Review on Energy Resilience

Contents lists available at ScienceDirect

Reliability Engineering and System Safety

journal homepage: www.elsevier.com/locate/ress

Literature review on modeling and simulation of energy infrastructures from a resilience perspective Jing Wanga, Wangda Zuoa,⁎, Landolf Rhode-Barbarigosb, Xing Lua, Jianhui Wangc, Yanling Lind a Department of Civil, Environmental and Architectural Engineering, University of Colorado Boulder, ECCE 247, UCB 428, Boulder, CO 80309-0428, USA b Department of Civil, Architectural, and Environmental Engineering, University of Miami, Miami, FL, USA c Department of Electrical Engineering, Southern Methodist University, Dallas, TX, USA d School of Electrical Engineering, Xi'an Jiaotong University, Xi'an, China

A R T I C L E I N F O

Keywords: Energy infrastructure Resilience Power grid Modeling and simulation Model evaluation Natural gas network

A B S T R A C T

Recent years have witnessed an increasing frequency of disasters, both natural and human-induced. This applies pressure to critical infrastructures (CIs). Among all the CI sectors, the energy infrastructure plays a critical role, as almost all other CIs depend on it. In this paper, 30 energy infrastructure models dedicated for the modeling and simulation of power or natural gas networks are collected and reviewed using the emerging concept of resilience. Based on the review, typical modeling approaches for energy infrastructure resilience problems are summarized and compared. The authors, then, propose five indicators for evaluating a resilience model; namely, catering to different stakeholders, intervening in development phases, dedicating to certain stressor and failure, taking into account different interdependencies, and involving socio-economic characteristics. As a supplement, other modeling features such as data needs and time scale are further discussed. Finally, the paper offers ob- servations of existing energy infrastructure models as well as future trends for energy infrastructure modeling.

1. Introduction

1.1. Critical infrastructure (CI) protection

A nation's health, wealth, and security rely on the production and distribution of goods and services. The array of physical assets, processes and organizations through which these goods and services move are called infrastructures [1]. Among all infrastructure systems, the critical infrastructures (CIs) are those systems “whose incapacity or destruction would have a debilitating impact on the defense and economic security” [2]. Presidential Policy Directives 21 Critical Infrastructure Security and Resi- lience (PPD-21) identified 16 critical sectors of infrastructures including: chemical, commercial facilities, communication, critical manufacturing, dams, defense industrial base, emergency services, energy, financial services, food and agriculture, government facilities, healthcare and public health, information technology, nuclear reactors, materials, and waste, transportation systems, and water and wastewater systems.

However, human-induced and natural disasters, such as the 9/11 terrorist attacks [3] in 2001 and Hurricane Katrina [4] in 2005, further highlighted the vulnerability of CI systems and raised the awareness about their protection. In the United States, the National Infrastructure Simulation and Analysis Center (NISAC) and the Department of

Homeland Security established in 2001 and 2002, respectively, aim at improving CI protection. PPD-8 and PPD-21 specifically addressed the national preparedness of CI systems.

Similar organizations and programs have also been developed in other regions and countries, such as the European Program on Critical Infrastructure Protection, the Critical Infrastructure Protection Implementation Plan in Germany and the Critical Infrastructure Resilience Program in the UK [5]. In Asia, recovering from the earth- quake and tsunami at Tokushima, the National Resilience Program of Japan dedicated $210 billion worth investment in 2013 to increase the overall resilience of energy, water, transportation and other CIs [6]. Being aware that the majority of outages have roots in the distribution system, the Chinese National Energy Administration allocated 20 tril- lion CNY for the distribution renovation during 2015–2020 to increase reliability, power quality, and resilience to disruptions. The modeling and simulation of CIs for protection and resilience purposes have thus received significant interests among universities, national laboratories and private companies.

1.2. The concept of resilience

Resilience, as an emerging concept in the area of engineering, was

https://doi.org/10.1016/j.ress.2018.11.029 Received 30 November 2017; Received in revised form 24 November 2018; Accepted 25 November 2018

⁎ Corresponding author. E-mail address: [email protected] (W. Zuo).

Reliability Engineering and System Safety 183 (2019) 360–373

Available online 28 November 2018 0951-8320/ © 2018 Elsevier Ltd. All rights reserved.

T

first introduced in 1973 by Holling into the fields of ecology and evo- lution [7]. This concept was first used to describe the ability of an ecosystem to continue functioning after changes. Nowadays, resilience has been broadly applied across many fields, including natural disaster and risk management [8], civil infrastructure studies [9–11], system engineering [12], energy systems [13,14], etc.

Though consensus on resilience definition is lacking [15], the essence of resilience definitions is generally the same, that is, it is an overarching concept that encompasses the system performance before and after dis- astrous events. Francis and Bekera [16] reviewed various approaches to defining and assessing resilience and identified three resilience capa- cities: adaptive capacity, absorptive capacity, and recoverability. Resi- lience therefore can be defined as “the ability of an entity to anticipate, resist, absorb, respond to, adapt to and recover from a disturbance” [17].

Resilience is a multi-dimensional concept. Its qualitative and quantitative studies often involve interdisciplinary efforts. Meerow et al. [18] reviewed the literature on urban resilience and concluded that “applying resilience in different contexts requires answering: Resilience for whom and to what? When? Where? And Why?” They, thus, pointed out the key considerations in the application of resilience: the stake- holder, the stressor, the temporal and spatial scale, and the motivation. Shaw and IEDM Team [19] developed a Climate Disaster Resilience Index to measure the existing level of climate disaster resilience of targeted areas. This index utilizes 25 variables in five resilience-based dimensions: natural, physical, social, economic and institutional. Carlson et al. [17] and McManus et al. [20] provided frameworks for system-level and region-level resilience overview to address personal, business, governmental, and infrastructure aspects of resilience. Roege et al. [21] formulated a scoring matrix to evaluate the system's cap- ability to plan, absorb, recover and adapt from the perspective of physical, information, cognitive and social.

In this work, reviewing energy infrastructure models from a resilience perspective implies utilizing different resilience-based dimensions and considerations during the evaluation of the selected models. Consequently, the models’ ability to promote resilience in energy infrastructures against short-term disruptions and long-term degradations is addressed, not only from a physical perspective, but also socio-economically.

1.3. Energy infrastructure resilience

Energy infrastructures include electric power, natural gas, and fuel networks. Among all the CI sectors, energy infrastructure might be identified as the most crucial one due to the enabling functions they provide across all other CI sectors (PPD-21). For example, water supply and sewer systems rely on electric power systems to operate their pump stations. Information and telecommunication systems rely on power networks to carry out information transmission tasks. Transportation systems rely on fuel networks to obtain power for all kinds of vehicles. The dependence of other critical infrastructures on the energy network can lead to its vulnerability: Disruptions in the energy system may transverse to other dependent infrastructure systems and possibly even back to itself, where the failure originated [22,23]. This cascading and escalating characteristic of failure adds to energy network's vulner- ability. Energy infrastructures are also vulnerable to climate change. For example, the rising sea level and increasing frequency of major storms lead to severe floods in coastal areas, where a lot of energy in- frastructures are located [24], such as power plants, natural gas facil- ities, and oil and gas refineries. Moreover, high-impact low-probability events, such as hurricanes and terrorist attacks, further threaten the operation of energy infrastructures.

Based on the above-mentioned importance and vulnerability, the study of energy infrastructure resilience has become an urgent and significant research topic. Different researchers approach this problem in various ways. Many scholars simulate energy infrastructure resi- lience as an optimal operation problem [25–30]. Some adopt agent- based modeling (ABM) technique to reveal the complex interactions

among energy system components [31–34]. Others improve traditional topological metrics of power grids by embodying its physical behavior [35]. Also, in response to the emergence of “big data” resources, some researches apply large-scale data analysis in the energy resilience stu- dies, especially for power grid studies [36,37].

