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.     

Component Criticality in Failure Cascade Processes of Network Systems

In this work, specific indicators are used to characterize the criticality of components in a network system with respect to their contribution to failure cascade processes. A realistic‐size network is considered as reference case study. Three different models of cascading failures are analyzed, differing both on the failure load distribution logic and on the cascade triggering event. The criticality indicators are compared to classical measures of topological centrality to identify the one most characteristic of the cascade processes considered.     

Testing Branching Process Estimators of Cascading Failure with Data from a Simulation of Transmission Line Outages

We suggest a statistical estimator to quantify the propagation of cascading transmission line failures in large blackouts of electric power systems. We use a Galton‐Watson branching process model of cascading failure and the standard Harris estimator of the mean propagation modified to work when the process saturates at a maximum number of components. If the mean number of initial failures and the mean propagation are estimated, then the branching process model predicts the distribution of the total number of failures. We initially test this prediction on failure data generated by a simulation of cascading transmission line outages on two standard test systems. We discuss the effectiveness of the estimator in terms of how many cascades need to be simulated to predict the distribution of the total number of line outages accurately.     

Spatial Risk Analysis of Power Systems Resilience During Extreme Events

The increased frequency of extreme events in recent years highlights the emerging need for the development of methods that could contribute to the mitigation of the impact of such events on critical infrastructures, as well as boost their resilience against them. This article proposes an online spatial risk analysis capable of providing an indication of the evolving risk of power systems regions subject to extreme events. A Severity Risk Index (SRI) with the support of real‐time monitoring assesses the impact of the extreme events on the power system resilience, with application to the effect of windstorms on transmission networks. The index considers the spatial and temporal evolution of the extreme event, system operating conditions, and the degraded system performance during the event. SRI is based on probabilistic risk by condensing the probability and impact of possible failure scenarios while the event is spatially moving across a power system. Due to the large number of possible failures during an extreme event, a scenario generation and reduction algorithm is applied in order to reduce the computation time. SRI provides the operator with a probabilistic assessment that could lead to effective resilience‐based decisions for risk mitigation. The IEEE 24‐bus Reliability Test System has been used to demonstrate the effectiveness of the proposed online risk analysis, which was embedded in a sequential Monte Carlo simulation for capturing the spatiotemporal effects of extreme events and evaluating the effectiveness of the proposed method.     

Using Graph Models to Analyze the Vulnerability of Electric Power Networks

In this article, we model electric power delivery networks as graphs, and conduct studies of two power transmission grids, i.e., the Nordic and the western states (U.S.) transmission grid. We calculate values of topological (structural) characteristics of the networks and compare their error and attack tolerance (structural vulnerability), i.e., their performance when vertices are removed, with two frequently used theoretical reference networks (the Erdös‐Rényi random graph and the Barabási‐Albert scale‐free network). Further, we perform a structural vulnerability analysis of a fictitious electric power network with simple structure. In this analysis, different strategies to decrease the vulnerability of the system are evaluated. Finally, we present a discussion on the practical applicability of graph modeling.     

考虑自适应行为的研发网络风险传播模型构建及仿真

构建风险视域下研发网络企业自适应行为规则，基于SIS模型构建研发网络风险传播模型，运用数值仿真的方法通过改变模型参数探索在考虑自适应行为的情况下研发网络的风险传播规律，研究结果表明：（1）C1策略增强了网络的层次性和社团强度，一定程度上抑制了研发网络中风险的传播；C2策略下节点之间新连接的建立更多是基于临近性的考量，容易陷入路径依赖和能力陷阱；（2）研发网络企业的自适应行为会导致社团强度的涨落，平均路径长度的下降以及平均聚类系数的增长充分体现出C1策略的有效性。（3）C1策略下，断边概率p与I*之间呈现"U"型相关关系；在C2策略下随着断边概率p的增长I*逐渐降低。（4）在C1策略和C2策略下，随着参数ζ的增长I*也随之增长，可知组织依赖水平是研发网络风险传播控制中需要重点关注的因素。本文揭示了在考虑自适应行为的情况下研发网络的风险传播规律，为网络化运作背景下研发网络治理提供理论依据。     

