Estimation of the Admittance Matrix in Power Systems Under Laplacian and Physical Constraints

Admittance matrix estimation in power networks enables faster control actions following emergency scenarios, energy-saving, and other economic and security advantages. In this paper, our goal is to estimate the network admittance matrix, i.e. to learn connectivity and edge weights in the graph representation, under physical and Laplacian constraints. We use the nonlinear AC power flow measurement model, which is based on Kirchhoff’s and Ohm’s laws, with power and voltage phasor measurements. In order to recover the complex-valued admittance matrix, we formulate the associated constrained maximum likelihood (CML) estimator as the solution of a constrained optimization problem with Laplacian and sparsity constraints. We develop an efficient solution using the associated alternating direction method of multipliers (ADMM) algorithm with an ℓ1 relaxation. The ADMM algorithm is shown to outperform existing methods in the task of recovering the IEEE 14-bus test case.