Minimax Flow Over Acyclic Networks: Distributed Algorithms and Microgrid Application

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. In addition, 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.

Automated summary

Given a flow network with variable suppliers and fixed consumers, the minimax flow problem aims to minimize the maximum flow between nodes, subject to flow conservation and capacity constraints. In this study, we address this problem in a distributed manner by introducing the concept of consensus problem between the maximum downstream flows. Additionally, we propose a distributed algorithm to estimate these quantities. Finally, we apply these theoretical results to design an online distributed controller for preventing overcurrent in microgrids.