Although some researches consider resilience and reliability of en- ergy infrastructures in the same topic [38,39], it is to note that resi- lience and reliability are not the same. While reliability is the ultimate goal that system designers and providers strive for, resilience is the way to achieve it by recovering fast from and adapting to disruptions [40]. The focus of this review paper is the modeling and simulation of energy infrastructure resilience.

1.4. Work scope and highlights

The modeling and simulation of CIs has been the topic of a few critical reviews. Eusgeld et al. [41] reviewed eight modeling and si- mulation techniques for interdependent CIs; namely, agent-based modeling, system dynamics, hybrid system modeling, input-output- model, hierarchical holographic modeling, critical path method, high level architecture and petri nets. They also proposed seven model evaluation criteria concerning modeling focus, methodical design strategies, type of interdependencies, types of events for simulation, event consequences, data needs and monitoring field. More recently, Ouyang [05] reviewed existing approaches for CI modeling and simu- lation grouping them into six types: empirical approaches, agent-based approaches, system dynamics based approaches, economic theory based approaches, network based approaches, and others. Existing studies were categorized and reviewed in terms of fundamental prin- ciples. Different approaches were further compared concerning the in- clusion of sampled resilience improvement strategies.

However, both aforementioned studies had a working scope of general CI systems rather than focusing on energy infrastructures. The work of Eusgeld et al. [41] only compared different modeling ap- proaches against each other without reviewing the details of specific models. The work of Ouyang [05] adopted several resilience improve- ment strategies to evaluate the modeling approaches but did not ad- dress other important issues of resilience such as the stakeholder or the temporal scale.

In this paper, we conduct a comprehensive review of 30 energy infrastructure models collected from open literature. In the overview part, we first summarize the modeling scenarios and the problems tackled by the models, as well as their typical assumptions. Based on the literature review, typical approaches to study energy infrastructure resilience are introduced with exemplary models. As the next step, we propose five selected resilience indicators; namely, catering to different stakeholders, intervening in development phases, dedicating to certain stressor and failure, taking into account different interdependencies and involving socio-economic characteristics. Other features are further discussed such as model type, data needs, etc. This review highlights the features and trends of existing models concerning their ability to address the multi-dimensional aspects of energy infrastructure resi- lience while stressing the characteristics of different modeling ap- proaches. From reading the paper, the readers could gain knowledge of: (1) what are the differences among major energy infrastructure models, (2) what are the modeling needs from a resilience perspective through the proposed resilience indicators, (3) what kind of energy infra- structure model is needed in the future to better equip energy infra- structure resilience studies.

The remainder of the paper is organized as follows: Section 2 in- troduces the model-collection procedure, provides an overview of the models and summarizes typical modeling approaches.Sections 3 pro- poses the resilience indicators, as well as other selected modeling fea- tures. Section 4 gives a discussion based on the proposed indicators and modeling features. Finally, concluding remarks and future trends in the field are stated in Section 5.

J. Wang et al. Reliability Engineering and System Safety 183 (2019) 360–373

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2. Reviewing existing energy infrastructure models

2.1. Collection of models

The review focus of this paper are models aiming at energy infra- structure operation, protection, or resilience enhancement. Three model collection methods have been applied: (1) searching literature with a variety of keywords, (2) checking the references and citations of the papers identified through method 1, (3) referring to the publica- tions of selected research groups in the field.

The keywords used in the literature search are listed in Table 1. The search strings accounted for the fact that different literature may use different terms for the same object (i.e. protection and security). As a result, 210 journal and conference papers from reliability, infra- structure and energy related journals were initially collected. Related papers citing or cited by the papers found in the first stage were re- viewed as well.

Models were also collected by reviewing the work done by active research groups in CI modeling and simulation field such as NISAC, ANL, Los Alamos National Laboratory (LANL), etc. NISAC experts use ad- vanced modeling and simulation capabilities to address CI inter- dependencies, vulnerabilities, and complexities in the U.S. Scientists at ANL use the ABM technique to study various aspects of energy network resilience. They also developed models for the natural gas and petroleum fuel networks [34]. The Interdependent Energy Infrastructure Simulation System [42] developed by LANL is an actor-based model that helps de- cision-makers understand and assess intrinsic vulnerabilities in CIs.

Through the above-mentioned procedure, this study identified 30 models for energy infrastructures. In the selected models, 17 are ap- plied on power networks, 3 on natural gas networks, 4 on both power and natural gas networks, and the remaining 6 are applied on other energy infrastructure systems. When looking at the detailed scenarios of the models, most models for power networks focus on power trans- mission networks. Nonetheless, the research on distribution systems is emerging. Some of the models integrate financial networks, human activity, or supervisory control and data acquisition (SCADA). The natural gas network models mainly focus on the analysis and restora- tion of natural gas transmission pipelines. The models for both power and natural gas networks are dedicated to studying the inter- dependencies between the two systems. Other models include energy generation and storage system model [43], coal distribution network model [44], crude oil and petroleum product transport pipeline model [34], and integrated urban energy systems model [32].

2.2. Model overview

To understand what problems the research community of energy infrastructure resilience is trying to tackle and how the researchers are approaching these problems, this section first summarizes the research problems of the selected models and their corresponding key assump- tions. Then, in the following section, the modeling approaches adopted by these models are introduced, representing typical methods for con- ducting energy infrastructure resilience studies.

Given that resilience describes a system's ability to sustain disruptions and to recover quickly from them, energy infrastructure resilience models concentrate on solving two major problems: (1) resource

allocation and hardening planning in the preparation stage, (2) power outage management and service restoration in the immediate aftermath and recovery stage. Due to the limitation of budgets, how to identify the most vulnerable components in the system, harden them with minimized economic costs and gain the most effects out of the hardening measures is one main topic the research community cares about. The second topic aims to mitigate the impacts of the disasters and to recover the services quickly. Typical implementations include models that simulate the re- storation process or that abstract the restoration process as an optimal control problem [25]. Common restoration measures include repair crew dispatch, distributed generation (DG), switch device remote control, etc.

Since the energy infrastructure sector is closely related to other CI sectors, an emerging number of researches focus on the study of in- terdependencies within the energy infrastructure sector and across CI sectors. Within the energy infrastructure sector, the interaction between the natural gas system and the power grid system is studied [45]. Across different sectors, researchers try to involve energy, water, transporta- tion and communication systems into the same modeling and simula- tion framework and find resilient solutions on a more holistic scale.

For different application focuses, the models are usually developed under various assumptions of the real world. In models of distributed generation or microgrid technologies, it is typically assumed that the remotely controlled automatic switch devices are available in the dis- tribution network so that lines can be opened/closed and loads can be connected/disconnected to form multiple microgrids. The switches are assumed to have local communication capabilities to exchange in- formation with its neighboring switches [27]. In most resilience models that simulate the defender and attacker activities, the decision maker has a budget to harden a maximum of power lines and to place a maximum of DG units and the system operators are aware of the status of all the components after the occurrence of the outage [30]. The worst-case attack scenario occurs and the hardened lines and nodes are assumed to be able to survive the disasters. For models that study the weather impact, it is usually assumed the system is exposed to the same weather conditions at any given time by modeling the weather event as a standstill event, which reduces the complexity of the modeling pro- cedure because no regional weather aspects are considered. The re- storation time during high and extreme wind speed events is equal to the restoration time during normal wind speeds [46,47]. For models studying interdependencies between power and gas systems, it is usually assumed that electricity generation consumes gas and gas compressors consumes electricity [30]. Other specific assumptions de- pend on the modeling objectives and the scale of the model.

