Several methods have been proposed for detection and classification of power quality (PQ) disturbances using wavelet, Hilbert transform, Gabor transform, Gabor-Wigner transform, S transform, and Hilbert-Haung transform. This paper presents a new method for detection and classification of single and combined PQ disturbances using a sparse signal decomposition (SSD) on overcomplete hybrid dictionary (OHD) matrix. The method first decomposes a PQ signal into detail and approximation signals using the proposed SSD technique with an OHD matrix containing impulse and sinusoidal elementary waveforms. The output detail signal adequately captures morphological features of transients (impulsive and oscillatory) and waveform distortions (harmonics and notching). Whereas the approximation signal contains PQ features of fundamental, flicker, dc-offset, and short- and long-duration variations (sags, swells, and interruptions). Thus, the required PQ features are extracted from the detail and approximation signals. Then, a hierarchical decision-tree algorithm is used for classification of single and combined PQ disturbances. The proposed method is tested using both synthetic and microgrid simulated PQ disturbances. Results demonstrate the accuracy and robustness of the method in detection and classification of single and combined PQ disturbances under noiseless and noisy conditions. The method can be easily expanded for compressed sensing based PQ monitoring networks. © 2014 IEEE.