TY - GEN
T1 - CRAMER-RAO BOUND FOR ADMITTANCE MATRIX ESTIMATION UNDER LAPLACIAN CONSTRAINTS
AU - Halihal, Morad
AU - Routtenberg, Tirza
N1 - Publisher Copyright:
© 2024 IEEE.
PY - 2024/1/1
Y1 - 2024/1/1
N2 - In this paper, we consider the problem of estimating the admittance matrix in power systems, accounting for Laplacian and physical constraints. We assume the nonlinear alternating current (AC) model, which accurately represents the power flow model. We develop a closed-form expression for the oracle Cramér-Rao bound (CRB) on the mean-squared-error (MSE) of any unbiased estimator of the admittance matrix. The proposed oracle CRB takes into account the Laplacian parametric equality constraints, including symmetry and the null space property, through a reparametrization of the estimation problem as an unconstrained optimization. The oracle CRB assumes knowledge of the locations of the nonzero entries of the Laplacian matrix, and, thus, provides a valid lower bound. We evaluate and compare the oracle CRB with the MSE of: 1) the constrained maximum likelihood estimator (CMLE), which integrates the equality, inequality, and joint-sparsity Laplacian constraints; and 2) the oracle CML estimator, which knows the location of the nonzero entries of the Laplacian matrix. It is shown that for data from the IEEE 33-bus power system, the MSEs of the estimators converge to the oracle CRB for a sufficient number of measurements.
AB - In this paper, we consider the problem of estimating the admittance matrix in power systems, accounting for Laplacian and physical constraints. We assume the nonlinear alternating current (AC) model, which accurately represents the power flow model. We develop a closed-form expression for the oracle Cramér-Rao bound (CRB) on the mean-squared-error (MSE) of any unbiased estimator of the admittance matrix. The proposed oracle CRB takes into account the Laplacian parametric equality constraints, including symmetry and the null space property, through a reparametrization of the estimation problem as an unconstrained optimization. The oracle CRB assumes knowledge of the locations of the nonzero entries of the Laplacian matrix, and, thus, provides a valid lower bound. We evaluate and compare the oracle CRB with the MSE of: 1) the constrained maximum likelihood estimator (CMLE), which integrates the equality, inequality, and joint-sparsity Laplacian constraints; and 2) the oracle CML estimator, which knows the location of the nonzero entries of the Laplacian matrix. It is shown that for data from the IEEE 33-bus power system, the MSEs of the estimators converge to the oracle CRB for a sufficient number of measurements.
KW - Admittance matrix estimation
KW - Cramér-Rao bound (CRB)
KW - power system topology identification
UR - https://www.scopus.com/pages/publications/85195387323
U2 - 10.1109/ICASSP48485.2024.10447538
DO - 10.1109/ICASSP48485.2024.10447538
M3 - Conference contribution
AN - SCOPUS:85195387323
T3 - ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
SP - 9871
EP - 9875
BT - 2024 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2024 - Proceedings
PB - Institute of Electrical and Electronics Engineers
T2 - 2024 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2024
Y2 - 14 April 2024 through 19 April 2024
ER -