Evaluating and Visualizing the Economic Impact of Commercial Districts Due to an Electric Power Network Disruption

Critical infrastructure networks enable social behavior, economic productivity, and the way of life of communities. Disruptions to these cyber–physical–social networks highlight their importance. Recent disruptions caused by natural phenomena, including Hurricanes Harvey and Irma in 2017, have particularly demonstrated the importance of functioning electric power networks. Assessing the economic impact (EI) of electricity outages after a service disruption is a challenging task, particularly when interruption costs vary by the type of electric power use (e.g., residential, commercial, industrial). In contrast with most of the literature, this work proposes an approach to spatially evaluate EIs of disruptions to particular components of the electric power network, thus enabling resilience‐based preparedness planning from economic and community perspectives. Our contribution is a mix‐method approach that combines EI evaluation, component importance analysis, and GIS visualization for decision making. We integrate geographic information systems and an economic evaluation of sporadic electric power outages to provide a tool to assist with prioritizing restoration of power in commercial areas that have the largest impact. By making use of public data describing commercial market value, gross domestic product, and electric area distribution, this article proposes a method to evaluate the EI experienced by commercial districts. A geospatial visualization is presented to observe and compare the areas that are more vulnerable in terms of EI based on the areas covered by each distribution substation. Additionally, a heat map is developed to observe the behavior of disrupted substations to determine the important component exhibiting the highest EI. The proposed resilience analytics approach is applied to analyze outages of substations in the boroughs of New York City.     

Integrating Operational and Organizational Aspects in Interdependent Infrastructure Network Recovery

Managing risk in infrastructure systems implies dealing with interdependent physical networks and their relationships with the natural and societal contexts. Computational tools are often used to support operational decisions aimed at improving resilience, whereas economics‐related tools tend to be used to address broader societal and policy issues in infrastructure management. We propose an optimization‐based framework for infrastructure resilience analysis that incorporates organizational and socioeconomic aspects into operational problems, allowing to understand relationships between decisions at the policy level (e.g., regulation) and the technical level (e.g., optimal infrastructure restoration). We focus on three issues that arise when integrating such levels. First, optimal restoration strategies driven by financial and operational factors evolve differently compared to those driven by socioeconomic and humanitarian factors. Second, regulatory aspects have a significant impact on recovery dynamics (e.g., effective recovery is most challenging in societies with weak institutions and regulation, where individual interests may compromise societal well‐being). And third, the decision space (i.e., available actions) in postdisaster phases is strongly determined by predisaster decisions (e.g., resource allocation). The proposed optimization framework addresses these issues by using: (1) parametric analyses to test the influence of operational and socioeconomic factors on optimization outcomes, (2) regulatory constraints to model and assess the cost and benefit (for a variety of actors) of enforcing specific policy‐related conditions for the recovery process, and (3) sensitivity analyses to capture the effect of predisaster decisions on recovery. We illustrate our methodology with an example regarding the recovery of interdependent water, power, and gas networks in Shelby County, TN (USA), with exposure to natural hazards.     

Systems Resilience for Multihazard Environments: Definition,Metrics, and Valuation for Decision Making

The United Nations Office for Disaster Risk Reduction reported that the 2011 natural disasters, including the earthquake and tsunami that struck Japan, resulted in $366 billion in direct damages and 29,782 fatalities worldwide. Storms and floods accounted for up to 70% of the 302 natural disasters worldwide in 2011, with earthquakes producing the greatest number of fatalities. Average annual losses in the United States amount to about $55 billion. Enhancing community and system resilience could lead to massive savings through risk reduction and expeditious recovery. The rational management of such reduction and recovery is facilitated by an appropriate definition of resilience and associated metrics. In this article, a resilience definition is provided that meets a set of requirements with clear relationships to the metrics of the relevant abstract notions of reliability and risk. Those metrics also meet logically consistent requirements drawn from measure theory, and provide a sound basis for the development of effective decision‐making tools for multihazard environments. Improving the resiliency of a system to meet target levels requires the examination of system enhancement alternatives in economic terms, within a decision‐making framework. Relevant decision analysis methods would typically require the examination of resilience based on its valuation by society at large. The article provides methods for valuation and benefit‐cost analysis based on concepts from risk analysis and management.     

