Centralized Optimization Methods Research Articles

Game theoretic operation optimization of photovoltaic storage charging station considering uncertainty and carbon trading

With the advancement of energy conservation and emission reduction efforts, the orderly charging of electric vehicles and the operation of photovoltaic-storage-charging stations associated with electric vehicles have become increasingly important topics. This study constructs an optimization model for the operation of stations under the synergy of electricity and carbon markets from a game theory perspective. Firstly, Latin hypercube sampling and Monte Carlo sampling are employed to handle the uncertainties in photovoltaic output and the stochastic nature of electric vehicles charging. Secondly, a ladder-type carbon trading mechanism is introduced, and a charging optimization model based on Stackelberg game theory is developed to describe the benefit interaction between charging stations and electric vehicles users. In this model, the upper level represents the charging station operator aiming to maximize joint electricity and carbon revenue while minimizing load fluctuations, whereas the lower level represents electric vehicles users aiming to maximize consumer surplus. Finally, a genetic algorithm nested with mixed-integer linear programming is used to solve the optimization model. The simulation results validate the model's effectiveness and superiority. The results indicate that, compared to centralized optimization methods, the Stackelberg game mechanism can increase consumer surplus by 119.40 %, reduce carbon emissions by 217.92 %, and achieve a win-win situation for both parties. Compared to a fixed carbon trading value, the ladder-type carbon trading mechanism can reduce carbon emissions by 23.84 % and smooth load fluctuations.

Distributed predefined-time economic dispatch based on event-triggered strategy for microgrids under directed graphs

The proliferation of new energy solutions and the enhanced accessibility of distributed power sources have significantly increased the complexity and variability of microgrid structures. Due to inherent limitations in its operational mode, the traditional centralized optimization method falls short in effectively addressing the economic dispatch problem in contemporary microgrids. In this paper, a distributed optimization method is devised to address the economic dispatch problem of microgrids under directed graphs by leveraging the consensus algorithm of multi-agent systems. We define the incremental cost of each microgrid unit as the consensus variable, achieving convergence through a pioneering combination of event-triggered strategy and predefined-time control theory. This approach not only optimizes resource use but also ensures timely and efficient solution convergence, addressing critical gaps in existing methodologies. This approach enables control over the upper bound of convergence time for optimal solutions by directly adjusting time parameters in the controller under the directed graph. Consequently, it achieves coordinated control of the power output in microgrids within a predefined time while reducing the communication resources between nodes with event-triggered mechanism. The effectiveness of the proposed algorithm is verified through simulation and analysis.

A Low-Carbon Collaborative Optimization Operation Method for a Two-Layer Dynamic Community Integrated Energy System

The traditional centralized optimization method encounters challenges in representing the interaction among multi-agents and cannot consider the interests of each agent. In traditional low-carbon scheduling, the fixed carbon quota trading price can easily cause arbitrage behavior of the trading subject, and the carbon reduction effect is poor. This paper proposes a two-layer dynamic community integrated energy system (CIES) low-carbon collaborative optimization operation method. Firstly, a multi-agent stage feedback carbon trading model is proposed, which calculates carbon trading costs in stages and introduces feedback factors to reduce carbon emissions indirectly. Secondly, a two-layer CIES low-carbon optimal scheduling model is constructed. The upper energy seller (ES) sets energy prices. The lower layer is the combined cooling, heating, and power (CCHP) system and load aggregator (LA), which is responsible for energy output and consumption. The energy supply and consumption are determined according to the ES energy price strategy, which reversely affects the energy quotation. Then, the non-dominated sorting genetic algorithm embedded with quadratic programming is utilized to solve the established scheduling model, which reduces the difficulty and improves the solving efficiency. Finally, the simulation results under the actual CIES example show that compared with the traditional centralized scheduling method, the total carbon emission of the proposed method is reduced by 16.34%, which can improve the income of each subject and make the energy supply lower carbon economy.

