Review on Energy Resilience

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Applied Energy

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

Sustainability of integrated energy systems: A performance-based resilience assessment methodology

Salim Moslehi⁎, T. Agami Reddy Arizona State University, School of Sustainable Engineering and the Built Environment, Tempe, AZ 85281, USA

H I G H L I G H T S

• A performance-based resilience assessment method is proposed for engineered systems. • System resilience quantified through functionality loss and associated monetary costs. • Resilience matrix is introduced where elements are resilience indices in different failure scenarios. • Methodology was applied to a large integrated energy system for an office building. • Methodology illustrated to evaluate two resilience enhancement measures.

A R T I C L E I N F O

Keywords: Resilience assessment Distributed generation Resilient design Functionality loss Optimization model Integrated energy systems

A B S T R A C T

One of the key elements of any community or facility is the integrated energy system (IES) which consists of utility power plants, distributed generation systems, and building heating and cooling systems. Assessing the sustainability of an IES would be of great value to decision-making relevant to design, future growth planning, and operation of such systems. This paper addresses one of the basic issues in this regard, i.e. resilience as- sessment and quantification of IES. A new performance-based method for characterizing and assessing resilience of multi-functional demand-side engineered systems is proposed in this study. Through modeling of system response to potential internal and external failures (called failure modes) during different operational temporal periods (such as different diurnal and seasonal periods of the year), the proposed methodology quantifies re- silience of the system based upon loss in the services which the system is designed to deliver. A three-dimen- sional matrix, called Loss Matrix, is introduced whose elements represent the undelivered system services under different scenarios, i.e. combinations of failure modes and different operational temporal periods. Assigning monetary penalty costs to such losses and including them in the objective function of an optimization model of the entire system allows the three-dimension loss matrix to be reframed into a two-dimensional Consequence Matrix where individual elements represent the imposed penalty costs to the system stakeholders due to un- delivered services and/or non-optimal system performance. Normalizing the individual elements results in the Resilience Matrix of the system for different scenarios. The developed methodology is illustrated for IES of a large office building serves to satisfy critical and noncritical electrical, heating, and cooling loads. The resilience assessment framework proposed in this paper would serve as a mean to identify critical components of a par- ticular IES, thereby facilitating resilient design and operation, and also to evaluate cost-effective resilience en- hancement strategies.

1. Introduction

Increased complexity of urban infrastructure systems on one hand, and more severe and more frequent natural disasters due to global climate change on the other hand, require analysis methods which can improve their preparedness, resistance, and rapid recovery against disruptions. The energy infrastructure, consisting of power generation

and distribution, transporting pipelines, and transportation systems (marine, railroad, truck lines, etc.), is critical for sustainable develop- ment under normal conditions, and in confronting natural and other types of extreme events and disasters. The world energy crisis, has been more pronounced in developing countries, particularly in rural areas, where people experience massive power outages in forms of planned, unplanned, unanticipated faults and burnouts. Absence of power results

https://doi.org/10.1016/j.apenergy.2018.06.075 Received 6 April 2018; Received in revised form 31 May 2018; Accepted 17 June 2018

⁎ Corresponding author. E-mail address: [email protected] (S. Moslehi).

Applied Energy 228 (2018) 487–498

Available online 28 June 2018 0306-2619/ © 2018 Elsevier Ltd. All rights reserved.

T

in drastic detrimental impacts on the economy, on education, on healthcare and, more generally, on sustainable development itself. Making infrastructure systems more resilient is thus an area of research which has gained considerable momentum in recent years.

The concept of resilience was first introduced in the 19th century in physics and material science as the ability of an object to resist loads without permanent distortion [1]. This concept has then been adopted in a variety of contexts such as, medicine, psychology, as well as in engineering. Such terms as ecological resilience, psychological resi- lience, disaster resilience, seismic resilience, family resilience, etc. have been introduced. The scope of this paper is, however, limited to resi- lience of engineered systems only.

Numerous studies have been conducted trying to characterize and assess resilience of different types of systems and proposed new defi- nition for resilience. In general, resilience assessment methods can be categorized in three groups: (i) structural assessment methods (ii) performance-based methods, and (iii) hybrid methods being a combi- nation of the first two ones. Structural assessment methods focus on the structure and general characteristics of the system and generally tend to be qualitative or semi-quantitative, in that, systems are scored using results of numerous questions categorized based on pre-identified re- silience metrics (e.g. vulnerability, capability, resourcefulness, etc.) [2]. On the other hand, performance-based assessment methods evaluate system resilience based upon the functionality of the system. Through a particular interruption scenario, this method measures, or simulates, the system performance during and after the disruption. The perfor- mance-based methods specifically consider the speed with which the system can return to the post-interruption condition, known as rapidity [3], as one of the basic aspects of resilience. The two general resilience evaluation methods, i.e. the structural and the performance-based methods, are complementary; while the structural assessment can ex- plain why a system is resilient, the performance-based approaches specify how much the system is resilient.

