The growing penetration of renewable energy sources (RESs) has increased the operational uncertainty of distribution networks. The impact of high-impact, low-probability extreme weather events on distribution networks is receiving increasing attention. To quantify the resilience level of renewable-integrated distribution networks under typhoon disasters, a resilience assessment framework considering emergency response and crew dispatch is proposed. First, a component failure model of renewable-integrated distribution networks is established to characterize the impact of the typhoon's spatiotemporal evolution on the system. Second, an intra-disaster network reconfiguration model and a post-disaster emergency crew dispatch model are proposed to simulate the system response behavior throughout the disaster. Finally, a set of metrics is defined to quantify the resilience of distribution networks and the impact of RESs against typhoon disasters. The proposed framework is validated on the IEEE 33-bus test feeder to verify the effectiveness of the assessment method and metrics.

Increasingly frequent extreme weather events pose significant risks of large-scale blackouts and substantial economic losses to power systems and electricity customers. In recent years, resilience insurance has emerged as an effective risk management tool to address this challenge. However, despite sufficient premium contributions from electricity customers, current insurance schemes may still expose insurance companies to high financial risks due to extreme tail events, thus demotivating them from entering the market. To this end, this paper develops a novel actuarial risk management framework consisting of risk assessment and insurance design to hedge against weather-induced catastrophe risks in transmission systems (TSs). Specifically, in the risk assessment phase, cascading failures and the aging effects of transmission lines, factors that exacerbate the heavy-tailed characteristics of weather-induced catastrophe risks, are comprehensively considered. A multi-stakeholder resilience insurance scheme is further designed, introducing reinsurance policies for the first time to alleviate insurers' financial burden, with the optimal retention derived from a risk-return Nash bargaining game. Numerical experiments on the modified IEEE 30-bus test system verify that the proposed method enables more accurate assessments for weather-induced catastrophe risks in TSs. Additionally, it helps mitigate insurers' insolvency risks while maintaining affordable premiums. Furthermore, the Nash bargaining game proves effective in helping insurers balance risk and return in decision-making. Finally, the proposed risk management framework exhibits excellent scalability when applied to large-scale real-world systems.

Extreme weather-driven cascading failures (CFs) in power systems can lead to catastrophic socioeconomic losses, yet integrating CF analysis directly into day-ahead proactive unit commitment (UC) is mathematically intractable. This difficulty arises from representing decision-dependent topology evolution within a tractable UC formulation. To address this challenge, a resilient UC framework is proposed, featuring a data-driven surrogate that encodes CF risks into a tractable polyhedral region. First, overload-induced CF simulations are performed offline across diverse commitment and dispatch states under contingencies. To capture nonlinear CF boundaries in the system's discrete-continuous operating space, a sequential training strategy is employed to construct a surrogate consisting of a series of linear classifiers. This surrogate identifies a polyhedral region with low CF risk, which can be directly integrated into the UC model as linear constraints for CF-aware decision-making. Case studies show that the proposed strategy significantly reduces the expected loss of load by proactively mitigating CF risks with only a marginal increase in operating costs, offering a streamlined yet effective pathway for enhancing power system resilience.

The energy storage self-scheduling (ESSS) problem is typically formulated as a mixed-integer linear programming (MILP) or quadratically constrained programming (QCP) model, reflecting the mutually exclusive nature of charging and discharging. However, as the problem scale increases, these formulations impose significant computational burdens, limiting their practical application. To tackle this challenge, this letter proposes a novel power decomposition (PD) model and an exact greedy (EG) algorithm for efficiently solving the ESSS problem with guaranteed accuracy. Numerical results demonstrate the superior computational efficiency of the proposed PD model and EG algorithm compared with the MILP and QCP models.

