Cascading blackout overall structure and some implications for sampling and mitigation

Cascading blackouts can be thought of as initiating events followed by propagating events that progressively weaken the power system. We briefly discuss the implications for assessing cascading risk by proper sampling from the various sources of uncertainty and for mitigating cascading risk by reducing both the initiating events and their propagation

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.

Predicting Cascading Failures in Power Grids using Machine Learning Algorithms

Although there has been notable progress in modeling cascading failures in power grids, few works included using machine learning algorithms. In this paper, cascading failures that lead to massive blackouts in power grids are predicted and classified into no, small, and large cascades using machine learning algorithms. Cascading-failure data is generated using a cascading failure simulator framework developed earlier. The data set includes the power grid operating parameters such as loading level, level of load shedding, the capacity of the failed lines, and the topological parameters such as edge betweenness centrality and the average shortest distance for numerous combinations of two transmission line failures as features. Then several machine learning algorithms are used to classify cascading failures. Further, linear regression is used to predict the number of failed transmission lines and the amount of load shedding during a cascade based on initial feature values. This data-driven technique can be used to generate cascading failure data set for any real-world power grids and hence, power-grid engineers can use this approach for cascade data generation and hence predicting vulnerabilities and enhancing robustness of the grid

Modeling Cascading Failures in Power Systems in the Presence of Uncertain Wind Generation

One of the biggest threats to the power systems as critical infrastructures is large-scale blackouts resulting from cascading failures (CF) in the grid. The ongoing shift in energy portfolio due to ever-increasing penetration of renewable energy sources (RES) may drive the electric grid closer to its operational limits and introduce a large amount of uncertainty coming from their stochastic nature. One worrisome change is the increase in CFs. The CF simulation models in the literature do not allow consideration of RES penetration in studying the grid vulnerability. In this dissertation, we have developed tools and models to evaluate the impact of RE penetration on grid vulnerability to CF. We modeled uncertainty injected from different sources by analyzing actual high-resolution data from North American utilities. Next, we proposed two CF simulation models based on simplified DC power flow and full AC power flow to investigate system behavior under different operating conditions. Simulations show a dramatic improvement in the line flow uncertainty estimation based on the proposed model compared to the simplified DC OPF model. Furthermore, realistic assumptions on the integration of RE resources have been made to enhance our simulation technique. The proposed model is benchmarked against the historical blackout data and widely used models in the literature showing similar statistical patterns of blackout size

Methodologies synthesis

This deliverable deals with the modelling and analysis of interdependencies between critical infrastructures, focussing attention on two interdependent infrastructures studied in the context of CRUTIAL: the electric power infrastructure and the information infrastructures supporting management, control and maintenance functionality. The main objectives are: 1) investigate the main challenges to be addressed for the analysis and modelling of interdependencies, 2) review the modelling methodologies and tools that can be used to address these challenges and support the evaluation of the impact of interdependencies on the dependability and resilience of the service delivered to the users, and 3) present the preliminary directions investigated so far by the CRUTIAL consortium for describing and modelling interdependencies

High Order Contingency Selection using Particle Swarm Optimization and Tabu Search

There is a growing interest in investigating the high order contingency events that may result in large blackouts, which have been a great concern for power grid secure operation. The actual number of high order contingency is too huge for operators and planner to apply a brute-force enumerative analysis. This thesis presents a heuristic searching method based on particle swarm optimization (PSO) and tabu search to select severe high order contingencies. The original PSO algorithm gives an intelligent strategy to search the feasible solution space, but tends to find the best solution only. The proposed method combines the original PSO with tabu search such that a number of top candidates will be identified. This fits the need of high order contingency screening, which can be eventually the input to many other more complicate security analyses. Reordering of branches of test system based on severity of N-1 contingencies is applied as a pre-processing to increase the convergence properties and efficiency of the algorithm. With this reordering approach, many critical high order contingencies are located in a small area in the whole searching space. Therefore, the proposed algorithm tends to concentrate in searching this area such that the number of critical branch combinations searched will increase. Therefore, the speedup ratio is found to increase significantly. The proposed algorithm is tested for N-2 and N-3 contingencies using two test systems modified from the IEEE 118-bus and 30-bus systems. Variation of inertia weight, learning factors, and number of particles is tested and the range of values more suitable for this specific algorithm is suggested. Although illustrated and tested with N-2 and N-3 contingency analysis, the proposed algorithm can be extended to even higher order contingencies but visualization will be difficult because of the increase in the problem dimensions corresponding to the order of contingencies

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

Real-time Prediction of Cascading Failures in Power Systems

Blackouts in power systems cause major financial and societal losses, which necessitate devising better prediction techniques that are specifically tailored to detecting and preventing them. Since blackouts begin as a cascading failure (CF), an early detection of these CFs gives the operators ample time to stop the cascade from propagating into a large-scale blackout. In this thesis, a real-time load-based prediction model for CFs using phasor measurement units (PMUs) is proposed. The proposed model provides load-based predictions; therefore, it has the advantages of being applicable as a controller input and providing the operators with better information about the affected regions. In addition, it can aid in visualizing the effects of the CF on the grid. To extend the functionality and robustness of the proposed model, prediction intervals are incorporated based on the convergence width criterion (CWC) to allow the model to account for the uncertainties of the network, which was not available in previous works. Although this model addresses many issues in previous works, it has limitations in both scalability and capturing of transient behaviours. Hence, a second model based on recurrent neural network (RNN) long short-term memory (LSTM) ensemble is proposed. The RNN-LSTM is added to better capture the dynamics of the power system while also giving faster responses. To accommodate for the scalability of the model, a novel selection criterion for inputs is introduced to minimize the inputs while maintaining a high information entropy. The criteria include distance between buses as per graph theory, centrality of the buses with respect to fault location, and the information entropy of the bus. These criteria are merged using higher statistical moments to reflect the importance of each bus and generate indices that describe the grid with a smaller set of inputs. The results indicate that this model has the potential to provide more meaningful and accurate results than what is available in the previous literature and can be used as part of the integrated remedial action scheme (RAS) system either as a warning tool or a controller input as the accuracy of detecting affected regions reached 99.9% with a maximum delay of 400 ms. Finally, a validation loop extension is introduced to allow the model to self-update in real-time using importance sampling and case-based reasoning to extend the practicality of the model by allowing it to learn from historical data as time progresses