Island microgrids face major challenges arising from the spatial mismatch between renewable generation and load centers as well as their heightened susceptibility to line failures. Traditional strategies such as full-line reinforcement are often impractical for islands due to the extremely high investment cost. This paper proposes a reliability-driven planning framework for microgrids under various failure scenarios, introducing Soft Open Points (SOPs) as flexible interconnection devices. Line failure rates are estimated based on component health indices and submarine cable lengths, and a scenario-based mixed-integer linear programming (MILP) model is developed to jointly optimize distributed energy resource scheduling and SOP siting and sizing. The proposed framework is validated on the Orkney Islands microgrid. Case studies demonstrate that optimal SOP deployment can reduce load shedding and renewable curtailment, improve voltage profiles, and lower total operational costs by over 50%, without the need for large-scale infrastructure upgrades. The results provide practical insights into enhancing the reliability and cost-effectiveness of island microgrids under reliability constraints.

This article addresses the privacy-preserving energy management problem of battery energy storage systems (BESSs). An autonomous privacy-preserving distributed optimization (APPDO) scheme is developed over time-varying networks with the aim of regulating the power output of local BESS to fulfill the total load demand at the minimum economic cost under battery capacity constraints without privacy leakage. To this end, a linearly convergent distributed algorithm is proposed by combining the gradient descent algorithm with leaderless and leader-following consensus schemes. This algorithm is applicable to both islanded and grid-connected modes of BESSs. Furthermore, a novel privacy-preserving approach is constructed by injecting well-designed perturbation sequences into the data exchanged between neighboring nodes, making it effective against malicious eavesdroppers. Furthermore, a comprehensive analysis framework is established to evaluate the convergence, optimality, and privacy-preserving performance of the APPDO algorithm. Finally, numerical studies are conducted to demonstrate the effectiveness of the developed APPDO scheme.

This article is concerned with the privacy-preserving distributed economic dispatch problem of microgrids. The main goal of this work is to develop a privacy-preserving distributed optimization algorithm over directed networks, aiming to achieve supply-demand balance at the lowest economic cost under practical constraints while preventing the leakage of power-sensitive information. For this purpose, a distributed optimization algorithm with aconstantstep size is proposed by combining the decentralized exact first-order algorithm with the push-sum protocol, which offers an advantage in terms of fast convergence. In addition, to ensure privacy preservation, a state-decomposition approach is employed by randomly dividing the state into two parts, where only partial state information is transmitted. Moreover, the effectiveness of the privacy-preserving scheme against honest-but-curious nodes and external eavesdroppers is demonstrated through rigorous analysis. Finally, simulation studies demonstrate the validity and superiority of the developed privacy-preserving distributed algorithm.

This article is concerned with the secure distributed economic dispatch (DED) problem of microgrids. A quantized distributed optimization algorithm using the Paillier encryption–decryption scheme is developed. This algorithm is designed to optimally coordinate the power outputs of a collection of distributed generators (DGs) in order to meet the total load demand at the lowest generation cost under the DG capacity limits while ensuring communication efficiency and security. First, to facilitate data encryption and reduce data release, a novel dynamic quantization scheme is integrated into the DED algorithm, through which the effects of quantization errors can be eliminated. Next, utilizing matrix norm analysis and mathematical induction, a sufficient condition is provided to demonstrate that the developed DED algorithm converges precisely to the optimal solution under finite quantization levels (and even the three-level quantization usingsigntransmissions). Moreover, an encryption–decryption scheme is developed based on quantized outputs, which ensures confidential communication by leveraging the homomorphic property of the Paillier cryptosystem. Finally, the effectiveness and superiority of the implemented secure distributed algorithm are confirmed through a simulated example.

