High renewable penetration and reduced system inertia introduce significant challenges for transient stability assessment and control. This article proposes a causality-aware, large language model–enhanced distribution-preserving graph representation learning framework (LLM-DP-GRL) for fast and accurate stability prediction and decision-making. The DP-GRL model captures both structural and distributional properties of network states, whereas large language models provide physics-informed priors that improve data efficiency and generalization under multicontingency and out-of-distribution scenarios. A causal intervention module further quantifies bus-level influence on stability margins, offering interpretable insights consistent with system dynamics. The learned surrogate model is integrated into a cooperative preventive–emergency control strategy, enabling real-time stability margin evaluation and optimization. Tests on the IEEE 39-bus and 118-bus systems show that LLM-DP-GRL achieves higher accuracy, faster convergence, and improved robustness compared with conventional machine learning, LSTM, and GNN-based methods. The proposed approach reduces online control computation from over 35 min (TDS-based) to 39 s while maintaining inference latency below 30 ms. These results demonstrate that combining graph learning, LLM-guided priors, and causal analysis provides an effective and scalable solution for stability assessment and emergency control in low-inertia, high-renewable power systems.

Distribution system state estimation (DSSE) plays a crucial role in the real-time monitoring, control, and operation of distribution networks. Besides intensive computational requirements, conventional DSSE methods need high-quality measurements to obtain accurate states, whereas missing values often occur due to sensor failures or communication delays. To address these challenging issues, a forecast-then-estimate framework of edge learning is proposed for DSSE, leveraging large language models (LLMs) to forecast missing measurements and provide pseudo-measurements. First, natural language-based prompts and measurement sequences are integrated by the proposed LLM to learn patterns from historical data and provide accurate forecasting results. Second, a convolutional layer-based neural network model is introduced to improve the robustness of state estimation under missing measurement. Third, to alleviate the overfitting of the deep-learning-based DSSE, it is reformulated as a multitask learning framework containing shared and task-specific layers. The uncertainty weighting algorithm is applied to find the optimal weights to balance different tasks. The numerical simulation on the Simbench case is used to demonstrate the effectiveness of the proposed forecast-then-estimate framework.

A novel architecture for smart meters in a Virtual Power Plant (VPP) is introduced in this research. By integrating blockchain technology, the system not only measures and quantifies diverse consumer data but also facilitates immediate control, hence improving demand responsiveness in a VPP environment. Mathematical models were created to optimize profit, battery reserve, and power balance. A novel transaction and security algorithm that enables peer-to-peer (P2P) transactions in a secure setting is used in conjunction with a power flow algorithm for real time monitoring and control to implement the proposed model. The lightweight characteristics of the algorithms enable faster and more effective computer processing. The unique identifier issued to each smart meter facilitates seamless integration with a blockchain smart contract, therefore enabling improved and secure P2P transactions. An innovative experimental setup demonstrated the framework’s ability to effectively manage energy flows while maintaining seamless wireless connection with the grid and executing transactions. The smart meter demonstrated exceptional efficiency in load management, resulting in an average loss of 1.9524W. A dedicated dapp was created just for this purpose. Through the strategic integration of algorithms and blockchain technology, this framework enhances the efficiency and reliability of the metering infrastructure, while also enabling secure transactions.

