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Electrical power analysis and the Durbin Watson (DW) statistic can be manipulated to diagnose the instability of the power quality parameters, and to discern between synchronous and asynchronous running of the generator. In this research, the computational techniques serve as a proper foundation of intelligent relay to anticipate and detect the generator Out-of-Step (OOS) situation following the fault presence. The protection strategy can identify sudden variations in several electrical waves in the OOS conditions, such as phase voltage, current, active power, reactive power, and power angle. To verify the performance of the method, a power model with real parameter data of its components is built using the software package of the Alternative Transient Program (ATP). The advanced algorithm is carried out and analyzed using the MATLAB application. Simulation results and analysis show that the protection plan has the ability to recognize the OOS events upon which the protective relay emits a tripping signal to both the annunciation panel and the generator circuit breakers. Whereas, it remains idle under acceptable synchronization conditions. As a consequence, the OOS is rapidly announced before the second pole-slipping occurrence. Furthermore, the algorithm is robust during the stable power swings, and the property of the protection redundancy is provided in this strategy. Additionally, it has the capability of estimating both the instability time and the frequency rate of the unstable power swings.<\/jats:p>","DOI":"10.1038\/s41598-025-03350-8","type":"journal-article","created":{"date-parts":[[2025,6,20]],"date-time":"2025-06-20T08:55:19Z","timestamp":1750409719000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Out-of-step detection for synchronous generators using electrical power analysis and Durbin Watson testing"],"prefix":"10.1038","volume":"15","author":[{"given":"R. A.","family":"Mahmoud","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"E. 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