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Convergence Analysis of Dual Decomposition Algorithm in distributed optimization: Asynchrony and Inexactness

IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2023年第8期68卷 4767-4782页

作者： Su, Yifan Wang, Zhaojian Cao, Ming Jia, Mengshuo Liu, Feng Tsinghua Univ Dept Elect Engn State Key Lab Power Syst Beijing 100084 Peoples R China Shanghai Jiao Tong Univ Dept Automat Key Lab Syst Control & Informat Proc Minist Educ China Shanghai 200240 Peoples R China Univ Groningen Fac Sci & Engn NL-9747 AG Groningen Netherlands Swiss Fed Inst Technol Power Syst Lab CH-8092 Zurich Switzerland

Dual decomposition is widely utilized in the distributed optimization of multiagent systems. In practice, the dual decomposition algorithm is desired to admit an asynchronous implementation due to imperfect communication, such as time delay and packet drop. In addition, computational errors also exist when the individual agents solve their own subproblems. In this article, we analyze the convergence of the dual decomposition algorithm in the distributed optimization when both the communication asynchrony and the subproblem solution inexactness exist. We find that the interaction between asynchrony and inexactness slows down the convergence rate from O(1/k) to O(1/v/k). Specifically, with a constant step size, the value of the objective function converges to a neighborhood of the optimal value, and the solution converges to a neighborhood of the optimal solution. Moreover, the violation of v/ the constraints diminishes in O(1/ k). Our result generalizes and unifies the existing ones that only consider either asynchrony or inexactness. Finally, numerical simulations validate the theoretical results.

关键词： Asynchronous algorithm distributed optimization dual decomposition inexact algorithm multiagent system (MAS)

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Event-Trigger-Based distributed optimization Approach for Two-Level Optimal Model of Isolated Power System With Switching Topology

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IEEE TRANSACTIONS ON SYSTEMS MAN CYBERNETICS-SYSTEMS 2023年第4期53卷 2339-2349页

作者： Zhang, Huifeng Yue, Dong Dou, Chunxia Xue, Yusheng Hancke, Gerhard P. Nanjing Univ Posts & Telecommun Inst Adv Technol Nanjing 210023 Jiangsu Peoples R China NARI Grp Corp State Grid Elect Power Res Inst Nanjing 210003 Jiangsu Peoples R China Nanjing Univ Posts & Telecommun Automat & Artificial Intelligence Dept Nanjing 210023 Jiangsu Peoples R China Univ Pretoria Dept Elect Elect & Comp Engn ZA-0002 Pretoria South Africa

Due to the uncertain output of intermittent energy resources and dynamic communication topology, it brings a great challenge for the optimal security control of isolated power system. To address this problem, this article proposes a two-level optimal control strategy with event-triggered switching mechanisms. For ensuring the security of the isolated power system, event-triggered switching mechanisms are proposed in the upper-level model to decrease potential risk of supply security and voltage stability, which can ensure system security as well as a low switching cost. In the lower-level model, a distributed optimization with switching topology is developed to minimize power generation cost under the above switching mechanisms, and the convergence ability of the proposed distributed optimization method is well proved with a uniformly globally exponentially stable condition. The obtained simulation results reveal that the proposed optimization approach can properly deal with the security issue of an isolated power system as well as dynamically minimize the economic cost.

关键词： Switches Security Costs optimization Energy storage Power system stability Topology distributed optimization event-triggered hybrid energy system optimal control switching topology

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Hierarchical and distributed optimization of distribution network considering spatial and temporal distribution of electric vehicle charging load

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ENERGY REPORTS 2023年 9卷 308-322页

作者： Liu, Shu Fang, Chen Jia, Shicheng Xiang, Yueping Yang, Jianwei State Grid Shanghai Municipal Elect Power Co Shanghai 200122 Peoples R China Southwest Jiaotong Univ Sch Elect Engn Chengdu 611756 Peoples R China

With the increasing penetration of electric vehicles (EV) and distributed generations (DG) in distribution networks, operation and control of distribution networks (DN) is faced with many new challenges. Considering the remarkable characteristics of distribution network layered by voltage level and the spatial and temporal distribution of EV charging load, a hierarchical and distributed optimization method for DN is proposed. Firstly, the spatial and temporal distribution prediction model of EV charging load is established, which is composed of three parts: the resident travel probability model, the vehicle mobility model and traffic network model. Secondly, these three parts runs jointly to simulate the charging demand generated by EV, and then the charging load is connected to the charging station in the low-voltage distribution station area. Thirdly, considering the operation characteristics of the new energy units, energy storage system (ESS), DG and EV charging station, a dynamic economic dispatching model is established. Fourthly, according to the hierarchical operation characteristics of the medium- and low-voltage distribution network (MLV), a distributed optimization algorithm of DN is proposed to realize the hierarchical and decoupled calculation, which transforms the traditional centralized serial computing mode into distributed parallel computing mode, and improves the computing efficiency of the system. At last, the effectiveness and superiority of the proposed strategy are verified by the simulation test. (c) 2023 The Author(s). Published by Elsevier Ltd. This is an open access article under theCCBY-NC-ND license (http://***/licenses/by-nc-nd/4.0/).

