Microgrids are susceptible to cascading failures triggered by various risks, which can severely compromise system resilience. Existing studies have extensively investigated cascading failures through propagation modeling, post-failure recovery, and mitigation strategies. Throughout the evolution of cascading failure, power redistribution plays a central role by reshaping post-disturbance power flow and influencing the subsequent propagation of failure. However, existing redistribution strategies primarily rely on network topology or updated operating states while overlooking the explicit enforcement of physical operating constraints. Consequently, redistributed power may still exceed system operating limits, resulting in persistent overloads and continued cascade propagation. To address this issue, this paper proposes a dynamic power redistribution strategy that proactively blocks cascading failures by eliminating overloads as they evolve. A two-stage stochastic programming model based on multi-objective optimal power flow is developed by integrating topological evolution with rigorous physical constraints. Comparative experiments demonstrate that (1) the proposed strategy effectively eliminates overloads and successfully blocks cascading failures; (2) it significantly enhances the microgrid resilience under diverse risk scenarios, achieving up to 56.8% higher resilience than benchmark strategies.

Ensuring frequency stability in microgrids (MGs) is becoming increasingly challenging due to the openness of networked control systems, the volatility of renewable energy sources, and the growing threat of hybrid cyber-physical attacks. This paper presents a delay-tolerant resilient model predictive control (MPC) approach for load frequency stability in MGs. First, a comprehensive MG load frequency control (LFC) model is developed, explicitly accounting for communication time delays. A control strategy that combines resilient MPC with delay compensation is proposed to enhance system resilience and dynamic performance. To address hybrid cyber-physical attacks, a resilient MPC-based output feedback controller is designed based on a hybrid H-2/H-infinity performance index, in which the H(2 )criterion is optimized online under a guaranteed H-infinity performance bound, ensuring robust frequency regulation. Feasibility and safety of the controller are guaranteed by reformulating the non-convex constraints via cone complementary linearization, and solving the controller using linear matrix inequality techniques. Stability and feasibility analyses of the algorithm are also provided. Finally, a series of comparative simulations under various attack scenarios and perturbation conditions are conducted to validate the robustness of the proposed method and demonstrate its effectiveness in enhancing the resilience of the MG system.

According to the dynamic interaction process between cyber flow and power flow in grid cyber-physical systems (GCPS), attackers could gradually trigger large-scale power failures through cooperative cyber-attacks, subsequently forming cross-domain cascading failures (CDCF) that cross cyber-domain and power-domain and endanger the stable running of GCPS. To reveal the evolutionary mechanism of CDCF, an optimal attack scheme evaluation method is proposed, considering the spatiotemporal synergy of multiple attack-event-chains. First, in accordance with the spatiotemporal synergy of multiple attack-event-chains, the CDCF evolutionary mechanism is analyzed from the attackers' perspective, and a CDCF mathematical model is established. Furthermore, an attack graph model of CDCF evolution and its hazard calculation method are proposed. Then, the attackers' decision-making process for the optimal attack scheme of CDCF is deduced based on the attack graph model. Finally, both the evaluation and implementation processes of the optimal attack scheme are simulated in the GCPS experimental system based on IEEE-39 bus systems.

Integrated sensing and communications (ISAC) has emerged as a promising paradigm for future wireless networks. Against this background, this paper proposes a probabilistic constellation shaping (PCS) framework for discrete Fourier transform-spread orthogonal frequency division multiplexing (DFT-s-OFDM)-based ISAC systems. We first derive a closed-form ambiguity function (AF) of DFT-s-OFDM waveforms, which reveals a direct relationship between velocity estimation accuracy and the constellation’s kurtosis. We formulate the PCS design as an optimization problem that maximizes communication throughput while constraining the kurtosis to explicitly control sensing performance. For nonlinear channels with power amplifier distortion, a surrogate-assisted evolutionary algorithm is proposed, which efficiently identifies the Pareto-optimal front with low computational complexity. Simulations demonstrate that our framework achieves a superior and highly tunable performance trade-off compared to conventional uniform constellations.