Inherent Costs and Interdependent Impacts of Infrastructure Network Resilience

Recent studies in system resilience have proposed metrics to understand the ability of systems to recover from a disruptive event, often offering a qualitative treatment of resilience. This work provides a quantitative treatment of resilience and focuses specifically on measuring resilience in infrastructure networks. Inherent cost metrics are introduced: loss of service cost and total network restoration cost. Further, “costs” of network resilience are often shared across multiple infrastructures and industries that rely upon those networks, particularly when such networks become inoperable in the face of disruptive events. As such, this work integrates the quantitative resilience approach with a model describing the regional, multi‐industry impacts of a disruptive event to measure the interdependent impacts of network resilience. The approaches discussed in this article are deployed in a case study of an inland waterway transportation network, the Mississippi River Navigation System.     

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.     

Integration of Critical Infrastructure and Societal Consequence Models: Impact on Swedish Power System Mitigation Decisions

Critical infrastructures provide society with services essential to its functioning, and extensive disruptions give rise to large societal consequences. Risk and vulnerability analyses of critical infrastructures generally focus narrowly on the infrastructure of interest and describe the consequences as nonsupplied commodities or the cost of unsupplied commodities; they rarely holistically consider the larger impact with respect to higher‐order consequences for the society. From a societal perspective, this narrow focus may lead to severe underestimation of the negative effects of infrastructure disruptions. To explore this theory, an integrated modeling approach, combining models of critical infrastructures and economic input–output models, is proposed and applied in a case study. In the case study, a representative model of the Swedish power transmission system and a regionalized economic input–output model are utilized. This enables exploration of how a narrow infrastructure or a more holistic societal consequence perspective affects vulnerability‐related mitigation decisions regarding critical infrastructures. Two decision contexts related to prioritization of different vulnerability‐reducing measures are considered—identifying critical components and adding system components to increase robustness. It is concluded that higher‐order societal consequences due to power supply disruptions can be up to twice as large as first‐order consequences, which in turn has a significant effect on the identification of which critical components are to be protected or strengthened and a smaller effect on the ranking of improvement measures in terms of adding system components to increase system redundancy.     

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.     

基于遗传算法的微电网负荷优化分配

负荷优化分配是电力系统中的一类重要优化问题,即在满足各类系统约束条件下,实现发电总成本最低。为了促进微电网的优化运行,本文研究了包含柴油发电机、微型燃气轮机、光伏发电机和风力发电机组成的微电网的负荷优化分配问题。首先简要分析了各个微电源的发电特征和成本函数,然后分别建立了孤岛模式和并网模式下的微电网负荷优化分配模型,孤岛模式下优化模型的目标函数是包含燃料成本和运行维护成本的总成本,约束条件包括发电能力约束和系统功率平衡约束,并网模式下的优化模型则在此基础上,在目标函数中增加了其与大电网交易的收入和支出,在约束条件中增加了电力交易约束。最后,通过遗传算法分别对两种模式下的优化模型进行仿真求解。结果表明,本文提出的负荷优化分配方法可以有效降低微电网的运行成本,促进微电网的优化运行。     

超负荷边带有崩溃概率的相继故障模型上袭击策略研究

考虑到现实网络中由于一些保护措施的存在,使得一些超负荷的边并不会立即从网络中移除,提出了超负荷边崩溃概率的机制,并构建了一个超负荷边带有崩溃概率的相继故障模型.对比了BA无标度网络和WS小世界网络上遭遇两种边袭击策略导致的全局相继故障现象,探讨了崩溃概率以及网络拓扑结构对边袭击策略的影响,并分析了网络有效预防相继故障发生的应对策略.数值模拟和理论解析的一致性也验证了结论的正确性.     

