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%.

This paper tackles denial-of-service (DoS) attacks and output constraints in secondary voltage control of islanded microgrids. While existing literature predominantly addresses communication security, it largely overlooks the operational boundaries of power converters. This oversight may result in control saturation, device failure and ultimately, compromised system stability. Furthermore, traditional consensus-based voltage regulation fails to facilitate necessary power interchange among sub-microgrids, limiting its practical applicability. To overcome these limitations, a novel distributed voltage control scheme based on the inclusion principle is proposed. Firstly, a distributed control system model incorporating output constraints is established. The nonlinearities of the system are effectively handled via a barrier Lyapunov function approach, ensuring strict adherence to the output voltage amplitude limits. Secondly, an adaptive state estimator with a switching mechanism is developed to mitigate intermittent communication failures induced by DoS attacks. The controller parameters are then obtained by solving a set of linear matrix inequalities, guaranteeing the semi-global uniform ultimate boundedness (SGUUB) of all closed-loop signals and the ultimate convergence of errors to a neighborhood of the origin. Simulation results verify that the proposed strategy effectively ensures voltage stability while simultaneously satisfying both output constraints and cybersecurity requirements.

Forecasting user-level multi-energy demand under data scarcity is challenging due to the strong spatial interdependencies among users and the complex coupling across heterogeneous energy carriers. To address the challenges, this paper proposes a few-shot forecasting approach for integrated electricity-gas-heat systems, enabling reliable prediction with limited historical data. First, a meta-learning graph neural network is developed to extract generalizable energy conversion features adaptively across user patterns, effectively alleviating data insufficiency. Second, to accurately capture system dynamics, a multi-relational spatiotemporal graph module is designed to hierarchically model intra-energy dynamics and inter-energy coupling, achieving adaptive fusion of heterogeneous spatiotemporal features. Furthermore, a knowledge-enhanced training mechanism is introduced by embedding physical energy conversion laws into meta-training via pseudo-tasks, enhancing physical consistency and preventing overfitting in few-shot adaptation. Extensive experiments on multi-energy datasets ultimately demonstrate that compared to state-of-the-art forecasting models, the proposed approach achieves significant improvements in average metrics 3.80% for MAE, 7.89% for RMSE, and 13.12% for MAPE).

To address the issues of insufficient stability, low power allocation accuracy, and resource constraints in dc microgrids, this article proposes a distributed optimal control method based on edge computing. Adaptive dynamic programming method is introduced to address the nonlinear control problem, improving the stability and power allocation accuracy. A three-level cloud-edge-device control framework is constructed to improve system efficiency and flexibility combining distributed control and edge computing. The improved event-triggered control mechanism is designed to reduce unnecessary computation and improve the real-time responsiveness of the system. The practicality of the method is verified using a hardware-in-the-loop simulation platform based on the edge intelligent terminal.

The operational optimization of integrated energy systems with high renewable energy penetration (IES-HREP) constitutes a complex systems engineering problem, primarily due to the absence of a well-defined cost model for renewable energy sources (RESs) generation and uncertainties affecting energy quality. To address these issues, this article proposes an entropy-based analysis and optimization framework to quantify RES uncertainty costs and system efficiency. First, an equivalent fuel (EF) cost model is introduced, integrating energy and information layers to quantify the cost of mitigating RES uncertainty. Building on this, entropy theory is employed to establish an information–energy quality coefficient (I-EQC) that evaluates RES energy quality by unifying thermodynamic and information entropy. In addition, a neurodynamics-based distributed algorithm is developed to perform multiobjective optimization for cost and exergy efficiency, enhancing computational speed while preserving data privacy. The simulation results demonstrate that the proposed framework reduces the cost by up to about 10% and improves the efficiency by up to about 5% compared to existing methods.

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.

Although rich collection of research results on sensor attack (SA) exist, no attack detection mechanism has ever been designed based on output error information to detect whether an attack has occurred. The primary objective of this article is to build a backstepping adaptive tracking control protocol for heterogeneous nonlinear uncertain multi-agent systems (HNUMASs) with partially SA. A dynamic SA detection mechanism by using output error information of agent only is developed to identify the SA. After locating the attack, to circumvent the effects of unknown time-varying output gain caused by SAs, we introduce the Nussbaum function in backstepping design to compensate the unknown time-varying output gain. The result shows that the developed SA detection mechanism is able to detect the occurrence of attack in a timely manner, while the derived adaptive backstepping tracking controller can effectively handle the adverse effects of SA and ensure that all signals are bounded in the closed-loop system. At last, the effectiveness and benefits of the presented approach are verified by simulation example. Note to Practitioners—This paper aims to achieve the adaptive tracking control for HNUMASs under SA, which can be widely used in practice, such as power systems, vehicular platoon systems, etc. The control protocol consists of a attack detection mechanism and Nussbaum function that compensates for the unfavorable effects caused by SAs. Moreover, the system may also be influenced by uncertainties from its neighboring agents in practical applications. Therefore, an additional estimator is designed in each subsystem to handle the uncertainties involved in its neighbor dynamics. This design avoids the exchange of information related to local neighborhood consensus errors among connected subsystems. A feasible strategy is provided for industrial applications.

