A distributed continuous-time gradient dynamics approach for the active power loss minimizations

In this paper, we consider the non-convex active power loss minimization problem. Under the existence of saddle points and certain mild conditions, we show that a solution to the active power loss minimization can be achieved by applying the gradient dynamics approach. An important feature of this approach is that it is naturally distributed, i.e., each bus in the network only requires the local information from its neighbors and itself for computation. A four-bus simulation example is given to illustrate the distributed structure and convergence of the gradient dynamics. The validity of our approach is also verified by distributedly computing the optimal solutions to the IEEE benchmark systems with 14, 30, and 57 buses.