Table 2 summarizes basic information for the selected models in- cluding name, developer/author, scenario, and purpose/problem tackled. “Scenario” gives the specific modeling object of a model. “Purpose/problem tackled” describes the targeted problem the model was developed to solve. Among all the models, 15% are for power outage management and service restoration, 21% are for vulnerability and reliability analysis, 18% are for resource allocation and hardening planning, 12% are for infrastructure interdependency analysis. The rest address problems such as electricity market studies, weather event impact studies, general presentation and analysis, etc.

2.3. Modeling approaches

In this section, we introduce typical modeling approaches for energy infrastructure resilience problems. The models collected in this paper adopt a variety of modeling approaches including optimal operation modeling, topological network modeling, agent-based modeling, prob- abilistic modeling, system dynamics modeling, empirical modeling, etc. Table 3 lists the modeling approaches and the corresponding models that were collected in this paper.

The most common four approaches will be introduced in detail in the following subsections. The rest approaches are introduced briefly in “other approaches”. It should be noted that since the review object of this paper is

Table 1 Keywords for literature search.

Model* Energy Infrastructure Simulat* Power Resilien* Electric* + Network + Vulnerab* Gas Protect* Fuel System Secur*

Risk

J. Wang et al. Reliability Engineering and System Safety 183 (2019) 360–373

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cl im

at e

ch an

ge .

14 El

ec tr

ic it

y M

ar ke

t C om

pl ex

A da

pt iv

e Sy

st em

(2 00

6) A

N L

El ec

tr ic

po w

er an

d fi na

nc ia

l ne

tw or

ks M

od el

in g

an d

si m

ul at

io n

of op

er at

io ns

in re

st ru

ct ur

ed el

ec tr

ic it

y m

ar ke

ts .

15 N

at ur

al G

as In

fr as

tr uc

tu re

To ol

se t

(2 00

6) A

N L,

In fr

as tr

uc tu

re A

ss ur

an ce

C en

te r

N at

ur al

ga s

ne tw

or ks

Pr ov

id e

an an

al ys

t w

it h

a qu

ic k

m et

ho d

to ac

ce ss

,r ev

ie w

,a nd

di sp

la y

co m

po ne

nt s

of th

e na

tu ra

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s ne

tw or

k; pe

rf or

m va

ry in

g le

ve ls

of co

m po

ne nt

an d

sy st

em s

an al

ys is

, an

d di

sp la

y an

al ys

is re

su lt s.

16 C ri

ti ca

l In

fr as

tr uc

tu re

M od

el in

g Sy

st em

(2 00

6) IN

L El

ec tr

ic po

w er

sy st

em , hu

m an

ac ti

vi ty

an d

SC A

D A

Pr ov

id e

de ci

si on

m ak

er s

w it

h a

hi gh

ly ad

ap ta

bl e

an d

ea si

ly co

ns tr

uc te

d ‘w

ar ga

m in

g’ to

ol to

as se

ss in

fr as

tr uc

tu re

vu ln

er ab

ili ti

es in

cl ud

in g

po lic

y an

d re

sp on

se pl

an s.

17 C ri

ti ca

l In

fr as

tr uc

tu re

Si m

ul at

io n

by In

te rd

ep en

de nt

A ge

nt s

(2 00

6) U

ni ve

rs it

y R

om a

Tr e

El ec

tr ic

po w

er sy

st em

an d

SC A

D A

A na

ly ze

sh or

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rm eff

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of fa

ilu re

s in

te rm

s of

fa ul

t pr

op ag

at io

n an

d pe

rf or

m an

ce de

gr ad

at io

n. 18

In te

gr at

ed en

er gy

sy st

em re

lia bi

lit y

ev al

ua ti

on m

od el

(2 01

6) Li

et al

. El

ec tr

ic it

y di

st ri

bu ti

on ne

tw or

k, di

st ri

bu te

d re

ne w

ab le

en er

gy sy

st em

,g as

sy st

em ,c

oo lin

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d he

at in

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s Pr

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ne w

re lia

bi lit

y ev

al ua

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oa ch

,i n

w hi

ch Sm

ar t

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nt C om

m un

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io n

is ba

se d

sy st

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co nfi

gu ra

ti on

is in

te gr

at ed

in to

th e

re lia

bi lit

y ev

al ua

ti on

pr oc

es s.

19 Sy

nC it

y (2

01 0)

Im pe

ri al

C ol

le ge

Lo nd

on U

rb an

en er

gy sy

st em

s Pr

ov id

e an

in te

gr at

ed ,s

pa ti

al ly

an d

te m

po ra

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ve rs

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pr es

en ta

ti on

of ur

ba n

en er

gy us

e w

it hi

n a

ge ne

ra liz

ed fr

am ew

or k

ac ro

ss al

l th

e de

si gn

st ep

s an

d in

a va

ri et

y of

pr ob

le m

en vi

ro nm

en ts

.

(c on tin ue d on

ne xt

pa ge

)

J. Wang et al. Reliability Engineering and System Safety 183 (2019) 360–373

363

T ab

le 2

(c on tin ue d)

N am

e D

ev el

op er

/A ut

ho r

Sc en

ar io

Pu rp

os e/

Pr ob

le m

Ta ck

le d

20 R

es ili

en ce

ev al

ua ti

on m

od el

(2 01

7) Pa

nt el

i an

d Pi

er lu

ig i

El ec

tr ic

po w

er sy

st em

s Pr

ov id

e a

co nc

ep tu

al fr

am ew

or k

fo r

ga in

in g

in si

gh t

in to

th e

re si

lie nc

e of

po w

er sy

st em

s w

it h

fo cu

s on

th e

im pa

ct of

se ve

re w

ea th

er ev

en ts

. Th

e eff

ec t

of w

ea th

er is

qu an

ti fi ed

w it

h a

st oc

ha st

ic ap

pr oa

ch . Th

e re

si lie

nc e

of th

e cr

it ic

al po

w er

in fr

as tr

uc tu

re is

m od

el ed

an d

as se

ss ed

w it

hi n

a co

nt ex

t of

sy st

em -o

f- sy

st em

s th

at al

so in

cl ud

e hu

m an

re sp

on se

as a

ke y

di m

en si

on .

21 M

ul ti

-m ic

ro gr

id re

lia bi

lit y

as se

ss m

en t

fr am

ew or

k (2

01 7)

Fa rz

in et

al .

M ul

ti -m

ic ro

gr id

di st

ri bu

ti on

sy st

em D

ev el

op a

ge ne

ra l fr

am ew

or k

fo r

re lia

bi lit

y as

se ss

m en

t of

m ul

ti -m

ic ro

gr id

(M M

G )

di st

ri bu

ti on

sy st

em s.

In ve

st ig

at e

re lia

bi lit

y im

pa ct

s of

co or

di na

te d

ou ta

ge m

an ag

em en

t st

ra te

gi es

in a

M M

G di

st ri

bu ti

on ne

tw or

k. 22

C ri

ti ca

l In

fr as

tr uc

tu re

s In

te rd

ep en

de nc

ie s

In te

gr at

or (2

00 2)

A N

L N

at ur

al ga

s pi

pe lin

es In

fr as

tr uc

tu re

re st

or at

io n

ti m

e an

d/ or

co st

es ti

m at

io n

co ns

id er

in g

an in

te rd

ep en

de nc

y an

al ys

is .

23 R

es to

re (2

01 1)

A N

L N

at ur

al ga

s pi

pe lin

es Es

ti m

at e

th e

ti m

e an

d co

st of

In fr

as tr

uc tu

re re

st or

at io

n. 24

A fr

am ew

or k

fo r

re lia

bi lit

y/ av

ai la

bi lit

y as

se ss

m en

t (2

01 7)

C ad

in i et

al .

