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Performance and Reliability of Electrical Power Grids under Cascading Failures
Abstract
The stability and reliability of electrical power grids are indispensable to the continuous operation of modern cities and critical for preparedness, response, recovery and mitigation in emergence management. Because present power grids in China are often running near their critical operation points, they are especially vulnerable and sensitive to external disturbances such as hurricanes, earthquakes and terrorist attacks, which may trigger cascading failures or blackouts. This paper describes a quantitative investigation of the stability and reliability of power grids with a focus on cascading failures under external disturbances. The 118-bus (substation) power network in Hainan, China is employed as a case study to investigate the risk of cascading failure of the regional power grids. System performance and reliability of the power grids are evaluated under two hypothetical scenarios (seismic impact and intentional disturbance) that could trigger cascading failures. By identifying the most vulnerable (critical) edges and nodes, the robustness of the power network is evaluated under the triggered cascading failures. It is found that the system reliabilities could decline as much as 95% during the triggered cascading failure. This paper also explores the use of concepts from modern complex network theories such as state transition graph and characteristic length to understand the complex mechanism of cascading failures. The findings could be useful for power industries and emergency managers to evaluate the vulnerability of power systems, understand the risk of blackout induced by cascading failures, and improve the resilience of power systems to external disturbances.
... Therefore, ignoring the correlation may cause unknown risk. There are no formal rules to deal with the interaction of the degradations among connected components [8]. ...
... If taking the average lifetimest 1 ,t 2 as the constraints, i.e., f 1 = t 1 , f 2 = t 2 , then the solutions become x 1 = 1/t 1 , x 2 = 1/t 2 for Equation (8). ...
... Note that not all the correlations and the moments can be fused by Equation (8). For example, one considers f 1 = t 1 , f 2 = t 2 , f 3 = t 1 t 2 and determines the Lagrange multipliers by these observed valuest 1 ,t 2 , and t 1 t 2 . ...
The degradation and recovery processes are multi-scale phenomena in many physical, engineering, biological, and social systems, and determine the aging of the entire system. Therefore, understanding the interplay between the two processes at the component level is the key to evaluate the reliability of the system. Based on the principle of maximum entropy, an approach is proposed to model and infer the processes at the component level, and is applied to repairable and non-repairable systems. By incorporating the reliability block diagram, this approach allows for integrating the information of network connectivity and statistical moments to infer the hazard or recovery rates of the degradation or recovery processes. The overall approach is demonstrated with numerical examples.
... Further, three categories are defined for data-driven interaction graphs based on the method used for analyzing the data.These include: (1) methods based on outage sequence analysis , (2) risk-graph methods [38][39][40][41], and (3) correlation-based methods [29,30,42,79]. The category of outage sequence analysis is further divided into four sub-categories including (i) consecutive failure-based methods [13][14][15][16][17][18][19][20], (ii) generation-based methods [21][22][23][24][25][26], (iii) influence-based methods [27][28][29][30], and (iv) multiple and simultaneous failure-based methods [31][32][33][34][35][36][37]. This novel taxonomy is used to classify thirty detailed research studies, including conference and journal publications, in the data-driven category into various subcategories. ...
... Consecutive Failures [13][14][15][16][17][18][19][20] Generation-based Failures [21][22][23][24][25][26] Influence-based [27][28][29][30] Multiple and Simultaneous Failures [31][32][33][34][35][36][37] Risk-graph [38][39][40][41] Correlation-based [29,30,42] 3.1. ...
... Other studies that consider the interaction among multiple failures at the same time are presented in [32,33]. In these works, the state of each component in the power grid, including buses and transmission lines/transformers, is represented by 0 for a failed condition and 1 for a working condition. ...
Understanding and analyzing cascading failures in power grids have been the focus of many researchers for years. However, the complex interactions among the large number of components in these systems and their contributions to cascading failures are not yet completely understood. Therefore, various techniques have been developed and used to model and analyze the underlying interactions among the components of the power grid with respect to cascading failures. Such methods are important to reveal the essential information that may not be readily available from power system physical models and topologies. In general, the influences and interactions among the components of the system may occur both locally and at distance due to the physics of electricity governing the power flow dynamics as well as other functional and cyber dependencies among the components of the system. To infer and capture such interactions, data-driven approaches or techniques based on the physics of electricity have been used to develop graph-based models of interactions among the components of the power grid. In this survey, various methods of developing interaction graphs as well as studies on the reliability and cascading failure analysis of power grids using these graphs have been reviewed.
... We show that REDRAW allows to effectively infer directed and weighted links among a group of coupled oscillators, and present an algorithm that allows to set the cut-off thresholds for removing false positives. We validate the method on a number of representative examples, including a set of real-world networks obtained from [30,31,32,33,34]. ...
... Finally, we used REDRAW to reconstruct some real-world networks existing in the current literature [30,31,32,33,34]. The values of the four metrics are detailed in Table 2 for different topologies characterized by a different number of nodes n and edges e, together with the value of the coupling strength c in the model described in Eq. (1), selected so that phase-locking could be achieved [37], and that of the thresholds ν and µ, selected as suggested by the proposed algorithm [40] -note how such thresholds converge towards each other as the number of nodes increases. ...
The formalism of complex networks is extensively employed to describe the dynamics of interacting agents in several applications. The features of the connections among the nodes in a network are not always provided beforehand, hence the problem of appropriately inferring them often arises. Here, we present a method to reconstruct directed and weighted topologies (REDRAW) of networks of heterogeneous phase-locked nonlinear oscillators. We ultimately plan on using REDRAW to infer the interaction structure in human ensembles engaged in coordination tasks, and give insights into the overall behavior.
... Instead, the accepted analysis approach is to generate a set of stochastic failures. The literature following this methodology has typically centered on simulations of targeted failures common to intentional attacks [27,30,31] random failures [32,33], or simulated component failures under seismic events [30]. ...
... Instead, the accepted analysis approach is to generate a set of stochastic failures. The literature following this methodology has typically centered on simulations of targeted failures common to intentional attacks [27,30,31] random failures [32,33], or simulated component failures under seismic events [30]. ...
The increasing occurrence of extreme weather events urges us to reevaluate the resiliency and vulnerability aspects of our most critical infrastructures — such as power grids — as their failures result in both economic loss and severe human hardship. Seen through the lens of alleviating human suffering, it is crucial to be able to identify critical system components of the infrastructure for targeted hardening given resource constraints. This effort is of particular importance in islanded areas such as Puerto Rico where hurricanes are frequent and resources are limited, and where the spatially diverse effects of power loss on human suffering are all the more severe. Recent studies on evaluating infrastructure networks during extreme weather events have taken a simulation based approach that incorporates a variety of component models, such as weather realizations, topological network models, fragility models, and power flow models to estimate expected loss of service. In this work, we expand such a Component Based Event Simulation (CBES) methodology proposed in the literature and integrate it with a social vulnerability modeling component. This paradigm-advancing approach of synthesizing the cutting edge capability of power network modeling and the social impacts of the power transmission network failure is demonstrated for the island of Puerto Rico. Our work exemplifies the efficacy of this integrated modeling framework in developing a decision metric for targeted transmission line hardening.
... In the view of the recoverability of the power grid system, some researchers focus on the measures to improve the flexibility of the power grid, including the preparation strategies before extreme situations and a series of operation strategies that can be adopted in some disasters [42][43][44][45][46][47]. Some researchers seek to propose various graded response mechanisms and recovery decision-making mechanisms after disasters [48][49][50][51]. While others focus on the research of power grid transmission framework topology such as power grid topology reconfiguration and dynamic topological analysis [52,53]. ...
... some disasters [42][43][44][45][46][47]. Some researchers seek to propose various graded response mechanisms and recovery decision-making mechanisms after disasters [48][49][50][51]. While others focus on the research of power grid transmission framework topology such as power grid topology reconfiguration and dynamic topological analysis [52,53]. ...
The safety and reliability of the power grid are related to national power security, economic development and people’s daily life. The occurrence of extreme weather changes the external environment greatly. Including generators and transmission lines, many power grid units cannot resist such a huge attack and get damaged easily, which forces units to quit from the power grid running system for a while. Furthermore, if the number of influenced units is high enough, the whole power system will be destroyed by cascading failure caused by extreme weather. Aiming at dealing with the cascading failure emergencies, this paper is trying to improve the traditional power structural vulnerability model so that it can be used to discuss extreme weather and propose a theoretical topological model to help scholars measure the damage caused by extreme cases. Based on previous research in this field, this paper utilizes complex network knowledge to build the power grid topology model. Then, considering extreme cases and the three attack modes simulation process, this paper makes use of the characteristic parameters of the power grid topology model and designs an algorithm, according to the realistic situation of the propagation mechanism of cascading failure of the power grid model as well as extreme weather research. Finally, taking IEEE-30 and IEEE-118 node bus system as examples, which shows that the structural vulnerability method proposed in this paper can properly address the mechanism of unbalanced load of cascading failure of power grid units under extreme conditions and can provide theoretical reference for preventing and reducing the impact of extreme cases on power grid which improves the reliability of the power grid.
... Chang et al. [10], presented the performance and the reliability assessment of part of China's southern power grid under cascading failures due to earthquakes and hypothetical terrorist attacks. The authors used the Matrix Based System Reliability (MBSR) method which based on OPA and CASCADE models. ...
... It's found by applying the proposed technique that, the failure probabilities' states are shown in Figs. (8,9,10,11). The failure probabilities' states from 2 to 1026 are shown in Fig.8, the failure probabilities' states from 1026 to state 1666 are shown in Fig.9, the failure probabilities' states from 1666 to state 2386 are shown in Fig.10, and the failure probabilities' states from 2386 to state 4096 are shown in Fig.11. ...
