The increasing integration of distributed generators (DGs) into AC microgrids (MGs) via power electronics reduces system inertia and causes frequency oscillations. To enhance the dynamic frequency response, this paper proposes a virtual asynchronous machine (VAM) control for the AC/DC interlinking converter (IC) that connects the MG and the heating system. Unlike conventional source-side methods (e.g., virtual synchronous generators) that provide inertia from generation units, this work addresses low inertia from the load side. The VAM emulates the slip-frequency regulation, natural damping, and self-regulating torque-speed characteristics of an asynchronous machine (AM). Furthermore, an adaptive virtual inertia and damping combination control is developed, which dynamically adjusts parameters based on frequency deviation and its rate of change. Meanwhile, the thermal inertia of buildings serves as a virtual energy buffer, allowing the VAM to temporarily reduce or increase power transmission to the heating system without compromising indoor thermal comfort. Simulation results demonstrate that the proposed VAM control reduces the maximum frequency deviation by 72% (from 0.25 Hz to 0.07 Hz) and the rate of change of frequency (RoCoF) by 64%.

Although the current sharing in islanded DC microgrids has been extensively studied, the low convergence rate and network attacks have hindered the consumption of renewable energy. Thus, this paper proposes a new fixed-time quasi-consensus control approach which can achieve accurate current sharing with a fast convergence rate under unknown denial of service (DoS) attacks. Firstly, the model of islanded DC microgrids with disturbances is built, where disturbances are caused by the renewable energy and three common loads (constant voltage, constant current and constant power loads). It is the basis for the subsequent design of the control scheme. Secondly, a dynamic compensator is developed in this paper to address the impact of unknown DoS attacks on islanded DC microgrids. Furthermore, a new fixed-time quasi-consensus approach with a new event-triggered mechanism is developed to realize accurate current sharing control with a fast convergence rate. Moreover, it can also realize low-bandwidth communication link and avoid continuous information exchange. Eventually, simulation and experimental results are given to verify the effectiveness of the proposed control approach for islanded DC microgrids under unknown DoS attacks.

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

The district heating network (DHN) can provide flexibility for electric power system (EPS) to accommodate power because of its slow dynamic and thermal energy storage characteristics. However, the traditional flexibility quantifications neglect the thermal temporal-spatial dynamic propagation and uncertainty parameters of DHN, resulting in inaccurate assessment of available flexibility capabilities. To address this issue, this article proposes a dynamic flexibility quantification method. First, three flexibility metrics including capacity, amplitude, and duration of power integration are modeled by simultaneously considering the temperature temporal and spatial dynamic propagation. Then, the discretized criteria are designed to reasonably linearize the temporal and spatial dynamic variables in the metrics. Thus, the evolution of flexibility metrics over time and space can be captured. Furthermore, the uncertainty parameters (e.g., mass flow, thermal resistance) in the metrics are modeled to account for their impact on the flexibility results. To this end, the maximum entropy principle combined with the probabilistic cumulant is developed to construct the probability distributions of metrics. With these effects, the flexibility provided by DHN can be elaborately quantified. Finally, case studies and simulation analysis are carried out on China Luhua network and Denmark 61-node network to verify the effectiveness of the proposed quantification method.

In this article, we research the output feedback consensus tracking control problem of nonlinear multiagent systems with unknown disturbance under event-triggered communication. An event-triggered mechanism with dynamic threshold utilizing only output information is proposed to reduce the controller updates and communication load between neighboring agent. This mechanism is combined with the state and disturbance observer to derive an output feedback-based adaptive backstepping event-triggered control protocol via dynamic filtering technique, which avoids the differentiation of virtual control protocol and eliminates Zeno behavior. Based on Lyapunov stability theory, it is proven that all signals of the closed-loop systems are bounded and output consensus tracking can be achieved. The effectiveness of the proposed control scheme is verified via a physical system example.

