I have been working on a tree message passing algorithm which uses dynamic programming to calculate optimal power flow in a tree network given an number of loads and generation units. Leaf nodes start by constructing a number of elements that contain a particular flow, carbon intensity and resulting carbon emission. They calculate it based on whether there is flow coming in from their parent, flow going out to their parent or whether there is no resultant flow between them and their parent. The leaf nodes send these elements to their parents and the parents then construct their own set of elements by merging the results from their children. This continues all the way up to the root of the tree, at which point the root can calculate the optimum state it should be in to produce the minimum carbon emission. This optimum state is propagated back down the tree and each node uses backtracking to determine what state they should be in given and optimum state from their parent. Once messages have propagated to the leaf nodes the algorithm terminates and each node will be outputting a certain power that satisfies loads in the tree and minimises carbon emissions.
The algorithm has nearly been fully implemented, I just need to code the merging of the elements for the root node and the decisions it has to make. I also need to thoroughly test this.
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