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This paper aims to develop a new idea for the classification of transient disturbances on power quality. The method is based on the combination of spectral kurtosis (SK) and artificial neural network (ANN). The SK is a high-order statistical moment which can detect the non-Gaussian components in a signal. Through the introduction of SK and its properties, we propose a classification plan for five transient disturbances combining SK and ANN. Firstly, the high frequency parts of five disturbance signals are extracted with DB4 wavelet transform (WT). Secondly, their SK values are respectively computed based on short time Fourier transform (STFT) and WT. Because the features of SK based on WT for five disturbance signals are not clearly distinguished, we propose a new computation method of SK based on Butterworth Distribution (BUD). Lastly, we choose the maximum, minimum and average values of SK based on STFT and BUD as the eigenvectors for the transient disturbance classification, which are input into RBF neural network. The simulation results show that the recognition rate of five transient disturbances is high, and the classification method proposed in the paper for transient power quality combining SK with ANN is efficient and feasible.