Buildings account for substantial global energy consumption, with heating, ventilation, and air conditioning (HVAC) systems as major contributors. We study the setpoint schedule optimization of HVAC systems that minimize both energy costs and occupant discomfort. Since building performance simulation (BPS) tools provide high-fidelity models of building dynamics, integrating simulation with optimization is expected to obtain an effective schedule for building energy management. Consequently, many simulation-based optimization methods that integrate BPS into optimization processes are proposed. However, these methods still face challenges due to non-analytical system dynamics, computational complexity, and the lack of theoretical convergence guarantees. To address these challenges, a Lagrangian relaxation-based simulation optimization (LRSO) method is developed in this paper. A dynamic linear surrogate model iteratively refines itself with simulation outputs, balancing tractability and accuracy. Within Lagrangian relaxation framework, the problem is decomposed into simulation and optimization subproblems, which can be solved in a coordinated and decomposed way. The surrogate subgradient method further ensures the convergence. Experimental results demonstrate its superior performance in minimizing energy cost and occupant discomfort across all test scenarios, with computational times suitable for real-time scheduling.

This paper studies the online management of the computational resources between multiple edge clouds to minimize the operational cost for a vehicle-to-network (V2N) service provider, subject to stochastic trajectories of vehicles, the quality-of-service (QoS) and the resource limit. Due to the random mobility of vehicles, it poses challenges in real-time migration management when the computational capacity of each edge cloud and the stringent delay requirement of V2N services are both constrained, resulting in strong temporal-spatial coupling of the migration decisions. The problem could even be intractable to solve as the number of vehicles grows. To tackle these issues, we first propose a multi-layered cloud framework to gather and coordinate migration information between vehicles. Then, a multiagent rollout with feasibility construction approach is developed, where the migration decision can be optimized sequentially for each vehicle based on the coordinated migration information from the central cloud. To handle the potentially infeasible solutions caused by the computational resource constraint, we propose a heuristic method to determine the migration priority at each overloading edge cloud, and an integer program is constructed that can be easily solved to produce feasible solutions. The numerical results show the efficiency of the proposed approach in both economical performance and computational complexity compared to the benchmarks.

As data traffic and information services surge, 5G base stations (BSs) have become primary energy consumers in wireless networks, with cooling accounting for 40% of BS power use and driving high operational expenditure. This underscores the need for energy-efficient optimization of cooling control. However, existing model-based and AI-driven optimization methods face critical limitations in real-world deployments, including limited generalizability across heterogeneous BSs resulting from their high scenario dependence, the inherent tradeoff between control stability and dynamic adaptability under complex operating conditions, and high deployment costs due to computational demands. To address these challenges, this article develops a three-stage hybrid learning (TSHL) approach that integrates imitation learning, ensemble learning, and deep reinforcement learning into a three-stage offline-to-online architecture, enabling expert knowledge transfer from data-rich BSs to generate high-quality initial policies for data-scarce ones, while online learning ensures continuous adaptation to local dynamics. In addition, we propose a cost-efficient deployment mechanism that leverages only existing monitoring data without additional hardware costs, employs hybrid experience policy updates within a deep Dyna-Q-based architecture to enhance learning efficiency, and incorporates a safety-constrained exploration to enhance policy reliability. Extensive evaluations on both a simulation testbed and a real-world 5G BS demonstrate that TSHL achieves over 18.36% cooling energy savings and outperforms baseline methods in cold-start effectiveness, online adaptability, operational reliability, and overall cost-efficiency. These results highlight TSHL as a practical solution for sustainable 5G BS operations, especially for data-scarce BSs, such as retrofitted or newly established sites, offering a scalable pathway to network-wide energy savings.

