Review on Energy Resilience

Sustainability and Resiliency Measures for Long-Term Investment Planning in Integrated Energy and

Transportation Infrastructures Diego Mejia-Giraldo1; Jose Villarreal-Marimon2; Yang Gu3; Yanyi He4;

Zhaoyang Duan5; and Lizhi Wang6

Abstract: Comprehensive and revealing performance measures are critical for the assessment of long-term investment plans. In this paper are defined three performance measures for long-term investment planning in integrated energy and transportation infrastructures: cost, sustainability, and resiliency. Whereas the first measure can be defined relatively straightforwardly, there exist significant ambiguity and discrepancy in the definitions of the last two in the existing literature. Different qualitative descriptions have been made in various research contexts, yet few studies have provided quantifiable definitions. This paper provides quantitative definitions of sustainability and resiliency measures that are appropriate for assessing long-term investment decisions in an integrated energy and transportation system. Sustainability is defined using the time duration for which the system will be able to satisfy operational and environmental requirements. Resiliency is mea- sured as the cost to transition from a precontingency state to a postrecovery state. A case study using representative U.S. coal transportation and electricity transmission networks is conducted to demonstrate the assessment methods. DOI: 10.1061/(ASCE)EY.1943-7897.0000067. © 2012 American Society of Civil Engineers.

CE Database subject headings: Sustainable development; Investments; Energy; Infrastructure; Transportation management.

Author keywords: Sustainability measure; Resiliency measure; Investment planning; Energy infrastructures; Transportation infrastructures.

Introduction

Long-term investment planning decisions in energy and transpor- tation systems will have increasingly overarching impacts on one another as a result of the growing interdependencies between the two systems. On the one hand, the fuel supply for the energy system relies on transportation infrastructures such as freight, rail, and barge. On the other hand, the current momentum toward transportational electrification exemplified by plug-in hybrid- electric vehicles will also enable the energy system to provide cheap, clean, and domestic electricity as an alternative transporta- tion fuel. Therefore, long-term investment planning for these two systems must be coordinated to leverage and strengthen their emerging interdependencies.

The effort to make “optimal” long-term investment decisions requires performance measures that are not only comprehensive to represent the balance of multiple objectives, but also revealing to indicate directions for potential improvement. For such purpose, three measures cost, sustainability, and resiliency—are identified as fundamentally important to capture the complementary character- istics of a healthy, interdependent, and integrated system of energy and transportation infrastructures. Whereas the cost measure can be defined relatively straightforwardly, there exist significant ambigu- ity and discrepancy in the definitions of sustainability and resil- iency measures in the existing literature. Different qualitative descriptions have been made in various research contexts, yet few studies have provided quantifiable definitions. Therefore, this study focuses on quantitative definitions of sustainability and resiliency measures that are appropriate for assessing long-term investment decisions in integrated energy and transportation systems. Sustain- ability is measured using the time duration for which the system will be able to serve demand without violating operational, envi- ronmental, and economic constraints. Resiliency is measured using the cost for the system to transition from a precontingency state to a postrecovery state.

This study is a component of a research project, “21st Century National Energy and Transportation Infrastructures—Balancing Sustainability, Costs, and Resiliency (NETSCORE-21),” at Iowa State University. The goal of this project is to formulate optimal infrastructure designs in terms of future power generation technol- ogies, energy transport and storage, and hybrid-electric transporta- tion systems, with balance in costs, sustainability, and resiliency.

In the remainder of this paper, existing definitions and measures of sustainability and resiliency in the literature are reviewed, and then definitions of the sustainability and resiliency measures are presented. Next, a case study is conducted using an integrated

1Dept. of Electrical and Computer Engineering, Iowa State Univ., Ames, IA 50011; and Universidad de Antioquia, Medellin, Colombia.

2XM, Compañía de Expertos en Mercados SA (Colombian System Operator), Medellin, Colombia.

3Midwest Independent Transmission System Operator, St. Paul, MN 55108.

4Dept. of Industrial and Manufacturing Systems Engineering, Iowa State Univ., Ames, IA 50011.

