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.

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.

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.

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.

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.

This paper investigates the issues of day-ahead and real-time cooperative energy management for multienergy systems formed by many energy bodies. To address these issues, we propose an event-triggered-based distributed algorithm with some desirable features, namely, distributed execution, asynchronous communication, and independent calculation. First, the energy body, seen as both energy supplier and customer, is introduced for system model development. On this basis, energy bodies cooperate with each other to achieve the objective of maximizing the day-ahead social welfare and smoothing out the real-time loads variations as well as renewable resource fluctuations with the consideration of different timescale characteristics between electricity and heat power. To this end, the day-ahead and real-time energy management models are established and formulated as a class of distributed coupled optimization problem by felicitously converting some system coordinates. Such problems can be effectively solved by implementing the proposed algorithm. With the effort, each energy body can determine its owing optimal operations through only local communication and computation, resulting in enhanced system reliability, scalability, and privacy. Meanwhile, the designed communication strategy is event-triggered, which can dramatically reduce the communication among energy bodies. Simulations are provided to illustrate the effectiveness of the proposed models and algorithm.

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, we propose a game theoretic approach for joint offloading and resource allocation optimization (JORAO) problem in mobile edge computing (MEC) system. This study not only investigates offloading strategy, but also considers cloud and wireless resource allocation. Specially, the concern of the JORAO problem is to minimize the energy consumption and monetary cost from mobile terminals' perspective. However, the JORAO problem is non-convex and NP hard. Therefore, it is formulated as a JORAO game. The existence of Nash equilibrium (NE) is proved for it. To obtain NE, we also concentrate on cloud and wireless resource allocation algorithm (CWRAA), which is the sub- algorithm of the JORAO game. For the CWRAA, on one hand, we take consideration of OFDM sub-channels allocation and uplink power allocation in radio access networks (RAN). On the other hand, the computation resource allocation in MEC is studied. Simulation results show that the distributed JORAO game algorithm can nearly minimize the total cost of all mobile terminals (MTs) with low complexity. In addition, the energy consumption and completion time are less when the size of data becomes larger compared with existing algorithms.

The problem of non-fragile pinning synchronization for complex networks is studied in this paper. Firstly, by using an inequality, which is introduced by using Newton-Leibniz formula, synchronization criterion is obtained by using novel mathematical skills. Secondly, a novel variable subintervals method is applied to expand the former results. Unlike previous results, the interval delay is divided into some dynamic variable sub-delays, which can introduce more weighting matrices. Thirdly, by resorting to Lyapunov function methods and some analysis techniques, the non-fragile pinning synchronization results are solved in terms of a set of LMI inequalities which are easy to be analyzed or computed. Finally, a numerical example is given to demonstrate the efficacy and efficiency of the proposed methods.

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.

This letter points out several fundamental mistakes in the above paper. It is shown that the proposed quantized control design method cannot guarantee the asymptotical stability of the impulsive fuzzy networked system in the above paper.

In this paper, a new delayed projection neural network with mixed delays is proposed for solving a class of quadratic programming (QP) problems. By the Lyapunov-Krasovskii theory and the linear matrix inequality (LMI) method, the proposed neural network is proved to be convergent to the optimal solution of the QP problems exponentially. The validity of the proposed neural network is verified by two simulation examples.

Graphics Processing Units (GPUs) that support general purpose program are promising platforms for high performance computing. However, the fundamental architectural difference between GPU and CPU, the complexity of GPU platform and the diversity of GPU specifications have made the generation of highly efficient code for GPU increasingly difficult. Manual code generation is time consuming and the result tends to be difficult to debug and maintain. On the other hand, the code generated by today's GPU compiler often has much lower performance than the best hand-tuned codes. A promising code generation strategy, implemented by systems like ATLAS~\cite{Whaley}, FFTW~\cite{FFTW_org}, SPIRAL~\cite{Pueschel:05} and X-Sort~\cite{Li:05}, uses empirical search to find the parameter values of the implementation, such as the tile size and instruction schedules, that deliver near-optimal performance for a particular machine. However, this approach has only proved successful when applied to CPU where the performance of CPU programs has been relatively better understood. Clearly, empirical search must be extended to general purpose programs on GPU. In this paper, we propose an empirical optimization technique for one of the most important sorting routines on GPU, the radix sort, that generates highly efficient code for a number of representative NVIDIA GPUs with a wide variety of architectural specifications. Our study has been focused on the algorithmic parameters of radix sort that can be adapted to different environments and the GPU architectural factors that affect the performance of radix sort. We present a powerful empirical optimization approach that is shown to be able to find highly efficient code for different NVIDIA GPUs. Our results show that such an empirical optimization approach is quite effective at taking into account the complex interactions between architectural characteristics and that the resulting code performs significantly better than two radix sort implementations that have been shown outperforming other GPU sort routines with the maximal speedup of 33.4\%.