The frequent blackouts around the world in the past 20 years have brought the security of the power grid to a head. Among various hazard situations, cascading failure is the one with critical threats due to its widespread propagation and long duration. An effective way to prevent cascading failure is to identify the vulnerable set, which is defined as the composition of transmission line combinations that can initialize the sequence of failures. In this paper, we first elaborate cascading failure model and its adaptation under the scenario of interest. Then a novel framework of data-driven identification model is developed to replace the traditional flow-based detection process, which is computationally heavy. Specifically, a method that seamlessly achieves the globally topological features embedding by designing a tailored messaging mechanism adjusted for the power grid is proposed, overcoming the otherwise problem of the constrained neighborhood in existing graph convolution networks (GCNs). Besides, with the proposed pruning optimization method, the sparsity of the vulnerable set can be naturally enforced and combinatorial explosion is readily alleviated. Numerical experiments are conducted on 30-bus, 200-bus, and 500-bus systems, including static and dynamic load scenarios. All of them verify the excellent performance of the identification model for both effectiveness and efficiency.Note to Practitioners—This paper is motivated by a practical need for mitigate the security threat of cascading failures to power grid through the vulnerable set identification. Existing methods for identifying the vulnerable set have limitations, including a limited number of vulnerabilities identified and challenges related to the high time complexity of cascading failure simulators and combinatorial explosion. To address this issue, we develop a data-driven identification model that integrates both the physical and topological features of the power grid. This model reduces the reliance on cascading failure simulators and enhances the efficiency of vulnerable set identification. Additionally, the pruning optimization method is proposed to further mitigate the high time complexity caused by combinatorial explosion. Simulative studies conduct in both dynamic and static load scenarios validate the performance of the developed data-driven model, demonstrating its ability to achieve rapid identification of the vulnerable set and thereby improve the overall robustness of the power grid against cascading failures.

With the popularity of electric vehicles (EVs) and renewable energy sources (RES), the flexibility of charging and discharging of EVs and the intermittency of RES have brought challenges to building operations. Considering the mobility of EVs as commuting tools between buildings and the uncertainty of RES, it is of great practical significance to coordinate multiple buildings with RES and EVs on the premise of meeting the state of energy (SOE) requirements of the future trip. We formulate this coordination problem as a stochastic centralized mixed integer linear programming problem. A polyhedral convex set is constructed to describe the SOE uncertainty of EVs. New nonanticipative constraints (NCs) are derived through forward recursion based on constructed scenarios to guarantee the all-scenario-feasibility (ASF) and nonanticipativity of the decision. A Lagrangian relaxation-based decentralized all-scenario-feasible (LR-DASF) algorithm is developed to solve the centralized optimization problem in a decomposition and coordination way. In this method, the optimal ASF solution can be obtained with a fast convergence rate by updating Lagrangian multipliers without solving all subproblems with NCs. The performance of the LR-DASF algorithm is verified by numerical results, which shows that the algorithm can guarantee the ASF of the solution, as well as promote computational efficiency. Note to Practitioners—EVs as energy storage devices bring energy exchanges between buildings accompanying the mobility of EVs which is an opportunity to improve the energy efficiency of multiple buildings. However, as commuting tools, the SOE of EVs must be guaranteed to be larger than the trip requirement over the randomness of RES generation. Furthermore, solving the coordinated optimization problem of multiple buildings with RES and EVs still faces computational complexity challenge due to the spatio-temperal coupling between EVs and buildings, which may lead to costly computational effort in the premise of guaranteeing the feasibility and nonanticipativity of the decision over the uncertainties in practice. Therefore, in order to overcome the above challenges, an LR-DASF algorithm is developed in this paper to solve the coordinated optimization problem of multiple buildings with RES and EVs. Based on the algorithm, for the system operator, it updates and broadcasts the Lagrangian multipliers information to the local coordinators of buildings. For each building, the local coordinator can make ASF decisions based on new NCs with the information obtained from the system operator independently to guarantee the SOE requirement. The method developed in this paper can make faster optimal decisions without perceivable degradation in accuracy and guarantee the SOE requirement of EVs simultaneously, to meet the requirements of feasibility and computational efficiency of decision making in practice. It is conducive to the future application of LR-DASF in the coordinated optimization of buildings and EVs at the city or regional scale.

