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A new method classifying power quality disturbances (PQD) based on random matrix transform (RMT) and sparse representation classification (SRC) by L1-minimization is presented. First, the PQD signals are characterized by random matrix lower-dimensional projection based on compressive sensing theory. Then, every test sample from feature vectors is represented as a sparse linear combination of training samples. The PQD type assign to the object class that minimizes the residual between test sample and its sparse representation by solving L1-minimization problem. RMT feature extraction method is extremely efficient to generate and independent of the training dataset. Compared with support vector machine (SVM), the SRC algorithm needs neither training process nor combination of two-class classifiers for multiclass classification. Simulation results show that the proposed feature extraction and classification method has high classification correct ratio in strong noise condition.