Master–Slave Game Optimal Scheduling for Multi-Agent Integrated Energy System Based on Uncertainty and Demand Response

With the transformation of the energy market from the traditional vertical integrated structure to the interactive competitive structure, the traditional centralized optimization method makes it difficult to reveal the interactive behavior of multi-agent integrated energy systems (MAIES). In this paper, a master–slave game optimal scheduling strategy of MAIES is proposed based on the integrated demand response. Firstly, a master–slave game framework of MAIES is established with an energy management agent as leader, an energy operation agent, an energy storage agent, and a user aggregation agent as followers. Secondly, in view of the wind and solar uncertainty, the Monte Carlo method is used to generate random scenarios, and the k-means clustering method and pre-generation elimination technology are used for scenario reduction. Then, according to different flexible characteristics of loads, a multi-load and multi-type integrated demand response model including electric, thermal, and cold energy is built to fully utilize the regulation role of flexible resources. On this basis, the transaction decision-making models of each agent are constructed, and the existence and uniqueness of the Stackelberg equilibrium solution are proved. Finally, the case simulations demonstrate the effectiveness of the proposed optimal scheduling strategy of MAIES. Compared to the scenario without considering the wind and solar uncertainty and the integrated demand response, the rate of renewable energy curtailment was reduced by 6.03% and the carbon emissions of the system were reduced by 1335.22 kg in the scenario considering the proposed method in this paper.

Local-coordinated voltage optimal control strategy of integrated PV and ESS system in distribution networks with π-type network simplification

With the increasing penetration of distributed photovoltaics (PVs) in distribution networks (DNs), the voltage violation and PV absorption difficulty have become great challenges for the security operation of DNs. In this context, the integrated photovoltaic and energy storage system (PESS) plays an increasingly important role in enhancing the DNs operational security and economy with its capability of flexible power regulation and energy transfer. Considering the incomplete online measurement of DNs, this paper proposes a local-coordinated voltage optimal control strategy that combines local optimization and real-time coordinated control. Firstly, a new π-type network simplification method is proposed, which is less demanding on the measurement device and doesn't add new virtual nodes for the convenience of modeling. Then the local rolling optimization model for PESS is established based on simplified network to solve the optimal local instruction, which only uses the measurement data of local node and the slack bus rather than global measurement. Next, a real-time coordinated voltage control method based on network loss sensitivity is proposed to eliminate voltage violation caused by random fluctuations of PV and load power. Finally, the IEEE 33-bus system and modified 123-bus system are used to verify the effectiveness and accuracy of the proposed voltage optimal control strategy, which is also compared with centralized optimization method with global measurement. The simulation results indicate that the proposed control strategy can effectively solve the voltage violation and improve the system operation economy, especially only relying on partial measurement.

A multi-objective decentralized optimization for voltage regulators and energy storage devices in active distribution systems

Centralized optimization methods have been widely used to manage the operation of distribution systems. However, these methods have some restrictions, such as the high computational cost, the reliance on a centralized computer system, and the lack of data privacy. To overcome these limitations, decentralized optimization methods have been proposed in recent years. Decentralized methods divide the control variables of the centralized optimization problem over several controllers, and each controller solves its own subproblem independently. This paper presents a multi-objective optimization framework for managing the operation of distribution systems. The primary objective of the proposed method is to optimize the tap positions of voltage regulators and charging and discharging powers for energy storage devices locally through a decentralized coordination process. The used objective functions take into account the voltage profile within the network, the lifetime of the devices, and the energy losses in the systems. Two decentralized methods, based on the Advanced Arithmetic Optimizer algorithm and the Profile Steering approach, are proposed to address the limitations of centralized optimization methods. The decentralized methods aim to improve the reliability and efficiency of the optimization process, while also minimizing communication and computational costs. The proposed methods are evaluated and compared to a centralized approach using the IEEE 33 and 69 bus systems. The results demonstrate that the proposed decentralized methods can effectively resolve voltage problems, minimize energy losses, and find high-quality solutions with improved computational efficiency compared to the centralized approach.