5Dept. of Industrial and Manufacturing Systems Engineering, Iowa State Univ., Ames, IA 50011.

6Dept. of Industrial and Manufacturing Systems Engineering, Iowa State Univ., Ames, IA 50011 (corresponding author). E-mail: lzwang@ iastate.edu

Note. This manuscript was submitted on June 24, 2011; approved on January 17, 2012; published online on May 15, 2012. Discussion period open until November 1, 2012; separate discussions must be submitted for individual papers. This paper is part of the Journal of Energy Engineering, Vol. 138, No. 2, June 1, 2012. ©ASCE, ISSN 0733-9402/2012/2-87–94/ $25.00.

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electricity generation/transmission network and a coal production/ transportation network, representing the contiguous United States. Conclusions are drawn at the end of the the paper.

Literature Review

Sustainability Definitions and Indicators

The word “sustainability” is derived from the Latin sustinēre, meaning to “hold up, endure and support” (Merriam-Webster Dictionary 2011). In 1970, the National Environmental Policy Act [42 U.S.C. 4321 et seq.] (NEPA) described sustainability as conditions under which humans and nature “can exist in productive harmony, and fulfill the social, economic and other requirements of present and future generations of Americans.” In 1981, the White House Council on Environmental Quality Report (White House Council 1981) stated that sustainable development “must proceed in a way that protects the natural resource base of developing coun- tries.” An often-quoted definition of sustainable development is from the 1987 United Nations report (World Commission on Environment and Development 1987): “Sustainable development is development that meets the needs of the present without com- promising the ability of future generations to meet their own needs.” The U.S. Environmental Protection Agency states that “Sustainability is based on a simple principal: Everything that we need for our survival and well-being depends, either directly or indirectly, on our natural environment” (U.S. EPA 2012). The 2005 World Summit refers to environmental sustainability, eco- nomic sustainability, and social sustainability as three “inter- dependent and mutually reinforcing pillars” of sustainable development. Brekke (1997) defines two categories of sustainabil- ity: “A development is … said to be weakly sustainable if the development is nondiminishing from generation to generation,” whereas “the second interpretation, known as ‘strong sustainabil- ity’, sees sustainability as nondiminishing life opportunities.”

Different indicators have been proposed to measure sustainabil- ity. Phillis et al. (2010) categorize 7 fundamental attributes of a system-of-systems into which sustainability models fall: opera- tional independence of the component systems, managerial inde- pendence of the component systems, geographical distribution, emergent behavior, evolutionary development, self-organization, and adaptation. Sustainability issues are particularly pressing in the energy and transportation sectors, which are respectively respon- sible for around 40 and 33% of total carbon dioxide emissions in the United States [Department of Energy/Energy Information Administration (DOE/EIA) 2008]. Jeon and Amekudzi (2005) address definitions, indicators, and metrics of sustainability in transportation systems. In the context of energy systems, Afgan et al. (2000) use 4 indicators to assess the sustainability of energy systems: resource, environment, social, and efficiency. Evans et al. (2009) define 7 sustainability indicators for renewable energy tech- nologies: price of electricity generation, greenhouse gas emissions, availability and technological limitations, efficiency of energy gen- eration, land use, water consumption, and social impacts. Vera and Langlois (2007) use 24 energy indicators to assess sustainable de- velopment: equity, accessibility, affordability, disparities, health, safety, use and production patterns, overall use, overall productiv- ity, supply efficiency, production, end use, diversification, prices, security, imports, strategic fuel stocks, atmosphere, climate change, air quality, land, soil quality, forest, solid-waste generation and management. Related literature also includes Altman (2009), Braun (2010), and Ilić et al. (2011), who discuss sustainability and its indicators in different contexts.

