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Once the power signals under measurement are corrupted by noises, the performance of the wavelet transform (WT) on recognizing power quality (PQ) events would be greatly degraded. Meanwhile, directly adopting the WT coefficients (WTCs) has the drawback of taking a longer time for the recognition system. To solve the problem of noises riding on power signals and to effectively reduce the number of features representing power transient signals, a noise-suppression scheme for noise-riding signals and an energy spectrum of the WTCs in different scales are used as features in this paper. The genetic k-means algorithm (GKA)-based radial basis function (RBF) network classification system is then used for PQ event recognition. The proposed GKA-based clustering approach can overcome the problem of oversensitivity to randomly initial partitions in the conventional methods. To determine a suitable number of centers in an RBF from the input data, the orthogonal least squares (OLS) learning algorithm was used in this paper. The success rates of recognizing PQ events from noise-riding signals have proven to be feasible in power system applications.