Extreme meteorological phenomena (e.g., cold waves) are low-probability, high-impact events that present significant operational and dispatch challenges for new-energy power systems. (1) Insufficient data on wind and photovoltaic power generation hinder data-driven modelling. (2) The uncertainty of small-sample wind and photovoltaic data is difficult to characterize. Therefore, a two-stage distributionally robust optimization dispatch strategy for a power system based on small-sample wind and solar data with uncertainty is developed. First, a generalized modelling method for a conditional generative adversarial network (CGAN) is proposed, which increases the generation of hourly output data for wind and photovoltaic power. Considering the drawback of large prediction errors for wind power and photovoltaic power in small-sample cases, a two-stage distributionally robust optimization model based on the Wasserstein metric is constructed, which embeds hard constraints (e.g., the capacity constraint of wind and solar transmission lines) and soft constraints (e.g., prediction errors). This model is nonconvex, and exactly solving it incurs a heavy computational burden. Duality theory and relaxation approximation are adopted here; the robust two-stage-distribution model is transformed into a mixed-integer linear programming model, and the iterative Taylor formula algorithm is used to linearize the constraint conditions. A numerical example is provided to demonstrate that the proposed model and solution algorithm can not only address the uncertainty of small-sample wind and photovoltaic data but also reduce the system operating costs and increase the model-solving efficiency.

With the increasing frequency of typhoon events and the continuous development of wind power generation, the safe and stable operation of the system has garnered extensive attention. Security risks are predominantly associated with abrupt fluctuations in wind power output, line outages, and compounded uncertainties. To address the operational risk of the power system with large-scale wind energy caused by typhoons, a typhoon-resilient coordinated dispatch of wind farm cluster (WFC) and hydrogen energy storage plant (HESP) driven by extreme scenarios (ESs) is developed. Firstly, the aggregated output of offshore wind power (OWP) is numerically simulated according to typhoon characteristic parameters, including meteorological and geographical parameters. In parallel, extreme N-1 line-outage scenarios are rigorously extracted through risk-informed contingency screening. Subsequently, a two-stage DRO dispatch strategy for N-1 line faults is proposed, which considers the supporting role of HESPs in emergency power supply. Specifically, systematic uncertainty error arising from wind power simulation and HESP forecasting is absorbed by flexible thermal units concurrently. Furthermore, Taguchi's orthogonal array testing (TOAT) method and Gumbel distribution are used to transform the worst expectation problem in DRO into an extreme-scenario-driven DRO model. Finally, the advantages of the proposed method are validated through experimental results in the improved IEEE-RTX-96 test system. The simulation results demonstrate that the HESP is superior in restoring power supply during extreme typhoon weather: when the key transmission line suffers N-1 faults under typhoon disturbances, the proposed coordinated dispatch method reduces the system load shedding by 88.44% compared with the traditional dispatch strategy.

The power consumption flexibility of distributed energy resources (DERs) must be aggregated to enable effective interaction with power systems. However, model heterogeneity, geographical dispersion, and the large number pose significant challenges to aggregation. This paper first models DER flexibility by explicitly incorporating heterogeneity in both state variables and available time periods, represented through polytopes of heterogeneous dimensions. The aggregation of DERs is then formulated as a standard projection maximal inner approximation (MIA) problem. To efficiently and accurately solve this problem, a novel linear programming (LP)-based algorithm is developed. Furthermore, a hierarchical framework is introduced to enable large-scale aggregation, within which a Minkowski-closed family is proven, allowing accurate and efficient secondary aggregation through vector addition. In addition, generalized operating envelopes (OEs) are proposed for distribution system operators (DSOs) to establish and communicate network constraints, enabling integration into the aggregation process without disclosing sensitive network information. Numerical experiments validate the proposed formulations and demonstrate superior accuracy and scalability of the proposed method while maintaining high computational efficiency.

