The increasing penetration of renewable energy generation (REG) introduces significant uncertainty into power grids, posing heightened risks for cascading failures. In this paper, a Markov tree model is proposed to assess the risk of cascading failure in power grid with uncertain REG. The model captures the diverse failure paths caused by REG uncertainty, representing the cascading failure process as a sequence of state transitions with probabilities reflecting the likelihood of state transitions. To identify critical tripping branches during cascading failure propagation, a hybrid probability-interval method is introduced. Probabilistic power flow analysis identifies branches with overload risk, while interval positional relationships rank their severity. To improve the efficiency of risk assessment, a risk-based depth-first search (R-DFS) method is proposed. This method uses estimated risk indices to prioritize high-risk failure paths while pruning low-risk paths, significantly reducing simulation time while maintaining assessment accuracy. Compared with existing models, the proposed model balances simulation efficiency and accuracy, effectively identifying high-risk failure paths under REG uncertainty. Simulation results demonstrate the impact of threshold selection on the retention of high-risk paths and simulation performance, providing insights into managing cascading failure risks in power grid with high REG penetration.

Distribution grid with electric vehicle (EV) charging infrastructure can be modeled as a coupled network consisting of the cyber network, distribution grid and traffic network. The interconnection of the coupled network allows attackers to launch cyber attacks and control numerous EVs to cause severe load fluctuations, thereby affecting the normal operation of the distribution grid and the traffic flow. To evaluate the cyber-physical security of the coupled network, we present a security assessment model formulated as a coupled Discrete Event System Specification (DEVS). In this model, the evolution of the coupled network is represented as state transitions triggered by events in a discrete-time process, while the interaction is achieved through event transmission, reception and processing. To determine the redistribution of states influenced by the selection of EV charging stations and moving paths, we propose a spatial-temporal evolution mechanism. Based on the assessment model, we propose an event-triggered simulation method. The efficiency of the proposed simulation method is evaluated by comparing it with the multi-layer synchronous simulation method. Compared with the existing security assessment models, the simulation results of our model are more accurate.

The frequent blackouts around the world in the past 20 years have brought the security of the power grid to a head. Among various hazard situations, cascading failure is the one with critical threats due to its widespread propagation and long duration. An effective way to prevent cascading failure is to identify the vulnerable set, which is defined as the composition of transmission line combinations that can initialize the sequence of failures. In this paper, we first elaborate cascading failure model and its adaptation under the scenario of interest. Then a novel framework of data-driven identification model is developed to replace the traditional flow-based detection process, which is computationally heavy. Specifically, a method that seamlessly achieves the globally topological features embedding by designing a tailored messaging mechanism adjusted for the power grid is proposed, overcoming the otherwise problem of the constrained neighborhood in existing graph convolution networks (GCNs). Besides, with the proposed pruning optimization method, the sparsity of the vulnerable set can be naturally enforced and combinatorial explosion is readily alleviated. Numerical experiments are conducted on 30-bus, 200-bus, and 500-bus systems, including static and dynamic load scenarios. All of them verify the excellent performance of the identification model for both effectiveness and efficiency.Note to Practitioners—This paper is motivated by a practical need for mitigate the security threat of cascading failures to power grid through the vulnerable set identification. Existing methods for identifying the vulnerable set have limitations, including a limited number of vulnerabilities identified and challenges related to the high time complexity of cascading failure simulators and combinatorial explosion. To address this issue, we develop a data-driven identification model that integrates both the physical and topological features of the power grid. This model reduces the reliance on cascading failure simulators and enhances the efficiency of vulnerable set identification. Additionally, the pruning optimization method is proposed to further mitigate the high time complexity caused by combinatorial explosion. Simulative studies conduct in both dynamic and static load scenarios validate the performance of the developed data-driven model, demonstrating its ability to achieve rapid identification of the vulnerable set and thereby improve the overall robustness of the power grid against cascading failures.

