Risk analysis and management in power outage and restoration: A literature survey

Electric Power Systems Research 107 (2014) 9–15

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Risk analysis and management in power outage and restoration: A literature survey Anya Castillo ∗ Johns Hopkins University, Baltimore, MD 21218, USA

a r t i c l e

i n f o

Article history: Received 20 May 2013 Received in revised form 31 August 2013 Accepted 2 September 2013 Keywords: Electric power system Power outage Power restoration Risk analysis Risk management Literature survey

a b s t r a c t Societies are highly reliant on power systems for their energy needs. Reliability assessment is performed in both planning and operation of these power systems. Although there has been increasing interest in hardening the power system to be resilient against power outages, the risk of power outages cannot be completely diminished. Numerous models and algorithms are available to predict hazards that subsequently result in loss of energy services to customers. Many quantitative and qualitative approaches to determining restoration strategies in the event of a power outage have been developed. Very few studies have assessed restoration strategies in response to the risk of predicted hazards. As a result of the hurricanes and storms that have damaged critical infrastructures in the U.S. in recent years, this has become a burgeoning area for active research. In this literature survey we present the various studies that have been completed to date and discuss potential areas for future research. Published by Elsevier B.V.

1. Introduction An electric power system is a large manmade electricity circuit that connects power providers and customers through transmission and distribution assets. The United States electric power system serves approximately 4184 TWh annually to hundreds of millions of customers across the nation [1]. It is a critical infrastructure because it is an asset essential for functioning of society and economy. The electric power system is interdependent on numerous other critical infrastructures, including but not limited to the gas infrastructure, water supply, telecommunications, financial services, security services, public health, agriculture, and transportations systems. Following a blackout, losses in electricity delivery can result in loss of service for numerous customers that may extend significant time periods. Only when the critical generating units can come online and the electricity infrastructure is structurally functional can full restoration of system load occur. Such disruptions result in direct and indirect losses. The effects of power outages can include economic, social, physical and psychological impacts; such consequences on providers and customers include premature death, injury, and indirect and direct economic losses. Reports by the Electric Power Research Institute (EPRI), Lawrence Berkeley National Laboratory (LBNL), and U.S. Department of Energy (DOE) have estimated $30–$400 billion per year in economic losses due to power outages in the occurrence of

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momentary interruptions and localized blackouts [2–4]. The widespread economic and non-economic losses of large-scale blackouts are not well-understood. Furthermore, assessing the hidden costs of poor power reliability is difficult because the industry does not currently track economic losses resulting from outages, and quantifying premature human death, human injury, and indirect economic and social impacts has always been a major source of dispute. Another issues is that the reliability metrics and standards vary significantly amongst regional entities in the U.S. and the electric reliability in the U.S. continues to fall behind other developed nations [4]. The Carnegie Mellon Electricity Industry Center reports using NERC 1984–2006 data that blackout sizes and durations are not correlated, but that there is a significant increase in blackout frequency during peak hours of the day, and also peak seasonal periods in the winter and summer months [5]. Furthermore, blackouts in the United States due to weather-related outages have significantly increased from between 5 and 20 each year during the 1990s, to between 50 and 100 each year in the past five years [6]. The increasing destruction caused by tropical storms and heavy rainfall is mainly due to longer storm lifetimes and greater storm intensities [7]. Although changes in extreme weather, infrastructure maintenance, and demographic trends may overall contribute to more frequent power outages, strong winds currently are the major contributor and account for approximately 80% of weatherrelated blackout incidents [6]. However the number of incidents alone does not correlate to the geographical spread or severity in duration and losses caused by such blackouts. Following hurricanes Katrina and Rita, the designated blackstart resource could not even

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initiate power restoration due to extensive damage. In the case of the Hyogoken–Nanbu earthquake, power outages increased even after the earthquake hit because of further damages caused by fires that engulfed overhead electric lines and buildings that collapsed on exposed cables [8]. The 1994 Northridge earthquake resulted in a power outage at the Van Norman water-supply pumping station which caused water shortages in the city of Los Angeles until the power was restored nearly 24 h later [9]. The northeast U.S. blackout of 2003 highlighted the fragility of the power grid infrastructure where the loss of electricity resulted in over 50 million without energy service, along with severe disruptions on other critical infrastructures. The extent and distribution of overall disruptions and subsequent losses due to power outages from natural disasters can be varying and pervasive. Moreover, the percentage of blackouts as a result of cascading failures is unknown [5]. Recent studies are also focusing on risk of power outages due to terrorist attacks because the vulnerability of power components and the overall system are targeted and compromised [10]. The Homeland Security Advisory Council’s Critical Infrastructure Task Force stated that critical infrastructure resilience is a top-level strategic objective of the nation’s critical infrastructure security efforts where resiliency is defined as the capability of a system to maintain its functions and structure in the face of internal and external change and to degrade gracefully when it must [11]. Power outages have caused disruptions in many other infrastructures and protecting against outages requires an infrastructure that is manageable and measurable, where both public and private stakeholders can best invest and mitigate such risks. Current restoration planning relies on both domain expert knowledge and analysis, with coordination amongst the system operator, and transmission and generation parties. For example, the United States does not have a “national power grid” but instead has three main interconnections, the Western Interconnect, Texas Interconnect, and the Eastern Interconnect, which are regions of interconnected AC power systems that operator at the same frequency and phase with one another during normal system conditions. Within these interconnects, the North American Electric Reliability Corporation (NERC) works with regional entities to improve the reliability and restoration strategy of the bulk power system, which includes generation and transmission assets but not distribution. Distribution network reliability and restoration is often managed by local utilities, the state public utilities commission, and other stakeholders. The Federal Energy Regulatory Commission recently approved three mandatory reliability standards to require that plans, facilities, and personnel are prepared to perform system restoration with the designated blackstart resources [12]. Such standards for required performance along with contractual agreements between parties specify responsibilities and compensation to maintaining system reliability. However, aligning incentives can be complicated and the dynamics of the power system makes optimal restoration scheduling for all power outage scenarios an unrealistic goal. Moreover, the NERC Regional Entities expect sufficient equipment and personnel available without outside assistance, but then vary from region to region in whether normal or extreme weather patterns set a baseline for restoration performance. Therefore better risk analysis and management can better prepare us for power outages and subsequent power restoration. The following survey covers decades of publications to assess how approaches determine the nature and extent of power outage risk, how risk analysis is applied in restoration planning, and opportunities for risk reduction. Whereas numerous studies have been completed in lifeline restoration of critical infrastructures, we focus here specifically on applications to address power outages. Several approaches have been applied to statistical modeling of historical data from extreme events and several approaches also have been