Reliable state estimation is essential for the secure and efficient operation of sustainable energy systems, especially under the increasing integration of renewable energy, distributed resources, and heterogeneous sensing devices. However, in practical power systems, SCADA, PMU, and AMI measurements often have different sampling rates, accuracies, communication delays, and availability levels, which makes reliable data completion and multi-source fusion difficult. This paper focuses on the state estimation problem of renewable-integrated distribution networks under multi-source heterogeneous measurement conditions. In such distribution networks, the increasing penetration of distributed renewable energy resources and the joint deployment of multiple measurement devices, including SCADA, PMU, and AMI, may lead to incomplete measurements, asynchronous sampling, differences in measurement accuracy, and reduced system observability. To address these issues, this paper proposes a model-based digital twin reference-guided physics-constrained DDPM framework to improve the quality of missing-measurement completion and the reliability of state estimation in distribution-network scenarios. A four-layer simulation-oriented cyber-physical framework is first constructed to integrate physical sensing, model-based digital twin reference mapping, AI-based measurement completion, and state estimation feedback. Within this framework, a physics-constrained self-supervised denoising diffusion probabilistic model is developed to recover missing measurements by combining observed data, digital twin reference measurements, real-time topology information, and power system operational constraints. The completed pseudo-measurements and physical measurements are then fused through a credibility-aware weighting strategy that considers timeliness, data integrity, measurement accuracy, and virtual-real consistency verification under simulation settings. Simulation results on the IEEE 14-bus system show that the proposed method improves pseudo-measurement completion and supports more reliable voltage magnitude and phase angle estimation under different measurement configurations. Under the tested simulation settings and multi-source measurement configurations, the results indicate that the proposed method can improve pseudo-measurement completion and support more reliable voltage magnitude and phase angle estimation. However, its performance under frequent topology switching, high missing-data ratios, and complex abnormal data conditions remains to be further evaluated.

Learning compact and reliable convex hulls from data is a fundamental yet challenging problem with broad applications in classification, constraint learning, and decision optimization. We propose Projection Convex Hull (PCH), a scalable framework for learning polyhedral trust regions in high-dimensional spaces. Starting from an exact MINLP formulation, we derive an unconstrained surrogate objective and show that, under suitable weight assignments, the optimal hyperplanes of the MINLP are recovered as stationary points of the surrogate. Building on this theoretical foundation, PCH adaptively constructs and refines hyperplanes by subregion partition, strategic weight assignment, and gradient-based updates, yielding convex hulls that tightly enclose the positive class while excluding negatives. The learned polyhedra can serve as geometric trust regions to enhance selective classification and constraint learning. Extensive experiments on synthetic and real-world datasets demonstrate that PCH achieves strong performance in accuracy, scalability, and model compactness, outperforming classical geometric algorithms and recent optimization-based approaches, especially in high-dimensional and large-scale settings. These results confirm the value of PCH as a theoretically grounded and practically effective framework for trust-region learning.

The real-time and accurate calculation of electricity indirect carbon emissions is not only the critical component for quantifying the carbon emission levels of the power system but also an effective mean to guide electricity users in carbon reduction and promote power industry low-carbon transformation. Fundamentally, calculating indirect carbon emissions involves allocating direct carbon emission data from the power source side, indicating that accurate indirect emission results rely on the precise measurement of power source emissions. However, existing research on indirect carbon emissions in large-scale power systems rarely accounts for variations in carbon emission characteristics under different operating conditions of power sources, such as rated/non-rated operating conditions and ramping up/down conditions, making it difficult to reflect source-side and load-side carbon emission information variation during providing ancillary services. Quadratic and exponential functions are proposed to characterize the energy consumption profiles of coal-fired and gas-fired power generation, respectively, to construct a refined carbon emission model for power sources. By leveraging the theory of power system carbon flow, we analyze how variable operating conditions of power sources impact indirect carbon emissions. Case studies demonstrate that changes in power source emissions under variable conditions have a significant effect on the indirect carbon emissions of power grids.