Regard to the vast growing technologies in the use of wind turbines and wind farms as a renewable energy source,
many searches had been proved its good impact on electrical transmission systems performance regarding congestion, power
losses, voltage stability, and voltage profiles. This paper aims to prove the positive effect of the connection of wind farms to
power system from the view of reliability and evaluates all the states of different generation’s probabilities for the power
systems. The proposed method used both block diagrams and the Markov chain techniques to assess the whole generation
system reliability, the generation buses reliabilities, the states of generation probabilities, the frequency and mean duration of
generation failure states, and the capacities of generation's system that are in or out of service for each failure state. Also, it is
assessed the system reliability, reliability indices, and analyzed the impact of forced outage rate for each wind turbine and the
number of used wind turbines in each wind farm. MATLAB code is developed using Markov chain construction. The
effectiveness of the proposed method is demonstrated through an updated version of IEEE_RTS_24_node with installed six
wind farms (IEEE_UV_EPS_24_bus_6_WFs). Each wind farm has power capacity of 200 MW. The proposed methodology by
using block diagram technique has been succeeded to reduce the number of system components from 434 to only 12
components and Markov’s states from infinity number to 4096 states. On the other hand, this proposed system is feasible
... Modeling the electrical grid and simulating events together with other types of simulation, such as weather forecasts, is an approach that helps to understand how the grid is affected in fault moments and will help to decrease the consequences. For instance, in 2012, Hurricane Sandy caused a catastrophic impact in New Jersey, with US $68 billion in damages, affecting the entire Atlantic coastline electrical infrastructure, with 69 and 102 electric substations damaged due to floods, 2500 transformers repaired, more than 4400 distribution poles replaced and 286 lives taken [47,131]. After this catastrophe, a control simulation and weather model were developed to try to understand the storm and future aspects to improve. ...
... To do this, monitoring and fault detection actions will be taken into consideration so the faults can be located, and grid components can be monitored. If the intensity of the event exceeds the withstanding capability of the grid components, the damaged part could lead to a cascading failure event, and it is important to know where the faults have occurred [131,132]. ...
One of the most critical infrastructures in the world is electrical power grids (EPGs). New threats affecting EPGs, and their different consequences, are analyzed in this survey along with different approaches that can be taken to prevent or minimize those consequences, thus improving EPG resilience. The necessity for electrical power systems to become resilient to such events is becoming compelling; indeed, it is important to understand the origins and consequences of faults. This survey provides an analysis of different types of faults and their respective causes, showing which ones are more reported in the literature. As a result of the analysis performed, it was possible to identify four clusters concerning mitigation approaches, as well as to correlate them with the four different states of the electrical power system resilience curve.
... Therefore, understanding the conditions or states that can lead the system to fail is crucial. Some papers, especially in the field of natural hazards, integrate both physical element failures (physical vulnerability) and system functionality (systemic vulnerability) [24,78], as seen in definition 8. Finally, we added a third group of definitions that focus on the measure of the system weakness to hazards: definitions 9-11. ...
... Accidental Hazard maps and affected areas Complex network analysis [78,172] Flow-based methods [3,24,215] Logical method [231] Intentional attacks Pointwise attack Intentional/strategic Critical component Complex network analysis [2, 8, 21, 40, 57, 78, 85, 91, 93, 130, 141, 147-150, 152, 153, 155, 158-162, 164, 166, 168, 170, 171, 174-176, 180, 181] Flow-based methods [3, 7, 56, 88, 184, 197, 198, 204-207, 209-212, 216, 217] Logical methods [117,220,221,226,235,236] Functional Methods [259,260,263, 265] Regional attack Intentional/strategic Critical area Complex network analysis [27,182] Logical method [235] Table 9 ...
The failure of a power system as a critical infrastructure causes considerable damage to society. Hence, the vulnerabilities of such facilities should be minimized to cope with several sources of disruption. Various methods have been proposed to identify and address the weaknesses of power systems to enhance their robustness and resilience. As the field is evolving quickly, understanding the pros and cons of each approach and the trends could be challenging. This paper aims to guide the reader toward choosing the most effective method according to the issue investigated. We focus on studies on power grids; however, research on other critical infrastructure could also benefit from this review. We identified three classes of events, namely natural hazards, intentional attacks, and random failures. These events affect the adopted method that can range from analytical approaches—complex network, flow-based, logical, and functional methods—to Monte Carlo simulations. At present, hybrid approaches are emerging with the growing complexities of power grids. Various methods are used in combination to benefit from the strengths of one another. We identified three emerging topics and challenges that require further investigations, namely the N-k problem, trade-off between robustness and optimality, and emerging drivers in power grids.
... In addition to climate-induced risks, other types of natural hazards must be considered regarding transmission line failure risk. Earthquakes are an example of natural hazards that cause power poles, towers, or transmission lines to collapse [9]. As a secondary hazard, they often trigger large urban or forest fires [51]. ...
... Localized failures or attacks on nodes can cause cascading failures and ultimately lead to the breakdown of a whole network, as widely researched in different types of networks [1]. This includes model descriptions [2][3][4], strategies for control or defense [5], and scenarios in real networks such as power grids [6][7][8], transportation infrastructure [9,10], and social networks [11,12]. In addition, the model was extended considering flows in interconnected networks or interdependent networks [13,14]. ...
One of the most challenging issues in contemporary complex network research is to understand the structure and vulnerability of multilayer networks, even though cascading failures in single networks have been widely studied in recent years. The goal of this work is to compare the similarities and differences between four single layers and understand the implications of interdependencies among cities on the overall vulnerability of a multilayer global logistics network. In this paper, a global logistics network model set as a multilayer network considering cascading failures is proposed in different disruption scenarios. Two types of attack strategies—a highest load attack and a lowest load attack—are used to evaluate the vulnerability of the global logistics network and to further analyze the changes in the topology properties. For a multilayer network, the vulnerability of single layers is compared as well. The results suggest that compared with the results of a single global logistics network, a multilayer network has a higher vulnerability. In addition, the heterogeneity of networks plays an important role in the vulnerability of a multilayer network against targeted attacks. Protecting the most important nodes is critical to safeguard the potential “vulnerability” in the development of the global logistics network. The three-step response strategy of “Prewarning–Response–Postrepair” is the main pathway to improving the adjustment ability and adaptability of logistics hub cities in response to external shocks. These findings supplement and extend the previous attack results on nodes and can thus help us better explain the vulnerability of different networks and provide insight into more tolerant, real, complex system designs.
... Also, a new index was introduced for comparing resiliency performances of the networks [69]. The plausible hazards and cascading failures on power systems due to seismic events and intentional disturbances were investigated by Chang and Wub [70] by employing the MSR method. The stability and reliability level of 118-bus high voltage transmission power system (TPS) in Hainan, China were determined. ...
... In the field of power systems, building a disaster risk model and a power system response model is a prerequisite for resilience analysis [9,10]. Chang and Wu [11] studied the robustness and reliability of the power grid under earthquake ground motions and evaluated its vulnerability under cascading failure. The functional evaluation standard and the rapid response strategy under the cascading effect provide an important reference for substation resilience evaluation. ...
... The power system has undergone continuous expansion, resulting in increasingly complex connection types [1,2]. In the event of a power system accident or a sequence of chain failures, the consequences extend beyond human casualties to encompass substantial societal property damage [3,4]. Within a power network, the presence of vulnerable nodes can exert a substantial influence on the incidence and propagation of faults. ...
A method for identifying vulnerable nodes in distribution networks is proposed, which is based on complex networks and optimized TOPSIS. This method aims to address the issues of one‐sided evaluation indicators and inaccurate indicator weights that are present in existing methods for identifying vulnerable nodes in distribution networks. Based on the theory of complex networks, a comprehensive set of vulnerability indicators for distribution network nodes is constructed by considering both the topology structure and system operation status of the distribution network. The TOPSIS comprehensive evaluation model for optimization is proposed to enhance the selection process of optimal and worst indicator values. The advantages and disadvantages of each indicator are characterized using Mahalanobis distance. The calculation of proximity is optimized by establishing a virtual negative ideal solution, which makes the identification of vulnerable nodes more reasonable. The simulation results demonstrate that this method is more effective in identifying vulnerable nodes in the power grid compared to traditional methods, and has significant practical applications.
... In reference [39], the relationship between topology and phase transition in power grid is analyzed, and the influence of topology on transition is evaluated by three spectral metrics. Chang et al. [40] studied the influence of key nodes or edges in topology on grid robustness. Reference [41] analyzes the relationship between the propagation rate of cascaded faults and the network topology parameters, and proves that the change of topology parameters is qualitatively consistent with the propagation rate of cascaded faults. ...
The safe and stable operation of power system is related to the national economy and people’s livelihood of the whole country. Blackouts are almost always caused by cascading failures. This paper first analyzes the global blackouts in the past 20 years, and points out that the scale and probability distribution of blackouts obey the power-law relationship. Secondly, it is concluded that transmission line fault, bus fault, large-scale power flow transfer and relay protection device misoperation are the main factors causing cascading failures. Then, the five stages of cascading failure evolution are analyzed, which are slow successive interruption process, fast successive interruption process, transient oscillation, avalanche blackout and long recovery. Finally, the research results of cascading failure at home and abroad in recent years are analyzed from three research points: small world network, topological network and two-layer coupling network.
