The increasing penetration of distributed renewable energy resources (REs) poses significant challenges to the voltage regulation and hosting capacity of modern distribution networks. Energy storage systems (ESSs), particularly when deployed across both user-side and grid-side levels, provide valuable flexibility for mitigating renewable fluctuations and supporting network operation. However, conventional state-of-charge (SoC) management strategies typically impose rigid terminal constraints, forcing ESSs to return to predefined states at the end of each scheduling horizon. This practice restricts intertemporal flexibility and limits the effective utilization of storage resources. To address these limitations, this study proposes a boundary-free SoC optimization framework for multi-source ESSs. By removing terminal SoC constraints, the proposed framework enables continuous multi-period operation and releases additional flexibility for renewable energy accommodation. To effectively utilize this flexibility, a multi-agent active/reactive power control model is developed to coordinate user-side ESSs, grid-side ESSs, and distributed renewable energy resources. Furthermore, a hybrid-attention multi-agent proximal policy optimization (HAMAPPO) algorithm is designed to support efficient decision-making. The hybrid attention mechanism enables heterogeneous agents to focus on role-specific information, thereby improving coordination performance and learning efficiency. Simulation results demonstrate that the proposed framework effectively reduces distribution network operational costs, user-side operating costs, and voltage deviations. These findings confirm the effectiveness of boundary-free SoC optimization in unlocking storage flexibility and improving distribution network hosting capacity under high renewable penetration conditions.

The increasing penetration of renewable energy resources and electric vehicles (EVs) introduces considerable uncertainty into distribution networks, where renewable intermittency and uncoordinated charging can cause voltage violations, congestion, and reduced hosting capability. Conventional static assessment methods, based on fixed operating assumptions, fail to capture the spatiotemporal interactions induced by renewable variability and aggregated charging demand under network constraints. To address these challenges, this study proposes a dynamic hosting domain (DHD) framework based on reinforcement learning. The DHD defines the time-varying feasible region of system states, providing a quantitative representation of admissible operating boundaries with explicit physical safety guarantees. It adapts to spatiotemporal charging variations and incorporates a margin-based index for hosting capacity evaluation. A station-level delay perception model is embedded into the reward design to account for aggregated service-quality constraints as macroscopic economic feedback, discouraging excessive charging postponement while preserving operational feasibility at the system level. Furthermore, a federated reinforcement learning architecture based on proximal policy optimization (PPO) enables collaborative policy learning among multiple charging stations without raw data sharing, thereby enhancing scalability, privacy preservation, and spatiotemporal coordination under non-IID conditions. Case studies on renewable-integrated distribution networks demonstrate faster convergence, enhanced voltage stability, and lower operational costs compared with benchmarks. The proposed DHD framework offers a unified pathway for secure, efficient, and behavior-aware EV charging management in renewable-energy-integrated systems.

To address the challenges of power fluctuations caused by the integration of distributed generation (DG) and the difficulty in simultaneously managing peak-valley load regulation due to diverse user energy demands in a microgrid system, this paper presents a coordinated optimal configuration method for serving a hybrid energy storage system (HESS), which explicitly considers the differentiated requirements from both the supply-side and the demand-side. In the presented method, an improved empirical mode decomposition (EMD) method is first presented to decompose the DG power into high-frequency, medium-frequency, and low-frequency bands. Based on the complementary technical and economic characteristics of different energy storage types, a coordinated regulation strategy for HESS in the multiple time-frequency domains is developed. Second, a coordinated optimal configuration model for HESS is further established. This model integrates key performance indicators, including maximum fluctuation and renewable energy utilization rate on the supply-side and the peak-valley difference reduction rate on the demand-side. Finally, a distributed optimization algorithm based on an improved alternating direction method of multipliers (ADMM) is developed to solve the coordinated configuration model. The experimental results demonstrate that the presented method can effectively smooth the DG power fluctuations and reduce the load peak-valley difference. The renewable energy utilization rate reaches 100%, and the peak-valley difference reduction rate reaches approximately 80%. The presented method successfully achieves the coordinated optimal configuration of HESS on both the supply and demand sides, providing a theoretical underlying infrastructure for the configuration of energy storage in the microgrid system with high penetration of renewable energy.

