In order to deal with the nonstationary signatures of phasor measurement units (PMU) signals, this paper presents a wavelet-based detection algorithm. Moreover, for an application to PMU for event detection purpose, it is necessary for us to classify detected events into unexpected real power related accidents, such as generator trip or automated control, such as reactive power injection. The proposed normalized wavelet energy function calculates the root mean square (RMS) of detail coefficients from time-synchronized voltage and frequency that reflect nonstationary occurrence of significant changes in signals. For a robust detection, wavelet-based detection parameter is designed with consideration of nonstationary characteristics of events. Also, there are distinct transients in voltage and frequency caused by different event types, and distinct results are key-idea of event classification. Besides the determination of event occurrences, one can obtain the information of event characteristics that include event types and zonal information of event from the proposed method. Moreover, successful results of detection and classification in real-world cases are presented in this paper.