Typhoons, among the most destructive extreme weather events, pose an increasing threat to the operational reliability and economic stability of power systems. While power catastrophe insurance has emerged as an effective supplement to traditional risk mitigation strategies, existing schemes are typically utility-centric and overlook the financial vulnerability of end users. Furthermore, the quantitative evaluation and trade-off of fairness in premium pricing remain critical yet unresolved challenges. To address these gaps, this paper proposes a novel customer-oriented and equity-aware catastrophe insurance scheme for typhoon risk management in power systems. To overcome historical data scarcity, an advanced Markov chains with kernel density estimation (KDEMC)-based synthetic typhoon simulation method is employed to generate high-fidelity typhoon scenarios, thereby facilitating subsequent probabilistic resilience assessment of power systems. A Gini coefficient-based fair premium pricing approach is developed to strike a balance between actuarial fairness and social equity in premium pricing, with optimal premium schemes derived via the NSGA-II algorithm. A comprehensive case study in Hong Kong validates the practical feasibility of the proposed scheme and clearly demonstrates its equitable and affordable premium schemes. This study establishes the first systematic methodology for customer-oriented catastrophe insurance in power systems, offering valuable insights and practical guidance for stakeholders in other typhoon-prone regions.

Maintaining a sufficient short-circuit ratio (SCR) is essential for the secure operation of high-voltage direct-current (HVDC) sending-end grids, particularly for mitigating transient overvoltages following DC-blocking faults. However, incorporating SCR requirements into unit commitment (UC) remains computationally challenging because rigorous SCR evaluation requires the inversion of a decision-dependent network admittance matrix, resulting in an implicit coupling between UC decisions and grid strength. To address this challenge, this paper proposes a novel SCR-constrained UC framework with a decoupled offline-mapping-to-online-optimization architecture, explicitly embedding grid strength requirements into system scheduling. Specifically, a combinatorial encoding technique is developed to establish an exact offline mapping between UC schemes and their corresponding short-circuit capacities (SCCs), thereby reformulating the implicit nonlinear SCR constraints into exact mixed-integer linear constraints. Numerical results demonstrate the effectiveness of the proposed framework and confirm that it preserves the standard MILP formulation of UC, enabling seamless integration into existing industrial UC frameworks.

Solving the AC optimal power flow (AC OPF) problem poses significant challenges in power system operations because of its inherent nonlinearity and complexity. This paper introduces a novel strategy to solve the AC OPF problem by utilizing a new problem decomposition framework combined with reinforcement learning (RL)-based cutting planes. The problem is decomposed into two sub-problems, DC OPF and AC power flow (AC PF) calculation sub-problems. To yield the AC-feasible solution, linear inequality constraints (i.e., cuts) are obtained by an RL agent and added into the DC OPF sub-problem. Then, the AC PF calculation is performed using the solution to the DC OPF sub-problem (i.e., power generation profiles) and voltage magnitude reference values, which is the output of the RL agent. Additionally, the action selection method is employed for the RL agent’s training efficiency. Case studies under various simulation scenarios are conducted to show the effectiveness of the proposed strategy compared to the conventional strategies. The simulation results indicate that the proposed strategy significantly enhances computational efficiency and solution feasibility compared to the conventional methods.

Grid interconnection is a key strategy for strengthening power system resilience to extreme weather events by facilitating intersystem mutual assistance. Despite the overall reduction in risk exposure, significant residual risks remain that could still lead to catastrophic consequences. While insurance offers a means to transfer these risks, conventional standalone models struggle to balance insurer solvency with premium affordability and fail to incentivize participation from lower risk areas. Inspired by spatial risk diversification, this article proposes a novel coalitional insurance framework for weather-related risk management of interconnected transmission systems (ITS). The framework is built on a joint resilience assessment model that quantifies power outage risks in ITS, accounting for intersystem mutual assistance. To solve this model with guaranteed convergence and well-preserved privacy, a distributed optimization approach based on the Bregman alternating direction method of multipliers and iterative optimization is developed. Furthermore, specially designed exante premium and expost indemnity policies ensure equitable allocation and promote coalition participation. Numerical experiments on the IEEE RTS-96 system validate the effectiveness and superiority of the proposed coalitional insurance scheme.

