ADMM Penalty Parameter Evaluation for Networked Microgrid Energy Management

TL;DR

This paper evaluates the performance of ADMM algorithms in networked microgrid energy management, focusing on penalty parameter selection and adaptive heuristics to improve convergence and solution quality.

Contribution

It compares three ADMM formulations and introduces an adaptive penalty heuristic, demonstrating improved robustness and solution accuracy in microgrid optimization.

Findings

OB-ADMM outperforms other methods in solution quality

Adaptive penalty heuristic enhances convergence stability

Objective-based ADMM is less sensitive to penalty parameter choice

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 \r{ho}, 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 \r{ho}, consistently yielding solutions closer to the centralized optimal benchmark by preventing premature algorithm stopping.