Out-of-step protection has been widely studied, and it remains an important topic in the field. Given the crucial modernization of the power systems and the evolution of protective relaying, it is crucial to merge from traditionally fixed parameters to novel approaches that allow flexibility and possible time-domain protection. This article presents a new methodology to implement an out-of-step protection algorithm through the geometrical understanding of a power system oscillation using Clarke's transformation. The article is an extension of a virtual relay solution previously developed and improves the swing center voltage solution in the αβ plane with enhanced selectivity. The result brings a functional virtual relay capable of detecting and reacting under stable and unstable power swing events through playback techniques. The contribution of this article relies on the application of the time-domain approach to improving the function ANSI 78 as an extension of ongoing research on virtualization of power system protection and real-time prototyping.