A distributed continuous-time algorithm for economic dispatch problem

In this paper, the economic dispatch problem over the undirected network is considered, which aims to minimize the total power generation cost. In order to solve the equality constraint, the Lagrangian dual problem is developed and a fast distributed continuous-time algorithm is designed for the dual variable based on the fixed-time stability theory. Furthermore, the optimal solution of the economic dispatch problem is obtained by a well-developed projector and the above proposed algorithm is initialization-free and privacy-guaranteed. Finally, several examples are provided for illustrating the effectiveness of our proposed algorithms.