... Resilience is intended as the set of attributes that allows the continuity and/or the restoration of the everyday life and business quality after a disrupting event. In fact, when it comes to earthquake engineering, there is a significant deal of research focusing on risk assessment of single utility distribution systems, as gas or electric networks (e.g., Esposito et al., 2015;Cavalieri et al., 2014a;Chang & Wu, 2011;Lanzano et al., 2014;D'onofrio et al., 2013;Ningxiong et al., 2007) and transportation networks (e. g., Argyroudis et al., 2015;Chang et al., 2012;Forte et al., 2015;Kiremidjian et al., 2007); in some cases, the interdependency of critical networks is also considered (e.g., Duenas-Osorio et al., 2007;Omidvar et al., 2014;Poljanšek et al., 2012). The study by Esposito et al. (2015) attempted to extend the probabilistic paradigm of performance-based earthquake engineering or PBEE (Cornell & Krawinkler, 2000), originally developed for buildings (i.e., point-like structures), to spatially distributed systems. ...
Data communication networks have large importance for the immediate post-earthquake emergency management and community resilience. In this study, the framework of simulation-based probabilistic seismic risk analysis of data communication infrastructure is applied to the real case of the inter-university data network of the Campania region (southern Italy). The network is constituted by point-like facilities (racks located within buildings and containing the device routing and managing traffic) and distributed links (buried fiber optic cables). The seismological, geological, and geotechnical features of the region were characterized together with the seismic vulnerability of each element of the network. The network performance is quantified in terms of traffic loss before and after the seismic event. Results are provided in terms of annual rate of events exceeding traffic loss thresholds and allow to identify the portion of the network mostly contributing to the seismic performance.
... Under such situations, sudden network disturbances can cause system blackouts (Kerin et al. 2009). Traditionally, these systems have been secured against low-impact, high-probability (LIHP) events caused by component failures, man-made errors, or minor exterior interferences (Panteli and Mancarella 2015a;Chang and Wu 2011). On the contrary, highimpact, low-probability (HILP) events can cause sporadic power outages, which can cause tremendous social and economic damage. ...
The electric power system is one of the most vital infrastructures, and its security is necessary for the proper functioning of society. The main goal for the electric power system has traditionally been continuity of the electrical power supply. However, in addition to this requirement, power systems must follow the requirements associated with vulnerability and resilience. Vulnerability deals with the assessment of risk, as it relates to physical and economic consequences, arising from the capability of the network to handle an undesirable incident. Resilience deals with the network capability to withstand unknown disturbances, and consequently, the ability to restore stable operating conditions. Despite some research on power system resilience and vulnerability, their basic concepts are still unexplored. This paper aims to discuss the essential concepts of vulnerability and resilience in electric power systems. Their assessment frameworks and quantification metrics are also described. Case studies, on standard test systems, to demonstrate the assessment of power system vulnerability and resilience, are also part of this research.
... Wang and Chen [14] explored the statistical characteristics of the avalanche size of a small world and scalefree network, and their findings have great generality for characterizing cascading-failure-induced disasters in nature. Chang and Wu [15] employed the 118-bus (substation) power network that is located in Hainan, China as a case study to investigate the risk of cascading failure to the regional power grids and found that the system reliabilities could decline by as much as 95% during the triggered cascading failure. Havlin et al. [16] modeled an interdependent network between an Italian power grid and an Internet communication network and presented analytical solutions for the critical fraction of nodes that, on removal, will lead to a failure cascade and a complete fragmentation of two interdependent networks. ...
Power grid system is one of the most important and complex infrastructure systems in our society. Catastrophic blackouts caused by cascading failures, however, still occur and lead to devastating effects. Here, for the first time, we investigate the robustness of the Chinese power grid (CPG) system under various attack and defence scenarios by considering cascading failures. The simulation results illustrate that the effect of the loading level of the power grid network has a large influence on the cascading process. When the initial load of the edge is smaller (α≤1.6), the ascending order strategy of the edge collective influence is the most effective attack strategy for triggering cascading failures over the CPG network. While when the initial load of the edge is larger (α≥1.6), the high load strategy appears to outperform the other strategies. To protect the national power grid from cascading failure, two approaches can be adopted: one approach is to improve the network load capacity, and the other approach is to protect the critical edges. The efforts needed to improve the cascading robustness of the CPG network within these two approaches are quantified. Our results can guide protective measures to avoid large cascading failures and are useful for the design of a robust national power grid network.
... This method helps to select the right PM actions for the component at the right time to reach the most cost efficient solution [4][5][6]. ...
... A. Dunant et al. probability of cascading occurrences is an emergent output of the model instead of the required input). Many publications already leverage graphical frameworks for risk studies in various disciplines where cascading effects can lead to compounding disruptions [42]: supply chains analysis [43], economic markets [44,45] and infrastructure systems [46][47][48][49] being few examples. But few publications use a network framework to constrain the multi-hazard part of the risk assessment ( [50] being one example which focuses on the topological aspect of the Fig. 2. Diagram of the network creation process [41]. ...
Probabilistic multihazard risk assessment from natural hazard is still a challenge today. Current limitations are the number of different hazards that can be included in the assessment, the capacity to output detailed spatial results and access to data for inverse fitting models. A novel quantitative multi-hazard framework is proposed which permit to model the interactions and triggering of perils of different types. Franz Josef on the West Coast of South Island, New Zealand, is used as a case study where the interactions and impacts of earthquake, rainfall, landslide, landslide dam and flooding hazards on the road network, stopbanks and housing is stochastically quantified. The results show that losses are earthquake-dominated, while rarer events show an influence of landsliding on the losses. Due to the complex interaction between hazards allowed by the modelling framework, while initial perils reach a “loss ceiling” with reducing probabilities, it also supercharges secondary perils that can cause greater and greater losses. Combining a network framework with iterative simulations is shown to provide inherent advantages by its discrete nature. In-depth exploration of the data outputs grants insight into the interconnected disaster system on a granular level. The risk assessment herein pointed out the seriousness of the multihazard threat to the Franz Josef township.
... Consequently, in the risk assessment of this kind of systems, these two different typologies of elements should be considered. However, Chang and Wu (2011) and Cavalieri et al. (2014) evaluated the seismic risk of electrical distribution networks accounting for the seismic vulnerabilities of the POPs and neglecting those related to cables: the former analyzes a simplified seismic scenario in which only substation fragilities are considered (according to Vanzi, 1996), while the latter discusses that, being the lines of the analyzed case study aerial lines, they can be considered not seismically vulnerable. On the other hand, Esposito et al. (2018) discuss the seismic performance of an existing data communication network, located in southern Italy (Rete di Interconnessione Multiservizio Interuniversitaria Campana, RIMIC). ...
The seismic risk assessment of spatially distributed infrastructures is gaining increasing research attention. Data communication networks, although less investigated than other infrastructures, have large importance for the immediate post-event emergency management and community resilience. In this study the framework of simulation-based probabilistic seismic risk analysis of data communication infrastructures is applied to a real case study; i.e., the interuniversity data network of the Campania region (southern Italy). The network is constituted by point-like facilities, that is, racks located within buildings and containing the devices routing and managing traffic, and distributed links, that is, buried fiber-optic cables. The network performance was assessed following the performance-based earthquake engineering framework extended to spatially distributed systems. The seismological, geological and geotechnical features of the region were characterized together with the seismic vulnerability of each element of the network. Moreover, to overcome the absence of available fragilities for buried fiber-optic cables, and as a difference with respect to previous work of the authors on the topic, the fragilities recently developed for buried electrical cables are adapted. The network performance is quantified in terms of traffic lost, that is the difference between traffic transferred through the network before and after the seismic event. Results indicate a relatively low level of losses when the network's region is hit by an earthquake and, according to the adopted models, a low influence of cables fragility on the performance of the network.
... Il est introduit dans le coût du composant. Ce dernier croît en fonction de l'intensité de la dépendance[5].LINGO aété conçu pour résoudre efficacement des modèles d'optimisation linéaires, non linéaires et entiers[25]. Il aété mis en place par Ghorabaee et al.[125] pour résoudre de tels problèmes de programmation mathématique. ...
Cette thèse porte sur les problèmes de conception et d’optimisation de la fiabilité des systèmes avec la prise en compte de la dépendance redondante. Nous nous intéressons d’abord à la conception de systèmes réparables dépendants de type parallèle et k sur n : G. Après avoir rappelé le modèle de la dépendance redondante présenté dans la littérature pour les systèmes parallèles, nous proposons un modèle plus général pour les systèmes k sur n : G. Ce modèle permet de quantifier la dépendance de défaillance entre les composants redondants du système. Nous évaluons également la disponibilité stationnaire du système avec la prise en compte de la dépendance à l’aide des modèles markoviens. Nous étudions ensuite la conception des systèmes réparables séries k sur n en considérant la notion de dépendance redondante. Ces problèmes sont traités sous deux approches d’optimisation : mono et multicritère. Dans l’approche monocritère, nous abordons, dans un premier temps, le problème de minimisation des coûts sous contrainte d’une disponibilité exigée. Nous proposons de le résoudre en utilisant le solveur LINGO et en développant des algorithmes génétiques et des algorithmes d'optimisation par colonies de fourmis. Ces algorithmes sont ensuite améliorés par une recherche locale. Dans un deuxième temps, nous étudions le problème dual de maximisation de la disponibilité que nous le résolvons à l’aide des algorithmes génétiques et LINGO. Dans l’approche multicritère, nous considérons simultanément les deux objectifs. Nous proposons des algorithmes multiobjectifs basés sur NSGA2 et SPEA2
... Volume 8, Issue 4, 686-700. with possible faults in the current situation of the system, while prognosis issue deals with the future system status which means predicting how would system behave in expected conditions to prevent malfunctions before its occurrence [1]. Electrical networks are wide spread systems which consist of large number of elements which exposes it to many disturbances affect its services, we can divide them into two categories internal and external affected factors. ...
