Normal and fault critical state vector sets in the power system state vector space facilitate research on system state evaluation, state screening and operational reliability analysis. Focusing on this state vector space, this study decomposes the system into the G-subsystem and L-subsystem to realize dimensionality reduction. It systematically investigates the properties of critical state vectors and related algorithms, and presents a method to identify critical state vector sets, which helps accelerate the calculation of power system reliability indices. Under the assumption that the L-subsystem is fully reliable, we derive the closed-form optimal value of the direct current optimal power flow model for the G-subsystem without numerical computation. Subsequently, the state vector spaces of both subsystems are reduced to obtain reduced regions covering all corresponding critical state vector sets. This paper presents an equivalent characterization for these sets and develops a search algorithm to locate critical state vectors. Furthermore, the invariance of fault critical state vectors is proven: each fault critical state vector of the subsystems can generate one corresponding fault critical state vector of the entire power system. Finally, an evaluation algorithm is established based on fault critical state vector sets. Numerical tests on standard test systems and a practical regional power system illustrate the performance of the presented method.

Reliability-constrained economic dispatch (RCED) requires evaluating multiple contingencies, but the number of possible combinations grows exponentially with system size. Traditional $\mathrm{N}-\mathrm{k}$ enumeration, such as $\mathrm{N}-2$, limits contingency order but cannot distinguish probability differences, which may lead to omitting important high-probability states. Existing probability-based selection methods also suffer from inefficient state generation in large systems. This paper proposes a Fast State Screening Method (FSSM) that constructs contingency states in a strictly ordered manner and uses a simple successor rule to generate at most two states. This enables efficient identification of the most probable contingencies and reduces the scale of the RCED model. Case studies show that FSSM significantly improves the computational efficiency of RCED while maintaining an accurate representation of system reliability.

The rapid development of wind energy in the power sectors raises the question about the reliability of wind turbines for power system planning and operation. The electrical subsystem of wind turbines (ESWT), which is one of the most vulnerable parts of the wind turbine, is investigated in this paper. The hygrothermal aging of power electronic devices (PEDs) is modeled for the first time in the comprehensive reliability evaluation of ESWT, by using a novel stationary "circuit-like" approach. First, the failure mechanism of the hygrothermal aging, which includes the solder layer fatigue damage and packaging material performance degradation, is explained. Then, a moisture diffusion resistance concept and a hygrothermal equivalent circuit are proposed to quantitate the hygrothermal aging behavior. A conditional probability function is developed to calculate the time-varying failure rate of PEDs. At last, the stochastic renewal process is simulated to evaluate the reliability for ESWT through the sequential Monte Carlo simulation, in which failure, repair, and replacement states of devices are all included. The effectiveness of our proposed reliability evaluation method is verified on an ESWT in a 2 MW wind turbine use time series data collected from a wind farm in China.

Cloud-edge collaboration enables virtual power plants (VPPs) to efficiently manage demand-side resources (DSRs). However, it also exposes VPPs to the threat of edge server distributed denial of service (DDoS) attacks, which can undermine the dispatchable power capability of a VPP by exhausting its computational resources. This article formulates an emergency computation offloading model to guide the collaboration between cloud servers and edge servers to maximize the dispatchable power of VPP. The model identifies analytically the range of attack intensities where a VPP can maintain full dispatchable power and where the VPP cannot. It also uncovers the convexity property of VPP’s dispatchable power. The proposed model is submodular so that an efficient submodular optimization algorithm can be developed to alleviate the curse of dimensionality inherent in the computation offloading problem. Numerical studies were carried out on the VPP with 9,951 DSRs to validate the effectiveness of the proposed method. A small-scale VPP was also selected to show that the proposed method offers comparable performance, but much less computational cost, to deep reinforcement learning methods.

The integration of information and communication technologies is transforming traditional distribution networks into cyber-physical distribution systems (CPDSs). A key challenge is the unified evaluation of multi-source cyber risks and their cascading impact on physical power supply reliability. Existing planning models often become computationally intractable when attempting to capture this intricate relationship. To address this, a novel reliability-oriented cyber-physical coordinated planning framework is proposed. A unified model is first developed to evaluate information link performance under multi-source cyber risks, from which a composite link invulnerability index is derived. Based on this index, an optimization-based reliability evaluation model is established by mapping information link invulnerability to fault isolation and load transfer durations. Finally, the reliability model is embedded into a coordinated planning framework to jointly optimize physical device deployment and the topology of a two-layer wireless-fiber hybrid cyber network. Case studies show that the proposed framework reduces annual EENS by up to 7.8456 MWh compared with single-cyber-risk-based planning, de creases planning computation time by more than 50% compared with planning using the minimal path-based reliability evaluation, and achieves 12.81% investment cost savings while further reduc ing annual EENS by 9.4022 MWh under multi-source cyber risks compared with a fiber-only cyber network. These results demon strate that the proposed framework enables cost-effective and re liability-oriented cyber-physical coordinated planning.