Optimizing distributed training strategies for large-scale deep learning models remains a critical challenge in both industry and academia, demanding extensive domain expertise and manual tuning. Existing automated distributed training frameworks are plagued by over-reliance on prior profiling, poor generalization across models/hardware, and scalability constraints stemming from vast search spaces, impeding real-world applicability. To address these challenges, we propose OptiCo, a model-driven multi-agent framework that leverages Large Language Models (LLMs) to enable automatic and explainable distributed training strategy configuration. OptiCo orchestrates a team of reasoning-driven agents, through a shared Global Message Pool facilitating persistent memory and coordination. By employing inception prompting and Chain-Of-Thought (COT) reasoning, agents iteratively refine configurations, detect bottlenecks, analyze failures, and optimize resource utilization. Evaluated across 25+ configurations spanning diverse model architectures, GPU types and scales, OptiCo outperforms expert-designed strategies within 20 iterations, achieving an average performance improvement of 1.84%, with gains ranging from 0.08% to 8.65%. The source codes are avaiable at https://github.com/TangZhe96/OptiCo-public.

Timely detection of spreading events and accurate inference of their sources are central challenges in multi-layer networks, where heterogeneous topologies and interactions across layers shape diffusion. We formulate these coupled tasks as the Multi-layer outbreak Detection and source Inference (MDI) problem. MDI is a bi-objective vital-node identification problem that selects observer sets of fixed cardinality to minimize detection time and inference cost under limited sensing resources. We propose MOEA/D-TCM, a decomposition-based multi-objective evolutionary framework tailored to node-set optimization in multi-layer networks. It represents each solution as an observer set and combines a set-structure-adaptive evolutionary strategy with stable-state replacement and neighborhood adjustment to coordinate exploration and exploitation. Whereas the baseline methods return a ranked list or a fixed observer set, MOEA/D-TCM returns multiple non-dominated observer sets that represent different trade-offs between detection timeliness and inference cost. Experiments on 128 synthetic and empirical multilayer networks show that MOEA/D-TCM outperforms nine representative baselines on average, with mean improvements of 21.84% on synthetic networks and 28.90% on real-world networks. These results support bi-objective vital-node identification as a useful framework for monitoring and source localization in multi-layer diffusion systems.

With the continuous increase in renewable energy penetration, the traditional distribution network is gradually evolving into the active distribution network. Facing increasingly severe regulation pressure, relying solely on resource allocation from a single side of the distribution network can no longer provide adequate flexibility support. As an effective carrier integrating sources and loads, collaborative mutual assistance between the microgrid and the distribution network has become an inevitable trend to tap the flexibility potential of multiple entities. However, the current insufficient coordination of multi-type flexibility resources and the lack of deep interaction between the distribution network and the microgrid limit system flexibility, affecting the secure operation of the power grid. Therefore, this paper proposes an active distribution network–microgrid collaborative planning method for flexibility enhancement. Firstly, a collaborative optimal allocation model of nodal and grid-level flexibility resources for the active distribution network is established. The upper tier minimizes the annualized comprehensive cost, while the lower tier minimizes the annual operational cost and optimizes flexibility indices, comprehensively considering constraints like equipment investment, system security, and flexibility supply–demand balance. Secondly, the coupling relationship between the distribution network and the microgrid is established through tie-lines to construct the active distribution network–microgrid collaborative planning model. Finally, an accelerated and robust analytical target cascading solution strategy is proposed. By constructing a balancing coefficient, it eliminates the algorithm’s sensitivity to initial penalty weights, effectively improving the stability and efficiency of the model solution. Case study analysis verifies the effectiveness of the proposed method.

With the development of new power systems, the "double high and double peak" characteristics of power loads are becoming increasingly pronounced. Reliable and accurate load forecasting is crucial for the operational planning of power systems. To more accurately predict power loads, this paper constructs an improved dual-layer optimization model for short-term power load forecasting using a multi-parameter GA-BP approach. Firstly, addressing parameter uncertainty, the GA-BP algorithm optimizes the number of neurons in the hidden layer, sigma, and lambda. Secondly, further optimization is conducted for weights and thresholds. Finally, error correction was enhanced using an improved step-by-step increment and decrement learning factor approach, leveraging the squeeze theorem. The results indicate that the Mean Absolute Error (MAE), Mean Square Error (MSE), Mean Absolute Percentage Error (MAPE), and Root Mean Square Error (RMSE) are 17.27, 611.26, 2.71 %, and 24.72, respectively.

