Inverse Power Flow Problem
  This paper formulates an inverse power flow problem which is to infer a nodal admittance matrix (hence the network structure of a power system) from voltage and current phasors measured at a number of buses. We show that the admittance matrix can be uniquely identified from a sequence of measurements corresponding to different steady states when every node in the system is equipped with a measurement device, and a Kron-reduced admittance matrix can be determined even if some nodes in the system are not monitored (hidden nodes). Furthermore, we propose effective algorithms based on graph theory to uncover the actual admittance matrix of radial systems with hidden nodes. We provide theoretical guarantees for the recovered admittance matrix and demonstrate that the actual admittance matrix can be fully recovered even from the Kron-reduced admittance matrix under some mild assumptions. Simulations on standard test systems confirm that these algorithms are capable of providing accurate estimates of the admittance matrix from noisy sensor data. 
Ye Yuan, Steven Low, Omid Ardakanian, Claire Tomlin
eess.SY cs.SY math.OC