Privacy leakage and Byzantine issues are two adverse factors to optimization and learning processes of multiagent systems (MASs). Considering an unsafe MAS with these two issues, this article targets the resolution of a category of nonconvex optimization problems under the Polyak-Łojasiewicz (P-Ł) condition. To address this problem, we first identify and construct the unsafe MAS model. Under this kind of unfavorable MASs, we mask the local gradients with Gaussian noise and adopt a resilient aggregation method, self-centered clipping (SCC), to design a differentially private (DP) and Byzantine-resilient (BR) decentralized stochastic gradient algorithm, dubbed DP-SCC-PL, aiming to address a class of nonconvex optimization problems in the presence of both privacy leakage and Byzantine issues. The convergence analysis of DP-SCC-PL is challenging, as the convergence error arises from the coupled effects of DP and BR mechanisms, as well as the nonconvex relaxation, which is resolved via seeking the contraction relationships among the disagreement measure of reliable agents before and after the SCC aggregation, together with the optimal gap. Theoretical results not only reveal the trilemma between algorithm utility, resilience, and privacy, but also show that DP-SCC-PL can achieve consensus among all reliable agents. It has also been proven that if there are no privacy issues and Byzantine agents, then the asymptotic exact convergence can be recovered. Numerical experiments verify the utility, resilience, and privacy of DP-SCC-PL by tackling a nonconvex optimization problem satisfying the P-Ł condition under various Byzantine attacks.

Decentralized stochastic gradient algorithms efficiently solve large-scale finite-sum optimization problems when all agents in the network are reliable. However, most of these algorithms are not resilient to adverse conditions, such as malfunctioning agents, software bugs, and cyber attacks. This article aims to handle a class of general composite optimization problems over multiagent systems (MASs) in the presence of an unknown number of Byzantine agents. Building on a resilient aggregation mechanism and the proximal-gradient mapping method, a Byzantine-resilient decentralized stochastic proximal-gradient algorithmic framework is proposed, dubbedProx-DBRO-VR, which achieves an optimization and control goal using only local computations and communications. To asymptotically reduce the noise variance arising from local gradient estimation and accelerate the convergence, we incorporate two localized variance-reduced (VR) techniques (SAGAandLSVRG) intoProx-DBRO-VRto designProx-DBRO-SAGAandProx-DBRO-LSVRG. By analyzing the contraction relationships among the gradient-learning error, resilient consensus condition, and convergence error in a unified theoretical framework, it is proved that bothProx-DBRO-SAGAandProx-DBRO-LSVRG, with a well-designed constant (resp., decaying) step-size, converge linearly (resp., sublinearly) inside an error ball around the optimal solution to the original problem under standard assumptions. A tradeoff between convergence accuracy and Byzantine resilience in both linear and sublinear cases is also characterized. In numerical experiments, the effectiveness and practicability of the proposed algorithms are manifested via resolving a decentralized sparse machine learning problem under various Byzantine attacks.

The end-edge-cloud orchestration of the virtual power plant (VPP) enables the edge server to timely serve community users. By deploying the community energy storage system (CESS) and the community peer-to-peer (P2P) market, prosumers can form energy communities to achieve self-sufficiency of energy and independence from fuel-based power generators. This article proposed a two-stage community energy trading model under end-edge-cloud orchestration. The community P2P trading is the first stage where the edge server can execute the automatic bidding process for multiple buyers and sellers based on the real-time users’ energy profiles and the Bayesian-game-based pricing mechanism. The trading between the retailer and energy communities is the second stage where the edge server can dynamically update the optimal operation of the CESS based on the dynamic pricing mechanism. An original centralized optimization problem is decomposed into subproblems for each stakeholder and solved through the alternating direction method of multipliers (ADMM). Considering ADMM needs multiple information exchanges, a general form of the communication-censored ADMM for sharing problems is proposed to decrease the communication cost. Numerical simulations prove that the proposed mechanism can effectively increase transaction efficiency, avoid the new demand peak brought by the utilization of the CESS, and decrease the communication cost.

With the increasing environmental issues, the energy consumption and carbon emissions of data centers have become a major concern. However, in previous works, the cost and carbon reduction potential of geographically dispersed data centers with renewable generations is not fully explored due to the difficulty in matching renewable generations with stochastic incoming jobs. In this paper, the temporal and spatial variability of the carbon footprint and electricity price is revealed. Integrated with the distributed characteristics of renewable generations and geographically dispersed feature of the data centers, the carbon emission reduction potential of data centers with renewable generations is explored, leading to triple uncertainties in electricity price, fuel mix and renewable generation. To navigate such a potential, a virtual queue algorithm is designed, which makes online strategies for job scheduling of the data centers. By introducing historical correction terms, high-precision matching of the workload and renewable generation can be achieved with triple uncertainties. This leads to the economic and environmental friendliness of the proposed mechanism, which can achieve O(T) expected regret and constraint violation. Simulations based on real-world data from several states of Australia demonstrate the effectiveness of the proposed framework in cost and carbon emission reduction with triple uncertainties.