Finding disjoint paths with related path costs

We consider routing in survivable networks that provide protection against node or link failures. In these networks resilience against failures is provided by routing connections on pairs of disjoint paths called primary and backup paths. The primary path of a connection carries its traffic under normal circumstances and in the eventuality of a network failure effecting the primary path the connection traffic (all or some portion of it) is rerouted over its backup path. In an online setting as connection requests arrive a pair of disjoint primary and backup paths of least total cost (under some link cost metric) are selected to route the connections. In many situations the cost metric used for the primary path differs from the cost metric used for the backup path. Also in many realistic settings these two cost metrics are related to each other. In this paper we study the problem of finding a pair of edge or node disjoint paths of least total cost where the cost of the primary path is the total cost of its links while the cost for the backup path is α times the sum of the cost of its links, for some given α < 1. We show that the problem is hard to approximate to within a factor for any positive . In addition we show that the problem is complete for a set of hard to approximate problems. On the positive side we show that a simple algorithm achieves an approximation ratio of for the problem.     

Multistage Stochastic Optimization for Production‐Inventory Planning with Intermittent Renewable Energy

A growing number of companies install wind and solar generators in their energy‐intensive facilities to attain low‐carbon manufacturing operations. However, there is a lack of methodological studies on operating large manufacturing facilities with intermittent power. This study presents a multi‐period, production‐inventory planning model in a multi‐plant manufacturing system powered with onsite and grid renewable energy. Our goal is to determine the production quantity, the stock level, and the renewable energy supply in each period such that the aggregate production cost (including energy) is minimized. We tackle this complex decision problem in three steps. First, we present a deterministic planning model to attain the desired green energy penetration level. Next, the deterministic model is extended to a multistage stochastic optimization model taking into account the uncertainties of renewables. Finally, we develop an efficient modified Benders decomposition algorithm to search for the optimal production schedule using a scenario tree. Numerical experiments are carried out to verify and validate the model integrity, and the potential of realizing high‐level renewables penetration in large manufacturing system is discussed and justified.     

Topological Performance Measures as Surrogates for Physical Flow Models for Risk and Vulnerability Analysis for Electric Power Systems

Critical infrastructure systems must be both robust and resilient in order to ensure the functioning of society. To improve the performance of such systems, we often use risk and vulnerability analysis to find and address system weaknesses. A critical component of such analyses is the ability to accurately determine the negative consequences of various types of failures in the system. Numerous mathematical and simulation models exist that can be used to this end. However, there are relatively few studies comparing the implications of using different modeling approaches in the context of comprehensive risk analysis of critical infrastructures. In this article, we suggest a classification of these models, which span from simple topologically‐oriented models to advanced physical‐flow‐based models. Here, we focus on electric power systems and present a study aimed at understanding the tradeoffs between simplicity and fidelity in models used in the context of risk analysis. Specifically, the purpose of this article is to compare performance estimates achieved with a spectrum of approaches typically used for risk and vulnerability analysis of electric power systems and evaluate if more simplified topological measures can be combined using statistical methods to be used as a surrogate for physical flow models. The results of our work provide guidance as to appropriate models or combinations of models to use when analyzing large‐scale critical infrastructure systems, where simulation times quickly become insurmountable when using more advanced models, severely limiting the extent of analyses that can be performed.     

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.     

冰雪灾害背景下电网投资优化和韧性提升模型

韧性研究尤其针对基础设施已经是当今越来越热门的研究话题，电网是社会正常运转的关键基础，雨雪冰冻等自然灾害会严重破坏电网系统，因此针对自然灾害下电网韧性提升至关重要。本文将从韧性视角对电网设施进行投资规划以减少电网系统损失，同时兼顾投资者的投资效益问题。通过建立一种设计者-攻击者-防御者三层数学模型，综合考虑电网韧性的吸收力与适应力提升，选取电网线路分级别保护和增添直流融冰设备作为投资策略来最小化雨雪冰冻的消极影响，实现了对电网系统差异化的动态保护。本文的三层优化模型通过设计的两层C&CG算法进行求解。通过对云南曲靖电网的算例结果进行分析，验证了从韧性视角综合考虑电网投资问题的合理性。     

