An Approximate Min-Sum Algorithm for Smart Grid Dispatch with Continuous Variables

We present a decentralized algorithm for solving economic dispatch problems in tree-shaped electrical distribution grids. Previous work used an extension of dynamic programming to trees, i.e. the min-sum algorithm, with discrete variables to solve these problems. We now present a novel, specially adapted, and efficient approximation scheme for continuous variables. Working with continuous variables is mandatory for many real world applications where line, consumption and generator capacities often have significantly different scales.