Structural vulnerability assessment of electric power grids

A topological investigation of phase transitions of cascading failures in power grids

Blackouts in power grids typically result from cascading failures. The key importance of the electric power grid to society encourages further research into sustaining power system reliability and developing new methods to manage the risks of cascading blackouts. Adequate software tools are required to better analyze, understand, and assess the consequences of the cascading failures. This paper presents MATCASC, an open source MATLAB based tool to analyse cascading failures in power grids. Cascading effects due to line overload outages are considered. The applicability of the MATCASC tool is demonstrated by assessing the robustness of IEEE test systems and real-world power grids with respect to cascading failures.

Current power grids suffer periodic disturbances that may trigger cascades of component failures, which, in turn, can result in blackouts of different scales. Understanding cascading failures and the ability to predict the risk of blackouts are therefore of great value in designing control and outage management systems for future smart grids. In this paper, a novel probabilistic approach is proposed to model the dynamics of cascading failures in power grids. The model characterizes the probability of reaching a blackout of an arbitrary size in any time interval starting from an initial grid state. The model exploits two power grid parameters: the maximum capacity of the set of failed lines and the grid loading ratio. Simulations have shown that these parameters largely affect the cascading failures. In addition, the number of failed lines and the maximum capacity of the failed lines are utilized to reduce the space of all possible grid configurations into a much smaller set of equivalence classes, thereby making the model scalable to large power grids. The results of the analytical model are in agreement with Monte Carlo simulations performed with the IEEE 118-bus system.

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.

Some critical lines can have important impact on the large-scale blackouts and cascading failures in power grid. Based on the newest progress in the field of complex network, a new vulnerability index called weighted line betweenness is proposed as vulnerability index in this paper. The weighted line betweenness of one line is defined as the sum of the loads acted on this line, which are brought by the shortest electric paths between generator nodes and load nodes that passing through this line. We revise the weighted line betweenness by increasing the betweenness to the highest betweenness in the neighboring lines before revision. Vulnerability analysis has been carried out on the IEEE 39 bus system and Huazhong-Chuanyu power grid. The time domain simulation results verify that the weighted line betweenness can not only identify the most critical lines but also find out those light loaded but critical lines due to their special position in the power grid.

Multilayer control of synchronization and 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.

The products of genes mutated or differentially expressed in cancer tend to occupy central positions within the network of protein-protein interactions, or the interactome network. Integration of different types of gene and protein relationships has considerably increased the understanding of the mechanisms of carcinogenesis, while also enhancing the applicability of expression signatures. In this scenario, however, it remains unknown how cancer develops, progresses and responds to therapies in a potentially controlled manner at the systems level. Here, by applying the concepts of load transfer and cascading failures in power grids, we examine the impact and transmission of cancer-related gene expression changes in the interactome network. Relative to random perturbations, this study reveals topological robustness associated with all cancer conditions. In addition, experimental perturbation of a central cancer node, which consists of over-expression of the α-synuclein (SNCA) protein in MCF7 breast cancer cells, also reveals robustness. Conversely, a search for proteins with an opposite topological impact identifies the autophagy pathway. Mechanistically, the existence of smaller shortest paths among cancer-related proteins appears to be a topological feature that partially contributes to the restricted perturbation of the network. Together, the results of this study suggest that cancer develops, progresses and responds to therapies following controlled, restricted perturbation of the interactome network.

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.

In smart power grid, power grid and communication network are connected and mutually dependent. The failure in power grid might cause failures in communication network, and vice versa. A tiny failure in either of them could trigger cascade of failures within the entire system. In this paper, we focus on understanding the structure of smart power grid and studying the underlying network model, their interactions, relationships and how cascading failures occur in the system. We propose a practical model for smart power grid as interdependent complex network. The interdependency between two networks is `oneto-multiple': each node in the communication network has only one support link from the power grid, while each node in power grid is connected to multiple communication nodes. We study the effect of cascading failures using percolation theory, and present detailed mathematical analysis of failure propagation in the system. We analyze the robustness of our model caused by random attacks or failures by calculating the size of functioning parts in both networks. Using simulations, we prove that there exists a threshold for the proportion of faulty nodes, beyond which the system collapses. Also we determine the critical values for different system parameters. To the best of our knowledge, this is the first work that models smart grid as interdependent complex networks and studies its fault tolerance.

