High-impact Low-probability Events Research Articles

Network hardening and optimal placement of microgrids to improve transmission system resilience: A two-stage linear program

This paper aims to develop a linear two-stage optimization problem based on an attacker-defender resilient planning (AD-RP) model to improve the power system's operational and infrastructural resilience in the face of low-probability high-impact events. In the developed model, attackers are natural phenomena that can cause the most severe damage to system performance, and defenders are actions that minimize system vulnerabilities. In the first stage, a stochastic model depending on Monte-Carlo simulation is developed to present a new index for selecting the most vulnerable transmission system components. This index is designed based on combining the worst possible case of attack, disaster statistical analysis, system structure and fragility curves. In the second stage, as defense operations, the hardening of vulnerable lines and microgrids placement in the proper places are carried out considering investment budget constraints. Minimizing load shedding and ensuring the resilience of the transmission network are the main objectives behind the second stage. In this regard, a comprehensive metric for the evaluation of the transmission system resilience is introduced. Thanks to a mixed-integer programming problem, the effectiveness of the proposed AD-RP model in increasing system resilience is demonstrated in the IEEE 30-bus and 118-bus test systems.

Microgrid resilience: a holistic and context-aware resilience metric

Microgrids present an effective solution for the coordinated deployment of various distributed energy resources and furthermore provide myriad additional benefits such as resilience, decreased carbon footprint, and reliability to energy consumers and the energy system as a whole. Boosting the resilience of distribution systems is another major benefit of microgrids. This is because they can also serve as a backup power source when the utility grid operations are interrupted due to either high-probability low-impact events like a component failure or low-probability high-impact events - be it a natural disaster or a planned cyberattack. However, the degree to which any particular system can defend, adapt, and restore normal operation depends on various factors including the type and severity of events to which a microgrid is subjected. These factors, in turn, are dependent on the geographical location of the deployed microgrid as well as the cyber risk profile of the site where the microgrid is operating. Therefore, in this work, we attempt to capture this multi-dimensional interplay of various factors in quantifying the ability of the microgrid to be resilient in these varying aspects. This paper, thus, proposes a customized site-specific quantification of the resilience strength for the individual microgrid capability to absorb, restore, and adapt to the changing circumstances for sustaining the critical load when a low-probability high-impact event occurs - termed as - context-aware resilience metric. We also present a case study to illustrate the key elements of our integrated analytical approach.

Post-event electric taxis dispatch for enhancing resilience of distribution systems

With the frequent occurrences of high-impact-low-probability (HILP) events such as typhoons, lightning strikes, and cyber attacks, people have the increasingly need of raising distribution network’s (DN) resilience. Deploying backup sources into the system can effectively improve the resilience of DNs. With the development of transportation electrification, the number of electric taxis (ETs) in urban transit is now growing. Besides, Vehicle-to-Grid (V2G) technology has also developed vigorously. Therefore, ETs can be dispatched to charging stations under unified command to feed power back to the grid when HILP events happen. To this end, we establish an optimization model for the post-event recovery of the DN using ETs. In this model, we combine the energy provided by V2G stations with the existing distributed generators and energy storage in the grid to restore the outage areas jointly. Topology reconfiguration technique and power flow balance of DN have also been fully considered in the modeling process. The whole grid is divided into several microgrids and powered by different sources. The multi-source multi-region power restoration method improves the stability of the DN restoration. It is easier to control the voltage and power quality. The method we proposed is tested on the modified IEEE 33-bus system. The simulation results verify the effectiveness and efficiency of our work.

Developing an innovating optimization framework for enhancing the long-term energy system resilience against climate change disruptive events

The energy system is one of the major sub-sectors of the economy in every society in which both supply with high reliability and compatibility of the energy sector with the environment is a necessity in the process of economic reconstruction and sustainable development. The energy system has been more susceptible to various disruptive events in recent years. Thus, designing a resilient energy system capable of resisting and recovering rapidly from high-impact low-probability (HILP) disruptive events is essential. This paper focuses on developing a two-stage long-term optimization framework for evaluating the energy system resilience as a crucial Critical Infrastructure (CI) system against HILP caused by climate change. The results show the share of electricity generation shift from coal and hydropower to PV in different scenarios based on the maximization of energy system resiliency. The faster occurring this shift, the greater vulnerability of the system. Furthermore, the sensitivity analysis of the optimum solution shows that the vulnerability of energy systems against HILP events depends on planner flexibility.

