Certifying global optimality of AC-OPF solutions via sparse polynomial optimization

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. • A hierarchy of SDP relaxations, named CS-TSSOS, is proposed to certify global optimality of AC-OPF solutions. • Numerical results for benchmarking CS-TSSOS on PGLiB AC-OPF instances are reported. • By fully exploiting sparsity, CS-TSSOS scales well with the problem size. • CS-TSSOS closes optimality gap for many challenging cases beyond Shor’s relaxation.