A leak fault is a safety risk to interrupt the operation of the transportation process for intelligent automation system. To judge the system failure, a fault diagnosis method based on mixed neural networks is proposed in this paper. First, the multi-attribute extraction module is proposed to provide the local and global data changes caused by the leak event for the following neural networks, which reduces the noise influence from the complex environment. Second, a feature-sharing neural network is proposed to capture the multi-scale features of data changes and further implement leak fault detection and location through the sequence information and the corresponding sequential dependencies. Third, the task-dependency loss function is proposed to update the network parameters of the joint learning of different network outputs in the whole training process. Based on the proposed network structure, the proposed method could achieve two different targets of fault detection and location simultaneously for long-time series data. Finally, different case studies of the collected acoustic data are studied, and the analysis results show the effectiveness of the proposed method for leak fault detection.Note to Practitioners—A leak event is considered a sudden system fault in the transportation-oriented intelligent automation system. In order to reduce and minimize the system damage influence, leak fault diagnosis is the key point to identify operation risks based on the analysis result of the collected data changes. Thus, a mixed neural networks-based method is proposed to achieve the detection and location of leak events in this paper. With the combination of different neural network structures, multi-scale data changes could enhance the analysis capability of the proposed method for different fault diagnosis targets in complex operation scenarios. The case results show that the proposed method is an implementation way to ensure system safety and is better than other detection methods through the comparisons of different evaluation metrics.

As the percentage of renewable energy in the Energy Internet (EI) gradually increases, how to deal with the uncertainty of renewable energy in the economic dispatch problem (EDP) becomes an important issue. This paper proposes a digital twin (DT) assisted economic dispatch strategy for EI with information entropy. First, we leverage the storage capacity of the DT and an extensive historical data set to provide a theoretical framework for quantifying uncertainty of renewable energy. Second, a renewable energy cost function based on the maximum entropy principle, confidence interval, and penalty factor is proposed to model the renewable energy resources considering the uncertainty. Further, we design a fully distributed Newton-surplus-based optimization algorithm. This algorithm achieves fast second-order convergence to ensure the real-time performance of the DT-assisted economic dispatch framework and overcome the asymmetry caused by the directed communication network. In addition, we give theoretical proof that the Newton-surplus-based algorithm can converge to the global optimal point. Finally, simulations validate the effectiveness of the proposed algorithm.Note to Practitioners—The essence of EDP is to minimize the total costs through optimal resource allocation while ensuring compliance with all operational constraints. With the increasing penetration of renewable energy resources, their strong stochasticity and uncertainty pose challenges to achieve reliable dispatch strategy. To address this issue, this paper presents the DT-assisted economic dispatch framework, model, and method to quantify the uncertainty of renewable energy resources and achieve distributed economic dispatch with fast convergence speed for EI. Our research is beneficial for practitioners to understand how to use the DT and information entropy to deal with the uncertain of renewable energy resources. The theory and simulation results demonstrate the correctness and effectiveness of the proposed method.

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 primary objective of this article is to construct a distributed adaptive cooperative fault-tolerant control (FTC) protocol for dynamic output-constrained nonlinear multi-agent systems (MASs) subject to actuator fault and unknown output dead zone (UODZ) in the presence of stochastic false data injection (SFDI) attacks. By establishing a unified universal barrier function (UUBF) upon output, the original constrained system is transformed into a fully equivalent non-constrained system, which not only eliminates the restrictive condition of the constraint boundaries/functions but also solves the output constraints problem without changing the control structure. To circumvent the effects of unknown time-varying output coefficient derived from UODZ, we introduce the Nussbaum function in backstepping design. An adaptive FTC strategy based on the parameter adaptive law compensation approach that does not require the lower and upper bounds of the unknown fault coefficient is developed, and it can tolerate SFDI attacks. The result shows that the derived adaptive backstepping FTC protocol can not only achieve the cooperative control for MASs subject to UODZ under SFDI attacks, but also guarantee that all signals are bounded in the closed-loop system and the output constraints are not violated. Finally, simulation examples validate the validity of the developed schemes.

