In direct-current (DC) microgrids (MGs), distributed secondary control is essential for achieving both voltage restoration and accurate current sharing, wherein precise parameter estimation plays a critical role in ensuring satisfactory control performance. To address system uncertainties, this paper presents a cascaded framework consisting of an adaptive parameter estimator and a distributed secondary controller for DC MGs. The proposed framework enables real-time online estimation of transmission line resistance and inductance while fulfilling the voltage restoration and current sharing. Since it is often challenging to validate the persistent excitation (PE) condition in practical DC MGs, we propose two parameter estimation algorithms. The first one is a standard gradient descent estimator, which requires strict PE to be satisfied. The second algorithm integrates preconditioning dynamics with gradient descent and only needs a weaker interval excitation (IE) condition to achieve effective estimation. Moreover, by integrating a dynamic average model with the virtual current derivative (VCD) approach, the DC MG system is reduced to a second-order model, which simplifies the joint design of parameter estimation and control, as well as facilitates closed-loop stability analysis. Finally, the effectiveness of the proposed method is verified through numerical simulations and experiments.

Distributed energy systems are shifting from stand-alone microgrids to networked multienergy microgrids (N-MEMGs), where energy management must handle multienergy coupling, renewable uncertainty, and strict device/network safety under distributed operation. A safety-guaranteed framework that couples a multi-actor single-critic multiagent deep reinforcement learning method with randomized ensembled double$Q$-learning (REDQ) and a model-based safety layer is proposed. Actors run locally at nodes for decentralized operation; a centralized REDQ-based critic module reduces$Q$-value overestimation and reliably guides policy updates; and the safety layer analytically enforces device, power balance, and multitimescale constraints, explicitly capturing inertia-induced effects along hydrogen device chains. On a five-node N-MEMG, the proposed method coordinates energy trading, hydrogen storage, and peak shaving, achieves zero observed safety violations over 12 000 evaluation steps, and outperforms mainstream baselines (multi-agent twin delayed deep deterministic policy gradient (MATD3), multiagent deep deterministic policy gradient, and multiagent soft actor critic) with an average daily adaptive normalized score of 98% across test days. The results point to a practical route to safe and scalable energy management in N-MEMGs.

Fault diagnosis of industrial equipment is crucial to ensure production safety, extend equipment life, and improve maintenance efficiency. Traditional acoustic diagnosis methods are susceptible to noise interference and domain offset in complex industrial scenarios, and their generalisation capability is limited. In this article, a cross-domain fault diagnosis method based on harmonic-percussion source separation (HPSS) and adaptive dual-channel feature fusion (ADFF) is proposed. Firstly, the HPSS algorithm is used to decompose the Log-Mel spectrogram into harmonic and percussion components to effectively separate the fault features from noise; secondly, the ADFF module is designed to dynamically fuse the time-frequency features of the two types of components through the dual-channel convolutional network and the squeeze-excitation (SE) attention mechanism to enhance the cross-domain generalisation capability. Experiments on a multi-condition drone fault dataset show that the diagnostic accuracy of the proposed approach in cross-equipment and cross-load scenarios is improved by up to 7.56% compared with the traditional approach.

Modern energy systems increasingly rely on complex, multi-energy microgrids incorporating diverse energy carriers, including hydrogen-based technologies, yet their efficient dispatch remains challenging due to the need for precise coordination across heterogeneous resources. Existing multi-agent reinforcement learning approaches often fail to capture the nuanced interactions between different energy vectors and agents. We propose an Attention-boosted Multi-Agent Twin Delayed Deep Deterministic Policy Gradient (MATD3) algorithm that enhances inter-agent coordination through self-attention mechanisms in the critic network, enabling more effective feature extraction and global value assessment. Comprehensive simulations demonstrate our approach significantly outperforms baseline methods, reducing operational costs by up to 37.67% and carbon emissions by 34.1%, while maintaining superior power balance across microgrids. These results establish attention-enhanced MATD3 as a promising solution for optimizing complex energy systems with high renewable penetration and diverse storage technologies.