Numerous qualitative and quantitative studies have been conducted to define and evaluate resilience of engineered systems. These studies are different in objective and scope based on type of the assessment (quantitative, qualitative, or semi-qualitative), type of the system, and type of the disruptive event. For example, Hatvani-Kovacsa et al. in- tegrated planning and design of infrastructures and buildings in addi- tion to public health and social research to qualitatively assess the heat stress resilience [4]; Bozza et al. proposed a framework to quantita- tively assess the disaster resilience of urban systems by introducing efficiency and quality of life as indicators to be identified before and after an extreme event and also during the recovery time [1]; Zobel and Khansa proposed a new resilience measure for multiple related dis- astrous events adopting the concept of resilience triangle which char- acterizes system resilience based on the functionality loss and duration of the recovery time [5]; Chang et al. have developed a practical ap- proach to evaluate infrastructure resilience at a community scale based on historical experiences and judgments of technical specialists to identify which critical services could be lost, to what extent, and for how long; they have also investigated the ripple effect, meaning that how disruption in one infrastructure sector can have impacts on downstream sectors [6]; Maliszewski and Perrings have investigated resilience of the power distribution systems suggesting that resilience of such systems depend on power distribution infrastructure and its

biophysical environment, and also on the priority given to restoration by the power company [7]; Cimellaro et al. proposed a framework for quantitatively evaluating resilience of health care facilities subjected to earthquakes by using an analytical function that fits both technical and organizational issues [8]; Attoh-Okine et al. formulated a resilience index for urban infrastructure using Belief function accounting for in- terdependencies among systems [9]; Cutter et al. developed a frame- work to assess disaster resilience at local or community scale focusing on social resilience [10]. Ouyang et al. developed a multi-stage fra- mework to assess and analyze infrastructure resilience. They defined resilience as the joint ability of a system/infrastructure to resist (pre- vent and withstand) any possible disruption or shock, absorb the initial damages, and recover to normal operation [11].

Resilience assessment frameworks are useful both during the design phase and during system retrofitting. Ouyang and Fang, improved on their earlier work, and developed a tri-level decision-making model which supports critical infrastructure resilience optimization in order to find the best defensive strategies by identifying vulnerable system components and protecting them against intentional [12] and spatially localized [13] attacks. They introduced the resilience metric based on the performance of the interdependent infrastructures under natural hazards (such as hurricanes [14]) and random failures relative to target performance of the system [15]. Lin and Bie proposed a new Defender- Attacker-Defender (DAD) model to identify hardening and operational restoration measures as two main resilience aspects of power systems [16]; they found that hardening strategies are strongly influenced by topology reconfiguration and the distributed generation installation. Alderson et al. developed a resilience assessment model which quan- tifies operational resilience of an infrastructure system and can help developers and policy makers identify critical vulnerabilities in the system [17]. Matelli and Goebel developed a conceptual framework for resilient design of a cogeneration system through stochastic failure propagation simulation [18].

Researchers from Sandia National Laboratory (for example, Vugrin et al. [19]; Vugrin et al. [20]) have developed complex resilience as- sessment models to quantify operational resilience of an infrastructure system and help developers and policy makers identify critical vulner- abilities in the system. They have developed detailed methodologies and operating software ranging from an individual infrastructure to a whole region with multiple infrastructures based on both network models as well as multiagent modeling approaches. The methodology requires extensive involvement of local experts in all relevant areas such as engineering, social and governance which is needed in both gathering necessary data as well as developing the interactions between infrastructures. A book by Biringer et al. [21] describes this general approach called IRAM (Infrastructure Resilience Assessment Metho- dology). It is an extension of RAMCAP originally developed for hostile threats on infrastructure systems. IRAM takes into account the fol- lowing considerations (which traditional methods tend to overlook): (i) Provides precise and actionable definition of resilience, (ii) Explicitly considers costs and resource requirements of adaptation and recovery, (iii) Proposes definitions and resulting measurement methods which are generally valid to all 18 infrastructure systems, (iv) Proposes a perfor- mance-based assessment that is flexible and uses different methods and models to generate performance metrics, (v) Minimizes subjective ele- ments, (vi) Meant not only to assess resilience but also to design

Nomenclature

DP disruption period f functionality FL functionality loss IC imposed costs IP interruption period

OC operational costs PC penalty costs Re resilience t time T time period x flow (electricity, fuel, heat, etc.)

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resilient systems. While most of the previous studies are focused on quantifying and

characterizing resilience of infrastructure systems at aggregated levels, the current study addresses how resilience of demand-side systems with multiple functions can be defined, characterized, and improved. A new quantitative performance-based resilience assessment framework is developed, and a resilience matrix is introduced which captures es- sential dimensions of resilience pertinent to engineered systems. The proposed methodology is illustrated for a typical integrated energy system (IES) and energy-related measures are assessed in terms of re- silience improvements.

2. Methodology

This section describes the methodologies and mathematical ap- proaches adopted in this study to quantitatively evaluate the resilience of demand-side engineered systems.

2.1. Definition of resilience

Earlier published literature viewed resiliency of a system as its ability recover once it has been compromised due to a short-acting shock. However, the concept has evolved and has been expanded greatly, it now includes additional set of characteristics and cap- abilities. Such capabilities can be classified into three groups relative to the occurrence of the disruption: (1) “Pre-disruption” phase: involve capabilities to anticipate shocks and adapt in order to respond properly while minimizing initial damages; adaptability and robustness are some examples of pre-disruption capabilities. (2) “During-the-disruption” phase: involve ability to minimize functionality losses through cap- abilities such as fail safe meant to prevent failure propagation, or re- sourcefulness enabling implementation of alternative sources to main- tain system functionality. (3) “Post-disruption” phase: involve the capacity to deal with the consequences of failure and with the rapidity i.e., how fast the interrupted system can be recovered. Numerous de- finitions have been proposed in the literature for resilience of systems to include these capabilities relative to the type of the interruption and to the type of the system itself.

