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This paper presents the idea and initial results of building decision trees (DTs) for detecting and identifying various transient dynamic events using the characteristic ellipsoid method. In this paper, the objective is to determine fault types, fault locations and clearance times in the system using DTs based on ellipsoids surrounding system transient responses in the system operating parameter space. The New England 10-machine 39-bus system is used to generate a sufficiently large number of transient events in different system configurations. Comprehensive transient simulations considering three fault types, two different fault clearance times and various fault locations were conducted in the study. Bus voltage magnitudes and monitored reactive and active power flows are recorded as the phasor measurements to calculate characteristic ellipsoids whose volume, eccentricity, center and projection of the longest axis on the parameter space coordinates are used as indices to build decision trees. The DTs performance is tested and compared for different sets of phasor measurement units (PMUs) locations. The results demonstrate that, depending on the number and location of PMUs in the model, the proposed approach is capable to detect the fault type, location, and clearance time in up to 99% of the cases which are not included in the training set used to build the DT.