Power system reliability assessment, which seeks to estimate the average impact of system states across the entire state space, is critical for system operation. Existing methods either neglect the mathematical structure of the state space or overlook the similarity between states, thus facing computational bottlenecks regarding evaluation efficiency and accuracy. To overcome these bottlenecks, we propose a state-similarity-based lattice space partitioning and reliability analysis method, termed SS-Dichotomy-FMCS, which linearizes over 95% of power flow calculations, thereby rapidly accomplishing state space partitioning and reliability assessment. Furthermore, to handle load fluctuations, we design the Adaptive Lattice Space Inheritance Strategy (ALSIS) that leverages intrinsic state space correlations across load levels to avoid repeated partitioning. Experiments on RBTS and RTS-79 systems demonstrate that the proposed methods maintains high accuracy (error <= 0.3%) while achieving 50-175 & times; higher computational efficiency than traditional methods.

The large-scale integration of wind power significantly reduces system inertia, resulting in deteriorated frequency dynamic performance during power disturbances caused by generator failures. This threatens the stable operation of frequency-sensitive synchronous units and, in turn, impacts system reliability. Thus, a coordinated frequency regulation model for DFIG wind turbines and energy storage systems considering frequency stability constraints is proposed in this paper, aiming to enhance the operational reliability of power systems with high wind power penetration. First, an active power frequency response model of the DFIG wind turbine is established, and its rapid power regulation capability is explored through an optimized power point tracking (OPPT) method. Furthermore, frequency stability constraints are introduced to guide the analysis of the system's dynamic frequency security boundaries, and a coordinated active power response mechanism between wind turbines and energy storage systems is constructed to ensure fast adjustment and stable operation during frequency fluctuations. Simulation results on the RTS79 system verify the effectiveness of the proposed model in improving system reliability.

The form of hybrid AC/DC is a trend in power distribution systems. The resilience against extreme weather depends on the coordination of cyber and physical systems. Therefore, it is necessary to study the post-disaster recovery of AC/ DC hybrid cyber-physical distribution systems (CPDSs). Voltage source converters (VSCs) are critical cyber-physical devices in hybrid AC/DC distribution systems (HDSs) that offer flexibility in post-disaster recovery. However, existing literature on the role of VSC commonly ignores the unreliable communication. In this paper, we quantify the impact of communication failures on VSCs and propose an adaptive switching model of VSC control modes that enhances both the emergency islanding and service restoration phases of post-disaster recovery. This paper also introduces a scheduling model of multi-type repair resources including power failure repair crews, communication failure repair crews, and emergency communication vehicles for joint the restoration of CPDSs. The system recovery model is also presented. Finally, a novel optimization framework combining adaptive switching of VSC control modes, scheduling of multi-type repair resources, and system recovery is proposed to improve the post-disaster recovery efficiency. The effectiveness and superiority of the proposed framework are demonstrated through numerical experiments in a modified IEEE 123-bus system.

Probalistic energy flow (PEF) analysis is an essential tool for assessing the impact of uncertainties on the steady-state operation of integrated electricity-gas systems (IEGS). Existing PEF studies primarily focus on the aleatory uncertainties in input variables, which are commonly represented by precise probability distributions. However, epistemic uncertainties arising from limited data and the resulting incomplete knowledge are often neglected, potentially leading to bias in risk assessment. Moreover, computationally efficient PEF analysis remains challenging when a large number of uncertain inputs are involved, due to the high computational burden of conventional methods. To address these issues, this paper proposes a data-driven PEF method for IEGS under mixed aleatory and epistemic uncertainties. An interval probability model based on bootstrap sampling is developed to characterize the uncertainties without strong prior assumptions. On this basis, arbitrary polynomial chaos (aPC) is employed to propagate uncertainties using the generated datasets. To alleviate its dimensionality issue, a compressive sensing model based on l(1)-l(2) minimization is adopted to construct a sparse aPC representation. Moreover, an adaptive sparse strategy is further developed to determine an appropriate sparsity level considering the different nonlinear properties of subsystems. Case studies demonstrate that the proposed method improves the computational efficiency of PEF analysis, while maintaining accurate risk assessment.