The increasing penetration of renewable energy generation (REG) introduces high levels of uncertainty into power grid, potentially causing significant impacts on the evolution of cascading failure. In this paper, we propose a failure tree model that encompasses all possible failure paths resulting from the uncertain power injections from REG to describe the dynamic process of cascading failure in power grid. In order to obtain the failure paths of cascading failure, we propose an interval overload tripping mechanism to model relay protection based on the uncertainty set of REG and dynamic interval power flow. On the basis of the proposed model, we design a forward-backward tree search to efficiently evaluate the impact of the uncertain REG on cascading failure. Compared with the probabilistic power flow (PPF) model and scenario-based model, the simulation results of our model are more accurate because the statistical distribution of demand loss in our model is closer to Monte Carlo simulation (MCS). The efficiency of the proposed simulation method is demonstrated by comparing our model with the MCS under various sample numbers and two existing models. Finally, we analyze the influence of REG uncertainty level and penetration level on cascading failure and simulation performance. Note to Practitioners—To achieve accurate and fast cascading failure analysis in power grid with renewable energy generation (REG), this paper develops a failure tree model that considers the impact of uncertain injected power of REG on the dynamic process of cascading failure. In the model, the dynamic interval power flow and interval overload tripping mechanism are proposed to simulate the physical responses during cascading failure, including power flow redistribution, transmission branch outage and frequency regulation. Therefore, the model is more accurate in describing the actual characteristics of cascading failure in power grid with REG. This will facilitate the development and evaluation of control strategies aimed at improving the stability of power grid. Meanwhile, the model provides a good example for researchers and engineers to simulate network systems without detailed information about the probability distribution of uncertain injection variables. Based on the proposed model, we develop a forward-backward tree search, which allows the decision-maker to make a satisfactory trade-off between accuracy and time consumption. This algorithm allows for fast control strategy implementation to prevent failure propagation.

This paper analyzes the evacuation process of people in a building, and constructs a discrete-time evacuation model that can accurately describe the evacuation problem according to evacuation scenarios. In the discrete time framework, the evacuation policy is dynamically adjusted based on the dynamic transfer of people. For the large-scale evacuation problem, this paper proposes a two-stage method to solve the evacuation policy of edge and node separately, which improves the solving efficiency. The results of case study prove the reliability and efficiency of our method. Note to Practitioners—In this paper, considering the influence of effective edge width and crowd density on the moving speed of people, a discrete time based evacuation model is constructed which accurately reflects the evacuation process. A two-stage method is proposed to solve the difficult problem of large-scale evacuation. The evacuation policy obtained by the two-stage method will be used as the evacuation plan, and the evacuation plan of different evacuation scenarios will be counted. When an evacuation event occurs, the distribution of people is matched with the scenario in the database, and the evacuation plan of the closest scenario is selected for evacuation.

The demands of electric vehicles (EVs) and building heating, ventilation, and air conditioning (HVAC) systems have considerable flexibility. Their flexibility is influenced by occupants’ behavior resulting in huge complementary and dispatchable capability. Therefore, the coordination of EVs and HVAC systems holds significant potential for optimizing the building demand profiles and energy cost under time-of-use (TOU) tariffs. However, solving the coordinated problem in practice still faces the challenges in computational complexity and global information requirement due to the spatio-temperal coupling constraints. In this paper, a mixed-integer linear programming model is developed to formulate the multi-building energy system with EVs and the impact of occupants’ behavior on the demand and flexibility of the system. The problem is converted into a three-level structure using Lagrangian relaxation framework. A dynamic programming-based Lagrangian relaxation (DPLR) algorithm is developed to independently solve all sub-problems of the three-level structure in a decomposition and coordination way while avoiding the iterative computation between the middle and lower level. The numerical results show the developed method can obtain a near-optimal solution in an efficient way without perceivable degradation in accuracy, which is 4% worse but at least three times faster, compared to the existing centralized algorithm. Note to Practitioners—The escalating demand for EVs and HVAC systems results in increased energy costs and challenges to existing power systems, such as frequency deviations and higher peak loads. Therefore, this paper focuses on the coordinated optimization of the EV charging and building HVAC system operation, while considering rooftop photovoltaic generation supply within the system. Optimal coordination of the above system can effectively reduce energy costs under TOU tariffs and enhance the ability to utilize renewable energy sources. However, solving the coordinated optimization problem still faces difficulties since the computational complexity will exponentially grow with increasing problem scale due to the spatio-temperal coupling between the demand of EVs and HVAC systems. Therefore, a DPLR algorithm is developed. There is a central coordinator that collects the demand information of EVs and HVAC systems and broadcasts the coordination information calculated according to the demand information. Every single EV and HVAC system can make decisions based on the coordination information independently. The DPLR algorithm decouples EVs and HVAC systems and avoids the curse of dimensionality. It has great improvement on computational efficiency and global information requirement reduction. The computational efficiency and effectiveness of the developed method is verified through multi-scale case studies. The numerical results show that compared with independent optimization of EVs and HVAC systems, coordinated optimization can reduce over 44% of the energy costs.