The spread of electric vehicles (EVs) could reduce greenhouse gas emissions and achieve sustainable travel patterns. However, the rapidly increasing charging demand will bring challenges to the operation of charging stations and power systems. Therefore, a two-stage EV management scheme is introduced in this article to overcome these challenges and promote sustainable transport. A charging dispatch model based on fuzzy multicriteria decision making is proposed in the first stage, where users' preferences are in the form of intuitionistic fuzzy sets to address the fuzziness and uncertainty of subjective factors and human judgment. A$\sigma$-cut similarity matrix is proposed to increase the users' satisfaction by excluding options with lower similarity. In the second stage, a noncooperative game model is proposed to incentive EVs to participate in supplementary frequency regulation (SFR). A fuzzy set is employed to reflect users' willingness to adjust charging power. The existence and uniqueness of the Nash equilibrium are investigated. Moreover, a distributed proximal best response algorithm with linear convergence is employed to find Nash equilibrium. Numerical simulations indicate that the proposed method can reduce charging costs while meeting users' preferences and facilitate EVs to participate in SFR.

Automatic generation control (AGC) is paramount in maintaining the stability and operation of power grids. Its dependence on communication systems makes it vulnerable to various cyberphysical attacks. False data injection attacks (FDIA) are particularly difficult to detect and represent a major threat to AGC systems. This article proposes a novel spatio-temporal learning algorithm that can learn the normal dynamics of the power grid with AGC system to deal with this problem. The algorithm first uses a long short-term memory autoencoder to learn the normal dynamics. It then utilizes this unsupervised learned model in detecting the various possibilities of FDIA affecting the AGC system by evaluating the reconstruction residual of each measurements sample. The proposed algorithm is data-driven which makes it resilient against AGC's parameters uncertainties and modeling nonlinearities. The effectiveness of the developed algorithm is evaluated through test cases with various basic and stealth FDIAs.

Memristive LSTM networks have been proven as a powerful Neuromorphic Computing Architecture (NCA) for various time series forecasting tasks and are recognized as the next generation of AI. However, a lack of model explainability makes it hard to properly interpret forecasting results for existing memristive LSTM networks, which makes this NCA unreliable, unaccountable and untrustworthy. In this paper, an interpretable memristive (IM) LSTM network design is proposed for time series forecasting, where the mixture attention technique is embedded into IM-LSTM cells for characterizing the variable-wise feature and the temporal importance. The updating rules and training approach are also presented for this interpretable memristive LSTM network. We evaluate this approach on a probabilistic residential load forecasting task incorporating PV. By improving model interpretability, the most influential predictive factors can be verified by Built Environment domain experts, demonstrating the effectiveness of our design.

To ensure a successful bid while maximizing profits, generation companies (GENCOs) need a self-scheduling strategy that can cope with a variety of scenarios. Therefore, distributionally robust optimization (DRO) is a good choice because it can provide an adjustable self-scheduling strategy for GENCOs in an uncertain environment, which can balance robustness and economics well compared to strategies derived from robust optimization and stochastic optimization. In this article, a novel moment-based DRO model with conditional value-at-risk is proposed to solve the self-scheduling problem under electricity price uncertainty. The size of the model mainly depends on the system size, and the computational burden increases sharply as the system size increases. For this drawback, two effective approximate models are proposed: one approximate model based on vector splitting (DRA-VS) and another based on the alternate direction multiplier method (DRA-ADMM). Both can greatly reduce calculation time and resources, while ensuring the quality of the solution, and DRA-ADMM only needs the information of the current area in each step of the solution, thus, private information is guaranteed. Simulations of three IEEE test systems are conducted to demonstrate the correctness and effectiveness of the proposed DRO model and two approximate models.

