The problem of distributed constrained optimisation over a network of agents, where the goal is to cooperatively minimise the sum of all local convex objective functions is studied. Each agent in the network possesses...
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The problem of distributed constrained optimisation over a network of agents, where the goal is to cooperatively minimise the sum of all local convex objective functions is studied. Each agent in the network possesses only its private local convex objective function and is constrained to a coupling equality constraint and its local inequality constraint. Moreover, the authors particularly focus on the scenario where each agent is only allowed to interact with their in-neighbours over a series of time-varying directed unbalanced networks. To collectively address the optimisation problem, a novel distributed primal-dual push-DIGing (integrated push-sum strategy with distributed inexact gradient tracking method) algorithm (termed as DPD-PD) in which agents employ uncoordinated step-sizes is proposed. Unlike other methods, DPD-PD allows not only the mixing matrices are column-stochastic, but also the step-sizes are uncoordinated. An important feature of DPD-PD is handling distributed constrained optimisation problems in the case of time-varying directed unbalanced networks. When objective functions are strongly convex and smooth, the authors demonstrate that DPD-PD converges linearly to the optimal solution given that the uncoordinated step-sizes are smaller than an upper bound. Explicit convergence rate is also conducted. Preliminary results on some numerical experiments validate the theoretical findings.
The DC Optimal Power Flow(DC-OPF) is at the heart of the actual centralized market clearing mechanisms used in Electrical Power Markets. Through the last decade several distributed clearing mechanisms have been propos...
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ISBN:
(纸本)9787564112493
The DC Optimal Power Flow(DC-OPF) is at the heart of the actual centralized market clearing mechanisms used in Electrical Power Markets. Through the last decade several distributed clearing mechanisms have been proposed in order to decentralise it. A common link in these approaches is that they address this problem as a decomposition of the whole system into subareas. Based on this decomposition they propose alternative methods to reach the global solution. However, in order to achieve their solution they add some constraints to the original problem. This document proposes a decentralized model for the DC-OPF which works in a bottom-up fashion without any additional constraint. The system is decomposed into its basic components. Next, by using the auxiliary problem principle a decentralized solution to the OPF is proposed. The application of this decomposition has a positive side effect: The complexity of the system, as a result of the network interconnectivity, is converted into local intercommunication tasks.
The DC Optimal Power Flow (DC-OPF) is at the heart of the actual centralized market clearing mechanisms used in Electrical Power Markets. Through the last decade several distributed clearing mechanisms have been propo...
详细信息
The DC Optimal Power Flow (DC-OPF) is at the heart of the actual centralized market clearing mechanisms used in Electrical Power Markets. Through the last decade several distributed clearing mechanisms have been proposed in order to decentralise it. A common link in these approaches is that they address this problem as a decomposition of the whole system into subareas. Based on this decomposition they propose alternative methods to reach the global solution. However, in order to achieve their solution they add some constraints to the original problem. This document proposes a decentralized model for the DC-OPF which works in a bottom-up fashion without any additional constraint. The system is decomposed into its basic components. Next, by using the auxiliary problem principle a decentralized solution to the OPF is proposed. The application of this decomposition has a positive side effect: The complexity of the system, as a result of the network interconnectivity, is converted into local intercommunication tasks.
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