An Affine Linear Solution of the Nonlinear Inverse Power Flow Problem in Resistive Networks

In the analysis of linear electrical networks, an inverse problem can be inferring all edge impedances only from known external voltage sources and measured resulting edge currents. Given all external edge voltages u(ext )and all resulting edge currents i, we present a new calculation method for the edge resistances R, with the assumption that the reactance is everywhere zero (e.g., a resistive network). Our considerations are based on affine subspaces and their intersection. We show, that in case of having a sequence of l >= 3 measurements (u(ext1), i1), & mldr; , (u(extl), i(l)), we can calculate R uniquely in every such network. For a sufficiently large but still small cuboid grid, we can reduce the number of needed measurements to 2.