Battery production line is crucial for determining the performance of batteries, further significantly affecting the industrial applications of relevant energy systems. As a complex and multidisciplinary system involving electrical, mechanical, and chemical processes, efficient prediction of manufactured battery properties and explainable analysis of strongly coupled battery production variables becomes an important but challenging issue for the wider application of batteries. In this article, an interpretable AI solution based on generalized additive model with interactive features and interpretability (GAM-IFI) is proposed to effectively predict battery capacities in the early phase of battery manufacturing and explain the effects of involved coating features. The designed solution is evaluated by using reliable production data from a real battery manufacturing line. Illustrative results show that the proposed solution is able to accurately predict three different types of battery capacities with an$R^{2}$over 0.98. Moreover, information regarding the importance ratio of both main effect and pairwise interaction terms derived from three coating features is identified, while global and local interpretations of the effects of these terms can be well explained. The developed interpretable solution opens a promising avenue to identify the importance of battery production features and explain how the variation of these features influences the properties of battery products. This can help engineers to better understand the underlying complex behaviors in battery production, which in turn will benefit the digitalization of battery manufacturing.

The technology of distributed cooperative consensus has been widely used in inverter-based microgrids. However, the traditional information interaction will lead to the problem of data disclosure. Although privacy issues have been widely researched in the tertiary control layer of microgrids, the issues of secondary control layer have not been properly addressed. To fill this gap, taking voltage restoration as the object, the privacy preserving consensus problem for secondary control layer of nDGs islanded microgrids is considered in this paper. Output mask approach, the basic idea of which is to insert a dynamic mask to the transmitted information, is adopted to achieve an accurate consensus rather than a pre-specified convergence accuracy level by differential private method. After that, a newly state decomposition mechanism is proposed, the DG agent is decomposed into two subagents, called$x^{\alpha} _{i}$and$x^{\beta} _{i}$. Among the agent pairs$(x^{\alpha} _{i}, x^{\beta} _{i})$, choose only one subagent of pair$i$arbitrarily connected to one subagent of its neighbor agent pair. Furthermore, only the communication lines among the agent pairs are masked. Compared with the existing literature, the constraint on the communication topology can be first removed without additional computational burden. Moreover, the consensus and privacy analysis of the controlled system are carried out. In the end, the simulation results verify the effectiveness of the proposed privacy preserving mechanism in the MATLAB/Simulink environment. Note to Practitioners—With the rapid development of information and intelligent technology, the information system and the physical system of MGs have been deeply integrated to get a higher efficiency of energy utilization. However, the traditional information interaction will lead to the problem of data disclosure. Although privacy issues have been widely researched in the tertiary control layer of microgrids, the issues of secondary control layer have not been properly addressed. Motivated by this, an improved privacy-preserving consensus strategy is proposed for secondary voltage control of islanded microgrids based on a newly node decomposition mechanism and the output mask method in this paper. And the theoretical results of this paper can be easily extended to other multi-agent systems.

This article studies the adaptive control about the geodetic fixed positions and heading of three-degree-of-freedom dual-propeller vessel. During the navigation of a vessel at sea, due to the unpredictable sea, on the one hand, it is important to ensure that the vessel can smoothly follow the desired geodesic fixed position and heading; on the other hand, when the sailing environment is harsh, it is even more important that the vessel can adapt to the desired geodesic fixed position and heading that change at any time for safe driving. Therefore, this article selects the time-varying function related to the desired geodesic fixed position and heading as the constraint condition, and the constraint condition will change in real time as the expected position and heading change. The design of the control strategy is difficult, and the designed control strategy will be more suitable for complex maritime navigation conditions. First, the article constructs a log-type barrier Lyapunov function. Second, by introducing an unknown external disturbance observer, the external disturbances caused by the environment that may be encountered during the vessel's voyage can be observed. Then, combined with the backstepping algorithm, a neural network (NN) control strategy and adaptive law are designed. Among them, for the uncertain function in the process of designing the control strategy, the NN is used to approximate it. Furthermore, through the Lyapunov stability analysis, it is shown that applying the designed control strategy to the vessel system in this article can ensure that the system is closed-loop stable. The final simulation experiment shows the effectiveness of the designed control strategy.