Multi-stage and resilience-based distribution network expansion planning against hurricanes based on vulnerability and resiliency metrics

Distribution networks should be expanded to supply reliable and cost-effective services for new and existing customers to respond to the rising demand. On the other hand, there is an increasing awareness of resilience in the face of high impact low probability events. Therefore, this paper presents a multistage, dynamic, and resilient distribution network expansion planning framework to expand a distribution network resiliently. The proposed model is constructed as a six-step structure. The first step develops a network expansion topology. The hurricane occurrence model is executed in the second one that introduces a novel vulnerability index to recognize the most vulnerable facilities. Resilient planning based on the resilience resources such as distributed generations, hardening actions, and distributed automation systems is performed as the third step to reinforce the network preventive capabilities. In the fourth step, a resilient operation is considered to decrease unserved loads and restore the distribution system rapidly. Resiliency evaluation based on technical, financial, and social welfare metrics is employed as the fifth step. Finally, the non-dominated sorting genetic algorithm II optimization method operators are implemented in the sixth step to optimize the problem. Numerical simulations are performed on a 20 nodes distribution system and a real network. The results demonstrate the effectiveness of the proposed method.

Resilient electrical distribution grid planning against seismic waves using distributed energy resources and sectionalizers: An Indian's urban grid case study

The urban and suburban advancement has increased the consumption of energy per capita gradually. Electrical distribution companies have expanded their network to cater to the demand, making the system more vulnerable to low probability high impact events. The extreme events occurred in last five year had shown us complete to partial blackout, which calls for resiliency enhancement. The presented study concentrates on the Dehradun, India, which listed as the most earthquake-prone region by Union Nations Development Programme. Hence, this paper proposes three main strategies to make a resilient distribution grid against an earthquake; (i) Hardening approach at grid side and demand side against earthquake disaster (ii) Monte-Carlo methodology for earthquake hazard model (iii) K-means algorithm with clustering quality index to identify the multiple vulnerable zones. Grid side hardening is performed using the optimal unit placement of the Solar PV plant (SPP) with storage and parallel cables with sectionalizers. For demand-side hardening, electric vehicles are considered storage after an event, duly taking their future growth rate into account. Furthermore, a Mixed Integer non-linear problem is formulated to identify the optimal sizing and sitting of SPP with storage. The proposed methodology is developed and applied to the distribution system (156-bus) of Dehradun, India.

A multi-objective resilience-economic stochastic scheduling method for microgrid

In this paper, the applicability of Microgrids (MGs) is reviewed for power system resilience against low-probability high-impact (LPHI) events. Financial issues have been always one of the major priorities in the scheduling of MGs. Although these systems can feed their loads in islanding mode, resilient operation of them under critical situations caused by LPHI events is a challenging problem. Improving resilience increases MG costs, therefore it is necessary to establish a trade-off between resilience and economic metrics. Therefore, the main purpose of this paper is to develop a novel multi-objective resilience-economic stochastic MG scheduling model. The proposed bi-level resilience-oriented stochastic scheduling integrates the economic perspective along with resilience function simultaneously using a multi-objective mixed-integer linear programming approach. The considered MG resilience function includes various metrics such as the ability to withstand, quick recovery, and the technical criteria in the face of low-probability high-impact events. The proposed method is tested on the modified IEEE 33-bus power system with a set of distributed energy resources, energy storage systems, and electric vehicle parking lots. The results outlined that, although, the integration of the resilience metrics in the MG scheduling problem has increased the operation cost of the MG approximately 25%, but improved the MG resilience more than 70%. On the other hand, the proper management of the independent distributed energy resources enhanced the resilience of the MG approximately 16% while decreased the operation cost of the MG by at least 28%.