The integration of graph-based fuzzy systems into power system state estimation (SE) remains underexplored, yet it offers strong potential for interpretable and resilient grid monitoring under cyber threats. As modern power grids become increasingly complex, ensuring accurate SE while defending against false data injection (FDI) attacks poses a critical challenge. Traditional SE techniques and bad-data detection methods, relying on linearized models and single-estimator residual checks, often fail to capture nonlinear topology-coupled dependencies and noise in practice, thereby limiting their ability to detect stealthy and coordinated attacks. To bridge this gap, we propose a Graph Fuzzy Competitive Equilibrium State Estimation (GF-CESE) framework that combines graph fuzzy reasoning with power grid topology to enhance interpretability and anomaly detection. By constructing fuzzy rules via virtual center nodes (VCNs) and embedding network connectivity into rule consequents through message propagation, GF-CESE models nonlinear state evolution in a topology-consistent manner. By further introducing a multi-estimator competitive-equilibrium mechanism and cross-estimator residual fusion with a sliding-window test, GF-CESE improves estimation stability and robustness against stealthy FDI attacks. Extensive experiments on IEEE 14-, 118-, and 300-bus systems validate the effectiveness, scalability, and robustness of the proposed approach under high measurement noise and large-scale coordinated multi-node attacks. Note to Practitioners-Power system state estimation (SE) plays a central role in grid monitoring and control. However, as modern grids become more interconnected and digitalized, they are increasingly exposed to cyber threats such as false data injection (FDI) attacks. These attacks can manipulate sensor data, degrade situational awareness, and mislead operator decisions. Traditional SE techniques, often based on simplified linear models, may struggle to provide reliable results under noisy or adversarial conditions. This paper presents a practical framework aimed at improving the robustness and interpretability of SE in the presence of such disturbances. The approach leverages the grid's physical topology and historical data to enhance anomaly detection and reduce estimation error, even under stealthy or coordinated attacks. In contrast to opaque learning models, our method provides explainable reasoning through interpretable fuzzy logic and graph-based processing. In real-world applications, this framework can be integrated into existing Supervisory Control and Data Acquisition (SCADA) or Energy Management System (EMS) platforms without requiring significant hardware or software upgrades. It operates on standard grid measurements such as power injections and bus voltages, and does not rely on additional sensors or infrastructure modifications. The model can be deployed as a software module within existing control centers, supporting real-time monitoring and scalable operation across large power networks. Engineers and system operators can apply this method to improve decision confidence, reduce false alarms, and strengthen resilience in critical infrastructure environments where cyber-physical risks are rising.

With the deep integration of power systems into cyber-physical systems (CPSs), the widespread deployment of measurement terminals and high-frequency information interactions has significantly expanded the attack surface. State estimation (SE), as a critical function, is increasingly vulnerable to severe cyber threats. To expose the security vulnerabilities of current SE processes, a covert data-tampering attack method without relying on prior knowledge is proposed in this article, addressing the limitations of previous attack methods, which generally face challenges in acquiring system models or lack theoretical guarantees for covertness. The core innovation lies in an adversarial attack framework that integrates an adversarial autoencoder (AAE) and a generative adversarial network (GAN), along with a bidirectional SE agent model designed to eliminate explicit reliance on accurate mechanistic models. Within this framework, an unsupervised generator deeply coupled with physical constraints is designed to jointly optimize attack strength and covertness through a composite loss function. The effectiveness of the proposed method is demonstrated through case studies, where high-threat and low-detectability attack vectors are generated in real time, misleading SE results while successfully evading conventional grid security protection mechanisms.

Synchrophasor estimation in distribution networks faces significant challenges under complex signal conditions, such as frequency deviation, harmonic distortion, and nonstationary disturbances. To address these issues, an adaptive state estimation algorithm combining the sliding Fourier transform (SFT) and a spectrum‐driven estimation via minimization of parameter residuals (SEMPR) mechanism was proposed. Dominant frequency components were identified through spectral analysis within a sliding window, a time‐varying signal model was constructed, and nonlinear parameter optimization was performed to estimate signal amplitude, frequency, phase angle, harmonics, and their dynamic evolution parameters. Compared with traditional static methods, frequency‐adaptive tracking and dynamic model updating were enabled, and improved fitting performance was observed; the estimation error was maintained within ±0.03 under clean conditions, within ±0.04 under mild pollution, and up to ±0.06 under severe pollution. The algorithm was validated under various simulation scenarios, and the results demonstrate superior performance in frequency tracking, harmonic identification, and fault detection tasks, supporting its applicability to synchrophasor measurement under complex operating environments.