Convergence acceleration is always a critical issue in distributed multi-area scheduling. The critical region projection (CRP) algorithm based on multi-parametric quadratic programming (MPQP) shows better convergence performance for multi-area static economic dispatch. However, its imperfect decomposition framework cannot be directly applied to dynamic economic dispatch. Therefore, this paper modifies the CRP algorithm to achieve fast distributed multi-area intra-day economic dispatch (MAIDED). First, we introduce slack variables to each area and add the corresponding penalty term into their objective functions to present a primal decomposition framework with penalty relaxation. It is more realistic than the decomposition framework of traditional CRP (TCRP). Then, an iterative algorithm of double spatial scale search (DSSS) is developed to improve the convergence rate of distributed solving based on the similar optimal value function in adjacent critical regions (CRs). Moreover, we design an initial value selection method based on data fitting to further reduce the number of iterations. Finally, three interconnected power systems of different sizes are used for numerical testing to demonstrate that the proposed modified CRP (MCRP) algorithm can meet the practical application and has higher convergence efficiency.Note to Practitioners—This paper is motivated by the problem of distributed MAIDED for power systems but it also applies to other multi-agent networks with a coordinator. The convergence speed of the existing distributed optimization algorithm is slow, which increases the risk of communication failure and attack. Meanwhile, more iterations will result in increased communication and computing costs. This paper modified the TCRP algorithm for high-efficient distributed MAIDED. The penalty relaxation is used to ensure that the decomposition framework is consistent with the actual system operation. The DSSS algorithm and the initial value selection method based on data fitting are designed to effectively reduce the number of iterations. In this paper, the DSSS is that the coordinator enlarges the CRs uploaded from each area to perform a rough optimization for approaching the global optimal solution fast, and then in the next iteration, conducts a precise optimization like the TCRP algorithm to determine the precise optimal solution. The numerical testing of the interconnected power systems of different sizes indicates that the MCRP algorithm has fewer iterations and calculation times than the TCRP algorithm. Future work will extend the MCRP algorithm to solve the distributed multi-area unit commitment problem.

Wireless communication system such as the 5G system incurs significant energy consumption due to increased bandwidth, channels, complex architecture, great density of base station (BS) sites, and antennas. This article reviews two main approaches to enhancing energy efficiency of wireless communication systems. Despite the great efforts made, the energy consumption and costs remain high, and energy savings are critical to sustainability of the 5G system. This article presents a new optimization-based approach to reducing the energy consumption and costs of wireless communication systems through the collaborative operation of telecom equipment and supporting infrastructure while satisfying the requirements of the operating environment of BS equipment based on their forecasted traffic loads and durations. The new approach is implemented in various types of the 5G BS sites in operation in Guang Dong Province, China. The meter measurement shows that with the new approach more than 12$\%$total energy cost reduction of the BS sites is achieved.