Coalition Game of Radar Network for Multitarget Tracking via Model-Based Multiagent Reinforcement Learning

Task assignment is crucial for multitarget tracking of the radar network and is mainly solved by centralized optimization methods, which results in the issues of robustness deficiency, high computational cost, and inflexible adaptability in complex environments. To overcome these issues, task assignment of the radar network for multitarget tracking is formulated as a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">multiagent decision-making and learning</i> problem, where each radar node in the network acts as an intelligent agent that can make the tracking decision according to its task preference and interact with other agents for the sake of the best network utility. To describe the decision references of radar nodes for various tasks, the criterion for the design of the utility function is presented, and a utility function under this criterion is devised based on the quality of service framework. Then, the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">coalition game with transferrable utility</i> is developed for task assignment, where the utility of the coalition is completely transferred to all coalition members. The existence of the stable coalition partition of the developed game is analyzed theoretically, and the model-based multiagent <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">random Fourier features reinforcement learning</i> (RFFRL) algorithm is proposed to solve the optimal solution to the game in the high dimensional state space, which is proven to be converged at a Nash-stable coalition partition. Some numerical simulation results are provided to illustrate the effectiveness of the proposed algorithm in terms of tracking performance and resource conservation.

Edge computing-based digital management system of game events in the era of Internet of Things

With the great development of Internet of Things (IoT) and edge computing, the development of sports activities depends on the development of information technology and it is inevitable to pay attention to the combination and optimization of resources. The combination of IoT and edge computing will be critical in sports activities. This paper elaborates on the application of network skill in sports event information management, that is, through the effective gathering of sports event data, to realize the use of sports event information, to achieve the purpose of information and digitization. Furthermore, the goal is to investigate the effect of sports event in the era of IoT. The impact of sports events on the economy and culture of the hosting city is investigated using IoT concept of edge computing. By analyzing the advantages and disadvantages of traditional centralized optimization method, we present a series of performance indicators and utility functions and show that the method is effective and achieves the optimal purpose. Through vital research, it is found that with the development of the edge computing and IoT industry, the scale of sports events is constantly expanding. By 2019, there has been a scale of 1,271 billion yuan. An increase of 981 billion yuan, compared with 290 billion yuan in 2013. Therefore, the use of the IoT technology in combination with edge computing to manage sports events will greatly encourage the expansion of sports activities. Furthermore, the holding of sporting events reflects a city’s overall strength and enhances the city’s exposure and fame. The investigation offers a certain reference point for cities looking to increase their influence through events.

Research on Low-Carbon Energy Sharing through the Alliance of Integrated Energy Systems with Multiple Uncertainties

It is of great significance to introduce the conception of a sharing economy into the electricity industry, which can promote the dispatch of multiple integrated energy systems. On the one hand, it is difficult to reveal the behaviors of complex players with multi-energy coupling through the traditional centralized optimization method of single electric energy. On the other hand, the uncertain fluctuations of renewable energy, such as wind power and photovoltaic, have posed great challenges to market transactions. First, the relationship and the functions of all stakeholders in the system are described in this paper, followed by the establishment of flexible resource models such as demand response and energy storage devices. On this basis, a low-carbon dispatching framework of multiple regional gas–electric integrated energy systems is then constructed under the guidance of cooperative game theory. The contribution indexes are established to measure the degree of energy sharing among the subsystems, and the method of asymmetric Nash bargaining is used to settle the interests of each subsystem. Second, a robust optimization model of multiple regional systems is established in response to multiple uncertainties from renewable energy and load. Finally, the numerical example proves that the proposed mechanism can increase the benefits of each integrated energy system player. Moreover, it helps the system to yield optimal benefits in the face of uncertainties and provides a reference on how to realize energy sharing under uncertainties from source load.

Distributed optimization of electricity-Gas-Heat integrated energy system with multi-agent deep reinforcement learning

The coordinated optimization problem of the electricity-gas-heat integrated energy system (IES) has the characteristics of strong coupling, non-convexity, and nonlinearity. The centralized optimization method has a high cost of communication and complex modeling. Meanwhile, the traditional numerical iterative solution cannot deal with uncertainty and solution efficiency, which is difficult to apply online. For the coordinated optimization problem of the electricity-gas- heat IES in this study, we constructed a model for the distributed IES with a dynamic distribution factor and transformed the centralized optimization problem into a distributed optimization problem in the multi-agent reinforcement learning environment using multi-agent deep deterministic policy gradient. Introducing the dynamic distribution factor allows the system to consider the impact of changes in real-time supply and demand on system optimization, dynamically coordinating different energy sources for complementary utilization and effectively improving the system economy. Compared with centralized optimization, the distributed model with multiple decision centers can achieve similar results while easing the pressure on system communication. The proposed method considers the dual uncertainty of renewable energy and load in the training. Compared with the traditional iterative solution method, it can better cope with uncertainty and realize real- time decision making of the system, which is conducive to the online application. Finally, we verify the effectiveness of the proposed method using an example of an IES coupled with three energy hub agents.