Resiliency Definitions sand Indicators

First introduced as a descriptive ecological term (Holling 1973, 1996; Brand and Jax 2007), the concept of resiliency has been fre- quently redefined and widely adopted as a critical characteristic of systems in various disciplines, such as engineering (Lovins and Hunter 1982; Dolev et al. 2006; Gunderson and Pritchard 2002), economics (Arthur 1999), psychology (Richardson 2002; Tugade et al. 2004), and sociology (Clark and Dickson 2003). Engineering resiliency “concentrates on stability near an equilibrium steady state, where resistance to disturbance and speed of return to the equilibrium are used to measure the property” (O’Neill et al. 1986). Economic resiliency “refers to the inherent and adaptive responses to disasters that enable individuals and communities to avoid some potential losses” (Rose 2004). Psychological resiliency refers to “the ability to bounce back from negative events by using positive emotions to cope” (Tugade et al. 2004). Social resiliency is defined as “the ability of social units to mitigate hazards, contain the effects of disasters when they occur, and carry out recovery activities in ways that minimize social disruption and mitigate the effectors of further earthquakes” (Bruneau et al. 2003).

Whereas the concept of engineering resiliency is similar to sta- bility (Kundur 1994), which is frequently used to describe the abil- ity of a system to return to a stable equilibrium state after the occurrence of a disturbance, ecological resiliency appears to be a more appropriate objective for the long-term investment planning purpose of energy and transportation infrastructures. As defined in Holling (1973), ecological resiliency “emphasizes conditions far from any equilibrium steady state, where instabilities can flip a sys- tem into another regime of behavior—that is, to another stability domain.” From a longer-term (e.g., 20 to 40 years) planning per- spective, energy and transportation infrastructures both behave like living systems that grow in an uncertain environment. The measure of resiliency should, therefore, focus on the system’s ability to with- stand unexpected events and possibly evolve into a better state rather than necessarily return to the same state before the events.

Various indicators have been proposed to measure resiliency. Holling (1973) proposes the resistance to disturbance and speed of getting to the equilibrium; Ives (1995) uses the variability in population densities resulting from interactions among species; Bruneau et al. (2003) compute reduced failure probability, reduced consequences from failure, and reduced time to recovery; Rose (2004) quantifies the extent to which the estimated direct output reduction deviates from the likely maximum; and Ludwig et al. (1997) argue that resiliency of a system depends on the objectives and functions of the system, the time scale of interest, the character- istics and magnitude of disturbances, and the underlying structure of the system, which need to be identified before the resiliency of a system can be assessed.

Sustainability and Resiliency Measures

Introduced first are four input factors that are necessary to define sustainability and resiliency measures: system of interest, Sym; expected demand, Dmd; projected events, Evt; and expected actions, Act.

The input factor Sym defines the subject of measurement, which can be represented by general mathematical programs. For conven- ience of exposition, this paper uses as an example the linear program

ζτ ¼ min x fc⊤τ x : Aτx ≥ bτ; x ≥ 0g ð1Þ

where x = decision variable; ζτ = objective value; and subscript τ = time period.

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The input factor Dmd represents all the requirements of the system, such as electricity demand, coal demand, emissions con- straints, clean water usage, and economic operation. Some of these (such as energy demand) may be the system demand, whereas others may be imposed by external authorities (such as emissions constraints). As such, the factor Dmd could include part of the right-hand-side parameters and/or some constraints in the sys- tem Sym.

For the sustainability measure, the input factor Evt includes uncontrollable events that are expected to happen to the system of interest, such as retirement of energy and transportation infra- structures,infrastructures and availability of fuel supply and renew- able resources. For the resiliency measure, this input factor also includes the set of unforeseeable high-consequence events (contin- gencies) that could happen to the system of interest.

For the sustainability measure, the input factor Act represents the planning strategies that will be carried out, such as retiring old inefficient fossil fuel power plants and building new transmis- sion lines. For the resiliency measure, this input factor also includes the expected reaction to a particular contingency, such as how much and how quickly new generators can be installed after the loss of a certain amount of generation capacity because of an an earthquake.

Sustainability Measure

Adopting the philosophy of the definition of sustainable develop- ment given by the World Commission on Environment and Devel- opment (1987), the sustainability measure is defined as follows.

Definition 1. For a given system of interest Sym, expected de- mand Dmd, projected events Evt, and expected investment actions Act, the sustainability of the system is measured by the duration of time that the system is able to meet demand by carrying out the investment plan under expected projected events. This measure is denoted by S (Sym, Dmd, Evt, Act).

