system reliability. assessment, optimization and applications. World Scientific, Singapore, SG (2003)

    Google Scholar 

  18. Xie, M., Dai, Y.-S., Poh, K.-L.: Multi-state system reliability. In: Computing system reliability. Models and Analysis. Kluwer Academic Publishers, New York, NY, 207–237 (2004)

    Google Scholar 

  19. Levitin, G., Lisnianski, A.: Optimization of imperfect preventive maintenance for multi-state system. Reliab. Eng. Syst. Saf. 67, 193–203 (2000)

    Article  Google Scholar 

  20. Zio, E., Marella, M., Podofillini, L.: A monte carlo simulation approach to the availability assessment of multi-state systems with operational dependencies. Reliab. Eng. Syst. Saf. 92, 871–882 (2007)

    Article  Google Scholar 

  21. Caldarola, L.: Coherent system with multi-state components. Nucl. Eng. Des. 58, 127–139 (1980)

    Article  Google Scholar 

  22. Veeraraghavan, M., Trivedi, K.S.: A combinatorial algorithm for performance and reliability analysis using multistate models. IEEE Trans. Comput. 43, 229–234 (1994)

    Article  Google Scholar 

  23. Reinske, K., Ushakov, I.: Application of graph theory for reliability analysis. Radio i Sviaz, Moscow, USSR (1988). (in Russian)

    Google Scholar 

  24. Zaitseva, E.: Reliability analysis of multi-state system. Dyn. Syst. Geom. Theor. 1, 213–222 (2003)

    MathSciNet  MATH  Google Scholar 

  25. Zaitseva, E., Levashenko, V., Kostlny, J., Kvassay M.: Analysis of Boundary States of Multi-State System by Direct Partial Logic Derivatives. In: Proceedings of 11th International Conference on ICT in Education, Research and Industrial Applications: Integration, Harmonization and Knowledge Transfer, CEUR Workshop, pp. 1356 (2015)

    Google Scholar 

  26. Miller, M.D., Thornton, M.A.: Multiple valued logic: concepts and representations. Morgan and Claypool Publishers, Synthesis Lectures on Digital Circuits and systems (2008)

    Google Scholar 

  27. Zaitseva, E., Levashenko, V.: Multiple-valued logic mathematical approaches for multi-state system reliability analysis. J. Appl. Logic 11, 350–362 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  28. Kvassay, M., Zaitseva, E., Levashenko, V.: Minimal cut sets and direct partial logic derivatives in reliability analysis, In: Proceedings of the Safety and Reliability: Methodology and Applications European Safety and Reliability Conference. CRC Press, pp. 241–248 (2014)

    Google Scholar 

  29. Kołowrocki, K.: Reliability of large and complex systems. Elsevier (2014)

    Google Scholar 

  30. Hung, J., Zuo, M.J.: Multi-State k-out-of-n System Model and its Applications. In: Ann. Reliability & Maintainability Symp. IEEE Pres, New York, 264–268 (2000)

    Google Scholar 

  31. Boedigheimer, R.A., Kapur, K.C.: Customer-Driven Reliability Models for Multistate Coherent Systems. IEEE Trans. Reliab. 43, 46–50 (1994)

    Article  Google Scholar 

  32. Nikolaidis, E. Ghiocel, D. M. Singhal, S. (eds.): Engineering Design Reliability, CRC Press (2005)

    Google Scholar 

  33. Natvig, B.: Multistate systems reliability theory with applications. Wiley, New York (2011)

    Book  MATH  Google Scholar 

  34. Ramirez-Marquez, J.E., Coit, D.W., Tortorella, M.: A generalized multistate based path vector approach for multistate two-terminal reliability. IIE Trans. 38, 477–488 (2006)

    Article  Google Scholar 

  35. Kuo, W., Zhu, X.: Importance measures in reliability, risk, and optimization: principles and applications, Wiley (2012)

    Google Scholar 

  36. Nourelfath, M., Chatelet, E., Nahas, N.: Joint redundancy and imperfect preventive maintenance optimization for series–parallel multi-state degraded systems. Reliab. Eng. Syst. Saf. 103, 51–60 (2012)

    Article  Google Scholar 

  37. Miller, M.D., Thornton, M.A.: Multiple Valued Logic: Concepts and Representations. Morgan and Claypool Publishers, Synthesis Lectures on Digital Circuits and systems (2008)

    Google Scholar 

  38. Zaitseva, E.: Importance Analysis of a Multi-State System Based on Multiple-Valued Logic Methods. In: Lisnianski, A., Frenkel, I. (eds.) Recent Advances in System Reliability: Signatures, Multi-state Systems and Statistical Inference, pp. 113–134. Springer, London, UK (2012)

    Chapter  Google Scholar 

  39. Wood, A.P.: Multistate Block Diagrams and Fault Trees, IEEE Trans on Reliability, R-34, pp. 236–240 (1985)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. National Aerospace University KhAI, Kharkiv, Ukraine

    Eugene Brezhnev & Vyacheslav Kharchenko

  2. Centre for Safety Infrastructure-Oriented Research and Analysis, Kharkiv, Ukraine

    Eugene Brezhnev & Vyacheslav Kharchenko

  3. O.M. Beketov National University of Urban Economy in Kharkiv, Kharkiv, Ukraine

    Herman Fesenko

  4. University of Žilina, Žilina, Slovakia

    Vitaly Levashenko & Elena Zaitseva

Authors
  1. Eugene Brezhnev
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Herman Fesenko
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Vyacheslav Kharchenko
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Vitaly Levashenko
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Elena Zaitseva
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Eugene Brezhnev .

Editor information

Editors and Affiliations

  1. KhAI 503, Department of Computer Systems & Network KhAI 503, Kharkiv, Ukraine

    Vyacheslav Kharchenko

  2. PMBSSU, 68th, Dept of Intelligent Information Systems PMBSSU, 68th, Mykolaiv, Ukraine

    Yuriy Kondratenko

  3. Sys Res Intit of Polish Acad of Science, Intelligent Systems Laboratory Sys Res Intit of Polish Acad of Science, Warszawa, Poland

    Janusz Kacprzyk

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Brezhnev, E., Fesenko, H., Kharchenko, V., Levashenko, V., Zaitseva, E. (2017). MSS Models of Smart Grids with Multi-level Degradation and Recovery. In: Kharchenko, V., Kondratenko, Y., Kacprzyk, J. (eds) Green IT Engineering: Concepts, Models, Complex Systems Architectures. Studies in Systems, Decision and Control, vol 74. Springer, Cham. https://doi.org/10.1007/978-3-319-44162-7_11

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-44162-7_11

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-44161-0

  • Online ISBN: 978-3-319-44162-7

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation