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33
Complex systems analysis of series of blackouts: cascading failure, critical points, and selforganization
 Chaos
, 2004
"... We give a comprehensive account of a complex systems approach to large blackouts caused by cascading failure. Instead of looking at the details of particular blackouts, we study the statistics, dynamics and risk of series of blackouts with approximate global models. North American blackout data sugg ..."
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Cited by 88 (14 self)
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We give a comprehensive account of a complex systems approach to large blackouts caused by cascading failure. Instead of looking at the details of particular blackouts, we study the statistics, dynamics and risk of series of blackouts with approximate global models. North American blackout data suggests that the frequency of large blackouts is governed by a power law. This result is consistent with the power system being a complex system designed and operated near criticality. The power law makes the risk of large blackouts consequential and implies the need for nonstandard risk analysis. Power system overall load relative to operating limits is a key factor affecting the risk of cascading failure. Blackout models and an abstract model of cascading failure show that there are critical transitions as load is increased. Power law behavior can be observed at these transitions. The critical loads at which blackout risk sharply increases are identifiable thresholds for cascading failure and we discuss approaches to computing the proximity to cascading failure using these thresholds. Approximating cascading failure as a branching process suggests ways to compute and monitor criticality by quantifying how much failures propagate. Inspired by concepts from selforganized criticality, we suggest that power system operating margins evolve slowly to near criticality and confirm this idea using a blackout model. Mitigation of blackout risk should take care to account for counterintuitive effects in complex selforganized critical systems. For example, suppressing small blackouts could lead the system to be operated closer to the edge and ultimately increase the risk of large blackouts. 1
LongTerm Effect of the n1 Criterion on Cascading Line Outages in an Evolving Power Transmission Grid
"... Abstract—Cascading transmission line outages contribute to widespread blackouts. Engineers respond to the risk of cascading line outages by applying policies such as the n1 criterion and upgrading lines involved in recent cascading outages. The transmission grid slowly evolves as these policies are ..."
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Cited by 19 (7 self)
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Abstract—Cascading transmission line outages contribute to widespread blackouts. Engineers respond to the risk of cascading line outages by applying policies such as the n1 criterion and upgrading lines involved in recent cascading outages. The transmission grid slowly evolves as these policies are applied to maintain reliability while the load grows. We suggest how to assess the longterm effect of these policies on the risk of cascading line outages by simulating both the cascading and the slow evolution of the transmission grid. The longterm effects of these policies on the probability distribution of outage size and the grid utilization are computed for the IEEE 118bus test system. The results show complex system selforganization of an evolving transmission grid. Index Terms—Complex system, failure analysis, network reliability, power system security, power transmission reliability, risk analysis. I.
Power grid vulnerability to geographically correlated failures  analysis and control implications
, 2011
"... We consider power line outages in the transmission system of the power grid, and specifically those caused by a natural disaster or a large scale physical attack. In the transmission system, an outage of a line may lead to overload on other lines, thereby eventually leading to their outage. While s ..."
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Cited by 14 (5 self)
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We consider power line outages in the transmission system of the power grid, and specifically those caused by a natural disaster or a large scale physical attack. In the transmission system, an outage of a line may lead to overload on other lines, thereby eventually leading to their outage. While such cascading failures have been studied before, our focus is on cascading failures that follow an outage of several lines in the same geographical area. We provide an analytical model of such failures, investigate the model’s properties, and show that it differs from other models used to analyze cascades in the power grid (e.g., epidemic/percolationbased models). We then show how to identify the most vulnerable locations in the grid and perform extensive numerical experiments with real grid data to investigate the various effects of geographically correlated outages and the resulting cascades. These results allow us to
Optimal Control of Cascading Power Grid Failures
"... Abstract — We study algorithms for computing optimal load shedding schedules in the event of a cascading power system failure. The algorithms compute an affine control at the onset of the cascade; the control is applied during the cascade as a function of observed state parameters such as line overl ..."
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Cited by 11 (2 self)
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Abstract — We study algorithms for computing optimal load shedding schedules in the event of a cascading power system failure. The algorithms compute an affine control at the onset of the cascade; the control is applied during the cascade as a function of observed state parameters such as line overloads. In the case of line outages that follow a deterministic rule, we obtain an efficient (polynomial time) algorithm for computing an optimal control. For the case of stochastic line outages we describe a stochastic gradients algorithm. We present computational experiments with a parallel implementation of our algorithms, tested on a snapshot of the U.S. Eastern Interconnect. A. Underlying approach I.
Towards quantifying cascading blackout risk
 Bulk Power System Dynamics and ControlVII
, 2007
"... Blackouts become widespread by initial failures propagating in a diverse and intricate cascade of rare events. We describe this complicated cascade using a bulk probabilistic model in which the initial failures propagate randomly according to a branching process. The branching process parameters can ..."
