Suboptimality of Decentralized Methods for OPF

We examine the fact that decentralized methods may converge to suboptimal solution. Observed in numerous studies of decentralized optimal power flow problem it has a simple explanation: the curse of non-convexity. We numerically assess the performance of decentralized interior point method (DIPM) and alternating direction method of multipliers (ADMM). The algorithms were tested in two situations: grid decomposition for a few areas associated with independent Transmission System Operators (TSOs) as in super grids and total decomposition till node level that models prosumers behavior. In particular, we demonstrate that the obtained optimal state and convergence rate depends on the starting point. The algorithms were tested on IEEE 9, 14, 118 bus systems. Besides, we discuss the advantages and drawbacks of decentralized optimization approaches.