Cascading Failures In Power Grids Research Articles

Geometric deep learning for online prediction of cascading failures in power grids

Past events have revealed that widespread blackouts are mostly a result of cascading failures in the power grid. Understanding the underlining mechanisms of cascading failures can help in developing strategies to minimize the risk of such events. Moreover, a real-time detection of precursors to cascading failures will help operators take measures to prevent their propagation. Currently, the well-established probabilistic and physics-based models of cascading failures offer low computational efficiency, hindering them to be used only as offline tools. In this work, we develop a data-driven methodology for online estimation of the risk of cascading failures. We utilize a physics-based cascading failure model to generate a cascading failure dataset considering different operating conditions and failure scenarios, thus obtaining a sample space covering a large set of power grid states that are labeled as safe or unsafe. We use the synthetic data to train deep learning architectures, namely Feed-forward Neural Networks (FNN) and Graph Neural Networks (GNN). With the development of GNNs, improved performance is achieved with graph-structured data, and GNNs can generalize to graphs of diverse sizes. A comparison between FNN and GNN is made and the GNNs inductive capability is demonstrated via test grids. Furthermore, we apply transfer learning to improve the performance of a pre-trained GNN model on power grids not seen in the training process. The GNN model shows accuracy and balanced accuracy above 96% on selected test datasets not used in the training. Conversely, the FNN shows accuracy above 85% and balanced accuracy above 81% on test datasets unseen during training. Overall, the GNN model is successful in determining, if one or several simultaneous outages result in a critical grid state, under specific grid operating conditions.

Optimal defense strategy for AC/DC hybrid power grid cascading failures based on game theory and deep reinforcement learning

This paper proposes a two-person multi-stage zero-sum game model considering the confrontation between cascading failures and control strategies in an AC/DC hybrid system to solve the blocking problem of DC systems caused by successive failures at the receiving end of an AC/DC system. A game model is established between an attacker (power grid failure) and a defender (dispatch side). From the attacker’s perspective, this study mainly investigates the problem of system line failures caused by AC or DC blockages. From the perspective of dispatch-side defense, the multiple-feed short-circuit ratio constraint method, output adjustment measures of the energy storage system, sensitivity control, and distance third-segment protection adjustment are used as strategies to reduce system losses. Using as many line return data as possible as samples, the deep Q-network (DQN), a deep reinforcement learning algorithm, is used to obtain the Nash equilibrium of the game model. The corresponding optimal dispatch and defense strategies are also obtained while obtaining the optimal sequence of tripping failures for AC/DC hybrid system cascading failures. Using the improved IEEE 39-node system as an example, the simulation results verify the appropriateness of the two-stage dynamic zero-sum game model to schedule online defense strategies and the effectiveness and superiority of the energy storage system participating in defense adjustment.

Mitigating Cascading Failures in Power Grids via Markov Decision-Based Load-Shedding With DC Power Flow Model

Despite the reliability of modern power systems, large blackouts due to cascading failures (CFs) do occur in power grids with enormous economic and societal costs. In this article, CFs in power grids are theoretically modeled proposing a Markov decision process (MDP) framework with the aim of developing optimal load-shedding (LS) policies to mitigate CFs. The embedded Markov chain of the MDP, established earlier to capture the dynamics of CFs, features a reduced state-space and state-dependent transition probabilities. We introduce appropriate actions affecting the dynamics of CFs and associated costs. Optimal LS policies are computed that minimize the expected cumulative cost associated with CFs. Numerical simulations on the IEEE 118 and IEEE 300 bus systems show that the actions derived by the MDP result in minimum total cost of CFs, compared to fixed and random policies. Moreover, the optimality of derived policies is validated by a CF simulation based on dc power flow for the IEEE 118 bus system. Therefore, such actions developed by the proposed theoretical MDP framework can serve as a baseline for devising optimal LS strategies to mitigate CFs in power grids.