The communication infrastructure is an important part to provide the reliability for energy management in the smart grid environment. With the aim of reducing the infrastructure cost for residential energy management, this article introduces a more complex multihop wireless remote metering network model. A novel evolutionary aggregation algorithm (EAA) is proposed to obtain the minimum number and locations of the local data centers (powerful nodes) in a 2-hop wireless remote metering network which has an arbitrary number of smart meters (ordinary nodes) with arbitrary transmission ranges. In the novel 2-hop EAA, the article designs and implements two novel adaptive operations (the switch operation and the shuffle operation) to improve the algorithm performance. Then the article extends the 2-hop EAA method to a more generic n-hop EAA which could obtain the optimal result in an n-hop (n > 2) smart meter network. Comprehensive case studies and numerical statistical analyses demonstrate that the EAA could efficiently achieve the optimal results in an n-hop (n> = 2) smart meter network environment; and the novel switch and shuffle operations could efficiently improve the performance of the evolutionary algorithm. The connectivity of the smart meter network could be fulfilled with the minimum number of the powerful nodes, from which the infrastructure cost for residential energy network could be minimized.

In this article, the problem of the distributed convex optimization is investigated, where the target is to collectively minimize a sum of local convex functions over an unbalanced directed multiagent network. Each agent in the network possesses only its private local objective function, and the sum of all local objective functions constitutes the global objective function. We particularly consider the scenario, where the underlying interaction network is strongly connected and the relevant weight matrix is row stochastic. To collectively figure out the optimization problem, a distributed accelerated convergence algorithm where agents utilize uncoordinated step-sizes is presented by incorporating consensus of multiagent networks into distributed inexact gradient tracking technique. Most of the existing methods require all agents to possess the out-degree information of their in-neighbors, which is impractical and hardly inevitable as interpreted in this article. By utilizing the small-gain theorem, we prove that if the maximum step-size is positive and sufficiently small (constrained by a specific upper bound), the proposed algorithm, termed as SGT-FROST, converges geometrically to the optimal solution given that the objective functions are smooth and strongly convex. A certain convergence rate is also shown. Simulations confirm the findings in this article.

The increased complexity of modern energy network raises the necessity of flexible and reliable methods for smart grid operation. To this end, this article is centered on the economic dispatch problem (EDP) in smart grids, which aims at scheduling generators to meet the total demand at the minimized cost. This article proposes a fully distributed algorithm to address the EDP over directed networks and takes into account communication delays and noisy gradient observations. In particular, the rescaling gradient technique is introduced in the algorithm design and the implementation of the distributed algorithm only resorts to row-stochastic weight matrices, which allows each generator to locally allocate the weights on the messages received from its in-neighbors. It is proved that the optimal dispatch can be achieved under the assumptions that the nonidentical constant communication delays inflicting on each link are uniformly bounded and the noises embroiled in gradient observation of every generator are bounded variance zero mean. Simulations are provided to validate and testify the effectiveness of the presented algorithm.

In the presence of several critical issues during data acquisition in industrial-informatics-based applications, like Internet of Things (IoT) and smart grid, this article proposes a novel framework based on compressive sensing (CS) and a cascade chaotic system (CCS). This framework can ensure low overhead, confidentiality, and authentication. Based on CS and the CCS, three technologies, including CCS-driven CS, CCS-driven local perturbation, and authentication mechanism, are introduced in the proposed data acquisition framework in this article. CCS-driven CS generates the measurement matrix with chaotic initial conditions and avoids the transmission of a large-size measurement matrix. CCS-driven local perturbation only perturbs a small number of elements in the original measurement matrix for each sampling and avoids the regeneration of the large-size measurement matrix. The authentication mechanism employs the authentication password and the access password to deal with the passive tampering attack and the active tampering attack, respectively. Moreover, the permutation-diffusion structure is used to encrypt the obtained measurements to enhance the security. Both theoretical and experimental analyses validate low overhead, confidentiality, and effective authentication of the proposed data acquisition framework for a number of industrial-informatics-based applications, such as IoT.

