Auto-tuned weighted-penalty parameter ADMM for distributed Optimal Power Flow

The Alternating Direction Method of Multipliers (ADMM) is widely utilized to solve the distributed Optimal Power Flow (OPF) problem, providing convergence under certain assumptions. ADMM relies on a penalty parameter $\rho$ to accelerate its convergence. The selection of appropriate values of $\rho$ is crucial for the quality of the final solution and for the efficiency of the iterative process. In this paper, we propose a weighted- $\rho$ ADMM, with its weights automatically determined by leveraging the nature of the optimal power flow problem. Specifically, the affinity matrix, a combination of the admittance matrix and Hessian matrix of the Lagrangian function of the associated OPF problem, is utilized to determine the penalty parameters. The convergence of the iterative scheme is analyzed and the effectiveness of the proposed methodology is validated through simulation experiments which show that the weighted- $\rho$ ADMM overcomes the necessity for suitable initial parameter selection.