An Event-Triggered Hybrid System Model for Cascading Failure in Power Grid

Cascading failure models are important for understanding the mechanism of blackouts and evaluating the control strategies to prevent the failure propagation. The evolution of cascading failure in actual power grid is a continuous dynamic process triggered by discrete events, such as initial disturbances and physical responses. In this paper, we develop an event-triggered hybrid system model to describe the dynamic process of cascading failure. In the model, the evolution of continuous states of power grid is described by differential algebraic equations and the discrete events are defined as transitions between discrete states of power grid. The model also integrates multiple physical responses including relay protection, frequency regulation and dispatching action. Based on the developed model, we propose an event-triggered simulation method of cascading failure to accelerate the simulation process. Compared with the DC power flow model, hidden failure model and topological model, the simulation results of our model are more accurate because the statistical distribution of demand loss in our model is closer to historical blackouts data. The efficiency of the proposed event-triggered method is demonstrated by comparing our model with the time-driven model and three existing models. The experimental results show that our model can trade off the simulation accuracy and time consumption. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This paper focuses on modeling the dynamic process of cascading failure with multiple physical responses in power grid. We develop an event-triggered hybrid system model for cascading failure. In the model, the continuous dynamics of power grid and discrete events triggering the evolution of cascading failure are all described by the framework of hybrid system, which is a good example of modeling the hybrid system for automation researchers and engineers. By this way, the model is more accurate in describing the actual characteristics of cascading failure in power grid, and thus supporting the design and evaluation of control strategies for improving the stability of power grid. Based on the developed model, we propose an event-triggered simulation method of cascading failure, which aims to improve simulation accuracy while potentially reducing time consumption. In practice, the model can make fast control strategies to prevent the failure propagation.

Importance evaluation of power network nodes based on community division and characteristics of coupled network

The identification of important nodes in the power and communication coupling network is beneficial to prevent the occurrence of cascading failures. It is of great significance to establish a robust and resilient coupling network. This paper proposes a new method for evaluating the importance of power information network nodes based on link-based community division and Betweenness Centrality Based on Neighbor Nodes (BCBNN) algorithm to prevent better power grid cascading failures. This method can evaluate the importance of nodes in the network, except the nodes whose node betweenness is zero. First of all, this article uses the link-based dividing method explores the overlapping communities in the power grid; secondly, it calculates the importance of nodes in a single-layer network based on BCBNN algorithm; finally, it proposes a characteristic node importance assessment method considering single-layer network topology, grid overlapping structure and dual-network coupling. In addition, this paper has conducted experiments on the standard IEEE30-node system and improved IEEE30-node system. Compared with the node shrinkage method and Max-Cas algorithm, the experimental results not only identify traditional nodes, but also mines potential nodes that could cause the grid to fail. It means that the proposed algorithm has a better degree of differentiation in terms of importance assessment.

A network-based structure-preserving dynamical model for the study of cascading failures in power grids

In this work we show that simple classic models of power grids, albeit frequently utilized in many applications, may not be reliable for investigating cascading failures problems. For this purpose, we develop a novel model, based on a structure-preserving approach, to obtain a network-based description of a power grid, where nodes correspond to generators and buses, while the links correspond to the physical lines connecting them. In addition, we also consider classic voltage and frequency protection mechanisms for lines and buses. Considering the Italian power grid as a case study of interest, we then investigate the propagation of an initial failure of any line of the power system, and compare the predicted impact of the failure according to different assumptions in the model such as the presence or absence of protection mechanisms and a simplified description of the system dynamics. In particular, it can be observed that more realistic models are crucial to determine the size of the cascading failure, as well as the sequence of links that may be involved in the cascade.

Micro-scale foundation with error quantification for the approximation of dynamics on networks

Epidemics, voting behaviour and cascading failures in power grids are examples of natural, social and technological phenomena that can be modelled as dynamical processes on networks. The study of such important complex systems requires approximation, but the assumptions that underpin the standard mean-field approaches are routinely violated by dynamics on real-world networks, leading to uncontrolled errors and even controversial results. Consequently, determining the approximation precision has been recognised as a key challenge. We present a micro-scale foundation for mean-field approximation of a wide range of dynamics on networks that facilitates quantification of approximation error, elucidating its connection to network structure and model dynamics. We show that our coarse-graining approach minimises approximation error and we obtain an upper bound on this uncertainty. We illustrate our approach using epidemic dynamics on real-world networks.

Control of cascading failures in dynamical models of power grids

In this paper, we introduce a distributed control strategy to prevent dynamically-induced cascading failures in power grids. We model power grids using complex networks and nonlinear dynamics to provide a coarse-grained description of the electro-mechanical phenomena taking place on them (in particular, we use coupled swing equations) and restrict our analysis to cascades of line failures, i.e., failures due to power flows exceeding the maximum capacity of a line. We formulate a distributed control protocol relying on the same topology of the physical layer and apply it to several power grid models, including a small-size illustrative example with five nodes, the Italian high-voltage (380kV) power grid, and the IEEE 118-bus system. Our results indicate that the approach is capable of preventing cascading failures, either controlling each node of the network or a suitable subset of them.

Identifying critical higher-order interactions in complex networks

Diffusion on networks is an important concept in network science observed in many situations such as information spreading and rumor controlling in social networks, disease contagion between individuals, and cascading failures in power grids. The critical interactions in networks play critical roles in diffusion and primarily affect network structure and functions. While interactions can occur between two nodes as pairwise interactions, i.e., edges, they can also occur between three or more nodes, which are described as higher-order interactions. This report presents a novel method to identify critical higher-order interactions in complex networks. We propose two new Laplacians to generalize standard graph centrality measures for higher-order interactions. We then compare the performances of the generalized centrality measures using the size of giant component and the Susceptible-Infected-Recovered (SIR) simulation model to show the effectiveness of using higher-order interactions. We further compare them with the first-order interactions (i.e., edges). Experimental results suggest that higher-order interactions play more critical roles than edges based on both the size of giant component and SIR, and the proposed methods are promising in identifying critical higher-order interactions.

