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88
A Markovian Dependability Model With Cascading Failures
"... Abstract — We develop a continuoustime Markov chain model of a dependability system operating in a randomly changing environment and subject to probabilistic cascading failures. A cascading failure can be thought of as a rooted tree. The root is the component whose failure triggers the cascade, its ..."
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Abstract — We develop a continuoustime Markov chain model of a dependability system operating in a randomly changing environment and subject to probabilistic cascading failures. A cascading failure can be thought of as a rooted tree. The root is the component whose failure triggers the cascade, its children are those components that the root’s failure immediately caused, the next generation are those components whose failures were immediately caused by the failures of the root’s children, and so on. The amount of cascading is unlimited. We consider probabilistic cascading, in the sense that the failure of a component of type i causes a component of type j to fail simultaneously with a given probability, with all failures in a cascade being mutually independent. Computing the infinitesimal generator matrix of the Markov chain poses significant challenges because of the exponential growth in the number of trees one needs to consider as the number of components failing in the cascade increases. We provide a recursive algorithm generating all possible trees corresponding to a given transition, along with an experimental study of an implementation of the algorithm on two examples. The numerical results highlight the effects of cascading on the dependability of the models. Index Terms — availability, reliability modeling, Markov processes, trees, cascading failures.
Exploring complex systems aspects of blackout risk and mitigation
 IEEE TRANSACTIONS ON RELIABILITY
"... Abstract—Electric power transmission systems are a key infrastructure, and blackouts of these systems have major consequences for the economy and national security. Analyses of blackout data suggest that blackout size distributions have a power law form over much of their range. This result is an i ..."
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Abstract—Electric power transmission systems are a key infrastructure, and blackouts of these systems have major consequences for the economy and national security. Analyses of blackout data suggest that blackout size distributions have a power law form over much of their range. This result is an indication that blackouts behave as a complex dynamical system. We use a simulation of an upgrading power transmission system to investigate how these complex system dynamics impact the assessment and mitigation of blackout risk. The mitigation of failures in complex systems needs to be approached with care. The mitigation efforts can move the system to a new dynamic equilibrium while remaining near criticality and preserving the power law region. Thus, while the absolute frequency of blackouts of all sizes may be reduced, the underlying forces can still cause the relative frequency of large blackouts to small blackouts to remain the same. Moreover, in some cases,
Topological Models and Critical Slowing Down: Two Approaches to Power System Blackout Risk Analysis
"... This paper describes results from the analysis of two approaches to blackout risk analysis in electric power systems. In the first analysis, we compare two topological (graphtheoretic) methods for finding vulnerable locations in a power grid, to a simple model of cascading outage. This comparison i ..."
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This paper describes results from the analysis of two approaches to blackout risk analysis in electric power systems. In the first analysis, we compare two topological (graphtheoretic) methods for finding vulnerable locations in a power grid, to a simple model of cascading outage. This comparison indicates that topological models can lead to misleading conclusions about vulnerability. In the second analysis, we describe preliminary results indicating that both a simple dynamic power system model and frequency data from the August 10, 1996 disturbance in North America show evidence of critical slowing down as the system approaches a failure point. In both examples, autocorrelation in the timedomain signals (frequency and phase angle), significantly increases before reaching the critical point. These results indicate that critical slowing down could be a useful indicator of increased blackout risk. I.
Cascading link failure in the power grid: A percolationbased analysis
 in 2011 IEEE International Conference on Communications Workshops (ICC
, 2011
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Statistical classification of cascading failures in power grids
 in Proceedings of the IEEE PES General Meeting
, 2011
"... Abstract—We introduce a new microscopic model of the outages in transmission power grids. This model accounts for the automatic response of the grid to load fluctuations that take place on the scale of minutes, when the optimum power flow adjustments and load shedding controls are unavailable. We de ..."