With the widespread deployment of phasor measurement units (PMUs), data-driven composite load modeling has gained increasing attention among researchers. Existing approaches mainly rely on optimization-based methods to produce point estimates, which lack the capability to quantify estimation uncertainty. Alternatively, sampling-based techniques can provide confidence intervals (CIs) but are computationally expensive for real-time applications. In addition, the theoretical interpretability of such CIs is still limited. To address these issues, we propose a decentralized Bayesian load modeling strategy utilizing trajectory sensitivity that achieves structural decoupling between the load model and the external network. It eliminates the effects associated with external uncertainties in the system while effectively providing a probabilistic description of the load parameters, without resorting to time-consuming sampling. Moreover, for the first time we derive an analytical relation between trajectory sensitivities, measurement Jacobians, priors, noise, and confidence levels, theoretically demonstrating the rationale of key parameter screening in a statistical manner. The simulation results for multiple load modeling cases reveal the excellent performance of the proposed method.

State estimation (SE) is vital for secure power system operation, but remains susceptible to stealthy false data injection attacks (FDIAs). Existing detection methods are primarily designed using prior attack knowledge, which limits their adaptability to unknown threats. This article introduces the concept of controllable uncertainty into SE, where uncertainty is actively regulated at inference time rather than passively induced by stochastic training effects, and proposes an attack-resilient SE model that enables active defense through an integrated estimation-detection-feedback mechanism. In the estimation stage, a spatiotemporal LSTM-GNN-based model equipped with Monte Carlo dropout executes multisample perturbation passes on identical inputs, whereas physics-consistency constraints enforce power-flow feasibility. In the detection stage, a detection index coupling mean shift and uncertainty expansion is introduced, with thresholds obtained via statistical calibration and perturbation-response bounds to ensure detectability without excessive false alarms. In the feedback stage, the dropout rate and the sampling density are adapted online in response to the detection statistics, amplifying attack signatures under anomalies and attenuating perturbations in normal scenarios to preserve estimation accuracy. Case studies on the standard test systems demonstrate consistently higher detection rates, lower false-alarm rates, and online latency compatible with operational requirements against single-snapshot, temporally optimal, and spatiotemporally coordinated FDIAs, without additional hardware investment. The results indicate that integrating physics consistency with actively controllable uncertainty offers a practical pathway toward enhancing the functional safety and resilience of SE.

Online estimation of region inertia is critical for frequency stability analysis and control in large-scale power systems. The fixed area division scheme for traditional region inertia estimation struggles to maintain the consistency of the dynamic response of bus frequencies within the evaluation region. To this end, this paper proposes a novel online region inertia estimation method founded on dynamic division principles. To accurately identify the frequency dynamic characteristics and reasonably divide the regions, we introduce a clustering method based on the amerced derivative dynamic time warping (ADDTW) indicator. The proposed new ADDTW effectively quantifies the fuzzy differences of the frequency spatial-temporal features. Then, to obtain the accurate center of inertia (COI) frequency in realtime during the inertia estimation process, the concept of the center range of inertia (CROI) frequency is introduced. It highly approximates the COI frequency using the shape-based distance (SBD) method and correction operations. Subsequently, to reduce the identification operation of disturbances in region inertia estimation and mitigate the impact of the power-frequency asynchronism phenomenon, we introduce a two-stage region inertia online estimation method, including the differential swing equation and data processing. Case studies conducted on a modified IEEE 145-bus system validate the effectiveness and robustness of the proposed method.

Carbon-intensity signals are increasingly incorporated into renewable-microgrid scheduling and carbon accounting, making their integrity relevant to both physical operation and low-carbon settlement. This study investigates time-sparse manipulation of imported-electricity carbon intensity in a network-constrained energy management system. We show that corrupted carbon information can induce a different but electrically feasible dispatch without introducing a deterministic signature into an electricity-only feasibility residual, revealing a cross-domain monitoring blind spot. By evaluating true and reported carbon accounts on the same realized dispatch, we derive an exact local quadratic law for settlement distortion and develop a carbon cyber-leverage metric and a network-aware global bound for exposure assessment. A sparse co-verification method further combines authenticated observations, independent temporal evidence, and data-calibrated uncertainty to recover compromised carbon signals. Tests on SimBench and SMART-DS show that modifying four of 24 carbon-intensity entries by at most 18% understates daily emissions by 4.44% and 4.54%, while nonlinear power flows remain feasible. Across 40 noisy attacked-day realizations, co-verification achieved 100% support recovery and reduced mean absolute settlement distortion by 92.4% and 93.1% in the two systems. The results show that carbon-intensity integrity affects both network-constrained dispatch and carbon settlement, making reliable carbon information an important consideration for resilient, carbon-aware microgrid operation.