In this paper, based on the deterministic learning (DL) theory, an approach for detection for small faults in a class of nonlinear closed-loop systems is proposed. First, the DL-based neural control approach and identification approach are employed to extract the knowledge of the control effort that compensates the fault dynamics (change of the control effort) and the fault dynamics (the change of system dynamics due to fault). Second, two types of residuals are constructed. One is to measure the change of system dynamics, another one is to measure change of the control effort. By combining these residuals, an enhanced residual is generated, in which the fault dynamics and the control effort are combined to diagnose the fault. It is shown that the major fault information is compensated by the control, and the major fault information is double in the enhanced residual. Therefore, the fault information in the diagnosis residual is enhanced. Finally, an analysis of the fault detectability condition of the diagnosis scheme is given. Simulation studies are included to demonstrate the effectiveness of the approach.

This paper considers solving a class of optimization problems which are modeled as the sum of all agents' convex cost functions and each agent is only accessible to its individual function. Communication between agents in multiagent networks is assumed to be limited: each agent can only interact information with its neighbors by using time-varying communication channels with limited capacities. A technique which overcomes the limitation is to implement a quantization process to the interacted information. The quantized information is first encoded as a binary sequence at the side of each agent before sending. After the binary sequence is received by the neighboring agent, corresponding decoding scheme is utilized to resume the original information with a certain degree of error which is caused by the quantization process. With the availability of each agent's encoding states (associated with its out-channels) and decoding states (associated with its in-channels), we devise a set of distributed optimization algorithms that generate two iterative sequences, one of which converges to the optimal solution and the other of which reaches to the optimal value. We prove that if the parameters satisfy some mild conditions, the quantization errors are bounded and the consensus optimization can be achieved. How to minimize the number of quantization level of each connected communication channel in fixed networks is also explored thoroughly. It is found that, by properly choosing system parameters, one bit information exchange suffices to ensure consensus optimization. Finally, we present two numerical simulation experiments to illustrate the efficacy of the algorithms as well as to validate the theoretical findings.

This paper considers the problem of designing adaptive learning algorithms to seek the Nash equilibrium (NE) of the constrained energy trading game among individually strategic players with incomplete information. In this game, each player uses the learning automaton scheme to generate the action probability distribution based on his/her private information for maximizing his own averaged utility. It is shown that if one of admissible mixed-strategies converges to the NE with probability one, then the averaged utility and trading quantity almost surely converge to their expected ones, respectively. For the given discontinuous pricing function, the utility function has already been proved to be upper semicontinuous and payoff secure which guarantee the existence of the mixed-strategy NE. By the strict diagonal concavity of the regularized Lagrange function, the uniqueness of NE is also guaranteed. Finally, an adaptive learning algorithm is provided to generate the strategy probability distribution for seeking the mixed-strategy NE.

Communication data rates and energy constraints are two important factors that have to be considered in the coordination control of multiagent networks. Although some encoder-decoder-based consensus protocols are available, there still exists a fundamental theoretical problem: how can we further reduce the update rate of control input for each agent without the changing consensus performance? In this paper, we consider the problem of average consensus over directed and time-varying digital networks of discrete-time first-order multiagent systems with limited communication data transmission rates. Each agent has a real-valued state but can only exchange binary symbolic sequence with its neighbors due to bandwidth constraints. A class of novel event-triggered dynamic encoding and decoding algorithms is proposed, based on which a kind of consensus protocol is presented. Moreover, we develop a scheme to select the numbers of time-varying quantization levels for each connected communication channel in the time-varying directed topologies at each time step. The analytical relation among system and network parameters is characterized explicitly. It is shown that the asymptotic convergence rate is related to the scale of the network, the number of quantization levels, the system parameter, and the network structure. It is also found that under the designed event-triggered protocol, for a directed and time-varying digital network, which uniformly contains a spanning tree over a time interval, the average consensus can be achieved with an exponential convergence rate based on merely 1-b information exchange between each pair of adjacent agents at each time step.

