ADMM Enhancement Techniques for Distributed Optimal Power Flow

This paper presents three techniques to enhance the convergence performance of distributed AC and DC optimal power flow (OPF) problems when solved using alternating direction method of multipliers (ADMM). The OPF problem is decomposed into subproblems, each representing a portion of the power grid. Motivated by the need for computational simplicity and the avoidance of sharing additional information between subproblems, while improving the convergence performance of distributed optimization, we have developed these straightforward yet effective techniques for AC and DC OPF applications. These techniques include (1) augmenting the Lagrangian function by incorporating surrogate penalties for tie-line power flow, (2) reformulating nodal power balance constraints at boundary buses to better model the power exchange behavior between subproblems, and (3) introducing an adaptive scaling mechanism that dynamically balances penalty terms with generation costs, eliminating the need for heuristic parameter tuning and improving convergence robustness under varying system conditions. Additionally, this paper extends these techniques to an exponential penalty formulation of ADMM, inspired by advancements in augmented Lagrangian approaches. Case studies demonstrate that the proposed techniques reduce iteration counts for quadratic and exponential penalty formulations. Combining these techniques results in superior performance across various power system scenarios and configurations. These findings establish the proposed methods as versatile solutions for accelerating ADMM-based distributed OPF computations.