With the increasing integration of cyber-physical systems (CPS) in smart grids, state estimation based on hybrid supervisory control and data acquisition (SCADA) and wide area measurement systems (WAMS) measurement has significantly enhanced observability and accuracy . However, this integration also exposes the power system to more sophisticated cyber threats, particularly coordinated false data injection attacks (FDIAs), which can bypass traditional bad data detection (BDD) mechanisms by collaborative tampering measurements. This paper investigates hybrid SCADA/WAMS measurement systems to elucidate their susceptibility to coordinated FDIA and proposes a robust detection framework towards the FDIA. First, from the attacker’s perspective, a FDIA vector is constructed based on a hybrid measurement state estimation model employing the weighted least squares (WLS) method, designed to maximize attack impact while evading detection. Second, from the defender’s perspective, to address the detection of coordinated FDIA, a graph attention network (GAT)-based detection model is proposed, integrating grid topology and measurement features for high-precision attack identification. Finally, comprehensive case studies are conducted to verify the feasibility of the coordinated attack strategy and the effectiveness of the detection model. Performance and sensitivity analyses are conducted, and model interpretability is corroborated through attention weight visualization.

ABSTRACT With increasing renewable energy penetration and more frequent extreme weather events, fault occurrences in distribution networks (DNs) have risen significantly, highlighting the urgent need to enhance distribution system resilience. However, existing fault recovery strategies are constrained by the lack of a coordinated scheduling mechanism across multiple resource types. To address this limitation, this paper proposes a source–grid–load (SGL) coordinated resilience enhancement strategy that leverages the spatiotemporal flexibility of data centre (DC) resources. A comprehensive SGL scheduling framework is established: on the source side, a mobile emergency generator (MEG) dispatch model is developed for rapid active power support; on the grid side, a coordinated optimisation model for network reconfiguration and islanding is formulated to enhance topological adaptability; on the load side, a DC workload migration model is proposed to flexibly regulate demand. A multiobjective optimisation problem is then constructed to minimise load shedding and DC operating costs, which is linearised and convexified for tractable solving. Case studies conducted on modified IEEE 33‐bus and PG&E 69‐bus systems under various fault scenarios validate the proposed method. Comparative results show that the SGL‐coordinated strategy significantly improves DN resilience and operational efficiency.

In traditional power system analysis, the decoupling of physical power flow and environmental attributes leads to the ambiguous definition of carbon responsibility and the misalignment between market trading and physical constraints. To address these challenges, this paper proposes a multi-agent collaborative dispatch framework based on electro-carbon coupling (ECC) theory. Firstly, the measurement model of generalized carbon emission flow (CEF) is established, utilizing a graph-theoretic topological sorting algorithm to overcome the computational bottleneck in large-scale networks and achieve accurate real-time carbon traceability. Secondly, to solve the deviation between commercial trading and physical transmission capacity, a green certificate validity verification mechanism and stepped carbon price model based on the carbon flow consistency index (CFCI) are introduced. To further bridge the timescale mismatch between market clearing and real-time operation, and aiming at the non-convexity of physics-market coupling constraints, a multi-time scale low-carbon dispatch strategy based on multi-agent deep reinforcement learning (MADRL) is proposed. The strategy innovatively quantifies the carbon responsibility time-shifting value of energy storage. The case study based on an integrated IEEE 14-bus transmission and 33-bus distribution system shows that the proposed framework effectively suppresses nominal-physical carbon mismatch, improves the overall low-carbon cost-effectiveness of the system, and verifies the effectiveness of energy storage in spatiotemporal carbon shifting.

The intricate coupling of meteorological volatility, decarbonization mandates, and communication irregularities significantly complicates power system risk assessment, yet a unified framework to model these interactions remains elusive. To bridge this gap, this paper develops a causality-aware spatiotemporal graph state-space model (GSSM) tailored for the coupled weather-power-carbon nexus. The proposed method explicitly aligns graph signals across three heterogeneous layers by employing semantic channel mapping. Directed, time-lagged interactions are captured via coupling matrices, where the underlying topology and intensity are quantified using transfer entropy. Distinctively, communication states are treated as exogenous security variables impacting observation and control channels, which allows for a robust distinction between benign natural degradation and malicious adversarial attacks. This architecture facilitates real-time diagnosis under diverse stress scenarios ranging from extreme weather and carbon-price shifts to cyber-physical disruptions. Empirical validation on IEEE 14-bus and 118-bus systems verified the event discrimination and detection performance through specialized situational indexes.

