Sparse recovery of an electrical network based on algebraic variety fitting and graph sparsification
The problem of recovering the topology and parameters of an electrical network from power and voltage data at all nodes is a problem of fitting both an algebraic variety and a graph which is often ill-posed. In case there are multiple electrical networks which fit the data up to a given tolerance, we seek a solution in which the graph and therefore the algebraic equations associated with the electrical network are sparse, i.e. with few edges and terms. From an applied point of view, frequently it is difficult for system operators to know the precise information of the network. On the other hand, improvements on measurement devices increasingly provide more data about voltage and power, so it is useful to use this amount of data to estimate the network. We propose an algorithm for recovering simultaneously a sparse topology and the cable parameters of any network, combining in an iterative procedure the resolution of algebraic fitting convex problems and techniques of spectral graph sparsification. The algorithm is tested on several electrical networks.