This article investigates the privacy-preserving distributed economic dispatch (DED) problem of islanded microgrids. To improve the convergence rate of the DED algorithm, anacceleratedconsensus scheme is adopted by utilizing a short memory. Then, a privacy-preserving strategy is introduced to prevent sensitive information leakage by adding well-designed perturbations into the proposed consensus algorithm at the initial time instant. The primary objective of this article is to design a privacy-preserving accelerated consensus scheme to achieve a balance between supply and demand at the globally minimized cost while preserving the initial local demand information. By virtue of rigorous algebra manipulation and mathematical induction, a unified framework is established under which the convergence, the optimal convergence rate, and the optimality of the proposed DED algorithm are simultaneously analyzed, and the main results are extended to satisfy the privacy-preserving needs. Furthermore, the proposed privacy-preserving DED algorithm is shown to be resilient against both internal (honest-but-curious) and external eavesdroppers. Finally, the effectiveness of the developed privacy-preserving accelerated consensus algorithm is validated on the IEEE 39-bus power systems.

This article is concerned with the distributed state estimation problem over wireless sensor networks (WSNs), where each smart sensor is capable of harvesting energy from the external environment with a certain probability. The data transmission between neighboring nodes is dependent on the energy level of each sensor, and the internode communication is deemed as a failure when the current energy level is inadequate to guarantee the normal data transmission. Considering the intermittent information exchange over WSNs, a novel distributed state estimator is first constructed via introducing a set of indicator functions, and then the evolution of the probability distribution of energy level and its steady-state distribution is systematically discussed by resorting to the eigenvalue analysis approach and the mathematical induction. Furthermore, the optimal estimator gain is derived by minimizing the trace of the estimation error covariance under known communication sequences. In addition, the convergence of the minimized upper bound of the expected estimation error covariance is analyzed under any initial condition. Finally, an illustrative example regarding the target tracking problem is provided to verify the validity of the obtained theoretical results.

This article is concerned with the differentially private average consensus (DPAC) problem for a class of multiagent systems with quantized communication. By constructing a pair of auxiliary dynamic equations, a logarithmic dynamic encoding-decoding (LDED) scheme is developed and then utilized during the process of data transmission, thereby eliminating the effect of quantization errors on the consensus accuracy. The primary purpose of this article is to establish a unified framework that integrates the convergence analysis, the accuracy evaluation, and the privacy level for the developed DPAC algorithm under the LDED communication scheme. By means of the matrix eigenvalue analysis method, the Jury stability criterion, and the probability theory, a sufficient condition (with respect to the quantization accuracy, the coupling strength, and the communication topology) is first derived to ensure the almost sure convergence of the proposed DPAC algorithm, and the convergence accuracy and privacy level are thoroughly investigated by resorting to the Chebyshev inequality and ϵ -differential privacy index. Finally, simulation results are provided to illustrate the correctness and validity of the developed algorithm.

In this article, the distributed formation-containment (FC) control issue is investigated for a class of discrete-time multiagent systems (DT-MASs) under the event-triggered communication mechanism. In order to save the communication cost and improve the utilization of communication resources, a novel dynamic event-triggered (DET) mechanism is developed by adding an auxiliary variable for each agent system, which is able to dynamically adjust the triggering threshold. A distributed FC control scheme under the DET mechanism is proposed for all the leaders and followers based on the available relative outputs. The purpose of the addressed problem is to design the FC controller such that all the leaders achieve a formation shape and all the followers converge into such a convex hull. To this end, the considered DT-MASs are first decoupled into a diagonal form by resorting to the property of the Laplacian matrix as well as the inequality technique. Then, two sufficient conditions are established to ensure the desired FC performance. Furthermore, the corresponding FC controller parameters are obtained in terms of the solutions to two matrix inequalities which only depend on the maximum and minimum nonzero eigenvalues of the Laplacian matrix. Finally, an illustrative example is provided to verify the validity of the developed control scheme.

This article focuses on the mean-square consensus control problem for a class of discrete-time multiagent systems (DT-MASs) over time-correlated multistate Markovian fading channels, where the packet loss probability is time-varying and depends on the current channel state. In order to save limited network bandwidth, a compressed coding scheme is developed by preprocessing the measurement output. With the aid of a stochastic Lyapunov–Krasovskii functional, a sufficient condition is first obtained under which the consensus error system is mean-square stable for DT-MASs over identical fading channels. Then, the consensus gain is formulated as the feasible solution to a set of linear matrix inequalities (LMIs) whose dimensions are independent of the number of agents. Furthermore, for the case that agents communicate over nonidentical fading channels, the mean-square consensus problem is transformed into an analyzable edge agreement issue in the mean-square sense by means of properties of the edge Laplacian combined with a mapping technique. Next, a sufficient condition is derived to ensure the mean-square consensus performance, based on which the existence of the controller can be guaranteed by the feasibility of a set of LMIs. Finally, the validity and feasibility of the developed design scheme are shown by two illustrative examples.