When supply-side systems, such as power generation infrastructure are targeted, fast recovery, would be an important resilience char- acteristic; but, when demand-side systems are investigated, robustness, reliability, and adoptability should be given more importance. For an IES, which can be considered a demand-side system, system perfor- mance depends on the performance of up-stream systems, i.e. the supply side electric grid and fuel distribution system and if they fail, the system performance will be adversely affected. In this case, the re- covery process is outside the control of the owner or user of the system. Internal failures (for example failure of a chiller), will also affect the system performance and can be addressed through reliability improve- ments aimed at lowering the probability of random failures (for ex- ample by performing regular maintenance), or through redundancy to prevent functionality losses (for example by having a stand-by chiller), and any other possible measure to help the system deliver its services/ products when disrupted. In transmission and distribution networks, the ability of the system to prevent propagation of failures is the main focus of resilience studies rather than recovery features [22]. Therefore, a new definition for resilience of engineered systems is proposed which is focused on functionality of the system of interest, rather than on the system characteristics as:

“Resilience is the ability of the system to meet as much of its in- tended functionalities as possible when interrupted by either ex- ternal or internal disruptions.”

This definition is holistic, in that it is not limited to the type of engineered system nor to a specific characteristic of the system, nor to a specific type of disruption. In other words, there are numerous

resilience characteristics pertinent to engineered systems and no defi- nition can contain them all. Instead, the suggested definition relates the system resilience to the level of system functionality losses since the primary goal is to maintain the system functionality at the desired level. On the other hand, quantification of resilience based on this definition, which is application and circumstance specific, will be more convenient and can be integrated into engineering practices (discussed below). The suggested definition can be adopted to different types of engineered systems, such as transportation or water distribution systems.

2.2. Quantification of resilience

Resilience of a demand-side system such as community scale in- tegrated energy systems (IES) can be characterized by its performance when stressed by internal or external disruptions. The term Interruption, then, refers to the system inability to deliver its functional service(s) during the disruption and afterwards. Fig. 1 schematically illustrates performance of a system when undergoes a disruption. Curve (1–3) represents the desired performance level identified by demand(s) pro- vided by the system, while curve (1–2–3) shows the actual system performance due to the disruption. Let the time interval t0 ≤ t ≤ t0 + TDP be the time of the disruption occurrence which es- sentially depends on nature of the event and can range from momentary ones, such as electric grid voltage drop, to long-lasting ones, like hur- ricanes and floods. Curve (1–2) shows how the system response to the disruption during this time; functional services loss rate might be slower at the beginning due to robustness of the system components. Curve (2–3) illustrates how the system bounces back to its desired state after a partial failure; depending on the disruption and the system characteristics, complete failure may occur, as illustrated by curve (2′–3′), and all functional services might be lost. The time interval t0 ≤ t ≤ t0 + TIP represents the interruption period during which the system cannot perform at its desired level. Note that the interruption period can be the same as disruption period meaning that the system is able to perform at the desired level right after the disruption is passed. At any moment during the interruption period, difference between the desired performance level and the actual performance identifies system functional service loss, denoted by floss(t). Therefore, the shaded area in Fig. 1 represents total functional service losses due to the disruption:

∫ ∫= − =+ +FL f t f t dt f t dt[ ( ) ( ) ]. ( ). t

t T desired actual t

t T loss

IP IP

0

0

0

0

(1)

Ideally, a resilient system would meet its performance targets throughout the interruption period. Two attributes characterize this attribute: (a) preparedness before the disruption, and (b) agility in re- covery after the disruption. However, we argue that not all kinds of

Fig. 1. Schematic of functionality and performance curves of an interrupted system under partial (curve 1–2–3) and complete failure (1–2′–3′); interruption period is assumed to be longer in the case of complete failure.

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interruptions require a recover period after the disruption is passed. For instance, if performance of a manufacturing unit is interrupted due to “lack of raw material” (disruption), it can start delivering its service as soon as the disruption is over. In this case, disruption and interruption periods are the same and there is no recovery process as such. Therefore, this analysis quantifies resilience of engineered system based upon the system performance during the interruption period, char- acterized by functional service losses, rather than solely based on spe- cific attributes or metrics (as in most of the published literature).

Infinite number of disruptions can be identified for a particular system and it would be impossible to analyze the system resilience in terms of all disruptions. Instead, for any system with given number of the system components, we can identify a finite number of failure modes. Regardless of cause of failures, i.e. the disruptions, analyzing effects of failures on system performance would be of great value. Therefore, in this study we focus on effects of system components failures rather than the inherent cause of the failure. Hence, a resilient system should be able to minimize losses in delivering its services, for any possible failure mode, and during all operational temporal periods. This can be represented as a three-dimensional matrix:

(2)

where arrays are service losses (each identified by Eq. (1) and shaded area in Fig. 1), j represent various failure modes correspond to failure of system components, k identifies system functional services (1 ≤ k), and i shows various operational temporal periods impacting the resilience of the system. Operational temporal periods may represent temporal variations in the system operation and are meant to reflect the extreme cases such as maximum demands in various seasons of the year. Hereafter, combinations of failure modes and operational temporal periods are referred to as scenarios.