The integration of large-scale inverter-based resources into power systems has led to reduced system inertia levels and increased spatial heterogeneity in inertia distribution. Conventional system-level inertia estimation methods are inadequate for assessing inertia with spatial distribution characteristics. This paper proposes a node-level inertia index evaluation method based on robust regression. First, a node-level inertia index is introduced and its dynamic properties are analyzed. Then, a robust regression-based estimation approach is developed to effectively evaluate the spatial distribution of inertia while mitigating the influence of outliers. Finally, the effectiveness and robustness of the proposed method are validated through tests on the IEEE 39-bus system and a provincial-level interconnected grid.

the scale of multiprocessor systems constantly increasing, the large number of interconnected processors (or nodes) makes faulty nodes inevitable. The fault diagnosis of multiprocessor systems therefore is a key technique for the system's robustness. In this paper, we first propose a novel diagnostic metric, the h-extra r-component diagnosability, denoted ECDrh (G), which characterizes one special pattern of faults. We derive some theoretical results for the ECD of hypercube, denoted ECDrh(Q(n)), under the PMC model. Diagnostic algorithms is proposed and implemented to detect faulty nodes that will disconnect hypercube Q(n) into r components each containing at least h + 1 nodes. We also test the ECD-PMC algorithm to the hypercube network with different number of faulty processors satisfying the h-extra r-component condition. Extensive simulation results show that our proposed method achieves very good performance in terms of ACCR, TPR, FPR, and TNR.

To adapt to the multi-dimensional uncertainties of the new-type power system, online security defense decision-making quantifies, decomposes, and compresses the defense decision-making criteria traditionally applied on a long-time scale into the real-time scale. Its data scale and execution speed exceed the feasible scope of manual inspection in traditional offline strategies, thus necessitating the establishment of an automated closed-loop detection mechanism to conduct quantitative evaluation on the trustworthiness of decision-making results. Therefore, this paper proposes a characterization system for the trustworthiness of decision-making closed-loop for the online security and stability defense decision-making system, providing a scientific and quantitative basis for improving the safety and reliability of online complex systems.

The increasing penetration of renewable resources and the deepening integration of multi-energy systems are transforming conventional power infrastructures into cyber-physical energy systems (CPES) that rely on distributed, data-driven and self-optimizing operation. As data flow across sensing, communication, control, and market layers, the security of data interactions has become a decisive factor for ensuring system stability and maintaining market reliability. Based on existing review studies that have provided valuable insights into specific system layers, attack categories, and defense techniques, this review presents a structured synthesis of exogenous threats, endogenous vulnerabilities, and resilience-oriented defense pathways for data-interaction security in renewable-dominated CPES. The mechanisms of data propagation and interaction within horizontal sensing processes, vertical control hierarchies, and market-level exchanges are first clarified. Major external threats are then examined, including measurement tampering, communication interference, model manipulation, coordinated data poisoning, and market intervention, together with their associated risk-amplification mechanisms. Building on this analysis, seven categories of endogenous vulnerabilities are defined to reveal the root causes of insecure data interaction. To mitigate these risks, a five-layer defense framework is proposed, integrating lightweight authentication, collaborative anomaly detection, interpretable and adversarially robust artificial intelligence (AI) models, system recovery mechanisms, and secure market feedback. Finally, research prospects are outlined in secure data management, trustworthy AI, cross-domain collaborative defense and standardized data-governance frameworks for CPES.

Modern power systems have evolved into cyber-physical power systems (CPPSs) requiring high-resolution spatial-temporal state awareness, driving the adoption of hybrid measurement-based state estimation (SE). However, such advancements introduce heightened cybersecurity requirements that demand systematic investigations from adversarial perspectives. This paper establishes a comprehensive attacker-defender framework with dual contributions. From the attacker's perspective, this paper proposes a multi-snapshot coordinated false data injection attack (MS-FDIA) strategy against hybrid measurement-based SE. The proposed attack model can effectively bypass both hybrid measurement synchronization checks and temporal data anomaly detection mechanisms, thereby achieving enhanced stealth and operational impact. From the defender's perspective, this paper develops a dynamic trusted phasor measurement unit (PMU) configuration scheme that adaptively reconfigures secure measurement matrix subsets against evolving multistage attacks. The defense mechanism is solved through two complementary approaches: a numerical algorithm based on matrix row transformations and a deep reinforcement learning (DRL)-based optimization method with temporal awareness. Comprehensive case studies on different standard test systems demonstrate the improved MS-FDIA mitigation capabilities and the defense scheme's effectiveness, and the test results reveal the matrix transformation algorithm's superiority in small-scale systems versus DRL's scalability advantages for large networks.