Fabric defect detection is a crucial step in the textile manufacturing process and serves as a key factor in ensuring high-quality fabric production. However, fabric defect images exhibit significant diversity, with defects often complex and irregularly distributed. Existing fabric defect detection algorithms face challenges such as low detection accuracy and slow processing speeds. In this paper, we propose a novel fabric defect detection algorithm based on YOLOv11, named YOLO-FEE. To reduce model parameters and computational overhead, we integrate a FasterNet module into YOLOv11. To enhance the model’s ability to represent discriminative features, we design the EMA module, which leverages a multi-scale attention mechanism to effectively capture detailed information at various scales. Furthermore, to improve the model’s stability and detection accuracy, we adopt the EIoU bounding-box loss function, which refines the IoU calculation method to more precisely evaluate the overlap between predicted and ground-truth bounding boxes. Experimental results demonstrate that even without applying quantization or other acceleration techniques, our approach shows significant potential to enhance the speed of inference and overall performance.

Despite the success of data-driven methods in detecting false data injection (FDI) attacks, the remarkable progress is inseparable from massive labeled and class-balanced measurements. However, the collected measurement datasets in smart grids typically exhibit skewed class distributions and are partially labeled due to the expensive labeling costs. Learning from such non-ideal datasets undoubtedly results in the degenerated detection performance of the data-driven methods. To cope with this issue, we propose an optimal transport (OT)-based framework named DeSSW to promote the utilization of plentiful unlabeled measurements through the self-training technique, which improves the ability to identify FDI attacks by producing distinguishable representations for normal and attacked measurements in the feature space. Specifically, DeSSW consists of a novel re-weighting algorithm and a debiased self-training strategy. The re-weighting algorithm ensures high-confidence unlabeled measurements dominate the self-training procedure, and the debiased self-training strategy mitigates bias accumulation in the iterative self-training procedure. Extensive experiments demonstrate that DeSSW achieves superior detection performance when facing the combinatorial challenge of partially labeled and class-imbalanced measurements, even if the measurements are noisy.

This article aims to develop a lightweight, decentralized federated learning (FL)-based strategy for electricity theft detection (ETD). Different from most of the existing ETD solutions, which typically deploy centralized deep learning models, our proposed method utilizes well-pruned lightweight networks and operates in a completely decentralized manner while maintaining the performance of the ETD model. Specifically, to protect data privacy, a novel sequential decentralized FL (SDFL) framework was designed, eliminating the centralized parameter aggregation node in traditional FL. Each client communicates model parameters only with its neighbors and trains its model locally. In addition, to facilitate deployment on edge devices, model pruning techniques are integrated with the sequential transmission characteristics of the SDFL framework. A progressive channel pruning technique is proposed, gradually reducing the number of model channels during training to promote model compression and simplify field deployment. Experiments demonstrate that our strategy compressed the model floating point operations from 18.32 to 3.60M and reduced the number of parameters from 8.61 to 3.47M, while protecting user privacy, and maintaining good performance. Deployment results on the edge devices, i.e., Raspberry Pi, indicate that our proposed strategy reduces the model inference time from 329.35 to 141.50 s, enhancing the detection efficiency by 57.04%.

Remote dc microgrids under integrated satellite terrestrial networks (ISTNs) as typical cyber-physical systems are vulnerable to cyberattacks and noises due to its broadcast nature and atmospheric interference. In this article, a distributed cyber resilient control strategy is proposed for such microgrids against denial of service (DoS) attacks and inherent noises associated with ISTNs. First, an intermediate observer is employed in each distributed generator (DG) to estimate its neighbors’ voltages and power sharing considering ISTN noises and DoS attacks. Then, a distributed resilient algorithm with a compensation component is proposed to mitigate the adverse effects of ISTN noises even with DoS attacks. It is theoretically demonstrated that the proposed control strategy can achieve voltage restoration and accurate power sharing in the presence of ISTN noises and DoS attacks. Finally, the effectiveness of the proposed control strategy is validated by extensive case studies conducted on the real-time OPAL-RT with digital signal processor controllers.

