Estimation of Complex-Valued Laplacian Matrices for Topology Identification in Power Systems

Morad Halihal, Tirza Routtenberg, H. Vincent Poor

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

In this paper, we investigate the problem of estimating a complex-valued Laplacian matrix with a focus on its application in the estimation of admittance matrices in power systems. The proposed approach is based on a constrained maximum likelihood estimator (CMLE) of the complex-valued Laplacian, which is formulated as an optimization problem with Laplacian and sparsity constraints. The complex-valued Laplacian is a symmetric, non-Hermitian matrix that exhibits a joint sparsity pattern between its real and imaginary parts. Thus, we present a group-sparse-based penalized log-likelihood approach for the Laplacian estimation. Leveraging the mixed ℓ2,1 norm relaxation of the joint sparsity constraint, we develop a new alternating direction method of multipliers (ADMM) estimation algorithm for the implementation of the CMLE of the Laplacian matrix under a linear Gaussian model. Next, we apply the proposed ADMM algorithms for the problem of estimating the admittance matrix under three commonly-used measurement models that stem from Kirchhoff's and Ohm's laws, each with different assumptions and simplifications: 1) the nonlinear alternating current (AC) model; 2) the decoupled linear power flow (DLPF) model; and 3) the direct current (DC) model. The performance of the ADMM algorithm is evaluated using data from the IEEE 33-bus power system data under different settings. The numerical experiments demonstrate that the proposed algorithm outperforms existing methods in terms of mean-squared-error (MSE) and F-score, thus providing a more accurate recovery of the admittance matrix.

Original languageEnglish (US)
Pages (from-to)3626-3640
Number of pages15
JournalIEEE Transactions on Signal Processing
Volume72
DOIs
StatePublished - 2024
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Signal Processing
  • Electrical and Electronic Engineering

Keywords

  • admittance matrix estimation
  • alternating direction method of multipliers (ADMM)
  • Estimation of complex-valued Laplacian matrix
  • topology identification

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