applied to determine power restoration strategies. Typically the output of these models is a restoration curve, such as the percentage of customers with service over time, or a reliability indicator, such as the system average interruption duration index (SAIDI). Modeling power outage events, consequences, and restoration is a complex, interdisciplinary problem that is difficult to address comprehensively and rigorously. Very few studies have incorporated both the risk of power outages and the subsequent power restoration as we note below.

2. Risk analysis of power outages Defining and therefore identifying risk has been a controversial task in itself. Numerous studies have developed criteria for “good” risk analysis; according to Haimes, studies should be comprehensive, adherent to evidence, logically sound, practical, open to evaluation, based on explicit assumptions and premises, compatible with institutions, conducive to learning, attuned to risk communication, and innovative [13]. Lowrance defines risk as a measure of the probability and severity of adverse effects [14]. In the first edition of Risk Analysis, Kaplan and Garrick published a seminal work in which they define risk as the set of a given scenario, the probability of that scenario, and the consequence or evaluation measure of that scenario, where a scenario can be defined as an identifiable outcome [15]. Kaplan and Garrick note that risk is subjective, and therefore can include the notion of uncertainty. Although risk can be thought of in qualitative terms, a quantitative definition of risk is necessary to make rational risk management decisions under uncertainties and with limited resources. Within this quantitative definition includes the power outage initiating event, the relationship between the outage and consequences of the outage, and the relationship of consequences to indirect and direct losses. A combination of outage and consequences can readily lead to worst case scenarios. From an economic perspective, eliminating all combinations of outage and consequences, in order to prevent such vulnerabilities or even correct blackouts in a timely manner, can be economically prohibitive. State-space methods have long been applied in power system reliability assessments. A power system is frequently represented as a network in which the components, such as generators, loads, electricity lines, and transformers, are connected together either in series, parallel, meshed, or a combination of these; however the reliability network applied to model the system may have a different topological structure [16]. Various events can cause power outages, and nominally the events have been broadly grouped into operational contingencies, man-made accidents, natural disasters, and terrorist attacks. The two-state model presented by Billinton and Allen to incorporate the effect of severe weather conditions has been extended to better capture variation in weather severity through a multi-state model [16–18]. However, power outages are typically not due to a single event but rather are due to a cascading failure in the system that is a result of strong coupling between the initiating event with subsequent events. Cascading outages can propagate through control areas resulting in significant loss of load and large-scale system collapse [19]. If corrective actions are not strategically applied by the grid operator during the power restoration, then the time to reenergize certain power components can increase due to thermal instability or damage. Therefore the dynamic behavior of power systems necessitates more powerful reliability analysis than traditional static models such as fault trees, event trees, and block diagrams. Often probabilistic methods do not correctly model dependencies that result in power outages; for example the failure rate of power components for a given system state depend on processes, such as temperatures, currents, and voltages.

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Although methods that are based on the analysis of detailed failure mechanisms or the physics of the failure are more accurate, using field data for reliability assessment and outage prediction is the more prominent practice. Given that transient stability is typically modeled as deterministic, such studies can also incorporate probabilistic methods to evaluate system-wide and component security, i.e., the ability to withstand sudden disturbances [24–27]. According to Billinton, assessments should be applied on a caseby-case basis, where a “single all-purpose reliability formula or technique which can be applied in all cases does not exist” [28]. A systematic approach to evaluating risk is a probabilistic risk assessment (PRA), which can describe discrete states along with process variables of the power system [29]. A PRA characterizes risk by the severity and likelihood of occurrence for an adverse outcome. Although a dynamic PRA explicitly accounts for time-related dependencies, Marais et al. contend that this chain-of-event modeling approach cannot account for indirect, nonlinear, and feedback relationships that are common to hazards in complex systems [30]. For example, in severe weather or extreme environmental conditions, the failure rates of the system or components evolve in relation to changes within the operating environment [31,32]. Another approach, that could even be extended within PRA, is to apply stochastic processes instead of probability distributions in order to determine the likelihood of component failure or power outage. In [31], Billinton applies discrete-state continuous-time stochastic Markov processes to perform a reliability assessment. Özekici and Soyer apply stochastic processes where the failure of components depends on the current state of the system, where the model parameters change randomly to represent a randomly changing environment [33]. Since in reality the life-time and repair times of components are not exponential, semi-Markov processes allows for such non-exponential distributions [34]. However unlike a PRA, these neglect the severity of failure occurrences, and therefore do not include a risk analysis but simply present a reliability assessment approach. Therefore a potential direction for future research would be to extend such reliability assessments to include a contextual risk assessment, which would be an important input to decision-making for power restoration. Garrick et al. recently advocated the use of PRA to analyze the risk of terrorist attacks [35]. In a recent study by Zimmerman et al. [10], the authors identify the risk of an electric power disruption occurring as: “the likelihood that attacks on electric power will occur, the vulnerability of components of the electric power system to being damaged in or targets of such attacks, and the likelihood and severity of those vulnerabilities being taken advantage of in attack strategies.” Based on their assessments of historical and expert elicited data, they concluded that transformers are the most difficult to replace. Salmeron and Baldick present a network-interdiction model to identify critical system components that when attacked, results in the maximal disruption given posited offensive resources [36]; such components are identified as candidates for hardening, but are highly dependent on the assumptions regarding the terrorists’ resources. Patterson and Apostolakis developed a ranking methodology to identify critical locations within multiple infrastructures, where an attack would affect more than one infrastructure [37]. Other studies have identified features of resilience and reliability through analyzing network topology [47–52]. For example, in investigating the network topology, Albert et al. determine that the power grid is robust to most perturbations, yet disturbances to critical substations dramatically reduce the security of operations [47]. However the aforementioned graph theoretic approaches neglect Kirchhoffs laws and other physics that conduct power systems. Natural disasters such as hurricanes, severe storms, and heat waves can be forecasted in advance with uncertainty in the severity, location, and time of the event. Numerous studies have developed