Distributed operation optimization of active distribution network with P2P electricity trading in blockchain environment

With the increasing integration of distributed generators and the rapid development of electricity markets, active distribution networks (ADNs) confront new challenges in operation optimization. Centralized optimization methods usually aggravate the computational burden when applied to large-scale distribution networks (DNs). A distributed operation optimization model incorporating peer-to-peer (P2P) electricity trading in a blockchain environment is proposed in this paper, where network usage fees considering electrical distance are specially addressed. Meanwhile, the private information security of prosumers is ensured by the Proof-of-Authority (PoA) consensus blockchain during P2P electricity trading. The trading information of adjustable prosumers should be sent to the proxy entity authorized by the DN using the blockchain platform. In addition, a network partitioning method via dynamic reconfiguration considering multi-level switching is offered to adapt to the required distributed manner. The operation network, as well as the corresponding market structure can be automatically updated according to the results of dynamic reconfiguration. Moreover, the unit price of network usage fees can be adjusted to derive a higher amount of P2P electricity trading with security constraints. Case studies on a practical 148-bus system and a 297-bus system verify that the proposed model maximizes the profits and reduces the computational time in the distributed operation optimization.

Distributed OPF for PET-Based AC/DC Distribution Networks With Convex Relaxation and Linear Approximation

A power electronic transformer (PET) can flexibly regulate the power flow of a network and facilitate the integration of distributed energy resources via AC/DC networks. With the continuous expansion of the scale of multiregional interconnection networks, the traditional centralized optimization method faces great challenges. This paper proposes a distributed convex optimal power flow (OPF) model by leveraging the hierarchical structural characteristics of PET enabled AC/DC distribution networks. An analytical target cascading method is introduced to divide the centralized OPF problem into several subproblems that can make the subnetworks operate individually and coordinate with each other. The PET flexibility is also harnessed to reduce network power loss and voltage deviation. To improve the computational efficiency and algorithm convergence, the convex relaxation and linear approximation methods are proposed. This allows us to transform the original nonconvex nonlinear problem into a successive convex programming problem, which can be easily solved by an iterative solution algorithm. Simulation results verify the feasibility and efficiency of the proposed approach.

Bi-layer optimal secondary frequency control approach for energy storage clusters considering wind power uncertainty

Increasing penetration of wind power with intermittency and variability threatens the stability of the power system frequency. The fast response capability of the energy storage system (ESS) makes it an effective measure to improve frequency regulation performance. However, designing an optimal control for numerous energy storage units (ESUs) with different power and energy characteristics is challenging. To solve the dilemma that the distributed control methods cannot achieve optimality over time horizons while the centralized optimization methods would cause high computational burdens, a bi-layer optimal control approach is proposed in this study. In the upper layer, a multi-area secondary frequency control (SFC) problem is established to determine control policies for ESS clusters under continuous wind power fluctuations and is solved by the Itô theory-based stochastic optimization (ITB-SO) method with high computational efficiency in a rolling-horizon manner. In the lower layer, the power output of ESUs is dispatched and coordinated using the distributed algorithm (DA) method via communication networks, considering different characteristics and the current state-of-charge (SoC) levels. Simulation studies carried out in a dual-region test system evidence the improvement of system frequency stability by compensating for rapid wind power fluctuations immediately via ESSs. The results show that the proposed ITB-SO method without scenario generation is suitable for real-time SFC for the ESS. The effectiveness of the DA method and its robustness in encountering loss of communication links are also verified.