On 18 August 2005, one of the biggest power outages in world history occurred in Java-Bali power grids system in Indonesia which impacts on almost 100 billion people for about 3 hours. A failure in the 500 kV transmission line between Saguling-Cibinong has caused the transmission line to break down resulting in the power grid network to dissolve into two separate networks, which in the end led to cascading failure along the whole grid. Power grid topology plays an important role in determining system behavior when one or more connections failed and impacting the whole network. In the worst case, cascading failure might take place which disturbs the whole networks. The objectives of the paper are to understand how a cascading failure incident takes place in power grids and find the correlation between key parameters using complex network theory to improve power grids robustness. The paper concentrate on an edge-based attack model as it has a resemblance with the Java-Bali power outages incident in 2005. The result indicates characteristics of small-world network from Java-Bali power grid, with different tunable parameters and load ratios, have an impact on network cascading failure likelihood.

• Transparent, reproducible workflow to build overhead power grids from public data. • Map electricity end users by integrating Google Places API and OpenStreetMap. • Novel distance–capacity method links end users to substations. • Cascading failures modelled via power flow analysis, beyond topological methods. • Estimate service disruptions via post-disruption electricity-served ratio. Cascading failures in power grids can escalate localized disruptions into extensive service outages. This study presents a transparent, reproducible framework to build power grids from publicly available data, integrating commissioned power plants, substations, transmission lines, and hypothetical transformers, for large-scale power system modelling. To assess how grid disruptions lead to service interruptions for industrial users, we combine Google Places API industrial points of interest with OpenStreetMap industrial zones, and link them to substations based on capacity and proximity. We model initial disruptions under two scenarios: 1) random disruptions, implemented through percolation analysis to assess network robustness under stochastic component removals; and 2) targeted disruptions, generated by Monte Carlo sampling of wind-induced fragility curves derived from the 2024 Typhoon Yagi wind field to produce probabilistic failures. The analysis reveals distinct spatial variation in grid vulnerability and traces the propagation of failures through the network, quantifying downstream service disruptions for industrial users. System-wide simulations further identify critical transmission corridors with higher failure and overload risks. These insights provide a basis for targeted investment, resilience assessment, and future research on multi-hazard and adaptive protection strategies.

Summary form only given. The most severe failures in power grids are often characterized as cascading failures where an initial event triggers consequent failures all along the grid often leading to blackouts. Upon identifying a failure and its cascade potential, timely control actions should be performed by the grid operators to mitigate the effect of the cascade. These actions have to be delivered to one or more control devices, creating a dependency between the power grid and its control network. This paper examines the dependency of the operation of the power grid on the control network. Different from literature studies on failure control, our dependency model captures the impact of networking parameters. We formulate an algorithmic model that describes the impact of this dependency on cascade control. Based on this model, we propose an efficient cascade control algorithm using load shedding with consideration of delays in the communication network for power grids. Finally, we evaluate the impact of the power-communication network dependency with uncontrolled grids, ideal/simple control grids and our proposed control scheme. The results demonstrate that the proposed algorithm can significantly reduce the failure of power lines while sustaining larger power demand for users.

Cascading failures in electrical power grids, comprising nodes and links, propagate nonlocally. After a local disturbance, successive resultant can be distant from the source. Since avalanche failures can propagate unexpectedly, care must be taken when formulating a mitigation strategy. Herein, we propose a strategy for mitigating such cascading failures. First, to characterize the impact of each node on the avalanche dynamics, we propose a novel measure, that of Avalanche Centrality (AC). Then, based on the ACs, nodes potentially needing reinforcement are identified and selected for mitigation. Compared with heuristic measures, AC has proven to be efficient at reducing avalanche size; however, due to nonlocal propagation, calculating ACs can be computationally burdensome. To resolve this problem, we use a graph neural network (GNN). We begin by training a GNN using a large number of small networks; then, once trained, the GNN can predict ACs efficiently in large networks and real-world topological power grids in manageable computational time. Thus, under our strategy, mitigation in large networks is achieved by reinforcing nodes with large ACs. The framework developed in this study can be implemented in other complex processes that require longer computational time to simulate large networks.

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.