Certifying Global Optimality of AC-OPF Solutions via sparse polynomial optimization

TL;DR

This paper demonstrates that the CS-TSSOS hierarchy, a sparse polynomial optimization method, can certify near-global optimality for large-scale AC-OPF problems, including instances with over 6,500 buses.

Contribution

It introduces the application of the CS-TSSOS hierarchy to certify 1% global optimality in large AC-OPF instances, showing scalability and effectiveness over existing relaxations.

Findings

Successfully certifies 1% global optimality for a 6515-bus AC-OPF instance.

Demonstrates scalability of the CS-TSSOS hierarchy to large real-world problems.

Provides tighter SDP relaxations than Shor's relaxation.

Abstract

We report the experimental results on certifying 1% global optimality of solutions of AC-OPF instances from PGLiB via the CS-TSSOS hierarchy -- a moment-SOS based hierarchy that exploits both correlative and term sparsity, which can provide tighter SDP relaxations than Shor's relaxation. Our numerical experiments demonstrate that the CS-TSSOS hierarchy scales well with the problem size and is indeed useful in certifying global optimality of solutions for large-scale real world problems, e.g., the AC-OPF problem. In particular, we are able to certify 1% global optimality for a challenging AC-OPF instance with 6515 buses involving 14398 real variables and 63577 constraints.