El ec

tr ic

po w

er tr

an sm

is si

on ne

tw or

ks C om

bi ne

an ex

tr em

e w

ea th

er st

oc ha

st ic

m od

el to

a re

al is

ti c

ca sc

ad in

g fa

ilu re

si m

ul at

or ba

se d

on a

di re

ct cu

rr en

t po

w er

fl ow

ap pr

ox im

at io

n an

d a

pr op

or ti

on al

re -

di sp

at ch

st ra

te gy

. D

yn am

ic s

of th

e ne

tw or

k is

co m

pl et

ed by

th e

in tr

od uc

ti on

of a

re st

or at

io n

m od

el ac

co un

ti ng

fo r

th e

op er

at in

g co

nd it

io ns

th at

a re

pa ir

cr ew

m ay

en co

un te

r du

ri ng

an ex

tr em

e w

ea th

er ev

en t.

25 In

te rd

ep en

de nt

En er

gy In

fr as

tr uc

tu re

Si m

ul at

io n

Sy st

em (2

00 6)

LA N

L El

ec tr

ic po

w er

an d

na tu

ra l ga

s in

fr as

tr uc

tu re

s A

ss is

t in

di vi

du al

s in

an al

yz in

g an

d un

de rs

ta nd

in g

in te

rd ep

en de

nt en

er gy

in fr

as tr

uc tu

re s.

26 Fr

am ew

or k

fo r

El ec

tr ic

it y

Pr od

uc ti

on V

ul ne

ra bi

lit y

A ss

es sm

en t

(2 00

9) Sh

ih et

al .

C oa

l di

st ri

bu ti

on ne

tw or

k U

se da

ta w

ar eh

ou si

ng an

d vi

su al

iz at

io n

te ch

ni qu

es to

ex pl

or e

th e

in te

rd ep

en de

nc ie

s be

tw ee

n co

al m

in es

, ra

il tr

an sp

or ta

ti on

, an

d el

ec tr

ic po

w er

pl an

ts .

27 C ri

ti ca

l In

fr as

tr uc

tu re

Pr ot

ec ti

on M

od el

in g

an d

A na

ly si

s (C

IP M

A )

Pr og

ra m

(2 00

6) A

us tr

al ia

n G

ov er

nm en

t -

A tt

or ne

y G

en er

al 's

D ep

ar tm

en t

C I

ne tw

or ks

an d

hi gh

pr io

ri ty

pr ec

in ct

s Su

pp or

tb us

in es

s an

d go

ve rn

m en

td ec

is io

n m

ak in

g fo

r C Ip

ro te

ct io

n, co

un te

r- te

rr or

is m

an d

em er

ge nc

y m

an ag

em en

t, es

pe ci

al ly

w it

h re

ga rd

to pr

ev en

ti on

,p re

pa re

dn es

s, an

d pl

an ni

ng an

d re

co ve

ry .

28 Pe

tr ol

eu m

Fu el

s N

et w

or k

A na

ly si

s M

od el

(2 00

6) A

N L,

In fr

as tr

uc tu

re A

ss ur

an ce

C en

te r

C ru

de oi

l an

d pe

tr ol

eu m

pr od

uc t

tr an

sp or

t pi

pe lin

es Pe

rf or

m hy

dr au

lic ca

lc ul

at io

ns of

pi pe

lin e

tr an

sp or

t of

cr ud

e oi

l an

d pe

tr ol

eu m

pr od

uc ts

.I nt

ro du

ct io

n of

pi pe

lin e

co m

po ne

nt de

pe nd

en ci

es in

to cr

it ic

al in

fr as

tr uc

tu re

an al

ys es

. 29

C ri

ti ca

l en

er gy

in fr

as tr

uc tu

re s

(2 01

4) Er

de ne

r et

al .

El ec

tr ic

it y,

na tu

ra l ga

s an

d oi

l sy

st em

s A

na ly

si s

of th

e im

pa ct

s of

in te

rd ep

en de

nc ie

s be

tw ee

n el

ec tr

ic it

y an

d na

tu ra

l ga

s sy

st em

s. Pr

op os

e an

in te

gr at

ed si

m ul

at io

n m

od el

th at

re fl ec

ts th

e dy

na m

ic s

of th

e sy

st em

s in

ca se

of di

sr up

ti on

s an

d ta

ke s

th e

ca sc

ad in

g eff

ec ts

of th

es e

di sr

up ti

on s

in to

ac co

un t.

30 Fa

st A

na ly

si s

In fr

as tr

uc tu

re To

ol (2

00 6)

Sa nd

ia N

at io

na l La

bo ra

to ry

(S N

L) El

ec tr

ic po

w er

, na

tu ra

l ga

s, an

d w

at er

w ay

sy st

em s

D et

er m

in e

th e

si gn

ifi ca

nc e

an d

in te

rd ep

en de

nc ie

s as

so ci

at ed

w it

h el

em en

ts of

th e

na ti

on 's

C I.

J. Wang et al. Reliability Engineering and System Safety 183 (2019) 360–373

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numerical models that could conduct simulations and predict system performance in the real world, no surveys or qualitative studies were in- cluded. In the remaining part of this section, each modeling approach is introduced with exemplary models to address their characteristics.

2.3.1. Optimal operation modeling Optimal operation modeling is one of the most widely used method

in the research area of energy infrastructure resilience. In this method, when the system is interrupted, achieving resilience can be interpreted as an optimization problem to restore the system within a short time while minimizing the load shedding ratio.

Arif et al. [25] solved the outage management problem by co-opti- mizing the repair, reconfiguration, and DG dispatch to maximize the picked-up loads and minimize the repair time considering reconfigura- tion and repair crew scheduling. Chen et al. [27] and Ding et al. [28] proposed a microgrid formation mechanism to restore critical loads after major faults at the grid caused by natural disasters. In this scheme, a mixed-integer linear program was formulated to maximize the total prioritized loads restored while satisfying self-adequacy and operation constraints of each microgrid. Similarly, Chen et al. [26] formulated a mixed-integer linear program model for the sequential service restora- tion problem. This model can generate the optimal restoration sequences to coordinate dispatchable DGs and switchgears to energize the system on a step-by-step basis. Manshadi and Khodayar [29] proposed a bi-level optimization methodology which took into consideration the inter- dependency between natural gas and electricity infrastructures. Through this model, the identification of most vulnerable components in the system, as well as the resilient generation and demand scheduling could be achieved. Yuan et al. [30] proposed a model for resilient distribution system planning with hardening and DG based on two-stage optimiza- tion. In this model, a multi-stage and multi-zone-based uncertainty set was used to capture the uncertainty of natural disasters.

To sum up, existing optimal operation models share common object functions such as maximizing picked-up loads, minimizing repair time and economic investments. For restoration strategy development purpose,

frequently considered measures include topology reconfiguration, DG dispatch, microgrid formulation, repair crew dispatch and switch device control. The problem is usually represented by mathematical models with equilibrium equations and certain constraints, including self-adequacy and operation constraints. An emerging number of researches focus on solving problems of demand scheduling and load flexibility in response to the adoption of building-to-grid, vehicle-to-grid technologies.

However, this type of model is usually focused on one single problem, either protection resource allocation or restoration, which are two sepa- rate stages of energy infrastructure resilience. On the other hand, the oc- currence of the disaster is usually not simulated. If all these characteristics are coupled together, the optimization problem might get very compli- cated and the computational time problem will arise. Nezamoddini et al. [48] compared the computational time of different scales of test systems. The computational time increases from 3 seconds to 4.2 hours when the system upgrades from IEEE 6-bus to IEEE 57-bus test system.