In power systems, faults are unavoidable events. They can cause disastrous problems to operations. In this study, we aim to reduce the bad effects resulting from these faults in order to raise the operation performance. Fuzzy petri nets (FPN) are very important tools used to diagnose and prognosis issues. However, they take constant certainty factors (CFs) and depend upon long-term statistical average values to describe initial places. A new method is introduced here to determine CFs and initial truth degrees in FPN, so they can reflect different operating states and adapt to any changes in conditions in order to improve the prognosis. For this purpose, we define new kinds of CFs in order to take various conditions into account and represent a wide range of their effects on the system. The main purpose of this study is to analyze the system operation at different states under different conditions to determine the state that may cause problems, and take convenient procedures to prevent them. The proposed method is applied on a reliability test system to show its ability to make the FPN model more flexible and cover a wide range of operation cases.
... To ensure resilience and improve reliability of power supply, European Union (EU) obliges its member states to develop a national risk assessment and a risk preparedness plan in the power supply sector. Stable electricity grids are indispensable to the normal functioning of modern cities and critical for preparedness, response, recovery, and mitigation in the emergence management (Chang and Wu 2011). ...
... Faber et al. (2003) proved that the FD between the sections of large-scale linear engineering structures is widespread. Studies have shown that FD is a significant problem to be handled appropriately in the process equipment systems with high-reliability requirements (Chang and Wu 2011;Gao et al. 2019a;Gao et al. 2019b). There are two forms: ...
Corrosion has made petrochemical infrastructure becomes a significant hazard of the surrounding environment. It is an excellent approach to reduce the risk of environmental pollution by improving the accuracy of determining the leakage probability of the equipment system. In this work, a reliability-based methodology was proposed to assess the system leakage probability with multiple pipe segments under the common cause failure (CCF). Specifically, the existence of FD between the pipe segments was examined under the CCF so that a system leakage assessment model was developed considering the FD. Thereby a novelty corrosion-induced leakage risk management framework was developed. After leakage evaluation for an oil pipeline, it was found that the results obtained were too conservative if ignoring FD, which will develop a wasteful maintenance plan. Overall, the findings in this work may be an opportunity for managers to improve maintenance efficiency.
... System reliability can be measured from three angles [78]: the reliability of structural elements, the connection reliability between node pairs, and system performance reliability, which means ensuring that the infrastructure equipment is not loaded or keeping a minimum water head (pressure) to meet maintenance requirements. For this reason, a power system must establish a relatively perfect four-dimensional index system, including a state dimension, degree dimension, hierarchical dimension and time dimension [77]. ...
Urban multi-energy systems (UMESs) are integrated energy systems (IESs) which can alleviate the current energy crisis, improve energy utilization and realize multi-energy complementarity of modern. Various subsystems involved in the coupling of UMESs, including power grids, gas pipeline networks, cold/heat networks, transportation networks, and energy cyber-physical system, exhibit coupling characteristics such as multi-energy source modeling, complex uncertainty factor modeling, mutual influence of information and physical coupling. At present, the modeling and reliability assessments of UMESs are the most urgent tasks. In this paper, the latest research results on the reliability modeling and evaluation of UMESs are analyzed by considering their coupling components. In addition, the reliability modeling methods and the evaluation indexes of UMESs, including power-gas systems, power-thermal systems, power-traffic systems, and energy cyber-physical systems, are presented in this paper, with specific UMES modeling methods divided into model-driven modeling and data-driven modeling. Finally, future challenges for the reliability modeling and evaluation of UMESs are proposed, such as the dispatch strategy of the coupling components needs to be developed and continuously optimized to improve the reliability of UMESs, and the resilience of UMESs under the extreme scenarios needs to be further studied.
... Based on the frequency and voltage control grid reliability index (Ahearne, 2011), many power system reliability studies have so far been published from the standpoint of cascading failures, such as from short-circuits or external disturbances (Sovacool, 2011;Kjølle et al., 2012;Chang and Wu, 2011). These existing reports have tended to mainly describe failures in the engineering or technical aspects of grid systems. ...
... The physical failure occurs when the intensity of the extreme weather event exceeds the withstanding capability of the grid component. The damaged part may lead to cascading failure because the other parts of the grid will burden additional loads, which may be larger than their maximum loading capacity [97][98][99][100][101][102][103]. ...
The occurrence of a Loss Of Offsite Power (LOOP) event can be a major threat to nuclear safety due to the dependence of auxiliary systems on electrical energy. Probabilistic safety assessments of nuclear power plants require, thus, estimates of the frequencies and durations of such LOOP events. These estimates are usually based on past statistical data, which is not always relevant. Model-based approaches are thus needed. This paper proposes an analytical method to estimate the frequency and duration of switchyard-centered LOOP events, which constitute one of the four main categories of LOOP events. The proposed method is mainly based on the identification of active minimal cut sets, considering the behavior of circuit breakers against faults according to their coordination and selectivity. Adapted versions of the Risk Reduction Worth and Fussel–Vesely importance factors are proposed to evaluate the impact of components on the switchyard-centered LOOP event frequency. Furthermore, uncertainty analysis is developed and performed. Various generic plant connection schemes are used for application. Results demonstrate the applicability of the methodology to estimate the frequency and duration of switchyard-centered LOOP events, and to identify optimal ways to reduce the risk by modifying the switchyard configuration.
This research aims to advance the field of vanadium redox flow batteries (VRFBs) by introducing a pioneering approach to optimize the microstructural characteristics of carbon cloth electrodes. Addressing the traditional challenge of developing high-performance electrode materials for VRFBs, this study employs a robust, generalizable, and cost-effective data-driven modeling and optimization framework. A novel sampling strategy using low-discrepancy Latin Hypercube and quasi-Monte Carlo methods generates a small-scale, high-fidelity dataset with essential space-filling qualities for training supervised machine learning models. This study goes beyond conventional methods by constructing two surrogate models: a random forest regressor and a gradient boosting regressor as objective functions for optimization. The integration of a non-dominated sorting genetic algorithm II (NSGA-II) for multi-objective optimization facilitates exhaustive exploration of the surrogate models, leading to the identification of electrode designs that yield enhanced energy efficiencies (EEs) under specific operating conditions. The application of NSGA-II in exploring surrogate models not only facilitates the discovery of realistic design combinations but also adeptly manages trade-offs between features. The mean pore diameter was reduced compared to the tested carbon cloth electrodes while maintaining a similar permeability value based on the results obtained using the developed algorithms. Based on this suggestion, a new type of carbon cloth electrode has been fabricated by introducing a carbonaceous binder into the woven fabric to make carbon cloths with more complex pore structures and reduced mean pore diameter. The new electrode demonstrates 24% and 66% reduction in average ohmic and mass transport resistances, respectively, validating the machine-learning recommendations. This research highlights the critical role of improved electrical conductivity and porosity in carbon materials, showing their direct correlation with increased EE. Overall, this study represents a significant step forward in developing more efficient and practical VRFBs, offering a valuable contribution to the renewable energy storage landscape.
Due to rapid advancements on the Internet of Things (IoT), unmanned aerial vehicles (UAVs), also known as drones, are transforming numerous military and civil application areas. UAVs aim to enhance the production efficiency, ensure safety, and reduce risk, particularly protecting human workforce in the case of harsh and dangerous environments. Due to the mission-critical, business-critical, or safety-critical nature of the UAV applications, it is pivotal that UAVs perform reliably to deliver the required service during the intended mission time. Therefore, reliability is one of the essential requirements for designing and operating UAVs. This paper presents a critical review of UAV reliability literature in both theoretical and practical research, pinpointing failure causes and reliability challenges of UAV systems, classifying and reflecting on the reliability modeling, analysis, and design methods for UAV systems and key subsystems. Some open research problems and opportunities are also discussed to highlight potential new challenges for designing reliable and resilient UAVs and UAV-assisted IoT systems.
Railway and power networks are among the most important critical infrastructures and their vulnerability under different types of disrupting events has been analyzed extensively. However, the increasing degree of interconnection between these two critical infrastructures makes it necessary to consider the multiple interdependencies when conducting vulnerability assessments. We propose an approach for the modeling and vulnerability analysis of interdependent railway and power networks which accounts for a realistic coupling through the traction power network, which acts as an interface. Moreover, we consider cascading failures within and between networks. With the proposed model, we show that failures in the power network have a considerable negative impact on the railway network. In addition, our analysis shows that the dependency of the railway network on the power network can considerably impact vulnerability and cascading failures dynamics of the power network.
Generic frequencies are used for Grid-related Loss of Offsite Power (GR-LOOP) in the Probabilistic Safety Analysis (PSA) of Nuclear Power Plants (NPPs). When historical databases are used, the influence of variation in the grid conditions over time and the impact of the NPP location are not considered in the estimation of GR-LOOP frequency. Therefore, relying purely on historical data induces uncertainty in total Core Damage Frequency (CDF).
This paper aims at assessing the influence of the dynamic load behavior on the GR-LOOP frequency, for different locations. For that purpose, sensitivity cases are defined. The occurrence frequency of GR-LOOP following the occurrence of a three-phase-short-circuit fault on a transmission line is evaluated via a probabilistic-deterministic methodology for all cases.
The minimum and maximum estimated values of the GR-LOOP frequency, 2.98E-04/year and 9.95E-03/year respectively, indicate the dependence on the variation in either the dynamic load behaviors or the NPP locations.
The results reveal that GR-LOOP frequency varies with load model in the initial grid. In the presented probabilistic-deterministic methodology it is beneficial to consider the influence of timely changes of the grid conditions on the GR-LOOP occurrence frequency for different NPPs’ locations, especially where relevant or sufficient generic databases are not available.