The capability of the system to serve the demand is determined by whether model (1) possesses a solution that satisfies all con- straints. Failure to satisfy any of these constraints will lead to infea- sibility. If in some year t þ 1 the system starts to be unable to meet demand (e.g., because of retirement of old generators and lack of new ones to fill the vacancy), then the system model is determined infeasible and the sustainability of the system is measured as t:

SðSym; Dmd; Evt; ActÞ ¼ maxft : ð1Þ is feasible; ∀ τ ¼ 1; …; tg ð2Þ

Strictly speaking, the parameters Aτ , bτ , and cτ and the objective value ζτ in (1) are determined by the input factors (Dmd, Evt, Act). For ease of exposition, this dependency is not explicitly expressed in models (1) and (2).

Resiliency Measure

After adoption of the ecological resiliency concept defined in Holling (1973), the resiliency measure is defined as follows.

Definition 2. For a given system of interest Sym, expected de- mand Dmd, contingency event Evt, and expected recovery action Act, the resiliency of the system is measured by the cost of tran- sition from the precontingency state to the postrecovery state while serving the demand. This measure is denoted by R (Sym, Dmd, Evt, Act).

In this definition, the precontingency state is right before the contingency occurs, whereas the postrecovery state is right after the recovery action has finished. The cumulative cost deviation from the nominal scenario, in which the contingency event did not happen, is used as the resiliency measure

R ¼ XN

τ¼0 βτðζτ � ζnominalτ Þ ð3Þ

where β = discount factor, which accounts for the time value of money; ζτ = total cost in year τ under the contingency; ζnominalτ = total cost in year τ reference under the nominal scenario; and N = duration of the recovery action Act. This resiliency measure has a unit of dollars, reflecting the increased cost caused by the contingency event. This definition is illustrated in Fig. 1, where shaded area indicates the resiliency measure.

Definition 2 follows the philosophy of ecological resiliency, which allows the system to grow and evolve after a contingency without necessarily returning to the precontingency state. It may be impossible to return or the system finds it better to transition to a different postrecovery state. The indicator used to measure the resiliency is thus the cost of this transition. It is assumed that the assessment of resiliency is subject to the choice of a specific event Evt and a recovery action Act. The former describes what contin- gency could possibly happen to the system, and the latter provides a recovery strategy that will be taken in response to the contingency.

Case Study

A case study was conducted on an integrated energy and transpor- tation system representing the contiguous United States to illustrate the proposed measures.

The following linear programming model is used to represent the integrated energy and transportation system, which is an in- stance of the system model (1):

