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Using inverse Lz-transform for obtaining compact stochastic model of complex power station for short-term risk evaluation

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  • Lisnianski, Anatoly
  • Ding, Yi

Abstract

In this paper a short-term risk evaluation is performed for electric power stations, where each power generating unit is presented by a multi-state Markov model. Risk is treated as the probability of loss of load or in other words, as the probability of system entrance in the set of states, where demand cannot be satisfied. The main obstacle for risk evaluation in such cases is a "curse of dimensionality" – a great number of states of entire power station that should be analyzed. Usually when the number of system states is increasing drastically, enormous efforts are required for solving the problem by using classical Markov methods or simulation techniques. Well known universal generating function technique also cannot be directly applied because this technique is primarily oriented to steady-state reliability analysis. By using such extension of UGF techniques as Lz-transform, one can find for the short-term such reliability characteristics as loss of load probability, expected energy not supplied to consumers etc. However risk function still cannot be obtained by using these techniques. This problem in many practical cases is a challenge for reliability researchers and engineers. In this paper, a special method based on inverse Lz-transform (LZ−1 transform) is developed in order to calculate risk function for such multi-state power systems. In order to illustrate the proposed approach, the short-term risk evaluation for a power station with different coal-fired generating units is presented.

Suggested Citation

  • Lisnianski, Anatoly & Ding, Yi, 2016. "Using inverse Lz-transform for obtaining compact stochastic model of complex power station for short-term risk evaluation," Reliability Engineering and System Safety, Elsevier, vol. 145(C), pages 19-27.
  • Handle: RePEc:eee:reensy:v:145:y:2016:i:c:p:19-27
    DOI: 10.1016/j.ress.2015.08.009
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    References listed on IDEAS

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    1. Ding, Yi & Wang, Peng & Lisnianski, Anatoly, 2006. "Optimal reserve management for restructured power generating systems," Reliability Engineering and System Safety, Elsevier, vol. 91(7), pages 792-799.
    2. Lisnianski, Anatoly & Elmakias, David & Laredo, David & Ben Haim, Hanoch, 2012. "A multi-state Markov model for a short-term reliability analysis of a power generating unit," Reliability Engineering and System Safety, Elsevier, vol. 98(1), pages 1-6.
    3. Gregory Levitin, 2005. "The Universal Generating Function in Reliability Analysis and Optimization," Springer Series in Reliability Engineering, Springer, number 978-1-84628-245-4, September.
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    Cited by:

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    2. Yan, Xiangbin & Qiu, Hui & Peng, Rui & Wu, Shaomin, 2020. "Optimal configuration of a power grid system with a dynamic performance sharing mechanism," Reliability Engineering and System Safety, Elsevier, vol. 193(C).
    3. Levitin, Gregory & Xing, Liudong & Dai, Yuanshun, 2017. "Optimal arrangement of connecting elements in linear consecutively connected systems with heterogeneous warm standby groups," Reliability Engineering and System Safety, Elsevier, vol. 165(C), pages 395-401.
    4. Peng, Rui & Xiao, Hui & Liu, Hanlin, 2017. "Reliability of multi-state systems with a performance sharing group of limited size," Reliability Engineering and System Safety, Elsevier, vol. 166(C), pages 164-170.
    5. Song, Xiaogang & Zhai, Zhengjun & Liu, Yidong & Han, Jie, 2018. "A stochastic approach for the reliability evaluation of multi-state systems with dependent components," Reliability Engineering and System Safety, Elsevier, vol. 170(C), pages 257-266.
    6. Levitin, Gregory & Xing, Liudong & Dai, Yuanshun, 2017. "Optimal loading of series parallel systems with arbitrary element time-to-failure and time-to-repair distributions," Reliability Engineering and System Safety, Elsevier, vol. 164(C), pages 34-44.
    7. Su, Peng & Wang, Guanjun & Duan, Fengjun, 2020. "Reliability evaluation of a k-out-of-n(G)-subsystem based multi-state system with common bus performance sharing," Reliability Engineering and System Safety, Elsevier, vol. 198(C).

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