This paper investigates the economic dispatch problem in interconnected microgrids (IMGs) subject to Byzantine attacks. While IMG enhances resource allocation through collaborative dispatch to overcome the supply-demand limitations of individual microgrids, it renders the system vulnerable to malicious information injection by Byzantine agents. To address this, a resilient consensus-based Byzantine fault-tolerant algorithm, termed RC-T, is proposed. Distinct from existing studies that require prior knowledge of the maximum number of attackers, RC-T leverages trusted agents to establish dynamic decision boundaries. This mechanism effectively filters anomalous data and ensures high convergence precision, even under unknown, heterogeneous, and time-varying communication delays. Theoretical analysis demonstrates that the RC-T algorithm converges to a neighborhood of the optimal dispatch solution, while simulation results further validate its effectiveness and superiority over benchmarks in handling both latencies and Byzantine attacks.

The scarcity of aging data and the inconsistency of aging trends during the second life lithium-ion batteries (SL-LIBs) echelon utilization process make state-of-health (SOH) estimation challenging, hindering accurate monitoring when deployed as energy storage in power systems. To address this issue, a cross-domain physical information network (CDPIN) method is proposed to estimate SOH of SL-LIBs. First, an internal parameter inference module is proposed to address the difficulty in directly and accurately measuring the internal state information of SL-LIBs, supervising inference of aging parameters with discretized degradation physical mechanism. Second, a memory-assisted domain alignment mechanism is proposed to address feature distribution differences caused by inconsistent aging trends. It enhances the unified representation capability of aging trends through the best aging feature replay strategy. Further, a framework for fine-tuning the SOH estimation model is proposed to address the distribution shift between SL-LIBs and the source domain, dynamically adjusting parameters through degradation process modeling feedback. CDPIN utilizes widely available first life lithium-ion battery data as the source domain, overcoming the limitation of SL-LIBs data scarcity for SOH monitoring during echelon utilization. Finally, the effectiveness of the proposed method is verified using actual aging data and a semiphysical hardware platform.

Localization of multipoint weak leakage in energy transportation systems remains challenging due to signal-source mismatch and weak responses of negative pressure waves (NPWs). To address this issue, this article proposes a novel physics-informed localization framework that combines an attenuation-based NPW matching algorithm with a prior-embedded maximum entropy adaptive dynamic programming (MEADP) scheme. First, a matrix transformation-based matching algorithm establishes physically coherent correspondences between inlet and outlet NPWs. Building on this foundation, a prior-embedded MEADP localization strategy incorporates Gaussian priors derived from the attenuation physics of NPWs to guide policy optimization. Furthermore, a Wasserstein-distance regularization term is introduced to stabilize policy learning and ensure reliable convergence. Experimental results demonstrate that the proposed method effectively resolves multileak signal mismatches and achieves high-precision localization, with the minimum localization error remaining below 0.5%.

Transient stability assessment is critical for supporting grid operator decisions and ensuring the secure operation of power systems. However, the high-dimensional complexity of system modeling and the limitations of binary classification hinder accurate evaluation. To address this, a physics-informed graph neural network is proposed to generate stagewise probabilistic trajectories of stability without relying on explicit prior models. First, a physics-graph collaborative framework is developed by embedding the swing equation to estimate rotor angles and suppress misjudgment. Second, within this framework, a distribution-aware aggregation module is proposed. It captures global power distribution and local state variations through recursive neighborhood updates and second-order pooling. Furthermore, to integrate physical laws with domain supervision and enhance physical consistency, a multiobjective interaction mechanism is designed, overcoming the limitations of purely data-driven methods in feature disentanglement. The proposed approach is validated on the IEEE 39-bus and IEEE 145-bus systems, demonstrating superior accuracy and effectiveness in comparison with baseline methods.

