Distributed Dual Gradient Tracking Method for Economic Dispatch Problem

In this paper, we focus on solving the economic dispatch problem (EDP) in the smart grid, which aims to minimize the total generation cost while ensuring the supply-demand coordination and generation capacity constraints. First, we develop a distributed optimization algorithm by employing the gradient tracking method. Different from most existing works, our proposed algorithm allows the objective function to be strongly convex only in the range of generation capacity constraint rather than in the whole interval. Then, we prove that the convergence rate of the proposed algorithm is $\mathcal{O}\left( {1/k} \right)$ with k being the number of iteration and becomes linear rate when the average value of optimization parameters for each agent falls into a closed interval. The closed interval consists of two endpoints, which are the minimum and the maximum gradients obtained from the cost function of all generations. Finally, numerical simulations are given to demonstrate the effectiveness of the proposed algorithm.