Accounting for uncertainties due to high-impact low-probability events in power system development

In the long-term development of the electric power system, system operators should consider the socio-economic balance between grid investment costs and security of supply, including the risk of power supply interruptions. Cost-benefit analyses conducted for this purpose are associated with many uncertainties but have traditionally focused on the expected value of the net socio-economic benefits of risk-reducing measures. This article focuses on the large uncertainties that are associated with the possible occurrence of high-impact low-probability interruption events (HILP events). The objective is to quantify and visualize the implications of uncertainties due to HILP events in the context of power system development. More specifically, this article describes a methodology accounting for uncertainties in socio-economic cost-benefit analysis of measures for reducing the risk of HILP events. The methodology accounts for the contributions of both aleatory and epistemic uncertainties and comprises a hybrid probabilistic-possibilistic uncertainty analysis method. Applying the methodology to a real case involving a grid investment decision, it is demonstrated how it provides additional insight compared to conventional cost-benefit analyses considering expected values where uncertainties are not accounted for explicitly. It is furthermore discussed how these results can help to better inform grid development decisions.

Probabilistic–proactive distribution network scheduling against a hurricane as a high impact–low probability event considering chaos theory

High impact–low probability (HILP) incidents, such as hurricanes, usually and gravely damage electric distribution networks. A resilient distribution network must have an ability to recover itself with a fast restoration methodology against the effects of HILP events. Due to improve the electric distribution network resiliency against HILP incidents, this paper suggests a probabilistic–proactive distribution network operation model based upon the chaos theory (P-PDNOMC(. Here, a resilience index based upon operational cost and load shedding cost is employed to decrease the effects of a hurricane as an HILP incident. P-PDNOMC is formulated as a framework that consists of a novel hurricane modelling and operation scheduling in normal and emergency conditions with uncertainties considering. It should be noted that a prediction approach based on the chaos theory and the least-squares support vector machine (LS-SVM) is also designed to consider the provisional and spatial behaviour of the hurricane. Furthermore, this paper proposes a novel optimization framework for damaged lines determination based upon the P-PDNOM C (DLsP-PDNOM C) by considering multi-zone and multi-period damaged equipment budget constraints. Here, the load shedding cost is applied to present the efficiency of the proposed model. The numerical results indicate the resiliency enhancement of the electric distribution network in the face of HILP incidents.

Robust Resiliency-Oriented Operation of Active Distribution Networks Considering Windstorms

Recent climate changes have created intense natural disasters, such as windstorms, which can cause significant damages to power grids. System resilience is defined as the ability of the system to withstand such high-impact low-probability events. This paper proposes a robust resilient operational schedule for active distribution networks against windstorms. In order to capture dynamic behaviors of these disasters, zonal disaster-specific uncertainty sets associated with the windstorm are proposed. Additionally, the unavailability uncertainties of N-K contingencies as well as the forecast uncertainties of load demand, wind power, and solar power are taken into account. Instead of committing micro-turbines and energy storage systems in the first stage ( here-and-now ) of the decision-making process, the proposed model considers these commitment decisions in the second stage ( wait-and-see ) of the decision-making process, which is more consistent with the fast response time of these units. Since the second stage of the proposed model has binary decision variables, recent KKT-based and duality-based methods are not applicable. Therefore, a new solution method based on block coordinate descent (BCD) and line search (LS) techniques is proposed to solve the bi-level problem. Eventually, IEEE 33-bus distribution test system is used to illustrate the effectiveness of the proposed model and solution method.

Radar-derived precipitation climatology for wind turbine blade leading edge erosion

Abstract. Wind turbine blade leading edge erosion (LEE) is a potentially significant source of revenue loss for wind farm operators. Thus, it is important to advance understanding of the underlying causes, to generate geospatial estimates of erosion potential to provide guidance in pre-deployment planning, and ultimately to advance methods to mitigate this effect and extend blade lifetimes. This study focuses on the second issue and presents a novel approach to characterizing the erosion potential across the contiguous USA based solely on publicly available data products from the National Weather Service dual-polarization radar. The approach is described in detail and illustrated using six locations distributed across parts of the USA that have substantial wind turbine deployments. Results from these locations demonstrate the high spatial variability in precipitation-induced erosion potential, illustrate the importance of low-probability high-impact events to cumulative annual total kinetic energy transfer and emphasize the importance of hail as a damage vector.

