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Research Papers

Resilience Analysis Framework for Interconnected Critical Infrastructures

[+] Author and Article Information
X. Liu

Chair on Systems Science
and the Energetic Challenge,
Foundation Electricité de France (EDF),
Laboratoire Genie Industriel,
CentraleSupélec,
Université Paris-Saclay,
Grande voie des Vignes,
Chatenay-Malabry 92290, France
e-mail: xing.liu@ecp.fr

E. Ferrario

Chair on Systems Science
and the Energetic Challenge,
Foundation Electricité de France (EDF),
Laboratoire Genie Industriel,
CentraleSupélec,
Université Paris-Saclay,
Grande voie des Vignes,
Chatenay-Malabry 92290, France
e-mail: elisa.ferrario@ecp.fr

E. Zio

Chair on Systems Science
and the Energetic Challenge,
Foundation Electricité de France (EDF),
Laboratoire Genie Industriel,
CentraleSupélec,
Université Paris-Saclay,
Grande voie des Vignes,
Chatenay-Malabry 92290, France
e-mail: enrico.zio@ecp.fr;
Department of Energy,
Politecnico di Milano and Via,
Ponzio, 34/3, Milano 20133, Italy
e-mail: enrico.zio@polimi.it

1Corresponding author.

Manuscript received December 4, 2015; final manuscript received August 5, 2016; published online February 20, 2017. Assoc. Editor: Konstantin Zuev.

ASME J. Risk Uncertainty Part B 3(2), 021001 (Feb 20, 2017) (10 pages) Paper No: RISK-15-1115; doi: 10.1115/1.4035728 History: Received December 04, 2015; Revised August 05, 2016

To investigate the resilience of interconnected critical infrastructures (CIs), a framework combining dynamic modeling and resilience analysis is proposed. Resilience is defined in this work as the capacity of a system to absorb the impacts of perturbations and recover quickly from disruptive states. It is seen as a property of the system, which depends on a number of design, operation, and control parameters. Within this framework, we introduce the concept of resilience regions in the parameters space: as long as the parameters values remain inside these regions during operation, the system visits only recoverable states or, in other words, it maintains nominal operation or recovers quickly to it. Based on this concept, we perform a resilience analysis of two interconnected critical infrastructures, a gas network and an electric power system. The analysis is performed by numerical calculation of the resilience conditions in terms of design, operation, and control parameters values for given failure scenarios. To render computationally feasible analysis, we resort to an abstract representation of the system dynamics by a linear model of switching dynamics. Although the high-level modeling adopted may suffer from predictive accuracy, the proposed framework can still provide valuable insights in the analysis of system resilience and its dependence on the design, operation, and control parameters under different failure scenarios, which can be valuable to inform the decision making process of CIs operators and other stakeholders.

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Figures

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Fig. 1

Resilience curves of interconnected CIs after a disruption

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Fig. 2

Resilience region (dotted area) and nonresilience region (white area), and two cases of resilient (case I) and nonresilient (case II) system

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Fig. 3

Schematic representation of the resilience analysis framework

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Fig. 4

Interconnected CIs

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Fig. 5

Interconnected gas-power systems

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Fig. 6

Evolution in time of the state of supplier S1 (top) and of users D1 and D2 (bottom left and right, respectively), with respect to a failure of supplier S1(Fs1 = 60 Mcf) and a linear recovery function with μs1 = 1 Mcf/h

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Fig. 7

Resilience region under a fixed configuration of parameters (μs1 = 1 Mcf/h, Hh = 50 h)

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Fig. 8

Resilience conditions with respect to different failure scenarios of supplier S1; the dots represent the combination of recovery rate, μs1, and time horizon, Hh, for which the system is resilient, whereas the stars those for which the system is not resilient

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Fig. 9

Resilience conditions for fixed levels of failure of supplier S1: (a) Fs1 = 40, (b) Fs1 = 45, (c) Fs1 = 50, (d) Fs1 = 55, (e) Fs1 = 60, and (f) Fs1 = 65

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