For DC microgrids (MGs) with multi-distributed generations (DGs), complex communication and physical networks among DGs result in input unknown. This paper studies the cooperative control problem of current sharing and voltage recovery for DC MGs with multi-DGs under input unknown. Different from most existing design methods of state observers, an unknown input observer is developed via applying augmented system to approximate the unmeasured state and disturbance information with high accuracy. The proposed cooperative control protocol is easy for implementation. It is also theoretically shown that all signals are bounded in the closed-loop system and the voltage recovery and current sharing can be achieved. The effectiveness of our present control method is verified via the simulation results.

This article proposes an observer-based event-driven fault-tolerant (OBEDFT) secondary control strategy for AC microgrids (MGs) to achieve load voltage regulation. First, the input-output feedback linearization method transforms the voltage regulation issue into an output feedback tracking problem for linear multiagent systems (MASs) with nonlinear dynamics. This transformation provides the necessary preprocessing for load voltage regulation. Then, an OBEDFT secondary control protocol that considers full-state immeasurability is proposed. The actuators of distributed generators (DGs) may experience partial loss of effectiveness (PLOE) and bias faults, and these fault parameters may be heterogeneous and time-varying. The protocol introduces adaptive techniques to avoid information related to fault parameters while using event-driven mechanisms to achieve discrete measurements of neighboring DG. Additionally, the protocol uses boundary layers to construct smooth controllers that prevent the chattering effect caused by nonsmooth controllers. Finally, simulation results confirm the effectiveness of this load voltage regulation strategy.

Although the current sharing control of dc microgrids has been widely studied, the high communication bandwidth and global communication network structure information demands hander the renewable energy consumption. Thus, this article proposes a fully distributed dynamic edge-event-triggered current sharing control strategy for multibus dc microgrids with power coupling. First, the system model with power coupling is built, which is further switched to the linear heterogeneous multiagent systems with unknown disturbance. It is an indispensable preprocessing for controller design. Furthermore, the fully distributed current sharing control strategy is proposed through adaptive coupling weights. Note that the global communication network structure information demand is eliminated. Moreover, the fully distributed dynamic edge-event-triggered mechanism is proposed to reduce communication bandwidth. Compared with the previous dynamic event-triggered mechanisms applied into dc microgrids, the continuous communication between neighboring agents is avoided, and controller updating frequency is reduced. Finally, the simulation and experimental results verify the proposed control performance.

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

Since most of the existing models based on the microgrids (MGs) are nonlinear, which could cause the controller oscillate, resulting in the excessive line loss, and the nonlinear could also lead to the controller design difficulty of MGs system. Therefore, this article researches the distributed voltage recovery consensus optimal control problem for the nonlinear MGs system with N -distributed generations (DGs), in the case of providing stringent real power sharing. First, based on the distributed cooperative control concept of multiagent systems and the critic neural networks (NNs), a novel distributed secondary voltage recovery consensus optimal control protocol is constructed via applying the backstepping technique and nonzero-sum (NZS) differential game strategy to realize the voltage recovery of island MGs. Meanwhile, the model identifier is established to reconstruct the unknown NZS games systems based on a three-layer NN. Then, a critic NN weight adaptive adjustment tuning law is proposed to ensure the convergence of the cost functions and the stability of the closed-loop system. Furthermore, according to Lyapunov stability theory, it is proven that all signals are uniform ultimate boundedness in the closed loop system and the voltage recovery synchronization error converges to an arbitrarily small neighborhood of the origin near. Finally, some simulation results in MATLAB illustrate the validity of the proposed control strategy.