Quantifying Community Resilience Using Hierarchical Bayesian Kernel Methods: A Case Study on Recovery from Power Outages

The ability to accurately measure recovery rate of infrastructure systems and communities impacted by disasters is vital to ensure effective response and resource allocation before, during, and after a disruption. However, a challenge in quantifying such measures resides in the lack of data as community recovery information is seldom recorded. To provide accurate community recovery measures, a hierarchical Bayesian kernel model (HBKM) is developed to predict the recovery rate of communities experiencing power outages during storms. The performance of the proposed method is evaluated using cross‐validation and compared with two models, the hierarchical Bayesian regression model and the Poisson generalized linear model. A case study focusing on the recovery of communities in Shelby County, Tennessee after severe storms between 2007 and 2017 is presented to illustrate the proposed approach. The predictive accuracy of the models is evaluated using the log‐likelihood and root mean squared error. The HBKM yields on average the highest out‐of‐sample predictive accuracy. This approach can help assess the recoverability of a community when data are scarce and inform decision making in the aftermath of a disaster. An illustrative example is presented demonstrating how accurate measures of community resilience can help reduce the cost of infrastructure restoration.     

Reframing Resilience: Equitable Access to Essential Services

We urgently need to put the concept of resilience into practice if we are to prepare our communities for climate change and exacerbated natural hazards. Yet, despite the extensive discussion surrounding community resilience, operationalizing the concept remains challenging. The dominant approaches for assessing resilience focus on either evaluating community characteristics or infrastructure functionality. While both remain useful, they have several limitations to their ability to provide actionable insight. More importantly, the current conceptualizations do not consider essential services or how access is impaired by hazards. We argue that people need access to services such as food, education, health care, and cultural amenities, in addition to water, power, sanitation, and communications, to get back some semblance of normal life. Providing equitable access to these types of services and quickly restoring that access following a disruption are paramount to community resilience. We propose a new conceptualization of community resilience that is based on access to essential services. This reframing of resilience facilitates a new measure of resilience that is spatially explicit and operational. Using two illustrative examples from the impacts of Hurricanes Florence and Michael, we demonstrate how decisionmakers and planners can use this framework to visualize the effect of a hazard and quantify resilience-enhancing interventions. This “equitable access to essentials” approach to community resilience integrates with spatial planning, and will enable communities not only to “bounce back” from a disruption, but to “bound forward” and improve the resilience and quality of life for all residents.     

An Optimization‐Based Framework for the Identification of Vulnerabilities in Electric Power Grids Exposed to Natural Hazards

This article proposes a novel mathematical optimization framework for the identification of the vulnerabilities of electric power infrastructure systems (which is a paramount example of critical infrastructure) due to natural hazards. In this framework, the potential impacts of a specific natural hazard on an infrastructure are first evaluated in terms of failure and recovery probabilities of system components. Then, these are fed into a bi‐level attacker–defender interdiction model to determine the critical components whose failures lead to the largest system functionality loss. The proposed framework bridges the gap between the difficulties of accurately predicting the hazard information in classical probability‐based analyses and the over conservatism of the pure attacker–defender interdiction models. Mathematically, the proposed model configures a bi‐level max‐min mixed integer linear programming (MILP) that is challenging to solve. For its solution, the problem is casted into an equivalent one‐level MILP that can be solved by efficient global solvers. The approach is applied to a case study concerning the vulnerability identification of the georeferenced RTS24 test system under simulated wind storms. The numerical results demonstrate the effectiveness of the proposed framework for identifying critical locations under multiple hazard events and, thus, for providing a useful tool to help decisionmakers in making more‐informed prehazard preparation decisions.     

Physical–cyber–human framework-based resilience evaluation toward urban power system: Case study from China

Because the increased frequency, intensity, and duration of extreme weather events have significantly challenged power systems, there has been an increased interest in resilient power systems. This article establishes a multicriteria resilience evaluation framework for urban power systems from a physical–cyber–human system perspective, in which the two principal elements responsible for power system function degradation are described, the three major domains comprising urban power systems are explained, four core capacities that positively contribute to power system resilience are proposed, and 15 (11 objective and four subjective) power system resilience evaluation indicators are identified. Fuzzy hesitant judgment and a Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) aggregation method are employed to minimize the expert divergence and maximize the group consensus. A validation method is designed and a comparison with commonly applied performance-based and attributes-based evaluation methods is conducted. The applicability of the evaluation framework is verified using data from four Chinese municipalities: Shanghai, Beijing, Chongqing, and Tianjin. It was found that Shanghai's resilience was the best, and Chongqing's physical resistance disadvantages would result in the greatest difficulties in coping with extreme event disturbances. Physical, cyber, and human domain resilience enhancement strategies are given for different cities separately. This study provides a practical tool to evaluate, compare, and enhance power system resilience for governments and public utilities.     