min ζ ¼ X

i∈Γ;j∈Ω;m∈S τmðCOMj þ ηjPfuelj ÞqEi;j;m þ αE

X

i∈Γ;m∈S ~ei;mτm

þ X

k∈Φ;m∈S τmPCk q

C k;m þ

X

s∈Θ;m∈S TCs f

C s;m þ αC

X

k∈Φ;m∈S τm~ck;m

ð4Þ

s:t: X

j∈Ω qEi;j;m �

X

r∈Ψ AEi;rf

E r;m þ ~ei;m ¼ DEi;m; ∀ i ∈ Γ; m ∈ S

ð5Þ

qCk;m � X

s∈Θ ACk;sf

C s;m þ ~ck;m ¼ DCk;m; ∀ k ∈ Φ; m ∈ S ð6Þ

f Er;m ¼ P i∈Γ

AEi;rδi;m

Xr Pbase; ∀ r ∈ Ψ; m ∈ S ð7Þ

Fig. 1. System response to a contingency event

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X

m∈S qEi;j;mτm ≤ γi;jCEi;j

X

m∈S τm; ∀ i ∈ Γ; j ∈ Ω ð8Þ

FEr;min ≤ f Er;m ≤ FEr;max; ∀ r ∈ Ψ; m ∈ S ð9Þ

FCs;min ≤ f Cs;m ≤ FCs;max; ∀ s ∈ Θ; m ∈ S ð10Þ

X

i∈Γ;m∈S ~ei;mτm ≤ σE

X

i∈Γ;m∈S DEi;mτm ð11Þ

X

i∈Γ;j∈Ω;m∈S τmEi;jqEi;j;m ≤ �M ð12Þ

0 ≤ qEi;j;m ≤ CEi;j; ∀ i ∈ Γ; j ∈ Ω; m ∈ S ð13Þ

0 ≤ qCk;m ≤ CCk ; ∀ k ∈ Φ; m ∈ S ð14Þ

� π ≤ δi;m ≤ π; ∀ i ∈ Γ; m ∈ S ð15Þ

~ei;m;~ck;m ≥ 0; ∀ i ∈ Γ; k ∈ Φ; m ∈ S ð16Þ The objective (4) is to minimize the total cost of the system.

The five cost terms are for electricity generation (including O&M and fuel), electricity demand not served, coal production, coal transportation, and coal demand not served, respectively. Constraint (5) imposes Kirchhoff’s current law, and constraint (6) requires the balance of coal demand and supply. Constraint (7) imposes Kirchhoff’s voltage law by formulating the DC power flow as a func- tion of voltage angle difference and line reactance. Constraint (8) means that electricity generation of any technology is limited by its capacity factor. Constraints (9) and (10) establish the lower and upper bounds for electricity transmission and coal transportation, respectively. Constraint (11) sets the maximally allowed percentages of energy demand not served. Constraint (12) limits the amount of emissions from electricity generation. Constraints (13) and (14) de- fine the lower and upper bounds of electricity generation and coal

production, respectively. Constraint (15) sets the range of voltage angle, and constraint (16) requires that the expected electricity and coal demand not served be nonnegative.

Data Sources

The system consists of 17 electricity nodes and 11 coal production nodes. The electricity nodes are illustrated in Fig. 2 of Zhou et al. (2011). Each electricity node represents an electrical subregion de- fined by the North American Electrical Reliability Corporation (NERC), with the exclusion of Canadian regions. Table 1 summa- rizes the regions that the 17 nodes represent. A total of 29 trans- mission paths are considered. The transmission capacities are set to be equal to the power flows under the nominal case scenario. All load blocks (base load, medium load, and peak load) are assumed to increase by 1.5% annually, and the demand at year t ¼ 0 is as- sumed to be 790 GW, approximately the 2007 U.S. peak demand level.

Eleven different types of power plants are considered: pulver- ized coal, oil (petroleum), natural gas combined cycle (NGCC), nuclear, hydro and pumped storage, biomass and wood, wind, so- lar, geothermal, other gases (e.g., lift gas), and others (e.g., fuel

Fig. 2. Three investment plans a) ActS1, no investment; b) Act S 2, 19.4% wind; (c) Act

S 3, renewables

Table 1. Electricity Nodes

Number Region Abbreviation

1 Northwest NWPP

2 California CA

3 Arizona AZNMSNV

4 Rocky Mountains RMPA

5 Mid-Continent MAPP

6 Southwest SPP

7 Texas ERCOT

8 Mid-America MAIN

9 East Central ECAR

10 Energy Electric System EES

11 Tennessee Valley Authority TVA

12 Virginia–Carolinas VACAR 13 Southern Company SOCO

14 Florida Reliability Coordinating FRCC

15 Mid-Atlantic Area Council MACC

16 New York ISO NYISO

17 ISO New England ISONE

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cells). Table 2 lists some of the data used for the computational experiment. The set of coal supply nodes is represented by the 11 production mines in Fig. 1 and Table 1 of Zhou et al. (2011). The model consists of 70 coal transportation paths between coal mines and electricity regions. Most of the data are taken from DOE/EIA (2008). The present computational experiment was coded in CVX (Grant and Boyd 2010), a Matlab-based convex optimization tool.

Sustainability Measure

The sustainability of the system is assessed respect to three invest- ment plans—ActS1, Act

S 2, and Act

S 3,—closed up to “which” which

are illustrated in Figs. 2(a)–2(c), respectively, and defined as follows: • ActS1: There is no investment in new generation capacity. The

existing level of generation capacity at t ¼ 0 is kept constant through the 40-year assessment horizon.