The estimation of the nodal admittance matrix is an important problem for the power grid operation and computing tasks. Some studies have shown that the admittance matrix can be fuzzily estimated only by the injection power measurements. Nevertheless, the estimation results of most existing efforts are not ideal because of the problem's nonconvex properties, and the effects of measurement observability on the accuracy of estimation methods are not clear either. In this article, we establish an ill-posed inverse dc power flow (IDCPF) problem model and propose an admittance matrix estimation method based on multimeasurements of the power grid, including measurements of injection power and voltage phasor. Our approach converts the original problem into solvable linear subproblems and improves the estimation models by considering various physical mechanisms of the power grid. Additionally, we develop an optimization algorithm that leverages alternating least-square and alternating direction methods of multipliers for solving the IDCPF problem. We also demonstrate the detailed analysis and proof of the effects of phasor measurement observability on the accuracy of the estimation. The effectiveness and performance of our method are verified based on experiments using IEEE 30-bus and 118-bus systems.

Renewable energy sources and electric vehicles provide an effective way to reduce the energy cost of an enterprise microgrid. However, the uncertainties of renewable energy sources and the time coupling characteristic of electric vehicles bring great challenges of non-anticipativity and feasibility for supply-demand coordination. To satisfy the non-anticipativity, we develop a supply-demand coordination optimal model using pre-scheduling method with virtual re-scheduling. In this model, the current decision only depends on the current and past realizations of random variables. Furthermore, we enhance the model with time-coupled robust constraints to guarantee the feasibility of the strategy under all possible realizations of the random variables. These time-coupled robust constraints bring high computational complexity to solve this model. So, we develop the method of combining forward recursion and backward recursion to decouple these time-coupled robust constraints in time. In this way, the coordination model is transformed to a mixed integer linear programming (MILP) model which can be efficiently solved. Finally, numerical test based on a real case is analysed and the results show that the energy cost of the enterprise is about 136129$\$ $if the flexible load is about 20% and load shifting and generators rescheduling can reduce the energy cost more than 6%. Note to Practitioners—This study is encouraged by the challenging problem caused by the multi-distributed energy introduced into an enterprise microgrid. In enterprises, as the large-area flat workshop roof assists in convenience for photovoltaics’ development and the EVs are widely used, the issue to best utilize renewable energy and EVs shows vital significance in reducing the energy cost. However, there exist the following three main challenges: (1) the non-anticipativity of the model, (2) the solution’s feasibility under all possible realizations, and (3) the effectiveness of the solution method. For the concerns of non-anticipativity, we develop the model using a pre-scheduling model with virtual re-scheduling in which the current decision only depends on the current and past realizations of random variables. To handle the second challenge, an ideal of scenario model with robust constraints is developed considering both feasibility and economy. In order to solve the model with robust constraints, the all-scenario-feasible method and a combination of the forward recursion and backward recursion method are used to deal with time-independent and the time-coupled robust constraints, respectively. The numeric results demonstrate that load shifting and generators rescheduling can reduce the energy cost more than 6%, and using the method with the forward and backward recursion process can reduce the energy cost more than 9%.

Green and sustainable development of Internet data centers (IDCs) has attracted more attention in both academia and industry. Full utilization of renewable energy sources is widely known as the most effective way to supply electrical and thermal energy while reducing carbon emission. However, the integration of renewable energy into IDCs is still challenging due to the mismatch between uncertain renewable supply and time-varying demand requirements, and high requirement of operation reliability against IDC failures. Therefore, in this paper a hydrogen-water-based energy (HWBE) system is developed and its integrated planning-and-operation problem is formulated as a mixed-integer linear programming problem to determine the optimal capacity of energy facilities in the HWBE system with considering IDC operation reliability. A hybrid physics-based and data-driven method is developed to accurately capture the electrical and thermal energy consumption characteristics and their coupling which are the basis for the optimal planning of the HWBE system. Furthermore, a Benders decomposition-based reliability improvement algorithm is developed to enhance the operation reliability, which decomposes the problem into the planning problem with normal operation as the master problem and the operation problem with IDC failure as the subproblem. The reliability can be enhanced using the solution obtained by the master problem with the feasibility cut obtained from the subproblem. Numerical results show that the developed HWBE system is energy-efficient with low carbon emission, since the power usage efficiency of IDCs could be as low as 1.09 and the carbon emission could be reduced by 74.9% as compared by the electricity-driven IDC energy system.Note to Practitioners—This paper focuses on the integrated planning-and-operation optimization of an HWBE system for the application in IDCs. We improve the energy consumption model of IDCs based on a hybrid physics-based and data-driven method, which can describe the interaction between the dynamic thermal process and electricity consumption of IDCs. In this way, both the high accuracy of the physics-based model and the lower computational effort of the data-driven method could be simultaneously achieved in the energy consumption model. Furthermore, in practice, the optimal planning problem of IDCs is necessary to take into account the operation reliability against data center failures, since the capital expenditure of the backup energy devices is generally significant. This means that a trade-off between the solution accuracy of the planning problem and the computational complexity caused by the operation problem should be considered. Therefore, we develop a Benders decomposition-based reliability improvement algorithm to address the trade-off mentioned above. This technique can integrate the feasibility cut obtained from the operation problem with IDC failure into the planning problem, in order to improve the operation reliability against the supply-demand mismatching and IDC failures while reducing the capital cost, as compared to the system designed by the conventional redundancy standard. Numerical results show the effectiveness of the developed method which can make full use of renewable energy sources and support the green and sustainable development of IDCs.