In this article, a novel online adaptive control scheme is developed for the optimal control issues of integrated electric-gas systems with partially unknown dynamics, by combining the decentralized event-triggered mechanism and adaptive dynamic programming techniques. Initially, the complex electric-gas coupling network is modeled in the state-space form. By virtue of neural networks (NNs), the NN-based identifier and the critic NN are designed to approximate the unknown drift dynamic and the optimal value function in an online fashion, respectively. Subsequently, the decentralized event-triggered control strategies are devised under the identifier-critic framework. Moreover, a novel decentralized event-triggered scheme with the dead-zone operation is proposed, which updates the controller and actuator signals only when the triggering condition is violated. As such, the computation complexity and the waste of communication resources can be significantly reduced. On the foundation of the Lyapunov theory, the uniform ultimate boundedness stability of the closed-loop control system and the exclusion of the Zeno behavior are proven. Finally, the effectiveness of the developed algorithm is verified through two numerical examples.

To achieve stable operation and current sharing in dc microgrids with communication networks of random packet losses, this article proposes a distributed event-triggered control (ETC) strategy based on data sampling mechanism and combined measurement. The proposed ETC consensus protocol achieves mean-square consensus of the distributed renewable power generation units (RGUs) by coupling the sampling interval, control gain, and packet loss probability. Moreover, the independent triggering of individual RGUs reduces communication burden during the control process and lowers the update frequency of converters. The proposed ETC strategy has the advantages of having fewer parameters, utilizing periodic data sampling mechanisms, avoiding the Zeno phenomenon in the control system and continuously monitoring the system state. Finally, detailed experimental tests are presented to demonstrate that the proposed distributed ETC strategy exhibits good capabilities in current sharing and robustness against random packet loss.

Although the P2P power transactions using the multiagent deep deterministic policy gradient (MADDPG) algorithm has been extensively studied, there are still challenges in privacy protection and training incentives. Furthermore, the stability and efficiency of the strategy decreases when dealing with nonindependent identically distribution (Non-IID) data from heterogeneous prosumers. Therefore, this article proposes a blockchain-enabled asynchronous federated learning-MADDPG (BEAFL-MADDPG) framework designed to enhance the training efficiency of heterogeneous prosumers while safeguarding data privacy. The framework includes a novel P2P energy trading model that facilitates energy trading amidst incomplete information while ensuring privacy assurances. In addition, a BEAFL-MADDPG algorithm is proposed, which accelerates training processes and enables parallel computation among agents. This algorithm enhances the efficiency of algorithm and empowers the training of diverse prosumers. Furthermore, a blockchain-enabled training mechanism and prosumer incentive scheme are proposed that not only encourage prosumer engagement in training but also ensure traceable transactions without the need for trust among participants. These mechanisms promote transparency and integrity, fostering a collaborative and secure environment for energy trading. Simulation results demonstrate that the framework achieves peak load reduction through optimized P2P trading, maintains computation efficiency across discount rates, and ensures secure transactions via blockchain-based incentives. These practical benefits support scalable and sustainable community microgrid operations.

As a burgeoning approach, droop control of interfacing inverters in microgrids has been widely adopted. However, droop control cannot achieve proportional reactive power sharing among distributed generators because of the difference of feeder impedances in actual microgrids. Hence, a novel distributed adaptive virtual impedance method based on average consensus algorithm is proposed to relieve feeder impedance mismatch. There into, virtual impedance is composed of static and adaptive inductance, which is designed to reshape equivalent impedance by creating additional control loops. Adaptive inductance unit is designed based on reactive power mismatch by applying multiagent consensus algorithm. By fully distributed adjustment to equivalent impedance, reactive power sharing accuracy can be improved. Then, proposed control method is applied to modified droop control, which is embedded designed dynamic voltage average consensus estimator, providing superior voltage restoration. At last, the effectiveness of proposed control method is shown by using simulation and further demonstrated through experiment study.

This article presents an adaptive prescribed-time dynamic surface control approach for a differential-driven unmanned surface vehicle (USV) with fully unknown parameters, which is a cascaded control system consisting of kinematic, kinetic, and motor-driven propeller layers. First, the control design of the kinematic layer determines the virtual surge and yaw velocities, which are filtered as the pseudocommands for the kinetic layer. By imposing a performance function for the position error of the USV, it can be driven into the preset precision region within the prescribed time. Second, the virtual force control laws designed in the kinetic layer give the desired motor angular speed commands, which are filtered as the pseudocommands for the propeller layer. Then, in the control design of the propeller layer, the actual command duty cycles are proposed to make the actual motor angular speed follow these pseudospeed commands of motors to apply in practice directly. By employing the fuzzy logic system to approximate the nonlinearities, we can establish a simpler control structure than the existing disturbance-observer-based controller due to the avoidance of virtual control laws and the adaptive compensations of modeling uncertainties. Finally, experimental results show that the proposed method makes the tacking task successful with user-defined performance.

