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The loss of stability-an instability-can become a critical cause of emergent cascading outages leading to wide-spread blackouts. Penetration of renewable energy sources makes the problem of instability more urgent because of the highly fluctuating nature of such sources. Here we show a data-based approach to stability assessment of power systems without models. This approach is enabled by Koopman mode analysis for nonlinear dynamical systems, which detects an instability based on the properties of the point spectrum of the Koopman operator. We apply the technique to data on physical power flows sampled from the two major accidents, the 2011 Arizona-Southern California grid outage and the 2006 system disturbance of the European interconnected grid, and successfully detect unstable power flow patterns that govern the complex dynamics occurring during the accidents.