Due to the increasing penetration of renewable power in the power grid, primary frequency regulation (PFR) resources are severely constrained, which threatens the operational safety of the power grid. Consequently, the PFR capability of coal-fired power plants, which have a decreasing share of installed capacity within the power grid, is of paramount importance. The PFR capability of coal-fired power plants tends to degenerate and the prediction error of the PFR model increases progressively under deep peak-shaving conditions. To reveal the degradation mechanism, both the steady-state and dynamic thermal storage characteristics were examined. As the load decreases from 75 % to 20 %, the frequency regulation time, maximum, and cumulative frequency deviation increase by 52.4 %, 287.0 % and 376.0 %, respectively, and the steady-state total thermal and exergy storage of the unit decrease by 111.0 GJ and 49.8 GJ, respectively. Moreover, during the step response of the high-pressure control valve, the transient release capacity of the thermal and exergy storage was substantially weakened by 73.4 %, ultimately contributing to the degradation of PFR capability. To enhance the prediction accuracy of the PFR capability under various conditions, a PFR margin prediction model was developed by integrating mechanism-driven and data-driven approaches, thereby improving both accuracy and efficiency, considering the variation in both live steam flow rate and work done per unit mass of live steam. The comprehensive prediction errors were reduced by 95.6 % compared to the standard model-based approach.

This paper studies the robust co-planning of proactive network hardening and mobile hydrogen energy resources (MHERs) scheduling, which is to enhance the resilience of power distribution network (PDN) against the disastrous events. A decision-dependent robust optimization model is formulated with min-max resilience constraint and discrete recourse structure, which helps achieve the load survivability target considering endogenous uncertainties. Different from the traditional model with a fixed uncertainty set, we adopt a dynamic representation that explicitly captures the endogenous uncertainties of network contingency as well as the available hydrogen storage levels of MHERs, which induces a decision-dependent uncertainty (DDU) set. Also, the multi-period adaptive routing and energy scheduling of MHERs are modeled as a mixed-integer recourse problem for further decreasing the resilience cost. Then, a nested parametric column-and-constraint generation (N-PC CG) algorithm is customized and developed to solve this challenging formulation. By leveraging the structural property of the DDU set as well as the combination of discrete recourse decisions and the corresponding extreme points, we derive a strengthened solution scheme with nontrivial enhancement strategies to realize efficient and exact computation. Numerical results on 14-bus test system and 56-bus real-world distribution network demonstrate the resilience benefits and economical feasibility of the proposed method under different damage severity levels. Moreover, the enhanced N-PC CG shows a superior solution capability to support prompt decisions for resilient planning with DDU models.

Microgrid formation-based distribution system (DS) restoration is a key strategy for restoring the power supply following extreme events. However, this restoration faces significant challenges when extreme disasters cause communication interruptions alongside power network failures. Such disruptions hinder the timely control and operation of power network of DS enabled by distribution automation. Therefore, the collaborative recovery of the communication network could enhance topology control capability of DS, leading to more effective power restoration. This paper proposes a novel cyber-physical collaborative framework for DS based on space-air-ground emergency communication resources. The proposed method utilizes uncrewed aerial vehicles (UAVs) equipped with emergency communication stations. These aerial relays establish emergency communication links with satellites in the air and ground base stations, thereby restoring the control capability for DSs in communication dead zones. UAVs, leveraging their flexible flight capabilities are dynamically deployed to achieve a sequential and collaborative restoration of communication and power network. To reduce computational complexity, the proposed method is divided into two steps. The first step determines the UAVs’ working sites with the maximum recovered load through topology reconfiguration. The second step schedule the UAVs’ optimal movement paths within their endurance. Moreover, an area division method is introduced to split the large-scale problems to reduce the complexity. Verification on IEEE 123-node test system outlines the efficiency of the proposed scheme.

High penetration of renewable energy sources, such as wind and solar energy, introduces significant uncertainty in power systems and increases the flexibility requirements of the system. To address this issue, this paper proposes a flexible multi-objective unit commitment (FMOUC) optimization model of the power system that simultaneously considers operating cost, renewable energy curtailment, and the flexibility of thermal power units. The augmented ε-constraint method is employed to solve the FMOUC optimization model and obtain the Pareto frontier. Then, the entropy weight double-base-point method is used to determine the most suitable unit commitment strategy. Numerical experiments on a modified 39-bus system demonstrate that the proposed model can effectively improve renewable energy accommodation while reducing operating costs.