2.3.2. Topological network modeling Power networks have been studied as a typical example of real-world

complex networks [51]. They can be modeled by extracting their topology. In this type of models, the power networks are represented by a set of vertices connected by a set of edges, where the vertices represent buses and the edges represent transmission lines. This type of model is typically applied in the structural vulnerability analysis of power networks.

Topological network models are easy to analyze due to their high level of abstraction and simplification. Buldyrev et al. [22] used the topology of the interdependent power system and communication system to demonstrate the cascading fault evolving between the two systems. Page et al. [43] proposed a simplified energy network mod- eling approach. Based on the topology of the original network, they used clusters that were aggregations of network nodes to build a less detailed model and calibrated it with detailed simulations. In this way, the number of variables was significantly reduced.

However, purely topological approaches fail to capture the physical properties and operational constraints of power systems and, therefore,

Table 3 Modeling approaches for energy infrastructure resilience problems.

Modeling approach Model name

1 Two-stage outage management model [25] 2 Microgrids formation scheme [27] 3 Sequential service restoration framework [26] 4 Optimal operation modeling Multiple energy resilient operation model [29] 5 Two-stage robust optimization model [30] 6 A risk optimization model [48] 7 The planner-attacker-defender model [49] 8 Attack structural vulnerability model [50] 9 CitInES [43] 10 Topological network modeling An improved model for structural vulnerability analysis [51] 11 Graph Model [52] 12 Tri-level defender-attacker-defender model [53] 13 A "proof-of-concept" model [24] 14 Electricity Market Complex Adaptive System [34] 15 Natural Gas Infrastructure Toolset [34] 16 Agent-based modeling Critical Infrastructure Modeling System [31] 17 Critical Infrastructure Simulation by Interdependent Agents [34] 18 Integrated energy system reliability evaluation model [33] 19 SynCity [32] 20 Resilience evaluation model [47] 21 Multi-microgrid reliability assessment framework [54] 22 Probabilistic modeling Critical Infrastructures Interdependencies Integrator [55] 23 Restore [56] 24 A framework for reliability/availability assessment [46] 25 Actor-Based Modeling Interdependent Energy Infrastructure Simulation System (IEISS) [42] 26 Empirical Modeling Framework for Electricity Production Vulnerability Assessment [44] 27 Other approaches System Dynamics Modeling CIPMA Program [34] 28 Physical Modeling Petroleum Fuels Network Analysis Model [34] 29 Integrated Simulation Platform Critical energy infrastructures [45] 30 Integrated Simulation Platform Fast Analysis Infrastructure Tool [34]

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can sometimes provide too optimistic analyses [35]. Hines et al. [57] compared purely topological network models and higher fidelity models in the vulnerability modeling of electricity infrastructures. They used three measures of vulnerability: characteristic path lengths, connectivity loss, and blackout sizes. Their conclusion was that evaluating vulner- ability in power networks using purely topological network models can be misleading. Chen et al. [50] proposed a hybrid model for structural vulnerability analysis of power networks. Their approach embodied the traditional topological methodology and took into account important characteristics of power transmission networks such as the power flow distribution. Consequently, their hybrid model better approximated real power grids compared with a traditional topological network model.

Topology modification, or known as reconfiguration, plays an im- portant role in the study of electric power system resilience, as a section can be reconnected to another power supply when an outage happens. Lin and Bie [53] proposed a tri-level defender-attacker-defender model to harden the distribution system under malicious attacks. In this model, resilient operational measures such as topology reconfiguration and DG were simulated to study their impact on distribution system resilience.

2.3.3. Agent-based modeling Agent-based models consist of dynamically interacting, rule-based

agents [58,59]. A general definition of agent is: “an entity with a loca- tion, capabilities and memory. The entity location defines where it is in a physical space… What the entity can perform is defined by its capabilities… the experience history (for example, overuse or aging) and data defining the entity state represent the entity's memory.” [60]. An agent-based model can exhibit complex behavior patterns [61] and provide valuable in- formation about the dynamics of the simulated real-world system [60].

The application of ABM in the modeling and simulation of energy infrastructures mainly focuses on the analysis of the interactions between interdependent systems. Casalicchio et al. [62] used ABM to model a system composed of a power grid and a communication network with agents representing the entire infrastructure, its subsystems and the hu- mans involved in the scenario. In this model, an agent is described by its attributes, the services it provides to other agents, and the services pro- vided by other agents. Li et al. [33] modeled the integrated energy system of electricity and natural gas system. A two-hierarchy smart agent model is built as the basis for the system reliability analysis. The lower hierarchy are the component smart agents which represent the power lines, transformers, and electricity loads while the higher hierarchy are the zone agents which form the system topology.

Another important application of ABM is to simulate the socio-eco- nomic activities, such as the electricity market and human activities within the energy infrastructure framework. Zhou et al. [63] simulated an electricity market with demand response from commercial buildings. In this model, agents were used to model different participants of the market such as power generation companies, load-serving entities, commercial building aggregators, and an independent system operator. SynCity [32] is a tool developed by Imperial College London for in- tegrated modeling of urban energy systems. This tool adopts agent-based micro-simulations to simulate the daily-activities of citizens of the city. Each citizen makes stochastic decisions based on the pre-defined rules and according to the environment around him/her. Solanki et al. [64,65] used agents to model different operators in restoring the electric system.

The ABM technique has proved its advantages in the following as- pects: (1) It can capture complicated interdependencies by simulating physical or economic flows among different infrastructures. (2) It en- ables the study of large-scale problems by avoiding complicated theo- retical analysis. (3) It allows behavior analysis of customers or decision- makers by making certain rules. However, ABM still has limitations in that it is difficult to validate, and not all types of interdependencies can be included in one single model. Most existing agent-based models can only simulate one type of interdependencies such as the physical or logical interdependency [66].

2.3.4. Probabilistic modeling In energy infrastructure resilience modeling, probabilistic algorithm

is necessarily applied to capture the uncertain characteristics of the system failure. Many models adopt sequential Monte Carlo simulation method [46,54,47]. A Monte Carlo simulation uses repeated sampling to determine the properties of some phenomenon or behavior [67]. The essential idea is to use randomness solving problems that might be deterministic in principle. It is useful for gathering information about random objects, estimating certain numerical quantities, and opti- mizing complicated objective functions [68].

Monte Carlo simulation in the field of energy infrastructure mod- eling is often employed for the simulation of weather events due to their high stochasticity. Panteli and Mancarella [47] developed a time-series simulation model based on sequential Monte Carlo method to assess the impact of weather events on power-system resilience. With the knowledge of the hurricane occurrence frequency and its impact on power system components, Li et al. [69] developed an algorithm to evaluate the risks of the power system in face of hurricanes. This method can be expanded to systems under other stochastic natural disasters. Similarly, Cadini et al. [46] used a sequential Monte Carlo simulation scheme to simulate historical failures caused by both normal and extreme weather events. The simulation results were then used to evaluate the reliability of the studied power transmission system.

Another common application of Monte Carlo simulation in energy infrastructure modeling is to simulate the restoration process of dis- rupted infrastructures. For example, the software tool Critical Infrastructures Interdependencies Integrator [55] developed by ANL used Monte Carlo simulation to estimate the time and cost required to restore a given infrastructure component, a specific infrastructure system, or a set of interdependent infrastructures.

It should be noted that Monte Carlo simulation can be integrated into other modeling frameworks, such as optimization-based models, to simulate the performance of energy systems. For example, Farzin et al. [54] evaluated the role of outage management with Monte Carlo si- mulation, while considering the optimal power flow problem of the electric distribution system.

