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The wavelet transform, the S-transform, the Gabor transform, and the Wigner distribution function are popular techniques for power quality (PQ) analysis in electrical power systems. They are mainly used to identify power harmonics and power disturbances and to estimate power quantities in the presence of nonstationary power components such as root-mean-square values and total harmonic distortions. Recently, the Hilbert-Huang transform has been also used in PQ analysis. These techniques have proven to be useful in PQ analysis; however, their performances depend on the types of PQ events. In this paper, a novel frequency-shifting wavelet decomposition via the Hilbert transform is introduced for PQ analysis. The proposed algorithm overcomes the spectra leakage problem in the discrete wavelet packet transform and can be used for estimating power quantities accurately and for detecting flickers. The effectiveness of the proposed algorithm was verified by computer simulations and experimental tests.