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This paper proposes a two-level distributed algorithmic framework for solvingthe AC optimal power flow (OPF) problem with convergence guarantees. Thepresence of highly nonconvex constraints in OPF poses significant challenges todistributed algorithms based on the alternating direction method of multipliers(ADMM). In particular, convergence is not provably guaranteed for nonconvexnetwork optimization problems like AC OPF. In order to overcome thisdifficulty, we propose a new distributed reformulation for AC OPF and atwo-level ADMM algorithm that goes beyond the standard framework of ADMM. Weestablish the global convergence and iteration complexity of the proposedalgorithm under mild assumptions. Extensive numerical experiments over somelargest test cases from NESTA and PGLib-OPF (up to 30,000-bus systems)demonstrate advantages of the proposed algorithm over existing ADMM variants interms of convergence, scalability, and robustness. Moreover, under appropriateparallel implementation, the proposed algorithm exhibits fast convergencecomparable to or even better than the state-of-the-art centralized solver.

A Two-level ADMM Algorithm for AC OPF with Global Convergence Guarantees