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statistical models to predict outages caused by natural disasters [29,38–46]. Nateghi et al. compare the predictive accuracy of two survival analysis models with three data mining techniques. Zhou et al. compare the predicted failure rates of overhead distribution lines using a Poisson regression model and a Bayesian network model [45]. Many explanatory variables can be included in a risk analysis, Liu et al. observed that if all the indicators are statistically significant, then the measures do not completely capture the relevant characteristics of their respective hazards. Furthermore Liu et al. observed that high resolution spatial data is not useful in predicting power outages [41]. Liu et al. were the first to implement a statistical regression that estimates restoration time prior to completing a damage assessment, which may take an uncertain amount of time due to resource constraints in available crew and accessibility to damaged assets [42]. Zhu et al. present a two-stage prediction method to classify and track various types of storms so that the grid operator can be proactive based on the errors between predicted storm outages and actual storm outages [46]. Han et al. apply negative binomial regression to estimate the spatial distribution of hurricanes for the purpose of improved utility preparation [39]. Balijepalli et al. applies a bootstrapping method to estimate lightning storm parameters and then applies a Monte Carlo simulation to assess the distribution of reliability indices [38]; other studies have also focused on how failure rates of power components affect system reliability indices [53–55]. In [55], Alvehag and Söder propose a time-sequential Monte Carlo reliability model that incorporates both failure rates and restoration times as a function of weather intensity and conclude that weather stochasticity has a significant impact on the variance in reliability indices for SAIDI and energy not supplied (ENS). A large body of work focuses on contingency-based outages, typically as a result of cascading failures from disturbances or undetected defects. Utilities have developed and implemented methodologies to screen multiple initiating contingencies in order to simulate the cascading process, evaluate system impacts, and rank the scenarios based on both the severity and likelihood of the risk [19]. The Oak Ridge National Laboratory, Power Systems Engineering Research Center at University of Wisconsin and University of Alaska have developed numerous cascading blackout models for practical applications [20–23]; in [23], Chen et al. develop a model to explore the characteristics of cascading events in order to suggest corresponding mitigation measures. Kirschen et al. provides a realistic estimate of expected ENS by including various environmental and operational factors in the Monte Carlo simulation; the subsequent probability indicator takes into account multiple contingencies, including cascading and sympathetic tripping, in order to help decision-makers assess the actual level of security of the power system [56]. Rei et al. apply a sequential Monte Carlo in order to represent non-Markovian processes such as remedial actions, restoration stages and cascading events, and calculate both the probability for restoration and also reliability indices depending upon consequences of disturbances and the nature of the component failure [57]. Li et al. applied fuzzy sets and Monte Carlo simulation to represent uncertainties for loads and system component outage parameters [58]. Issicaba et al. present an adequacy and security evaluation in order to assess the impact of device protection and controls on reliability indices and other performance metrics for distribution systems under various operational states [59]. Masiello et al. [60] propose a way to use a measure of risk over future time that can be updated as conditions change. The authors remark that transition probabilities and the non-stationary nature of the model introduces some uncertainty in dealing with complex and hard-to-observe phenomena. However they claim that making the model deliberately simple results in better intuition of operational and non-engineering effects, and a better fit to the subset of power outage observations.

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3. Risk management in power restoration In 1967 DyLiacco established that the power system could be classified as operating in a preventive (normal), emergency, or restorative state with associated controls [61]; this classification has become standard terminology in power systems. Certain actions have been taken in an effort to reduce the risk of power outages and maintain operations in a preventive state. For example, investment in power lines made of aluminum rather than steel have greater resiliency to sagging. Apt et al. make the case for installing sensors every 10 miles of transmission line, which would increase the average residential electricity bill by less than 0.1% but would minimize delays in failure detections by operators [62]. Remedial actions such as generation rescheduling, voltage correction, and load curtailment are used when operating limits are violated and to re-establish a preventive state. Other strategies such as identifying and hardening key power components, learning from accident models, improving real-time decision support platforms, increasing staff training, enhancing situational awareness in the organizational culture, enabling dynamic infrastructure topology (e.g., transmission switching), allocating for system redundancy, automating response mechanisms, and maintaining communications infrastructure can improve the resilience of the system against power outage; however there are few studies that quantify such ˜ and investments. In the studies by Ouyang and Duenas-Osorio Ouyang et al., the authors examine the nonlinear features in timedependent resilience of the power system to resist various hazards, or to absorb initial damage from hazards and recover to a preventive operating state [63,64]. The authors determine that under limited resources, adopting better restoration planning is the overall optimal single strategy. Accordingly there is a substantial effort in restoration planning, which can occur after the power system enters an emergency state. Often the risk management is addressed separately from the outage prediction. Two primary objectives in power restoration is to restore supply to the maximal number of customers in accordance with their importance, and to accomplish this as quickly as possible. According to Haimes, risk-based decision-making is a systemic process that assesses uncertainties through various distributional impacts and ramifications, and addresses such uncertainties in formulating policy options [13]. Furthermore Aven states that risk management is to protect people, the environment and assets from undesirable consequences, as well as to balance divergent concerns [65]. In power restoration, underestimating repair needs can result in excessive delays in service restoration, and overestimation can lead to suboptimal expenditures. In practice, a restoration plan undergoes both steady-state and harmonic analysis. In the steady-state restoration strategy, the required voltage levels, reserve levels and reactive power capabilities must be met. The service of critical loads is often considered an initial priority [66]. Given that system specific regulations and the voltage or frequency violations which may occur, the restoration strategy for a given power network or power outage situation may differ drastically. A natural disaster or terrorist attack may bring power components offline, resulting in undesirable operating points where the system is liable to collapse due to dynamic fluctuations. Since the topology and functionality of the system is constantly altering the dynamic and steady-state operations due to sequential and simultaneous restoration actions, it is difficult to assess risks during restoration with a high degree of certainty. From a mathematical perspective, the restoration problem has been modeled as a combinatorial multi-objective, multi-stage, linear or nonlinear constrained optimization problem. It is a highly complex decision and control problem. Prior studies have included algorithmic methods and knowledge-based approaches into system restoration plans. Restoration strategies that are derived from