In this paper, we consider the event-triggered distributed average-consensus of discrete-time first-order multiagent systems with limited communication data rate and general directed network topology. In the framework of digital communication network, each agent has a real-valued state but can only exchange finite-bit binary symbolic data sequence with its neighborhood agents at each time step due to the digital communication channels with energy constraints. Novel event-triggered dynamic encoder and decoder for each agent are designed, based on which a distributed control algorithm is proposed. A scheme that selects the number of channel quantization level (number of bits) at each time step is developed, under which all the quantizers in the network are never saturated. The convergence rate of consensus is explicitly characterized, which is related to the scale of network, the maximum degree of nodes, the network structure, the scaling function, the quantization interval, the initial states of agents, the control gain and the event gain. It is also found that under the designed event-triggered protocol, by selecting suitable parameters, for any directed digital network containing a spanning tree, the distributed average consensus can be always achieved with an exponential convergence rate based on merely one bit information exchange between each pair of adjacent agents at each time step. Two simulation examples are provided to illustrate the feasibility of presented protocol and the correctness of the theoretical results.

This paper proposes a generalized Hopfield network for solving general constrained convex optimization problems. First, the existence and the uniqueness of solutions to the generalized Hopfield network in the Filippov sense are proved. Then, the Lie derivative is introduced to analyze the stability of the network using a differential inclusion. The optimality of the solution to the nonsmooth constrained optimization problems is shown to be guaranteed by the enhanced Fritz John conditions. The convergence rate of the generalized Hopfield network can be estimated by the second-order derivative of the energy function. The effectiveness of the proposed network is evaluated on several typical nonsmooth optimization problems and used to solve the hierarchical and distributed model predictive control four-tank benchmark.

Dynamic security assessment (DSA) is an important issue in modern power system security analysis. This paper proposes a novel pattern discovery (PD)-based fuzzy classification scheme for the DSA. First, the PD algorithm is improved by integrating the proposed centroid deviation analysis technique and the prior knowledge of the training data set. This improvement can enhance the performance when it is applied to extract the patterns of data from a training data set. Secondly, based on the results of the improved PD algorithm, a fuzzy logic-based classification method is developed to predict the security index of a given power system operating point. In addition, the proposed scheme is tested on the IEEE 50-machine system and is compared with other state-of-the-art classification techniques. The comparison demonstrates that the proposed model is more effective in the DSA of a power system.

In this paper, global exponential synchronization of a class of discrete delayed complex networks with switching topology has been investigated by using Lyapunov-Ruzimiki method. The impulsive scheme is designed to work at the time instant of switching occurrence. A time-varying delay-dependent criterion for impulsive synchronization is given to ensure the delayed discrete complex networks switching topology tending to a synchronous state. Furthermore, a numerical simulation is given to illustrate the effectiveness of main results.

Chaotic simulated annealing (CSA) is a relatively new heuristic optimization technique and has been widely applied to optimization problems because of its simplicity and capability of finding fairly good solutions rapidly. However, currently only experimental results are used for verifying its superiority. In this paper, a new of chaotic simulated annealing method (CSA) is introduced and then a mathematic proof is given. It shows that the Markov Chain associated with the algorithm is weakly ergodic, which guarantees that the asymptotic behavior of the algorithm is independent of initial states. Furthermore, the theoretical analysis of the proposed CSA is very important to understand the essential features which make the algorithm work well.