The increasing penetration of renewable energy generation (REG) introduces high levels of uncertainty into power grid, potentially causing significant impacts on the evolution of cascading failure. In this paper, we propose a failure tree model that encompasses all possible failure paths resulting from the uncertain power injections from REG to describe the dynamic process of cascading failure in power grid. In order to obtain the failure paths of cascading failure, we propose an interval overload tripping mechanism to model relay protection based on the uncertainty set of REG and dynamic interval power flow. On the basis of the proposed model, we design a forward-backward tree search to efficiently evaluate the impact of the uncertain REG on cascading failure. Compared with the probabilistic power flow (PPF) model and scenario-based model, the simulation results of our model are more accurate because the statistical distribution of demand loss in our model is closer to Monte Carlo simulation (MCS). The efficiency of the proposed simulation method is demonstrated by comparing our model with the MCS under various sample numbers and two existing models. Finally, we analyze the influence of REG uncertainty level and penetration level on cascading failure and simulation performance. Note to Practitioners—To achieve accurate and fast cascading failure analysis in power grid with renewable energy generation (REG), this paper develops a failure tree model that considers the impact of uncertain injected power of REG on the dynamic process of cascading failure. In the model, the dynamic interval power flow and interval overload tripping mechanism are proposed to simulate the physical responses during cascading failure, including power flow redistribution, transmission branch outage and frequency regulation. Therefore, the model is more accurate in describing the actual characteristics of cascading failure in power grid with REG. This will facilitate the development and evaluation of control strategies aimed at improving the stability of power grid. Meanwhile, the model provides a good example for researchers and engineers to simulate network systems without detailed information about the probability distribution of uncertain injection variables. Based on the proposed model, we develop a forward-backward tree search, which allows the decision-maker to make a satisfactory trade-off between accuracy and time consumption. This algorithm allows for fast control strategy implementation to prevent failure propagation.

Over the past two decades, frequent blackouts have highlighted the critical importance of ensuring the security of power grid. The integration of cyber and physical domains through intelligent devices has increased the risk of asynchronous attacks that can trigger cascading failures. One effective approach to mitigating this threat is to identify vulnerable sequences, which are sequences of transmission lines that can cause large-scale failures in the power grid. This article proposes an event-triggered hybrid system model to characterize the generation and propagation mechanism of sequential cascading failures. In addition, the problem of identifying vulnerable sequences is formulated as a Markov decision process. To solve the sequential decision problem in approximately contiguous states, a vulnerable sequence identification method based on reinforcement learning is designed. Furthermore, a topological feature embedding algorithm based on matrix decomposition is proposed to improve identification performance. To evaluate the effectiveness of the proposed method, various numerical experiments are conducted on IEEE 30-bus and ACTIVSg 200-bus systems. The results of these experiments demonstrate the excellent performance of the proposed method.

Cascading failures pose a significant security threat to networked systems, with recent global incidents underscoring their destructive potential. The security threat of cascading failures has always existed, but the evolution of cyber-physical systems (CPSs) has introduced novel dimensions to cascading failures, intensifying their threats owing to the intricate fusion of cyber and physical domains. Addressing these threats requires a nuanced understanding achieved through failure modeling and vulnerability analysis. By analyzing the historical failures in different CPSs, the cascading failure in CPSs is comprehensively defined as a complicated propagation process in coupled cyber and physical systems, initialized by natural accidents or human interference, which exhibits a progressive evolution within the networked structure and ultimately results in unexpected large-scale systemic failures. Subsequently, this study advances the development of instructions for modeling cascading failures and conducting vulnerability analyses within CPSs. The examination also delves into the core challenges inherent in these methodologies. Moreover, a comprehensive survey and classification of extant research methodologies and solutions are undertaken, accompanied by a concise evaluation of their advancements and limitations. To validate the performance of these methodologies, numerical experiments are conducted to ascertain their distinct features. In conclusion, this article advocates for future research initiatives, particularly emphasizing the exploration of uncertainty analysis, defense strategies, and verification platforms. By addressing these areas, the resilience of CPSs against cascading failures can be significantly enhanced.

Past 20 years has witnessed some exorbitant fallout and large-scale blackouts in power system, particularly due to cascading failures and their propagation in the crucial yet complex and networked infrastructure. A pivotal prevention measure to steer clear from cascading events is the identification of vulnerable set, defined as the composition of specific line combinations that can trigger sequence of errors. By nature, the identification problem is NP-hard and a resort to approximation algorithms is necessary. In this article, we first construct a general yet rigorous formalism for the mathematical analysis of cascading failure in networked systems. With a tailored treatment of the propagation mechanism, a fast identification algorithm (FIA) for vulnerable set is then designed based on a key observation revealing the correlation structure among different N-kcontingencies. By analyzing the monotonic nondecreasing, quasi-submodular property of the propagation process, a theoretical lower bound of our algorithm is given in specific order. Besides, we show that the optimization framework of our algorithm can be readily extended to incorporate prior information. Numerical experiments on IEEE 30-, 118-, and 200-bus systems are performed to verify the effectiveness and efficiency of both FIA and its optimization framework.

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.Note to Practitioners—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.