# Feasibility vs. Optimality in Distributed AC OPF - A Case Study Considering ADMM and ALADIN

## TL;DR

This paper examines how initial feasibility and penalty parameters affect distributed optimization methods like ADMM and ALADIN in solving power system OPF problems, highlighting potential slow convergence issues.

## Contribution

It provides an analysis of ADMM's behavior under large penalization and compares it with ALADIN in the context of distributed AC OPF, supported by case studies.

## Key findings

- Large consensus-violation penalization can slow ADMM convergence.
- ADMM's behavior is influenced by initial guesses and penalty parameters.
- ALADIN shows different convergence characteristics compared to ADMM.

## Abstract

This paper investigates the role of feasible initial guesses and large consensus-violation penalization in distributed optimization for Optimal Power Flow (OPF) problems. Specifically, we discuss the behavior of the Alternating Direction of Multipliers Method (ADMM). We show that in case of large consensus-violation penalization ADMM might exhibit slow progress. We support this observation by an analysis of the algorithmic properties of ADMM. Furthermore, we illustrate our findings considering the IEEE 57 bus system and we draw upon a comparison of ADMM and the Augmented Lagrangian Alternating Direction Inexact Newton (ALADIN) method.