Optimizing infrastructure resilience under budgetary constraint

Communities located in regions prone to natural and man-made disasters endure hardship and financial loss in the face of these events. Investment to enhance infrastructure resilience is vital to reduce the consequences of these low probability high-impact events. Budget and resources are limited, and they must be allocated wisely to infrastructure components to build a resilient community. The complexity of infrastructure makes it difficult to show the effects of component enhancements on system resilience. This paper proposes a mathematical programming model aimed at optimizing infrastructure resilience against a set of adverse events by optimally allocating budget to the infrastructure components. Investment, component enhancement, and corresponding functionality are combined with the resilience-based component importance to tackle the system complexity. Three utility functions are presented to determine the possible component enhancement alternatives for an allocated budget and to choose the optimal alternative. A resilience-based component importance metric is introduced, which is used in the budget allocation optimization problem. This approach establishes a relationship between amount allocated to a component and changes in its absorption and recovery, and the aggregate of all such changes on the components on the system functionality. The results show that the utility function of a component impacts the resilience enhancement of the system.

Black swan models for the entertainment industry with an application to the movie business

Success in popular entertainment is highly unpredictable. Yet it is the high-impact low-probability events—known as ‘black swans’—that drive entertainment industry profitability because success is highly concentrated on a small number of winners. In this research, we apply recently developed statistical tools to model motion-picture success; these tools explicitly account for rare extreme events while permitting valid statistical inferences to be made on how product attributes are associated with product success. The specific empirical application relates the attributes of a film and its theatrical release to the distribution of worldwide cumulative box-office revenue. A regression model with skew-stable random disturbances is applied to a large sample of motion pictures to quantify the correlates of film success while explicitly accounting for skewness and heavy tails. The skew-stable estimates are compared to estimates obtained from symmetric-stable regression, ordinary least-squares regression, and several alternative robust-to-outliers regression models. Failure to control explicitly for heavy tails and skewness generates misleading statistical inferences, particularly regarding the impact of production budget, opening week screens, and star power on a film’s success at the box-office.

A viable controlled splitting strategy to improve transmission systems resilience against blackouts

An effective strategy for intentional islanding of a transmission system is proposed in this paper to boost its resilience under low-probability high-impact events such as man-made attacks and natural disasters, which can cause catastrophic blackouts. This strategy considers two main aspects of islanding, i.e. time and scheme. To realize the appropriate time that the system need to be intentionally islanded, a new algorithm based on analysis of the rotor angles of its generators is first presented to distinguish coherent groups of the generators. The main advantage of this algorithm is its independence to the predefined degree of coherency and number of the groups. The information obtained by grouping the generators is then used to compute a new defined indicator, whose sign change specifies the islanding time. To decide about the lines that must be disconnected for fulfillment of the islanding scheme, the initial islands are first formed by tracing the active power produced by the generators. Then, the intended scheme is devised by solving a binary linear programming (BLP) problem that minimizes the disruption of the power transferred between these islands. Comparing the proposed scheme with some existing ones shows that the proposed strategy splits two IEEE test systems into stable islands with a better voltage profile and lower imbalance between the active power generation and demand by disconnecting fewer lines, which have smaller amounts of the power flows.

Energy Storage Planning for Enhanced Resilience of Power Distribution Networks Against Earthquakes

Energy infrastructures are perceived continuously vulnerable to a range of high-impact low-probability (HILP) incidents-e.g., earthquakes, tsunamis, floods, windstorms, etc.- the resilience to which is highly on demand. Specifically suited to battery energy storage system (BESS) solutions, this paper presents a new resilience-driven framework for hardening power distribution systems against earthquakes. The concept of fragility curve is applied to characterize an earthquake hazard, assess its impact on power distribution systems, and estimate the unavailability of the network elements when exposed to extreme earthquakes. A new metric is defined to quantify the network resilience taking into account the uncertain nature of such HILP events. A linear programming optimization problem is formulated to determine the capacity and location of the BESSs for enhanced resilience against earthquakes. Efficacy of the proposed framework is numerically analyzed and verified through application to a real-world distribution power grid.

Optimal allocation of limited resources to biosecurity surveillance using a portfolio theory methodology

Newly arrived pests and diseases pose a continuous threat to agriculture and the environment, and there are limited resources available for early detection programs. We formulate an optimal resource-allocation framework for early detection. The approach is based on the principles of portfolio theory although, unlike standard portfolio theory and its previous applications to biosecurity problems, return is modelled using a flexible mixed-distribution and an uncertainty measure is defined using the Chernoff bound. The Chernoff bound does not assume underlying symmetry and allows sensitivity to both stochasticity and parameter uncertainty to be incorporated systematically into the optimisation process. Optimisation is a trade-off between expected return values and uncertainty while, at the same time, hedging against low-probability high-impact events. In an application to the islands of Torres Strait (Australia), we demonstrate how uncertainty, stochasticity and linkages between surveillance locations interact to significantly alter relative allocation, when compared with allocation based on expected values alone. Locations of particular interest for biosecurity are identified and results lead to a more even spread of resources, or greater surveillance ‘diversification’.