expert knowledge and operational experience are incorporated into these plans. Such policies and plans include islanding the system into several subsystems based on blackstart and power balancing capabilities [67]; often a damage assessment can take substantial time to perform even before repair and restoration can be pursued [68]. Conventional restoration techniques on meshed networks generally employ a build-upward, build-downward, build-inward, build-outward, or build-together restoration strategy [69–71]. A build-upward approach defines islands and then resynchronizes the system following the restoration of each island. The build-downward approach requires the startup of blackstart units, reenergization of the network, and then cranking of non-blackstart units. The build-inward approach utilizes available tie-line assistance to restart generating units. The build-outward approach is employed when tie-line assistance is unavailable and system restoration must proceed from the ring outward. In the build-together approach, the network is reenergized in stages as non-blackstart units near the load are restored. Pham et al. propose a build-together approach where the restoration process is carried out simultaneously in both the transmission and distribution networks; however a criticism of this approach is that often the capacity on the distribution network is rarely enough to reenergize all the loads connected to a particular feeder, which may lead to inequitable priority loading [72]. Whichever restoration strategy is employed, the primary three tasks are to startup the generating units, restore the network, and pickup the load [71]. Fink et al. provide a more extensive list of critical tasks: start blackstart units, determine critical paths, energize transmission lines, pick-up loads, synchronize subsystems, reconnect tie-lines, crank non-blackstart units, and energize busbars [66]. Distribution system restoration often entails the transfer of reenergized loads through network reconfigurations to nearby supporting feeders, without violating operational and electrical constraints. Distribution grid operators aim to restore service to outage areas as soon as possible with minimal switching operations [73]. Therefore at the distribution level, restoring service has often been treated as a network reconfiguration problem where operators transfer maximum load from the faulted to the unfaulted part by operating the sectionalizing switches within a feeder, or by reclosing the tie switches between otherwise de-energized feeders [72]. Prior studies have focused on restoration strategies with an emphasis on response to generator and transmission contingencies more than disaster recovery [67,70,74–81]. Heuristic methods have also been applied to reduce the combinatorial complexity [82–87]. Another approach is to apply optimization methods for restoration strategies. Studies [88–90] combine optimization with power flow analysis and expert knowledge to create a decision support tool for power outages. Liu et al. developed optimization modules to automate and adapt actual restoration by providing decision support analysis on generation capability optimization, transmission path search, constraint checking, and distribution system restoration [90]. Hou et al. present generic restoration milestones (GRMs) to reduce restoration times through decision support based on actual system conditions [89]. These GRMs include restarting available non-blackstart units, reenergizing the transmission grid, maximizing the load pickup, sectionalizing islands, synchronizing islands, and connecting with neighboring systems. The studies in [68,91–93] optimize resource allocation during the restoration process. Alternatively, numerous studies have applied knowledgebased systems without optimization or heuristic techniques [67,74,76–78,80,81,94–96]. The earlier works primarily describe real-time expert systems, often integrated with supervisory control and data acquisition (SCADA), for restoration guidance. Winkler et al. demonstrate that topological metrics coupled with fragility

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models of power components can elucidate the contribution of spatial factors and the system layout to overall power reliability [96]. Furthermore, the above studies differ in the measure of restoration efficiency, and this aspect remains controversial due to varying stakeholder priorities in restoration speed, load interruption, impact on customers, and other factors [90]. Thus objectives have included but are not limited to: minimizing the restoration time and unserved loads [105,79], minimizing the number of switching operations [83,85], minimizing the imbalance of spare capacity amongst the power sources while maximizing the minimum system voltage [86], minimizing the out-of-service area, minimizing the deviation of the bus voltage, minimizing the line current, minimizing the loading of the transformers [83], and minimizing real power losses while also minimizing the bus voltage deviation.

4. An integrated risk analysis and management paradigm Recent studies demonstrate that more than 70% of major disturbances cascade due to incorrect relay operations, which could occur due to undetected defects that remain dormant until abnormal operating conditions are reached; alternatively, cascading disturbances could also occur due to poor remedial and restorative strategies [100]. Although major disturbances are relatively rare, the impacts can be catastrophic. Furthermore, a study by Dobson et al. demonstrate that societal and economic influences should not be underestimated and could self-organize the system to be near criticality, i.e. the operational limit with respect to a cascading failure [97]. The authors contend that the efforts to mitigate power outage risk should not only take into account the physics of the power system but also these broader societal and economic dynamics. Similarly stated, Kirschen and Strbac note that although the level of security in power systems has not changed in the United States due to deregulation, the deregulated markets have resulted in “bigger, longer, and more frequent transactions” that have “increased the probability of blackouts” [98]. Thus managing the tradeoff between costs and the risk of widespread catastrophic cascading failure is difficult without further developments and practical application in both understanding and managing the risk [97]. Therefore, decision-makers need integrated studies that incorporate both risk analysis of power outages and risk management in power restoration. There are very few studies that attempt this integrated paradigm. Shinozuka et al. use Monte Carlo simulation techniques and take into consideration the fragility curves of power components and the network power flows under earthquake scenarios that result in varying states of network damage [99]. Furthermore the authors consider joint performance of the water and power infrastructures, where the system restoration is simulated in order to assess economic loss resulting from system disruption. Using a Poisson regression model for spatial data within a Bayesian hierarchical framework, Li et al. incorporate uncertainties in their damage forecasts through random errors in the interpolation process of point weather information to substation areas; they present outage predictions and then use the forecast in further analysis and visualization for emergency management planning [40]. Xu et al. adopt the earthquake scenarios and damage states of the LADWP electric power system from the works by Chang et al. and Dong, and then apply a stochastic integer program to optimize resourceconstrained scheduling for power restoration [101,102,68]. Koonce et al. extended Patterson and Apostolakis’ approach in [37] to assess the bulk power grid, and identified the number and type of customers affected along with the duration of the power outage; the authors then applied a multi-attribute utility theory to value the

