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This paper presents a power swing detection algorithm in multi-machine power systems, which uses wide-area synchrophasor measurements and is based on Zubov’s stability boundaries. Zubov’s boundary method, an approximation of the famous Lyapunov function, is very common for numerical analyses of power system stability. This work extends the concept of Zubov’s approximation boundaries to online protection applications. First, the proposed protection algorithm constructs a series of Zubov’s stability boundaries on power angle–frequency ($\delta$ – $\omega$) plane for generators based on real-time measurements from phasor measurement units/merging units. Then, it tracks the trajectory of each generator in the $\delta$ – $\omega$ plane after the disturbance to differentiate out-of-step (OOS) conditions from stable swings. The proposed approach is suitable for online applications, which is a significant improvement over the existing methods for swing detection since it does not require offline studies and network reduction. Effectiveness of the proposed method is shown using a single-machine infinite bus and New-England 10-machine 39-bus systems. The proposed method is also implemented in a hardware-in-the-loop setup with a customized IEC 61850-based OOS relay, and performance is compared with a commercially available relay. [ABSTRACT FROM AUTHOR]