The variation in multivariate time series (MTS) under wind turbine (WT) operational conditions makes it challenging for traditional anomaly detection methods to model expected behavior under normal conditions, resulting in failure to identify anomalies. To address this, an online anomaly detection method based on multiscale spatiotemporal graph learning is proposed, enabling prompt anomaly detection. First, an adaptive multiscale graph correlation forecasting network is introduced, which autonomously learns temporal and feature dependencies at each scale. Next, a dynamic spatiotemporal graph variational autoencoder is presented to model the MTS’s spatiotemporal correlations and capture the normal operation patterns. In addition, we propose a nonparametric dynamic threshold updating mechanism using Welch’s t-test to adapt to changing operating conditions based on anomaly scores. The proposed method jointly optimizes the forecasting and pattern reconstruction networks to derive spatiotemporal graph representations and anomaly scores, effectively identifying anomalies that deviate from normal operating states. Experiments on real WT data demonstrate the method’s ability to detect anomalies earlier, with evaluation metrics showing at least a 2% improvement in anomaly detection accuracy compared to existing methods.

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.

Communication network failure, e.g., persistent packet loss, may considerably affect the safe and stable operation of smart grids. This may degrade the performance of various components and applications, including energy management and economic dispatch. We propose a switched surplus-based distributed security dispatch approach to cope with the persistent packet loss under an unreliable communication network environment. First, we jointly consider the packet loss sequence and the dynamic triggering sequence to define actual affected periods caused by the persistent packet loss. Then, we outline an incentive scheme, integrate primal-dual analysis and eigenvalue perturbation theory to design the switched surplus-based distributed security dispatch algorithm. Further, we design a dynamic triggering mechanism that enables the proposed algorithm to dynamically switch to different modes according to the change in network state. With those components, the proposed method offers strong robustness against persistent packet loss. In addition, we provide the convergence and optimality proofs of the algorithm. Finally, simulation results are provided to validate the proposed method and to demonstrate its effectiveness.

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 paper investigates one type of distributed constrained optimization problem, e.g., the economic dispatch problem, in the presence of DoS attacks. Therein, multiple DoS attackers are collaborative to impede the communication transmission and change the communication topology at will. Consequently, the convergence and/or optimality of distributed algorithm may be compromised. To reduce the effect of this kind of DoS attacks, a distributed resilient initialization-free Jacobi descent algorithm is proposed. It is designed with three switched control protocols which enable the proposed algorithm reasonably employing the estimations to replace the missing information when attacks occur. Meanwhile, the proposed method is embedded with second order information, resulting in faster convergence speed. Moreover, theoretical analysis results are provided to show that the proposed algorithm can exponentially converge to the global optimal solution of the studied problem. Finally, simulation results tested in IEEE 30-bus system validate its effectiveness and flexibility.Note to Practitioners—The economic dispatch is a key issue in smart grid, which can be formulated as a kind of distributed constrained optimization problem. Since the distributed algorithms work under distributed sensor networks, they are easier to undergo DoS attacks. To address this issue, this paper presents a distributed resilient initialization-free Jacobi descent algorithm, which features strong robustness to resist DoS attacks and faster convergence. Meanwhile, the proposed method is shaped for common constrained optimization problem with better expansibility. We conduct the global convergence and optimality proofs, which benefits the practitioners to estimate the convergence performance, e.g., the convergence rate. Simulations further show the correctness and effectiveness of the proposed method. In future, we will pay more attention on the non-convex constrained optimization problem.

The transition of the power system into a low-carbon power system (LCPS) with a high penetration of renewable energy resources addresses several issues related to energy and climate. However, due to the uncertainty associated with renewable power generation (RPG), deriving an accurate effective locational marginal pricing (LMP) for an LCPS remains a challenge. To address this challenge, we propose a novel information theory-based framework for LMP calculation that quantifies the fluctuations in the LMP due to uncertainty associated with RPG and random loads in an LCPS. First, based on the information entropy levelized cost of energy, we introduce the equivalent cost of RPG to ensure that the cost of RPG is not zero under the LMP mechanism so that it can bid reasonably in the market to provide accurate price signals. We, then, design a security-constrained economic dispatch model incorporating the RPG equivalent cost to balance uncertainty and energy demand in the LCPS electricity market. Furthermore, we propose an uncertainty-constrained model of buses and branches in LCPS based on information theory that is developed to clarify the physical significance of the information that reduces generation and load uncertainty within the LMP framework.

