Smart Grid Seminar

As emerging technologies such as, electric vehicles, battery storage, and distributed renewable generation disrupt established power networks, real-time network optimization is emerging as a critical aspect of future energy systems.  Unfortunately, these optimization tasks are challenging to compute, due to the non-convex nonlinear nature of AC power flows.  Convex relaxations of the AC power flow equations such as, the Semi-Definite Programming (SDP) and Second-Order Cone (SOC) relaxations, have attracted significant interest in recent years to address these computational challenges.  Indeed, these convex optimization problems benefit from both theoretical guarantees and industrial-strength optimization software.

This talk introduces the recent Quadratic Convex (QC) power flow relaxation, which is constructed by composing intuitive convex-envelopes of non-convex functions.  A theoretical analysis is presented to demonstrate that the QC relaxation is stronger than the established SOC relaxation and neither dominates nor is dominated by the SDP relaxation. A comprehensive computational study on the AC Optimal Power Flow problem is presented to illustrate the trade offs of computation time and relaxation strength of all three methods.