To achieve carbon neutrality by 2060, balancing energy demand with emission reduction, while fostering technological innovation to address climate change, the retrofitting of coal-fired power plants with Carbon Capture, Utilization, and Storage (CCUS) retrofitting has emerged as a critical strategy for mitigating CO2 emissions. Given the anticipated rapid advancement and widespread deployment of coal-fired power CCUS retrofitting in China over the coming decades. It is essential to quantify the carbon lock-in effects associated with planned coal-fired power plants resulting from CCUS retrofitting under different power planning scenarios. In this study, a source-sink matching model incorporating the Levelized Cost of CO₂ Abatement(LCOA) is developed to evaluate the pipeline layout and deployment costs for CCUS retrofits under scenarios of uncertain coal power capacity expansion. The findings reveal that scaling up the coal power CCUS capacity from 200 GW to 350 GW by 2060 leads to an increase of over 80% in both pipeline length and deployment costs. Furthermore, due to inevitable delays in CCUS deployment, CO2 emissions from fossil fuel power generation will continue to accumulate throughout the transition period. Although the net-zero emissions target remains achievable by 2060, cumulative CO2 emissions over the transition period could be approximately 8% higher. These findings underscore the need for prudent decision-making regarding new coal power capacity, with particular attention to the impacts of power development pathways shape CCUS infrastructure layout and retrofitting investment requirements.

Optimization of the membrane electrode assembly (MEA) is critical for enhancing hydrogen production and energy conversion efficiency in unitized regenerative fuel cells (URFCs). High-porosity bifunctional MEAs can be effectively fabricated by physically mixing Pt and IrO2catalysts and depositing them onto a proton exchange membrane. The MEAs were characterized using cyclic voltammetry and electrochemical impedance spectroscopy (EIS), with EIS data further analyzed via the distribution of relaxation times method to separate high-frequency processes that are otherwise difficult to distinguish, thereby providing a basis for establishing an equivalent circuit model for URFCs. Experimental results indicate that the round-trip efficiency (RTE) of URFCs under constant electrode configuration is highly sensitive to the composition of the anode catalyst layer. When the mixed catalyst layer contains IrO2and Pt in a 5:5 ratio, with a total catalyst loading of 2 mg/cm2 and an ionomer content of 15%, the effective electrochemical surface areas of Pt and IrO2reach their maximum values of 13.6 m2/g and 80.25 m2/g, respectively. Under this configuration, the URFC achieves a RTE of 45.94% at 1 A/cm2 during cycling between water electrolysis and fuel cell modes. Moreover, EIS comparisons reveal that the anode composition significantly influences the overall HFR and charge transfer process in FC mode, indicating that optimizing the anode composition in URFCs is a key factor for enhancing FC mode performance.

Customer baseline load (CBL) estimation holds the key to the successful implementation of demand response (DR) programs. In traditional control group methods, non-DR users are clustered into sub-clusters. DR users are matched with those in sub-clusters showing similar load patterns, and the matched users' load data is used to estimate DR users' CBL. In general, the existing methods can generate relatively accurate CBL estimation results as long as the number of matched users is adequate. However, the current control group methods suffer from two major limitations, which not only undermine the estimation accuracy but may also render the methods entirely ineffective: 1) these methods are highly vulnerable to uneven distribution of sub-clusters; 2) load data of the non-DR participating users is under-exploited. To this end, this paper proposes a CBL estimation method based on variance transformation principle and contrastive learning framework. Firstly, the variance transformation principle is revealed, which is the basis to generate enough samples showing correlation with the DR users. Secondly, a neural network model based on contrastive learning framework is established to further recognize the non-DR participating users showing highly similar load pattern to the DR users and extract the high-dimensional load features from the DR users and the matched users. Finally, the CBL estimation results can be obtained by the feature similarity-weight calculation. The effectiveness and robustness of the proposed method is validated by using multi-source datasets and comprehensive evaluation indicators.

