Achieving linear convergence for distributee dispath response in power systems over directed graphs

Inspired by potential application in power systems and a fully distributed primal-dual method, we investigate how a novel distributed optimization algorithm can be used to solve the dispath response problem in power systems with a distributed manner, whose main target is to minimize the generation cost of the whole network. The problem we study here can be formulated as a kind of optimization problem, and its global objective function is a sum of all local agents' individual cost function and the individual cost function is only known by itself. The agents' communication graph in the networks is directed, strongly connected and the weight matrix is row-stochastic matrix that means each agent in the network only needs to know its in-degree which also means the total information it received from its neighbors. Our main contribution of this paper is to design a novel distributed optimization algorithm with fixed step-size, which combines with the distributed primal-dual method. If all agents' individual cost functions are convex and smooth, we prove that the convergence rate of our method can achieve a geometrical rate to the optimal solution. Finally, simulation test is presented to illustrate the efficacy of our method as well as testify the theoretical finding.