A robust adaptive control method for a certain type of quarter active suspension system (ASS) is proposed in this work. The constraint issue of ASS is put into consideration primarily. Due to the limitation of the traditional barrier Lyapunov functions (BLFs), the integral barrier Lyapunov function (iBLF) is introduced to exert direct constraints on state variables in each stage under the backstepping frame, and neural networks (NNs) are applied to identify those unknown functions. Then, an adaptive law based on the projection operator is defined to eliminate the influence caused by the actuator failure. It is widely known that only the vertical displacement and velocity constraints are not violated, can the ASSs become stable and secure. It can be ultimately confirmed that all signals in the closed-loop system are bounded, and the control goals are satisfied. Last but not least, the feasibility of the approach is illustrated directly through a contrast simulation example.

This economic dispatch problem has been tended to be solved by using distributed optimization algorithms which are easier to suffer from diversified cyberattacks, e.g., the denial-of-service (DoS) attacks. It leads to enormous secure risks for the economic operation of smart grid. To address this issue, this article aims to propose a distributed secure dispatch method to effectively defend the DoS attacks. First, considering the coexistence of the attack sequence and triggering sequence, the actual affected period and actual safe period are analyzed and defined. It provides an analysis model for the subsequent algorithm design. Then, by designing switched system dynamics along with hybrid-triggering concept, a novel distributed secure dispatch strategy is presented. The proposed method can enable each distributed generator (DG) to reasonably use estimation values and switched rate of system evolution to mitigate the effect of the DoS attacks. Meanwhile, contributed by the designed hybrid-triggering communication strategy, the proposed method takes advantages of reduced communication costs, flexible execution, and fast and reliable communication recuperation among DGs. With those efforts, the proposed method is capable of high robustness to resist the DoS attacks well. Moreover, theoretically analytic results are proposed to verify the correctness of the proposed method. Finally, simulation results are provided to show the feasibility and effectiveness of the proposed method.

Though voltage-regulation and current-sharing of distributed generations (DGs) in dc-microgrids have been widely studied, additional communication links or independent modulation circuit should be added to achieve information transmission. To accomplish precise current-sharing/voltage-regulation without additional communication devices, this article proposes a communication-free intelligent edge control regarding voltage and current for dc-microgrids. First, the power-information dual modulation (PIDM) is designed to achieve information exchange among DGs and eliminate additional communication devices. Second, the cooperative control problem with two coupled targets, i.e., accurate voltage-regulation and current-sharing, is converted into a matter of optimal control. Therefore, the voltage-regulation and current-sharing could be solved concurrently. In addition, the control objective function of each DG is switched to provide the optimal controller and minimize the voltage/current control deviation, which is further switched to solve the Hamilton–Jacobi–Bellman (HJB) function. In order to solve this HJB function, which is difficult to obtain analytical solution, an intelligent edge control strategy with PIDM is proposed to solve the HJB function. Therefore, the precise voltage-regulation and current-sharing can be accomplished. Finally, the proposed control approach is verified through simulation results.

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

The security and economy of multienergy systems (MESs) are directly threatened by the potential cyberattacks. It is of great importance to investigate the effects of cyberattacks, e.g., denial of service (DoS) attacks, on distributed energy management algorithms. To this end, this article focuses on exploring how the frequency and the time of duration of DoS attacks influence the behavior of Newton–Raphson-based distributed energy management (NRBDEM) algorithm for MES and in which condition the optimal operations can still be obtained. First, a switched NRBDEM algorithm is presented, which is composed of the normal operation mode and the attack mode. In the attack mode, the attackers are able to change the communication structure at will and make it unconnected to destroy the convergence of the switched NRBDEM algorithm. Then, by making use of automatons to generate the hybrid time domain, the switched NRBDEM algorithm is further modeled and formulated as a hybrid dynamical system, which provides a mathematical model for the subsequent convergence analysis. Therein, the generated hybrid time domain satisfies the average dwell-time constraint and time-ratio constraint to limit the persistent attacks. Furthermore, we analyze the restrained conditions for persistent attacks, under which the optimality and convergence of the switched NRBDEM algorithm can be guaranteed still. Finally, simulation results demonstrate the effectiveness of the proposed method. Note to Practitioners—The multienergy system (MES) is viewed as a typical cyber-physical system. Since it works in a networked environment, the convergence and optimality of the corresponding distributed energy management algorithms are easily destroyed by various cyberattacks, such as the DoS attack. Few noticeable studies have been documented to investigate the distributed energy management problem for MES under persistent DoS attacks. To address this issue, this article proposes a switched NRBDEM algorithm subject to persistent DoS attacks, which is made up of normal operation mode and attack mode. Moreover, sufficient conditions are derived for the tolerable frequency of attack and the time of duration. It is helpful for the practitioners to know in which conditions the global convergence and optimality can be maintained still. Several simulations are provided to verify the correctness of the proposed theoretical analysis results. Our future work will aim at analyzing the performance of different energy management algorithms under different cyberattacks.

