Asynchronous ADMM for Distributed Non-Convex Optimization in Power Systems

TL;DR

This paper introduces an asynchronous distributed ADMM algorithm tailored for large-scale non-convex optimization problems in power systems, enabling more scalable and efficient solutions without requiring synchronization.

Contribution

It develops a novel asynchronous ADMM method that converges to KKT points under mild conditions and demonstrates improved convergence speed over synchronous methods in power system applications.

Findings

Asynchronous ADMM converges to KKT points in non-convex problems.

The method outperforms synchronous schemes in large-scale power system tests.

Validation on Optimal Power Flow shows faster convergence in practice.

Abstract

Large scale, non-convex optimization problems arising in many complex networks such as the power system call for efficient and scalable distributed optimization algorithms. Existing distributed methods are usually iterative and require synchronization of all workers at each iteration, which is hard to scale and could result in the under-utilization of computation resources due to the heterogeneity of the subproblems. To address those limitations of synchronous schemes, this paper proposes an asynchronous distributed optimization method based on the Alternating Direction Method of Multipliers (ADMM) for non-convex optimization. The proposed method only requires local communications and allows each worker to perform local updates with information from a subset of but not all neighbors. We provide sufficient conditions on the problem formulation, the choice of algorithm parameter and network delay, and show that under those mild conditions, the proposed asynchronous ADMM method asymptotically converges to the KKT point of the non-convex problem. We validate the effectiveness of asynchronous ADMM by applying it to the Optimal Power Flow problem in multiple power systems and show that the convergence of the proposed asynchronous scheme could be faster than its synchronous counterpart in large-scale applications.