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Research Papers

Reliability and Component Importance in Networks Subject to Spatially Distributed Hazards Followed by Cascading Failures

[+] Author and Article Information
Anke Scherb

Engineering Risk Analysis Group,
Technische Universität München,
Theresienstr. 90,
Munich 80333, Germany
e-mail: anke.scherb@tum.de

Luca Garrè

DNV GL,
Veritasveien 1,
Høvik 1363, Norway
e-mail: luca.garre@dnvgl.com

Daniel Straub

Engineering Risk Analysis Group,
Technische Universität München,
Theresienstr. 90,
Munich 80333, Germany
e-mail: straub@tum.de

1Corresponding author.

Manuscript received December 5, 2016; final manuscript received February 28, 2017; published online March 24, 2017. Assoc. Editor: Konstantin Zuev.

ASME J. Risk Uncertainty Part B 3(2), 021007 (Mar 24, 2017) (9 pages) Paper No: RISK-16-1144; doi: 10.1115/1.4036091 History: Received December 05, 2016; Revised February 28, 2017

We investigate reliability and component importance in spatially distributed infrastructure networks subject to hazards characterized by large-scale spatial dependencies. In particular, we consider a selected IEEE benchmark power transmission system. A generic hazard model is formulated through a random field with continuously scalable spatial autocorrelation to study extrinsic common-cause-failure events such as storms or earthquakes. Network performance is described by a topological model, which accounts for cascading failures due to load redistribution after initial triggering events. Network reliability is then quantified in terms of the decrease in network efficiency and number of lost lines. Selected importance measures are calculated to rank single components according to their influence on the overall system reliability. This enables the identification of network components that have the strongest effect on system reliability. We thereby propose to distinguish component importance related to initial (triggering) failures and component importance related to cascading failures. Numerical investigations are performed for varying correlation lengths of the random field to represent different hazard characteristics. Results indicate that the spatial correlation has a discernible influence on the system reliability and component importance measures, while the component rankings are only mildly affected by the spatial correlation. We also find that the proposed component importance measures provide an efficient basis for planning network improvements.

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Figures

Grahic Jump Location
Fig. 1

Plots of the IEEE 39 bus system with geo referenced nodes. Left: line thicknesses indicate the reactance values of the lines and right: thicknesses indicate the line capacities, which are proportional to the number of shortest paths passing through the lines.

Grahic Jump Location
Fig. 2

Spatial random field realizations of component failure probabilities for selected values of the correlation length, together with the projected IEEE 39 bus system; scale unit is kilometers

Grahic Jump Location
Fig. 3

Finally versus initially failed lines for the case of independence (left) and full dependence (right); based on 10,000 samples with α=1.5; gray circles indicate the frequency of the data points in the sample space

Grahic Jump Location
Fig. 4

Network performance as a function of the correlation length with varying α value. Left: mean overall graph efficiency E[Enorm] and right: standard deviation of overall graph efficiency, based on 10,000 samples per correlation length value and α value combinations.

Grahic Jump Location
Fig. 5

CI weighted graph at a correlation length of 100 km. Left: CI(i) with respect to initial failures and right: CI(c) with respect to cascading failures, with α=1.5 and tE=0.9, based on 10,000 samples.

Grahic Jump Location
Fig. 6

ES importance weighted graph at a correlation length of 100 km. Left: ES(i) with respect to initial failures and right: ES(c) with respect to cascading failures, with α=1.5, based on 10,000 samples.

Grahic Jump Location
Fig. 7

CI as a function of correlation length. Left: CI(i) with respect to initial failures; right: CI(c) with respect to cascading failures, with α=1.5 and tE=0.9 each and based on 10,000 samples per correlation length value.

Grahic Jump Location
Fig. 8

ES as a function of correlation length. Left: ES(i) with respect to initial failures and right: ES(c) with respect to cascading failures, with α=1.5 each and based on 10,000 samples per correlation length value.

Grahic Jump Location
Fig. 9

Mean efficiency as a function of correlation length for different network improvement strategies. Left: line strengthening (decreasing the initial failure probability during the hazard event) of five selected lines and right: increasing line capacity (increasing the tolerance parameter α) of five selected lines.

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