This study introduces a novel unified framework for simultaneous denoising and compression of electric power system disturbance signals using sparse signal decomposition and reconstruction on overcomplete hybrid dictionary (OHD) matrix. In the proposed method, the power quality signal is first decomposed into deterministic sinusoidal components and non-deterministic components using the OHD matrix, including discrete impulse dictionary (I), cosine dictionary (C), sine dictionary (S) and the l(1)-norm optimisation algorithm. Then, the hard-thresholding, uniform threshold dead-zone quantisation, modified index coding and Huffman coding techniques are used for compression of significant detail signal samples and approximation coefficients. To justify the selection of OHD matrix, four compression methods are implemented using the decomposition techniques based on the dictionaries psi = {[}I C S] and psi = {[}I C], the wavelet transform (WT) and the discrete cosine transform (DCT). The performance of each method is tested and validated using a wide variety of typical power quality disturbance (PQD) signals taken from the IEEE-1159-PQE and GIM-PQE databases and generated using the Microgrid model. The results show that the method with dictionary psi = {[}I C S] is capable of effectively compressing the PQD signals as well as suppressing the noise components in the signals.