Past 20 years has witnessed some exorbitant fallout and large-scale blackouts in power system, particularly due to cascading failures and their propagation in the crucial yet complex and networked infrastructure. A pivotal prevention measure to steer clear from cascading events is the identification of vulnerable set, defined as the composition of specific line combinations that can trigger sequence of errors. By nature, the identification problem is NP-hard and a resort to approximation algorithms is necessary. In this article, we first construct a general yet rigorous formalism for the mathematical analysis of cascading failure in networked systems. With a tailored treatment of the propagation mechanism, a fast identification algorithm (FIA) for vulnerable set is then designed based on a key observation revealing the correlation structure among different N-kcontingencies. By analyzing the monotonic nondecreasing, quasi-submodular property of the propagation process, a theoretical lower bound of our algorithm is given in specific order. Besides, we show that the optimization framework of our algorithm can be readily extended to incorporate prior information. Numerical experiments on IEEE 30-, 118-, and 200-bus systems are performed to verify the effectiveness and efficiency of both FIA and its optimization framework.

Pedestrian trajectory prediction has become an essential underpinning in various human-centric applications including but not limited to autonomous vehicles, intelligent surveillance system and social robotics. Previous research endeavors mainly focus on single camera trajectory prediction (SCTP), while the problem of multi-camera trajectory prediction (MCTP) is often overly simplified into predicting presence in the next camera. This paper addresses MCTP from a more realistic yet challenging perspective, by redefining the task as a joint estimation of both future destination and possible trajectory. As such, two major efforts are devoted to facilitating related research and advancing modeling techniques. Firstly, we establish a comprehensive multi-camera Scenes Pedestrian Trajectory Dataset (mcScenes), which is collected from a real-world multi-camera space combined with thorough human interaction annotations and carefully designed evaluation metrics. Secondly, we propose a novel joint prediction framework, namely HM3GAT, for the MCTP task by building a tailored network architecture. The core idea behind HM3GAT is a fusion of topological and trajectory information that are mutually beneficial to the prediction of each task, achieved by deeply customized networks. The proposed framework is comprehensively evaluated on the mcScenes dataset with multiple ablation experiments. Status-of-the-art SCTP models are adopted as baselines to further validate the advantages of our method in terms of both information fusion and technical improvement. The mcScenes dataset, the HM3GAT, and alternative models are made publicly available for interested readers.

This paper presents a dynamic pricing mechanism in the industrial park with demand response programs. A Lagrangian relaxation based dynamic pricing model for electricity and thermal coupled industrial park is formulated, taking into account energy balance, feeder exchange and other systems operating constraints. Considering two-markets clearing mechanism and two types of demand response programs, a dynamic prices prediction model is proposed by long short-term memory (LSTM) technique. Based on the prediction model, we proposed a real-time prices spike detection model for industrial park, which can detect prices spike hourly by history data and give rolling prices spike warning for next short-term operating horizon. Simulation experiments validate the theoretic results and show the effectiveness of the dynamic prices spike detection model.Note to Practitioners—This paper focuses on the dynamic pricing mechanism and prices spike detection for the customers in the industrial park. We improve the pricing model based on the Lagrangian relaxation method and develop a dynamic prices prediction model to handle the uncertainty in real-time. Furthermore, we develop a prices spike detection mechanism, which can achieve rolling detect whether the electricity and thermal prices may exceeded the threshold in the next short-term operating horizon. This technique can give the customers a prices spike early warning service and let them to reschedule their own strategy to minimize their operation cost with respect to the uncertainties in the energy price. Experimental results show that the proposed prices spike detection mechanism can issue spike warnings correctly in most supply-demand mismatching cases.