This article proposes an interpretable deep reinforcement learning (DRL) method for energy management of low-carbon community energy systems (LCCES), which effectively addresses the transparency limitations caused by the black-box nature of traditional DRL neural network structures, thereby overcoming a key constraint in energy system applications. First, we develop a hybrid integer dynamic decision DRL algorithm to solve the low-carbon scheduling problem in community energy systems with continuous-discrete hybrid action spaces. Second, we construct an interpretable artificial intelligence framework, where the temporal attention mechanism is used to process and extract features to provide macro-level decision contribution analysis. These features are input into the decision tree for extracting device-level rules. Building upon this, we design an ensemble decision tree architecture with temporal attention mechanism to effectively identify critical time periods influenced by system inertia and energy fluctuations, thereby achieving interpretable optimization strategies while enhancing decision robustness under state fluctuations. Simulation results based on the independent test set demonstrate that, in comparison with alternative methods, the proposed approach yields a 22.1% cost reduction and a 32.4% carbon emission reduction rate relative to twin delayed deep deterministic policy gradient (TD3), and a 14.7% improvement in explanation accuracy compared with static decision trees.

Input convex neural networks (ICNNs) are increasingly used as surrogates for stability indices and embedded as constraints in power-system optimization. This letter clarifies two recurring formulation limitations that can negate ICNN convexity benefits: (i) applying generic Big-M mixed-integer reformulations introduces auxiliary binaries that are unnecessary for enforcing ICNN sublevel constraints; and (ii) reversing the stability inequality transforms a convex sublevel set into a generally nonconvex superlevel set, invalidating global-convergence guarantees of cut-based methods. After clarifying the limitations, we provide (i) an exact LP-based epigraph reformulation for ReLU-ICNNs, (ii) an outer-approximation scheme with global guarantees under the sublevel convention, and (iii) a feasibility-preserving inner-approximation scheme for the superlevel convention, with simulations on IEEE 14- and 118-bus unit commitment instances.

The influence of reactive power on carbon emissions in power flows has been largely underestimated, limiting the assessment of grid-side carbon reduction potential and hindering effective emission accountability. To address this, this study develops an operator-oriented framework to quantify the maximum carbon reduction potential of regional power grids through optimal reactive power compensation, considering operational constraints. The framework models how reactive power affects voltage profiles, power flow distribution, and network losses, and accordingly establishes a carbon flow accounting method aligned with actual network power distribution. Carbon-reactive power sensitivity indices are introduced to identify critical buses where compensation yields the greatest emission reduction. Based on these insights, a constrained optimization model is formulated to search for the maximum boundary of system-level carbon reduction. Due to nonlinear objectives, discrete decision variables, and mixed equality-inequality constraints, conventional solvers are insufficient. To address this, an exponential-trigonometric optimization (ETO) algorithm, leveraging a two-stage explorationexploitation mechanism, is employed to efficiently search for the theoretical boundary of carbon reduction potential. Case studies on IEEE 30-bus and 118-bus systems demonstrate emission reductions of 1.06 t/h and 8.38 t/h, respectively, while maintaining voltage stability. Results show that even limited investments in reactive power devices can achieve substantial emission reductions, providing a cost-effective pathway for grid-side decarbonization. Comparative analysis confirms that the proposed framework outperforms alternative approaches in accounting accuracy, emission reduction, and operational reliability. Overall, the framework offers grid operators a practical and precise tool for low-carbon operation under realistic operational constraints.