Battery energy storage systems (BESS) could enhance the reliability of renewable energy-dominated power systems. However, they also expose power systems to the risks of catastrophic safety incidents like thermal runaway, fires, and explosions. To address this issue, this paper proposes a reliability evaluation model for power systems considering the state of safety (SoS) of BESS. First, a generalized Pareto distribution-based scenario generation method is presented to capture the variability of renewable energies. Then, the SoS constraint is derived based on the scenario and system operational parameters. Finally, the SoS constraint is included into the reliability evaluation model for power systems. Case studies based on a modified IEEE 30-bus system demonstrate that the proposed model can efficiently reflect the risks related to BESS and provide more accurate reliability evaluation results.

Contingency screening is a crucial step in reliability assessment, risk-constrained dispatch, and stability control of power systems. The increasing integration of renewable energy has made the rapid identification of high-impact contingencies more challenging because of the associated operating uncertainty. To address this issue, this paper proposes an efficient contingency screening method (ECSM) based on component severity quantification. First, a component severity quantification scheme is developed by integrating component failure probabilities and component importance factors that reflect the impacts of component outages on system power-supply capability. Accordingly, state severity coefficients are calculated to quantify the impact of each contingency on the system. Furthermore, the ECSM ranks contingencies in descending order of their state severity coefficients. The core of the ECSM is an enhanced neighborhood state generation rule, which ensures that states can be searched without repetition or omission. Case studies validate the efficiency and effectiveness of the ECSM in screening high-impact contingencies.

The increasing integration of wireless communication technologies enables virtual power plants (VPPs) to coordinate distributed energy resources efficiently. However, it introduces communication uncertainties that may significantly degrade the operational reliability of VPPs. Existing VPP reliability assessment methods mainly focus on the interactions between physical components and wired communications, which cannot capture the time-varying characteristics of wireless communications. To fill this gap, this paper develops an operational reliability evaluation method for VPPs considering communication uncertainties. A stochastic communication model capturing equipment failures, signal collisions, and bandwidth constraints is established and integrated into the state analysis model via an optimal information flow formulation. An improved uniform design-based sampling scheme is then proposed to generate representative system states with near space-filling properties and polynomial computational complexity. Furthermore, a Rayleigh-Ritz-based analytical dynamic reliability model is developed to directly compute time-dependent reliability indices without repeated sequential simulations. Case studies demonstrate that the proposed method achieves near-enumeration accuracy while reducing computational time by more than 95% compared with Monte Carlo methods. The results also reveal that neglecting communication uncertainties leads to systematically biased reliability assessments.

Extreme rainstorms can trigger secondary flooding, causing cascading failures in power distribution networks (PDNs). Existing restoration strategies primarily focus on weather-induced damage to PDNs and assume complete fault information (FI), i.e., fixed fault locations and repair time. However, they generally neglect the impacts of secondary disasters and incomplete FI under severe cyber failures. This paper introduces a dynamic damage-aware restoration strategy for flooded cyber-physical distribution systems (CPDSs) under incomplete FI. First, a FI perception model under cyber failures is developed. Specifically, a disaster scenario simulation based on the shallow water equations is established to characterize the spatiotemporal damage risk of electrical components during rain storms and flood events. Then, a damage-aware model integrating disaster consequence inversion with drone-assisted inspection is proposed to perceive FI under limited observability. Furthermore, a stochastic repair time model is introduced to capture uncertainty in damage extent and repair processes. Finally, an event-driven and model predictive control-based restoration model is developed to coordinate FI perception, fault repair, and waterlogging evolution, where an improved Floyd algorithm and a restoration coefficient model quantify waterlogging effects, forming a closed-loop perception-restoration co-optimization that adapts to waterlogging-induced traffic disruptions and restrictions. Comparative simulations validate the effectiveness of the proposed strategy.

The integration of distributed renewable energy sources into distribution networks is a key approach to achieving sustainable and low-carbon power systems. However, high renewable penetration significantly increases the volatility and uncertainty of distribution systems, posing challenges to renewable energy accommodation and reliable operation. To address these challenges, active control of distribution networks is required, which in turn relies on accurate system states. In practice, the limited number and accuracy of measurement devices in distribution networks make dynamic state estimation a critical technology for sustainable distribution systems. In this paper, a novel dynamic state estimation method for sustainable distribution systems is proposed, incorporating spatiotemporal data correlation and adaptiveness to process and measurement noise. A CNN-BiGRU-Attention model is developed to reconstruct high-accuracy real-time pseudo-measurements, compensating for insufficient sensing infrastructure. Furthermore, a noise adaptive dynamic state estimation method is proposed based on an improved unscented Kalman filter. An amplitude modulation factor (AMF) is applied to track time-varying process noise, while an evaluation method based on robust Mahalanobis distance (RMD) is embedded to deal with non-Gaussian measurement noise. Finally, simulation studies on the IEEE 33-bus three-phase unbalanced distribution network demonstrate the effectiveness and robustness of the proposed method.

