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We formulate an inverse power flow problem that infers a nodal admittance matrix 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). We propose an effective algorithm to uncover the actual admittance matrix of a radial system with hidden nodes from its Kron-reduced admittance matrix.
Yuan et al. (Mon,) studied this question.