Analyzing and studying a three-dimensional matrix would be in- convenient, especially for large systems with numerous many compo- nents and failure modes. We, therefore, suggest assigning monetary penalty costs to functional service losses and thereby reducing the matrix order to two. To do so, at any given i and j, i.e. for a given scenario, we estimate total imposed costs due to functional service losses and non-optimal system operations as:

∑= + × − =

IC f OC FL PC OC| [ ( ) ]i j j i j k

K

i j k i k i desired, , 1

, , , (3)

where IC f|i j j, denotes the imposed costs due to failure mode j, OCi j, is the operational costs during failure mode j and time period i, K is the total number of system functional services, and PCi k, represents the penalty costs associated with one unit of k functional service loss during time period i. Further, we have assumed that the penalty costs do not vary based on the failure modes, but may vary depending on the time period. For instance, penalty costs of unmet electrical loads (in $/unmet kWh) in a commercial unit is independent of why the system is unable to meet the loads (i.e. the failure mode) but may vary throughout the day de- pending on criticality of electrical loads during different hours of the day. OCi desired is the operational cost for uninterrupted system running optimally during time period i. More detailed discussions on identifi- cation of failure modes and calculation of imposed costs are provided below. Note that repair and replacement recovery costs of failed or damaged systems can be included in estimating the imposed costs in real-case applications. Also, more complex penalty cost functions can be used to estimate the imposed costs but linear penalty cost functions were used in this study.

Using Eq. (3), the three-dimensional Loss Matrix can be reduced to a two-dimensional matrix called “Consequence Matrix” which includes the imposed monetary costs associated with different scenarios:

= ⎡

⎣

⎢ ⎢

⋯ ⋮ ⋱ ⋮

⋯

⎤

⎦

⎥ ⎥

Consequence Matrix IC IC

IC IC

J

I I J

1,1 1,

,1 , (4)

Therefore, resilience of the system can be characterized by the Consequence Matrix containing total monetary costs incurred to the system stakeholders (users, owners, etc.) under different scenarios. Such failures could range from random failure of the system compo- nents, to deliberate attacks, to personnel mistakes. In any case, one or multiple system components would fail whereby functionality of the system is compromised if the system is not fully resilient. Failing in delivering the functional services at the desired level may cause con- siderable damages to assets, products, or even to reputation of the provider. Such damages can be often expressed in monetary penalty costs. For instance, according to Hamachi LaCommare and Eto, eco- nomic costs associated with power interruption to the U.S electricity customers is estimated to be about $80 billion annually [23].

Imposed costs can be used to develop a quantitative resilience index. Since resilience is a positive attribute, higher numbers should reflect better performance while higher imposed costs ought to re- present poorer resilience in dealing with disruptions. Therefore, in this analysis, the resilience index is defined pertinent to each scenario as:

Fig. 2. Schematic of the imposed costs curves of an interrupted system under (a) partial failure (curve 1–2–3) and (b) complete failure (1–2′–3′).

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= −

Re IC IC

IC i j

i Max

i j

i Max,

,

(5)

where ICi Max is the maximum possible imposed costs in each scenario,

i.e. if all functional services during operational temporal period i are lost. Fig. 2 schematically illustrates the resilience index as (Shaded Area Hatched Area/ ). Therefore, resilience index ranges be- tween 0 and 1, and corresponds to the worst and best level of resilience respectively. Re = 0 reflects the situation that system would not be able to deliver any of its functional services, and Re = 1 indicates that functionality of the system would not be interrupted at all.

The Resilience Matrix which includes resilience indices for all iden- tified scenarios can be represented as:

=

⎡

⎣

⎢ ⎢ ⎢ ⎢

⋯

⋮ ⋱ ⋮

⋯

⎤

⎦

⎥ ⎥ ⎥ ⎥

= ⎡

⎣

⎢ ⎢

⋯ ⋮ ⋱ ⋮

⋯

⎤

⎦

⎥ ⎥

− −

− −

Resilience Matrix Re Re

Re Re

IC IC IC

IC IC IC

IC IC IC

IC IC IC

J

I I J

1,1 1,

,1 ,

Max

Max

Max J Max

I Max I

I Max

I Max I J

I Max

1 1,1

1

1 1,

1

,1 ,

(6)

Note that the proposed methodology is a performance-based ap- proach. Expressing resilience of the system in monetary terms will en- able planners and designers to perform cost-effectiveness analysis of various resilience enhancement options more conveniently.

2.2.1. Failure modes In this study, disruptions are defined based on failure of individual

system components regardless of the causes and type of events which caused them. It should be noted that while cause of failures for various system components are not explicitly involved in the analysis, in- vestigating causes of various components failures would be of great

value in reducing failure risks. This will improve predictive and adaptive performance of the system in order to reduce the probability of failures and thereby enhance resilience of the system. In addition, improving robustness of individual components against prevailing disruptions can improve resilience of the whole system.

Failure of any set of system components can be considered as a system failure mode. Total number of single-component failures dis- ruption scenarios can be as large as number of system components. Since system complexity is often defined as number of components and their connections, the proposed framework also accounts for complexity of the system considered as an important factor affecting system resi- lience.

This study is more focused on single-component failures in order to identify the critical components of the system and the level of func- tionality losses. This should not be confused with “cascading failures” which are considered in this analysis through system performance si- mulation during different failure modes; cascading failure (or some- times referred to as ripple effects) occurs when failure of one compo- nent propagates to other components of the system and causes additional failures. In this analysis, cascading effects are modeled. Multiple-components failures are left for future extensions of this study as proper sampling methods and prior domain knowledge regarding simultaneous failures, especially for systems will large number of components, is required.

2.2.2 Imposed costs calculation Imposed costs due to system failures would have many different

aspects and may vary depending on type of failure, type of undelivered functions, and failure duration. The imposed costs are those forced on the system stakeholders due to disruptions and ought to be

Fig. 3. A typical integrated energy system diagram which includes utility electricity and Natural Gas inputs, on-site power generation, heating and cooling equipment, and the facility loads.

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distinguished from operational costs of the system during normal op- erations.