Cloud-edge collaborative distributed optimal dispatching strategy for an electric-gas integrated energy system considering carbon emission reductions

To reduce carbon emissions and improve the energy efficiency of energy systems, integrated energy systems (IESs) have been promoted in recent years. However, the data of different energy networks cannot be fully shared. The data privacyprotection is attracting more attention in demand side. It is difficult for centralized dispatching strategies, which must obtain all the data of energy systems during optimization, to be applied. To solve these issues, a cloud-edge collaborative distributed optimal dispatching strategy for electric-gas IESs is proposed in this paper. The centralized IES scheduling problem is reasonably divided into multiple subproblems. Considering information barrier, the cloud computing centers are separately set in different energy networks to solve energy flow optimization subproblems. Considering prosumer privacy protection, edge computing units are separately set in energy hubs to deal with cost and carbon emissions minimization of regional integrated energy systems (RIESs). Based on the proximal Jacobian alternating direction method of multipliers, the common optimization variables interactive iteration and parallel solution of multiple dispatching models are developed. The simulation results show that the proposed distributed optimization method can achieve the same accuracy as the centralized optimization method and improve problem-solvingefficiency in general.

Parallel and Distributed Optimization Method With Constraint Decomposition for Energy Management of Microgrids

Energy management in power systems is a thorny optimization problem. With the sizes of systems rising, centralized optimization methods are restricted by their complexities of communications, while distributed optimization methods have emerged as a powerful tool for dealing with increasingly complex systems. However, convergence rates of some widely used distributed optimization methods, such as the standard alternating direction method of multipliers (ADMM), still have room for improvement. In this paper, a parallel and distributed optimization method for energy management of microgrids (MGs) is proposed to boost the convergence rate without sacrificing the accuracy of the optima, in which agents calculate, exchange and update in parallel. At first, a decomposition method is presented, where the objective functions and constraints of an original optimization problem with separable variables are decomposed into local objective functions and constraints for agents, which is the key to our method. Further, agents solve their local optimization problems independently and then exchange determined optima with their neighbors. Finally, the method is evaluated to solve economic dispatch with demand response for microgrids. The simulation results show that compared to the standard ADMM, for a given accuracy, the number of iterations in our method is only one third or even less than that of ADMM. Furthermore, our method can minimize the cost functions of distributed generation on supply side and maximize the profit functions of flexible loads on the demand side.

Distributed Task Offloading Optimization With Queueing Dynamics in Multiagent Mobile-Edge Computing Networks

Task offloading decision making plays a key role in enabling mobile-edge computing (MEC) technologies in Internet of Things (IoT). However, it meets the significant challenges arising from the stochastic dynamics of task queueing in the application layer and coupled wireless interference in the physical layer in a distributed multiagent network without any centralized communication and computing coordination. In this article, we investigate the distributed task offloading optimization problem with consideration of the upper layer queueing dynamics and the lower-layer coupled wireless interference. We first propose a new optimization model that aims at maximizing the expected offloading rate of multiple agents by optimizing their offloading thresholds. Then, we transform the problem into a game-theoretic formulation, which further leads to the design of a distributed best-response (DBR) iterative optimization framework. The existence of Nash equilibrium strategies in the game-theoretic model has been analyzed. For the individual optimization of each agent's threshold policy, we further propose a programming scheme by transforming a constrained threshold optimization into an unconstrained Lagrangian optimization (ULO). The individual ULO is integrated into the DBR framework to enable agents to cooperate and converge to a global optimum in a distributed manner. Finally, simulation results are provided to validate the proposed method and demonstrate its significant advantage over other existing distributed methods. The numerical results also show that the proposed method can achieve comparable performance to a centralized optimization method.

Augmented Lagrangian coordination for energy-optimal allocation of smart manufacturing services

• Energy-optimal service allocation model in smart manufacturing is constructed. • The diverse production domains of manufacturing tasks are considered. • A distributed optimization method is adopted to solve the proposed problem. • The performance of the proposed method is verified by a case study. The rapid development of information and communication technologies has triggered the proposition and implementation of smart manufacturing paradigms. In this regard, efficient allocation of smart manufacturing services (SMSs) can provide a sustainable manner for promoting cleaner production. Currently, centralized optimization methods have been widely used to complete the optimal allocation of SMSs. However, personalized manufacturing tasks usually belong to diverse production domains. The centralized optimization methods could hardly include related production knowledge of all manufacturing tasks in an individual decision model. Consequently, it is difficult to provide satisfactory SMSs for meeting customer's requirements. In addition, energy consumption is rarely considered in the SMS allocation process which is unfavorable for performing sustainable manufacturing. To address these challenges, augmented Lagrangian coordination (ALC), a novel distributed optimization method is proposed to deal with the energy-optimal SMS allocation problem in this paper. The energy-optimal SMS allocation model is constructed and decomposed into several loose-coupled and distributed elements. Two variants of the ALC method are implemented to formulate the proposed problem and obtain final SMS allocation results. A case study is employed to verify the superiority of the proposed method in dealing with energy-optimal SMS allocation problems by comparing with the centralized optimization method at last.