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˜ consequences [103]. In a more recent study Ouyang and DuenasOsorio integrate a hurricane model, component fragility model, a robustness model of system performance response immediately following the hurricane event, and a system restoration model. The authors calibrate and verify the model with real outage and restoration data for the power system in Harris County, Texas as a result of hurricane Ike in 2008 [104]. Furthermore, the breadth of these studies typically trade-off for the more detailed treatment of physical and operational constraints of certain methods listed in above sections. 5. Conclusion The research to date on power outage and restoration typically focus on the risk analysis or the risk management but rarely incorporate both. It has been difficult to apply the methodologies in both types of studies into a single study because there has not been an effective and unanimous approach in how to relate reliability and resiliency to market efficiency and economic losses. Reliability metrics and standards vary significantly amongst regional entities in the U.S. From an economic perspective, it is not well understood how to make improved reliability and resiliency a fungible asset. Often transmission and generation planning, as well as restoration planning, is requirement driven and must be balanced with factors that drive grid investments. Future work in this area can further address integrating the risk analysis into investment and restoration planning decisions in order to better incorporate grid resilience targets, restoration strategies, the adoption of smart grid techniques, and hardening of critical components. Acknowledgements The author gratefully acknowledges the anonymous reviewers for their time and expertise in versioning this manuscript. This research was supported by the US National Science Foundation through EFRI Grant 0835879. References [1] International Energy Agency (IEA), Statistics Electricity Information, 2010. [2] K.H. LaCammare, J.H. Eto, Understanding the Cost of Power Interruptions to U.S. Electricity Consumers, Ernest Orlando Lawrence Berkeley National Laboratory, University of California Berkeley, Berkeley, California, 2004. [3] D. Lineweber, S. McNulty, The Cost of Power Disturbances to Industrial and Digital Economy Companies, Consortium for Electric Infrastructure to Support a Digital Society, An Initiative by EPRI and the Electricity Innovation Institute, Palo Alto, California, 2001. [4] G. Rouse, J. Kelly, Electricity Reliability: Problems, Progress and Policy Solutions, Galvin Electricity Initiative, Chicago, Illinois, 2011, February. [5] P. Hines, J. Apt, S. Talukdar, Large blackouts in North America: historical trends and policy implications, Energy Policy 37 (2009) 5249–5259. [6] North American Electric Reliability Corporation (NERC), Events Analysis: System Disturbance Reports, 1992–2010. [7] T.R. Karl, G.A. Keehl, C.D. Miller, S.J. Hassol, A.M. Waple, W.L. Murray, Weather and Climate Extremes in a Changing Climate. Regions of Focus: North America, Hawaii, Caribbean, and U.S. Pacific Islands. A Report by the U.S. Climate Change Science Program and the Subcommittee on Global Change Research, Department of Commerce, NOAA’s National Climatic Data Center, Washington, DC, 2008. [8] T.D. O’Rourke, Lessons learned for lifeline engineering from major urban earthquakes, in: Eleventh World Conference on Earthquake Engineering, No. 2172, 1996. [9] T.D. O’Rourke, Critical infrastructure, interdependencies, and resilience, Bridge–Washington–National Academy of Engineering 37 (1) (2007) 22–29. [10] R. Zimmerman, C. Restrepo, N. Dooskin, R. Hartwell, J. Miller, W. Remington, J. Simonoff, L. Lave, R. Schuler, Electricity Case: Main Report – Risk, Consequences, and Economic Accounting, 2005, May, CREATE Report, FEMA Grant EMW-2004-GR-0112. [11] W. Webster, Report of the Critical Infrastructure Task Force, Homeland Security Advisory Council, Washington, D.C, 2006. [12] Federal Energy Regulatory Commission, EOP-001-1 (Emergency Operations Planning), EOP-005-2 (System Restoration from Blackstart Resources), EOP006-2 (System Restoration Coordination), March 2011.

