{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,7]],"date-time":"2026-10-07T17:25:39Z","timestamp":1791393939342,"version":"4.3.3"},"reference-count":70,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2023,1,26]],"date-time":"2023-01-26T00:00:00Z","timestamp":1674691200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"The Israel Ministry of National Infrastructure, Energy, and Water Resources"},{"name":"The BGU Cyber Security Research Center"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>This paper considers the problem of estimating the states in an unobservable power system, where the number of measurements is not sufficiently large for conventional state estimation. Existing methods are either based on pseudo-data that is inaccurate or depends on a large amount of data that is unavailable in current systems. This study proposes novel graph signal processing (GSP) methods to overcome the lack of information. To this end, first, the graph smoothness property of the states (i.e., voltages) is validated through empirical and theoretical analysis. Then, the regularized GSP weighted least squares (GSP-WLS) state estimator is developed by utilizing the state smoothness. In addition, a sensor placement strategy that aims to optimize the estimation performance of the GSP-WLS estimator is proposed. Simulation results on the IEEE 118-bus system show that the GSP methods reduce the estimation error magnitude by up to two orders of magnitude compared to existing methods, using only 70 sampled buses, and increase of up to 30% in the probability of bad data detection for the same probability of false alarms in unobservable systems The results conclude that the proposed methods enable an accurate state estimation, even when the system is unobservable, and significantly reduce the required measurement sensors.<\/jats:p>","DOI":"10.3390\/s23031387","type":"journal-article","created":{"date-parts":[[2023,1,27]],"date-time":"2023-01-27T01:27:58Z","timestamp":1674782878000},"page":"1387","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":33,"title":["State Estimation in Partially Observable Power Systems via Graph Signal Processing Tools"],"prefix":"10.3390","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1993-6629","authenticated-orcid":false,"given":"Lital","family":"Dabush","sequence":"first","affiliation":[{"name":"School of Electrical and Computer Engineering, Ben-Gurion University of the Negev, Beer Sheva 8410501, Israel"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ariel","family":"Kroizer","sequence":"additional","affiliation":[{"name":"School of Electrical and Computer Engineering, Ben-Gurion University of the Negev, Beer Sheva 8410501, Israel"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7238-7764","authenticated-orcid":false,"given":"Tirza","family":"Routtenberg","sequence":"additional","affiliation":[{"name":"School of Electrical and Computer Engineering, Ben-Gurion University of the Negev, Beer Sheva 8410501, Israel"},{"name":"Department of Electrical and Computer Engineering, Princeton University, Princeton, NJ 08544, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,1,26]]},"reference":[{"key":"ref_1","unstructured":"Dekker, M. 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