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

2021/09/21 by Wang, Jie, Magron, Victor, Lasserre, Jean B. · 2 citations
#12D15 #14P10 #90C22 #90C23 #90C26 #FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.2109.10005

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.

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Related

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• Proving Global Optimality of ACOPF Solutions
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