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Abstract—We introduce a new microscopic model of the outages in transmission power grids. This model accounts for the automatic response of the grid to load fluctuations that take place on the scale of minutes, when the optimum power flow adjustments and load shedding controls are unavailable. We describe extreme events, initiated by load fluctuations, which cause cascading failures of loads, generators and lines. Our model is quasistatic in the causal, discrete time and sequential resolution of individual failures. The model, in its simplest realization based on the Directed Current description of the power flow problem, is tested on three standard IEEE systems consisting of 30, 39 and 118 buses. Our statistical analysis suggests a straightforward classification of cascading and islanding phases in terms of the ratios between average number of removed loads, generators and links. The analysis also demonstrates sensitivity to variations in line capacities. Future research challenges in modeling and control of cascading outages over realworld power networks are discussed. Index Terms—Power system dynamics, Power system faults, Power system reliability
Determining the vulnerabilities of the power transmission system
 Fortyfifth Hawaii International Conference on System Sciences, Maui
, 2011
"... Determining the vulnerabilities in power transmission systems requires two distinct steps because most large blackouts have two distinct parts, the triggers/initiating event followed by the cascading failure. Finding the important triggers for large blackouts is the first and standard step. Next, th ..."
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Determining the vulnerabilities in power transmission systems requires two distinct steps because most large blackouts have two distinct parts, the triggers/initiating event followed by the cascading failure. Finding the important triggers for large blackouts is the first and standard step. Next, the cascading part of the extreme event (which can be long or short) is critically dependent on the “state ” of the system; how heavily the lines are loaded, how much generation margin exists, and where the generation exists relative to the load. However, during large cascading events there are some lines whose probability of overloading is higher that the others. Statistical studies of blackouts using the OPA code allow the identification of such lines or groups of line for a given network model, thereby providing a technique for identifying at risk (or critical) clusters. This paper addresses both parts of the vulnerability question. 1.
Multicontingency cascading analysis of smart grid based on selforganizing map
 IEEE Trans. Inf. Forensics Security
, 2013
"... Texas Power grid shown in ArcMap 10.0 with substations and transmission lines (top) and its clustering result with the selforganizing map (SOM) approach (bottom), as seen in "MultiContingency Cascading Analysis of Smart Grid Based on SelfOrganizing Map," ..."
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Texas Power grid shown in ArcMap 10.0 with substations and transmission lines (top) and its clustering result with the selforganizing map (SOM) approach (bottom), as seen in "MultiContingency Cascading Analysis of Smart Grid Based on SelfOrganizing Map,"
Exact and efficient algorithm to discover extreme stochastic events . . .
, 2011
"... In this manuscript we continue the thread of . . . 2011] and suggest a new algorithm discovering most probable extreme stochastic events in static power grids associated with intermittent generation of wind turbines. The algorithm becomes EXACT and EFFICIENT (polynomial) in the case of the proporti ..."
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Cited by 4 (3 self)
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In this manuscript we continue the thread of . . . 2011] and suggest a new algorithm discovering most probable extreme stochastic events in static power grids associated with intermittent generation of wind turbines. The algorithm becomes EXACT and EFFICIENT (polynomial) in the case of the proportional (or other low parametric) control of standard generation, and logconcave probability distribution of the renewable generation, assumed known from the wind forecast. We illustrate the algorithm’s ability to discover problematic extreme events on the example of the IEEE RTS96 model of transmission with additions of 10%,20 % and 30 % of renewable generation. We observe that the probability of failure may grow but it may also decrease with increase in renewable penetration, if the latter is sufficiently diversified and distributed.
Cascading Failures in Smart Grid Benefits of Distributed Generation
"... Abstract—Smart grid is envisioned to incorporate local distributed power generation for better efficiency and flexibility. Distributed generation, when not used carefully, however, may compromise the stability of the grid. Recently, researchers have proposed innovative architectures (e.g., microgrid ..."
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Abstract—Smart grid is envisioned to incorporate local distributed power generation for better efficiency and flexibility. Distributed generation, when not used carefully, however, may compromise the stability of the grid. Recently, researchers have proposed innovative architectures (e.g., microgrid, LoCal grid) that virtualize a local generator as a constant load, source, or zero load to the grid, thus offering great promise to connect distributed generation into the grid without sacrificing its reliability. In fact, intuitively, using these architectures, distributed generation may enhance the stability of the power grid. In this paper, we develop a simulation model to quantify how much distributed generation can mitigate cascading failures. Applying this model to IEEE power grid test cases, we find that local power generation, even when only using a small number of local generators, can reduce the likelihood of cascading failures dramatically. I.
Validating OPA with WECC data
"... We validate the OPA cascading blackout simulation on a 1553 bus WECC network model by establishing OPA parameters from WECC data and comparing the blackout statistics obtained with OPA to historical WECC data. 1. ..."
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We validate the OPA cascading blackout simulation on a 1553 bus WECC network model by establishing OPA parameters from WECC data and comparing the blackout statistics obtained with OPA to historical WECC data. 1.