The device faults commonly exist in microgrids (MGs) and often undermine the system stability. However, the existing distributed methods generally design control protocols based on the absence of faults or only considering actuator faults, which limits the applicability of controllers in MG systems. Therefore, this paper investigates an adaptive prescribed fixed-time performance (PFTP) consensus fault-tolerant control (FTC) problem for the voltage regulation of a nonlinear islanded MG inverter-based distributed generators (DGs) with output contactor and actuator fault via the state event-triggered mechanism. The PFTP method for the voltage restoration synchronization error is proposed by constructing a novel performance function to increase the speed of voltage recovery. Based on the estimation properties of fuzzy logic system, an unknown nonlinear function and the residual term of output contactor are estimated. Then, an adaptive state event-triggering mechanism is designed to reduce the communication burden, and its main advantage is that the control protocol is updated in the aperiodic way at the triggering instants. Further, according to backstepping technology, a novel adaptive event-triggered consensus FTC protocol is constructed to achieve the voltage regulation of islanded MG, and a parameter adaptive law is designed to compensate the adverse effects of the output contactor fault. Based on the Lyapunov stability theory, it is proved that the voltage recovery synchronization error satisfies the PFTP, and all signals in the closed-loop systems are cooperatively uniformly ultimately bounded. Finally, the proposed control strategy is also validated by using the MATLAB.

Although the cyber-physical system stability is widely studied, scholars focus more on system stability with communication time delay. Therein, grid-connected inverters with the digital control system are regarded as one simplest and typical cyber-physical system. Meanwhile, the switching/sampling frequency of the inverter is always selected as low as possible from an efficiency viewpoint, resulting in unavoidable delay time. This delay time is apt to cause the system instability, which is more prone to severity under weak grid. To this end, this paper provides a minimum switching/sampling frequency for grid-connected inverters. Firstly, the system impedance model with equivalent delay time is constructed, which is based on padé approximate approach. This equivalent delay time consists of three parts, i.e., sampling delay time in cyber/physical level, calculation delay time in cyber level and pulsewidth modulation delay time in physical level, which reflects the cyber-physical interaction impact. Furthermore, the stability forbidden criterion is applied to make the switching/sampling frequency solving process become Hurwitz matrix identification problem through space mappings. Based on these space mappings, an adaptive step search approach is adopted to obtain the minimum switching/sampling frequency. Finally, the proposed approach can well evaluate the system stability under different frequencies through simulation and experiment.

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

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

Although privacy-preserving is often considered in energy management and energy scheduling of microgrids (MGs), to the best of authors’ knowledge, there are almost no literatures on distributed secondary control of MGs with privacy-preserving. To fill this gap, this article investigates the privacy-preserving problem for voltage restoration of an ac MG. First, the model of the MG is transformed into a linear multiagent system model by feedback linearization. Furthermore, output mask approach, which avoids divulging the initial condition by inserting a dynamic mask on the exchanged state information, is adopted to make the distributed generator agents exactly converge to the reference value rather than the value with a preset certain convergence error by differential private. Meanwhile, the sliding mode control scheme with simple structure is adopted to accelerate the convergence speed of the masked system. However, it is difficult to design the controller directly because of the strong nonlinearity brought by the mask function. To solve this problem, we first implement the controller for the original system, and then extend it to the masked system. After that, we carry out the consensus analysis of the controlled masked system. Finally, the effectiveness of the proposed control scheme is validated in the MATLAB/Simulink environment.

