Discovery of Energy Network Topology from Uncertain Flow Measurements.

The objective we focus on here consists in discovering the topology of an energy distribution network modeled by a flow digraph from which we only know the set of arcs without identification of their extremities. We also have as inputs a set of temporal series of flow measures on these arcs and the correlation matrix of the arcs, with possible errors. From these inputs, we consider the graph which incidence matrix is the correlation one. If the correlation matrix contains no errors, this graph is the line graph of the network to be discovered. Thus, given this graph, we then propose here algorithms determining the graph with the same vertex set being a line graph and maximizing the set of similar edges with the initial correlation graph. We then evaluate the performances of this approach by simulation on 50 networks, randomly generated.