A Review of Matrix Algebra for Power and Energy Applications

TL;DR

This paper reviews matrix algebra techniques implemented in Julia, focusing on their application to power and energy systems, emphasizing practical coding practices and fundamental concepts like quadratic forms and norms.

Contribution

It provides a concise overview of matrix algebra applications in power systems using Julia, highlighting best practices and essential concepts for convergence analysis.

Findings

Effective visualization and matrix operations in Julia

Understanding quadratic forms and norms for power flow convergence

Practical coding guidelines for power system analysis

Abstract

This report presents a brief review of matrix algebra and its implementation in Julia for power and energy applications. First, we present basic examples of data visualization, followed by conventional operations with matrices and vectors. Then, we study quadratic forms and norms, two main concepts required in the convergence study of the power flow in power and energy applications. After that, we give good practices to create a neat code in Julia. There is an extensive set of examples available on the Internet related to these basic aspects, so we avoid repeating what is well documented. Hence, we show only basic examples to create our first scripts.