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A situational awareness system is essential to provide accurate understanding of power system dynamics, such that proper actions can be taken in real time in response to system disturbances and to avoid cascading blackouts. Event analysis has been an important component in any situational awareness system. However, most state-of-the-art techniques can only handle single event analysis. This paper tackles the challenging problem of multiple event detection and recognition. We propose a new conceptual framework, referred to as event unmixing, where we consider real-world events mixtures of more than one constituent root event. This concept is a key enabler for analysis of events to go beyond what are immediately detectable in a system, providing high-resolution data understanding at a finer scale. We interpret the event formation process from a linear mixing perspective and propose an innovative nonnegative sparse event unmixing (NSEU) algorithm for multiple event separation and temporal localization. The proposed framework has been evaluated using both PSS/E simulated cases and real event cases collected from the frequency disturbance recorders (FDRs) of the Frequency Monitoring Network (FNET). The experimental results demonstrate that the framework is reliable to detect and recognize multiple cascading events as well as their time of occurrence with high accuracy.