A survey on conic relaxations of optimal power flow problem

Conic optimization has recently emerged as a powerful tool for designing tractable and guaranteed algorithms for power system operation. On the one hand, tractability is crucial due to the large size of modern electricity transmission grids. This is a result of the numerous interconnections that have been built over time. On the other hand, guarantees are needed to ensure reliability and safety for consumers at a time when power systems are growing in complexity. This is in large part due to the high penetration of renewable energy sources and the advent of electric vehicles. The aim of this paper is to review the latest literature in order to demonstrate the success of conic optimization when applied to power systems. The main focus is on how linear programming, second-order cone programming, and semidefinite programming can be used to address a central problem named the optimal power flow problem. We describe how they are used to design convex relaxations of this highly challenging non-convex optimization problem. We also show how sum-of-squares can be used to strengthen these relaxations. Finally, we present advances in first-order methods, interior-point methods, and nonconvex methods for solving conic optimization. Challenges for future research are also discussed. (C) 2020 Elsevier B.V. All rights reserved.