In the case of label space alignment, the existing domain adaptation (DA)-based fault diagnosis approaches have achieved high accuracy. In real industrial scenarios, however, the label space of the target domain is usually a subset of the label space of the source domain, called partial DA (PDA). The main challenge of PDA lies in how to separate common samples from private samples. In existing works, different weights are usually assigned to different samples based on the prediction score of the classifier, but the negative transfer caused by the data distribution alignment of private and common samples is ignored. To address this problem, class-consistency matching is proposed in this article, which uses label consensus score to identify classes in target clusters to discover common and private samples. In addition, parameter-free cosine attention wavelet blocks (PCAWBs) are designed to learn the complementary spatial-domain and frequency-domain features to enrich the domain-invariant features extracted by the shared encoder. Experiments on the real motor system demonstrate that the proposed method significantly outperforms state-of-the-art PDA fault diagnosis approaches.

In this paper, the optimal power allocation and frequency restoration problem for islanded alternating-current (AC) microgrids (MGs) is addressed under false data injection (FDI) frequency sensor attacks. Firstly, a distributed proportional and integral secondary controller is developed without considering the FDI attack. In addition to the advantages of the traditional distributed structure, this controller also has more advantages, such as simple tuning and robustness to external disturbances. Also, the theoretical analysis proves that the developed controller can drive the system frequency to the reference value, while the optimal power distribution is realized. Then, a distributed intermediate-estimate-based resilient secondary control strategy is further designed to enhance the resilience of cyber-physical AC MG to FDI attacks on frequency sensors. Compared to most of existing resilient control strategies, our proposed controller can not only maintain the frequency stability, but also ensure the accuracy of optimal power sharing among distributed generators (DGs). Finally, an islanded AC MG test system is built on a real-time testing platform to illustrate and verify the effectiveness of the developed methods.

Privacy preservation for distributed optimization in multiagent systems has been widely concerned in recent years. In this article, the accumulated noise privacy-preserving alternating direction method of multipliers (ANPPM) algorithm is proposed to preserve the private information of each agent. The masked states of each agent are sent to its neighbors with a designed noise-adding mechanism, and an accumulated term is introduced to confuse the gradients at each iteration. With ANPPM, all the agents can achieve privacy preservation for the information of real states and subgradients. Moreover, the states of all the agents can be guaranteed to converge to the optimal solution. The convergence rate of is consistent with standard ADMM, hence no adverse effect is induced by the privacy-preserving mechanism. Numerical results are provided to validate the effectiveness of the proposed ANPPM algorithm.

This article is concerned with developing a privacy-preserving distributed-learning-based fault diagnosis approach for power transformers. Due to the constraints of data privacy, it is not possible to have enough labeled samples for training. Recently, the emergence of federated learning (FL) has provided a secure and distributed learning framework. However, the unbalanced data from multiple power stations may reduce the overall performance of FL while an untrusted central server can threaten the data privacy and security of clients. To address such challenges, a privacy-preserving FL scheme is developed for transformer fault diagnosis, where a multistep data-sharing strategy and an adaptive differential privacy technology are proposed. Specifically, amounts of shared data and noise perturbation will be designed according to the quantity of local data by the central server. The experimental results on the dataset generated according to IEC publication 60599 show that the proposed method has high diagnostic accuracy across various categories of transformer faults and even on training datasets with extremely unbalanced data quantity where the average accuracy is as high as 95.28%.

Privacy preservation for distributed optimization algorithms in multi-agent systems has warranted widespread concern in recent years due to the urgent security requirements. In this paper, a novel distributed subgradient privacy-preserving algorithm is proposed, where the weight matrix is row stochastic. The proposed algorithm holds an advanced noise-adding mechanism, where locally balanced noise is adopted to mask the real data that agents transmit to neighbors. It is shown that all the agents converge to an optimal solution of the optimization problem, while the subgradients and cost functions are preserved simultaneously.

