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High-impedance faults (HIFs) on distribution systems create unique challenges to protection engineers. HIFs do not produce enough fault current to be detected by conventional overcurrent relays or fuses. A method for HIF detection based on the nonlinear behaviour of current waveforms is presented. Using this method, HIFs can be distinguished successfully from other similar waveforms such as nonlinear load currents, secondary current of saturated current transformers and inrush currents. A wavelet multi-resolution signal decomposition method is used for feature extraction. Extracted features are fed to an adaptive neural fuzzy inference system (ANFIS) for identification and classification. The effect of choice of mother wavelet is also analysed by investigating a large number of wavelet families. Various simulation results, which are obtained using an appropriate model, are summarised and efficiency of the proposed algorithm for dependable and secure HIF detection is determined.