• ActS2: Wind penetration is 19.4% annually with high presence of NGCC.

• ActS3: Investment is made in nuclear and renewable energy technologies. System model (4)–(16) is solved for 40 years under all three

investment plans. This model may become infeasible either because of a lack of generation capacity to serve energy demand, violating constraint (11) with σE ¼ 0:01, or because of a high level of CO2 emissions in the power system, violating constraint (12). The

emissions cap is set to be �M ¼ 1929:7 MMeTon (2127.1 million short tons) of CO2 in Year 1 and reduced by 10% annually. In all cases, optimal solutions can be obtained by removing the violated constraints, if any. The percentage of energy demand served and the amount of emissions are shown in Fig. 3. Plan ActS1 violates con- straint (11) in the sixth year and constraint (12) in the second year, resulting in a sustainability measure of 1 year. Plan ActS2 violates only constraint (12) in the third year, so its sustainability measure is 2 years. Plan ActS3 does not violate any constraint, so its sustain- ability measure is at least 40 years. Results are summarized in Table 3.

Resiliency Measure

A nominal scenario is assumed as a reference case for resiliency evaluation. The capacity growth under the investment plan of the nominal scenario is shown in Fig. 4(a). This scenario was ob- tained by assuming a constant growth rate in capacity of each tech- nology throughout the planning horizon, favoring renewable resources such as wind power, geothermal, and nuclear. Electric transmission capacity is assumed to expand at a yearly rate of 2%.

Three contingency events are defined in terms of losses in capacities of generation units, electricity transmission, and coal transportation at specified locations of the event, which are detailed in Table 4. The magnitudes of losses are intentionally assumed to be severe enough to represent high-consequence events such as earth- quakes, tsunamis, and hurricanes. All contingencies are assumed to occur in Year t ¼ 1. The transmission and coal transportation losses to which the table refers are the losses of capacity in the set of paths that link the specified region with the rest of the system.

For each of the three contingency events, two recovery plans are considered. A recovery plan is defined as the investment actions to be carried out to restore the capacities of the system over a specified period in response to the occurrence of a high-consequence event. The first recovery plan, ActR1 , recovers 100% of the capacity losses within 5 years of occurrence of the contingency. The second

Table 2. Electricity Generation Technology Data

Technology O&M cost Heating rate Emissions ($∕MWh) (MBTU∕MWh) (lb∕MBTU)

Coal 4.7 9.2 215.0

Oil 3.2 9.3 160.0

NGCC 2.0 6.8 117.1

Nuclear 0.5 10.5 0.0

Hydro 2.5 9.9 0.0

Biomass + wood 6.9 9.5 100.0

Wind 2.1 9.9 0.0

Solar 3.0 9.9 0.0

Geothermal 3.0 33.0 0.0

Other gases 0.0 13.6 115.0

Other 49.0 7.9 100.0

0.0%

0.2%

0.4%

0.6%

0.8%

1.0%

1.2%

1.4%

1.6%

1.8%

Plan 1 Plan 2 Plan 3 Upper limit

Time (year)

P er

ce nt

ag e

of e

xp ec

te d

en er

gy s

er ve

d

0

500

1,000

1,500

2,000

2,500

3,000

1 (a) (b)

2 3 4 5 6 7 8 1 5 9 13 17 21 25 29 33 37

Plan 1 Plan 2 Plan 3 Upper limit

C ar

bo n

E m

is si

on s

(M M

eT on

)

Time (year)

Fig. 3. Sustainability constraints (a) energy; (b) emissions

Table 3. Sustainability Measures

Plan

First year violated

S (years)Constraint (11) Constraint (12)

ActS1 6 2 1

ActS2 — 3 2 ActS3 — — ≥ 40

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recovery plan, ActR2 , is similar to Act R 1 except that all recovery ac-

tivities are delayed by 5 years, so ActR2 takes 10 years and there is no recovery effort in the first 5 years. Fig. 4 shows the recovery process in terms of total generation capacity for contingency event EvtR1 . Those for events Evt