Public wireless communication networks enable power systems to manage demand-side resources (DSRs) efficiently. However, such networks are also vulnerable to random communication disruptions caused by cyberattacks or device faults. These disruptions may lead to the loss of control over large numbers of DSRs, thereby increasing the risk of frequency instability. To address this issue, this paper proposes a local-centralized collaborative control method for DSRs. First, the random characteristics of communication disruptions are incorporated into the frequency dynamic model of power systems with DSRs. Second, unlike existing research that relies on static local control, an adaptive stochastic local control strategy is introduced to guide the responses of DSRs when communication is unavailable. The aggregated behavior of these DSRs is then estimated and leveraged to centrally control the remaining DSRs, thereby avoiding uncoordinated or conflicting actions. Furthermore, a communication disruption threshold is defined to quantify the maximum level of disruption that does not impair the frequency performance. The effectiveness of the proposed method is validated through case studies under various disruption scenarios.

End-consumers, as the primary drivers of carbon emissions, are receiving increasing attention for decarbonization of energy systems. Most of the existing studies on carbon pricing overlook the impact of energy consumption behavior of consumers and fail to leverage the potential of demand-sides to achieve greater carbon emission reductions. This paper proposes a low-carbon demand response (LCDR) framework for decarbonization of power-hydrogen integrated energy systems (PH-IESs) and an equitable allocation of carbon responsibility to various types of consumers. A consumer-based carbon pricing strategy with improved marginal carbon intensity is first developed to quantify the impact of the amount and behavior of energy consumption on carbon responsibility and costs. Then, a consumer-based LCDR model is proposed for demand-side energy aggregators (DSEAs) who adjust flexible loads to reduce operation costs and carbon emissions based on the determined carbon price. Finally, a low-carbon operation model is formulated to schedule the PH-IESs considering the responses of DSEAs. To capture renewable uncertainties and reduce decision conservatism, distributionally robust joint chance constraints are established capitalizing on heterogeneous information (i.e., moment, unimodality, and mode skewness). Case studies verify the effectiveness of the proposed LCDR framework.

Incorporating reliability constraints in economic dispatch is challenging considering massive system states resulting from random component failures and renewable energy (RE) uncertainties. Traditionally, only N-1 or N-2 failures are considered to reduce complexity, and the consequence is remarkable accuracy losses. This paper aims to achieve low complexity and precise characterization of reliability constraints with fewer system states. First, the initial system state space is constructed, and the limit state function is proposed to define the boundary between reliable and unreliable domains. Then, the limit state function is converted to constraints on a particular set of system states defined as limit system states (LSS). Moreover, by revealing the distribution regulations of system states, the “worst of the best” principle is proposed to identify LSS. In the first step, a chance-constrained optimal power flow model is established to screen the better system states (BSS) considering RE uncertainties. In the second step, the worst ones among the BSS are targeted based on the capacity of failed components and the tolerance to RE uncertainties. Finally, the reliability constraint is converted to the condition that none of the LSS suffers load loss, which is convenient to formulate and incorporate in the dispatch model. Case studies have been conducted to verify the validity of the proposed methods.

The large-scale integration of renewable energy has intensified the electricity market price fluctuation and encouraged strategic offering behaviors of generation companies (GenCos), including capacity withholding. This paper systematically investigates the load shedding risk driven by both physical outage and capacity withholding. First, a data-driven multi-state reliability model of generators is proposed to quantify the available capacity of power systems. Then, a novel load shedding risk assessment and responsibility allocation framework is proposed to quantify the load shedding risk and the corresponding responsibility of GenCos. Furthermore, to address the curse of dimensionality, a novel physics-informed neural networks (PINNs)-based load shedding risk assessment method is introduced. This approach significantly reduces the computation burden while enabling dynamic load shedding risk assessment and responsibility allocation that account for strategic offering behaviors. Finally, a modified IEEE 30-bus system is developed to validate the effectiveness of the proposed approach.