This article proposes a hierarchical distributed control to address the voltage control and current allocation issues in the islanded DC microgrid cluster with hybrid energy storage systems (HESSs). The primary control is droop control, which utilizes a low-pass filter to achieve high/low-frequency decomposition of the HESSs reference power. A threshold management strategy based on the charge state partitioning of supercapacitors is studied. Furthermore, the droop coefficient of the batteries is adjusted based on their state of charge. The second control is the distributed control, which consists of two parts: average voltage control and proportional current control. Consensus algorithm is employed to dynamically adjust droop control in the second control, where adjacent microgrids exchange their state information through a communication network. Simulations are conducted, which verify the correctness of the analysis and the feasibility of the proposed method.

This paper proposes a thermal management strategy for proton exchange membrane fuel cell based on nonlinear model predictive control (NMPC). To handle the highly coupled and nonlinear nature of the thermal management system, we adopt NARMAX model and introduce BP neural network to fit the nonlinear prediction model. Then in rolling optimization stage, an optimization problem consisting of two inputs and single output is established, for which an improved particle swarm optimization method is employed in combination with a mutation mechanism and an improved parameter update mechanism. Simulation results validate the effectiveness of the proposed NMPC-based thermal management strategy.

This article presents an intelligent fault diagnosis method for wind turbine (WT) gearbox by using wavelet packet decomposition (WPD) and deep learning. Specifically, the vibration signals from the gearbox are decomposed using WPD and the decomposed signal components are fed into a hierarchical convolutional neural network (CNN) to extract multiscale features adaptively and classify faults effectively. The presented method combines the multiscale characteristic of WPD with the strong classification capacity of CNNs, and it does not need complex manual feature extraction steps as usually adopted in existing results. The presented CNN with multiple characteristic scales based on WPD (WPD-MSCNN) has three advantages: 1) the added WPD layer can legitimately process the nonstationary vibration data to obtain components at multiple characteristic scales adaptively, it takes full advantage of WPD and, thus, enables the CNN to extract multiscale features; 2) the WPD layer directly sends multiscale components to the hierarchical CNN to extract rich fault information effectively, and it avoids the loss of useful information due to hand-crafted feature extraction; and 3) even if the scale changes, the lengths of components remain the same, which shows that the proposed method is robust to scale uncertainties in the vibration signals. Experiments with vibration data from a production wind farm provided by a company using condition monitoring system (CMS) show that the presented WPD-MSCNN method is superior to traditional CNN and multiscale CNN (MSCNN) for fault diagnosis.

Keypoints matching is a pivotal component for many image-relevant applications such as image stitching, visual simultaneous localization and mapping (SLAM), and so on. Both handcrafted-based and recently emerged deep learning-based keypoints matching methods merely rely on keypoints and local features, while losing sight of other available sensors such as inertial measurement unit (IMU) in the above applications. In this paper, we demonstrate that the motion estimation from IMU integration can be used to exploit the spatial distribution prior of keypoints between images. To this end, a probabilistic perspective of attention formulation is proposed to integrate the spatial distribution prior into the attentional graph neural network naturally. With the assistance of spatial distribution prior, the effort of the network for modeling the hidden features can be reduced. Furthermore, we present a projection loss for the proposed keypoints matching network, which gives a smooth edge between matching and un-matching keypoints. Image matching experiments on visual SLAM datasets indicate the effectiveness and efficiency of the presented method.

Currently, a nonconvex economic dispatch problem is one of the research focuses in the field of smart grid (SG). A variety of algorithms are developed to solve it. However, these algorithms are prone to suffering from high computation cost and slow convergence rate, which creates an inevitable gap between theoretical analysis and practical real-time operations. In this article, we aim at providing an ensemble deep-learning-based approach to tackle such a challenging issue. First, a novel ensemble method is presented to explore the ground truth of nonconvex economic dispatch problems. Second, considering the time-varying total load demand, cost coefficients, and dispatchability of all generation units in a practical SG system as the features, a new deep neural network structure is proposed to learn the complex mapping from instant features to an optimal nonconvex economic dispatch solution. If such a mapping is well approximated by the designed deep neural network, no significant effort is required to solve a new economic dispatch problem, and the solution is obtained on the scale of milliseconds. Third, analyzing that a single deep neural network may be weak to a small part of the mapping space of the nonconvex economic dispatch problem, we further present an ensemble of multiple parallel deep neural networks trained sequentially with a simplified Adaboost.R2 algorithm. Finally, case studies reveal that the proposed approach achieves orders of magnitude speedup in computational time while guaranteeing similar or better performance on minimizing the overall generation cost compared to the state-of-the-art nonconvex economic dispatch algorithms.

