Strengthening QC relaxations of optimal power flow problems by exploiting various coordinate changes

Motivated by the potential for improvements in electric power system economics, this dissertation studies the AC optimal power flow (AC OPF) problem. An AC OPF problem optimizes a specified objective function subject to constraints imposed by both the non-linear power flow equations and engineering limits. The difficulty of an AC OPF problem is strongly connected to its feasible space\u27s characteristics. This dissertation first investigates causes of nonconvexities in AC OPF problems. Understanding typical causes of nonconvexities is helpful for improving AC OPF solution methodologies. This dissertation next focuses on solution methods for AC OPF problems that are based on convex relaxations. The quadratic convex (QC) relaxation is one promising approach that constructs convex envelopes around the trigonometric and product terms in the polar representation of the power flow equations. This dissertation proposes several improvements to strengthen QC relaxations of OPF problems. The first group of improvements provides tighter envelopes for the trigonometric functions and product terms in the power flow equations. Methods for obtaining tighter envelopes includes implementing Meyer and Floudas envelopes that yield the convex hull of trilinear monomials. Furthermore, by leveraging a representation of line admittances in polar form, this dissertation proposes tighter envelopes for the trigonometric terms. Another proposed improvement exploits the ability to rotate the base power used in the per unit normalization in order to facilitate the application of tighter trigonometric envelopes. The second group of improvements propose additional constraints based on new variables that represent voltage magnitude differences between connected buses. Using \u27bound tightening\u27 techniques, the bounds on the voltage magnitude difference variables can be significantly tighter than the bounds on the voltage magnitudes themselves, so constraints based on voltage magnitude differences can improve the QC relaxation --Abstract, page iv