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[13] Y.Y. Haimes, Risk Modeling, Assessment, and Management, John Wiley & Sons, Inc., Hoboken, New Jersey, 2011. [14] W.W. Lowrance, Of Acceptable Risk: Science and the Determination of Safety, W. Kaufmann, Inc., Los Altos, California, 1976. [15] S. Kaplan, B.J. Garrick, On the quantitative definition of risk, Risk Analysis 1 (1) (1981) 11–27. [16] R. Billinton, R.N. Allan, Reliability Evaluation of Power Systems, 2nd ed., Plenum, New York, 1996. [17] R. Billinton, C. Wu, G. Singh, Extreme adverse weather modeling in transmission and distribution system reliability evaluation, in: Proceedings of the 14th Power Systems Computational Conference, 2002. [18] R. Billinton, J. Acharya, Consideration of multi-state weather models in reliability evaluation of transmission and distribution systems, in: Proceedings of the Canadian Conference of Electrical and Computer Engineering, 2005. [19] R.C. Hardiman, M. Kumbale, Y.V. Makarov, An advanced tool for analyzing multiple cascading failures, in: Proceedings of the 8th International Conference on Probabilistics Methods Applied to Power Systems, 2004. [20] I. Dobson, B.A. Carreras, V.E. Lynch, D.E. Newman, An initial model for complex dynamics in electric power system blackouts, in: Proceedings of the 34th Hawaii International Conference on System Sciences, 2001. [21] B.A. Carreras, V.E. Lynch, M.L. Sachtjen, I. Dobson, D.E. Newman, Modeling blackout dynamics in power transmission networks with simple structure, in: Proceedings of the 34th Hawaii International Conference on System Sciences, 2001. [22] B.A. Carreras, V.E. Lynch, I. Dobson, D.E. Newman, Critical points and transitions in an electric power transmission model for cascading failure blackouts, Chaos 12 (4) (2002) 985–994. [23] J. Chen, J.S. Thorp, I. Dobson, Cascading dynamics and mitigation assessment in power system disturbances via a hidden failure model, Electric Power and Energy Systems 27 (2005) 318–326. [24] R. Billinton, P.R.S. Kuruganty, Probabilistic assessment of transient stability in a practical multimachine system, IEEE Transactions on Power Apparatus and Systems 7 (1981) 3634–3641. [25] P.R.S. Kuruganty, R. Billinton, Protection system modeling in a probabilistic assessment of transient stability, IEEE Transactions on Power Apparatus and Systems 5 (1981) 2163–2170. [26] P.M. Anderson, K.J. Timko, A probabilistic model of power system disturbances, IEEE Transactions on Circuits and Systems 29 (11) (1982) 789–796. [27] Y.Y. Hsu, C.L. Chang, Probabilistic transient stability studies using the conditional probability approach, IEEE Transactions on Power Systems 3 (4) (1988) 1565–1572. [28] R. Billinton, Power System Reliability Evaluation, Gordon and Breach (1970). [29] P. Henneaux, P.-E. Labeau, J.-C. Maun, Role of thermal effects in blackout probabilistic risk assessment, 2011 IEEE Electrical Power and Energy Conference (2011) 266–271. [30] K. Marais, Karen, N. Dulac, N. Leveson, Beyond normal accidents and high reliability organizations: the need for an alternative approach to safety in complex systems, in: Engineering Systems Division Symposium, Massachusetts Institute of Technology, 2004. [31] R. Billinton, K.E. Bollinger, Transmission system reliability using Markov processes, IEEE Transactions on Power Apparatus and Systems 87 (1968) 538–547. [32] D.P. Gaver, F.E. Montmeat, A.D. Patton, Power system reliability I – measures of reliability and methods of calculation, IEEE Transactions on Power Apparatus and Systems 83 (1964) 727–737. [33] S. Özekici, R. Soyer, Network reliability assessment in a random environment, Naval Research Logistics 50 (6) (2003) 574–591. [34] C. Singh, R. Billinton, S.Y. Lee, The method of stages for non-Markov models, IEEE Transactions on Reliability R-26 (2) (1977) 136–137. [35] B. Garrick, J. Hall, M. Kilger, J. McDonald, T. O’Toole, P. Probst, E. Parker, R. Rosenthal, A. Trivelpiece, L. Arsdale, E. Zebroski, Confronting the risks of terrorism: making the right decisions, Reliability Engineering and System Safety 86 (2) (2004) 129–176. [36] J. Salmeron, K. Wood, R. Baldick R., Analysis of electric grid security under terrorist threat, IEEE Transactions on Power Systems 19 (2) (2004) 905–912. [37] S.A. Patterson, G.E. Apostolakis, Identification of critical locations across multiple infrastructures for terrorist actions, Reliability Engineering and System Safety 92 (2007) 1183–1203. [38] N. Balijepalli, S. Venkatta, C. Richter Jr., R. Christie, V. Longo, Distribution system reliability assessment due to lightning storms, IEEE Transactions on Power Delivery 50 (3) (2005) 2153–2159. [39] S. Han, S.D. Guikema, S.M. Quiring, K. Lee, D. Rosowsky, R.A. Davidson, Estimating the spatial distribution of power outages during hurricanes in the Gulf coast region, Reliability Engineering and System Safety 94 (February (2)) (2009) 199–210. [40] H. Li, L.A. Treinish, J.R.M. Hosking, A statistical model for risk management of electric outage forecasts, IBM Journal of Research and Development 54 (May/June (3)) (2010), Paper 8. [41] H. Liu, R.A. Davidson, D.V. Rosowsky, J.R. Stedinger, Negative binomial regression of electric power outages in hurricanes, Journal of Infrastructure Systems 11 (4) (December 2005) 258–267. [42] H. Liu, R.A. Davidson, T.V. Apanasovich, Statistical forecasting of electric power restoration times in hurricanes and ice storms, IEEE Transactions on Power Systems 22 (4) (November 2007) 2270–2279.