This article investigates the distributed state estimation problem for large-scale power systems with the appearance of bad data. The power system is decomposed into several nonoverlapping agents and these agents interact with each other through transmission lines to form an interconnected multiagent power system (IMAPS). The measurement at each agent is local measurement, and the measurement in transmission line is edge measurement. To obtain an accurate state estimation of each agent in a distributed manner when the measurements are coupled with bad data, a bad data detection process should be designed. The difficulty is how to detect the bad data in edge measurement in a distributed scheme. To solve this problem, the characteristics of the edge measurement residual is analyzed, and a distributed bad data detection strategy is presented based on a novel iterative distributed Kalman-like filter (IDKF). It is proved that the IDKF algorithm can converge in finite steps when the communication graph of the IMAPS is acyclic, and the estimation accuracy is similar to that of the centralized Kalman filter. In addition, the IDKF algorithm shows excellent performance even when bad data appears. Simulation tests conducted on the IEEE 118-bus power system verify the theoretical findings.

Currently, numerical optimization methods are used to solve distributed optimal power allocation (OPA) problems for islanded microgrid (MG) systems. Most of them are developed based on rigorous mathematical derivation. However, the complexity of such optimization algorithms inevitably creates a gap between theoretical analysis and real-time implementation. In order to bridge such a gap, in this article we provide a new distributed learning-based framework to solve the real-time OPA problem. Specifically, inspired by the human-thinking scheme, distributed deep neural networks (DNNs) together with a dynamic average consensus algorithm are first employed to obtain an approximate OPA solution in a distributed manner. Then a distributed balance generation and demand algorithm is designed to fine-tune it to obtain the final optimal feasible solution. In addition, it is theoretically proved that the proposed DNN can well approximate one existing OPA algorithm (Guo et al. 2018), where quantitative numbers of at most how many hidden layers and neurons are provided. Several experimental case studies show that our proposed distributed learning framework can achieve similar optimal results to those obtained by using typical existing distributed numerical optimization methods while it is superior in terms of simplicity and real-time capability.

This article tries to provide a new alternative approach to solve the economic dispatch (ED) problem in a smart grid system. Such a problem has been widely studied recently with several advanced numerical optimization algorithms being proposed. However, most of these numerical algorithms may suffer from high computational cost for on-line optimization. In this article, we aim to address this problem by proposing a learning-based optimization strategy. The key idea is to regard the optimization strategy of the ED problem as an unknown mapping relationship. With the help of traditional ED optimization algorithms to obtain the ground truth, we employ a deep neural network (DNN) to learn the ED optimization strategy and use it for online ED. In particular, our main contribution in this article is to theoretically show that one popular ED algorithm, i.e.,$\lambda $-iteration algorithm, can be accurately approximated by a well-constructed DNN with finite network size. Moreover, dynamic units status of dispatchable generators is also considered and can be well solved by our proposed approach. Furthermore, several simulation case studies implemented on a 3-unit power system and an IEEE-30 bus power system validate the effectiveness of our proposed method.

This article presents a distributed consensus-based successive convex approximation (DSCA) algorithm to solve nonconvex nondifferentiable economic dispatch (ED) problems. The ED model formulated incorporates generation constraints, valve-point effects, and multiple fuel types. A perturbation technique enables the proposed DSCA to tackle such a nondifferentiable and nonconvex optimization, which paves the way to solving more complicated optimization problems that occur in practical applications. The local generation constraint is taken care by a local surrogate convex optimization directly. The global equality constraint is handled based on a consensus protocol, where the local generation-demand mismatch among all dispatchable generators (DGs) is shared in a distributed manner. As a result, the power distribution of DGs is updated, and the generation cost is minimized. Several case studies show that the proposed DSCA algorithm can achieve superior ED solutions and computational efficiency over existing nonconvex optimization algorithms.