The development of low-carbon power systems has not only elevated the investment costs of power enterprises, but also generated a vast amount of electricity data. The electricity data trading holds promising potential as a primary means to cover investment costs. However, there is a lack of research on the electricity data trading. To address this issue, this article designs an electricity data trading method based on price game and blockchain for low-carbon power systems. It encompasses a data trading framework and the corresponding trading mechanism. The proposed trading framework contains data providers, data consumers, and a blockchain-based information system that plays the role of the data servicer to handle the transactions between data providers and consumers. The proposed trading mechanism mainly consists of three parts: 1) valuation; 2) pricing; and 3) copyrights confirmation. Those parts are executed sequentially to complete the electricity data trading process from valuation to clearing. Specially, the information theory is employed to realize multidimensional electricity data valuation. Further, the data trading game pricing is formulated as a multiobjective optimization problem considering market power constraints to solve. In addition, the digital watermarking combined with blockchain is designed to protect the electricity data copyright. With those components, the designed electricity data trading method enables the power enterprises to make profit from the low-carbon smart energy systems. Finally, experiments demonstrate the effectiveness of the proposed method.

As the number of ships docking at ports and using onshore power grows, there is a pressing need for efficient economic dispatch within the port microgrid (PMG). The computing power network (CPN) leverages ubiquitous computing resources, presenting new opportunities for handling complex tasks, such as the economic dispatch problem (EDP) more efficiently. However, integrating CPNs into PMGs raises significant concerns about data security and privacy. To address these issues, this article proposes a distributed prescribed-time optimization (PPDPTO) algorithm specifically designed for the EDP in the integrated PMG and CPN. This algorithm ensures both high computation efficiency and enhanced privacy security. Specifically, this algorithm combines the distributed prescribed-time optimization theory and the privacy-preserving technique, which can protect the sensitive energy information of the berthing ships while ensuring fast convergence. Moreover, based on the proposed mask function protecting the power demand information of the berthing ships, the optimal solution of the EDP can be obtained with limited decoding resources. A smooth piecewise mask function is proposed to promote the nonvulnerability of the system and the bias in the optimal steady states of the proposed algorithm is reduced. Furthermore, the prescribed-time convergence of the PPDPTO algorithm is proven; meanwhile, the supply and demand balance constraints of the EDP can be guaranteed under the mask function. Finally, simulations undermine the effectiveness of the PPDPTO algorithm.

This article proposes a multienergy trading market model based on price matching, aiming to foster multienergy collaboration and enhance energy utilization through individual participation. With the ongoing advancements in energy distribution and marketization, the energy Internet necessitates improved applicability and efficiency for personalized energy responses. To address these requirements, a multienergy trading market model is proposed, which enables the avoidance of user information disclosure and guarantees user trading autonomy. In addition, a joint trading mechanism is designed that accounts for multiple time scales and energy types, consequently reducing trading failures caused by overlooking energy transmission processes. By performing the proposed trading mechanism, the market operator can match various energy types using conversion devices, thereby augmenting matching efficiency. An income mechanism is also established to deter the operator from purposefully evading potential trading opportunities for personal gain. To address the proposed model, an improved hierarchical reinforcement learning algorithm is employed, which effectively overcomes challenges associated with large state action spaces and sparse rewards. Numerical examples are provided to confirm the efficacy of the proposed approach.

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.

The integrated energy system based on ubiquitous power Internet of Things (IoT) has the characteristics of ubiquitous connection of everything, complex energy conversion mode, and unbalanced supply-demand relationship. It brings strong random disturbance to the power grid, which deteriorates the comprehensive control performance of automatic generation control. Therefore, a novel deep reinforcement learning algorithm, namely, collaborative learning actor–critic strategy, is proposed. It is oriented to different exploration horizons, has the advantage on experience sharing mechanism and can continuously coordinate the key behavioral strategies. Simulation tests are performed on the two-area integrated energy system and the four-area integrated energy system based on ubiquitous power IoT. Comparative analyses show that the proposed algorithm can efficiently solve the problem of strong random disturbance, and has better convergence characteristic and generalization performance. Besides, it can realize the optimal cooperative control of multiarea integrated energy system efficiently.