Toward Disaster‐Resilient Cities: Characterizing Resilience of Infrastructure Systems with Expert Judgments

Resilient infrastructure systems are essential for cities to withstand and rapidly recover from natural and human‐induced disasters, yet electric power, transportation, and other infrastructures are highly vulnerable and interdependent. New approaches for characterizing the resilience of sets of infrastructure systems are urgently needed, at community and regional scales. This article develops a practical approach for analysts to characterize a community's infrastructure vulnerability and resilience in disasters. It addresses key challenges of incomplete incentives, partial information, and few opportunities for learning. The approach is demonstrated for Metro Vancouver, Canada, in the context of earthquake and flood risk. The methodological approach is practical and focuses on potential disruptions to infrastructure services. In spirit, it resembles probability elicitation with multiple experts; however, it elicits disruption and recovery over time, rather than uncertainties regarding system function at a given point in time. It develops information on regional infrastructure risk and engages infrastructure organizations in the process. Information sharing, iteration, and learning among the participants provide the basis for more informed estimates of infrastructure system robustness and recovery that incorporate the potential for interdependent failures after an extreme event. Results demonstrate the vital importance of cross‐sectoral communication to develop shared understanding of regional infrastructure disruption in disasters. For Vancouver, specific results indicate that in a hypothetical M7.3 earthquake, virtually all infrastructures would suffer severe disruption of service in the immediate aftermath, with many experiencing moderate disruption two weeks afterward. Electric power, land transportation, and telecommunications are identified as core infrastructure sectors.     

Optimization of Cascade‐Resilient Electrical Infrastructures and its Validation by Power Flow Modeling

Large‐scale outages on real‐world critical infrastructures, although infrequent, are increasingly disastrous to our society. In this article, we are primarily concerned with power transmission networks and we consider the problem of allocation of generation to distributors by rewiring links under the objectives of maximizing network resilience to cascading failure and minimizing investment costs. The combinatorial multiobjective optimization is carried out by a nondominated sorting binary differential evolution (NSBDE) algorithm. For each generators–distributors connection pattern considered in the NSBDE search, a computationally cheap, topological model of failure cascading in a complex network (named the Motter‐Lai [ML] model) is used to simulate and quantify network resilience to cascading failures initiated by targeted attacks. The results on the 400 kV French power transmission network case study show that the proposed method allows us to identify optimal patterns of generators–distributors connection that improve cascading resilience at an acceptable cost. To verify the realistic character of the results obtained by the NSBDE with the embedded ML topological model, a more realistic but also more computationally expensive model of cascading failures is adopted, based on optimal power flow (namely, the ORNL‐Pserc‐Alaska) model). The consistent results between the two models provide impetus for the use of topological, complex network theory models for analysis and optimization of large infrastructures against cascading failure with the advantages of simplicity, scalability, and low computational cost.     

Improving the resilience of power grids against typhoons with data-driven spatial distributionally robust optimization

In recent years, the increased frequency of natural hazards has led to more disruptions in power grids, potentially causing severe infrastructural damages and cascading failures. Therefore, it is important that the power system resilience be improved by implementing new technology and utilizing optimization methods. This paper proposes a data-driven spatial distributionally robust optimization (DS-DRO) model to provide an optimal plan to install and dispatch distributed energy resources (DERs) against the uncertain impact of natural hazards such as typhoons. We adopt an accurate spatial model to evaluate the failure probability with regard to system components based on wind speed. We construct a moment-based ambiguity set of the failure distribution based on historical typhoon data. A two-stage DS-DRO model is then formulated to obtain an optimal resilience enhancement strategy. We employ the combination of dual reformulation and a column-and-constraints generation algorithm, and showcase the effectiveness of the proposed approach with a modified IEEE 13-node reliability test system projected in the Hong Kong region.     

Selecting Indicators for Assessing Community Sustainable Resilience

Communities are complex systems subject to a variety of hazards that can result in significant disruption to critical functions. Community resilience assessment is rapidly gaining popularity as a means to help communities better prepare for, respond to, and recover from disruption. Sustainable resilience, a recently developed concept, requires communities to assess system‐wide capability to maintain desired performance levels while simultaneously evaluating impacts to resilience due to changes in hazards and vulnerability over extended periods of time. To enable assessment of community sustainable resilience, we review current literature, consolidate available indicators and metrics, and develop a classification scheme and organizational structure to aid in identification, selection, and application of indicators within a dynamic assessment framework. A nonduplicative set of community sustainable resilience indicators and metrics is provided that can be tailored to a community's needs, thereby enhancing the ability to operationalize the assessment process.     