Post-disruption restoration of critical infrastructures (CIs) often faces uncertainties associated with the required repair tasks and the related transportation network. However, such challenges are often overlooked in most studies on the improvement of CI resilience. In this paper, two-stage risk-averse and risk-neutral stochastic optimization models are proposed to schedule repair activities for a disrupted CI network with the objective of maximizing system resilience. Both models are developed based on a scenario-based optimization technique that accounts for the uncertainties of the repair time and the travel time spent on the underlying transportation network. Given the large number of uncertainty realizations associated with post-disruption restoration tasks, an improved fast forward algorithm based on a wait-and-see solution methodology is provided to reduce the number of chosen scenarios, which results in the desired probabilistic performance metrics. To assess the risks associated with post-disruption scheduling plans, a conditional value-at-risk (CVaR) metric is incorporated into the optimization models through a scenario reduction algorithm. The proposed restoration framework is applied to the French RTE electric power network with a DC power flow procedure, and the results demonstrate the added value of using the stochastic optimization models incorporating the travel times related to repair activities. It is essential that risk-averse decision-making under uncertainty largely impacts the optimum schedule and the expected resilience, especially in the worst-case scenarios.
This paper presents a new online scheme for estimating critical contingencies caused by extreme windstorms aiming at improving the microgrid (MG) resiliency. The proposed scheme benefits from an online and non-model-based index by which the fragility metrics of MGs and the loads are evaluated at each time moving window. Also, four indices based on dynamic evaluation of the network are proposed which two indices correspond to the failure period and the two other are related to the network recovery period. By evaluation of these indices, correction actions aiming at improving the resilience of MG are provided. Finally, the proposed method is assessed in the case of different generation locations and the outage probability of system components. The results evidence that the proposed scheme shows a 15% reduction in the total load failure index and a 7% reduction in the critical load failure index if compared to the base case. It also shows a 23% improvement in the total load recovery in the presence of severe storms.
Loss of Offsite Power (LOOP) is the most dominant initiating event in the Core Damage Frequency (CDF) of Nuclear Power Plants (NPPs). Since the frequency of occurrence of LOOP depends on the grid configuration, outage schedule, load flow, etc., even a relevant generic frequency may result in significant uncertainty.
In this study, an analytical hybrid methodology, which combines the probabilistic and deterministic modules, is introduced to systematically estimate the frequency of Grid-related LOOP. The proposed probabilistic module develops the relevant event-trees and fault-trees in SAPHIRE7 to identify the LOOP sequences upon the response of the distance protection system to a fault on the transmission lines. Meanwhile, the identified scenarios are confirmed based on the simulation results from the deterministic module in DIgSILENT-PowerFactory15.1.
15-out-of-48 scenarios (100-out-of-300 sequences) are identified as grid-related LOOP upon faults on the four transmission lines of the test grid, and result in 1.76E-06/yr for the grid-related LOOP frequency. The developed methodology enables us to trace a LOOP chain, from a primitive presumed fault through the progress of the cascade. The grid-related LOOP scenarios in a certain network can be ranked probabilistically, with the desired level of details in both deterministic and probabilistic modules.
In this paper, we develop a new method for evaluating the reliability polynomial of a hammock network. The method is based on a homogeneous absorbing Markov chain and provides the exact reliability for networks of width less than 5 and arbitrary length. Moreover, it produces a lower bound for the reliability polynomial for networks of width greater than or equal to 5. To investigate how sharp this lower bound is, we compare our method with other approximation methods and it proves to be the most accurate in terms of absolute as well as relative error. Using the fundamental matrix, we also calculate the average time to absorption, which provides the mean length of a network that is expected to work.
Recent hurricane events have caused unprecedented amounts of damage on critical infrastructure systems and have severely threatened our public safety and economic health. The most observable (and severe) impact of these hurricanes is the loss of electric power in many regions, which causes breakdowns in essential public services. Understanding power outages and how they evolve during a hurricane provides insights on how to reduce outages in the future, and how to improve the robustness of the underlying critical infrastructure systems. In this article, we propose a novel scalable segmentation with explanations framework to help experts understand such datasets. Our method, CnR (Cut-n-Reveal), first finds a segmentation of the outage sequences based on the temporal variations of the power outage failure process so as to capture major pattern changes. This temporal segmentation procedure is capable of accounting for both the spatial and temporal correlations of the underlying power outage process. We then propose a novel explanation optimization formulation to find an intuitive explanation of the segmentation such that the explanation highlights the culprit time series of the change in each segment. Through extensive experiments, we show that our method consistently outperforms competitors in multiple real datasets with ground truth. We further study real county-level power outage data from several recent hurricanes (Matthew, Harvey, Irma) and show that CnR recovers important, non-trivial, and actionable patterns for domain experts, whereas baselines typically do not give meaningful results.
The Internet of Things (IoT) aims to transform the human society toward becoming intelligent, convenient, and efficient with potentially enormous economic and environmental benefits. Reliability is one of the main challenges that must be addressed to enable this revolutionized transformation. Based on the layered IoT architecture, this paper first identifies reliability challenges posed by specific enabling technologies of each layer. The paper then presents a systematic synthesis and review of IoT reliability related literature. Reliability models and solutions at four layers (perception, communication, support, and application) are reflected and classified. Despite the rich body of works performed, the IoT reliability research is still in its early stage. Challenging research problems and opportunities are then discussed in relation to current under-explored behaviors and future new aspects of evolving IoT system complexity and dynamics.
With the rise of the resilience concept, scholars and practitioners have paid increasing attention to resilient city, which has become a new means of coping with hazards. As the cornerstone of modern cities, urban critical infrastructure networks (CINs) are prerequisites for resilient cities due to the huge economic losses and social impacts caused by their incapacities. In recent years, researches on the resilience of CINs have considerably increased, resulting in various resilience definitions, approaches, and enhanced strategies. This work reviews literature on six CINs, namely, water, drainage, gas, transportation, electric, and communication networks. The resilience definitions, hazard categories, methodologies, and enhanced measures for each CIN are analyzed in detail. Research challenges and future directions are also presented.
This paper focuses on the planning and scheduling of restoration efforts provided by infrastructure networks in the aftermath of disruptive events. Two mathematical formulations are presented to assign restoration crews to disrupted components and maximize network resilience progress in any given time horizon. In the first formulation, the number of assigned restoration crews to each component can vary to increase the flexibility of models in the presence of different disruption scenarios. Along with considering the assumptions of the first formulation, the second formulation models the condition where the disrupted components can be partially active during the restoration process. We test the efficacy of our formulations on the realistic dataset of 400-kV French electric transmission network and 32 realistic size datasets illustrating scale-free, small-world, lattice, and random networks. The results indicate that the proposed formulations can be used for a wide variety of infrastructure networks and for real-time restoration process planning.
Electrical substations and vital components, e.g., disconnect switches, experienced severe damage that caused blackouts during past earthquakes. To improve the seismic resiliency of power grids and use probabilistic decision-making frameworks, comprehensive fragility data for the different substation equipment are needed. The objective of this study is to investigate the seismic performance of and develop component and system fragility curves for a critical substation component: disconnect switches. The seismic vulnerability of two common switch types was evaluated and two operational configurations were considered. Detailed nonlinear finite element models for the full switches were calibrated using previous experimental data and used to conduct incremental dynamic analysis and carry out the fragility assessment. A total of 160 triaxial ground motions representing four sets of different ground motion characteristics were used. The switches’ fragility curves were developed and presented to be readily used for new substation design, prioritizing retrofit/maintenance activities and reliability assessment of power grids.
A blackout is usually the result of increasing load beyond the transmission capacity of the power system. One of the main reasons for power blackouts is voltage collapse. To avoid this problem, the proper corrective measures called load shedding is required. In critical and extreme emergencies, under voltage load shedding (UVLS) is performed as a final remedy to avoid a larger scale voltage collapse. Therefore, UVLS is considered state of the art to achieve voltage stability. This review summarizes and updates the important aspects of UVLS; it also provides principle understanding of UVLS, which are critical in planning such defense schemes. Moreover, this article provides a discussion on recent state‐of‐art UVLS schemes applied in various power industries. Additionally, the pros and cons of the conventional and computational intelligence techniques are discussed. It is envisioned that this work will serve as one‐stop information for power system engineers, designers, and researches.
Recent extreme weather events have emphasized the need for new methods and metrics to assess the power system resilience in response to high-impact low-probability (HILP) events. Microgrids (MGs) have been instrumental in such occasions for maintaining the power supply continuity to local customers. This paper provides a quantitative framework for assessing the MG resilience in response to HILP windstorms. The proposed framework jointly employs fragility curves of overhead distribution branches and windstorm profile to quantify the degradation in the MG performance (particularly supplied load in this work). The proposed analytical method is simple and computationally efficient which offers a quick means for getting knowledge about adverse impacts of an approaching windstorm and taking preventive measures accordingly. A set of normalized metrics is defined which provides a comparable tool for assessing the resilience in various operating conditions and power systems. The impacts of restorative actions, the system reinforcement, and the event severity on resilience curves and metrics are also investigated. The effectiveness of the proposed approach in response to an extreme windstorm is examined on a real-scale MG test bed.
In order to improve the reliability of civil infrastructure systems against deterioration and natu- ral or man-made hazards, it is important to identify their critical components and cut sets. There exist various measures of component importance, which often relate to the relative contribution of a component or cut set to the failure probability of the system. Recently, the authors developed a linear programming (LP) approach for computing bounds on the failure probability of general systems in terms of the marginal and joint compo- nent failure probabilities. This paper shows that bounds on the well-known importance measures can be ob- tained by solving an LP that is modified or parameterized from the one used for estimating the system failure probability. Also introduced is a new component importance measure that estimates the upgrading of system performance that can be achieved by a fixed cost. The new measure involves the sensitivities of system failure probability with respect to the marginal and joint component failure probabilities, which are byproducts of the LP for the system failure probability. Example applications to an electrical substation system demonstrate the methods proposed for the existing and the new importance measures.