With renewable energy becoming more and more important, the heat and electricity integrated energy system (HE-IES) has been widely used because of its potential benefit in accommodating renewable energy. This work for the first time formulated a dynamic optimal energy flow (OEF) problem for the HE-IES with hybrid AC/DC sources. Firstly, to effectively and accurately assess the operation state of district heating network (DHN), the temperature dynamics are focused and solved with a set of difference equations where an adaptive discretization method is proposed. The method based on the delay characteristics of pipelines is proposed to select temporal and spatial steps for reasonable approximation of DHN, and to achieve satisfactory accuracy results with a lower computational burden. Secondly, a two-stage OEF model for HE-IES with new linear approximations is developed. In this model, a detailed converter station model coupled AC grid and DC grid is investigated, and a linearization constraint method is proposed to handle the highly nonlinear of converter station by adding extended branches to the AC grid. Finally, simulations demonstrate that the effectiveness of the proposed model, which can provide more intact information of state variables for optimal planning.Note to Practitioners—This work is motivated by the demand for optimal energy management in heat and electricity integrated energy system (HE-IES). On the one hand, the slow dynamic characteristic of the district heating network (DHN) is crucial for calculating the optimal results. On the other hand, the improvement of electronic technology has diversified energy supplies and enriched the way of using electricity, such as converter-based generators for electric power grid (EPG) and converter-based boilers for DHN. Therefore, the model of HE-IES exhibits highly nonlinearity, which brings huge challenges to optimal energy flow analysis, especially for the real-time OEF analysis with state information updated every 15–30 min. Existing studies focus on computing optimal energy flow without considering the slow dynamic characteristic of DHN or the hybrid AC/DC scenarios brought by the converter-based sources. This paper presents an optimal energy flow problem that integrates the slow dynamic characteristic and the converter-based sources to retain the complete state information of the system as much as possible in the optimization process. The work is used on an integrated IEEE-33 bus and Denmark-61 node system to show the effectiveness.

In this paper, the problem of secondary voltage restoration in an islanded microgrid (MG) is considered, in which the actuator of the distributed generators (DGs) may coexist with partial loss of effectiveness (PLOE) fault and bias fault. For each DG, an adaptive event-triggered fault-tolerant (ETFT) control protocol is designed to compensate for the effects of actuator faults in the DGs, thereby restoring the voltage to the reference value. The dependent event triggering mechanism saves the processor’s computational resources. A desirable feature of the protocol proposed in this paper is that the control protocol relies only on relative information between neighboring DG’s, independent of global information about the network graph, fault boundaries, and network scale. It means that the protocol is implemented in a fully distributed framework. The protocol fully applies to the common ETFT consensus control problem of linear multiagent systems (MASs) with actuator faults. Furthermore, comprehensive theoretical arguments for consensus stability and analysis of Zeno behavior ensure the approach’s feasibility. The simulation results verify the effectiveness of the algorithm.Note to Practitioners—This paper aims to propose a fully ETFT control protocol for secondary voltage restoration of an islanded MG. The control protocol consists of a linear term and a nonlinear time that compensates for the multiplicative and additive fault of the actuator. Moreover, DGs’ communication structure and global fault boundaries may be unknown in practice. Hence, adaptive coupling gains that depend only on the sampled relative information of DGs are introduced to estimate the controller gain, thus avoiding global information. A feasible strategy is provided for industrial applications.

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.

Privacy issues and the cyberattacks are two typical threats in network operation, but the problem considering both of them has not been properly addressed. To fill this gap, this article investigates the privacy-preserving consensus strategy against the false data injection attacks (FDIAs) for secondary control of microgrids. An integral sliding mode observer and its supporting controller are developed to against the FDIAs on local units. Since the sliding motion is independent of the controller signal, the proposed strategy has a natural advantage for the FDIAs on the controller command. Furthermore, an observer-based resilient control strategy is proposed to against the FDIAs on the communication lines. It is worth mentioning that the$H_\infty$performance can be obtained by regarding the consensus errors as disturbance. Moreover, the edge-based privacy-preserving algorithm along with the observed-based resilient strategy is proposed. Finally, some simulation examples are used to verify the theoretical results.

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.

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.

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.

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.

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 algorithms are increasingly being used to solve the economic dispatch problem of integrated energy systems (IESs) because of their high flexibility and strong robustness, but those algorithms also bring more risk of cyber-attacks in IESs. To solve this problem, this article investigates the distributed robust economic dispatch problem of IESs under cyber-attacks. First, as the first line of defense against attacks, a privacy-preserving protocol is designed for covering up some vital information used for economic dispatch of IESs. On this basis, a distributed robust economic dispatch strategy is presented to achieve the energy management of IESs in the presence of misbehaving units, which consists of a neighbor-observe-based detection process and a reputation-based isolation process. The proposed strategy is implemented in a fully distributed fashion and possesses strong robustness against various colluding and noncolluding attacks. In addition, the strategy can not only ensure the reliability of information transmission among energy units, but also solve the problem of incorrect measurement of distributed local load data caused by cyber-attacks. Finally, the effectiveness of the proposed strategy is illustrated by simulation cases on a 39-bus 32-node power–heat IES.