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Cited by 10 (5 self)
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Blackouts become widespread by initial failures propagating in a diverse and intricate cascade of rare events. We describe this complicated cascade using a bulk probabilistic model in which the initial failures propagate randomly according to a branching process. The branching process parameters can be statistically estimated from observed data or simulations and then used to efficiently predict the probability distribution of blackout size. We review the current testing of these methods on simulations and observed data and discuss the next steps towards achieving verified and practical methods for quantifying cascading failure of electric power systems. The ability to efficiently quantify cascading blackout risk from observed data and simulations could offer new ways to monitor power transmission system reliability and quantify the reliability benefit of proposed improvements. 1
Reliability analysis of electric power systems using an objectoriented hybrid modeling approach,” arXiv preprint arXiv:1201.0552
, 2012
"... Abstract The ongoing evolution of the electric power systems brings about the need to cope with increasingly complex interactions of technical components and relevant actors. In order to integrate a more comprehensive spectrum of different aspects into a probabilistic reliability assessment and t ..."
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Cited by 8 (0 self)
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Abstract The ongoing evolution of the electric power systems brings about the need to cope with increasingly complex interactions of technical components and relevant actors. In order to integrate a more comprehensive spectrum of different aspects into a probabilistic reliability assessment and to include timedependent effects, this paper proposes an objectoriented hybrid approach combining agentbased modeling techniques with classical methods such as Monte Carlo simulation. Objects represent both technical components such as generators and transmission lines and nontechnical components such as grid operators. The approach allows the calculation of conventional reliability indices and the estimation of blackout frequencies. Furthermore, the influence of the time needed to remove line overloads on the overall system reliability can be assessed. The applicability of the approach is demonstrated by performing simulations on the IEEE Reliability Test System 1996 and on a model of the Swiss highvoltage grid.
Realistic control of network dynamics
 Nat. Commun
, 1942
"... The control of complex networks is of paramount importance in areas as diverse as ecosystem management, emergency response and cell reprogramming. A fundamental property of networks is that perturbations to one node can affect other nodes, potentially causing the entire system to change behaviour or ..."
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Cited by 5 (0 self)
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The control of complex networks is of paramount importance in areas as diverse as ecosystem management, emergency response and cell reprogramming. A fundamental property of networks is that perturbations to one node can affect other nodes, potentially causing the entire system to change behaviour or fail. Here we show that it is possible to exploit the same principle to control network behaviour. Our approach accounts for the nonlinear dynamics inherent to real systems, and allows bringing the system to a desired target state even when this state is not directly accessible due to constraints that limit the allowed interventions. Applications show that this framework permits reprogramming a network to a desired task, as well as rescuing networks from the brink of failure—which we illustrate through the mitigation of cascading failures in a powergrid network and the identification of potential drug targets in a signalling network of human cancer.
Simulation models and implementation of a simulator for the performability analysis of electric power systems considering interdependencies
 IN: 10TH IEEE HIGH ASSURANCE SYSTEMS ENGINEERING SYMPOSIUM
, 2007
"... Electric Power Systems (EPS) become more and more critical for our society, since they provide vital services for the human activities. At the same time, obtaining dependable behaviour of EPS is an highly challenging task, both in terms of defining effective business management and in terms of analy ..."
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Cited by 4 (3 self)
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Electric Power Systems (EPS) become more and more critical for our society, since they provide vital services for the human activities. At the same time, obtaining dependable behaviour of EPS is an highly challenging task, both in terms of defining effective business management and in terms of analysis of dependability and performability attributes. A major concern when dealing with EPS is the understanding and the evaluation of the interdependencies between Electric Infrastructures (EI) and the Computerbased Control System (CCS), which controls the status and the activities of EI. Studies on these interdependencies are only at an early stage of development. Major difficulties are the complexity of the infrastructures under analysis and the lack of wellestablished models and tools for dealing with them. This paper presents an adhoc simulator for the evaluation of dependability and performability measures in EPS. The system model the simulator is based on focuses on interdependencies between EI and CCS. Most existing modeling approaches in EPS does not provide explicit modeling of interdependencies among the composing subsystems, so that the cascading or escalating phenomena cannot be deeply analyzed. Our stochastic model is composed by separated and simple, but representative, submodels representing the dynamics of EI and different policies of reactions to disruptions and reconfigurations triggered by CCS. In this way, the simulator aims at providing explicit modeling of the interdependencies between the main subsystems, so the impact on the dependability and performability of the cascading or escalating failures can be analyzed. In this paper, we describe the simulator and highlight the design choices.
Calculation of the autocorrelation function of the stochastic single machine infinite bus system
 in North American Power Symposium
, 2013
"... Abstract—Critical slowing down (CSD) is the phenomenon in which a system recovers more slowly from small perturbations. CSD, as evidenced by increasing signal variance and autocorrelation, has been observed in many dynamical systems approaching a critical transition, and thus can be a useful signal ..."
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Cited by 4 (2 self)
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Abstract—Critical slowing down (CSD) is the phenomenon in which a system recovers more slowly from small perturbations. CSD, as evidenced by increasing signal variance and autocorrelation, has been observed in many dynamical systems approaching a critical transition, and thus can be a useful signal of proximity to transition. In this paper, we derive autocorrelation functions for the state variables of a stochastic single machine infinite bus system (SMIB). The results show that both autocorrelation and variance increase as this system approaches a saddlenode bifurcation. The autocorrelation functions help to explain why CSD can be used as an indicator of proximity to criticality in power systems revealing, for example, how nonlinearity in the SMIB system causes these signs to appear. I.