With the proposal of global low-carbon goals, research on new energy systems has become a major focus. As an emerging technology, electric vehicle (EV) can effectively reduce fossil energy consumption and enhance the integration of renewable energy sources. However, since EV usage patterns are highly dependent on human behavior, their uncertainty and complexity pose new challenges to the safe operation of distribution networks. Existing studies mainly focus on optimizing EV scheduling and orderly charging while overlooking the comprehensive carrying capacity of the distribution network for EV. Therefore, this paper proposes a method to enhance EV carrying capacity based on multi-agent cooperative control in the distribution network. First, a comprehensive EV carrying capacity index system is constructed, covering safety, stability, and quality aspects, and the Delphi method is used to integrate multiple indicators into a single optimization objective. Then, an improved particle swarm optimization (PSO) algorithm is applied to solve the multi-agent cooperative control model, aiming to enhance the EV hosting capacity of the distribution network. Finally, case studies based on the IEEE 33-bus system validate the effectiveness of the proposed method. The results demonstrate that the proposed approach significantly improves the maximum EV acceptance capacity and grid penetration rate while ensuring the safe, stable, and high-quality operation of the distribution network with minimal economic cost variation, providing effective support for the further development and deployment of EV.

ObjectiveThe Energy Router (ER) is an intelligent power electronic device featuring bidirectional regulation and multi-port interconnection, enabling efficient coordination of diverse energy types and voltage levels. However, ER planning involves multiple coupled factors—such as deployment location, connection topology, and capacity allocation—which result in a complex, high-dimensional optimization problem. To tackle this challenge, a two-stage planning method is proposed aiming to integrates network partitioning, source-load centroid identification, and bi-level optimization modeling to determine optimal ER deployment and configuration.MethodsThe proposed planning method is structured in two stages to address the complexity of ER deployment and configuration under high DG penetration. In the first stage, the distribution network is abstracted as a weighted graph, where the line weights are constructed based on electrical betweenness. A Louvain-based community detection algorithm is applied to partition the network into subregions. Within each subregion, the power source and load centroid are identified by relaxing the source-load distribution and calculating a synthetic centroid. The centroid nodes are then mapped to actual physical nodes, which serve as candidate locations for ER deployment. The number of ERs is determined by the number of subregions. In the second stage, a bilevel optimization model is established. The upper level determines the port number and interconnection scheme of each ER, with the objective of minimizing the total system cost, including ER investment and operational expenses. Based on the upper-level decisions, the lower level optimizes the port capacity configuration and dispatch strategy under uncertain conditions of wind, solar, and load. A two-stage adjustable robust optimization model is employed to ensure operational feasibility across a range of worst-case disturbance scenarios. The column-and-constraint generation (C&CG) algorithm and duality theory are adopted to iteratively solve the robust model, ensuring both computational tractability and robustness of the planning solution.Results and Discussions Case studies on a modified IEEE-33 bus system demonstrate the effectiveness of the proposed method. Compared with a baseline case without ER deployment, the proposed method reduces the annual system cost by 27.14% and improves ER return on investment (ROI) by 81.9% over existing single-ER strategies. The proposed ER planning also ensures 100% DG utilization and significantly reduces voltage deviation, with the maximum voltage offset decreasing by 48.73% compared to the baseline. The ERs operate at near-full capacity during peak hours, achieving average operational efficiency of 96.1% and extended periods of full-load operation. Sensitivity analyses indicate that deploying two ERs strikes an optimal balance between cost and ROI, outperforming both under- and over-deployment scenarios. Reducing the unit port capacity (e.g., to 10 kVA) improves voltage regulation and enhances port utilization due to increased configuration flexibility. Under different DG penetration levels (from 1.0 to 1.6), the ER layout remains largely stable. Higher penetration levels yield greater cost reduction and ROI, with maximum ROI observed under the 1.6 scenario. Although higher port capacities introduce some redundancy during low-output periods, overall efficiency remains above 92%, demonstrating robust adaptability to varying DG outputs.ConclusionsThe proposed two-stage ER planning method effectively addresses the challenges posed by high DG penetration in radial distribution networks. By combining network partitioning, gravity center-based deployment, and robust bi-level optimization, the method enhances economic efficiency, renewable energy accommodation, and voltage stability. Simulation results verify its adaptability, cost-effectiveness, and scalability under diverse operating conditions, making it a practical solution for next-generation distribution network planning.