R 2 and Evt

R 3 are similar in pattern and,

thus, are omitted. Figs. 5(a) and 5(b) show the response of the system to each con-

tingency under the presence of a recovery plan. Event EvtR1 seems to be the most severe for the system, resulting in a higher cost when the system transitions from the precontingency to the postrecovery state. The resiliency measure can be computed according to Eq. (3), which is the present value of the area between the contingency tra- jectory and the nominal one. Table 5 shows this computation using β ¼ 0:9. According to the results, the system is more resilient to event EvtR2 under both recovery plans. This is so partly because the installed capacity at region 11 (where event EvtR2 occurs) is less

than those at regions 2 and 14 (where the other two events occur), so the consequence of event EvtR2 is expected to be smaller. Moreover, the resiliency measures are almost tripled for all three contingency events under recovery plan ActR2 compared with ActR1 , indicating the importance of preparedness for making quick responses after a contingency.

The sensitivity of the resiliency measure defined in Eq. (3) to the discount factor, β, is analyzed. Because β is used only in (3), system model (4)–(16) does not need to be recalculated. Tables 6 and 7 summarize the results for a larger and a smaller β value, respectively.

Although the conclusions regarding the importance of the re- covery plans remain intact, the numerical values of R do respond to β. In particular, the resiliency measure for recovery plan ActR2 , which delays recovery activities by 5 years, exhibits a higher sen- sitivity to the discount factor.

Fig. 4. Expansion and recovery plans (a) nominal expansion scenario; (b) recovery plans for contingency even EvtR1

0.00

(a) (b)

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

1 5 9 13 17 21 25 29 33 37 41

Nominal Event 1 Event 2 Event 3

Time (year)

T ot

al C

os t

($ tr

il li

on )

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

1 5 9 13 17 21 25 29 33 37 41

Nominal Event 1 Event 2 Event 3

Time (year)

T ot

al C

os t

($ tr

il li

on )

Fig. 5. Recovery plan total costs under (a) recovery plan ActR1 and (b) recovery plan Act R 2

Table 4. Catastrophic Events

Event Region

Loss in capacity

Generation Transmission Transportation

EvtR1 2 80% 80% 80%

EvtR2 11 80% 80% 80%

EvtR3 14 80% 80% 80%

Table 5. Resiliency Measures for β ¼ 0:9 R ($trillion)

EvtR1 Evt R 2 Evt

R 3

ActR1 0.48 0.17 0.22

ActR2 1.17 0.52 0.64

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Conclusions

Three measures—cost, sustainability, and resiliency—have been proposed assess long-term investment plans for integrated energy and transportation infrastructures. These measures focus on different yet complementary perspectives of a healthy invest- ment plan. Because of the lack of existing sustainability and resil- iency measures suitable for this purpose, the focus of this paper has been to quantitatively establish these two measures. Use of these measures was demonstrated in a case study of an integrated energy and transportation system representing the contiguous United States.

This paper’s definition of the sustainability measure has three prominent features that make it particularly suitable for not only energy and transportation but other systems as well. First, rather than having a high-dimensional indicator that may be specific to a particular system of interest, the present definition is a one- dimensional scaler: the duration of time for which the system is able to sustain. The succinctness of this measure makes it easier to balance the trade-off with the other two measures, cost and resil- iency, which are equally important for assessing an investment plan. Second, this definition is flexible enough to adopt to other systems, as the sustainability constraints can be modified to reflect specific requirements of a particular system without affecting the definition of the measure. Third, this definition not only indicates for how long the system will sustain, but also reveals which con- straints are bottlenecks to further improvement.

Our resiliency measure also has the advantages of being succinct, flexible, and revealing. Moreover, this measure captures not only the magnitude of the impact of the contingency on the system but also the duration of the impact. The resiliency mea- sure thus reveals the system’s capability to adjust to the contin- gency by transitioning to a postrecovery state in a timely and smooth manner.