Digital twin-driven service model and optimal allocation of manufacturing resources in shared manufacturing

The sharing economy has been recognized a mutually beneficial economic mode. Deriving from the concept of sharing economy, shared manufacturing was proposed under the support of advanced information and manufacturing technologies. As a core part of implementing shared manufacturing, manufacturing resource allocation aims to coordinate cross-organizational resources to provide on-demand services for personalized manufacturing requirements. However, some challenges still hinder effective and efficient resource allocation in shared manufacturing. Traditional centralized optimization methods with only one decision model are difficult to maintain autonomous decision rights of resource providers. Thus, they could hardly adapt to the situation of cross-organizational resource coordination. In addition, the credit of resource providers is rarely considered in the resource allocation process, which is unfavorable for promoting more reliable trades in shared manufacturing. To address these issues, this study proposes an integrated architecture to promote the resource allocation in shared manufacturing. A digital twin-driven service model is built to perform the seamless monitoring and control of shared manufacturing resources. The resource allocation model is constructed based on the consideration of the credit of resource providers. To keep the decision autonomy of resource providers, augment Lagrangian coordination is adopted to analyze the constructed resource allocation model. A case study is further employed to validate the effectiveness and efficiency of the proposed method in performing the resource allocation in shared manufacturing.

A real-time optimal control strategy for multi-zone VAV air-conditioning systems adopting a multi-agent based distributed optimization method

Determining the proper trade-off among thermal comfort, Indoor Air Quality (IAQ) and energy use is important for optimal control of air-conditioning systems. The number of optimization variables increases as systems become increasingly complex, as with multi-zone VAV (Variable Air Volume) air-conditioning systems, leading to large-scale mathematics programming challenges and inconveniences in the implementation of conventional centralized optimization strategies. This paper therefore proposes a real-time optimal control strategy adopting a multi-agent based distributed optimization method for multi-zone VAV air-conditioning systems. The proposed strategy consists of three novel schemes. First, a temperature set-point reset scheme adopts a linear rule to correlate the resetting of the temperature set-points in individual zones to simplify the optimization problem while applying proper optimization in individual zones. Second, a multi-objective optimization scheme optimizes the fresh air ratio of the supply air and the temperature set-point in the critical zone by formulating the multi-objective optimization problem. Third, a multi-agent distributed optimization scheme is developed to solve the optimization problem in a distributed manner, facilitating the deployment of local control devices of limited capacity. A TRNSYS-MATLAB co-simulation testbed is constructed to test and validate the proposed strategy. Test results show that the strategy is effective in properly balancing thermal comfort, IAQ and energy use while largely reducing programming challenges. The distributed optimization method can provide almost the same optimal outputs as conventional centralized optimization methods.

Optimal flexibility dispatch of demand side resources with high penetration of renewables: a Stackelberg game method

To promote the utilization of renewable energy, such as photovoltaics, this paper proposes an optimal flexibility dispatch method for demand-side resources (DSR) based on the Stackelberg game theory. First, the concept of the generalized DSR is analyzed and flexibility models for various DSR are constructed. Second, owing to the characteristics of small capacity but large-scale, an outer approximation is proposed to describe the aggregate flexibility of DSR. Then, the optimal flexibility dispatch model of DSR based on the Stackelberg game is established and a decentralized solution algorithm is designed to obtain the Stackelberg equilibrium. Finally, the actual data are utilized for the case study and the results show that, compared to the traditional centralized optimization method, the proposed optimal flexibility dispatch method can not only reduce the net load variability of the DSR aggregator but is beneficial for all DSR owners, which is more suitable for practical applications.