In this article, we consider a convex optimization problem which minimizes the sum of local agents' cost functions subject to certain local constraints. Besides, both the local cost function and local constraints are only known by the local agent itself. To solve this problem, a new accelerated distributed gradient-based algorithm is proposed, which is inspired by the “momentum” phenomena in nature and aims to accelerate the convergence speed of conventional distributed gradient algorithms. Sufficient conditions for the stepsizes and the acceleration gains are derived to ensure the convergence of the proposed algorithm. Furthermore, based on this proposed fast distributed algorithm, a new decentralized approach is proposed to solve economic dispatch problem, especially for a large-scale power system. Based on the idea of virtual agent, it is proved that this decentralized algorithm is equivalent to the original fast distributed gradient method. Several case studies implemented on IEEE 30-bus, IEEE 118-bus power systems, and a large-scale power system consisting of 1000 generators are conducted to validate the proposed method.

High-voltage direct current (HVDC) is increasingly utilized for long-distance electric power transmission, mainly due to its low resistive losses. In this paper, a decentralized control strategy is proposed to address the secondary frequency restoration and real power sharing problem for multi-terminal direct current (MTDC) transmission systems. We establish a sufficient stability condition to guarantee that the designed decentralized leaky integral controller can restore the frequency to its nominal value. Furthermore, the proposed controller can adjust the real power sharing ratio according to different working conditions. An MTDC system consisting of 4 AC systems is built in MATLAB Simulink environment. Numerical simulations are conducted to validate the effectiveness of proposed decentralized control approach.

This paper presents a decentralized secondary control scheme to solve the voltage restoration and current sharing problem in islanded DC microgrid (MG) systems. The existing solutions to this problem are either centralized control or distributed control based approaches. For these methods, communication and information exchange is inevitable. In order to improve the system robustness and reduce the system implementation cost, a decentralized communication-free leaky integral control is proposed in this paper, which is able to realize the same control goals without any communication. The stability of overall system together with proposed decentralized controller is analysed. A test DC MG system is built in Matlab Simulink to validate the effectiveness of proposed control method.

In this paper, reciprocal collision avoidance is studied for nonholonomic mobile robots to achieve an efficient navigation. Two strategies are proposed to respectively adjust the linear and angular velocities so that a collision-free navigation can be achieved. By characterizing the collision-free navigation as a set of changing ratios for linear velocities, it is shown that collision can be avoided if the changing ratio of linear velocities is inside this set. Moreover, the strategy of the adjusting angular velocities is established following TTC-based method. With the combination of these two strategies, a simulation is done for four robots crossing the intersection, which shows the effectiveness of the proposed method.

In this paper, a new hierarchical decentralized optimization architecture is proposed to solve the economic dispatch problem for a large-scale power system. Conventionally, such a problem is solved in a centralized way, which is usually inflexible and costly in computation. In contrast to centralized algorithms, in this paper we decompose the centralized problem into local problems. Each local generator only solves its own problem iteratively, based on its own cost function and generation constraint. An extra coordinator agent is employed to coordinate all the local generator agents. Besides, it also takes responsibility to handle the global demand supply constraint based on a newly proposed concept named virtual agent. In this way, different from existing distributed algorithms, the global demand supply constraint and local generation constraints are handled separately, which would greatly reduce the computational complexity. In addition, as only local individual estimate is exchanged between the local agent and the coordinator agent, the communication burden is reduced and the information privacy is also protected. It is theoretically shown that under proposed hierarchical decentralized optimization architecture, each local generator agent can obtain the optimal solution in a decentralized fashion. Several case studies implemented on the IEEE 30-bus and the IEEE 118-bus are discussed and tested to validate the proposed method.

