Certifying Global Optimality of Ac-Opf Solutions Via the Cs-Tssos Hierarchy

In this paper, we report the experimental results on certifying 1% global optimality of solutions of AC-OPF instances from PGLiB with up to 24464 buses 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 1% global optimality of solutions for large-scale real world problem; e.g., the AC-OPF problem. In particular, we are able to certify 1% global optimality for an AC-OPF instance with 6515 buses involving 14398 real variables and 63577 constraints.

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