This article focuses on the finite-horizonH∞bipartite consensus control problem for a class of discrete time-varying cooperation-competition multiagent systems (DTV-CCMASs) with the round-robin (RR) protocol. The cooperation-competition relationship among agents is characterized by a signed graph, whose edges are with positive or negative connection weights. Specifically, a positive weight corresponds to an allied relationship between two agents and a negative one means an adversary relationship. The data exchange between each agent and its neighbors is orchestrated by an RR protocol, where only one neighboring agent is authorized to transmit the data packet at each time instant, and therefore, the data collision is prevented. This article aims to design a bipartite consensus controller for DTV-CCMASs with the RR protocol such that the predeterminedH∞bipartite consensus is satisfied over a given finite horizon. A sufficient condition is first established to guarantee the desiredH∞bipartite consensus by resorting to the completing square method. With the help of an auxiliary cost combined with the Moore-Penrose pseudoinverse method, a design scheme of the bipartite consensus controller is obtained by solving two coupled backward recursive Riccati difference equations (BRRDEs). Finally, a simulation example is given to verify the effectiveness of the proposed scheme of the bipartite consensus controller.

In this paper, the distributed state estimation problem is studied for a class of state-saturated power systems subject to Denial-of-Service (DoS) attacks. The randomly occurring DoS attacks is modeled by a series of Bernoulli distributed stochastic variables with known probability distributions. The aim of this paper is to design a distributed estimator ensure, in the presence of both cyber-attacks and state saturations, the desired estimation performance is satisfied. By virtue of some typical matrix inequalities, a tight upper bound of estimation error covariance is derived. The estimation parameters are obtained with the help of the solution of a set of Riccati-like difference equations. The developed recursive algorithm is independent of the global information and thus satisfies the requirements of scalability and online application. Finally, a practical example is developed to verify the validity of the designed estimator.

This paper investigates the finite-horizon H∞containment control issue for a general discrete time-varying linear multiagent systems with multileaders. All followers in such a system are driven into a convex hull spanned by multiple leaders, which can be transformed into a problem of tracking a virtual trajectory generated by these leaders. For this purpose, a local state observer is put forward to estimate the state of each agent itself. Then, the estimated state is transmitted to corresponding neighbors governing by an innovation-based event-triggered scheduling protocol. The purpose of the addressed problem is to design both an event-based distributed controller and a state observer such that a prescribed H∞containment index can be achieved over a given finite horizon. First, with the help of the completing the square method, a sufficient condition is established to ensure the desired H∞containment performance. Then, by resort to a novel nominal energy cost index combined with Moore-Penrose pseudoinverse method, the desired controller and observer parameters are obtained by solving two coupled backward recursive Riccati difference equations. Two positive scalars in proposed nominal energy cost index provide a tradeoff among the controlled tracking errors, the energy of transformed control inputs, and the precision of estimated states. Finally, a simulation example is given to illustrate the usefulness of the proposed theoretical results.

This paper addresses the distributed resilient filtering problem for a class of power systems subject to denial-of-service (DoS) attacks. A novel distributed filter is first constructed to practically reflect the impact from both cyber-attacks and gain perturbations. For all possible occurrence of DoS attacks and gain perturbations, an upper bound of filtering error covariance is derived by resorting to some typical matrix inequalities. Furthermore, the desired filter gain relying on the solution of two Riccati-like difference equations is obtained with the help of the gradient-based approach and the mathematical induction. The developed algorithm with a recursive form is independent of the global information and thus satisfies the requirements of scalability and distributed implementation online. Finally, a benchmark simulation test is exploited to check the usefulness of the designed filter.