In the Industrial Internet of Things (IIoT), data loss may occur in edge devices due to network latency, communication failures, and other factors. Therefore, a mask asymmetric transformer generative adversarial network (MATGAN) is proposed for imputing missing data at edge devices closer to the data source. First, an online collaborative architecture based on generative adversarial networks is proposed, progressively enhancing resolution and reducing embedding dimensions through a hierarchical structure, effectively mitigating excessive memory overhead. Then, to reduce initial computational costs, an asymmetric lightweight masked autoencoder is designed to achieve sparse sampling by randomly masking edge data, reducing the initial computational cost and learning the reconstruction of spatiotemporal patches. Moreover, a dynamic weighted loss is proposed, which assigns weights based on the difficulty of distinguishing patch imputation, and minimizing multi-scale similarity from easy to hard, thereby improving the recovery capability of complex textures and sharp edge regions. Experimental results demonstrate that the proposed imputation method effectively recovers data and reduces imputation errors and transmission latency.

The power fluctuation and system inertia degradation in a short time put forward higher requirements on the rapidity and robustness of frequency control. This paper proposes an online multiplayer Stackelberg game control framework to achieve frequency control of multi-area power system with the uncertainties of load, renewable energy and line loss. Firstly, an optimal frequency control model incorporating efficient management of load aggregators (LA) is designed based on Stackelberg game, where the LA acts as the leader and all micro-turbines act as the followers. The two-level optimization problem of leader and followers is converted into solving the coupled Hamilton-Jacobi equations with the constraints of the follower’s costate equation. Then, an improved integral reinforcement learning is designed to enhance the wide adaptability of the control strategy online by introducing a general function with uncertainty upper bounds and line losses for all players, while satisfying the uniform ultimate bounded stability of the closed-loop system. A single critic neural network structure is utilized to obtain the optimal strategy. And the convergence of neural network weights is proven. Last, comparative simulation results verify the effectiveness of the proposed method.Note to Practitioners—High accuracy and robustness in frequency control of power systems is important for system safety. Demand-side participation in the interactive regulation of the system makes frequency control strategies more flexible and diversified. However, unreasonable control allocation schemes can incur large payment costs, while changes in control can cause dynamic changes in line losses to affect the supply-demand balance, leading to frequency deviations. This paper proposes an intelligent frequency control method based on the Stackelberg game. The designed IRL algorithm is able to solve the trade-off between system control performance and payment costs online without the priori knowledge of the system and with wide adaptability to uncertainty. Simulation results show that the proposed method outperforms non-game strategies and is robust.

This article considers the hierarchical containment control (HCC) for flexible mirrored collaboration, which accommodates the bipartite cluster consensus behavior in two symmetric convex hulls formed by multiple leaders. First, to achieve the mirrored collaboration in symmetric convex hulls, the layer-signed digraph is generated by involving the antagonistic interaction. Benefiting from the hierarchical structure, the antagonistic interaction in the assistant-layer replaces the assumption of in-degree balance for the existing cluster consensus issues. Second, the existing types of control protocols and the framework of cooperative output regulation limit the achievement of the studied hierarchical mirrored collaboration. To solve this problem, the hierarchical cooperative output regulation is extended based on the formulated hierarchical mirrored collaborative errors. Third, the layer-signal compensator is designed estimating the states of leaders as well as guaranteeing the convergence of collaborative behaviors. Combining with the designed layer-signal compensator, a novel HCC protocol is proposed so that the bipartite cluster consensus behavior can be achieved simultaneously in two symmetric convex hulls. Finally, theoretical results are verified by performing the numerical simulation.

This article proposes the row-stochastic event-based quantized (RSEQ) algorithm to address the distributed optimization problem with multiple communication constraints, including limited communication costs and bandwidth. In RSEQ, a novel event-based dynamic quantizer is designed to resist the negative effects of communication constraints on the algorithm. The quantizer encompasses the event generator and the dynamic encoder/decoder, which collectively adapt the frequency and size of information sharing based on real-time state. The RSEQ only requires the construction of a row-stochastic weight matrix, which leads to lower conservatism compared to algorithms based on column-stochastic matrices. Additionally, the introduction of an acceleration term enables RSEQ to linearly converge to the globally optimal solution without the deployment of the average gradient estimator. Instead, a Perron vector estimator needs to be employed to counteract the unbalancedness of the directed network. With the effect of the event generator, the Perron vector estimator can also be left inactive after a certain number of iterations, which means that the transmission of only state information between agents can linearly converge to the global optimal solution under directed networks. Finally, the effectiveness of the algorithm is demonstrated through an economic dispatch problem in smart grids.