In order to estimate losses in functional services, the investigated system has to be modeled at the appropriate granularity and fidelity levels. The system model should be able to realistically reflect behavior of the system during normal operation, as well as during each failure mode. Network systems modeling, also known as graph models, can be used to simulate the interactions between various components within the system and with upstream systems.

Performance of engineered systems are constrained by economic, physical, and operational limitations which can be easily formulated and incorporated into an optimization model reflective of how the system can and ought to perform. Applying physical and practical con- straints requires background knowledge of the system, and relatively detailed component and interaction models are needed. The objective of the optimization model will reflect desired performance of the system which can be minimum operational costs, maximum revenue, etc. Defining the resilience index in terms of monetary costs enables us to formulate the objective function of the optimization model as minimum imposed costs for each failure mode during each operational temporal period. Since the penalty costs associated with functional service losses are included in the imposed costs, the optimization model will set the system status, i.e. load of different components, such that those losses are minimal. Therefore, the system will adopt and actively respond to each failure. Further discussions and mathematical for- mulations are provided in Section 3.

2.2.3. Penalty costs The costs imposed to the stakeholders, due to failing in delivering

functional services, damages to the system, and non-optimal operation are used to quantify the resilience index. This would essentially depend on type of products and/or services provided by the system and the assigned monetary values to losses in delivery of those services. One example can be economic values of uninterrupted electricity services which can be estimated through various perspectives and methods [24]; these methods include: (i) surveying customers to assign dollar values to the costs that might incurred during an outage. This can be direct costs such as loss of production in an industrial unit, for which market prices are available, or contingent costs for services with no market value. In the latter case, “willingness to accept” or “willingness to pay” concepts are often used in order to monetize the damages. (ii) Proxy methods through which cost of the outage is evaluated by an observable

behavior such as the amount of money industrial customers would in- vest on back-up generators to prevent loss of functional services and damages due to electric grid failures. Such back-up systems are usually sized based one the critical functions (critical functions/outputs are those that will impose huge cost to the stakeholders if interrupted) such as life safety loads in a health care hospital. Further discussions on critical loads can be found in “critical loads securing” literature (such as studies by Pipattanasomporn et al. [25] and by Sujil et al. [26]).

3. System modeling and simulation

To estimate the system functional service losses due to a disruptive event, i.e. to identify how failure of each individual system component affects the whole system functionality, a realistic model of the entire system with proper level of fidelity is required. Scope and purpose of the analysis identifies how detailed such a system model should be. As discussed earlier, optimization model of the system is suggested in this study as it provides several advantages [17]. Such models not only are able to capture topological features of the system, i.e. number of system components and their interconnections, but also, they account for physical and operational limitations through model constraints. With inclusion of penalty costs (due to undelivered functional services) in the objective function of the optimization model, adaptation would be an in- built capability of the system to respond to various failure modes. Ad- ditionally, prioritizing different functional services of the system can be easily accomplished by assigning proper penalty costs to undelivered services proportional to their criticality. This is one of the unique fea- tures of the current study.

The proposed resiliency assessment methodology is illustrated for an integrated energy system (IES) shown in Fig. 3. The system includes various types of on-site power generation systems, such as combined heat and power (CHP) and solar photovoltaics (PV), electrical energy storage systems, and heating and cooling equipment. The energy system loads, i.e. heating, cooling, and electrical loads, are classified as critical and noncritical loads. This classification will help in prioritizing various types of services and to treat them differently when maximizing system resilience. Loads classification depends on type of the system and should be specified by the stakeholders. On the other hand, multiple number of equipment of each type are usually installed in order to provide redundancy and also to achieve more efficient performance. The corresponding network representation of the IES is shown in Fig. 4. System components are shown as nodes and linked through vectors or

Fig. 4. Network representation of the IES shown in Fig. 3.

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edges. Depending on type of the system, these vectors can be electric transmission lines, pipelines, roads, etc.

Fig. 4 illustrates the network model of the IES. Node 0 and node 21 are imaginary nodes added to the network model to fulfill the con- servation laws for the energy system network. Node 0 represents total energy enters the system and node 21 is an energy sink which captures all energy losses from system components. By connecting all the system outputs and the sink node (node #21) to the source node (node #0), the conservation law for the entire system will be fulfilled. A mixed integer linear programming (MILP) optimization model was developed in this study which incorporates different systems and components perfor- mance as well as physical system constraints [27]. Component perfor- mance (or efficiency) models identify the lost portion of the input en- ergy to that component. Various linear (constant efficiency) and non- linear (variable efficiency based on the system part-load ratio) models for each component type can be found in the literature (see [28,29] for more detailed discussions on component models and control optimi- zation of integrated energy systems). Segmented-linear models were used in this study in order to reduce the computational burdens while accounting for non-linear nature of efficiency performance of these components. The developed optimization models have been validated by independent evaluations with two other research groups form Pa- cific Northwest National Lab (PNNL) and Washington State University (WSU) [27].

Fig. 4 is the connected directed graph for the IES assumed in Fig. 3. The network shows energy flows between system components. In this case, the optimization model objective function includes both opera- tional and penalty costs associated with different functions of the system which enables the model to adapt and prioritize the functions based on their criticality in case of disruptions.

