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

TL;DR

This paper introduces a novel two-level ADMM algorithm for solving the nonconvex AC optimal power flow problem, providing global convergence guarantees and demonstrating superior scalability and robustness in large-scale tests.

Contribution

The paper presents a new distributed reformulation and a two-level ADMM algorithm that guarantees convergence for AC OPF, surpassing existing methods in scalability and robustness.

Findings

Proposed algorithm converges globally under mild conditions.

Demonstrated scalability on large test cases up to 30,000 buses.

Achieved convergence speed comparable or superior to centralized solvers.

Abstract

This paper proposes a two-level distributed algorithmic framework for solving the AC optimal power flow (OPF) problem with convergence guarantees. The presence of highly nonconvex constraints in OPF poses significant challenges to distributed algorithms based on the alternating direction method of multipliers (ADMM). In particular, convergence is not provably guaranteed for nonconvex network optimization problems like AC OPF. In order to overcome this difficulty, we propose a new distributed reformulation for AC OPF and a two-level ADMM algorithm that goes beyond the standard framework of ADMM. We establish the global convergence and iteration complexity of the proposed algorithm under mild assumptions. Extensive numerical experiments over some largest test cases from NESTA and PGLib-OPF (up to 30,000-bus systems) demonstrate advantages of the proposed algorithm over existing ADMM variants in terms of convergence, scalability, and robustness. Moreover, under appropriate parallel implementation, the proposed algorithm exhibits fast convergence comparable to or even better than the state-of-the-art centralized solver.