This article addresses the cooperative output regulation problem for discrete-time multiagent systems with unknown parameters, a challenge that arises in many practical applications where system models are unavailable. Unlike existing techniques, a model-free Q-learning algorithm is devised to iteratively obtain the optimal policy. This algorithm operates independently of system parameters, and its immediate cost formulation excludes the necessity of solving regulator equations. Consequently, it achieves a streamlined structure, facilitating direct determination of the optimal policy. Subsequently, the stability of each iteration of the algorithm is formally established, along with the derivation of a unique condition for the Q-function matrix. Additionally, to address the challenge of obtaining a stable policy when the initial policy is unstable, an innovative data-driven algorithm is introduced that effectively computes the initial stable gains, ensuring convergence to stability throughout the learning process. Meanwhile, we focus on demonstrating that the distributed observer and the excitation noise do not introduce bias. Finally, the efficacy of the proposed algorithm is validated through two simulation examples.

As a burgeoning approach, droop control of interfacing inverters in microgrids has been widely adopted. However, droop control cannot achieve proportional reactive power sharing among distributed generators because of the difference of feeder impedances in actual microgrids. Hence, a novel distributed adaptive virtual impedance method based on average consensus algorithm is proposed to relieve feeder impedance mismatch. There into, virtual impedance is composed of static and adaptive inductance, which is designed to reshape equivalent impedance by creating additional control loops. Adaptive inductance unit is designed based on reactive power mismatch by applying multiagent consensus algorithm. By fully distributed adjustment to equivalent impedance, reactive power sharing accuracy can be improved. Then, proposed control method is applied to modified droop control, which is embedded designed dynamic voltage average consensus estimator, providing superior voltage restoration. At last, the effectiveness of proposed control method is shown by using simulation and further demonstrated through experiment study.

Leakage localization in energy interconnection systems remains a significant challenge since the efficacy of traditional time-based methods is compromised by the requirements for high sampling frequency. To overcome this issue, a novel localization framework that eliminates the reliance on timestamp data is proposed in this article. This framework utilizes neural networks to model the attenuation patterns of negative pressure waves (NPWs) along the pipeline, transforming the localization problem into a consistency issue between the NPWs at both ends. First, the Bayesian neural network is employed to model the attenuation patterns, not only reducing overfitting and quantifying uncertainty, but also enhancing the optimization process by incorporating probabilistic reasoning. Furthermore, an innovative maximum entropy adaptive dynamic programming algorithm is developed. This algorithm integrates the variance of theQ-function into policy improvement and incorporates policy entropy to enhance exploration and mitigate convergence to suboptimal solutions. Finally, experimental results on a long-distance pipeline demonstrate that the proposed approach achieves high localization accuracy.

The variation in multivariate time series (MTS) under wind turbine (WT) operational conditions makes it challenging for traditional anomaly detection methods to model expected behavior under normal conditions, resulting in failure to identify anomalies. To address this, an online anomaly detection method based on multiscale spatiotemporal graph learning is proposed, enabling prompt anomaly detection. First, an adaptive multiscale graph correlation forecasting network is introduced, which autonomously learns temporal and feature dependencies at each scale. Next, a dynamic spatiotemporal graph variational autoencoder is presented to model the MTS’s spatiotemporal correlations and capture the normal operation patterns. In addition, we propose a nonparametric dynamic threshold updating mechanism using Welch’s t-test to adapt to changing operating conditions based on anomaly scores. The proposed method jointly optimizes the forecasting and pattern reconstruction networks to derive spatiotemporal graph representations and anomaly scores, effectively identifying anomalies that deviate from normal operating states. Experiments on real WT data demonstrate the method’s ability to detect anomalies earlier, with evaluation metrics showing at least a 2% improvement in anomaly detection accuracy compared to existing methods.

