Minimax Flow over Acyclic Networks: Distributed Algorithms and Microgrid Application

TL;DR

This paper introduces a distributed approach to minimize the maximum flow in acyclic networks, with applications to microgrid overcurrent prevention, by reformulating the problem as a consensus task and developing new algorithms.

Contribution

It recasts the minimax flow problem as a novel consensus problem and provides a distributed algorithm for estimating maximum downstream flows, enabling effective microgrid control.

Findings

Distributed algorithms successfully estimate maximum downstream flows.

The approach effectively prevents overcurrent in microgrids.

Numerical validation confirms practical applicability.

Abstract

Given a flow network with variable suppliers and fixed consumers, the minimax flow problem consists in minimizing the maximum flow between nodes, subject to flow conservation and capacity constraints. We solve this problem over acyclic graphs in a distributed manner by showing that it can be recast as a consensus problem between the maximum downstream flows, which we define here for the first time. Additionally, we present a distributed algorithm to estimate these quantities. Finally, exploiting our theoretical results, we design an online distributed controller to prevent overcurrent in microgrids consisting of loads and droop-controlled inverters. Our results are validated numerically on the CIGRE benchmark microgrid.