Multiple pricing schemes are proposed to guide resource allocation in the economic dispatch (ED) of power systems. However, implementing a single pricing scheme often fails to meet the diverse economic preferences of ED participants, while the coexistence of multiple pricing schemes within a power system leads to inconsistent valuation standards. This contradiction causes unreasonable profit allocation of ED participants, which brings economic losses. In this paper, the economic losses of multiple pricing coexistence are derived as the optimality gap between the ED and self-dispatch models of ED participants. Then, the gap is proven to stem from 1) the linearization error of the ED model, and 2) the deviation from the employed pricing schemes to LMP. Consequently, an LMP-related factor in the ED objective is discovered, which can reduce the linearization error and naturally renders LMP as a decision variable. By establishing a price constraint aimed at guiding the multiple pricing schemes to equal LMP, an ED model minimizing the economic losses of multiple pricing coexistence is formulated, whose performance is verified in numerous test systems.

Climate change-induced extreme temperature events are posing severe threats to the frequency stability of low-inertia power systems. Inverter-based thermostatically controlled loads (ITCLs), as the dominant electricity consumption units during extreme weather, present a potential solution to this challenge due to their vast adjustable potential. However, existing strategies for utilizing loads to provide frequency support generally rely on either complex control algorithms or high-speed communication, hindering their large-scale engineering application. To address this challenge, this article proposes a synthetic inertia (encompassing both inertial and droop responses) aggregation control strategy for ITCL cluster. Its core innovation lies in a hybrid architecture that is lightweight in both computation and communication, coupled with a corresponding ordered frequency-threshold sequencing scheme. This strategy guides massive numbers of load terminals to autonomously and sequentially trigger power adjustments during system disturbances by preconfiguring them with ordered thresholds based on the rate of change of frequency and frequency deviation. Consequently, without relying on complex control algorithms or high-speed communication, the aggregated power dynamics of the cluster can accurately emulate the synthetic inertia characteristics of synchronous generators. Hardware-in-the-loop experimental validation demonstrates that the proposed strategy enables the cluster consisting of 500 ITCL units to achieve an equivalent inertia time constant of 2.71 s and a droop coefficient of 2.62. Under a 0.1 p.u. step disturbance, the synthetic inertia support lifts the frequency nadir from 49.61 to 49.69 Hz, corresponding to a 20.5% reduction in frequency deviation compared with the single-response modes, and cuts the average CPU utilization by 77% relative to the conventional centralized architecture. This provides a technically promising pathway with strong engineering application prospects for addressing power grid frequency security risks under extreme climate conditions.

As a critical porous component of proton exchange membrane fuel cells (PEMFCs), the gas diffusion layer (GDL) plays an essential role in electron conduction, heat dissipation, and liquid-water transport. To quantitatively evaluate how microstructural features influence these transport behaviors, a three-dimensional stochastic reconstruction model with controllable porosity and fiber diameter was developed based on statistical fiber-orientation distributions. Effective through-plane electrical conductivity, thermal conductivity, and intrinsic permeability were subsequently calculated on a unified geometric basis, with both dry (gas-solid) and wet (liquid-solid) conditions considered. It is found that the relative electrical conductivity decreases by approximately 96% as porosity increases from 0.5 to 0.85, while the thermal conductivity shows an even greater reduction of about 97%. In contrast, permeability exhibits a strong nonlinear increase, rising by more than one order of magnitude across the same porosity range. Under fixed porosity, the influence of fiber diameter remains comparatively minor, altering electrical and thermal conductivities by less than 23% and affecting permeability far less than the changes driven by porosity. Dry-wet comparisons show that liquid water produces a negligible change (<0.2%) in electrical conductivity but dramatically enhances thermal conductivity by over 500%. This work provides a unified and directly comparable electro-thermal-hydraulic assessment framework, offering quantitative guidance for multi-objective GDL design and multiphysics optimization in PEMFCs.