The increasing deployment of distributed energy resources has driven significant interest in peer-to-peer (P2P) energy trading frameworks, particularly for optimizing distributed energy storage service provision (DESSP). Traditional bidding concession mechanisms primarily employ linearized models that oversimplify real-world market interactions and fail to capture the nonlinear relationship between participants’ concession strategies and market-clearing dynamics. To address this gap, this study proposes a novel P2P market design integrating a two-stage framework and a bidding concession model. Initially, we construct an iterative bidding model to quantify the nonlinear relationship between concession behavior and clearing prices, minimizing market mismatches and reducing dependence on the distribution network. We then introduce a two-stage P2P trading framework, incorporating day-ahead and intraday markets to mitigate deviations in renewable generation and load through DESSP. Finally, we construct a cross-framework credit mechanism, integrating credit into the trading rank to enhance transaction completion and market integrity and regulate pricing practices. Experimental results demonstrate that the proposed framework decreases reliance on the distribution network by 26.29%, improves local energy matching, and reduces total operational costs by 12.12%. The credit mechanism further stabilizes market dynamics, reducing operational costs by an additional 3.36%. These findings demonstrate the effectiveness of our proposed approach in enhancing the efficiency, stability, and fairness of P2P energy markets, providing valuable insights for future distributed energy trading systems.

Considering the uncertainty of wind power generation (WPG) and the specific operation behaviors of trading microgrids, this paper presents a blockchain-enabled robust-game electricity transaction model in a multi-microgrid system (MMS) to obtain optimal bidding-dispatching strategies, and achieve a transparent and decentralized electricity transaction. Combining blockchain technology and a non-cooperative game model, the established MMS electricity transaction architecture provides a complete information game environment for all game microgrids and facilitates the transparent, efficient, orderly, spontaneous management of MMS electricity transactions without the intervention of a third trusted party. Based on the distributed transaction architecture, an MMS robust-game model is presented to achieve the optimal day-ahead bidding-dispatching (DA-BD) strategies, in which the individual microgrid two-stage adjustable robust-game bidding-dispatching (ARG-BD) model characterizes the WPG uncertainty by employing uncertain interval and adjustable robust parameters. The binary expansion method, duality theory, big M method, and column-and-constrain generation algorithm (C&CG) are employed to solve the individual microgrid two-stage ARG-BD model. An alternating robust-game procedure integrating the C&CG algorithm and non-cooperative game model is developed to solve the MMS robust-game model. Case studies demonstrate the transparent and decentralized transaction, economic mutual benefits, and solution robustness of the presented method.

In order to cope with the challenges of source-load bilateral uncertainty on power system dispatch such as wind power and load output fluctuation, this paper constructs a distributionally robust optimization model for electricity-heatcooling microgrid based on data-driven and imprecise Dirichlet model. Firstly, to address the problem of limited historical data samples, a diffusion model is used to generate wind power historical data to fully expand the dataset. Secondly, an imprecise Dirichlet model is constructed based on the generated data to obtain the uncertainty set of wind power output and accurately portray its fluctuation characteristics. Finally, a distributionally robust optimization algorithm is used to solve for the optimal operation of the electric-heat-cooling microgrid a few days before. The proposed method can provide data-driven uncertainty support for microgrid scheduling, effectively guarantee the safety and economy of the system under the uncertainty environment, and expand the new path of microgrid source-load bilateral uncertainty modelling and optimal operation.