[43] H. Liu, R.A. Davidson, T.V. Apanasovich, Spatial generalized linear mixed models of electric power outages due to hurricanes and ice storms, Reliability Engineering and System Safety 93 (6) (June 2008) 875–890. [44] R. Nateghi, S.D. Guikema, S.M. Quiring, Comparison and validation of statistical methods for predicting power outage durations in the event of hurricanes, Risk Analysis 31 (12) (2011) 1897–1906. [45] Y. Zhou, A. Pahwa, S. Yang, Modeling weather-related failures of overhead distribution lines, IEEE Transactions on Power Systems 21 (November (4)) (2006) 1683–1690. [46] D. Zhu, D. Cheng, R.P. Broadwater, C. Scirbona, Storm modeling for prediction of power distribution system outages, Electric Power Systems Research 77 (June (8)) (2007) 973–979. [47] R. Albert, I. Albert, G.L. Nakarado, Structural vulnerability of the North American power grid, Physical Review E 69 (2) (2004), 10 pp. [48] D.P. Chassin, C. Posse, Evaluating North American electric grid reliability using the Barabasi–Albert network Model, Physica A: Statistical Mechanics and Its Applications 355 (2005) 667–677. [49] P. Crucitti, V. Latora, M. Marchiori, A topological analysis of the Italian electric power grid, Physica A: Statistical Mechanics and Its Applications 338 (2004) 92–97. [50] A.J. Holmgren, Using graph models to analyze the vulnerability of electric power networks, Risk Analysis 26 (4) (2006) 955–969. [51] R. Kinney, P. Crucitti, R. Albert, V. Latora, Modeling cascading failures in the North American power grid, The European Physical Journal B – Condensed Matter and Complex Systems 46 (July (1)) (2005) 101–107. [52] M.I. Rosas-Casals, S. Valverde, R.V. Sole, Topological vulnerability of the European power grid under errors and attacks, International Journal of Bifurcation and Chaos 17 (7) (2007) 2465–2475. [53] R.E. Brown, S. Gupta, R.D. Christie, S.S. Venkata, R. Fletcher, Distribution system reliability assessment: momentary interruptions and storms, IEEE Transactions on Power Delivery 12 (4) (1997) 1569–1575. [54] D.A. Reed, Electric utility distribution analysis for extreme winds, Journal of Wind Engineering and Industrial Aerodynamics 96 (1) (2008) 123–140. [55] K. Alvehag, L. Söder, A reliability model for distribution systems incorporating seasonal variations in severe weather, IEEE Transactions on Power Delivery 26 (2) (2011) 910–919. [56] D.S. Kirschen, D. Jayaweera, D.P. Nedic, R.N. Allan, A probabilistic indicator of system stress, IEEE Transactions on Power Systems 19 (3) (2004) 1650–1657. [57] A.M. Rei, A.M.L. da Silva, J.L. Jardim, J.C. de Oliveira Mello, Static and dynamic aspects in bulk power system reliability evaluations, IEEE Transactions on Power Systems 15 (1) (2000) 189–195. [58] W. Li, J. Zhou, K. Xie, X. Xiong, Power system risk assessment using a hybrid method of fuzzy set and Monte Carlo simulation, IEEE Transactions on Power Systems 23 (May (2)) (2008) 336–343. [59] D. Issicaba, J.A.P. Lopes, M.A. da Rosa, Adequacy and security evaluation of distribution systems with distributed generation, IEEE Transactions on Power Systems 27 (3) (2012) 1681–1689. [60] R. Masiello, J. Spare, A. Roark, S. Brattini, Reliability @ risk: a new paradigm for assessing reliability, Electricity Journal 17 (December (10)) (2004) 71–84. [61] T.E. DyLiacco, The adaptive reliability control system, IEEE Transactions on Power Apparatus and Systems (May) (1967) 517–531. [62] J. Apt, L.B. Lave, S. Talukdar, M.G. Morgan, M. Ilic, Electrical blackouts: a systemic problem, Issues in Science and Technology 20 (Summer (4)) (2004) 55–61. ˜ [63] M. Ouyang, L. Duenas-Osorio, Time-dependent resilience assessment and improvement of urban infrastructure systems, Chaos 22 (033122) (2012), 11 pp. ˜ [64] M. Ouyang, L. Duenas-Osorio, X. Min, A three-stage resilience analysis framework for urban infrastructure systems, Structural Safety 36–37 (2012) 23–31. [65] T. Aven, Quantitative Risk Assessment: The Scientific Platform, Cambridge University Press, New York, New York, 2011. [66] L.H. Fink, K.L. Liou, C.-C. Liu, From generic restoration actions to specific restoration strategies, IEEE Transactions on Power Systems 11 (2) (1995) 745–752. [67] K. Matsumoto, T. Sakaguchi, R.J. Kafka, M.M. Adibi, Knowledge-based systems as operational aids in power system restoration, Proceedings of the IEEE 80 (5) (1992) 689–697. [68] N. Xu, S.D. Guikema, R.A. Davidson, L.K. Nozick, Z. Cagnan, K. Vaziri, Optimizing scheduling of post-earthquake electric power restoration tasks, Earthquake Engineering and Structural Dynamics 36 (2007) 265–284. [69] M.M. Adibi, L.H. Fink, C.J. Andrews, F. Arsanjani, M.W. Lanier, J.M. Miller, T.A. Volkman, J. Wrubel, Special consideration in power system restoration, IEEE Transactions on Power Systems 141 (1992) 9–1427. [70] M.M. Adibi, L.H. Fink, Power System Restoration Planning, IEEE Transactions on Power Systems 9 (1) (1994) 22–28. [71] Y. Hou, C.-C. Liu, P. Zhang, K. Sun, Constructing power system restoration strategies, International Conference on Electrical and Electronics Engineering (2009), I-8-I-13. [72] T.T. Ha Pham, Y. Besanger, N. Hadjsaid, New challenges in power system restoration with large scale of dispersed generation insertion, IEEE Transactions on Power Systems 24 (1) (2009) 398–406. [73] K.N. Miu, H.-D. Chiang, B. Yuan, G. Darling, Fast service restoration for largescale distribution systems with priority customers and constraints, IEEE Transactions on Power Systems 13 (3) (1998) 789–795.

