# Convex Relaxations in Power System Optimization, A Brief Introduction

## Abstract

Convex relaxations of the AC power ow equations have attracted signi cant 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 ow 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 speci c convex relaxations, but rather focus on ideas that are common to all convex relaxations of the AC optimal power ow problem. The videos assume minimal prerequisite knowledge and are designed to be accessible to a variety of disciplines (e.g. power system engineers, industrial engineers and computer scientists). They are designed to be modular, such that interested listeners can either watch the series as a whole, or choose only the subset that matches their interest. The following sections provide a brief overview of the topics and references covered in each video.

- Authors:

- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

- Publication Date:

- Research Org.:
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

- Sponsoring Org.:
- USDOE Office of Electricity Delivery and Energy Reliability (OE)

- OSTI Identifier:
- 1461380

- Report Number(s):
- LA-UR-18-26601

- DOE Contract Number:
- AC52-06NA25396

- Resource Type:
- Technical Report

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICS AND COMPUTING; Computer Science; Mathematics

### Citation Formats

```
Coffrin, Carleton James, and Roald, Line Alnaes.
```*Convex Relaxations in Power System Optimization, A Brief Introduction*. United States: N. p., 2018.
Web. doi:10.2172/1461380.

```
Coffrin, Carleton James, & Roald, Line Alnaes.
```*Convex Relaxations in Power System Optimization, A Brief Introduction*. United States. doi:10.2172/1461380.

```
Coffrin, Carleton James, and Roald, Line Alnaes. Thu .
"Convex Relaxations in Power System Optimization, A Brief Introduction". United States. doi:10.2172/1461380. https://www.osti.gov/servlets/purl/1461380.
```

```
@article{osti_1461380,
```

title = {Convex Relaxations in Power System Optimization, A Brief Introduction},

author = {Coffrin, Carleton James and Roald, Line Alnaes},

abstractNote = {Convex relaxations of the AC power ow equations have attracted signi cant 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 ow 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 speci c convex relaxations, but rather focus on ideas that are common to all convex relaxations of the AC optimal power ow problem. The videos assume minimal prerequisite knowledge and are designed to be accessible to a variety of disciplines (e.g. power system engineers, industrial engineers and computer scientists). They are designed to be modular, such that interested listeners can either watch the series as a whole, or choose only the subset that matches their interest. The following sections provide a brief overview of the topics and references covered in each video.},

doi = {10.2172/1461380},

journal = {},

number = ,

volume = ,

place = {United States},

year = {2018},

month = {7}

}