For the integrated energy system (IES) formed by a cluster of energy hubs (EHs), the outputs of EHs and system parameters, which greatly influence the security performance, should be properly adjusted. In this article, an event-triggered distributed hybrid control scheme is proposed to achieve security and economic operation for the IES. First, the EH output control is designed based on the features of energy networks as well as the containment and consensus algorithms. According to the control of outputs, the electricity and heat load power can be accurately shared without knowing the network parameters. Second, the pressure is bounded within an acceptable range, and the frequency is reverted to the reference value by implementing the proposed control method. Third, an event-triggered communication strategy is employed to design the corresponding protocols, resulting in reduced communication cost. Finally, the control of devices based on the equal incremental principle is proposed to achieve the minimal economic cost for each EH with considering energy prices. The results of numerical case studies are presented to validate the performance of the proposed control method.

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.

This article investigates the energy operation problem based on We-Energy (WE), a novel full-duplex model in Energy Internet (EI). A dual-objective optimal energy operation model of WE is formulated with the consideration of economical benefit and security operation under different time scenarios. Due to the inaccurate model of distributed generation devices and loads, a multipolicy convex hull reinforcement learning (MCRL) algorithm is proposed. It can find the multiobjective strategy set with model-free feature. Moreover, considering the limitations of artificial intelligence technology and the human advantages in information processing for complex task, a two-channel Human-in-the-loop (HITL) method is designed to combine with MCRL to avoid decision-making risks. The one channel of HITL can evaluate the operation strategy by human under normal conditions so that the understanding of human for complex operating conditions can be incorporated into the machine learning algorithms to improve the confidence of intelligent systems. The other channel of HITL can allow human to participate in real-time adjustment under abnormal conditions to avoid system out of control. Simulation studies of modified EI are confirmed that the proposed algorithm can improve system performance effectively.

This article investigates a distributed adaptive dual control that employs both consensus algorithm and improved equal incremental principle (IEIP), to guarantee the security operation while reducing the energy consumption of the energy Internet (EI). Since the security operation is a critical factor of the EI with the energy hub (EH), it is necessary for the EI to adjust the outputs of EHs and the system parameters, which have a great influence on the performance. The consensus-based control of the EI can resolve the energy-coupling issue and accurately share the electricity and heat loads power without requiring the information of the network parameters, which is hard to know. Meanwhile, the variations of system parameters caused by the droop action greatly impact the security operation of the EI. It can be adaptively recovered by executing the proposed control strategy. Furthermore, in order to reduce the energy consumption, the equipment in hubs should also be managed in view of the features of EH. The minimal loss of the energy can be achieved by utilizing the control of devices via the IEIP by considering the coupling characteristics of devices. The performance of the proposed method is demonstrated through numerical case studies.

This paper investigates the situation awareness issue of power system with massive measured data. To address this issue, first, a graph-theory-based network partitioning algorithm is proposed to realize decentralized detection in a faster response speed, while using power flow characteristics highlights the independency of different groups. Further, a hierarchical event detection method is proposed to judge voltage change and locate event position according to spectral distribution change of established multidimensional matrix. With the proposed method, the system situation can be assessed and the knowledge of the system model is not required. In addition, the accurate result of weak event happened in system could also be obtained. The simulation results are presented to illustrate the effectiveness of the proposed detection method.

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.

A distributed optimization problem based on a continuous-time multiagent system (MAS) disturbed by general noise is considered in this paper. The general noise, under some relaxed assumptions, which may be a stationary process, is proposed to describe the disturbance among agents more accurately. The noise-to-state (NOS) stability of the concerned MAS is analyzed based on an improved theoretical result of random differential equations. Furthermore, the relative sufficient conditions in the form of linear matrix inequality are developed with less conservatism, from which the minimum estimation error between the optimal solution and the NOS stable state of the proposed MAS with general noise can be obtained by choosing some appropriate distributed optimization parameters. One example is used to verify the effectiveness of the proposed approach.

This paper investigates the residential energy management problems in the power-heat-coupling system. For better solving this issue, based on the novel concept of We-Energy (WE) for energy Internet (EI), this paper proposes a residential WE (R-WE) framework faced by the terminal users who play an important role in renewable energy consumption. Inspired by the full-duplex feature of R-WE, the power and heat supply-demand balance constraints are fulfilled in a regional unit of EI, but it may be inequality constraints for corresponding consumer, producer, or WE operation modes in only one R-WE. The R-WE framework can be classified into four operation modes, which is island mode, consumer mode, producer mode, and WE mode. On this basis, the R-WE models cooperate to achieve the objective of minimizing the operation costs, smoothing out the loads’ variations, and renewable resource fluctuations. Specifically, the R-WE framework with respect to the heat-power-coupling problem can be solved in the distributed double-consensus algorithm (DDCA), which is designed two sets of consensus algorithms by using four completely different consensus variables to calculate the power and heat multipliers, evaluate the power and heat generations and, thereby, further obtain the power mismatches of electricity and heat. Also, the Karush-Kuhn-Tucker (KKT) optimal conditions of the proposed DDCA is further proved. Meanwhile, a novel projection operation method for combined heat and power devices is designed to take the infeasible solutions mapped into the feasible region. Finally, the simulation results in different cases further demonstrate that the proposed R-WE frame can be an appropriate method to analyze the terminal consumers and harmonize multienergy producers in the process of constructing EI projects. And an R-WE framework of the campus has experimented with minority loads in island mode.