关键词： Spatial and temporal distribution distributed optimization Medium and low voltage distribution network Economic dispatching of distribution network ADMM

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distributed optimization for Two Types of Heterogeneous Multiagent Systems

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IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2021年第3期32卷 1314-1324页

作者： Sun, Chao Ye, Maojiao Hu, Guoqiang Nanyang Technol Univ Sch Elect & Elect Engn Singapore 639798 Singapore Nanjing Univ Sci & Technol Sch Automat Nanjing 210094 Peoples R China

This article studies distributed optimization algorithms for heterogeneous multiagent systems under an undirected and connected communication graph. Two types of heterogeneities are discussed. First, we consider a class of multiagent systems composed of both continuous-time dynamic agents and discrete-time dynamic agents. The agents coordinate with each other to minimize a global objective function that is the sum of their local convex objective functions. A distributed subgradient method is proposed for each agent in the network. It is proved that driven by the proposed updating law, the agents' position states converge to an optimal solution of the optimization problem, provided that the subgradients of the objective functions are bounded, the step size is not summable but square summable, and the sampling period is bounded by some constant. Second, we consider a class of multiagent systems composed of both first-order dynamic agents and second-order dynamic agents. It is proved that the agents' position states converge to the unique optimal solution if the objective functions are strongly convex, continuously differentiable, and the gradients are globally Lipschitz. Numerical examples are given to verify the conclusions.

关键词： optimization Multi-agent systems Vehicle dynamics Power system dynamics Linear programming Heuristic algorithms Sun distributed optimization heterogeneous system hybrid system multiagent system subgradient descent

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distributed optimization for Distribution Grids With Stochastic DER Using Multi-Agent Deep Reinforcement Learning

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IEEE ACCESS 2021年 9卷 63059-63072页

作者： Al-Saffar, Mohammed Musilek, Petr Univ Alberta Dept Elect & Comp Engn Edmonton AB T6G 2V4 Canada Univ Hradec Kralove Dept Cybernet Hradec Kralove 50003 Czech Republic

This article develops a special decomposition methodology for the traditional optimal power flow which facilitates optimal integration of stochastic distributed energy resources in power distribution systems. The resulting distributed optimal power flow algorithm reduces the computational complexity of the conventional linear programming approach while avoiding the challenges associated with the stochastic nature of the energy resources and loads. It does so using machine learning algorithms employed for two crucial tasks. First, two proposed algorithms, Dynamic distributed Multi-Microgrid and Monte Carlo Tree Search based Reinforcement Learning, constitute dynamic microgrids of network nodes to confirm the electric power transaction optimality. Second, the optimal distributed energy resources are obtained by the proposed deep reinforcement learning method named Multi Leader-Follower Actors under Centralized Critic. It accelerates conventional linear programming approach by considering a reduced set of resources and their constraints. The proposed method is demonstrated through a real-time balancing electricity market constructed over the IEEE 123-bus system and enhanced using price signals based on distribution locational marginal prices. This application clearly shows the ability of the new approach to effectively coordinate multiple distribution system entities while maintaining system security constraints.

关键词： optimization Microgrids Heuristic algorithms Stochastic processes Power systems Real-time systems Convex functions distributed architecture distributed optimization Monte Carlo tree search multi-agent deep reinforcement learning optimal power flow

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distributed optimization of Average Consensus Containment with Multiple Stationary Leaders

Distributed Optimization of Average Consensus Containment wi...

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European Control Conference (ECC)

作者： Chatterjee, Sushobhan Kalaimani, Rachel Kalpana Indian Inst Technol Madras Dept Elect Engn Chennai 600036 Tamil Nadu India

ISBN: (数字)9783907144077

ISBN: (纸本)9783907144077

In this paper, we consider the problem of containment control of multi-agent systems with multiple stationary leaders, interacting over a directed network. While, containment control refers to just ensuring that the follower agents reach the convex hull of the leaders' states, we focus on the problem where the followers achieve a consensus to the average values of the leaders' states. We propose an algorithm that can be implemented in a distributed manner to achieve the above consensus among followers. Next we optimize the convergence rate of the followers to the average consensus by proper choice of weights for the interaction graph. This optimization is also performed in a distributed manner using Alternating Direction Method of Multipliers (ADMM). Finally, we complement our results by illustrating them with numerical examples.

