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Partial discharge (PD) may cause insulation deteriorations in power facilities and may demonstrate impact on the reliability. Therefore PD detection with pattern recognition is seen as an effective approach in the high-voltage (HV) insulation diagnostics of power systems. Based on an extension method, a PD recognition system for HV power cables is proposed in this study. A PD detector is used to measure raw three-dimension PD patterns of cross-linked polyethylene (XLPE) power cables using an L sensor, according to which two fractal features (the fractal dimension and the lacunarity) and the mean discharge are extracted as critical PD features that form the cluster domains of defect types. The matter-element models of the PD defect types are then built according to the PD features derived from practical experimental results. The PD defect type can be directly identified by the correlation degrees between a tested pattern and the matter-element models. The recognition ability is investigated on 160 sets of PD patterns of XLPE power cables and compared with a multilayer neural network and K-means method. The results show that a high accuracy together with a high tolerance in the presence of noise interference is reached by use of the extension method.