Distributed Feasibility Algorithms with Application to Power Flow Problems

Abstract

Given a network of interconnected nodes, each with its own value (such as a measurement, position or vote) and with constraints between each node and its neighbors, a feasibility algorithm assigns a value to each node such that constraints between neighboring nodes are satisfied simultaneously. This paper presents two novel feasibility algorithms that are based on the Method of Alternating Projections (MAP) and the Projected Consensus algorithm. Our algorithms solve convex feasibility problems by distributing computation among nodes and require only local information exchanges. A well-motivated application discussed throughout the paper is the power flow problem, which is vital to the operation of electric power grids. Although the power flow problem is a non-convex feasibility problem, our algorithms are demonstrated to be effective heuristics using various IEEE test beds.