Wind power data often suffers from missing values due to sensor faults and unstable transmission at edge sites. While federated learning enables privacy-preserving collaboration without sharing raw data, it remains vulnerable to anomalous updates and privacy leakage during parameter exchange. These challenges are amplified in open industrial environments, necessitating zero-trust (ZT) mechanisms, where no participant is inherently trusted. To address these challenges, this work proposes ZTFed-MAS2S, a ZT federated learning framework that integrates a multihead attention-based sequence-to-sequence imputation model. ZTFed integrates verifiable differential privacy with noninteractive zero-knowledge proofs and a confidentiality and integrity verification mechanism to ensure verifiable privacy preservation and secure model parameters transmission. A dynamic trust-aware aggregation mechanism is employed, where trust is propagated over similarity graphs to enhance robustness, and communication overhead is reduced via sparsity- and quantization-based compression. MAS2S captures long-term dependencies in wind power data for accurate imputation. Extensive experiments on real-world wind farm datasets validate the superiority of ZTFed-MAS2S in both federated learning performance and missing data imputation, demonstrating its effectiveness as a secure and efficient solution for practical applications in the energy sector.

Mobile energy storage systems (MESSs) represent a proactive approach to load restoration of faulted microgrids. Existing studies mainly focus on minimizing the overall cost of the MESS fleet but fail to guarantee that self-interested MESSs are willing to follow the optimal social cost solution. Hence, this article allows MESSs to make independent decisions and formulates a nonconvex game. In particular, we incorporate the maximum tolerable service waiting time and construct a potential function to prove that the selfish actions of MESSs converge to a Nash equilibrium. We derive a small upper bound on the price of anarchy (PoA), demonstrating that granting MESSs the autonomy to make self-interested Nash decisions does not significantly increase the overall social cost. Moreover, we model subjective behaviors under uncertain grid power availability, accounting for both loss-sensitive and gain-seeking tendencies. Simulation results show that for different MESS fleet sizes and battery anxiety extents, Nash equilibria are always achieved, with all PoA values below the theoretical bound. Higher MESS numbers or battery anxiety extents improve load restoration performance. Under uncertain surplus energy, gain-seeking MESSs behave more aggressively and earn higher average profits.

The operation and control of active distribution networks (ADNs) are becoming increasingly important due to the high penetration of renewable energy (RE). The inherent uncertainty of RE can affect the stability and efficiency of ADN operations. To mitigate the inherent uncertainty and rapid variability of the high RE penetration in ADNs, this article uses an online ADN reconfiguration (ADNR) approach to ensure swift responses to RE fluctuations. Unlike traditional deep reinforcement learning (DRL)-based methods, which typically model the ADNR as a Markov decision process (MDP) and rely on historical ADN data to train the DRL agent, this approach may lead to a mismatch between the MDP's characteristics and the actual ADNR and pose challenges in handling scenarios that do not exist in the training data. To address this issue, this article proposes an online-offline DRL framework for online ADNR. Initially, during the offline stage, ADNR is formulated as a state-driven Markov decision process, which incorporates the operational characteristics of the ADN. Following this, a state-driven proximal policy optimization (SD-PPO) algorithm is proposed to enhance the generalization capability of DRL. In the subsequent step, we present the optimized action proximal policy optimization (OA-PPO) algorithm, which performs personalized training based on SD-PPO to further improve DRL performance in the online stage. The proposed approach is applied to three IEEE ADN systems. Numerical results demonstrate the effectiveness of our approach in reducing power loss and enhancing RE accommodation. Furthermore, detailed comparisons with other DRL and traditional ADNR algorithms confirm the superior computational performance of our proposed method.