Cascading failure models are important for understanding the mechanism of blackouts and evaluating the control strategies to prevent the failure propagation. The evolution of cascading failure in actual power grid is a continuous dynamic process triggered by discrete events, such as initial disturbances and physical responses. In this paper, we develop an event-triggered hybrid system model to describe the dynamic process of cascading failure. In the model, the evolution of continuous states of power grid is described by differential algebraic equations and the discrete events are defined as transitions between discrete states of power grid. The model also integrates multiple physical responses including relay protection, frequency regulation and dispatching action. Based on the developed model, we propose an event-triggered simulation method of cascading failure to accelerate the simulation process. Compared with the DC power flow model, hidden failure model and topological model, the simulation results of our model are more accurate because the statistical distribution of demand loss in our model is closer to historical blackouts data. The efficiency of the proposed event-triggered method is demonstrated by comparing our model with the time-driven model and three existing models. The experimental results show that our model can trade off the simulation accuracy and time consumption.Note to Practitioners—This paper focuses on modeling the dynamic process of cascading failure with multiple physical responses in power grid. We develop an event-triggered hybrid system model for cascading failure. In the model, the continuous dynamics of power grid and discrete events triggering the evolution of cascading failure are all described by the framework of hybrid system, which is a good example of modeling the hybrid system for automation researchers and engineers. By this way, the model is more accurate in describing the actual characteristics of cascading failure in power grid, and thus supporting the design and evaluation of control strategies for improving the stability of power grid. Based on the developed model, we propose an event-triggered simulation method of cascading failure, which aims to improve simulation accuracy while potentially reducing time consumption. In practice, the model can make fast control strategies to prevent the failure propagation.

Microgrid usually associated with distributed renewable energy sources plays a key role in reducing the requirement of traditional power sources and the emission of CO2. Connecting multiple microgrids to the electric power grid can facilitate a more powerful and reliable operation. Microgrids need decentralized dispatch with the requirement of security and privacy, and at the same time, they need to cooperate to satisfy the constraints from the power grid. We consider online decentralized and cooperative dispatch problem in this paper. In order to capture the randomness in the wind and solar power generation and the system dynamics, we formulate the problem as a decentralized Markov decision process (Dec-MDP). We propose a new method to calculate the approximate Q-value functions by constructing the initial feasible policy with reasonable space and time complexity. Bayesian games (BGs) is applied to model the decentralized dispatch with delayed communication in order not to slow down the online decision-making. Also, the alternating minimization method is used to solve this BGs based on the approximate Q-value functions. Numerical results demonstrate that the proposed algorithm is very effective in reducing the state space and computing time and achieving the requirement of real-time scheduling. Motivated by the problem of decentralized dispatch of multi-microgrids in grid-connected mode, we consider the online decentralized operation and pay special attention to the grid tie-line power fluctuation. This problem is challenging due to the randomness of the renewable power generation, the global constraints about multiple microgrids, and the correlation among stages. We model the decentralized dispatch problem as a rolling horizon Dec-MDP and provide an approximate solution method, namely, alternately minimizing among different microgrids at the online stage and calculating approximate value functions in the offline preparation process. The approximate value functions make the online decision turn out to be a single-stage decentralized decision problem. Online decision calculation based on delayed communication is to guarantee all the microgrids to start conducting an action immediately while receiving the information related to them. We hope this paper brings insight onto the tie-line power fluctuation stabilization while multiple microgrids connecting to the same point of interconnection.