Abstract

The alternating direction method of multipliers (ADMM) is a powerful algorithm for solving decentralized optimization problems including networked microgrid energy management (NetMEM). However, its performance is highly sensitive to the selection of its penalty parameter ρ, which can lead to slow convergence, suboptimal solutions, or even algorithm divergence. This paper evaluates and compares three district ADMM formulations to solve the NetMEM problem, which explore different methods to determine appropriate stopping points, aiming to yield high-quality solutions. Furthermore, an adaptive penalty heuristic is also incorporated into each method to analyze its potential impact on ADMM performance. Different case studies on networks of varying sizes demonstrate that an objective-based ADMM approach, denominated as OB-ADMM, is significantly more robust to the choice of ρ, consistently yielding solutions closer to the centralized optimal benchmark by preventing premature algorithm stopping.

Index Terms

Alternating Direction Method of Multipliers, Decentralized Optimization, Energy Management, Networked Microgrids.

Cite this paper:

Jesus Silva-Rodriguez and Xingpeng Li, “ADMM Penalty Parameter Evaluation for Networked Microgrid Energy Management”, arXiv, Nov. 2025.