Convex Relaxations of AC Optimal Power Flow under Uncertainty

High penetration of renewable energy sources and the increasing share of stochastic loads require the explicit representation of uncertainty in tools such as the optimal power flow (OPF). Current approaches follow either a linearized approach or an iterative approximation of non-linearities. We propose a semidefinite relaxation of a chance constrained AC-OPF which is able to provide guarantees for (near-)global optimality. Using a piecewise affine approximation, we can ensure tractability, accurately model large power deviations, and determine suitable corrective control policies for active power, reactive power, and voltage. We state a tractable formulation of the chance constraints using two different methods: A combination of robust and randomized optimization, and an analytical reformulation assuming a Gaussian distribution of the forecast errors. To include security constraints, we propose an iterative solution algorithm to recover a feasible solution. Furthermore, we investigate the applicability of our framework to interconnected AC and HVDC grids. We demonstrate the performance of our approach on the IEEE 24 and 118 bus system using realistic day-ahead forecast data and obtain tight near-global optimality guarantees.
Andreas Venzke received the M.Sc. degree in Energy Science and Technology from ETH Zurich with distinction in 2017. He is currently working towards the Ph.D. degree at the Department of Electrical Engineering, Technical University of Denmark (DTU). His research interests include power system operation under uncertainty and convex relaxations of optimal power flow.