2.3.5. Other modeling approaches Actor-based modeling: Similar to an agent-based model, an actor-

based model is composed of actors that can make local decisions, create more actors, send messages and determine how to respond to messages received. The Interdependent Energy Infrastructure Simulation System (IEISS) [42] developed by LANL is an actor-based infrastructure mod- eling, simulation, and analysis tool designed to understand inter- dependent energy infrastructures. The actors can realistically simulate the dynamic interactions within each of the infrastructures, with a specialization in simulating the interdependent electric power and natural gas infrastructures.

Empirical modeling: Empirical models are built based on historical data or expert experience. Shih et al. [44] adopted data warehousing technique to conduct vulnerability assessment of interdependencies be- tween coal mines, rail transportation, and electric power plants. A data warehouse is a system used for reporting and data analysis. It has the capability of bringing various datasets together and managing historical data. In this case, the data warehouse allowed an interactive analysis of historical and multi-dimensional data of varied granularities.

System dynamics modeling: System dynamics is a method for studying the behavior and the underlying structure of a complex system over time [70]. It is widely used in the analysis of CI interdependencies. For example, the CIPMA program [71] in Australia adopts the system dy- namics model to examine the relationships and dependencies within and between CI systems, and to demonstrate how a failure in one sector can greatly affect the operations of other CI sectors.

Physical modeling: Petroleum Fuels Network Analysis Model (PFNAM) [34] is a physical model developed by ANL to perform hy- draulic calculations of pipeline transport of crude oil and petroleum

J. Wang et al. Reliability Engineering and System Safety 183 (2019) 360–373

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products. Main outputs of the model include pressure and pipeline ca- pacity estimates along the pipeline.

Integrated simulation platform: Some models are implemented in a way that several approaches are adopted for component models and then coupled together. Erdener et al. [45] proposed an integrated si- mulation model for electricity and gas systems. The electricity and gas systems are first modeled separately and then linked by an (MATLAB- based) interface. The Fast Analysis Infrastructure Tool (FAIT) devel- oped by SNL [34] consists of a dependency model and an economic model. The dependency model is an object-oriented expert system model of infrastructure interdependencies. The economic model utilizes the input-output method for estimating the economic consequences of the disruption of an asset. An input-output model is a quantitative economic technique that represents the interdependencies between different branches of a national economy or regional economies [72]. This economics-based method has been applied on CIs to capture the cascading economic effects of a disruption across different sectors [66].

3. Proposed resilience indicators and other features

3.1. Resilience indicators

To address energy infrastructure resilience, a model should take into account certain dimensions of resilience. Sharifi [73] proposed a fra- mework for the analysis of community resilience assessment (CRA) tools. Within this framework, six criteria were proposed to evaluate the selected CRA tools. These include comprehensiveness in addressing multiple dimensions of community resilience, considering connections between different spatial scales, ability to measure changes across temporal scales, developing suitable measures for capturing un- certainties, collaboration with stakeholders, and leading to action plans. Cutter et al. [08] measured the inherent resilience of counties in the United States according to six capitals identified in the extant lit- erature: social, economic, housing and infrastructure, institutional, community, and environmental. Hosseini et al. [15] identified four domains of resilience: organizational, social, economic, engineering.

Although different researchers may emphasize various aspects when assessing resilience, they do share some common grounds. Based on lit- erature review, this paper proposes five indicators for energy infra- structure models from the resilience perspective. A model that success- fully helps enhance energy infrastructure resilience should: be dedicated to certain stakeholders, intervene in one or more resilient infrastructure development phases, be able to simulate a certain stressor and the failure it caused, address interdependencies within or between infrastructure sectors, and integrate socio-economic characteristics.

Indicator 1 – Catering to different stakeholders: Urban infrastructures are owned and operated by different stakeholders who may not be aware of the interdependencies between their own infrastructure system and other systems [74]. Different stakeholders tend to have different priorities and considerations, when making decisions related to infrastructure investment, protection, or restoration. Hence, it is necessary to identify the stakeholder of a selected model before diving into further details. A stakeholder-oriented lens helps better understand a model's values and limitations. Francis and Bekera [16] included stakeholder engagement as a key component in the analysis framework of engineered and infrastructure systems. Hasan and Foliente [74] classified stakeholders according to their scales and roles into: inter- national union, federal/state/local government, advocacy organiza- tions, donors/financial institutions, insurance, utility companies, busi- ness, and households, individuals and communities.

Indicator 2 – Intervening in development phases: This indicator evaluates in which phase of infrastructure development a model can be employed. Four phases are distinguished: design, operation, restoration, and adap- tation. Compliance with this indicator is decided as follows. If the model helps designers recognize the most vulnerable components in an infra- structure system and enhance the infrastructure resilient design, then the

model is dedicated to the design phase. If the model focuses on the modeling and simulation of CI operational status, then the model is dedicated to the operation phase. If the model simulates restoration processes and helps develop restoration strategies, then the model is dedicated to the restoration phase. If the model integrates resilience enhancement techniques and considers the long-term adaptation of CIs to certain stressors, then the model is dedicated to the adaptation phase.

Indicator 3 – Dedicating to certain stressor and failure: In the research field of resilience, a stressor represents the source that causes the system to change its original status. For CIs, there are generally two kinds of stressors: human-induced stressors such as terrorism and maloperations, and nature-induced stressors such as the climate change and extreme weather events. Identifying the stressor that a model is dealing with helps further evaluate the failure mode.

There are three types of infrastructure failures; namely, cascading failure, escalating failure, and common cause failure [55,75,76]. The cascading failure refer to the disruption of one single infrastructure that is caused by a component failure, which is common in power grid disrup- tions. An escalating failure is a disruption in one infrastructure that ex- acerbates independent disruptions in other infrastructures. This kind of escalating effect is due to the complex interdependencies among infra- structure sectors and often leads to a longer time of restoration. A common cause failure is a disruption of two or more infrastructures at the same time resulted from a common cause. Existing models typically don't dis- tinguish between “cascading failure” and “escalating failure”, englobing them all under the concept of “cascading failure”. In this paper, they are distinguished to investigate a models’ temporal scale and the feature in simulating escalating effects of disasters. For example, a model for esca- lating failure not only simulates the immediate effects of a disruption, but also the propagated effects of a disaster among different sectors.

Indicator 4 – Taking into account different interdependencies: The in- terdependency between CIs is defined by Rinaldi et al. [77] as “a bi- directional relationship between two infrastructures through which the state of each infrastructure influences or is correlated to the state of the other.” Due to the complex relationships among different CI sectors, the vul- nerability of CI systems is raised. The failure of one single component can lead to the failure of the entire system, even of the systems that rely on it. Some research results have proved the necessity to consider in- terdependencies between infrastructure systems when evaluating resi- lience and reliability [45,33].

There are four types of interdependencies: physical, cyber, geo- graphic, and logical [77]. Physical interdependency expresses the physical reliance on material flow from one infrastructure to another. Typically, the output of one infrastructure may be the input of another infrastructure for operation. Cyber interdependency expresses the re- liance on information transfer between infrastructures. An infra- structure has cyber interdependency if its state depends on information transmitted through the communication infrastructure. Geographic in- terdependency exists if a local environmental event can affect multiple infrastructures. That is, elements of multiple infrastructures are in close spatial proximity. Logical interdependency is a dependency that exists if two infrastructures depend on each other via a mechanism that fall into none of the above categories. It may be more closely linked to a control schema that links one infrastructure to another infrastructure without any direct physical, cyber, or geographic connection. Com- pliance with this indicator is confirmed if a model considers any of the four types of interdependencies inner the energy sector, or between energy and other sectors.