The massive electric power blackout in the northeastern United States and Canada on August 14-15, 2003 resulted in the U.S. electricity system being called ''antiquated'' and catalyzed discussions about modernizing the grid. Industry sources suggested that investments of 100 billion would be needed. This report seeks to quantify an important piece of information that has been missing from these discussions: how much do power interruptions and fluctuations in power quality (power-quality events) cost U.S. electricity consumers? Accurately estimating this cost will help assess the potential benefits of investments in improving the reliability of the grid. We develop a comprehensive end-use framework for assessing the cost to U.S. electricity consumers of power interruptions and power-quality events (referred to collectively as ''reliability events''). The framework expresses these costs as a function of: (1) Number of customers by type in a region; (2) Frequency and type of reliability events experienced annually (including both power interruptions and power-quality events) by these customers; (3) Cost of reliability events; and (4) Vulnerability of customers to these events. The framework is designed so that its cost estimate can be improved as additional data become available. Using our framework, we estimate that the national cost of power interruptions is about 30 billion to more than $130 billion. Because of this large range and the enormous cost of the decisions that may be based on this estimate, we encourage policy makers, regulators, and industry to jointly under take the comparatively modest-cost improvements needed in the information used to estimate the cost of reliability events. Specific areas for improvement include: coordinated, nationwide collection of updated information on the cost of reliability events; consistent definition and recording of the duration and frequency of reliability events, including power-quality events; and improved information on the costs of and efforts by consumers to reduce their vulnerability to reliability events.
Bounds on system probability in terms of marginal or joint component probabilities are of interest when exact solutions cannot be obtained. Currently, bounding formulas employing unicomponent probabilities are available for series and parallel systems, and formulas employing bi- and higher-order component probabilities are available for series systems. No theoretical formulas exist for general systems. It is shown in this paper that linear programming ~LP! can be used to compute bounds for any system for any level of information available on the component probabilities. Unlike the theoretical bicomponent and higher-order bounds, the LP bounds are independent of the ordering of the components and are guaranteed to produce the narrowest possible bounds for the given information. Furthermore, the LP bounds can incorporate any type of information, including an incomplete set of component probabilities or inequality constraints on component probabilities. Numerical examples involving series, parallel and general structural systems are used to demon- strate the methodology.
Abstract The state - space of a discrete dynamical network is connected into basins of attraction, mathematical objects that can be computed and shown as graphs for small networks Multiple attractors explain how the same genetic regulatory network can maintain di?erent stable patterns of gene activation, the cell types in multi - cellular organisms Ideas of modularity suggest that the overall genetic network is actually made up of semi - independent sub - networks Each sub - network also settles into one of a range attractors according to its current state, which if perturbed can cause the dynamics to jump to alternative attractors A network's \memory", its ability to categorize, is provided by its separate basins of attraction, and also by the topology of the tr
Civil infrastructure systems such as power systems are the essential urban elements and also highly vulnerable to natural and man-made disasters such as earthquakes and terrorist attacks. With the provincial level power grid data from Chinese power utilities including 118 buses (substations) and more than 180 branches (transformers and transmission lines), we studied the system reliability and performance of the power systems in Province A, China in two scenarios — under a given scenario earthquake and a hypothetical terrorist attack. Seismic reliability of the substations (nodes) was evaluated under the impact of earthquake. Power flow (load flow) analysis was then conducted on the power network. The most vulnerable (critical) edges and nodes were identified with complex network theory. The results can be used to estimate cascading failure and economic loss induced by the damaged power system. The findings could also be useful for local planning department and power industries to evaluate the most vulnerable nodes/edges of the power system and improve their seismic performance under economic constrains.
In efforts to estimate the risk and reliability of a complex structure or infrastructure network, it is often required to evaluate the probability of a ‘system’ event, i.e. a logical function of multiple component events. Its sensitivities with respect to design parameters are also useful in decision-making processes for more reliable systems and in reliability-based design optimisation. The recently developed, matrix-based system reliability (MSR) method can compute the probabilities of general system events including series, parallel, cut-set and link-set systems, and their parameter sensitivities, by use of efficient matrix-based procedures. When the component events are statistically dependent, the method transforms the problem into an integral in the space of random variables which cause the statistical dependence, termed as the common source random variables (CSRVs). One can identify CSRVs by fitting a generalised Dunnett-Sobel (DS) model to a given correlation coefficient matrix. This article introduces two further developments of the MSR method: First, for efficient evaluation, it is proposed that the integral in the CSRV space can be performed using the first- or second-order reliability methods. Second, a new matrix-based procedure is developed to compute the sensitivity of the system failure probability with respect to the parameters that affect the correlation coefficients between the components. In addition, an extensive parametric study is performed to investigate the effect of the error in fitted generalised DS model on the accuracy of the estimates by the MSR method. The further developed MSR method is demonstrated by two examples: system reliability analysis of a three-storey Daniels system structure, and finite element reliability analysis of a bridge pylon system.
An algorithm is developed to obtain a simplified reliability expression for a general network. All the success paths of the network are determined; then they are modified to be mutually disjoint. The reliability expression follows directly from the disjoint paths. The algorithm is easy and computationally economical. The reliability expression involves fewer terms and arithmetic operations than any of the existing methods. This is an advantage, considering the size of the system a reliability engineer normally handles and the frequency with which the expression is used for reliability studies.
Power grids are prone to failure. Time series of reliability measures such as total power loss or energy not supplied can give significant account of the underlying dynamical behavior of these systems, specially when the resulting probability distributions present remarkable features such as an algebraic tail, for example. In this paper, seven years (from 2002 to 2008) of Europe's transport of electricity network failure events have been analyzed and the best fit for this empirical data probability distribution is presented. With the actual span of available data and although there exists a moderate support for the power law model, the relatively small amount of events contained in the function's tail suggests that other causal factors might be significantly ruling the system's dynamics. Comment: 4 pages 1 figure
Thesis (Ph.D. in Engineering-Civil and Environmental Engineering)-- University of California, Berkeley, Spring 2004. Includes bibliographical references (leaves 240-245).
Urban infrastructure systems such as utility networks for electricity-, water-, sewage- and gas-services, transportation systems and telecommunication networks are critical backbones of modern societies. However, these systems are often susceptible to natural and man-made hazards. Structural damages of components in these infrastructure networks not only disrupt residential and commercial activities, but also impair post-disaster response and recovery efforts, resulting in substantial socio-economic losses. Therefore, estimating the reliability of these infrastructure systems is vital to urban stakeholders such as utility companies, urban planners, and policy makers as well as to residents and business owners. Evaluation of the performance and connectivity of such urban infrastructure systems is complex in nature due to the large number of network components, complex network topology and component/system interdependencies. Due to this complexity, network reliability analysis is often performed by repeated network analyses for random samples of hazard scenarios and component status, which prevents rapid risk assessment and near-real-time risk-informed decision making. In this paper, an analytical, i.e. non-sampling-based network reliability analysis method is proposed for urban infrastructure systems. First, a review of previous research on network reliability analysis is given, followed by a brief summary of the recursive decomposition algorithm (RDA) and the matrix-based system reliability (MSR) method that constitute the proposed network reliability analysis methodology. As a case study, the proposed methodology is applied to a Memphis Light, Gas and Water (MLGW) natural gas network of Shelby County of Tennessee. Based on seismic hazard maps from the Mid-America Earthquake Center’s risk management software MAEviz and the topological characteristics of an MLGW gas network, the reliability of the network components are computed by use of a geographic information system, ArcGIS. All the disjoint cut sets and link sets of the simplified MLGW gas network are efficiently identified by use of the RDA. The MSR method, which can account for statistical dependence between components and incomplete information, is employed to evaluate the connectivity reliability of the gas network in an efficient manner. The results of the system reliability analysis are presented for earthquake scenarios with different magnitudes. By integrating the MSR method with an advanced network analysis algorithm such as the RDA, we can perform network reliability analysis for a complex infrastructure system without random samplings. This approach will enable us to perform risk analysis and various statistical inferences rapidly. Based on the results of the case study, further research is in progress to (1) account for the statistical dependence between seismic intensities at adjacent network components, (2) estimate the average downtime and socio-economic losses, (3) account for the interdependency between different infrastructure systems, and (4) provide useful information for decision making on disaster planning, response, recovery, and mitigation using the proposed methodology. published or submitted for publication is peer reviewed
Cascading failures in large-scale electric power transmission systems are an important cause of blackouts. Analysis of North American blackout data has revealed power law (algebraic) tails in the blackout size probability distribution which suggests a dynamical origin. With this observation as motivation, we examine cascading failure in a simplified transmission system model as load power demand is increased. The model represents generators, loads, the transmission line network, and the operating limits on these components. Two types of critical points are identified and are characterized by transmission line flow limits and generator capability limits, respectively. Results are obtained for tree networks of a regular form and a more realistic 118-node network. It is found that operation near critical points can produce power law tails in the blackout size probability distribution similar to those observed. The complex nature of the solution space due to the interaction of the two critical points is examined.(c) 2002 American Institute of Physics.
As power system loading increases, larger blackouts due to cascading outages become more likely. The authors investigate a critical loading at which the average size of blackouts increases sharply to examine whether the probability distribution of blackout sizes shows the power tails observed in real blackout data. Three different models are used, including two simulations of cascading outages in electric power transmission systems. They also derive and use a new, analytically solvable model of probabilistic cascading failure which represents the progressive system weakening as the cascade proceeds.
The primary objective of any electric utility company in the new competitive environment would be to increase the market value of the services it provides with the right amount of reliability, and at the same time, lower its costs for operation, maintenance, and construction of new facilities in order to provide lower rates for customers. The electric utility company will strive to achieve this objective via many different means, one of which is to defer the capital distribution facility requirements in favor of a distributed generation (DG) solution by an independent power producer (IPP) to meet the growing customer load demand. In this case, the distribution capital investment deferral credit received by the IPP will be dependent on the incremental system reliability improvement rendered by the DG solution. In other words, the size, location and the reliability of the DG will be based on the comparable incremental reliability provided by the distribution solution under considerations. This paper presents a reliability model for determining the DG equivalence to a distribution facility for use in distribution system planning studies in the new competitive environment.
