Convex Relaxations in Power System Optimization: A Brief Introduction

TL;DR

This paper introduces convex relaxations of AC power flow equations, explaining their mathematical foundations and applications in power system optimization to aid researchers in understanding and developing these methods.

Contribution

It provides a high-level overview of convex relaxations in power system optimization, focusing on common ideas and applications rather than detailed methods.

Findings

Convex relaxations simplify AC power flow equations.

They enable more efficient power system optimization.

The paper serves as an introductory resource for researchers.

Abstract

Convex relaxations of the AC power flow equations have attracted significant interest in the power systems research community in recent years. The following collection of video lectures provides a brief introduction to the mathematics of AC power systems, continuous nonlinear optimization, and relaxations of the power flow equations. The aim of the videos is to provide the high level ideas of convex relaxations and their applications in power system optimization, and could be used as a starting point for researchers who want to study, use or develop new convex relaxations for use in their own research. The videos do not aim to provide an in-depth tutorial about specific convex relaxations, but rather focus on ideas that are common to all convex relaxations of the AC optimal power flow problem.