Resilience Analysis of a Remote Offshore Oil and Gas Facility for a Potential Hydrocarbon Release

Resilience is the capability of a system to adjust its functionality during a disturbance or perturbation. The present work attempts to quantify resilience as a function of reliability, vulnerability, and maintainability. The approach assesses proactive and reactive defense mechanisms along with operational factors to respond to unwanted disturbances and perturbation. This article employs a Bayesian network format to build a resilience model. The application of the model is tested on hydrocarbon‐release scenarios during an offloading operation in a remote and harsh environment. The model identifies requirements for robust recovery and adaptability during an unplanned scenario related to a hydrocarbon release. This study attempts to relate the resilience capacity of a system to the system's absorptive, adaptive, and restorative capacities. These factors influence predisaster and postdisaster strategies that can be mapped to enhance the resilience of the system.     

Implementation of Equity in Resource Allocation for Regional Earthquake Risk Mitigation Using Two‐Stage Stochastic Programming

This article presents a new methodology to implement the concept of equity in regional earthquake risk mitigation programs using an optimization framework. It presents a framework that could be used by decisionmakers (government and authorities) to structure budget allocation strategy toward different seismic risk mitigation measures, i.e., structural retrofitting for different building structural types in different locations and planning horizons. A two‐stage stochastic model is developed here to seek optimal mitigation measures based on minimizing mitigation expenditures, reconstruction expenditures, and especially large losses in highly seismically active countries. To consider fairness in the distribution of financial resources among different groups of people, the equity concept is incorporated using constraints in model formulation. These constraints limit inequity to the user‐defined level to achieve the equity‐efficiency tradeoff in the decision‐making process. To present practical application of the proposed model, it is applied to a pilot area in Tehran, the capital city of Iran. Building stocks, structural vulnerability functions, and regional seismic hazard characteristics are incorporated to compile a probabilistic seismic risk model for the pilot area. Results illustrate the variation of mitigation expenditures by location and structural type for buildings. These expenditures are sensitive to the amount of available budget and equity consideration for the constant risk aversion. Most significantly, equity is more easily achieved if the budget is unlimited. Conversely, increasing equity where the budget is limited decreases the efficiency. The risk‐return tradeoff, equity‐reconstruction expenditures tradeoff, and variation of per‐capita expected earthquake loss in different income classes are also presented.     

Probabilistic Multiple Hazard Resilience Model of an Interdependent Infrastructure System

Multiple hazard resilience is of significant practical value because most regions of the world are subject to multiple natural and technological hazards. An analysis and assessment approach for multiple hazard spatiotemporal resilience of interdependent infrastructure systems is developed using network theory and a numerical analysis. First, we define multiple hazard resilience and present a quantitative probabilistic metric based on the expansion of a single hazard deterministic resilience model. Second, we define a multiple hazard relationship analysis model with a focus on the impact of hazards on an infrastructure. Subsequently, a relationship matrix is constructed with temporal and spatial dimensions. Further, a general method for the evaluation of direct impacts on an individual infrastructure under multiple hazards is proposed. Third, we present an analysis of indirect multiple hazard impacts on interdependent infrastructures and a joint restoration model of an infrastructure system. Finally, a simplified two‐layer interdependent infrastructure network is used as a case study for illustrating the proposed methodology. The results show that temporal and spatial relationships of multiple hazards significantly influence system resilience. Moreover, the interdependence among infrastructures further magnifies the impact on resilience value. The main contribution of the article is a new multiple hazard resilience evaluation approach that is capable of integrating the impacts of multiple hazard interactions, interdependence of network components (layers), and restoration strategy.     

Assessing Engineering Resilience for Systems with Multiple Performance Measures

Recently, efforts to model and assess a system's resilience to disruptions due to environmental and adversarial threats have increased substantially. Researchers have investigated resilience in many disciplines, including sociology, psychology, computer networks, and engineering systems, to name a few. When assessing engineering system resilience, the resilience assessment typically considers a single performance measure, a disruption, a loss of performance, the time required to recover, or a combination of these elements. We define and use a resilient engineered system definition that separates system resilience into platform and mission resilience. Most complex systems have multiple performance measures; this research proposes using multiple objective decision analysis to assess system resilience for systems with multiple performance measures using two distinct methods. The first method quantifies platform resilience and includes resilience and other “ilities” directly in the value hierarchy, while the second method quantifies mission resilience and uses the “ilities” in the calculation of the expected mission performance for every performance measure in the value hierarchy. We illustrate the mission resilience method using a transportation systems‐of‐systems network with varying levels of resilience due to the level of connectivity and autonomy of the vehicles and platform resilience by using a notional military example. Our analysis found that it is necessary to quantify performance in context with specific mission(s) and scenario(s) under specific threat(s) and then use modeling and simulation to help determine the resilience of a system for a given set of conditions. The example demonstrates how incorporating system mission resilience can improve performance for some performance measures while negatively affecting others.     

