The emerging smart grid, cyber-physical infrastructure, provides a steady, secure, and reliable power system over the current power grid. Synchrophasor systems, like Phasor Measurement Units (PMUs), are a key element of smart grids. They have the capability to measure time-coherent phasors of a grid. The key advantage of PMUs is the fast sampling rate that they provide over traditional Supervisory control and data acquisition (SCADA) systems which can be in the range of 30-120 samples/second. These higher sampling rates come at the cost of higher data quantities. Generating large amounts of data per day poses a challenge in making the most efficient use of information. In this paper, this problem has been addressed utilizing machine learning techniques, Logistic Regression Analysis, on PMU data. Identifying system anomalies in smart power grids is the primary focus of this paper. The standard IEEE 39 Bus system has been modified using the RT-LAB environment to generate faults and to produce synthetic synchrophasor data. Archived/offline mode data from a Phasor data concentrator (PDC) database is being used to train and test the algorithm. Additionally, the algorithm has been tested in real-time using an OPAL-RT digital real-time simulator.