Stochastic Dynamics of Cascading Failures in Electric-Cyber Infrastructures

Emerging smart grids consist of tightly-coupled systems, namely a power grid and a communication system. While today\u27s power grids are highly reliable and modern control and communication systems have been deployed to further enhance their reliability, historical data suggest that they are yet vulnerable to large failures. A small set of initial disturbances in power grids in conjunction with lack of effective, corrective actions in a timely manner can trigger a sequence of dependent component failures, called cascading failures. The main thrust of this dissertation is to build a probabilistic framework for modeling cascading failures in power grids while capturing their interactions with the coupled communication systems so that the risk of cascading failures in the composite complex electric-cyber infrastructures can be examined, analyzed and predicted. A scalable and analytically tractable continuous-time Markov chain model for stochastic dynamics of cascading failures in power grids is constructed while retaining key physical attributes and operating characteristics of the power grid. The key idea of the proposed framework is to simplify the state space of the complex power system while capturing the effects of the omitted variables through the transition probabilities and their parametric dependence on physical attributes and operating characteristics of the system. In particular, the effects of the interdependencies between the power grid and the communication system have been captured by a parametric formulation of the transition probabilities using Monte-Carlo simulations of cascading failures. The cascading failures are simulated with a coupled power-system simulation framework, which is also developed in this dissertation. Specifically, the probabilistic model enables the prediction of the evolution of the blackout probability in time. Furthermore, the asymptotic analysis of the blackout probability as time tends to infinity enables the calculation of the probability mass function of the blackout size, which has been shown to have a heavy tail, e.g., power-law distribution, specifically when the grid is operating under stress scenarios. A key benefit of the model is that it enables the characterization of the severity of cascading failures in terms of a set of operating characteristics of the power grid. As a generalization to the Markov chain model, a regeneration-based model for cascading failures is also developed. The regeneration-based framework is capable of modeling cascading failures in a more general setting where the probability distribution of events in the system follows an arbitrarily specified distribution with non-Markovian characteristics. Further, a novel interdependent Markov chain model is developed, which provides a general probabilistic framework for capturing the effects of interactions among interdependent infrastructures on cascading failures. A key insight obtained from this model is that interdependencies between two systems can make two individually reliable systems behave unreliably. In particular, we show that due to the interdependencies two chains with non-heavy tail asymptotic failure distribution can result in a heavy tail distribution when coupled. Lastly, another aspect of future smart grids is studied by characterizing the fundamental bounds on the information rate in the sensor network that monitors the power grid. Specifically, a distributed source coding framework is presented that enables an improved estimate of the lower bound for the minimum required communication capacity to accurately describe the state of components in the information-centric power grid. The models developed in this dissertation provide critical understanding of cascading failures in electric-cyber infrastructures and facilitate reliable and quick detection of the risk of blackouts and precursors to cascading failures. These capabilities can guide the design of efficient communication systems and cascade aware control policies for future smart grids

Cascading Failures in Interdependent Infrastructures: An Interdependent Markov-Chain Approach

Many critical infrastructures are interdependent networks in which the behavior of one network impacts those of the others. Despite the fact that interdependencies are essential for the operation of critical infrastructures, such interdependencies can negatively affect the reliability and fuel the cascade of failures within and across the networks. In this paper, a novel interdependent Markov-chain framework is proposed that enables capturing interdependencies between two critical infrastructures with the ultimate goal of predicting their resilience to cascading failures and characterizing the effects of interdependencies on system reliability. The framework is sufficiently general to model cascading failures in any interdependent networks; however, this paper focuses on the electric-cyber infrastructure as an example. Using this framework it is shown that interdependencies among reliable systems, i.e., systems with exponentially distributed failure sizes, can make the individually reliable systems behave unreliably as a whole with power-law failure-size distributions

Stochastic Analysis of Cascading-Failure Dynamics in Power Grids

A scalable and analytically tractable probabilistic model for the cascading failure dynamics in power grids is constructed while retaining key physical attributes and operating characteristics of the power grid. The approach is based upon extracting a reduced abstraction of large-scale power grids using a small number of aggregate state variables while modeling the system dynamics using a continuous-time Markov chain. The aggregate state variables represent critical power-grid attributes, which have been shown, from prior simulation-based and historical-data-based analysis, to strongly influence the cascading behavior. The transition rates among states are formulated in terms of certain parameters that capture grid\u27s operating characteristics comprising loading level, error in transmission-capacity estimation, and constraints in performing load shedding. The model allows the prediction of the evolution of blackout probability in time. Moreover, the asymptotic analysis of the blackout probability enables the calculation of the probability mass function of the blackout size. A key benefit of the model is that it enables the characterization of the severity of cascading failures in terms of the operating characteristics of the power grid.

Efficient Interconnectivity Among Networks Under Security Constraint

Interconnectivity among networks is essential for enhancing communication capabilities of networks such as the expansion of geographical range, higher data rate, etc. However, interconnections may initiate vulnerability (e.g., cyber attacks) to a secure network due to introducing gateways and opportunities for security attacks such as malware, which may propagate from the less secure network. In this paper, the interconnectivity among subnetworks is maximized under the constraint of security risk. The dynamics of propagation of security risk is modeled by the evil-rain influence model and the SIR (Susceptible-Infected-Recovered) epidemic model. Through extensive numerical simulations using different network topologies and interconnection patterns, it is shown that the efficiency of interconnectivity increases nonlinearly and vulnerability increases linearly with the number of interconnections among subnetworks. Finally, parametric models are proposed to find the number of interconnections for any given efficiency of interconnectivity and vulnerability of the secure network

On the Dynamics of Transmission Capacity and Load Loss during Cascading Failures in Power Grids

In this paper, a novel analytical model is proposed to predict the average transmission-capacity loss and load loss during a cascading failure as a function of time and their steady state values. Cascading failures in the power grid are described using a Markov-chain approach, in which the state transition probabilities depend on the number and capacities of the failed lines. The transition matrix is characterized parametrically using Monte Carlo simulations of cascading failures in the power grid. The severity of cascading failure is estimated using two metrics: the expected number of transmission-line failures and the amount of load shedding/load loss (inferred from the average transmission capacity loss) in the steady state. These two metrics provide critical information regarding the severity of a cascading failure in a power grid (in terms of both the distribution of blackout sizes and the amounts of load shedding). One of the benefits of this model is that it enables the understanding of the effect of initial failures and of the operating parameters of the power grid on cascading failures