Critical Infrastructure Vulnerability to Spatially Localized Failures with Applications to Chinese Railway System

This article studies a general type of initiating events in critical infrastructures, called spatially localized failures (SLFs), which are defined as the failure of a set of infrastructure components distributed in a spatially localized area due to damage sustained, while other components outside the area do not directly fail. These failures can be regarded as a special type of intentional attack, such as bomb or explosive assault, or a generalized modeling of the impact of localized natural hazards on large‐scale systems. This article introduces three SLFs models: node centered SLFs, district‐based SLFs, and circle‐shaped SLFs, and proposes a SLFs‐induced vulnerability analysis method from three aspects: identification of critical locations, comparisons of infrastructure vulnerability to random failures, topologically localized failures and SLFs, and quantification of infrastructure information value. The proposed SLFs‐induced vulnerability analysis method is finally applied to the Chinese railway system and can be also easily adapted to analyze other critical infrastructures for valuable protection suggestions.     

Agent‐Based Recovery Model for Seismic Resilience Evaluation of Electrified Communities

In this article, an agent‐based framework to quantify the seismic resilience of an electric power supply system (EPSS) and the community it serves is presented. Within the framework, the loss and restoration of the EPSS power generation and delivery capacity and of the power demand from the served community are used to assess the electric power deficit during the damage absorption and recovery processes. Damage to the components of the EPSS and of the community‐built environment is evaluated using the seismic fragility functions. The restoration of the community electric power demand is evaluated using the seismic recovery functions. However, the postearthquake EPSS recovery process is modeled using an agent‐based model with two agents, the EPSS Operator and the Community Administrator. The resilience of the EPSS–community system is quantified using direct, EPSS‐related, societal, and community‐related indicators. Parametric studies are carried out to quantify the influence of different seismic hazard scenarios, agent characteristics, and power dispatch strategies on the EPSS–community seismic resilience. The use of the agent‐based modeling framework enabled a rational formulation of the postearthquake recovery phase and highlighted the interaction between the EPSS and the community in the recovery process not quantified in resilience models developed to date. Furthermore, it shows that the resilience of different community sectors can be enhanced by different power dispatch strategies. The proposed agent‐based EPSS–community system resilience quantification framework can be used to develop better community and infrastructure system risk governance policies.     

Integrating Risk and Resilience Approaches to Catastrophe Management in Engineering Systems

Recent natural and man‐made catastrophes, such as the Fukushima nuclear power plant, flooding caused by Hurricane Katrina, the Deepwater Horizon oil spill, the Haiti earthquake, and the mortgage derivatives crisis, have renewed interest in the concept of resilience, especially as it relates to complex systems vulnerable to multiple or cascading failures. Although the meaning of resilience is contested in different contexts, in general resilience is understood to mean the capacity to adapt to changing conditions without catastrophic loss of form or function. In the context of engineering systems, this has sometimes been interpreted as the probability that system conditions might exceed an irrevocable tipping point. However, we argue that this approach improperly conflates resilience and risk perspectives by expressing resilience exclusively in risk terms. In contrast, we describe resilience as an emergent property of what an engineering system does, rather than a static property the system has. Therefore, resilience cannot be measured at the systems scale solely from examination of component parts. Instead, resilience is better understood as the outcome of a recursive process that includes: sensing, anticipation, learning, and adaptation. In this approach, resilience analysis can be understood as differentiable from, but complementary to, risk analysis, with important implications for the adaptive management of complex, coupled engineering systems. Management of the 2011 flooding in the Mississippi River Basin is discussed as an example of the successes and challenges of resilience‐based management of complex natural systems that have been extensively altered by engineered structures.