Indicator 5 – Involving socio-economic characteristics: Socio-economic characteristics are significant aspects of resilience. According to the City Resilience Framework [78], economy and society is one of the four basic elements of resilience, which is also recognized as the organiza- tional resilience. The other three categories include the health and wellbeing of individuals, urban systems and services and, finally, lea- dership and strategy, which emphasize the role of people, place and knowledge in constructing a resilient city. When evaluating the

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resilience of energy infrastructures, a place-based perspective con- sidering the people, as well as the socio-economics is more compre- hensive. Many researchers point out that the socio-economic impacts resulting from the infrastructure disruptions can be very significant and needs serious considerations [79,80]

This indicator examines if a selected energy infrastructure model considers the socio-economic impacts of the infrastructure failures or involves socio-economic activities in the simulation. Typical socio- economic characteristics include age, ethnic, religion, income, disaster insurance, and community resources.

3.2. Other modeling features

In order to further evaluate the models and gain insights into the characteristics of different modeling approaches in the context of energy infrastructure modeling, some more features of the models are discussed in this section; namely, data needs, model type, and time scale. Furthermore, whether the model is dynamic or static and whether the damage and re- store processes are endogenous or exogenous are also discussed.

Data needs: The input data of a model usually include information about the layout of the simulated system, commodity flows, func- tioning, as well as numerical values for modeling parameters [41]. Data needs can vary largely according to the modeling approaches. A model with high data needs relies on high quality and large quantity of input data to provide reasonable outputs. On the contrary, a model with low data needs can provide plausible outputs, even when little data is ac- cessible. This indicator analyzes the data needs of modeling approaches for energy infrastructures. For example, if a model requires databases as inputs, then the data demand level is high. If a model only has a few input variables, or only requires a small amount of profile data, then the data demand level is low. If the situation lies in between, then the demand level is regarded as medium.

However, it should be noted that there is a trade-off between a model's data need and its accuracy. High-fidelity models that reproduce the state and behavior of the real world better will rely more on high quantity and quality of data [41]. On the other hand, a model with lower data need might sacrifice its accuracy due to more assumptions. The data need of a model from a developer's angle is dependent on the development purpose. In the context of energy infrastructure resilience, for example, a model intended for impact analysis of weather events on the energy system will require more data than an optimization model that is developed for re- storation strategy design. At last, a model's data need is also highly de- pendent on the data availability. Sometimes, developers have to make reasonable assumptions to compensate for the inaccessible data.

Model type: This indicator evaluates the computational mechanism of the models. Three types of models are distinguished: white box, black box, and grey box, which is their combination. In the white-box

approach, the model uses governing laws of physics and the detailed knowledge of the underlying process [81]. In the black-box approach, the system performance data is collected under normal use or under a specific test and a relationship is found between the input and output variables using mathematical methods [82]. In the grey-box approach, the model structure is formed using physics-based methods and the parameters are determined using estimation algorithms based on the measured data [81].

Time scale: The simulation time step and time horizon vary with the purpose and scenario of the energy infrastructure model. Holmgren [52] simulated different hazard scenarios and gave their time scales. For major technical failure that disables a station in the sub-transmission or distribution grid, the corresponding vertices in the model are removed for 10 hours. For human factors and regular technical failures, the time scale is 1 to 2 hours. For snowstorm and lightning, the time scales are 8 hours and 0.5 h, respectively. As for the repair time, it usually lasts hours depending on the damaged component in the system. Li et al. [33] stu- died the reliability problem of integrated energy systems and gave the repair time of different components. Each kilometer of gas or heat pi- peline will take 5 hours to repair. However, for gas-fired boiler, steam turbine, or absorption cooling plant, it will take 200 to 300 hours to repair. This indicator examines the time scale each model is designed to simulate over. Time step and time horizon are distinguished.

Dynamic or static: Dynamic models simulate the system performance in a time-dependent way, while static models calculate the system in equilibrium. Given the dynamic characteristics of energy infrastructure systems and the time-dependent instinct of resilience problems, most energy infrastructure resilience models are built dynamically. However, there do exist some static models. Manshadi and Khodayar [29] simu- lated the resilient microgrid operation problem in a static way to identify the vulnerable components and the optimal operation plan considering the interdependency between power and gas systems. Nezamoddini et al. [48] solved a resilient distribution network planning problem in equili- brium to coordinate the hardening and distributed generation resource allocation with the objective of minimizing the system damage. The physical model Petroleum Fuels Network Analysis Model (2006) con- ducts the hydraulic calculation of fuel pipelines in an equilibrant way.

Endogenous or exogenous damage/restore: The simulation of damage and restore processes are dealt with either endogenously or exogenously in resilience models. Models that don't obtain the disruption signal from outside but rather embed the disruptions inside the model are en- dogenous. Typically, the damage of the energy infrastructure is re- presented by the disconnection of lines, open switch devices, or ran- domly or intentionally removed nodes. Specially, in some agent-based models, different types of faults are propagated by agents. In exogenous models, the damage is generated by external random or non-random events, such as unit outages or system disruptions. Li et al. [33] adopted

Fig. 1. Number distribution of models with different stakeholders.

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Monte Carlo simulation to evaluate power system reliability by gen- erating stochastic errors. The Fast Analysis Infrastructure Tool (FAIT) (2006) couples with other models to get the duration and magnitude of the disruption and recovery and conducts regional economic analysis.

4. Discussions

This section applies the above-proposed resilience indicators and other modeling features to evaluate the collected energy infrastructure models. The evaluation results can be found in Appendices 1 and 2. Findings regarding the resilience-related performance of the models and comparisons between different modeling approaches are discussed in the following text.

Stakeholder: Regarding “resilience for whom”, Fig. 1 shows the number of models with different stakeholders revealing that the stake- holders taken into account by most selected models are the decision- makers, including the government. They serve the decision-makers during the infrastructure protection tasks, investment-related proce- dures, or when faced with infrastructure emergencies. The second most common stakeholders are infrastructure providers and operators, as over one third of the selected models were developed for their needs. Infra- structure providers and operators have significant impact on energy in- frastructure resilience as they take charge of the operation and main- tenance of infrastructures. Only two models include the consumers as relevant stakeholders. Although both decision-makers (especially the government), as well as providers and operators are in the service of consumers, surprisingly little attention has been paid to energy

consumers when developing energy infrastructure models. Given that the ultimate goal of energy infrastructure resilience promotion is to better serve the consumers, it would be beneficial to consider their demands on energy supply and their response to energy infrastructure emergencies when seeking a holistic solution of energy resilience. Other stakeholders include research institutes, emergency responders, and engineers.

Intervention phase: Regarding the infrastructure development phase in which a model is employed, most models in this study are found to be dedicated to the operation phase (Fig. 2). Another considerable proportion of models conduct restoration simulations of the energy infrastructures. The least number of models take adaptational evolutions of energy in- frastructures into account. This distribution indicates that existing energy infrastructure models for resilience studies have been focusing on the operation phase. On the other hand, they are limited in integrating long- term adaptation strategies into the modeling framework, which should be an important dimension of resilience enhancement.

Stressor: Nearly 40% of the models simulating general disruptions of energy infrastructures. Instead of identifying a specific cause, these models focus on the failure of the infrastructure after the occurrence of a disaster and are generally applicable for disruption studies. 28% of the models are developed against intentional attacks while 19% are against extreme weather events such as natural disasters. Only 3% of the selected models take economic disruptions as the stressor.

Failure: 40% of the models simulate cascading failures of energy in- frastructures while 27% are for common cause failures, where several locations of disruptions occur together. However, only 16% of the models are able to simulate escalating failures of the critical infrastructures

Fig. 2. Number distribution of modeling approaches intervening in different phases.

Fig. 3. Number distribution of modeling approaches with different data needs.

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revealing that most existing energy infrastructure models don't account for the escalating effects of a failure. They tend to only focus on the immediate effects of a disruption. The varying temporal scale in the aftermath of disasters have been neglected by most selected models.