∑⎧ ⎨ ⎩

+ ⎛

⎝ ⎜ ×

⎞

⎠ ⎟

⎫ ⎬ ⎭=

OC FL PCmin i j k

K

i j k i k, 1

, , , (7)

This optimization model is subject to physical and operational constraints such as energy and mass balances, component capacity constraints, and ramping constraints. Interconnections among system components are captured by conservation laws as:

∑ ∑− = = …x x for q N0 1, 2, , p

pq r

qr (8)

where xpq represents flows enter the node q and xqr represents flows leave the node q and N shows total number of nodes (i.e. system components). Eq. (8) can be expressed in the matrix form as:

=× ×A X[ ] [ ] 0N M M 1 (9)

where matrix A is the node-edge incidence matrix, i.e. rows represents nodes and columns represents edges and entries are −1 or +1 or 0 (refer to a graph theory textbook such as [30] for further details). The matrix X arrays, i.e. xpq s are flows (energy flows in this case) from node p to node q (p, q = 1, 2, …, N) and M denotes total number of edges (connections) in the graph. Depending on type of the system, other operational and physical constraints should also be included in the optimization model. Detailed discussions on the IES optimization model constraints can be found in [28,29].

When IES are analyzed, functional service losses would be unmet heating, cooling, and electrical loads (both normal and critical). As discussed earlier, proper penalty cost values should be assigned to unmet loads (in Dollar per unmet MJ) reflective of criticality of loads. The optimization model, then, minimizes the operational and penalty costs during each scenario (recall that each scenario is a combination of

Fig. 5. Flowchart illustrating the various steps of the proposed resilience assessment framework.

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a failure mode occurring during a particular operational temporal period). For instance, one failure mode can be electric grid failure; depending on the facility loads at each operational temporal period, on- site power generation components, such as the CHP system and the solar PVs might not be able to entirely cover the loads. Therefore, the optimization model will prioritize different system functions based on the assigned penalty costs and will try to cover the more critical ones first such that the penalty costs are minimum.

The operational costs, i.e. electricity and fuel costs, should also be determined from the optimization model, modified to treat the condi- tional case where one or more nodes and/or one or more links are broken. Under such cases, the needed services can be met by operating the numerous equipment differently. For instance, when the electric grid fails, cooling loads can be met by electric chillers fed by on-site generated power or by the absorption chiller which can use the heat generated by the boiler or recovered from the CHP system. The opti- mization model identifies which alternative would be more economical. Note that the assigned penalty costs to unmet loads should be larger than operational costs otherwise the optimization model would choose not to meet the loads in order to minimize the objective function.

The flowchart depicted in Fig. 5 summarizes all the steps in the proposed resilience assessment methodology.

4. Case study

The integrated energy system shown in Fig. 3 is assumed in order to illustrate the capabilities of the developed framework. A large office building with 5500 m2 floor area located in Boston, MA is assumed whose IES consists of two CHP systems, two boilers, two vapor com- pression (VC) chillers, and one absorption chiller (Table 1) [28,29]. The baseline case does not include solar PVs and electrical battery storage systems.

In this case study, four operational temporal periods have been se- lected representative of various seasonal and diurnal operational con- ditions of the system. The Summer and Winter design days were se- lected to be July 24th and February 2nd respectively. In addition, six system functional services have been considered in the current study as specified in Table 2. Penalty costs associated with critical and non- critical electrical unmet loads were taken from prior research which assigned monetary costs to electric utilities service reliability for dif- ferent types of customers across the U.S. [31]. However, we could not find similar penalty costs for heating and cooling unmet loads; there- fore, the values listed in Table 2 are assumed only for the purpose of this analysis. Note that these penalty costs are case-specific and the best practice would be to conduct surveys and asking system stakeholders to decide on the operational temporal scenarios, load classifications, and the assigned penalty costs.

Table 3 summarizes hourly critical and noncritical loads of the studied IES averaged during the specified time interval of each opera- tional temporal periods (these were determined by a detailed hourly building energy simulation program described in [25]). Note that the case study is conducted on an hourly basis due to unavailability of data on failure durations for most of the failure modes and large un- certainties associated with those for which data could be found (e.g. power grid failure).

Ten specific failure modes were considered in this analysis: 1 – electric power grid failure; 2 – natural gas distribution grid failure; 3 – reciprocating engine (prime mover) failure; 4 – turbine (prime mover) failure; 5 – both prime movers failure; 6 – one boiler failure; 7 – both boilers failure; 8 – one vapor compression chiller (VC) failure; 9 – both VCs failure; and 10 – absorption (Abs.) chiller failure. The IES was si- mulated through each of these failure modes and deficiencies in desired functional services were evaluated for all scenarios.

5. Results and discussion

5.1. Baseline case

The Loss Matrix (Eq. (2)) is generated for this case study as a 4 × 6 × 10 matrix (shown in Fig. 6); each array identifies unmet loads (in GJ) due to one failure mode and during one operational temporal period.

Zero values in the loss matrix imply that the corresponding load or service is being fully met. It can be seen that critical electrical loads are all met during all scenarios. Using an optimization model of the system along with proper penalty cost values enable the system to prioritize different functionalities based on their criticality and manage available sources to first satisfy more critical ones. As noted from the Loss Matrix, none of the unmet critical loads are greater than noncritical ones for any given scenario which identifies that the model is capable of prioritizing different tasks based on their criticality.

Consequence Matrix for the investigated IES is shown in Fig. 7. Using Eq. (3) and the penalty cost values given in Table 2, imposed costs were calculated for each failure mode and operational temporal period. It is obvious from the results that the “Electric Grid Failure” mode would cause the highest imposed costs mainly due to high elec- trical loads, specifically during the “Summer Day” and “Winter Day” operational temporal periods. The “NG Grid Failure” mode would be the next critical failure mode followed by the “Both VC Chillers Failure” mode which would impose penalty costs due to unmet cooling loads during the “Summer Day” operational temporal period. It is worth mentioning that failure modes 3, 4, 5, and 10 would not impose any penalty costs, and all the imposed penalty costs are due to non-optimal performance of the IES. All other failure modes result in some amount of penalty costs. Comparing failure mode 6 with failure mode 7, and failure mode 8 with 9, demonstrate that the provided redundancy can reduce the unmet loads due to failure of the equipment thereby im- proves resilience of the IES.