This paper investigates the economic dispatch problem of microgrids in a distributed fashion. To address this issue, a delay-free-based distributed algorithm is presented to optimally assign the whole energy demand among local generation units with the objective of minimizing the agminated operation cost. By implementing the proposed algorithm, each component can find its own optimal operations by only requiring local computation and communication. As a result, it enhances the system robustness, flexibility, privacy, etc. More importantly, the time-varying delays model is considered and embedded into the design of our distributed algorithm, such that the components can employ the delays information to achieve the collaborative operation, which are more general and applicable for practical power systems. In addition, we have proved that the proposed algorithm can converge to the global optimal point under some sufficient conditions. Finally, several simulations are provided to demonstrate the correctness and effectiveness of the proposed algorithm.

In this paper, a novel discrete-time deterministic Q -learning algorithm is developed. In each iteration of the developed Q -learning algorithm, the iterative Q function is updated for all the state and control spaces, instead of updating for a single state and a single control in traditional Q -learning algorithm. A new convergence criterion is established to guarantee that the iterative Q function converges to the optimum, where the convergence criterion of the learning rates for traditional Q -learning algorithms is simplified. During the convergence analysis, the upper and lower bounds of the iterative Q function are analyzed to obtain the convergence criterion, instead of analyzing the iterative Q function itself. For convenience of analysis, the convergence properties for undiscounted case of the deterministic Q -learning algorithm are first developed. Then, considering the discounted factor, the convergence criterion for the discounted case is established. Neural networks are used to approximate the iterative Q function and compute the iterative control law, respectively, for facilitating the implementation of the deterministic Q -learning algorithm. Finally, simulation results and comparisons are given to illustrate the performance of the developed algorithm.

A hybrid power supply system (HPSS) based on the quasi-Z-source network is proposed for aluminum electrolysis, which can reduce energy consuming and carbon emission through the use of renewable energy. An ac–dc integrate controller is designed in the HPSS that contains a two-layer control. The first layer control is responsible for maintaining the dc bus voltage and current, which can mitigate negative effects caused by anode effect in aluminum electrolysis. The independent maximum power tracking for PV array and the dc-bus voltage balance for each quasi-Z-source dc–dc converter can be achieved by using the PV-voltage controller and dc-bus voltage controller for the PV System. To maintain the voltage of dc bus within the require voltage range of aluminum electrolysis production and ensure high input power quality of ac System, the quasi-Z-rectifier controller is employed, which can reduce the harmonic injection. The power allocation is addressed in the second control layer and a power scheme algorithm (PSA) is carried out to maximize the system efficiency and economic benefit. At last, the simulation and experimental results are provided to verify the effectiveness of the designed HPSS and the proposed PSA.

Based on the hierarchical control structure in islanded Micro-Grid (MG) systems, the coupling/tradeoff effects in different levels are analyzed in details. In the primary level, analyses of the coupling effects among droop control gains, line impedance differences, output reactive power and voltage magnitudes are provided specifically. In the secondary level, the tradeoffs between accurate reactive power sharing and voltage magnitudes regulation are further detailed. The analysis results can provide a guideline for the design of MG structure and its control parameters. In addition, novel containment-based controller is proposed to control the voltage into a reasonable range which is the first time to apply this algorithm in MG. Furthermore, dynamic-consensus-based controller is used to guarantee accurate reactive power sharing. The combination of controllers offers a coordinated distributed operation and enhanced system performance. Finally, experimental results are shown to validate the effectiveness of the proposed method.

As system transient stability is one of the most important criterions of microgrid (MG) security operation, and the performance of an MG strongly depends on the placement of its energy storage devices (ESDs); optimal placement of ESDs for improving system transient stability is required for MGs. An MG structure preserving energy function is first developed for voltage source inverter-based MGs since the existing energy functions, based on synchronous generators and the conventional power system, are not applicable for MGs. The concept of internal potential energy of distributed energy resource is presented instead of the kinetic energy term in traditional energy function. Then, a novel approach for the optimal placement of ESDs is proposed based on MG structure preserving energy function for improving MG transient stability. Simulation and experimental results show that the proposed method can be used to find the optimal placement of ESDs and improve the system stability effectively.