This article investigates the issue of privacy preservation in distributed optimization, where each node possesses a local private objective function and collaborates to minimize the sum of those functions. A novel dynamic average consensus-based distributed Newton algorithm is introduced to achieve consensus, optimality, and differential privacy. Each node utilizes its local gradient and Hessian as time-varying reference signals, facilitating information exchange with neighbors for tracking the average. To safeguard privacy, persistent Laplace noise is introduced into the exchanged data, affecting the estimated optimal solution, gradient, and Hessian averages. To counteract the noise’s impact, the internode coupling strength is adaptively reduced over time through decay factors, allowing for noise attenuation as the algorithm progresses. The algorithm’s convergence to the optimal solution, assuming global function smoothness and strong convexity, is theoretically proven. The algorithm’s accurate convergence to the optimal solution, assuming global function smoothness and strong convexity, is theoretically proven. Furthermore, the efficiency and reliability of the algorithm are empirically validated through simulations of an IEEE 14-bus test system.

This article investigates the distributed constrained optimization problem with event-triggered communication over time-varying weight-unbalanced directed graphs. A more generalized network model is considered where the communication topology may be variable and unbalanced over time, the information flows across agents are subject to time-varying communication delays, and agents are not required to know their out-degree information accurately. To address the above challenges, we propose a novel discrete-time distributed event-triggered delay subgradient algorithm. To facilitate convergence analysis, a consensus-only “virtual” agent technique is employed, dynamically adjusting its state (active or asleep) to ensure a delay-free information flow among agents. Additionally, an augmentation approach is proposed to ensure that the augmented time-varying weight matrix is row-stochastic. It is shown that the agents’ local decision variables converge to the same optimal solution, in the case of reasonable communication delays and event-triggering thresholds. Numerical examples show the efficiency of the proposed algorithm.

In traditional leak location methods, the position of the leak point is located through the time difference of pressure change points of both ends of the pipeline. The inaccurate estimation of pressure change points leads to the wrong leak location result. To address it, adaptive dynamic programming is proposed to solve the pipeline leak location problem in this article. First, a pipeline model is proposed to describe the pressure change along pipeline, which is utilized to reflect the iterative situation of the logarithmic form of pressure change. Then, under the Bellman optimality principle, a value iteration (VI) scheme is proposed to provide the optimal sequence of the nominal parameter and obtain the pipeline leak point. Furthermore, neural networks are built as the VI scheme structure to ensure the iterative performance of the proposed method. By transforming into the dynamic optimization problem, the proposed method adopts the estimation of the logarithmic form of pressure changes of both ends of the pipeline to locate the leak point, which avoids the wrong results caused by unclear pressure change points. Thus, it could be applied for real-time leak location of long-distance pipeline. Finally, the experiment cases are given to illustrate the effectiveness of the proposed method.

In the real-time status monitoring of pipeline network, incomplete pressure data are unavoidable due to some device or communication errors. To solve this problem, a hierarchical data recovery method based on generative adversarial networks (GANs) is proposed in this article. First, a hierarchical data recovery framework is proposed to handle different numbers of incomplete data due to the structure of the semicentral pipeline network. Second, a joint attention module is presented to capture both interior nature and correlation relationships of multivariate pressure series and further guarantee the consistency of pressure data. Third, the macromicrodual discriminators are proposed to evaluate the recovery result through the combination of the local and global variation in temporal and spatial dependencies. Based on the novel structures, the proposed model is able to recover incomplete data with abnormal fluctuation values, unreasonable fixed values, or missing values. Finally, under a series of data recovery experiments, the efficiency of the proposed method is evaluated. Experimental results demonstrate that the proposed method is a practical way to ensure data recovery performance in the pipeline network.Note to Practitioners—Status monitoring based on pressure data is of great importance for safe and efficient operation in a pipeline network. However, due to unexpected situations, the appearance of incomplete pressure data affects the subsequent data processing and status analysis, resulting in an incorrect decision. In this article, a deep learning-based method is proposed to recover the incomplete data. With the help of the spatiotemporal dependencies of multivariate pressure series, the proposed method can recover different numbers of incomplete data through the no-missing part of pressure data. The experiment results show that the proposed method is better than the similar data recovery methods through three different evaluation metrics. In the future, we will address the data recovery problem without the complete data pairs in the training process.

