Initial Evidence for Self-Organized Criticality in Electric Power System Blackouts

We examine correlations in a time series of electric power system blackout sizes using scaled window variance analysis and R/S statistics. The data shows some evidence of long time correlations and has Hurst exponent near 0.7. Large blackouts tend to correlate with further large blackouts after a long time interval. Similar effects are also observed in many other complex systems exhibiting self-organized criticality. We discuss this initial evidence and possible explanations for self-organized criticality in power systems blackouts. Self-organized criticality, if fully confirmed in power systems, would suggest new approaches to understanding and possibly controlling blackouts

Blackouts, risk, and fat-tailed distributions

We analyze a 19-year time series of North American electric power transmission system blackouts. Contrary to previously reported results we find a fatter than exponential decay in the distribution of inter- occurrence times and evidence of seasonal dependence in the number of events. Our findings question the use of self-organized criticality, and in particular the sandpile model, as a paradigm of blackout dynamics in power transmission systems. Hopefully, though, they will provide guidelines to more accurate models for evaluation of blackout risk.blackout, risk, fat-tailed distribution, power grid

Stochastic Model for Power Grid Dynamics

We introduce a stochastic model that describes the quasi-static dynamics of an electric transmission network under perturbations introduced by random load fluctuations, random removing of system components from service, random repair times for the failed components, and random response times to implement optimal system corrections for removing line overloads in a damaged or stressed transmission network. We use a linear approximation to the network flow equations and apply linear programming techniques that optimize the dispatching of generators and loads in order to eliminate the network overloads associated with a damaged system. We also provide a simple model for the operator's response to various contingency events that is not always optimal due to either failure of the state estimation system or due to the incorrect subjective assessment of the severity associated with these events. This further allows us to use a game theoretic framework for casting the optimization of the operator's response into the choice of the optimal strategy which minimizes the operating cost. We use a simple strategy space which is the degree of tolerance to line overloads and which is an automatic control (optimization) parameter that can be adjusted to trade off automatic load shed without propagating cascades versus reduced load shed and an increased risk of propagating cascades. The tolerance parameter is chosen to describes a smooth transition from a risk averse to a risk taken strategy...Comment: framework for a system-level analysis of the power grid from the viewpoint of complex network

On the Inability of Markov Models to Capture Criticality in Human Mobility

We examine the non-Markovian nature of human mobility by exposing the inability of Markov models to capture criticality in human mobility. In particular, the assumed Markovian nature of mobility was used to establish a theoretical upper bound on the predictability of human mobility (expressed as a minimum error probability limit), based on temporally correlated entropy. Since its inception, this bound has been widely used and empirically validated using Markov chains. We show that recurrent-neural architectures can achieve significantly higher predictability, surpassing this widely used upper bound. In order to explain this anomaly, we shed light on several underlying assumptions in previous research works that has resulted in this bias. By evaluating the mobility predictability on real-world datasets, we show that human mobility exhibits scale-invariant long-range correlations, bearing similarity to a power-law decay. This is in contrast to the initial assumption that human mobility follows an exponential decay. This assumption of exponential decay coupled with Lempel-Ziv compression in computing Fano's inequality has led to an inaccurate estimation of the predictability upper bound. We show that this approach inflates the entropy, consequently lowering the upper bound on human mobility predictability. We finally highlight that this approach tends to overlook long-range correlations in human mobility. This explains why recurrent-neural architectures that are designed to handle long-range structural correlations surpass the previously computed upper bound on mobility predictability

Revisiting and modeling power-law distributions in empirical outage data of power systems

The size distribution of planned and forced outages and following restoration times in power systems have been studied for almost two decades and has drawn great interest as they display heavy tails. Understanding of this phenomenon has been done by various threshold models, which are self-tuned at their critical points, but as many papers pointed out, explanations are intuitive, and more empirical data is needed to support hypotheses. In this paper, the authors analyze outage data collected from various public sources to calculate the outage energy and outage duration exponents of possible power-law fits. Temporal thresholds are applied to identify crossovers from initial short-time behavior to power-law tails. We revisit and add to the possible explanations of the uniformness of these exponents. By performing power spectral analyses on the outage event time series and the outage duration time series, it is found that, on the one hand, while being overwhelmed by white noise, outage events show traits of self-organized criticality (SOC), which may be modeled by a crossover from random percolation to directed percolation branching process with dissipation, coupled to a conserved density. On the other hand, in responses to outages, the heavy tails in outage duration distributions could be a consequence of the highly optimized tolerance (HOT) mechanism, based on the optimized allocation of maintenance resources.Comment: 16 pages, 8 figure

Cascading Failures in Complex Networks

Cascading failure is a potentially devastating process that spreads on real-world complex networks and can impact the integrity of wide-ranging infrastructures, natural systems, and societal cohesiveness. One of the essential features that create complex network vulnerability to failure propagation is the dependency among their components, exposing entire systems to significant risks from destabilizing hazards such as human attacks, natural disasters or internal breakdowns. Developing realistic models for cascading failures as well as strategies to halt and mitigate the failure propagation can point to new approaches to restoring and strengthening real-world networks. In this review, we summarize recent progress on models developed based on physics and complex network science to understand the mechanisms, dynamics and overall impact of cascading failures. We present models for cascading failures in single networks and interdependent networks and explain how different dynamic propagation mechanisms can lead to an abrupt collapse and a rich dynamic behavior. Finally, we close the review with novel emerging strategies for containing cascades of failures and discuss open questions that remain to be addressed.Comment: This review has been accepted for publication in the Journal of Complex Networks Published by Oxford University Pres