# CONICOPF: Conic relaxations for AC optimal power flow computations

## TL;DR

This paper introduces and compares two convex conic relaxations, TCR and QCR, for solving large-scale AC optimal power flow problems efficiently, demonstrating TCR's superior performance across various test cases.

## Contribution

The paper presents a new MATLAB package, CONICOPF, and provides a comprehensive comparison of TCR and QCR relaxations for AC optimal power flow.

## Key findings

- TCR outperforms QCR on most test cases.
- CONICOPF package is publicly available on GitHub.
- Convex relaxations balance speed and optimality effectively.

## Abstract

Computational speed and global optimality are key needs for practical algorithms for the optimal power flow problem. Two convex relaxations offer a favorable trade-off between the standard second-order cone and the standard semidefinite relaxations for large-scale meshed networks in terms of optimality gap and computation time: the tight-and-cheap relaxation (TCR) and the quadratic convex relaxation (QCR). We compare these relaxations on 60 PGLib-OPF test cases with up to 1,354 buses under three operating conditions and show that TCR dominates QCR on all 20 typical (TYP) test cases, on 18 out of 20 active power increase (API), and 12 out of 20 small angle difference (SAD). Selected state-of-the-art conic relaxations are implemented in the new MATLAB-based package CONICOPF available on GitHub.