The performance of engineering systems is not deterministic but rather controlled by the uncertainties in the variables affecting that performance. The evaluation of the probability of non-performance can be carried out implementing methods of reliability theory. This work presents a brief discussion of these methods and their applications to four problems relevant to risk analysis of power components and systems: transmission towers, pole distribution lines, the calibration of factored equations for performance-based design, and the reliability updating of existing structures under change of service conditions.
The blackout has become worldwide concerned problem. We focus on the aspects of causes and restoration. In this paper, we reviewed the blackout in Hainan Island power system and analyzed the causes and restoration procedure. Some experience was summed. At last we put forward to some exposed problem and gave some suggestion.
Using a matrix-based system reliability (MSR) method, one can estimate the probabilities of complex system events by simple matrix calculations. Unlike existing system reliability methods whose complexity depends highly on that of the system event, the MSR method describes any general system event in a simple matrix form and therefore provides a more convenient way of handling the system event and estimating its probability. Even in the case where one has incomplete information on the component probabilities and/or the statistical dependence thereof, the matrix-based framework enables us to estimate the narrowest bounds on the system failure probability by linear programming. This paper presents the MSR method and applies it to a transportation network consisting of bridge structures. The seismic failure probabilities of bridges are estimated by use of the predictive fragility curves developed by a Bayesian methodology based on experimental data and existing deterministic models of the seismic capacity and demand. Using the MSR method, the probability of disconnection between each city/county and a critical facility is estimated. The probability mass function of the number of failed bridges is computed as well. In order to quantify the relative importance of bridges, the MSR method is used to compute the conditional probabilities of bridge failures given that there is at least one city disconnected from the critical facility. The bounds on the probability of disconnection are also obtained for cases with incomplete information.
τ —penetration time L —sample length ∝ — gas viscosity P i —inlet pressure n —porosity P o — outlet pressure ξ — penetration depth k — permeability
For structural systems that may fail in any one of several possible modes, reliability analysis is greatly simplified by use of upper and lower bound techniques. General bounds based on all the single mode failure probabilities and all the pairwise mode intersection failure probabilities are established. For systems where the single mode limit state surfaces are hyperplanes in the space of basic variables, a simple geometrical interpretation of the correlation between mode safety margins combined with a well-known geometrical interpretation of the single mode reliability index makes the practical calculation of the system reliability bounds easy. This is particularly true when the set of basic variables is jointly normally distributed. Examples show very narrow bounds which, in the practically important domain of high reliability, are almost coincident.
Dealing with the transmission network of electric power systems, this paper identifies the sequential failures of receiving station components under a severe earthquake. Such failures progressively degrade the power network performance, potentially leading to a network blackout. Hence, in this paper, these components are incorporated into the network systems analysis taking their seismic vulnerability into consideration in the form of fragility curves for the evaluation of the network performance under seismic conditions. Specifically, most critical to the operation of transmission network, transformers, disconnect switches, circuit breakers and buses are integrated into the systems analysis, exploring the possibility of progressive failures of these components. The scenarios of these component failures can make it possible to estimate quantitatively direct cost of damage, emergency repair and restoration, and duration of power interruption and attendant economic losses and societal disruption. Copyright © 2006 John Wiley & Sons, Ltd.
A new probabilistic analytical approach to evaluate seismic system reliability of large lifeline systems is presented in this paper. The algorithm takes the shortest path from the source to the terminal of a node weight or edge weight network as decomposition policy, using the Boolean laws of set operation and probabilistic operation principal, a recursive decomposition process then could be constructed. For a general weight network, the modified Torrieri method (NTR/T method) is introduced to combine with the suggested algorithm. Therefore, the recursive decomposition algorithm may be applied to evaluate the seismic reliability of general lifeline systems. A series of case studies, including a practical district electric power network system and a large urban water supply system, show that the suggested algorithm supplies a useful probabilistic analysis means for the seismic reliability evaluation of large lifeline systems. Copyright © 2002 John Wiley & Sons, Ltd.
In this paper a method for assessing the struc-tural vulnerability of two coupled energy distribution systems is proposed. The co-existing of an electric power distribution system and a district heating system is described and modelled, under the assumption that the operation of the district heating system is directly dependent on electric power. The structural vulnerability of the two systems subject to single failures or a set of simultaneous failures in the power system is found. Thus, the consequences of power system failures for the energy supply as a whole are quantified.
In past works the authors set up a refined model for electric power networks under earthquake action. The procedure models the fragility of components with respect to earthquake action, the complex behaviour of the stations and the network, the power flow, the network capability to feed the nodes in a damaged condition, the earthquake damage on the territory, the need to deliver electric power to the municipalities where most damage has occurred. In later works the method was improved towards design goals: nonetheless complexity of the network seismic behaviour, a procedure to maximize safety of selected nodes and minimize economic expenses was constructed, allowing identification of which components, within each station, had to be upgraded to obtain the maximum economic convenience. The procedure was programmed within the ASK4ELP computer code (National Information Service for Earthquake Engineering, University of California, Berkeley, U.S.A., 1999) using late 1990s state-of-the-art knowledge for both the earthquake and the structural behaviour models.
Recently the method has gone through a thorough updating, partially still in progress. Among the results, it is now more clear how important is a correct soil geotechnical model to predict the system response and safety. This paper presents, together with a short summary of the ASK4ELP procedure, these latest advancements and results and shows, through a real example, the sensitivity of the predicted safety to soil modelling. Copyright
This chapter sets forth a new approach for transmission network expansion planning that accounts for increasingly plausible
deliberate outages. Malicious attacks expose the network planner, a centralized entity responsible for expansion decisions
of the entire transmission network, to a new challenge: how to expand and reinforce the transmission network so that the vulnerability
against intentional attacks is mitigated while meeting budgetary limits. Two vulnerability-constrained transmission expansion
models are presented in this chapter. The first model allows the network planner to analyze the tradeoff between economic-
and vulnerability-related issues and its impact on the expansion plans. The uncertainty associated with intentional outages
is modeled through scenarios. Vulnerability is measured in terms of the system load shed. In the second model, the risk associated
with the nonrandom uncertainty of deliberate outages is incorporated through the minimax weighted regret criterion. The proposed
models are formulated as mixed-integer linear programs for which efficient solvers are available. Illustrative examples show
the performance of both models.
KeywordsDeliberate outages-Minimax weighted regret-Mixed-integer linear programming-Risk-Scenario-Transmission network expansion planning-Vulnerability
The concept of state transition graph is used to analyze the cascading failure of electrical power grids in different load level. State transition graph is introduced first, then the state transition model of electrical power system DC flow is designed. The IEEE 9-bus sample system is used to show the state transition graph evolution by aggravating the load level. Some general conclusion is drawn by this method.
Security of energy supply is a main concern worldwide, given the strong dependence on society functioning on its adequate delivery. Surges in fuel prices, political conflicts, wars and natural disasters threaten directly energy supply, and countries look at ways to protect themselves. On February 2010 an 8.8 Richter scale earthquake hit the central part of Chile and a tsunami following the earthquake hit coastal areas, affecting the most populated area of the country. Main supplies collapsed, electricity, water, gas, telephones, contributing to make matters worse for the suffering population. This paper illustrates events that took place in electricity supply during and after the earthquake in Chile, its impact on the generation, transmission and distribution infrastructure, and the lessons to be learned. The challenges in reconstruction are also discussed. The main interconnected system, generation and main transmission grid, was able to resume partial operation within a few hours, although in a weak condition. Damage took place in some main substations, and alternative paths and operational conditions had to be found. Security criteria had to be degraded in the system operation and handling of the main grid. The Chilean codes impose strict anti seismic standards for all electricity infrastructure construction, but the earthquake strength still produced damage in some grid installations. However, the most severe damage took place in the distribution networks, vast areas were left with no supply for weeks, including the large city of Concepcion being severely affected.
Distributed Generation (DG) is generally considered as an alternative to bulk power transport. The basic idea is that the presence of electricity generation inside the distribution systems leads to a reduction of the local electricity needs, which consequently leads to a reduced need for power transmission capacity and thus a deferral of investments in transmission lines. However, due to the different operational characteristics of the plethora of types of distributed generation, this hypothesis may prove invalid. Controllable distributed generation, defined as local generation of which the power output can be regulated by the system operator (e.g. stand-alone gas-fired combustion units) will certainly have a positive impact on this direction. However, in reality different types of DG technologies could de implemented in the distribution systems, such as partially or stringently controlled micro-combined heat and power (micro-CHP) units operating according to different local control modes (e.g. thermal-led control) or non-controllable (stochastic) DG units, such as wind power plants. The operation of such units may lead to an opposite effect regarding the necessary transmission capacity. In this paper we first define four types of DG regarding their level of controllability. We then look into the effect on the transmission system of both stringently-controlled DG (i.e. micro-CHP) and stochastic DG (i.e. wind turbines). It is shown that micro-CHP systems may have a positive effect to the dimensioning of the transmission system, while the presence of wind power plants may instead lead to increased investment needs in power transport capacity.
This paper proposes a model and implements a computational procedure to assess the reliability of electric power networks subjected to seismic load. A general electric network is first described and its functioning under ordinary conditions and under seismic action is analyzed. A reliability model to assemble small into larger components is proposed, which drastically simplifies the analysis. Power flow equations in the network are presented and modified to account for the current configuration of the network under seismic action. Seismic hazard is computed with the Cornell model. The whole procedure is applied to a real electric network and a simulation procedure is used to assess its reliability, measured via the probability distributions of suitable performance indexes.