Extreme weather conditions can significantly affect the operational resilience of power systems. The resilience assessment of transmission systems has been widely studied as a foundation for resilience planning and operation. However, scenario-based simulation methods often suffer from heavy computational burden and lack intuitive insights into the factors influencing resilience. To address these issues, this paper proposes an explainable spatial-temporal graph attention network (ST-GAT) framework for online resilience evaluation of transmission systems. First, the evolutionary process of the system is modeled as a Markov Decision Process (MDP), with the value function utilized as the resilience metric to quantify the effort required for recovery. Second, we augment the GAT network with the topology coding and temporal convolutional network to efficiently capture spatial-temporal features of systems under extreme events, enabling accurate estimation of resilience metrics. Finally, a gradient-based explanation method is proposed for the critical component identification, thereby offering intuitive guidance for resilience enhancement. Case studies validate the effectiveness of the explainable ST-GAT. Furthermore, the explanation method could highlight key elements influencing resilience assessment outcomes.

Energy storage (ES) is typically modeled as either a mixed-integer linear programming (MILP) problem involving binary variables or a quadratic constraint programming (QCP) problem with complementarity constraints due to the mutually exclusive characteristics of charging and discharging. The MILP model is an NP-hard problem that suffers from the curse of dimensionality. The solution time for QCP problems increases rapidly as the problem scale expands. To address these challenges, this paper proposes the energy storage network flow (ES-NF) model. Initially, the conditional MILP (C-MILP) model is derived from the MILP through variable substitution. Next, the conditional extreme point is introduced and proven equivalent to the extreme point of MILP. The ES-NF model is then established as a directed acyclic state transition diagram. Finally, the network flow algorithms can solve the ES-NF model efficiently. Numerical results indicate that when ES participates in independent scheduling, the proposed model significantly enhances computational efficiency without compromising accuracy. Compared with the MILP and QCP models, the proposed ES-NF model can effectively reduce the average solution time.

High-level penetration of intermittent renewable energy sources (RESs) has introduced significant uncertainties into modern power systems. In order to rapidly and economically respond to the fluctuations of power system operating state, this paper proposes a safe deep reinforcement learning (SDRL) algorithm for the real-time optimal power flow problem. First, this problem is formulated as a Constrained Markov Decision Process model. Second, primal-dual proximal policy optimization (PD-PPO) is proposed to realize adaptively tuned binding effects on policy security constraints while achieving policy enhancement. Utilizing a cost critic network to evaluate policy security, actor gradients are estimated by a Lagrange advantage function derived from economic reward and violation cost critic networks with higher accuracy. Moreover, the performance of the PD-PPO method is further improved with an effective knowledge-driven action masking technique, which explicitly identifies critical action dimensions based on the physical model to encourage the policy in the safety direction with nonconservative exploration. Numerical tests are carried out on the IEEE 9-bus, 30-bus, 118-bus, and ACTIVSg2000 test systems. The results show that the well-trained SDRL agent can significantly improve the computation efficiency while satisfying security constraints and optimality requirements as much as possible.

As modern power systems rapidly evolve into cyber-physical power systems (CPPS), the integration of advanced communication networks introduces significant opportunities alongside critical vulnerabilities. The escalating complexity of CPPS cyber-physical infrastructure heightens susceptibility to extreme events such as cyberattacks and natural disasters, potentially compromising system stability and resilience. Consequently, enhancing CPPS resilience requires addressing not only the physical network layer but also strengthening cyber-network recovery and resistance capabilities. To address this requirement, this paper investigates the role of software-defined networking (SDN) in bolstering CPPS resilience. Specifically, we examine how SDN provides key resilience-enabling attributes—including recoverability, flexibility, scalability, and adaptive network control—that stem from its centralized architecture. This architecture enables dynamic resource allocation and rapid fault detection, capabilities critical for maintaining system performance during cross-layer threats. Then, we review existing SDN applications in power systems, highlighting implementations for real-time monitoring, fault isolation, and resource optimization that demonstrate SDN's viability for CPPS resilience enhancement. Through analysis of current research and future trends, this paper underscores SDN's potential to substantially improve CPPS resilience, enabling more effective disruption resistance and recovery to ensure continuous, secure power supply. Finally, we discuss integration challenges and potential solutions, outlining open issues and future research directions.