In the context of the accelerating convergence of the global digital economy and new urbanization, this study focuses on China and aims to address the challenges of its coordinated development. A review of extant studies reveals limitations in both theory and practice. The present study proposes an evaluation index system for the digital economy and new urbanization, employing the entropy weight method to calculate development indicators. The Coupled Coordination Degree (CCD) model is employed to assess their synergistic relationship, while recurrent neural network (RNN) and long short-term memory (LSTM) machine learning models are utilized for prediction. The findings indicate that from 2011 to 2023, China's digital economy development index and new urbanization construction level exhibited an upward trend, though notable regional variations were observed. The CCDL between the two shows a slight downward trend, indicating an imbalance and a transitional development stage. Preliminary analyses suggest that the CCDL will persist in demonstrating a downward trend. To promote coordinated development, it is imperative to optimize policies, reallocate resources, and innovate systems. This study provides a foundation for China to achieve high-quality urbanization and balanced regional development.

The ensemble learning technologies represented by bagging show notable performance in the field of high-performance electrical load classification researches. However, bagging frequently encounter classifier redundancy issue which significantly impacts classification accuracy. Therefore, to research a suitable base, classifier selection strategy is one of the most important directions to improve the effectiveness of ensemble learning participating in the load classification tasks. Therefore, aiming at solving the redundancy issue of the base classifiers in the bagging-based ensemble learning, this article presents a META learning-based dynamic selective ensemble strategy. First, the class labels of the load data samples can be achieved using the exponential similarity (Esim) distance-based spectral clustering and k-medoids clustering. Second, according to the labeled load samples, an ensemble-based back propagation neural network (BPNN) load classification model can be constructed. Afterward, a META learning-based dynamic selective ensemble strategy of optimizing the base classifiers ensemble is presented. Specifically, META feature sets (MFSs) of base classifiers are defined and extracted. And then, a META discriminator is trained using the MFSs, which is finally able to select suitable base classifiers ensemble for the classification for each individual sample to be classified. Ultimately, case studies are carried out using the UCI Electrical Grid Stability Simulated Dataset (EGSSD) and UCI Electricity Load Diagrams 2011-2014 Dataset (ELDD). According to the experimental result, the effectiveness of presented strategy of improving the classification performance can be identified.

In the context of modern power systems, examining low-carbon scheduling strategies for multiicro-mgrids, while considering uncertain wind power output, helps mitigate the influence of such scheduling uncertainty on the low-carbon and economic aspects. In order to make the microgrid operation more inclined to use low-carbon units and new energy units for energy production. The initial focus of this paper is on the involvement of microgrids in the carbon trading market, constructs a stepwise carbon trading model, and establishes a two-phase DRO scheduling model for microgrids aiming at minimizing the day-ahead operation cost, real-time regulation cost and carbon trading cost. Secondly, a DRO scheduling problem is decoupled into master and sub-problems using the column constraint generation algorithm, which are then solved iteratively. At last, the efficiency of the proposed DRO model is validated by highlighting its advantages in enhancing the low-carbon and economic performance of microgrids.

Although renewable energy, especially wind power, enables environmentally friendly power generation, its uncertainty remarkably influences the economy of the integrated energy system (IES) dispatching. Together with the naturally existing load uncertainty issue, the economy of IES could severely deteriorate. However, in recent years the cyber-physical system has been deeply coupled with IES to form the cyber-physical integrated energy system (CPIES). Therefore, driven by the comprehensive data flows, it is possible to model and analyze the uncertainties in energy flows using data-driven approaches. To analyze and solve the wind power generation (WPG) uncertainty and the load uncertainty issues in CPIES dispatching, this paper develops and introduces a distributionally robust optimization approach to realize the optimized economic dispatching for CPIES. First, the ambiguity set based on the imprecise Dirichlet theory is adopted. Further, aiming at solving the potential issue arising from the insufficiency of the WPG data samples utilized for constructing the ambiguity set, a gradient penalty-based Wasserstein generative adversarial network is presented to generate additional samples to enhance the uncertainty depicting the ability of the ambiguity set. Moreover, to improve the processing efficiency, deep-embedded clustering is also adopted to carry out the sample clustering to obtain the typical WPG scenarios. On the basis of the clustering results, ambiguity sets describing the uncertainties of different WPG scenarios and the uncertainty of the load are finally constructed, which are ultimately involved in implementing the optimized economic dispatching model for CPIES. At last, the model is solved using the duality theory, the column and constraint generation algorithm, and the Big-M method. The case studies demonstrate that the work presented in this paper can effectively improve the dispatching economy of CPIES.