Power systems currently face static voltage stability issues due to increased renewable integration. The shortest distance from a current operating state to the voltage collapse boundary is a crucial metric for system operators to evaluate safety. To attain a less conservative and more realistic assessment, the shortest distance should be evaluated within a feasible operating region, not within the entire mathematical space. We propose a new optimization-based framework to address this challenge. A Slope-induced Iterative Distance Estimation (SIDE) algorithm is proposed based on the framework. In each iteration, the SIDE algorithm solves a simple optimization problem to obtain the most dangerous power injection variations related to voltage collapse. The feasible operating region, which can be composed of complex operation laws, is integrated into the optimization problem as constraints to ensure the physical feasibility of the results. Different from classical eigenvector-based methods, the approach presented in this paper provides a framework for formulating various physical operation constraints in the assessment algorithm through mathematical optimizations, which is a promising perspective and can be easily extended to include other constraints. In addition, the SIDE algorithm is guaranteed to converge within finite iterations, and extensive numerical results verify its efficiency and scalability for large-scale power systems.

Recently, electric vehicles (EVs) have been playing an increasingly important role in the secure operation and renewable energy accommodation in distribution networks (DN). Generally, EV aggregators in DN can coordinate the charging/discharging behavior of massive EVs. However, the potential battery degradation diminishes EV owners' participation. Thus, it is essential to consider battery degradation to better reflect the actual scheduling costs for distribution system operators (DSOs) and fairly allocate profit to participated EVs. To this end, we propose an EV aggregation model that can accurately estimate EVs' battery degradation while efficiently coordinating heterogeneous EVs. Specifically, we first develop the flexibility region of individual EVs and adopt stochastic optimization to assess the costs of battery degradation. Then, we formulate the aggregated flexibility region of EV fleets based on an affine transformation algorithm, each point within which is associated with a battery degradation cost. Finally, we apply the aggregation model to DN scheduling which aims at minimizing operation costs. Numerical tests in a modified IEEE 33-bus system illustrate that the proposed aggregation model can achieve high accuracy in assessing battery degradation and reduce operation costs compared to the scenario where battery degradation is not considered.

Most renewable energy power systems are created to provide more resilient, reliable, economical, sustainable and secure power support services for loads. However, owing to the inherent forecasting errors of wind and photovoltaic (PV) power, existing optimal dispatch decisions based on forecasting errors have biases. To address this issue, this paper proposes the distributed proximal policy optimization (DPPO) model with embedded dual rules for optimal power dispatch that considers wind and PV power forecasting error correction. The proposed model embeds forecasting and error correction information into the DPPO state space. Moreover, considering the physical characteristics and operational security constraints of the power grid, power balance and flow constraints are embedded in the DPPO network in a regular form. Finally, by integrating the established rules, wind and PV forecasting, and error correction information, the proposed model achieves optimal dispatch decisions through the calculation of state and execution of prescribed actions. The proposed method is applied and tested on a modified IEEE-30 bus system using actual data from a provincial power grid. The numerical results demonstrate that the proposed method effectively addresses optimal dispatch decisions caused by wind and PV forecasting errors. Compared with three other advanced methods, the proposed approach has significant advantages in promoting wind power accommodation, reducing operating costs, and enhancing the adaptability of optimal dispatch to uncertainty.

Cold waves lead to significant deviations in wind power prediction and load surge of electric-heat systems, which seriously affect the system's power supply and heat supply. In this paper, a distributionally robust chance-constrained optimization model for integrated electricity-heat systems (IEHSs) based on hierarchical reserve is proposed. Firstly, an optimization model for the IEHSs based on hierarchical reserve is constructed. Secondly, a Wasserstein distance-based ambiguity set is formulated to characterize wind power prediction errors during cold wave events, enabling the construction of a distributionally robust optimization model with ambiguous chance constraints for IEHSs. Finally, the proposed methodology employs duality theory and conditional value-at-risk (CVaR) approximation techniques to reformulate the original distributionally robust optimization model as a computationally tractable linear programming problem. The effectiveness of the proposed method is verified using the improved IEEE 24-bus and Barry Island 32-node test system. The results show that compared with the robust optimization (RO), stochastic optimization (SO), and deterministic optimization (DO) models, the proposed method can reduce overall operating costs to mitigate the uncertainty caused by the wind power prediction error during cold waves, and effectively balance economic efficiency and robustness of IEHSs.