A. Castillo / Electric Power Systems Research 107 (2014) 9–15 [74] K. Hotta, H. Nomura, H. Takemoto, K. Suzuki, S. Nakamura, S. Fukui, Implementation of a real-time expert system for a restoration guide in a dispatching center, IEEE Transactions on Power Systems 5 (3) (1990) 1032–1038. [75] A. Ketabi, H. Asmar, A.M. Ranjbar, R. Feuillet, An approach for optimal units start-up during bulk power system restoration, in: IEEE Large Engineering Systems Conference on Power Engineering, New York, 2001, pp. 190–194. [76] Y. Kojima, S. Warashina, M. Kato, H. Watanabe, The development of power system restoration method for a bulk power system by applying knowledge engineering techniques, IEEE Transactions on Power Systems 4 (3) (1989) 1228–1235. [77] C.C. Liu, S.J. Lee, S.S. Venkata, An expert system operational aid for restoration and loss reduction of distribution systems, IEEE Transactions on Power Systems 3 (2) (1988) 619–626. [78] T.K. Ma, C.C. Liu, M.S. Tsai, R. Rogers, S.L. Muchlinski, J. Dodge, Operational experience and maintenance of an on-line expert system for customer restoration and fault testing, IEEE Transactions on Power Systems 7 (2) (1992) 835–842. [79] T. Nagata, S. Hatakeyama, M. Yasuoka, H. Sasaki, An efficient method for power distribution system restoration based on mathematical programming and operation strategy, in: Proceedings of the International Conference on Power System Technology, 2000, pp. 1545–1550. [80] T. Sakaguchi, K. Matsumoto, Development of a knowledge based system for power system restoration, IEEE Transactions on Power Systems PAS-102 (2) (1983) 320–329. [81] K. Shimakura, J. Inagaki, Y. Matsunoki, M. Ito, S. Fukui, S. Hori, A knowledgebased method for making restoration plan of bulk power system, IEEE Transactions on Power Systems 7 (2) (1992) 337–343. [82] A.S. Bretas, A.G. Phadke, Artificial neural networks in power system restoration, IEEE Transactions on Power Delivery 18 (October (4)) (2003) 1181–1186. [83] Y.-T. Hsiao, C.-Y. Chien, Enhancement of restoration service in distribution systems using a combination fuzzy-GA method, IEEE Transactions on Power Systems 15 (November (4)) (2000) 1394–1400. [84] K. Prasad, R. Ranjan, N.C. Sahoo, A. Chaturvedi, Optimal reconfiguration of radial distribution systems using a fuzzy mutated genetic algorithm, IEEE Transactions on Power Delivery 20 (April (2)) (2005) 1211–1213. [85] T.D. Sudhakar, N.S. Vadivoo, S.M.R. Slochanal, Heuristic based strategy for the restoration problem in electric power distribution systems, in: 2004 International Conference on Power System Technology, Singapore, November, 2004. [86] S. Toune, H. Fudo, T. Genji, Y. Fukuyama, Y. Nakanishi, Comparative Study of Modern Heuristic Algorithms to Service Restoration in Distribution Systems, IEEE Transactions on Power Delivery 17 (January (1)) (2002) 173–181. [87] J.S. Wu, C.C. Liu, K.L. Liou, R.F. Chu, A Petri Net algorithm for scheduling of generic restoration actions, IEEE Transactions on Power Systems 12 (February (1)) (1997) 69–76. [88] F.F. Wu, A. Monticelli, Analytical tools for power system restorationconceptual design, IEEE Transactions on Power Systems 3 (1988) 10–26.

15

[89] Y. Hou, C.-C. Liu, K. Sun, P. Zhang, S. Liu, D. Mizumura, Computation of milestones for decision support during restoration, IEEE Transactions on Power Systems 26 (3) (2011) 1399–1409. [90] C.C. Liu, W. Sun, Development and Evaluation of System Restoration Strategies from a Blackout, 2009, PSERC Publication 09-08. [91] S. Wang, B. Sarker, L. Mann Jr., E. Triantaphyllou, Resource planning and a depot location model for electric power restoration, European Journal of Operational Research 155 (2004) 22–43. [92] J. Wu, T. Lee, C. Tsai, T. Chang, S. Tsai, A fuzzy rule-based system for crew management of distribution systems in large-scale multiple outages, in: Proceedings of the 2004 International Conference on Power System TechnologyPOWERCON, Singapore, 2004, pp. 1084–1089. [93] M. Yao, K.J. Min, Repair-unit location models for power failures, IEEE Transactions on Engineering Management 45 (1) (1998) 57–65. [94] D.S. Kirschen, T.L. Volkmann, Guiding a power system restoration with an expert system, IEEE Transactions on Power Systems 6 (2) (1991) 558–566. [95] K.-L. Liou, C.-C. Liu, Tie line utilization during power system restoration, IEEE Transactions on Power Systems 10 (February (1)) (1995) 192–199. ˜ [96] J. Winkler, L. Duennas-Osorio, R. Stein, D. Subramanian, Performance assessment of topologically diverse power systems subjected to hurricane events, Reliability Engineering and System Safety 95 (2010) 323–336. [97] I. Dobson, B.A. Carreras, V.E. Lynch, D.E. Newman, Complex systems analysis of series of blackouts: cascading failure, criticality, and self-organization, in: Proceedings of the 6th Bulk Power System Dynamics and Control, 2004. [98] D. Kirschen, G. Strbac, Why investments do not prevent blackouts, Electricity Journal 17 (2) (2004) 29–36. [99] M. Shinozuka, S.E. Change, T.C. Cheng, M. Feng, T.D. O’Rourke, M.A. Saadeghvaziri, X. Dong, X. Jin, Y. Wang, P. Shi, Resilience of integrated power and water systems, Multidisciplinary Center for Earthquake Engineering Research (2003) 65–86. [100] North American Electric Reliability Corporation (NERC), Disturbances Analysis Working Group Database, 2004. [101] S.E. Chang, M. Shinozuka, J. Moore, Probabilistic earthquake scenarios: extending risk analysis methodologies to spatially distributed systems, Earthquake Spectra 16 (2000) 557–572. [102] X.J. Dong, The Seismic Performance Analysis of Electric Power Systems, University of Southern California, 2002 (Ph.D. dissertation). [103] A.M. Koonce, G.E. Apostolakis, B.K. Cook, Bulk power grid risk analysis: ranking infrastructure elements according to their risk significance, in: Engineering Systems Division Working Paper Series ESD-WP-2006-19, Massachusetts Institute of Technology, 2006. ˜ [104] M. Ouyang, L. Duenas-Osorio, Probabilistic resilience model of electric power systems subjected to hurricane hazards, in: Proceedings of PMAPS 2012, Istanbul, Turkey, June 10–14, 2012. [105] T. Nagata, H. Sasaki, R. Yokoyama, Power system restoration by joint usage of expert system and mathematical programming approach, IEEE Transactions on Power Systems 10 (August (3)) (1995) 1473–1479.