Inverse Power Flow Problem

TL;DR

This paper introduces a method to uniquely identify and recover the network structure of power systems by inferring the nodal admittance matrix from voltage and current measurements, even with hidden nodes, using graph theory algorithms.

Contribution

It presents novel algorithms for inverse power flow problems that can recover the admittance matrix of power systems, including cases with hidden nodes, with theoretical guarantees and practical effectiveness.

Findings

Algorithms accurately recover admittance matrices from noisy data.

Unique identification of admittance matrices from measurements under certain conditions.

Effective for radial systems with hidden nodes, confirmed by simulations.

Abstract

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.