Finally, the values of the Resilience Matrix, calculated according to Eqs. (5) and (6) are shown in Fig. 8. Recall that Re = 0 means total loss in functional services and that Re = 1 implies no loss in delivered services.

As expected, resilience indices correspond to “electric Grid Failure” during “Summer Day” and “Winter Day” are the lowest among all in- vestigated scenarios. We can conclude that resilience improvement strategies should be focused on strengthening against these scenarios. On the other hand, natural grid distribution network is more reliable compared to electric grids and other forms of energy transport systems mostly because it is underground [32].

5.2. Resilience improvement measures

Since the “Electric Grid Failure” mode is found to be by far the most critical one, it is reasonable to focus on improving the system resilience against this failure mode. Therefore, two improvement strategies, called Resilience Improvement Measures (RIM), were considered: RIM1: adding a solar PV system; and RIM2: adding an electrical battery sto- rage. The PV system and the battery system are sized such that the initial costs are equal for both RIMs. First, a 700-kW PV system was modeled using PVWatts calculator developed by NREL [33] (standard panel type, fixed mount with 42° tilt angle equal to the location

Table 1 Equipment specifications for IES case study.

Prime mover Boilers VC chiller Abs. chiller

Quantity 1 (reciprocating engine) + 1 (turbine)

2 (identical) 2 (identical) 1

Capacity (unit)

788 + 242 (kW) 7063.7 MJ/h 600 Ton 155 Ton

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latitude); the PV system capacity was selected such that it can cover 30% of the peak total electrical loads during the Summer design day (July 24th); then, the initial cost of the PV system was calculated based on $3/Watt (according to [34]) which was found to be around $2 million. Battery system capacity, calculated based on similar initial investment ($2 million), was found to be 7000 kWh (battery price was assumed to be $300/kWh [35]). We assumed that 10% of battery charge is always available for emergency situations, such as sudden grid failure.

It should be noted that solar PVs and battery storage systems are reliable systems. According to Vazquez and Roy-Stolle, solar PVs failure rates are in the order of 10-3 failures per year [36]. Reliability of battery storage systems drops sharply after certain number of cycles which depends on storage system configuration and management strategies [37]; before reaching to such point, battery systems are reliable if sized and maintained properly. On the other hand, failure of the PV or the battery components would degrade the whole system performance to the baseline case. Therefore, PV and battery storage failure modes were not considered for the improved IES. In general, adding a new com- ponent to the baseline case should be considered by defining an addi- tional failure mode.

Fig. 9 assembles the results of the constrained optimization for unmet noncritical electrical loads for the three cases. Both the RIMs have reduced the unmet loads for the two “Summer Day” and “Winter Day” operational temporal periods with battery option being more ef- fective. However, for the two night periods, there is no unmet loads in all three instances. The uncertainty bands shown for RIM1 reflects the variability of the PV system output during each operational temporal period; the upper limit corresponds to zero PV output (say due to overcast sky) and the lower limit is when the PV system generates at its maximum capacity during that operational temporal period. Such variability is a drawback of PV systems, or any other non-dispatchable power generation technology, with regards to resilience performance. No critical electrical load is left unmet in all cases (i.e. the baseline as well as the two improved cases) suggesting that on-site power genera- tion (CHP system) has improved system resilience during “Electric Grid Failure” mode; such capability is often referred to as self-sufficiency or adaptability.

Results of the first RIM, i.e. solar PV implementation, corresponds to electric grid failure are

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Consequence Matrix RIM

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RIM2 can improve the resilience index of the system by 18.1% for both “Summer Day” and “Winter Day” periods while RIM1 improves the system resilience by 9.5% during the “Summer Day” and by 6.7% during the “Winter Day”. Thus, we conclude that implementation of battery storage can result in much lower imposed costs and higher re- silience indices. Therefore, from the resilience standpoint, having a battery storage would be a better option compared to the PV system. In addition, PV system output is stochastic and may not be available during the grid failure mode should it be cloudy. Thus, we would conclude that battery storage system has a better value in term of en- hancing the IES resilience. Other types if RIMs can be evaluated in a similar fashion.

In dealing with electric grid outages, frequency and duration of outages, which considerably varies by country and region, would be decisive factors. Such statistics are usually collected, tracked, and published by federal and governmental authorities. American Public Power Association (APPA) has published grid reliability data for var- ious U.S. regions [38]. Customer Average Interruption Duration Index (CAIDI), reported in minutes, and System Average Frequency Inter- ruption Index (SAIFI), reported in number of occurrences per annum, are particularly helpful regarding end-use energy systems. The large office building studied here is located in Boston, MA, in the APPA re- gion 8 for which the CAIDI is 65 min and the SAIFI is 0.51 (almost once in two years with average during around one hour). This information can be used to assess the real value of the resilience improvement measures over the lifecycle of the energy system. For instance,

Table 2 Case study operational temporal periods, system functions, and assigned penalty costs.

Operational temporal periods IES functional services

Noncritical elec. ($/kWh)

Critical elec. ($/kWh)

Noncritical heating ($/GJ)

Critical heating ($/GJ)

Noncritical cooling ($/GJ)

Critical cooling ($/GJ)

1 – Summer-Day (6 AM–5 PM) 20 200 50 500 100 1000 2 – Summer-Night (6 PM–5 AM) 10 200 25 500 50 1000 3 – Winter-Day (6 AM–5 PM) 20 200 50 500 100 1000 4 – Winter-Night (6 PM–5 AM) 10 200 25 500 50 1000

Table 3 Critical and noncritical loads of the case study energy system.