Distributed renewable energy source is an advisable solution for dc microgrids to reduce fuel consumption and CO2emission. In such microgrids, the installation of two or more battery energy storage (BES) units is utilized to compensate the power imbalance between the sources and loads. Nevertheless, energy management with numerous BES units does not simultaneously consider the impacts of distributed generators (DGs) and constant power loads (CPLs). Since the inaccurate current sharing will shorten the lifetime of the batteries and cause instability problem, this article proposes a distributed secondary$H_{\infty }$consensus approach based on the dynamic event-triggered communication method to realize accurate current sharing and efficient operation in the presence of numerous DGs and CPLs. First, the whole state-space function model of the dc microgrid consisting of DGs, batteries, resistive loads, and CPLs, is first built in detail. This model is further transformed into standard linear heterogeneous multiagent systems, which provides an indispensable preprocessing for advanced control strategy application. Then, the distributed secondary$H_{\infty }$consensus approach based on the foresaid systems is designed to achieve accurate current sharing. For reducing the communication among batteries and the controller updating frequency, the dynamic event-triggered communication method is proposed. Compared with existing event-triggered methods, the communication and controller updating frequency of the proposed dynamic event-triggered method have been reduced a lot. Additionally, the proposed method can not only avoid the Zeno behavior, but also obtain the lowest bound of the sampled time interval. Finally, the numerical simulation results and experimental results verify the effectiveness of the proposed control strategy.

The high penetration of renewable energy sources always leads to the fluctuation of the droop coefficients which are designed in inverse proportion to their rated capacity, and power electronics devices are prone to static instability. Although the impedance-based approaches have been widely studied to deal with this problem, the stability-oriented droop coefficients region identification due to the fluctuation of renewable energy sources is not provided. Thus, this article proposes an impedance-based approach to assess the droop coefficients stability region in the power system consisting of numerous distributed generators (DGs). First, the modified phase margin and opposing argument (MPMOA) forbidden criterion is constituted to acquire the complementary space of the droop coefficients stability region. The MPMOA forbidden criterion is first transformed into the condition that the generalized return-ratio matrix is Hurwitz through mirror, rotation, and translation mapping. In comparison with the previous simplified stability criteria, the conservatism of the proposed criterion is reduced a lot. Thereafter, the droop coefficients stability region is directly calculated by the generalized return-ratio matrix and guardian map theory. Eventually, the simulation and experimental results are provided to validate the conservatism and effectiveness of the impedance-based stability region identification approach. Therein, the simulation results illustrate that the proposed droop coefficients stability operation criterion has lower conservatism than these of the previous simplified stability criteria. Furthermore, the simulation and experimental results illustrate that the proposed stability-oriented droop coefficients region identification approach can provide an effective parameter stability region.

In this paper, the problems of stability and control for a class of uncertain nonlinear systems with unknown state time-delay are studied by using the fuzzy logic systems. Because the dynamic surface control technique is introduced to deal with the uncertain time-delay systems, the designed adaptive fuzzy controller can avoid the issue of "explosion of complexity", which comes from the traditional backstepping design procedure. Compared with the existing results in the literature, the robustness to the fuzzy approximation errors is improved by adjusting the estimations of the unknown bounds for the approximation errors. It is shown that the resulting closed-loop system is stable in the sense that all the signals are bounded and the system output track the reference signal in a small neighborhood of the origin by choosing design parameters appropriately. Three simulation examples are given to demonstrate the effectiveness of the proposed techniques.