recent years, renewable energy sources (RESs) have been increasingly integrated into power systems to address energy crises and environmental concerns. However, the inherent uncertainty and volatility of RESs pose significant challenges to the secure and cost-effective operation of power systems, such as increased risk of curtailment and supply shortages. Enhancing power system flexibility is an effective way to address these challenges. However, existing studies on flexibility primarily focus on its evaluation, while limited research has considered incorporating flexibility directly into scheduling models. To address this issue, this paper proposes a day-ahead scheduling model with flexibility chance constraints (DASFCC), driven by wind power forecast errors. First, historical wind power data are used to model the forecast error and derive a probability density function characterizing the flexibility demand. Next, the flexible supply capabilities of coal-fired units are analyzed. Then, the DASFCC model is formulated and reformulated as a mixed-integer linear programming problem. Finally, numerical results demonstrate the validity of the DASFCC model in improving the accommodation of wind power and reducing operational costs.

Successful post-disaster restoration for distribution systems (DS) cannot be accomplished without the assistance of communications. As a result of the disaster, part of the communication infrastructure may be damaged, leading to the failure of distribution automation functions. This paper proposes a cyber-physical coordinated emergency restoration strategy based on unmanned aerial vehicle (UAV) relay communications with a decode-and-forward relay strategy to achieve longer distance and higher quality power data transmission. This restoration problem is a complex non-convex optimization problem. In this paper, a deep neural network approach is introduced to transform the problem into mixed-integer linear programming. The results show that the joint restoration strategy can fully exploit the UAV communication recovery potential and enhance DS resilience based on the IEEE 33-node test system.

Distribution networks with inverter-based distributed energy resources may increasingly face extreme events. While localized and islanded energy supply can enhance grid resilience, post-contingency distribution networks may struggle with efficient communication capabilities and energy sources owing to inevitably tight cyber-physical interdependence. Currently, post-contingency distribution networks do not comprehensively integrate cyber-physical self-organization capabilities using mobile resources. Therefore, in this paper, we propose a drone-assisted distribution network self-organization framework to enable operational data collection and control implementation, further maximizing the system resilience margin. Specifically, post-contingency communication services, i.e., data collection and control actuation, are scheduled via a multi-drone flight trajectory optimization considering drone recharging needs. Due to recharging periods with no emergency communication services, a resilience-oriented optimization is developed to co-optimize power injections and generator parameters for both static optimality and dynamic stability. This involves a compromised objective function that balances long-term energy consumption with short-term tolerant power imbalance. Finally, the proposed communication-control service provision framework is demonstrated through comprehensive case studies.

Due to lack of historical data and manuals, the parameters of the frequency-response model in an emergently-formed microgrid for restoration after extreme events may not all be known, making it difficult to provide basis for black start and topology reconfiguration scheduling. To address the issue, an aggregated frequency response model is constructed firstly, taking account of synchronous generators, and inverters operating in droop as well as virtual synchronous machine modes. Subsequently, two methods based on Fourier and Laplace Transform are utilized to identify the partial unknown parameters through appropriate formula derivation and numerical calculations. The methods’ applicability to deal with cold load pick-up (CLPU) process is also discussed. Fourier transform requires high signal integrity to avoid spectral distortion. However, the CLPU process takes a significant amount of time to complete. In this case, the method based on the Laplace Transform could alleviate the effects of spectral distortion and is less dependent on the measurement duration. The identification accuracy and fitting effectiveness of proposed methods are validated with numerical simulation.