Robust optimization (RO) has been widely used in the hydrogen-data-center microgrid (H2-DCMG) optimal operations. However, the operation results based on RO are too conservative. Statistical feasibility can be introduced into RO to reduce conservatism. Therefore, statistical feasibility-based RO is adopted in the H2-DCMG operations optimization. In this study, a data-driven statistical-feasibility-based robust rolling optimization framework is constructed for the optimal operations of the c-DCMG. In this framework, DC temperature is influenced by the uncertain outside temperature, and an uncertainty set is needed to express the uncertain outside temperature. Unfortunately, the existing studies that construct the uncertainty set satisfying statistical feasibility only constructs the ellipsoid uncertainty sets. The ellipsoid uncertainty sets will be converted into the second-order cone constraints, which will increase the complexity when solving. In this study, the Statistical-Guarantee-based Vertex Link (SGVL) algorithm is proposed to construct the polyhedron uncertainty sets, which are used to describe the uncertainty of the outside temperature. Moreover, statistical feasibility-based DC temperature bound is guaranteed by the optimal operations obtained based on these uncertainty sets. Compared with the traditional ellipsoid uncertainty set, the polyhedron uncertainty set can reduce the complexity of the optimization problem and improve the efficiency of the solution process. Case studies based on the real-world temperature dataset are processed. The results show that the introduction of statistical feasibility can reduce the total operation cost by 0.29%~0.64%. The average solving time of the optimization problems based on the polyhedron uncertainty sets constructed using the SGVL algorithm also reduces by 7%~13%. The cases also verify that other uncertainty parameters and different kinds of forecasters do not influence the performance and effectiveness of the framework. Note to Practitioners—This paper focuses on optimizing the operations of a hydrogen-data center microgrid (H2-DCMG) to minimize its operation cost in the way of statistical feasibility-based robust optimization. The statistical feasibility is introduced into the framework for the relaxation of the data center (DC) temperature bound. The Statistical-Guarantee-based Vertex Link (SGVL) algorithm is proposed to construct the uncertainty set of outside temperature that guarantees the dispatch results satisfying statistical feasibility. In practice, the settings of the framework and the data used in the SGVL are significant. Firstly, in the rolling dispatch, the length of the forecasting period needs also to be set after the trade-off between the solving efficiency, the dispatch economy and the DC temperature stability. Secondly, the pre-set DC temperature bound is advisable to be set below the maximum temperature that does not harm its normal operation. When constructing the uncertainty sets, the two parameters of the statistical feasibility need also to be set after the trade-off between the economics of dispatch results and the acceptability of constraint violations. The dataset and the actual forecasting error need to remain equally distributed to guarantee the performance of the dispatch of the proposed framework. The proposed framework can be readily implemented and integrated into the actual dispatch of H2-DCMG.

The accurate characterization of net load uncertainty can ensure the economy and stability of renewable power systems operation. In existing studies, Gaussian mixture model (GMM) and Dirichlet process mixture model (DPMM) are powerful tools for characterizing the uncertainty of monthly net load. However, the correlation among the Gaussian components and the common distribution characteristics among the monthly net load are not considered in these studies, which may lead to lower characterization accuracy. To solve these issues, we propose a hierarchical uncertainty characterization method for monthly net load considering Gaussian component reduction and correlation. Firstly, the method obtains the Gaussian mixture components and the label information of the annual net load by the Expectation-Maximum (EM) algorithm. Then, the Gaussian components of the monthly net load are corrected by the label information, which helps extract the common distribution characteristics among the monthly net load. On this basis, the corrected Gaussian components are considered as the base distribution. A component-preserving Expectation-Maximum (CPEM) algorithm is developed for component reduction. This realizes the uncertainty characterization of the monthly net load with high accuracy and lower time consumption. Importantly, the temporal correlation of net load is converted into the correlation among the Gaussian components, which are explicitly characterized by the Spearman coefficient. Finally, the superiority of the proposed method is verified with actual data collected in Australia. Note to Practitioners—In this article, we address the issue of monthly net load uncertainty characterization in renewable power systems. A hierarchical uncertainty characterization method is proposed to enable the distribution characteristic extraction of monthly net load. Most existing works on uncertainty characterization use GMM and DPMM, where the internal information in the net load data (e.g., distribution and component correlation information) is poorly utilized. This poses a considerable challenge for accurately analyzing the net load uncertainty. To this end, the article proposes a hierarchical uncertainty characterization method for monthly net load considering Gaussian component reduction and correlation. In this method, the common and typical distribution characteristics of monthly net load are considered by the CPEM algorithm. Moreover, the temporal information of the net load is transformed as the correlation among the Gaussian components, which are integrated into the E-step in the proposed CPEM algorithm. Since more internal information is utilized, the proposed method is helpful in characterizing the net load uncertainty by means of high accuracy and lower time consumption. The results of the uncertainty characterization can be readily implemented in the planning operation and real-time dispatch of renewable power systems.