A new generation rescheduling approach for preventive control of power system is presented which can reallocate power generation for multiple unstable contingencies based on graph theory. The objective of preventive control is to prepare the system when it is still in normal operation, so that the system is able to face future uncertain events in a satisfactory way. The generator rescheduling is based on the outage of links from one generator area to the other without violating line overloads. The quantity of generation shifting from one generator area to other is calculated by the proportionality assumption. When rescheduling of generators fails to provide a feasible solution for secure operation, optimal load shedding/switching off disturbed area, called islanding formation, is resorted to. The suitability of the proposed method is demonstrated with the help of six bus three machine power system and IEEE 30-bus power system.
Complex systems are characterized by large numbers of components, cut sets or link sets, or by statistical dependence between the component states. These measures of complexity render the computation of system reliability a challenging task. In this paper, a decomposition approach is described, which, together with a linear programming formulation, allows determination of bounds on the reliability of complex systems with manageable computational effort. The approach also facilitates multi-scale modeling and analysis of a system, whereby varying degrees of detail can be considered in the decomposed system. The paper also describes a method for computing bounds on conditional probabilities by use of linear programming, which can be used to update the system reliability for any given event. Applications to a power network demonstrate the methodology.
We verify and examine criticality in a 1000 bus network with an AC blackout model that represents many of the interactions that occur in cascading failure. At the critical loading there is a sharp rise in the mean blackout size and a power law probability distribution of blackout size that indicates a significant risk of large blackouts.
Ontologies in current computer science parlance are computer based resources that represent agreed domain semantics. Unlike data models, the fundamental asset of ontologies is their relative independence of particular applications, i.e. an ontology consists ...
The first book to explore the hot new science of networks and their impact on nature, business, medicine, and everyday life. }In the 1980's, James Gleick's Chaos introduced the world to complexity. Now, Albert-Lszl Barabsi's Linked reveals the next major scientific leap: the study of networks. We've long suspected that we live in a small world, where everything is connected to everything else. Indeed, networks are pervasive--from the human brain to the Internet to the economy to our group of friends. These linkages, it turns out, aren't random. All networks, to the great surprise of scientists, have an underlying order and follow simple laws. Understanding the structure and behavior of these networks will help us do some amazing things, from designing the optimal organization of a firm to stopping a disease outbreak before it spreads catastrophically.In Linked, Barabsi, a physicist whose work has revolutionized the study of networks, traces the development of this rapidly unfolding science and introduces us to the scientists carrying out this pioneering work. These "new cartographers" are mapping networks in a wide range of scientific disciplines, proving that social networks, corporations, and cells are more similar than they are different, and providing important new insights into the interconnected world around us. This knowledge, says Barabsi, can shed light on the robustness of the Internet, the spread of fads and viruses, even the future of democracy. Engaging and authoritative, Linked provides an exciting preview of the next century in science, guaranteed to be transformed by these amazing discoveries.From Linked:This book has a simple message: think networks. It is about how networks emerge, what they look like, and how they evolve. It aims to develop a web-based view of nature, society, and technology, providing a unified framework to better understand issues ranging from the vulnerability of the Internet to the spread of diseases. Networks are present everywhere. All we need is an eye for them...We will see the challenges doctors face when they attempt to cure a disease by focusing on a single molecule or gene, disregarding the complex interconnected nature of the living matter. We will see that hackers are not alone in attacking networks: we all play Goliath, firing shots at a fragile ecological network that, without further support, could soon replicate our worst nightmares by turning us into an isolated group of species...Linked is meant to be an eye-opening trip that challenges you to walk across disciplines by stepping out of the box of reductionism. It is an invitation to explore link by link the next scientific revolution: the new science of networks. }
Power grids are prone to failure. Time series of reliability measures such as total power loss or energy not supplied can give significant account of the underlying dynamical behavior of these systems, specially when the resulting probability distributions present remarkable features such as an algebraic tail, usually considered the footprint of self-organization and the existence of critical points. In this paper, 7 years (from 2002 to 2008) of Europe’s transport of electricity network failure events have been analyzed and the best fit for this empirical data probability distribution is presented. With the actual span of available data and although there exists a moderate support for the power-law model, the relatively small amount of events contained in the function’s tail suggests that causal factors other than self-organization or a critical state might be significantly ruling these systems’ dynamics. Peer Reviewed Postprint (author’s final draft)
Massachusetts Institute of Technology. Dept. of Civil Engineering. Thesis. 1974. Civ. E. Bibliography: leaves XX.
A new technique for determining the terminal reliability of probabilistic networks is derived and discussed. The technique uses set-theoretic concepts to partition the space of all graph realizations in a way which permits extremely fast evaluation of the source-to-terminal probability. If not allowed to run to completion, the algorithm yields rapidly converging upper and lower bounds on that probability. Comparison with algorithms in the recent literature shows a decrease of one or two orders of magnitude in required CPU time.
For calculating terminal-pair reliability, most published
algorithms are based on the sum of disjoint products. However, these
tree-based partitions lack the capability to avoid redundant computation
due to the isomorphic sub-problems. To overcome these problems, an
efficient methodology to evaluate the terminal-pair reliability, based
on edge expansion diagrams using OBDD (ordered binary decision diagram)
is presented. First, the success path function of a given network is
constructed based on OBDD by traversing the network with diagram-based
edge expansion. Then the reliability of the network is obtained by
directly evaluating on this OBDD recursively. The effectiveness of this
approach is demonstrated by performing experiments on benchmarks
collected by previous works including the larger networks (from 4 to 2
99 paths). A dramatic improvement, as demonstrated by the
experimental results for a 2-by-n lattice network is that the number of
OBDD nodes is only linearly proportional to the number of stages, and is
much better than previous algorithms which have exponential complexity
by using the sum of disjoint products. The CPU time of reliability
calculation for a 100-stage lattice network is only about 2.5 seconds
with 595 nodes generated on a SPARC 20 workstation with 128 MBytes of
memory. Thus, with this approach, the terminal-pair reliability of large
networks can be efficiently evaluated better than thought possible
A new efficient method that compensates for unreliable nodes in
network reliability computations is presented. This method can be
embedded in the modified Dotson algorithm or any algorithm that
generates a symbolic reliability expression for networks with perfect
nodes. Its cost increases linearly with the number of links, and the
effect of unreliable nodes can be directly computed. This method
supplants the Aggarwal method and other methods of compensating for
unreliable nodes in the calculation of node-pair reliability. When
combined with the modified Dotson algorithm, this method provides
accurate reliability estimates for networks so large that the
Theologou-Carlier algorithm cannot complete its computations in a
reasonable amount of time. For such networks, the new method can be
embedded in the modified Dotson algorithm to estimate both the node-pair
reliability and the error in this estimate even if the algorithm is
terminated before completion
Four algorithms for the terminal-pair-reliability problem are
compared. Nelson (1970), Lin (1976), Shooman (1968), and Dotson (1979)
algorithms are used in this study. It is shown that the Dotson algorithm
is the fastest among the terminal-pair reliability algorithms analyzed.
The Dotson algorithm is suited not only for numerical reliability, but
for obtaining symbolic expression for the terminal-pair reliability with
no additional effort. By modifying the Dotson algorithm the efficiency
can be further improved. The modifications to this algorithm are listed
and the reliability of the modified Dotson algorithm is computed
The author considers a specific maze shown as a figure. The question is to enumerate all 46 paths between two specificn points. It is supposed that if one tries manually, that he will probably find about three-fourths of all the paths and then become bogged down with redundancy. In the remainder of this letter, the author not only shows how to enumerate all paths from some starting nodet to some end node in a straightforward one-pass technique, but also how to determine the total number of paths between any two specific nodes. The second piece of information is determined essentially for no additional cost. The matrix technique of Murchland (1965) for generating all paths in maze or graph requires the eliminaotion of paths produced which contain a loop. Consequently, the author believes that the method proposed here is more efficient. Also, this new technique has a simpliclty, as found in Moore??s Shortest Route Algorithm (1957), which is not found in Murchland??s.
Seismic response and reliability of electrical substation equipment and systems. Berkeley (CA): Pacific Earthquake Engineering Research (PEER) Center, University of California
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Song J, Der Kiureghian A, Sackman JL. Seismic response and reliability of electrical substation equipment and systems. Berkeley (CA): Pacific Earthquake Engineering Research (PEER) Center, University of California; 2004.
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Netherlands: Rotterdam; 2008. L. Chang, Z. Wu / Electrical Power and Energy Systems 33 (2011) 1410–1419
Modeling earthquake impact on urban lifeline systems: advances and integration in loss estimation. In: Earthquake engineering frontiers in the new millennium. Netherlands: Swets & Zeitlinger
- Chang Se
- Rose Az M Shinozuka
- Tierney
- Kj
Chang SE, Rose AZ, Shinozuka M, Tierney KJ. Modeling earthquake impact on urban lifeline systems: advances and integration in loss estimation. In: Earthquake engineering frontiers in the new millennium. Netherlands: Swets & Zeitlinger; 2001.
Introduction to lifeline earthquake engineering
- Lin C G Liu
- Li H Zhou
Liu C, Lin G, Li H, Zhou J. Introduction to lifeline earthquake engineering. Dalian (China): Dalian University of Technology Press; 2005.
Estimation of the economic impact of multiples lifeline distribution: Memphis light, gas and water division case study
- Chang Se
- Ha Seligson
- Eguchi
Chang SE, Seligson HA, Eguchi RT. Estimation of the economic impact of multiples lifeline distribution: Memphis light, gas and water division case study. Technical report NCEER-96-001. Buffalo (NY): National Center for Earthquake Engineering Research (NCEER); 1996.