Optimal Power Flow in Uncertain DC Networks

This paper addresses the optimal power flow problem in direct current networks with uncertain load demands. This is a non-convex optimization problem which becomes further complicated due to the presence of uncertain loads. We construct affine control policies using which power converters adjust the bus voltages. Using S–Lemma, semidefinite programming relaxations, and penalization techniques, uncertain variables are eliminated and the problem is cast as a deterministic convex optimization using which the affine policies are calculated. The convexified problem can be readily solved using off-the-shelf solvers. The proposed control policies are numerically verified on modified IEEE 4-, 14-, and 30-bus networks, and experimentally validated using a controller/hardware-in-the-loop setup for the 4-bus network.