Monitoring of abnormal events in a distribution feeder by using a single technique is a challenging task. Many abnormal events can cause unsafe operation, including a high impedance fault (HIF) caused by a downed conductor touch ground surface, an incipient fault (IF) caused by partial breakdown to a cable insulation, and a circuit breaker (CB) malfunction due to capacitor bank de-energization to cause current restrikes. These abnormal events are not detectable by conventional protection schemes. In this dissertation, a new technique to identify distribution feeder events is proposed based on the complex Morlet wavelet (CMW) and on a decision tree (DT) classifier. First, the event is detected using CMW. Subsequently, a DT using event signatures classifies the event as normal operation, continuous and non-continuous arcing events (C.A.E. and N.C.A.E.). Additional information from the supervisory control and data acquisition (SCADA) can be used to precisely identify the event. The proposed method is meticulously tested on the IEEE 13- and IEEE 34-bus systems and has shown to correctly classify those events. Furthermore, the proposed method is capable of detecting very high impedance incipient faults (IFs) and CB restrikes at the substation level with relatively short detection time. The proposed method uses only current measurements at a low sampling rate of 1440 Hz yielding an improvement of existing methods that require much higher sampling rates.