Leader–follower equilibria to examine investment decisions in grid resilience-enhancing measures

Large-area, long-duration power outages are increasingly common in the United States, and cost the economy billions of dollars each year. Building a strategy to enhance grid resilience requires an understanding of the optimal mix of preventive and corrective actions, the inefficiencies that arise when self-interested parties make resilience investment decisions, and the conditions under which regulators may facilitate the realization of efficient market outcomes. We develop a bi-level model to examine the mix of preventive and corrective measures that enhances grid resilience to a severe storm. The model represents a Stackelberg game between a regulated utility (leader) that may harden distribution feeders before a long-duration outage and/or deploy restoration crews after the disruption, and utility customers with varying preferences for reliable power (followers) who may invest in backup generators. We show that the regulator's denial of cost recovery for the utility's preventive expenditures, coupled with the misalignment between private objectives and social welfare maximization, yields significant inefficiencies in the resilience investment mix. Allowing cost recovery for a higher share of the utility's capital expenditures in preventive measures, extending the time horizon associated with damage cost recovery, and adopting a storm restoration compensation mechanism shift the realized market outcome toward the efficient solution. If about one-fifth of preventive resilience investments is approved by regulators, requiring utilities to pay a compensation of $365 per customer for a 3-day outage (about seven times the level of compensation currently offered by US utilities) provides significant incentives toward more efficient preventive resilience investments.     

Opportunities and Challenges for Public Libraries to Enhance Community Resilience

This study bridges a gap between public library and emergency management policy versus practice by examining the role of public libraries in the community resource network for disaster recovery. Specifically, this study identifies the opportunities and challenges for public libraries to fulfill their role as a FEMA‐designated essential community organization and enhance community resilience. The results indicate there are several opportunities for libraries to enhance community resilience by offering technology resources and assistance; providing office, meeting, and community living room space; serving as the last redundant communication channel and a repository for community information and disaster narratives; and adapting or expanding services already offered to meet the changing needs of the community. However, libraries also face challenges in enhancing community resilience, including the temptation to overcommit library capacity and staff capability beyond the library mission and a lack of long‐term disaster plans and collaboration with emergency managers and government officials. Implications for library and emergency management practice and crisis research are discussed.     

Decision‐Making Analytics Using Plural Resilience Parameters for Adaptive Management of Complex Systems

It is critical for complex systems to effectively recover, adapt, and reorganize after system disruptions. Common approaches for evaluating system resilience typically study single measures of performance at one time, such as with a single resilience curve. However, multiple measures of performance are needed for complex systems that involve many components, functions, and noncommensurate valuations of performance. Hence, this article presents a framework for: (1) modeling resilience for complex systems with competing measures of performance, and (2) modeling decision making for investing in these systems using multiple stakeholder perspectives and multicriteria decision analysis. This resilience framework, which is described and demonstrated in this article via a real‐world case study, will be of interest to managers of complex systems, such as supply chains and large‐scale infrastructure networks.     

Stochastic Measures of Network Resilience: Applications to Waterway Commodity Flows

Given the ubiquitous nature of infrastructure networks in today's society, there is a global need to understand, quantify, and plan for the resilience of these networks to disruptions. This work defines network resilience along dimensions of reliability, vulnerability, survivability, and recoverability, and quantifies network resilience as a function of component and network performance. The treatment of vulnerability and recoverability as random variables leads to stochastic measures of resilience, including time to total system restoration, time to full system service resilience, and time to a specific α% resilience. Ultimately, a means to optimize network resilience strategies is discussed, primarily through an adaption of the Copeland Score for nonparametric stochastic ranking. The measures of resilience and optimization techniques are applied to inland waterway networks, an important mode in the larger multimodal transportation network upon which we rely for the flow of commodities. We provide a case study analyzing and planning for the resilience of commodity flows along the Mississippi River Navigation System to illustrate the usefulness of the proposed metrics.