In this paper, we propose a new distributed event-trigger consensus protocol for linear multiagent systems with external disturbances. Two consensus problems are considered: one is a leader-follower case and the other is a nonleader case. Different from the existing results, our proposed scheme enables each agent to decide when to transmit its state signals to its neighbors such that continuous communication between neighboring agents is avoided. Clearly, this can largely decrease the communication burden of the whole communication network. Besides, since the control signal for each agent is discontinuous because of the event-triggering mechanism, the existence of a solution for the closed-loop system in the classical sense may not be guaranteed. To solve this problem, we employ a nonsmooth analysis technique including differential inclusion and Filippov solution. Through nonsmooth Lyapunov analysis, it is shown that uniformly bounded consensus results are derived and the bound of the consensus error is adjustable by choosing suitable design parameters.

This paper presents a distributed voltage unbalance compensation method for an islanded microgrid (MG) system. By using hierarchical control concept, we design a distributed compensation scheme in the secondary control layer, while the traditional inverter control methods including voltage and current PR control, droop control, virtual impedance are implemented in the primary layer. Different from most existing centralized compensation methods, no specified individual centralized secondary controller exists. We decompose the traditional centralized controller into several local secondary controllers. A novel distributed PI controller with negative sequence current feedback is designed in each secondary controller. By allowing them to exchange information with their neighboring controllers respectively, the unbalanced voltage in the sensitive load bus (SLB) can be compensated by all the distributed generators (DGs) cooperatively. In addition, the compensation effort of each DG is designed to be proportional to their power ratings respectively. An islanded microgrid system consisting of 4 DGs is built in MATLAB to validate the proposed method.

In this paper, we present a distributed economic dispatch strategy for a large-scale power system. At first, we treat each generator and load in the grid as an "agent". By decomposing the centralized optimization into optimizations at local agents, a scheme is proposed for each agent to iteratively estimate a solution of the optimization problem in a distributed manner. Due to the large number of the agents, the agents are sorted into several clusters and each cluster has a leader to communicate with the leaders of its neighboring clusters. The agents in the same cluster can conduct local optimization and communicate with its neighboring agents in parallel. After that, the leader agents of each cluster exchange their information simultaneously. It is shown that the estimated solutions of all the agents reach consensus of the optimal solution asymptomatically. Compared to our previous work in [14], where the leader agent in each cluster conducts the optimization in a sequential way, the proposed scheme in this paper allows them communicate and conduct optimization simultaneously, which greatly improves the algorithm efficiency. A case study implemented on IEEE 30-bus power system are discussed and tested to validate the proposed method.

This paper presents a distributed secondary control scheme for voltage unbalance compensation in the islanded microgrid (MG) systems. Conventionally, the voltage unbalance compensation is realized in a centralized way, which has certain intrinsic disadvantages such as poor fault tolerance ability and higher computational and communication cost. In order to overcome these drawbacks, a distributed secondary control scheme for voltage unbalance compensation is proposed. A finite-time average consensus algorithm is used for each local controller to obtain global information. The proposed scheme not only achieves similar voltage unbalance compensation performance as the centralized one but also shares the compensation efforts among local compensators dynamically in a distributed fashion. In addition, our proposed scheme has fault tolerance ability in the sense that when some compensators fail to work, the rest compensators can still ensure balanced voltage output in the sensitive load bus (SLB). Simulation results are presented to validate our proposed scheme.

This paper presents a distributed cooperative control scheme for voltage unbalance compensation (VUC) in an islanded microgrid (MG). By letting each distributed generator (DG) share the compensation effort cooperatively, unbalanced voltage in sensitive load bus (SLB) can be compensated. The concept of contribution level (CL) for compensation is first proposed for each local DG to indicate its compensation ability. A two-layer secondary compensation architecture consisting of a communication layer and a compensation layer is designed for each local DG. A totally distributed strategy involving information sharing and exchange is proposed, which is based on finite-time average consensus and newly developed graph discovery algorithm. This strategy does not require the whole system structure as a prior and can detect the structure automatically. The proposed scheme not only achieves similar VUC performance to the centralized one, but also brings some advantages, such as communication fault tolerance and plug-and-play property. Case studies including communication failure, CL variation, and DG plug-and-play are discussed and tested to validate the proposed method.