Optimal power flow (OPF) is an important problem in the operation of electric power systems. The solution to an OPF problem provides a minimum cost operating point that satisfies both engineering limits and the power flow equations corresponding to the network physics. Optimal power flow is a non-convex, NP-hard optimization problem that may have multiple local optima. Many recent research efforts have applied convex relaxation techniques to compute bounds on the optimal objective values, certify problem infeasibility, and, in some cases, obtain the globally optimal decision variables of OPF problems. The first part of this presentation surveys the OPF relaxation literature with a focus on recent developments.

With growing penetrations of renewable generation, OPF problems are increasingly influenced by the forecast uncertainty and short-term fluctuations that are inherent to many renewable energy sources. Thus, reliable and efficient operation of power systems requires the solution of OPF problems that incorporate uncertainty. The second part of this presentation describes a recently proposed iterative algorithm for the OPF problem that uses convex relaxation techniques to obtain a solution with robust feasibility guarantees.

Information: Daniel Molzahn is a computational engineer in the Energy Systems Division at Argonne National Laboratory. Prior to his current position, Daniel was a Dow Sustainability Fellow at the University of Michigan. Daniel received the B.S., M.S. and Ph.D. degrees in Electrical Engineering and the Masters of Public Affairs degree from the University of Wisconsin–Madison, where he was a National Science Foundation Graduate Research Fellow. His research interests are in the application of optimization techniques to electric power systems.