Interdependency: Regarding CI interdependencies, 43% of the se- lected models consider some types of interdependencies. The model “Critical energy infrastructures” [45] studies the interdependency inner the energy sector between the natural gas and electric power system. Other models consider interdependencies between energy and other sectors such as transportation ([32,43,44,55,56]) and telecommunica- tion ([34,55,56]). The rest of the models do not consider inter- dependencies but rather focus on the energy sector.

Socio-economic characteristics: 50% of the selected models involve socio-economic characteristics during the modeling and simulation process. However, most of these models only consider economic char- acteristics, such as economic impacts of infrastructure disruptions [83,34] and investment optimization [49,48,43]. Only four of all the selected models consider social impacts of a disaster, such as public hazards [25] or effects on population and housing [24,32,34].

Data needs: Fig. 3 depicts the number distribution of modeling ap- proaches with different data needs. Agent-based models tend to have the highest data needs, as 86% of them fall in medium and high data need columns. As for optimal operation models, topological network models and probabilistic models, most of them fall in the columns of low or medium data needs. This phenomenon is consistent with the characteristics of ABM, as historical data and attribute data will be needed to define each agent and certain interaction rules,

Model type: Concerning the model type, 93.3% of the selected models are white box. Only 3.3% of them are grey box and 3.3% are black box. In the grey box model [47], historical weather data are used to first determine the frequency distribution of certain weather events. The weather profile is then used as an input of the physics-based model. In the black box model [44], data warehousing and visualization techniques are used to manage non-spatial historical data which are then merged with geospatial data to model the potential impacts of a disruption to one or more mines, rail lines, or power plants.

Other features: When looking at other features of the models, the time horizon varies from the short term of several hours to the long term of several years, depending on the problem tackled. Accordingly, the time step ranges from 1 minute or 1 h to 1 week. Most models deal with energy infrastructure resilience problems dynamically. 63.3% of the models have endogenous damage or restoration while 16.7% have exogenous. For more details, the reader could refer to Appendix 2.

5. Conclusions

Energy infrastructures are becoming more vulnerable due to the rising frequency of both nature- and human-induced disasters. Hence, the resi- lience of energy infrastructures has gained much attention in recent years. This paper reviewed 30 energy infrastructure models from a resilience perspective. Through the review, research problems tackled by the models and typical modeling approaches adopted by researchers were summar- ized. Specifically, the authors proposed five resilience-based indicators to comprehensively address a model's capability in promoting energy infra- structure resilience. At last, other modeling features such as data needs and time scale were discussed to further evaluate the models.

The models collected in this work involve representative state-of- the-art energy infrastructure models implemented through various ap- proaches. The addressed problems include optimal resource allocation and hardening planning, interdependency analysis, outage manage- ment and restoration, weather impact study, etc. The models intervene across planning, operation, restoration and adaptation phases of energy infrastructures. Based upon the review, the following observations are gained: The dominant stakeholder of the models are decision-makers, including government and regulators. Most selected models serve en- ergy consumers indirectly as little attention is paid to energy consumers

during the development stage. Most selected models focus on the op- eration and restoration phases of energy infrastructures. Long-term adaptation strategies are not integrated into the modeling framework by most models. Existent models tend to only consider immediate ef- fects of system disruptions. The study on the propagated effects of the failure among different sectors is typically neglected. Although many selected models involve economic impact evaluation, only a few models take into account social parameters or consider social impacts of dis- asters. Concerning other modeling features, physics-based models are still the trend in energy infrastructure modeling, rather than data- driven techniques. Among others, agent-based models tend to have higher data needs than topological models and optimal operation models. The time horizon and time step vary significantly among the models, ranging from several hours to several years.

Based on the discussions above, future trends in the modeling and simulation of energy infrastructures are as follows:

Addressing larger temporal and spatial scale: As most existing energy infrastructure models focus on immediate effects of disruptions but are limited in capturing the dynamic behavior during longer terms, it remains to be explored how the models could be scaled over a larger temporal scale. Also, including the complex interactions across multiple CI sectors over different spatial scales helps making the model more realistic. However, the challenge of scalability lies in the computational time. How to employ more complexity in the model while reducing the computational time remains a challenge for future researchers. Integrating more human and social aspects: Though existent models serve mostly the needs of decision-makers, energy consumers’ be- havior and potential in helping achieving energy infrastructure re- silience would be more considered in the future. The emerging focus on human-in-loop control and demand response technologies also implies this trend. Also, since the impact of disasters eventually take place on the human and the society, it would be drawing more at- tention to integrate social characteristics in the modeling frame- works and study the social impacts of CI disruptions. However, the uncertainty in human behavior and the quantification of social factors remain a challenge. Employing more smart resources and solutions: It was noticed from the review that smart technologies such as energy storage, demand re- sponse with flexible loads (e.g. electrical vehicles, flexible building loads) are integrated by some models to explore future possibilities of energy resilience. In the future, as these technologies develop and become more accepted, involving them in energy infrastructure models would be a trend.

Due to the limited number of models collected in this paper, there are certain limitations of the work: only four of the commonly used modeling approaches are deeply analyzed and the working scope is limited to the energy sector. In the future, the same evaluation meth- odology could be applied to transportation, water supply and sewer, communication and other CI sectors.

Acknowledgment

This research was supported by the National Science Foundation under Award no. OAC-1638336.

Supplementary materials

Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.ress.2018.11.029.

Appendices

Appendices 1 and 2.

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A p p en

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Appendix 2. Other modeling features and the evaluation results of the selected models.

Modeling approach Data needs Model type Output format Time scale Dynamic or static

Endogenous or exogenous damage/Restore

1 Medium White box Data charts Several-hour time horizon Dynamic Endogenous 2 Low White box Plan N/A Dynamic Endogenous 3 Optimal operation

modeling Medium White box Plan N/A Dynamic Endogenous

4 Medium White box Plan N/A Static Endogenous 5 Medium White box Data and plan N/A Dynamic Endogenous 6 Low White box Data and plan N/A Static Endogenous 7 Low White box Plan N/A Static Endogenous 8 Low White box Data charts N/A Dynamic Endogenous 9 High White box Potential costs and CO2

emission N/A Dynamic N/A

10 Topological network modeling

Low White box Data charts N/A Dynamic Endogenous

11 Low White box Data charts Several-hour time horizon Dynamic Endogenous 12 Medium White box Plan N/A Static Endogenous 13 Medium White box Metrics 1-week time step Dynamic N/A 14 Medium White box Economic impacts 1-hour time step Dynamic Exogenous 15 Low White box GIS N/A Dynamic Exogenous 16 Agent-based modeling High White box 3D visualized model N/A Dynamic Endogenous 17 High White box Graphic models N/A Dynamic Endogenous 18 Medium White box Data charts 1-minute or 1-hour time

step Dynamic Exogenous

19 High White box Map 1-year time horizon Dynamic N/A 20 Low Grey box Index 10-hour to 50-hour time

horizon Dynamic Endogenous

21 Probabilistic modeling Medium White box Plan 1-hour time step Dynamic Endogenous 22 Low White box Graphs and tables N/A Dynamic Endogenous 23 Low White box Graphs N/A Dynamic Endogenous 24 High White and grey

box* Data charts 1 year Dynamic Endogenous

25 High White box Map N/A Dynamic N/A 26 Other modeling

approaches High Black box GIS Between 1-month and 5-

year time horizon Dynamic Endogenous

27 High White box GIS N/A Dynamic N/A 28 High White box Graphs and tables N/A Static N/A 29 Medium White box Data charts N/A Dynamic Exogenous 30 Medium White box Reports 1-week to 1-month time

horizon Dynamic Exogenous

N/A: not enough information provided. ⁎ :This model has two sub-models that adopt different modeling methods. The restoration model is white box and the cascading failure model is grey box.

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