TY - JOUR
T1 - Power Systems Topology and State Estimation by Graph Blind Source Separation
AU - Grotas, Sivan
AU - Yakoby, Yair
AU - Gera, Idan
AU - Routtenberg, Tirza
N1 - Funding Information:
Manuscript received August 9, 2018; revised December 30, 2018 and January 27, 2019; accepted February 13, 2019. Date of publication February 25, 2019; date of current version March 7, 2019. The associate editor coordinating the review of this manuscript and approving it for publication was Prof. Tao Jiang. This work was supported in part by the Israel Science Foundation (ISF) under Grant 1173/16 and in part by the BGU Cyber Security Research Center. The work of S. Grotas was supported under a Grant from the Ministry of Science and Technology of Israel. (Corresponding author: Tirza Routtenberg.) The authors are with the Department of Electrical and Computer Engineering, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel (e-mail:, sivangr@post.bgu.ac.il; yairyak@post.bgu.ac.il; idange@post.bgu. ac.il; tirzar@bgu.ac.il). Digital Object Identifier 10.1109/TSP.2019.2901356
Publisher Copyright:
© 1991-2012 IEEE.
PY - 2019/4/15
Y1 - 2019/4/15
N2 - In this paper, we consider the problem of blind estimation of states and topology (BEST) in power systems. We use the linearized dc model of real power measurements with unknown voltage phases (i.e., states) and an unknown admittance matrix (i.e., topology) and show that the BEST problem can be formulated as a blind source separation (BSS) problem with a weighted Laplacian mixing matrix. We develop the constrained maximum likelihood (ML) estimator of the Laplacian matrix for this graph BSS problem with Gaussian-distributed states. The ML-BEST is shown to be only a function of the states' second-order statistics. Since the topology recovery stage of the ML-BEST approach results in a high-complexity optimization problem, we propose two low-complexity methods to implement it: First, two-phase topology recovery, which is based on solving the relaxed convex optimization and then finding the closest Laplacian matrix, and second, augmented Lagrangian topology recovery. We derive a closed-form expression for the associated Cram\acute{\text{e}}r-Rao bound (CRB) on the topology matrix estimation. The performance of the proposed methods is evaluated for three case studies: the IEEE-14 bus system, the IEEE 118-bus system, and a random network, and compared with the oracle minimum mean-squared-error state estimator and with the proposed CRB.
AB - In this paper, we consider the problem of blind estimation of states and topology (BEST) in power systems. We use the linearized dc model of real power measurements with unknown voltage phases (i.e., states) and an unknown admittance matrix (i.e., topology) and show that the BEST problem can be formulated as a blind source separation (BSS) problem with a weighted Laplacian mixing matrix. We develop the constrained maximum likelihood (ML) estimator of the Laplacian matrix for this graph BSS problem with Gaussian-distributed states. The ML-BEST is shown to be only a function of the states' second-order statistics. Since the topology recovery stage of the ML-BEST approach results in a high-complexity optimization problem, we propose two low-complexity methods to implement it: First, two-phase topology recovery, which is based on solving the relaxed convex optimization and then finding the closest Laplacian matrix, and second, augmented Lagrangian topology recovery. We derive a closed-form expression for the associated Cram\acute{\text{e}}r-Rao bound (CRB) on the topology matrix estimation. The performance of the proposed methods is evaluated for three case studies: the IEEE-14 bus system, the IEEE 118-bus system, and a random network, and compared with the oracle minimum mean-squared-error state estimator and with the proposed CRB.
KW - Graph blind source separation (GBSS)
KW - Laplacian mixing matrix
KW - Topology identification
KW - constrained maximum likelihood
KW - power system state estimation
UR - http://www.scopus.com/inward/record.url?scp=85062688795&partnerID=8YFLogxK
U2 - 10.1109/TSP.2019.2901356
DO - 10.1109/TSP.2019.2901356
M3 - Article
AN - SCOPUS:85062688795
SN - 1053-587X
VL - 67
SP - 2036
EP - 2051
JO - IEEE Transactions on Signal Processing
JF - IEEE Transactions on Signal Processing
IS - 8
M1 - 8651352
ER -