Currently, renewable energy sources (RES) have been widely deployed in the smart grid, especially in the active distribution network (ADN). However, the inherent uncertainty of the renewable energy output significantly impacts the economy of the ADN operation. It is suggested that the utilization of flexible resources (FR) can effectively even out the uncertainty of RES. Nevertheless, the non-marketization of FR may prevent the emerging park-level integrated energy systems (PIES), important entities in ADN, from sufficiently offering their potential flexibilities. Therefore, this paper presents a two-stage local flexibility trading mechanism for motivating multi-PIESs to provide their flexible resources (PFR) to improve the operational flexibility of ADN. The first stage determines the dispatching plan of ADN according to the day-ahead forecasted values of RES. The second stage enables the multi-PIESs to trade their PFR with ADN to adjust the day-ahead dispatching plan in real-time to correct the forecasted errors of RES. In terms of implementing the two stages, firstly, the capacity of PFR with involving the adjustable tie line power of PIES is quantified using an optimization-based as sessment model. Secondly, based on the change of the operation cost before and after the sale of PFR, a pricing model of PFR is established. And then, to determine the trading amount of PFR, a real-time ADN economic dispatching model with the network constraints is further constructed, which aims at minimizing the comprehensive operation cost. Afterwards, a marginal-based method is employed to obtain the clearing price of PFR. Finally, to ensure the feasibility of the trading results and to provide the accurate dispatching strategies for the PFR trading in next time interval, a rolling dispatch for the multi-PIESs is carried out. Case studies demonstrate that the presented flexibility trading mechanism significantly reduces the power curtailment of ADN, the operation costs of ADN and the multi-PIESs.

At present, the park operation optimisation mechanism is still immature, and the utilisation rates of distributed energy equipments are low. At the same time, the power trading suffers from the problems of strong individual tendency and uncertainty in the output of units. Therefore, their economy and users' participation are seriously affected. To this end, firstly, an optimal operation strategy based on the multi-energy coupling at the park level is presented to improve the economic efficiency of the park; secondly, a mechanism for distributed power transaction based on reputation value is developed, which improves the motivation of users to participate in the market and enhance their autonomy while taking into account the economic efficiency of all entities. Finally, the feasibility and reasonableness of the proposed integrated energy operation mechanism of the park are verified using the simulations.

To promote wind power consumption and enhance energy efficiency in integrated energy systems, this paper proposes an Imprecise Dirichlet model data-driven two-stage adjustable robust optimization method based on an improved uncertainty set using Wasserstein generative adversarial networks. First, Wasserstein generative adversarial networks is used to expand the historical statistical data set, and the data-driven uncertainty set is constructed to describe the uncertainty of wind power output. Second, to enhance the operational economy of the integrated energy systems, a two-stage adjustable robust economic dispatch model based on improved uncertainty sets is developed. Third, the column and constraint algorithm, duality theory, and Big-M method are employed to solve the two-stage model. Finally, the effectiveness of the proposed model and method is validated through the example analysis.

With the popularity of distributed clean energy such as wind and solar in industrial parks, the fluctuating, intermittent and stochastic characteristics of distributed energy bring challenges to energy management. A hybrid energy storage optimal configuration strategy for industrial parks is proposed to address the output fluctuation problem of distributed energy sources. First, empirical mode decomposition is used to allocate the distributed generation original power into supercapacitor power task and lithium battery capacity task. Next, based on the allocation results, a hybrid energy storage optimal configuration model considering the maximum fluctuation quantity constraint with the objective of minimizing the annual comprehensive cost is established. Finally, the proposed configuration strategy is validated and analyzed with an actual industrial park as a case study, and the results show that the proposed capacity configuration scheme can effectively stabilize the fluctuation of distributed power output.