Convergence analysis of a distributed gradient algorithm for economic dispatch in smart grids

•We propose a fresh distributed algorithm to solve the EDP, which not only allows the utilization of constant step-size, but also provides a wider range of its selection.•If the cost functions meet the strongly convex and smooth condition, theoretical analysis indicates that the algorithm can achiev...

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Vydáno v:International journal of electrical power & energy systems Ročník 134; s. 107373
Hlavní autoři: Zhang, Hao, Liang, Shan, Liang, Jing, Han, Yiyan
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier Ltd 01.01.2022
Témata:
Constant step-size
Distributed algorithm
Economic dispatch
Linear convergence
Smart grids
Constant step-size
Linear convergence
Economic dispatch
Smart grids
Distributed algorithm
ISSN:0142-0615
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Shrnutí:•We propose a fresh distributed algorithm to solve the EDP, which not only allows the utilization of constant step-size, but also provides a wider range of its selection.•If the cost functions meet the strongly convex and smooth condition, theoretical analysis indicates that the algorithm can achieve the optimal dispatch at a linear convergence rate.•The linear convergence rate of the algorithm is tunable, and a relationship among the linear rate, cost functions, network topology, weight matrix and constant step-size is established. The increasingly complex modern energy network arouses the need of flexible and dependable approaches to solve the economic dispatch problem (EDP) in the smart grids. Toward this end, this paper develops a fresh distributed algorithm with constant step-size, which aims to schedule the power generation among generators by complying with individual generation capacity limits to satisfy the total load demand at the minimized cost. The convergence of the proposed algorithm is analyzed through utilizing the Lyapunov method and the spectral decomposition technique. When the selected constant step-size is smaller than a specifically provided upper bound, the theoretical analysis demonstrates that the proposed algorithm can linearly achieve the optimal solution of the EDP under the smooth and strongly convex assumption on generation cost functions. In particular, the linear convergence rate of the proposed algorithm is tunable, and a relationship among the linear convergence rate, generation cost functions, network topology, weight matrix and constant step-size is established. The availability of the proposed algorithm is verified through simulation experiments.
ISSN:0142-0615
DOI:10.1016/j.ijepes.2021.107373