The rapid development of renewable energy sources (RESs) has led to their increased integration into microgrids (MGs), emphasizing the need for safe and efficient energy management in MG operations. We investigate the methods of MG energy management, primarily categorized into model-based and model-free approaches. Due to a lack of incremental knowledge, model-based methods need to be reengineered for new scenarios during the optimization process, leading to reduced computational efficiency. In contrast, model-free methods can obtain incremental knowledge via trial-and-error in the training phase, and output energy management scheme rapidly. However, ensuring the safety of the scheme during the training phases poses significant challenges. To address these challenges, we propose a safe reinforcement learning (SRL) framework. The proposed SRL framework initially includes a safety assessment optimization model (SAOM) to evaluate scheme constraints and refine unsafe schemes for ensuring MG safety. Subsequently, based on SAOM, the MG energy management issue is formulated as an assess-based constrained Markov decision process (A-CMDP), enabling the SRL can be adopted in this issue. After that, we adopt a Lyapunov-based safety policy optimization for agent policy learning to ensure that policy updates are confined within a safe boundary, theoretically ensuring the safety of the MG throughout the learning process. Numerical studies highlight the superior performance of our proposed method. Specifically, the SRL framework effectively learns energy management policy, ensures MG safety, and demonstrates outstanding outcomes in the economic operation of MG.

Privacy of user is becoming increasingly significant in constructing efficient multiagent energy management systems for multimicrogrid (MMG). As an emerging privacy-protection method, federated learning (FL) has been used to prevent data breaches in the MMG-related field. However, with the ever-growing participants, the underlying communication burden existing in FL is evident. Besides, since the neural network layers collectively determine an agent's performance, the possible difference in layer convergence speeds would cause the inconsistency problem, that is, the FL may degrade the convergence rate of those fast-convergent layers, which weakens the overall performance of the agent. To address these issues, a communication-efficient FL (CEFL) algorithm is proposed in this study. Considering the cooperative relationship among layers, a layer evaluation (LE) mechanism is developed in CEFL to evaluate layer contribution through the Shapley value (SV), a profit distribution approach for coalitions. In this way, only partial layers with the highest contributions are selected to be uploaded to the server. In addition, instead of average parameters aggregation, a communication-efficient parameter aggregation method is proposed in CEFL to update the parameters of the global model (GM), in which an aggregation model (AM) is developed to receive parameters for aggregation. The performance of the proposed CEFL is verified by the numerical analysis of MMGs with 3-8 MGs participating. Furthermore, experiments investigate the influence of the hyperparameter in the CEFL and also demonstrate performance improvements, compared with the other four state-of-the-art algorithms.

With increasing deployment of distributed energy resources, the energy market which aims for local generation and load profile redistribution is facing the challenge to accommodate various types of participants. To realize social welfare maximization with privacy preserving in a dynamic energy market, this article propose a multiagent reinforcement learning (MARL) method for quotation decision optimization in continuous double auction (CDA)-based peer-to-peer (P2P) energy market. To address the nonstationarity and privacy violation brought by multiagent context, we utilize mean-field approximation to abstract the unauthorized local information of other agents from the public market dynamics. An abstract Q-value function is developed for each agent to infer the neighbor agents' local observation and action through the public clearing results in the dynamic CDA market. Moreover, to avoid sparse reward so as to stabilize the learning process, we propose a dynamic potential-based reward shaping term in the reward. Without altering the learnt optimal policies, the agents can be informed with the additional energy storage state as the reward shaping in each time instants. To validate the effectiveness and economy of our proposed method, simulation studies are conducted on a real-world dataset. Simulation results show that the proposed MARL method produces up to 17% more convergent episodic reward and 67% less energy bills which indicates competitive convergence performance and significant economic benefits.

The utilization of large-scale distributed renewable energy (RE) promotes the development of the multimicrogrid (MMG), which raises the need of developing an effective energy management method to minimize economic costs and keep self energy sufficiency. The multiagent deep reinforcement learning (MADRL) has been widely used for the energy management problem because of its real-time scheduling ability. However, its training requires massive energy operation data of microgrids (MGs), while gathering these data from different MGs would threaten their privacy and data security. Therefore, this article tackles this practical yet challenging issue by proposing a federated MADRL (F-MADRL) algorithm via the physics-informed reward. In this algorithm, the federated learning (FL) mechanism is introduced to train the F-MADRL algorithm, thus ensures the privacy and the security of data. In addition, a decentralized MMG model is built, and the energy of each participated MG is managed by an agent, which aims to minimize economic costs and keep self energy sufficiency according to the physics-informed reward. At first, MGs individually execute the self-training based on local energy operation data to train their local agent models. Then, these local models are periodically uploaded to a server and their parameters are aggregated to build a global agent, which will be broadcasted to MGs and replace their local agents. In this way, the experience of each MG agent can be shared and the energy operation data are not explicitly transmitted, thus protecting the privacy and ensuring data security. Finally, experiments are conducted on Oak Ridge National Laboratory distributed energy control communication laboratory MG (ORNL-MG) test system, and the comparisons are carried out to verify the effectiveness of introducing the FL mechanism and the outperformance of our proposed F-MADRL.