Contingency Inventory Reservation for Low-Probability High-Impact Events

This article investigates reservation contracts for contingency inventory management between two buyers and a single supplier under a game theoretic framework. Two channel structures are considered in this context. In the first setting, the buyers simultaneously move to offer reservation fees to the supplier, who in turn, decides on the inventory amount she wants to carry for each buyer. In the second setting, the supplier moves first and offers nonrefundable-deductible reservation fees for the buyers, who respond with their respective reservation quantities. By reserving through a shared supplier, the buyers enable a contingency inventory pool which alleviates overage risk for the supplier and enables availability of products after low-probability high-impact events. Conditions for successful implementation of contingency reservation contracts are investigated. The results obtained for both channel structures were contrasted. It is shown that in a market where the buyers have more negotiation power, reservation contracts are more likely to achieve inventory buildup under relatively lower event probabilities.

Risk-based probabilistic-possibilistic self-scheduling considering high-impact low-probability events uncertainty

In recent years, examining the ruinous consequence of extreme weather events on the power system is one of the most challenging issues that researchers have confronted to. Considerable extreme conditions are generally the missing part of a realistic self-scheduling problem. Considering high-impact low-probability (HILP) events into the model have at least two benefits: first, generation companies (GenCos) can elude from financial disadvantages of upcoming HILP events and then the ISO can better clear energy and reserve markets with a preventive-oriented process to enhance power system resilience. This paper provides a pre-extreme condition self-scheduling for a price-taker generation company with renewable generation units which participates in the day-ahead energy and spinning reserve markets. Uncertainties associated with electricity prices and wind power production are characterized by multiple stochastic scenarios. The stochastic behavior of wind power is presented by using the Beta probability density function (PDF). In order to model the uncertainty of forced outages of generating units due to HILP events and the probability of being called for reserve deployment, a possibilistic approach is proposed. By comparing the generation scheduling under different risk factors and according to the financial disadvantages of HILP events, the conditional value-at-risk (CVaR) risk-averse strategy is considered into the model.

Proactive Resilience of Power Systems Against Natural Disasters: A Literature Review

The increase in power outages caused by high-impact low-probability events, such as extreme weather-related climate variation events, is the main reason behind studying power system resilience. However, the concepts of resilience as well as the proactive procedures that can be carried out to address these events are such have not so far been satisfactorily investigated notwithstanding their growing benefits. This paper exhibits a review of the current research on power system resilience; which predominantly focuses on proactive resilience against natural disasters. Firstly, it gives a theoretical framework to acquire insights into power system resilience and its key features. Secondly, it presents frameworks for proactive resilience of power systems with a spotlight on the extreme weather events and their effect. Finally, various strategies for preparing, hardening and enhancing proactive resilience with a focus on microgrids for improving power system resilience are reviewed.

Maintaining Electric System Safety Through An Enhanced Network Resilience

Global environmental variations in the past two decades have contributed to a significant deviation of classic ecological patterns, leading to severe electricity outages triggered by extreme weather-driven phenomena. This has highlighted an urgent need for enhancing the resilience and robustness of the interconnected electricity grid against such high impact low probability (HILP) incidents. From the electrical safety point of view, it is essential to increase the operators’ awareness on a better understanding of such hazards and grid vulnerabilities, and enhance their preparedness on how to respond or mitigate the probable outages. This paper proposes a temporary, yet agile, restoration strategy in response to the forecasted HILP events, founded based on efficient utilization of the grid existing infrastructure, and aimed at improving its resilience against such extreme emergencies. The applied concept of reconfiguration is proactively planned to recover the electricity outages in a timely manner. In the meantime, two sets of metrics are proposed to quantify both the grid operational and infrastructure resilience. The presented framework aids the system operator to evaluate the outage recovery plans considering their impacts on system resilience and decide on the final implementation. The proposed approach is applied to the IEEE 118-bus test system facing an HILP event, where results reveal its applicability and efficiency.