In daily pipeline inspection, it is significant to ensure good network communication and security. With the development of drone technology, it is possible to apply drones as air routers to collect information from pipeline networks and transmit it to pipeline inspectors. It is also crucial to achieve optimal drone deployment in pipeline networks. This article proposes a two-phase evolution optimal 3-D drone layout algorithm to deploy drones in pipeline networks. First, a 3-D pipeline graph model is designed to represent the possible projection position of drones, and the objective function is proposed for optimal drone deployment. Then, in the first phase, based on the features of the 3-D pipeline graph, the drone flight rules and constraint conditions are presented to calculate the number of drones and the initial layout sequence. In the second phase, according to the objective function and the above results, every drone is continuously moved in a small area to achieve a tradeoff between signal coverage and interference. Moreover, the key parameters of the objective function can be discussed to further optimize drone deployment. Simulation results are presented to illustrate the effectiveness and advantages of the proposed algorithm.

The microgrid with the high proportion of renewable sources has become the trend of the future. However, the negative features, such as renewable energy perturbation, nonlinear counterpart, and so on, are prone to causing the low-power quality of the ac microgrid. To deal with these problems, this article proposes an event-triggered consensus control approach. First, the nonlinear state-space function regarding the ac microgrid is built, which is further transformed into the standard linear multiagent model by using the singular perturbation method. It provides indispensable preprocessing for the direct application of advanced linear control approaches. Then, based on this standard linear multiagent model, the secondary consensus approach with the leader is designed to compensate for the output voltage deviation and achieve accurate power sharing. In order to decrease the communication among various distributed generators, the event-triggered communication method is further proposed. Meanwhile, the Zeno behavior is avoided through the theoretical proof. Finally, simulation results are presented to demonstrate the effectiveness of the proposed approach.

In terms of pipeline leak detection, the unavoidable fact is that existing data could not provide enough effective leak data to train a high accuracy model. To address this issue, this article proposes mixed generative adversarial networks (mixed-GANs) as a practical way to provide additional data, ensuring data reliability. First, multitype generative networks with heterogeneous parameter-updating mechanisms are designed to explore a variety of different solutions and eliminate the potential risks of instable training and scenario collapse. Then, based on expert experience, two data constraints are proposed to describe leak characteristics and further evaluate the quality of generated leak data in the training process. Through integrating the particle swarm optimization algorithm into generative model training, mixed-GAN has better generation performance than the conventional gradient descent algorithm. Based on the above-mentioned contents, the proposed model is able to provide satisfactory leak data with different scenarios, contributing to data quantity expansion, data credibility enhancement, and data variety enrichment. Finally, extensive experiments are given to illustrate the effectiveness of the proposed generative model for pipeline network leak detection.

This paper investigates the situation awareness issue of power system with massive measured data. To address this issue, first, a graph-theory-based network partitioning algorithm is proposed to realize decentralized detection in a faster response speed, while using power flow characteristics highlights the independency of different groups. Further, a hierarchical event detection method is proposed to judge voltage change and locate event position according to spectral distribution change of established multidimensional matrix. With the proposed method, the system situation can be assessed and the knowledge of the system model is not required. In addition, the accurate result of weak event happened in system could also be obtained. The simulation results are presented to illustrate the effectiveness of the proposed detection method.