Accurate spatiotemporal traffic flow forecasting is significant for the modern traffic management and control. In order to capture the spatiotemporal characteristics of the traffic flow simultaneously, we propose a novel spatiotemporal residual graph attention network (STRGAT). First, the network adopts a deep full residual graph attention block, which performs a dynamic aggregation of spatial features regarding the node information of the traffic network. Second, a sequence-to-sequence block is designed to capture the temporal dependence in the traffic flow. The traffic flow data with weekly periodic dependencies are also integrated and STRGAT is used for traffic forecasting of traffic road networks. The experiments are conducted on three real data sets in California, USA. Results verify that our proposed STRGAT is able to learn the spatiotemporal correlation of traffic flow well and outperforms the state-of-the-art methods.

With the increasing penetration of renewable energy and flexible loads in smart grids, a more complicated power system with high uncertainty is gradually formed, which brings about great challenges to smart grid operations. Traditional optimization methods usually require accurate mathematical models and parameters and cannot deal well with the growing complexity and uncertainty. Fortunately, the widespread popularity of advanced meters makes it possible for smart grid to collect massive data, which offers opportunities for data-driven artificial intelligence methods to address the optimal operation and control issues. Therein, deep reinforcement learning (DRL) has attracted extensive attention for its excellent performance in operation problems with high uncertainty. To this end, this article presents a comprehensive literature survey on DRL and its applications in smart grid operations. First, a detailed overview of DRL, from fundamental concepts to advanced models, is conducted in this article. Afterward, we review various DRL techniques as well as their extensions developed to cope with emerging issues in the smart grid, including optimal dispatch, operational control, electricity market, and other emerging areas. In addition, an application-oriented survey of DRL in smart grid is presented to identify difficulties for future research. Finally, essential challenges, potential solutions, and future research directions concerning the DRL applications in smart grid are also discussed.

The optimal frequency control of autonomous microgrids (MGs), i.e., to achieve fast frequency recovery and dynamic power adjustment of the distributed generators in proportion to predefined participation factors, can be achieved in a fully distributed way based on the subgradient consensus protocol. However, such a distributively controlled MG is susceptible to different types of cyber attacks infiltrated from different locations. In this article, a robust and resilient distributed optimal frequency control scheme is proposed to address the threat of cyber attacks. It is facilitated by introducing an auxiliary networked system interconnecting with the original cooperative control system. On condition that the cyber attacks are within certain ranges, the robust design can maintain the functionalities by significantly attenuating the impact. Otherwise, the cyber attacks can be easily detected, and resilient reactions can be taken to mitigate their influences via isolation. Simulation results in a modified IEEE 34-bus MG validate the effectiveness of the proposed approach.

In this article, the approach of an adjustable uncertainty set is proposed to deal with the uncertainty of renewable energy (RE) in unit commitment (UC). Demand response (DR) is co-optimized to reduce the operation risk of load shedding and RE curtailment when the RE falls out of the adjustable uncertainty set. In comparison with existing approaches with an adjustable uncertainty set, the proposed approach further incorporates DR requires no predefined parameters to constrain the deviation from the forecast RE. It divides the maximum RE set into subintervals, and bounds of the adjustable uncertainty set are determined among these subintervals with the consideration of DR in reducing the operation risk. The original mixed-integer nonlinear problem of UC scheduling is transformed to be a mixed-integer linear problem to be effectively solved. The performance of the proposed approach is verified on the IEEE 6-bus, 30-bus, and 300-bus systems. Through the comparison with existing methods, the effectiveness of the proposed approach in reducing the conservativeness is verified. The effectiveness of the proposed approach in the reduction of the operation risk of load shedding and RE curtailment is verified through the comparison between situations with and without DR.

