A distributed stochastic gradient algorithm for economic dispatch over directed network with communication delays

•We propose a distributed primal-dual algorithm to solve constrained optimization problems over directed network.•The proposed algorithm adopts stochastic gradient descent method to update values of nodes for dealing with noise.•Theoretical analysis indicates that the algorithm can exactly seek the...

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Bibliographic Details
Published in:International journal of electrical power & energy systems Vol. 110; pp. 759 - 771
Main Authors: Zhang, Hao, Li, Huaqing, Zhu, Yifan, Wang, Zheng, Xia, Dawen
Format: Journal Article
Language:English
Published: Elsevier Ltd 01.09.2019
Subjects:
Communication delays
Directed network
Distributed optimization algorithm
Economic dispatch problem (EDP)
Stochastic gradient descent
Uncoordinated step-sizes
Uncoordinated step-sizes
Distributed optimization algorithm
Stochastic gradient descent
Directed network
Economic dispatch problem (EDP)
Communication delays
ISSN:0142-0615, 1879-3517
Online Access:Get full text
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Summary:•We propose a distributed primal-dual algorithm to solve constrained optimization problems over directed network.•The proposed algorithm adopts stochastic gradient descent method to update values of nodes for dealing with noise.•Theoretical analysis indicates that the algorithm can exactly seek the optimal solution to EDP with probability one.•The algorithm allows uncoordinated step-sizes for local optimization of each node.•To demonstrate the robustness and scalability of the proposed algorithm, we extend the algorithm to the network with communication delays. Economic dispatch problem (EDP) is one of the fundamental optimization problems in power systems, which involves a coupling linear constraint and several individual box constraints. In this paper, we propose a distributed stochastic gradient descent algorithm based on consensus theory to solve the EDP under directed network, where the convex cost function for each generator only needs to satisfy the condition that the function is strictly convex with Lipschitz continuous gradient. The proposed algorithm utilizes stochastic gradient descent to update values of generators for dealing with the noise which is incurred during the gradient estimation, and the step-sizes are heterogeneous. Under strictly convex assumption on objective functions, the algorithm can seek the exact optimal solution with probability one at the rate of OlnKK, where K is the number of iteration. Furthermore, the algorithm is also suitable and effective to the network with communication delays if the communication delays are bounded. Simulation results illustrate the effectiveness of the algorithm.
ISSN:0142-0615
1879-3517
DOI:10.1016/j.ijepes.2019.03.024