Estimating Nodal Admittance Matrix for Ill-Posed Inverse Power Flow Problem in Power Grid

The estimation of the nodal admittance matrix is an important problem for the power grid operation and computing tasks. Some studies have shown that the admittance matrix can be fuzzily estimated only by the injection power measurements. Nevertheless, the estimation results of most existing efforts are not ideal because of the problem's nonconvex properties, and the effects of measurement observability on the accuracy of estimation methods are not clear either. In this article, we establish an ill-posed inverse dc power flow (IDCPF) problem model and propose an admittance matrix estimation method based on multimeasurements of the power grid, including measurements of injection power and voltage phasor. Our approach converts the original problem into solvable linear subproblems and improves the estimation models by considering various physical mechanisms of the power grid. Additionally, we develop an optimization algorithm that leverages alternating least-square and alternating direction methods of multipliers for solving the IDCPF problem. We also demonstrate the detailed analysis and proof of the effects of phasor measurement observability on the accuracy of the estimation. The effectiveness and performance of our method are verified based on experiments using IEEE 30-bus and 118-bus systems.