Vulnerability Assessment of Power Grids Against Cost-Constrained Hybrid Attacks

The frequent occurrences of cascading failures in power grids have been receiving continuous attention in recent years. An urgent task for us is to assess the vulnerability of power grids against various kinds of attacks, which trigger cascading failures. In this brief, we formulate a cost-constrained hybrid attack in power grids, where both nodes and links are targeted with a limited total attack cost. Based on the consequence and cost of removing a component (node or link), we propose an attack centrality metric for components, which can be either local or global depending on the depth of cascading failures. We further propose a greedy hybrid attack and another optimal hybrid attack by applying the attack centrality. Simulation results on IEEE bus test data demonstrate that the optimal attack is more efficient than the greedy one. Furthermore, we find, counterintuitively, that the local centrality based attack algorithms perform better than the global centrality based ones when attack cost is a concern. Our work can help in the robustness optimization of power systems by revealing the worst-case attack vulnerability and most vulnerable components.

Interaction Graphs for Cascading Failure Analysis in Power Grids: A Survey

Understanding and analyzing cascading failures in power grids have been the focus of many researchers for years. However, the complex interactions among the large number of components in these systems and their contributions to cascading failures are not yet completely understood. Therefore, various techniques have been developed and used to model and analyze the underlying interactions among the components of the power grid with respect to cascading failures. Such methods are important to reveal the essential information that may not be readily available from power system physical models and topologies. In general, the influences and interactions among the components of the system may occur both locally and at distance due to the physics of electricity governing the power flow dynamics as well as other functional and cyber dependencies among the components of the system. To infer and capture such interactions, data-driven approaches or techniques based on the physics of electricity have been used to develop graph-based models of interactions among the components of the power grid. In this survey, various methods of developing interaction graphs as well as studies on the reliability and cascading failure analysis of power grids using these graphs have been reviewed.

Publisher's Note: "Don't go chasing artificial waterfalls: Artificial line limits and cascading failures in power grids" [Chaos 29, 113117 (2019)

Publisher's Note: "Don't go chasing artificial waterfalls: Artificial line limits and cascading failures in power grids" [Chaos 29, 113117 (2019)

Don't go chasing artificial waterfalls: Artificial line limits and cascading failures in power grids.

Research on cascading failures in power-transmission networks requires detailed data on the capacity of individual transmission lines. However, these data are often unavailable to researchers. Consequently, line limits are often modeled by assuming that they are proportional to some average load. However, there is scarce research to support this assumption as being realistic. In this paper, we analyze the proportional loading (PL) approach and compare it to two linear models that use voltage and initial power flow as variables and are trained on the line limits of a real power network that we have access to. We compare these artificial line-limit methods using four tests: the ability to model true line limits, the damage done during an attack, the order in which edges are lost, and accuracy ranking the relative performance of different attack strategies. We find that the linear models are the top-performing method or are close to the top in all the tests we perform. In comparison, the tolerance value that produces the best PL limits changes depending on the test. The PL approach was a particularly poor fit when the line tolerance was less than two, which is the most commonly used value range in cascading failure research. We also find indications that the accuracy of modeling line limits does not indicate how well a model will represent grid collapse. The findings of this paper provide an understanding of the weaknesses of the PL approach and offer an alternative method of line-limit modeling.

Revealing Impacts of Cyber Attacks on Power Grids Vulnerability to Cascading Failures

Cascading failures in power grids are typically triggered by initiating contingencies (ICs). Traditional assumption is that those multiple-component ICs have low chances of occurring. However, considering the increasing cyber events in power grids, this brief reveals that smart attackers can target at critical ICs and implement well-designed cyber attacks to highly increase the ICs’ occurrence probabilities by overloading key branches in the grid. This will greatly increase the grid vulnerability to cascading failures. In this brief, such issue is revealed and analyzed using a two-step approach, which consists of a high-probability IC screening and a deterministic cascading testing. The simulation results on the IEEE 118-bus systems verify the effectiveness of the proposed approach and highlight the increased risk imposed by cyber-attacks.