The measures defined in this paper are used to assess exog- enously determined long-term investment plans rather than to directly obtain the optimal one. Future research should be directed toward addressing the interdependencies between energy and trans- portation systems and evaluating the benefit of coordinating invest- ment in these two systems. Another important next step is to extend the definitions of the two indicators presented in this paper to ac- commodate imperfect information, such as uncertain input factors Sym, Dmd, Evt, and Act. This will make the indicators less sensi- tive to the choice of scenarios under consideration. Stochastic programming and dynamic programming could be useful methods for such a purpose.

Acknowledgments

This research is partially supported by the U.S. National Science Foundation under Grant No.EFRI-0835989.

Notation

The following symbols are used in this paper: AEi;r = element (i, r) of the electricity network incidence matrix∀i ∈ Γ, r ∈ Ψ, unitless; ACk;s = element (k, s) of the coal network incidence matrix∀k ∈ Φ, s ∈ Θ, unitless; CEi;j = capacity available of power plants with technology j ∈ Ω

located at node i ∈ Γ, MW; COMj = operation and maintenance cost of power plants with

technology j ∈ Ω, $million∕MWh; CCk = coal production capacity at node k ∈ Φ, short tons∕h; ~ck;m = expected coal demand not served at node k ∈ Φ

during load duration curve (LDC) step m ∈ S, short tons∕h;

DEi;m = expected electricity demand at node i ∈ Γ during LDC step m ∈ S, MW;

DCk;m = expected coal demand at node k ∈ Φ during LDC step m ∈ S, MBTU∕h;

Eij = emission rate of electricity generation at node i ∈ Γ by technology j ∈ Ω, short tons∕MWh;

~ei;m = expected electricity demand not served at node i ∈ Γ during LDC step m ∈ S, MW;

FCs;max = maximum coal transportation flow by transmission path s ∈ Θ, short tons∕h;

FCs;min = minimum coal transportation flow by transmission path s ∈ Θ, short tons∕h;

FEr;max = maximum electricity capacity flow by transmission path r ∈ Ψ, MW;

FEr;min = minimum electricity capacity flow by transmission path r ∈ Ψ, MW;

f Cs;m = coal flowing through transportation paths s ∈ Θ during step m ∈ S of LDC, short tons∕h;

f Er;m = power flowing through transmission line r ∈ Ψ during step m ∈ S of LDC, MW;

�M = emissions cap, short tons of CO2; Pbase = base power of the electricity system, MW; PCk = mine-mouth coal price at node k ∈ Φ, $million∕short ton;

Pfuelj = fuel price of power plants with technology j ∈ Ω, $million∕MBTU;

qEi;j;m = electricity generation at node i ∈ Γ by technology j ∈ Ω during step m ∈ S of LDC, MW;

qCk;m = coal production at coal node k ∈ Φ during step m ∈ S of LDC, short tons∕h;

S = set of LDC steps; TCs = coal transportation cost of path s ∈ Θ, in $million∕ton; Xr = reactance of the transmission path r ∈ Ψ, p.u.; αC = cost of expected carbon demand not served,

$million∕short ton; αE = cost of expected electricity demand not served,

$million∕MWh; Γ = set of electricity generation nodes; γij = capacity factor of power plants with technology j ∈ Ω

located at node i ∈ Γ in %, unitless; δi;m = voltage angle at node i ∈ Γ during step m ∈ S of LDC,

rads; ηj = heating rate of plants with technology j ∈ Ω,

MBTU∕MWh;

Table 7. Resiliency Measures for β ¼ 0:8696 R ($trillion)

EvtR1 Evt R 2 Evt

R 3

ActR1 0.45 0.16 0.21

ActR2 1.01 0.46 0.56

Table 6. Resiliency Measures for β ¼ 0:9524 R ($trillion)

EvtR1 Evt R 2 Evt

R 3

ActR1 0.54 0.18 0.24

ActR2 1.51 0.65 0.82

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Θ = set of coal transportation paths; σE = upper bound of energy demand not served, %; τm = duration of LDC step m ∈ S, h; Φ = set of coal production nodes; Ψ = set of electricity transmission paths; and Ω = set of electricity generation technologies.

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