Convex relaxation and decomposition in large resistive power networks with energy storage

A fundamental challenge of a smart grid is: to what extent can moving energy through space and time be optimized to benefit the power network with large-scale storage integration? In this paper, we study a dynamic optimal power flow problem with energy storage dynamics in resistive power networks. We first propose a second order cone programming convex relaxation to solve this nonconvex problem optimally. Then, we apply optimization decomposition techniques to decompose and decouple the problem and obtain the global optimal solution in a distributed manner. The optimization decomposition offers new interesting insight over space and time between the dual solution and energy storage dynamics. We investigate the efficiency of the SOCP relaxation in several IEEE benchmark systems and verify that the distributed algorithms can converge fast to the global optimal solution by numerical simulations.