This paper presents a newly developed compressive sensing (CS), maximum likelihood (ML), and rule-based method for classification of power quality disturbances (PQDs). The first PQD signals are sampled using compressive sampling method and reduced PQD signal dimensionally, and then the data are directly used as features for the classification. PQD signals are divided into two groups: at first, impulsive, oscillatory, harmonics notch, flicker and DC offset, and the second, sag, swell, and interruption. Compressive sensing maximum likelihood (CSML) classifier is used for the classification of the first group and the rule-based method is used for the classification of the second group. CSML classifier and the rule-based method are tested utilizing 1000 PQD events under noiseless and noisy environment. About 100% correct classification rate is achieved without noise and 99.8% correct classification result is obtained with noise. In both methods, noise was considered from 20 to 40 dB. Results show that the proposed CS and ML algorithms and rule-based method can be efficiently used for PQD classification.