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Power components, power factors, and pollution factor are defined according to the IEEE standard 1459-2000 based on the fast Fourier transform (FFT). However, the FFT in the presence of nonstationary power quality (PQ) disturbances results in inaccurate values due to its sensitivity to the spectral leakage problem. In this paper, a new perspective for the IEEE standard 1459-2000 definitions is introduced using the stationary wavelet transform (SWT). As a time-frequency transform, the SWT can provide variable frequency resolution while preserving time information without spectral leakage as the FFT. Moreover, unlike other time-frequency transforms, such as discrete wavelet transform (DWT), SWT possesses the time-invariance property that keeps the time and frequency characteristics throughout all of the decomposition levels. Results of different case studies including stationary, nonstationary of synthetic, and real PQ disturbances proves the effectiveness of applying the SWT over FFT or DWT.