This paper investigates the residential energy management problems in the power-heat-coupling system. For better solving this issue, based on the novel concept of We-Energy (WE) for energy Internet (EI), this paper proposes a residential WE (R-WE) framework faced by the terminal users who play an important role in renewable energy consumption. Inspired by the full-duplex feature of R-WE, the power and heat supply-demand balance constraints are fulfilled in a regional unit of EI, but it may be inequality constraints for corresponding consumer, producer, or WE operation modes in only one R-WE. The R-WE framework can be classified into four operation modes, which is island mode, consumer mode, producer mode, and WE mode. On this basis, the R-WE models cooperate to achieve the objective of minimizing the operation costs, smoothing out the loads’ variations, and renewable resource fluctuations. Specifically, the R-WE framework with respect to the heat-power-coupling problem can be solved in the distributed double-consensus algorithm (DDCA), which is designed two sets of consensus algorithms by using four completely different consensus variables to calculate the power and heat multipliers, evaluate the power and heat generations and, thereby, further obtain the power mismatches of electricity and heat. Also, the Karush-Kuhn-Tucker (KKT) optimal conditions of the proposed DDCA is further proved. Meanwhile, a novel projection operation method for combined heat and power devices is designed to take the infeasible solutions mapped into the feasible region. Finally, the simulation results in different cases further demonstrate that the proposed R-WE frame can be an appropriate method to analyze the terminal consumers and harmonize multienergy producers in the process of constructing EI projects. And an R-WE framework of the campus has experimented with minority loads in island mode.

A hybrid power supply system (HPSS) based on the quasi-Z-source network is proposed for aluminum electrolysis, which can reduce energy consuming and carbon emission through the use of renewable energy. An ac–dc integrate controller is designed in the HPSS that contains a two-layer control. The first layer control is responsible for maintaining the dc bus voltage and current, which can mitigate negative effects caused by anode effect in aluminum electrolysis. The independent maximum power tracking for PV array and the dc-bus voltage balance for each quasi-Z-source dc–dc converter can be achieved by using the PV-voltage controller and dc-bus voltage controller for the PV System. To maintain the voltage of dc bus within the require voltage range of aluminum electrolysis production and ensure high input power quality of ac System, the quasi-Z-rectifier controller is employed, which can reduce the harmonic injection. The power allocation is addressed in the second control layer and a power scheme algorithm (PSA) is carried out to maximize the system efficiency and economic benefit. At last, the simulation and experimental results are provided to verify the effectiveness of the designed HPSS and the proposed PSA.

As system transient stability is one of the most important criterions of microgrid (MG) security operation, and the performance of an MG strongly depends on the placement of its energy storage devices (ESDs); optimal placement of ESDs for improving system transient stability is required for MGs. An MG structure preserving energy function is first developed for voltage source inverter-based MGs since the existing energy functions, based on synchronous generators and the conventional power system, are not applicable for MGs. The concept of internal potential energy of distributed energy resource is presented instead of the kinetic energy term in traditional energy function. Then, a novel approach for the optimal placement of ESDs is proposed based on MG structure preserving energy function for improving MG transient stability. Simulation and experimental results show that the proposed method can be used to find the optimal placement of ESDs and improve the system stability effectively.

A fuzzy min-max neural network based on data core (DCFMN) is proposed for pattern classification. A new membership function for classifying the neuron of DCFMN is defined in which the noise, the geometric center of the hyperbox, and the data core are considered. Instead of using the contraction process of the FMNN described by Simpson, a kind of overlapped neuron with new membership function based on the data core is proposed and added to neural network to represent the overlapping area of hyperboxes belonging to different classes. Furthermore, some algorithms of online learning and classification are presented according to the structure of DCFMN. DCFMN has strong robustness and high accuracy in classification taking onto account the effect of data core and noise. The performance of DCFMN is checked by some benchmark datasets and compared with some traditional fuzzy neural networks, such as the fuzzy min-max neural network (FMNN), the general FMNN, and the FMNN with compensatory neuron. Finally the pattern classification of a pipeline is evaluated using DCFMN and other classifiers. All the results indicate that the performance of DCFMN is excellent.