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This paper deals with the detection of incipient faults in underground distribution systems using online voltage and current measurements. The approach presented in this paper is based on the numerical modeling of incipient fault patterns established from the oscillographic data. Specific energy features in the wavelet domain were extracted and used in the modeling task using the self-organizing map technology. The modified modeling errors are used as a chronologically ordered sequence in the change detection problem specifically formulated for this application. Three modified change detection algorithms, namely, cumulative sum, exponentially weighted moving averages, and generalized likelihood ratio were investigated and assessed as to the performance using field-recorded data from an underground cable lateral. The detection results demonstrate the detectability of these faults and application of the approach for real fault scenarios.