关键词： Containment control distributed control leader-follower average consensus distributed optimization ADMM directed graphs

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distributed optimization Using ALADIN for MPC in Smart Grids

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IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY 2021年第5期29卷 2142-2152页

作者： Jiang, Yuning Sauerteig, Philipp Houska, Boris Worthmann, Karl ShanghaiTech Univ Sch Informat Sci & Technol Shanghai 201210 Peoples R China Tech Univ Ilmenau Inst Math D-98693 Ilmenau Germany

This article presents a distributed optimization algorithm tailored to solve optimization problems arising in smart grids. In detail, we propose a variant of the augmented Lagrangian-based alternating direction inexact Newton (ALADIN) method, which comes along with global convergence guarantees for the considered class of linear-quadratic optimization problems. We establish local quadratic convergence of the proposed scheme and elaborate its advantages compared with the alternating direction method of multipliers (ADMM). In particular, we show that, at the cost of more communication, ALADIN requires fewer iterations to achieve the desired accuracy. Furthermore, it is numerically demonstrated that the number of iterations is independent of the number of subsystems. The effectiveness of the proposed scheme is illustrated by running both an ALADIN and an ADMM-based model predictive controller on a benchmark case study.

关键词： optimization Batteries Convergence Power demand Smart grids Benchmark testing distributed optimization model predictive control (MPC) smart grid

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distributed optimization of Second-Order Nonlinear Multiagent Systems With Event-Triggered Communication

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IEEE TRANSACTIONS ON CONTROL OF NETWORK SYSTEMS 2021年第4期8卷 1954-1963页

作者： Li, Shiling Nian, Xiaohong Deng, Zhenhua Cent South Univ Sch Automat Changsha 410075 Hunan Peoples R China

In this article, we study the event-triggered distributed optimization problem of second-order nonlinear multiagent systems under undirected and connected communication topologies. To reduce the cost of information exchange in an optimization problem, a distributed event-triggered communication-based algorithm is proposed. In an event-triggered mechanism, the information interaction process of the network is controlled by a set of trigger conditions. The trigger condition of each agent only requires its own state information and its neighboring agents' state information. Each agent updates its own states only at the triggering time. In order to achieve the optimal result of the optimization problem and reduce the cost of communicatio, we propose a distributed event-triggered algorithm based on gradient descent. Moreover, we analyze the convergence of the algorithm by constructing a suitable Lyapunov function. Furthermore, we prove that the Zeno behavior can be avoid. Finally, we provide examples to validate the effectiveness of the obtained result.

关键词： distributed optimization event-triggered control nonlinear systems second-order systems zeno behavior

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distributed optimization Using Reduced Network Equivalents for Radial Power Distribution Systems

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IEEE TRANSACTIONS ON POWER SYSTEMS 2021年第4期36卷 3645-3656页

作者： Sadnan, Rabayet Dubey, Anamika Washington State Univ Dept Sch Elect Engn & Comp Sci Pullman WA 99164 USA

The limitations of centralized optimization methods for power systems operation have led to the distributed computing paradigm, particularly in power distribution systems. The existing techniques reported in recent literature for solving distributed optimization problems are not viable for power distribution systems applications. The essential drawback remains a large number of required communication rounds, i.e., macro-iterations among the computing agents to solve one instance of the optimization problem;the typical number of macro-iterations are in the order of 10(2)similar to 10(3). In this paper, a new and scalable distributed optimization method based on Equivalent Network Approximation (ENApp) is proposed to solve optimal power flow (OPF) for a balanced radial distribution system. Specifically, the distribution system's radial topology is leveraged to reduce the decomposed systems into upstream and downstream network equivalents. The proposed innovations reduce the required number of macro-iterations/communication-rounds for convergence by order of magnitude. The approach is validated using IEEE 123-bus and IEEE 8500-node test systems and is shown to converge to the same optimal solution as obtained using an equivalent centralized OPF (C-OPF) model.

关键词： distributed Energy Resources (DERs) distributed optimization loss minimization optimal power flow

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distributed optimization without boundedness of gradients for second-order multi-agent systems over unbalanced network

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INFORMATION SCIENCES 2021年 565卷 177-195页

作者： Mo, Lipo Hu, Haokun Yu, Yongguang Ren, Guojian Beijing Technol & Business Univ Sch Math & Stat Beijing 100048 Peoples R China Guizhou Inst Technol Key Lab Power Big Data Guizhou Prov Guiyang 550003 Peoples R China Beijing Jiaotong Univ Dept Math Beijing 10044 Peoples R China

This paper is mainly devoted to the distributed second-order multi-agent optimization problem with unbalanced and directed networks, where the gradient of the private objective functions might be unbounded. To deal with this problem, a new distributed algorithm is proposed based on the local neighbor information and the private objective functions. By a coordination transformation, the closed-loop system is divided into two simple first order subsystems. Under the assumption of the strong connectivity of networks, it is proved that all agents can collaboratively converge to some optimal solution of the team objective function. At last, we give two numerical examples to show the effectiveness of our proposed algorithm. (c) 2021 Elsevier Inc. All rights reserved.

关键词： distributed optimization Second-order multi-agent systems Unbalanced network

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