Dynamical economic dispatch using distributed barrier function-based optimization algorithm

In this paper, we study the distributed economic dispatch problem where the supply demand balance, capacity constraints and ramp-rate constraints are considered. In order to accommodate varying power load and power storage in reality, we introduce two variables where each variable is time-varing and has its own dynamics. The renewable power is also considered. Barrier functions are introduced to deal with the local constraints by means of imposing penalty terms into the objective function to ensure that the optimal solution satisfies the corresponding constraints. Based on the Langrange dual theory, the primal optimization problem is transformed into the dual problem, which is solved by the primary-dual algorithm proposed in this paper. Under the assumption that the communication graph is an undirected and connected graph, we analyze the convergence of the proposed algorithm. The simulations on IEEE six-bus test systems are carried out to verify the performance of the algorithm, which shows that the proposed algorithm converges to the optimal solution, while all the constraints are met.