Operational temporal periods Hourly average loads

Noncritical elec. (kWh) Critical elec. (kWh) Noncritical heating (GJ) Critical heating (GJ) Noncritical cooling (GJ) Critical cooling (GJ)

1 – Summer-Day 1480 295 1.4 0.3 9.7 1.9 2 – Summer-Night 530 106 1.0 0.2 4.2 0.9 3 – Winter-Day 1482 296 6.8 1.4 3.5 0.7 4 – Winter-Night 650 130 4.3 0.9 1.8 0.4

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according to SAIFI of the given location, 12 outages are expected during lifespan of the PV system (assumed to be is 25 years). Note that APPA region 8 has one of the most reliable electric grids in the U.S, and thus, resilience improvements measure would be more significant in other regions. For example, the SAIFI for region 3 is 1.63 and therefore 41 outages would be expected during the 25-year horizon. Average inter- ruption duration is also higher in region 3 (191.25 min); resilience improvements would be crucial in such regions.

6. Summary and future work

Sustainable and resilient infrastructure systems are critical to achieve sustainable development under normal conditions, and in confronting extreme events and disasters. Improving infrastructure systems resilience, as a crucial attribute of sustainable systems, is thus an area of research which has gained considerable momentum in recent years. Developing quantitative resilience assessment methods in sup- port of decision-analysis regarding operation, design, and retrofitting resilient engineered systems would be one of the first steps towards this goal.

In this study, resilience is regarded as an umbrella term which covers several concepts including reliability, robustness, adaptability, self-sufficiency, etc. A new simple and comprehensive definition is

proposed for resilience of engineered systems which can be adopted to different types of systems and captures different operational and structural resilience characteristics. This paper proposed a mathema- tical resilience assessment framework for multi-functional demand-side engineered systems. Through modeling and constrained optimization of system response to potential internal and external failures, the proposed methodology allows resilience to be quantified in terms of functional loss and monetary costs arising from loss in services which the system is designed to deliver. A three-dimensional matrix, called Loss Matrix, is introduced which represents undelivered system services under dif- ferent scenarios, i.e. combination of the specified failure modes during different operational temporal periods (such as different diurnal and seasonal periods of the year). By assigning monetary cost penalties to different service losses for different temporal periods, the three-di- mension loss matrix to be reframed into a two-dimensional Consequence Matrix where individual elements represent the imposed penalty costs to the system stakeholders due to undelivered services and/or non- optimal system performance under different scenarios. Normalizing the individual elements results into the Resilience Matrix of the system whose elements range between 0 and 1, with 0 denoting total loss in all functional services and 1 denoting no loss under the corresponding scenario.

The developed methodology was applied to assess resilience of an

Fig. 6. Loss Matrix associated with the case study IES. Functional service losses are in GJ/h.

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integrated energy system of a large office building, composed of on-site power generation, electricity and natural gas inputs from utility, and heating and cooling equipment serve to satisfy critical and noncritical electrical, heating, and cooling loads (i.e., six end-use services in all). Performance of the IES case study was simulated during four opera- tional temporal periods and 10 failure modes using a constrained op- timization model capable of capturing economic, physical, and prac- tical limitations. Critical components of the IES was identified, as those which their failure causes the most imposed costs, and two resilience improvement measures, i.e. adding solar PV system and adding elec- trical battery storage, were evaluated. Results showed that adding battery storage system would be a more effective strategy to improve IES resilience.

The proposed resilience assessment framework offers several ad- vantages compared to the existing ones: (i) through a constraint opti- mization model of the system, the system performance during disrup- tion can be realistically modeled accounting for physical, economic, and operational limitations; such models are usually available for op- erational control and optimization and can be modified to include penalty costs and possible failure scenarios to be used for resilience assessment purposes; (ii) the developed framework can be implemented for different types of engineered systems and is able, and meant to, handle multi-functional systems; (iii) quantification of resilience per- formance in monetary terms facilitates resilience considerations to be

incorporated in cost-effectiveness analyses; (iv) it directly targets system performance when confronted a disruption, rather than focusing on system characteristics, e.g. faster recovery, which may or may not improve the system respond to the disruption.

Note that assigning penalty costs ought to be based on the condition and type of building/facility and ranges from “loss in personnel

Fig. 7. Consequence Matrix for the case study IES.

Fig. 8. Resilience Matrix for the case study IES for different failure modes and operational temporal periods.

Fig. 9. Unmet noncritical electrical loads comparison along with uncertainty bands associated with PV outputs.

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productivity” to “loss of lives”. For instance, in a residential building located in an extreme cold weather, heating loads are more critical as residents may lose their lives in the absence of heat supplies; in this case, different, and potentially very high, penalty costs would be as- signed to the critical heating loads. Value of Statistical Life (VSL), which is an economic value used to quantify the benefit of avoiding fatalities, can be used to estimate the associated penalty costs to the critical heating loads.

The methodology proposed in this paper can be extended/improved in a number of ways: (i) more subtle consideration of the criticality of loads (rather than simply considering them as critical and non-critical) and expressing associated service loss penalties as a non-linear function with relevant uncertainties stated as, say fuzzy numbers, (ii) extending the current methodology which is limited to events that cause little or no physical damage to more extreme events including disasters, (iii) including frequency of occurrences of different failure modes and their duration which is important for resilience-enhancing investment.

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