The complexity and randomness of the power system with distributed energy resources have led to the difficulties for fast optimal power flow (OPF) analysis. As a remedy, in this paper, we develop an interior point Powerball algorithm to accelerate the OPF solution process. To achieve better convergence characteristics, the proposed IPPB algorithm which is based on the Powerball optimization method, improves the search directions during iterative optimization by a nonlinear transformation. Also, a Newton—Raphson Powerball algorithm is derived for a faster power flow calculation, which is a basic yet critical part of the OPF problem. Numerical case studies are conducted on benchmark power systems with different scales to validate the proposed algorithms. Performances of the proposed algorithms to address improper initial points are studied by randomly picking the initial bus voltages. Numerical study results verify the feasibility and superiority of the proposed algorithms.

The irregular and truncated probabilistic characteristics of wind power uncertainty lead to unknown influences on the power system operation. In this article, we propose a new probabilistic optimal power flow (POPF) framework, which can cope with such uncertainties, while taking into account the correlations among the wind generation power in multiple wind farms. A truncated multivariate Gaussian mixture model (Trun-MultiGMM) is designed to describe the irregular and multimodal wind power distributions with its typical truncation feature. Then an efficient Markov chain quasi-Monte-Carlo (MCQMC) sampler is developed to deliver wind power samples from the customized Trun-MultiGMM. Numerical simulations are conducted on the publicly available wind generation datasets and multiple benchmark power systems. The results have verified the effectiveness and efficiency of Trun-MultiGMM as well as the proposed POPF framework with MCQMC sampler.

Power quality events are usually associated with more than one disturbance and their recognition is typically based on multilabel learning. In this study, we propose a new method for recognizing multiple power quality disturbances (MPQDs) based on variational mode decomposition (VMD) and a random discriminative projection extreme learning machine for multilabel learning (RDPEML). First, VMD is employed to decompose the MPQDs into several intrinsic mode functions and the standard energy differences of each mode are extracted as features that form the input vectors of the classifier. Second, a novel multilabel classifier called RDPEML is constructed by combining a random discriminative projection multiclass extreme learning machine (ELM) and a thresholding learning method-based kernel ELM. In order to obtain better classification performance, a tenfold cross-validation embedded particle swarm optimization approach is utilized to search for the optimal values of the structural parameters. Finally, a test study was conducted using MATLAB synthetic signals and real signals sampled from a three-phase standard source under different noise conditions. Compared with the several recent state-of-the-art multilabel learning algorithms, RDPEML achieved better classification performance with superior computational speed.

In this paper, the distributionally robust optimization approach (DROA) is proposed to schedule the energy consumption of the heating, ventilation and air conditioning (HVAC) system with consideration of the weather forecast error. The maximum interval of the outdoor temperature is partitioned into subintervals, and the proposed DROA constructs the ambiguity set of the probability distribution of the outdoor temperature based on the probabilistic information of these subintervals of historical weather data. The actual energy consumption will be adjusted according to the forecast error and the scheduled consumption in real time. The energy consumption scheduling of HVAC through the proposed DROA is formulated as a nonlinear problem with distributionally robust chance constraints. These constraints are reformulated to be linear and then the problem is solved via linear programming. Compared with the method that takes into account the weather forecast error based on the mean and the variance of historical data, simulation results demonstrate that the proposed DROA effectively reduces the electricity cost with less computation time, and the electricity cost is reduced compared with the traditional robust method.

Microgrid (MG) represents one of the major drives of adopting Internet of Things for smart cities, as it effectively integrates various distributed energy resources. Indeed, MGs can be connected with each other and presented as a system of multimicrogrid (MMG). This paper proposes the optimal operation of MMGs by a cooperative energy and reserve scheduling model, in which energy and reserve can be cooperatively utilized among MMGs. In addition, values of Shapely are introduced to allocate economic benefits of the cooperative operation. Finally, a case study based on a system of MMGs is conducted, and simulation results verify the effectiveness of the proposed cooperative scheduling model.

In this paper, a new classification approach for detection and classification of complex power quality disturbances (PQDs) using a three-level multiply connected Bayesian network is proposed. First, the model consisting of features evidence layer, disturbances state layer, and circumstance evidence layer is established, which represent the features extracted from the sample signal, the state of each single label of PQDs and the circumstance factors that may affect the PQDs, respectively. Second, the parameters of three-level multiply connected Bayesian network (TLBN) are studied from statistical data and Monte Carlo simulations. Finally, the classification is determined by computing the posterior marginal probabilities of each event given observed evidences. The new method not only utilizes the existing features extracting methods, but also takes the historical data, and other surrounding factors into account. Simulation results and real-life PQ signal tests show that the performances of TLBN classification of complex disturbances are better than the other approaches in existing literatures.