Impacts of Operators’ Behavior on Reliability of Power Grids During Cascading Failures

Human operators play a key role in the reliable operation of critical infrastructures. However, human operators may take actions that are far from optimum. This can be due to various factors affecting the operators’ performance in time-sensitive and critical situations such as reacting to contingencies with significant monetary and social impacts. In this paper, an analytic framework is proposed based on Markov chains for modeling the dynamics of cascading failures in power grids. The model captures the effects of operators’ behavior quantified by the probability of human error under various circumstances. In particular, the observations from historical data and information obtained from interviews with power-system operators are utilized to develop the model as well as identify its parameters. In light of the proposed model, the noncritical regions of power-system's operating characteristics with human-factor considerations are characterized under which the probability of large cascading failures is minimized.

Dynamically induced cascading failures in power grids

Reliable functioning of infrastructure networks is essential for our modern society. Cascading failures are the cause of most large-scale network outages. Although cascading failures often exhibit dynamical transients, the modeling of cascades has so far mainly focused on the analysis of sequences of steady states. In this article, we focus on electrical transmission networks and introduce a framework that takes into account both the event-based nature of cascades and the essentials of the network dynamics. We find that transients of the order of seconds in the flows of a power grid play a crucial role in the emergence of collective behaviors. We finally propose a forecasting method to identify critical lines and components in advance or during operation. Overall, our work highlights the relevance of dynamically induced failures on the synchronization dynamics of national power grids of different European countries and provides methods to predict and model cascading failures.

Analyzing Cascading Failures in Power Grids under the AC and DC Power Flow Models

In this paper, we study cascading failures in power grids under the nonlinear AC and linearized DC power flow models. We numerically compare the evolution of cascades after single line failures under the two flow models in four test networks. The cascade simulations demonstrate that the assumptions underlying the DC model (e.g., ignoring power losses, reactive power flows, and voltage magnitude variations) can lead to inaccurate and overly optimistic cascade predictions. Particularly, in large networks the DC model tends to overestimate the yield (the ratio of the demand supplied at the end of the cascade to the initial demand). Hence, using the DC model for cascade prediction may result in a misrepresentation of the gravity of a cascade.

Impacts of Wind Power Uncertainty on Grid Vulnerability to Cascading Overload Failures

Higher penetration of renewables like wind power generation will introduce an unprecedented amount of uncertainty into the grid that might severely affect the grid vulnerability to cascading failures. In this study, we propose a mixed OPF-stochastic approach to analyze and simulate cascading failures in power grid and to evaluate the impact of wind generation in terms of its penetration and uncertainty level. The proposed approach incorporates both thermal stability model for transmission line outage and automatic power balance algorithms. Numerical simulation results on the IEEE 300 bus system indicate that uncertainty coming from wind energy has severe impacts on grid vulnerability to cascading overload failures under different contingency scenarios. Results also suggest that higher penetration levels of wind energy, if not managed appropriately, will add to this severity because higher uncertainties may be injected into weaker lines in a grid.

Distributed monitoring for the prevention of cascading failures in operational power grids

Electrical power grids are vulnerable to cascading failures that can lead to large blackouts. The detection and prevention of cascading failures in power grids are important problems. Currently, grid operators mainly monitor the states (loading levels) of individual components in a power grid. The complex architecture of a power grid, with its many interdependencies, makes it difficult to aggregate the data provided by local components in a meaningful and timely manner. Indeed, monitoring the resilience of an operational power grid to cascading failures is a major challenge.This paper attempts to address this challenge. It presents a robustness metric based on the topology and operative state of a power grid to quantify the robustness of the grid. Also, it presents a distributed computation method with self-stabilizing properties that can be used for near real-time monitoring of grid robustness. The research thus provides insights into the resilience of a dynamic operational power grid to cascading failures during real-time in a manner that is both scalable and robust. Computations are pushed to the power grid network, making the results available at each node and enabling automated distributed control mechanisms to be implemented.

Modeling and impact analysis of interdependent characteristics on cascading failures in smart grids

Smart grids are increasingly interactive with communication networks and have even become interdependent networks. The majority of previous research has assumed that a minor failure might evolve into cascading failures through interactive interdependency. However, in the interdependent power grids and communication networks, the point-to-point interdependency is embedded based on certain topological characteristics rather than at random. This paper aims to analyze the impacts of different interdependencies and structure characteristics of communication networks on cascading failures in power grids. An interactive cascading model for power grids and coupled communications systems is proposed based on the redistribution of DC power flow and the routing of the open shortest path first (OSPF) strategy with consideration of the abnormal transmission, and the interdependency is analyzed numerically. Quantification of the different types of interdependencies illustrates that greater interdependency leads to a lower probability of a large blackout. Furthermore, a threshold value for the transmission inefficiency of communication networks is shown in the cascading process. The most of the power system can be functional when the transmission inefficiency is under the threshold value. Comparison of the threshold values in the double-star and the mesh communication networks illustrates that the heterogeneous characteristics of the double-star structure provide better control to mitigate cascading failures.